[
    {
        "q_id": "8972_mmlu_math",
        "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": [
            [
                6.962256248871951e-06,
                1.6701423831188846e-05,
                3.5356254914330094e-05,
                6.605212095972449e-05,
                2.7535684532815695e-05,
                2.7535700932494338e-05,
                1.4738976698006875e-05,
                1.4738985483128763e-05,
                4.0063692165808155e-05,
                9.610238046617398e-05
            ],
            [
                1.4738983724146862e-05,
                4.539785778740889e-05,
                0.9740426454865795,
                0.9995121427795796,
                5.829129321831856e-05,
                0.995929861493203,
                8.48110816558695e-05,
                2.430024355427424e-05,
                1.147876675466972e-05,
                0.00010889690915033367
            ],
            [
                8.481102095191198e-05,
                8.481105131283225e-05,
                0.00013982212336406024,
                2.7535700939406174e-05,
                0.00012339457426802834,
                7.484624502565293e-05,
                2.7535704219423216e-05,
                0.0001233945743452308,
                1.47389819699641e-05,
                0.9998766054547225
            ],
            [
                4.53978577543791e-05,
                0.9999339478238656,
                4.0063677800452475e-05,
                1.892514823013346e-05,
                0.9999756997505882,
                3.1201900168900725e-05,
                3.535626755428014e-05,
                0.9999785550592983,
                0.9999599363221718,
                1.3007126906982452e-05
            ],
            [
                2.4300246513165137e-05,
                1.89251482372248e-05,
                4.785096205778054e-06,
                1.1478772230407462e-05,
                5.422217677028889e-06,
                2.1444948410303962e-05,
                0.00013982207367803525,
                1.6701421841259862e-05,
                0.00026119024493071347,
                6.144173136729416e-06
            ],
            [
                2.1444943285915917e-05,
                0.9998204720344616,
                9.610240292700156e-05,
                6.605215238359538e-05,
                7.484626279663136e-05,
                2.4300237828059798e-05,
                1.6701429804744246e-05,
                7.48462538226543e-05,
                7.484623592480082e-05,
                1.3007134663521234e-05
            ],
            [
                2.7535694350223355e-05,
                0.9999151889184854,
                0.0031726821355852987,
                5.8291251573808804e-05,
                1.3007123807302014e-05,
                0.00012339454459356464,
                0.00013982212288394296,
                1.0129987354882753e-05,
                5.1442238137271045e-05,
                0.998967768943438
            ],
            [
                2.7535681231364308e-05,
                3.120191135264947e-05,
                3.1201922517673344e-05,
                5.144221363703851e-05,
                5.144219521911119e-05,
                2.753568124458694e-05,
                1.4738985478678359e-05,
                1.4738983719053027e-05,
                0.9940889302161554,
                0.00020342699346314472
            ],
            [
                5.144219522247965e-05,
                0.9995121429430667,
                1.892514147046736e-05,
                2.4300237828059798e-05,
                7.484623602717382e-05,
                0.00010889696038787034,
                0.9770226292118533,
                1.4738987238893715e-05,
                1.8925150492616083e-05,
                0.9988304896646378
            ],
            [
                0.9999417087067342,
                3.1201903900940664e-05,
                8.939695236983711e-06,
                3.1201903930339314e-05,
                7.889264466230069e-06,
                2.430024072648329e-05,
                6.962254589104433e-06,
                1.147877086073156e-05,
                3.726637951126493e-06,
                1.670142781244497e-05
            ],
            [
                1.300712846411008e-05,
                4.006368740256958e-05,
                5.82912516391202e-05,
                5.829127937441555e-05,
                5.144221362094481e-05,
                2.1444940736477737e-05,
                5.829129322340776e-05,
                2.753569437686898e-05,
                5.82912723385944e-05,
                2.1444945848226808e-05
            ],
            [
                4.006369693473136e-05,
                5.144223202577919e-05,
                0.00012339454510166436,
                4.0063701693307245e-05,
                0.00015843627271653116,
                0.00023050665908071752,
                3.120190389378964e-05,
                6.605212092416299e-05,
                0.0002034268994173227,
                0.00017952790096184096
            ],
            [
                0.9324533074525657,
                5.4222170304318e-06,
                6.9622537593854575e-06,
                6.144172403827636e-06,
                8.939696303758459e-06,
                1.47389819699641e-05,
                5.829126544654401e-05,
                1.4738978454172926e-05,
                0.9241418215456966,
                6.144173135896795e-06
            ],
            [
                2.1444943297072005e-05,
                0.00010889690904258862,
                4.539785232659414e-05,
                7.484620931490225e-05,
                3.120191879107958e-05,
                0.0002611904303242687,
                3.120190763025685e-05,
                6.605216031188985e-05,
                2.4300243625614346e-05,
                5.829125846925035e-05
            ],
            [
                5.144221976237626e-05,
                2.4300252297461515e-05,
                8.93970056565517e-06,
                0.0003353500694285664,
                2.4300243622255085e-05,
                1.3007134664514934e-05,
                9.610240332972338e-05,
                0.0001584362350152198,
                0.9999687980849312,
                0.999954602136865
            ],
            [
                4.7850950649408664e-06,
                1.1478770859624945e-05,
                5.42221767672807e-06,
                5.4222215552470286e-06,
                1.1478768124324254e-05,
                8.93969630362837e-06,
                1.012999580884213e-05,
                4.222831934248571e-06,
                1.0129988564099116e-05,
                4.785094494463623e-06
            ],
            [
                3.1201915071864306e-05,
                1.8925150486764003e-05,
                2.4300237829827827e-05,
                1.1478772229781076e-05,
                8.481105137391814e-05,
                1.5534984917424775e-06,
                7.889266346287306e-06,
                1.3007126912826352e-05,
                6.605212885485651e-05,
                1.473898548194914e-05
            ],
            [
                0.00013982210707059006,
                9.610242628137363e-05,
                8.481101091470089e-05,
                4.006369694959736e-05,
                5.144221972045777e-05,
                0.00020342694853270045,
                5.144223816384438e-05,
                0.00020342702138448633,
                3.120192623257619e-05,
                4.006368737910463e-05
            ],
            [
                0.0001233946186127645,
                9.610243777782634e-05,
                0.000261190213962137,
                3.120192251903545e-05,
                7.484626288702458e-05,
                5.8291286317783706e-05,
                5.144221974927673e-05,
                3.120190017276001e-05,
                3.1201915071864306e-05,
                0.0002611903680906888
            ],
            [
                9.61024607064122e-05,
                2.4300232029003796e-05,
                5.829124465589078e-05,
                3.5356254903911806e-05,
                7.484623613063591e-05,
                3.1201922523121745e-05,
                0.00015843615952272183,
                6.605214463262879e-05,
                9.610241483875839e-05,
                5.8291251608160896e-05
            ],
            [
                4.539785237613882e-05,
                2.4300249417247375e-05,
                9.610239167316494e-05,
                1.3007126911335805e-05,
                0.00012339454405494303,
                0.0010322309231937054,
                0.00010889694761215425,
                2.4300252304268445e-05,
                9.610238037737944e-05,
                0.00013982209038651802
            ],
            [
                8.939693106329072e-06,
                3.535626333989112e-05,
                3.535625912717466e-05,
                6.605212093617702e-05,
                2.430024072091399e-05,
                5.422221554926484e-06,
                3.5356254919217684e-05,
                5.8291279411736364e-05,
                9.610244923163104e-05,
                7.484623605603429e-05
            ],
            [
                3.12019076377484e-05,
                4.006370168019018e-05,
                1.0129989770662257e-05,
                6.605217600172698e-05,
                9.610242620376576e-05,
                9.610240332972338e-05,
                7.48462093285157e-05,
                2.4300249409733237e-05,
                0.00012339454520938868,
                0.00020342706904670477
            ],
            [
                1.3007130012980722e-05,
                0.9840936049934791,
                1.473898723508674e-05,
                0.9998766054403412,
                5.1442238133528324e-05,
                1.3007128463352975e-05,
                1.8925148238808306e-05,
                2.753570419988976e-05,
                1.4738983725406915e-05,
                1.6701419849933667e-05
            ],
            [
                5.829127240390582e-05,
                2.430023203740195e-05,
                8.9396941718352e-06,
                1.3007131561425676e-05,
                3.5356254916002164e-05,
                2.7535684525803696e-05,
                3.5356254894393866e-05,
                8.481102103150874e-05,
                1.6701425824307884e-05,
                3.535623804623613e-05
            ],
            [
                5.144223190750916e-05,
                2.7535694366751658e-05,
                4.006368259662828e-05,
                0.08509905022775231,
                4.006367784140681e-05,
                1.8925155005051806e-05,
                8.315281416007088e-07,
                4.5397863201321984e-05,
                6.605214461148412e-05,
                4.006369216362198e-05
            ],
            [
                1.1478766755734576e-05,
                4.006368260129212e-05,
                5.1442195225848094e-05,
                2.43002494076116e-05,
                1.3007133114602719e-05,
                1.670142183934597e-05,
                4.006370152161956e-05,
                0.00010889696096937699,
                5.4222202621161125e-06,
                5.82912515784739e-05
            ],
            [
                0.9971990727773052,
                0.000179527900998409,
                0.00012339458889340497,
                0.00023050671299894272,
                1.6701419851270353e-05,
                0.00010889688273853931,
                1.012999459815081e-05,
                3.5356246471407274e-05,
                0.9149009625340366,
                0.9988304898922845
            ],
            [
                0.9999417087206773,
                0.9998911030910144,
                0.9990889487923009,
                2.144495351097679e-05,
                0.00015843623510281685,
                6.605217612378949e-05,
                0.00010889693471601869,
                4.0063677765182186e-05,
                0.9706877664927535,
                3.120190763922401e-05
            ],
            [
                2.4300246523066122e-05,
                0.0001795280508231233,
                0.9324533158993962,
                1.892514823488397e-05,
                1.3007123809644304e-05,
                0.9859363761205792,
                0.0007096703896889902,
                0.9998911031190266,
                6.144177531208195e-06,
                6.605213666348852e-05
            ],
            [
                6.962256247098965e-06,
                2.1444948406091176e-05,
                4.22283344433731e-06,
                1.1478773597640625e-05,
                2.1444940737257882e-05,
                1.012999460108057e-05,
                1.6701421842566163e-05,
                2.1444945848226808e-05,
                2.4300243624818735e-05,
                6.144172404380855e-06
            ],
            [
                1.3007123812317831e-05,
                3.288749065209246e-06,
                1.0129995809247506e-05,
                1.6701429806475863e-05,
                1.3007125362820425e-05,
                1.670141785651155e-05,
                1.3007126912826352e-05,
                4.785094494576774e-06,
                5.4222202621161125e-06,
                8.939699499627926e-06
            ],
            [
                0.9999646437324458,
                0.9997694933143458,
                8.481101090606248e-05,
                3.5356242266024216e-05,
                9.610240339544534e-05,
                9.610240349752414e-05,
                7.484623604187633e-05,
                4.539786862564012e-05,
                0.9997965731022224,
                6.605214463262879e-05
            ],
            [
                1.0129995807699706e-05,
                3.1201903922734266e-05,
                1.3007126907455643e-05,
                2.1444950957402623e-05,
                8.93969630011598e-06,
                1.1478769487840372e-05,
                4.785096775998733e-06,
                1.147876812069122e-05,
                1.0129993394314164e-05,
                2.4300232038197563e-05
            ],
            [
                5.144223814063949e-05,
                4.539786853134004e-05,
                2.7535681236473055e-05,
                1.4738988992031526e-05,
                1.4738980209347228e-05,
                6.144173868312501e-06,
                3.120191135264947e-05,
                1.1478769492392108e-05,
                4.5397890270732005e-05,
                0.00010889687012128086
            ],
            [
                5.1442195248304415e-05,
                4.006370648569653e-05,
                5.829129329168791e-05,
                1.892514597832254e-05,
                5.829128632668981e-05,
                1.8925148237775583e-05,
                1.892514822620912e-05,
                0.00015843627271653116,
                6.9622587393661365e-06,
                3.535626335108113e-05
            ],
            [
                3.120191508321514e-05,
                3.535624226936835e-05,
                2.4300249418927004e-05,
                2.1444950962395557e-05,
                3.535626335108113e-05,
                1.3007131565140219e-05,
                4.0063711285810896e-05,
                1.1478769491598686e-05,
                3.5356254905712496e-05,
                2.7535700945316292e-05
            ],
            [
                1.8925148239772175e-05,
                0.9324533093296393,
                1.4738985479214553e-05,
                2.7535704220525098e-05,
                1.670141586907437e-05,
                2.4300252316291068e-05,
                0.9984988175855166,
                3.5356250704701545e-05,
                6.144174600985344e-06,
                3.2887482811220126e-06
            ],
            [
                1.0129987355564522e-05,
                2.4300243615448162e-05,
                1.8925141467679015e-05,
                5.8291293252246584e-05,
                6.9622562492265485e-06,
                3.1201915067096954e-05,
                0.9859363747904815,
                3.5356246478738656e-05,
                1.0129988561906404e-05,
                1.8925148238808306e-05
            ],
            [
                1.8925152750176348e-05,
                6.144176066521288e-06,
                1.6701419852090592e-05,
                4.006369216143581e-05,
                1.670141587068447e-05,
                5.422220908703723e-06,
                3.5356246487099006e-05,
                4.785096205717126e-06,
                2.430023783309869e-05,
                5.422217676925328e-06
            ],
            [
                6.60521288918597e-05,
                6.9622562478334885e-06,
                6.9622537593854575e-06,
                4.222833947774596e-06,
                0.9859363716912245,
                5.422221555069497e-06,
                8.481104122255304e-05,
                2.430024071781994e-05,
                1.4738987238893715e-05,
                1.6701417857058377e-05
            ],
            [
                2.7535681242383173e-05,
                5.829125853074485e-05,
                5.144219521911119e-05,
                3.1201911351060354e-05,
                2.7535700933696396e-05,
                1.6701425798607075e-05,
                2.7535694366751658e-05,
                0.9971990726101743,
                6.605215248979934e-05,
                1.6701419835959236e-05
            ],
            [
                1.3007123812554424e-05,
                2.753570420970657e-05,
                4.5397884859458064e-05,
                5.8291251611977796e-05,
                5.82912863088776e-05,
                2.430025231469984e-05,
                1.4738981969240237e-05,
                0.9525741226150287,
                5.422218323019487e-06,
                4.539785781036459e-05
            ],
            [
                7.48462272100267e-05,
                0.0001584362726565963,
                0.00026119027604368705,
                4.539787399744151e-05,
                8.481106146543261e-05,
                0.00010889689613219725,
                4.006369694347607e-05,
                0.00013982202373365993,
                8.93969621451772e-06,
                4.539787401263522e-05
            ],
            [
                1.473898899742027e-05,
                1.8925152749659986e-05,
                6.1441731363550164e-06,
                1.8925157261545463e-05,
                5.144223811518898e-05,
                1.892514372479069e-05,
                2.753569437145972e-05,
                4.222834954607099e-06,
                3.120192252437034e-05,
                8.939695237504067e-06
            ],
            [
                3.120191880379252e-05,
                4.006368260595596e-05,
                1.0129987355343409e-05,
                1.2098652508287273e-06,
                1.4738987234550548e-05,
                2.430023203572232e-05,
                1.8925141466439755e-05,
                1.3007134665674251e-05,
                1.0129993393319151e-05,
                1.670141785237998e-05
            ],
            [
                0.00013982214030853883,
                4.006368261047406e-05,
                4.5397874009662535e-05,
                2.4300243623139103e-05,
                1.8925143724239906e-05,
                7.484626284672882e-05,
                5.8291272379732106e-05,
                4.53978686205205e-05,
                5.829129325648758e-05,
                1.8925157259824262e-05
            ],
            [
                3.12019225022362e-05,
                1.1478768118310953e-05,
                2.7535697654881812e-05,
                0.00013982203972806446,
                1.8925143719695944e-05,
                0.9996646497826501,
                3.120192623110058e-05,
                5.144221975938208e-05,
                1.4738988972889425e-05,
                4.5397890221682726e-05
            ],
            [
                8.481108166450792e-05,
                3.53562633126235e-05,
                2.7535681240079227e-05,
                3.535624227425594e-05,
                9.610246065397443e-05,
                9.610244922114349e-05,
                0.9986749775596796,
                0.0001088969608980751,
                2.7535687791694597e-05,
                3.1201915085825835e-05
            ],
            [
                1.0129995809431767e-05,
                1.8925157262061825e-05,
                0.00010889686972832847,
                0.9740426451569193,
                4.539786319306454e-05,
                4.006370169826257e-05,
                1.4738985482753428e-05,
                5.8291258547708845e-05,
                6.962255419279419e-06,
                6.962255418924822e-06
            ],
            [
                1.670141985166528e-05,
                0.9995121429470971,
                8.481101100478711e-05,
                3.5356238038776134e-05,
                3.120191507481552e-05,
                6.605216037820727e-05,
                0.00020342692268608288,
                8.481104127376647e-05,
                0.9999687980812043,
                4.006370648788271e-05
            ],
            [
                8.481101090606248e-05,
                3.5356254910985954e-05,
                4.006370171895837e-05,
                4.006370647870077e-05,
                7.484620937425679e-05,
                3.5356259116499136e-05,
                5.829127241747701e-05,
                5.144220745705777e-05,
                2.4300232038993178e-05,
                9.610246049386444e-05
            ],
            [
                1.3007125360809367e-05,
                2.144494329566774e-05,
                1.3007123811229494e-05,
                5.82912515784739e-05,
                3.120191877791261e-05,
                1.0129995805359584e-05,
                1.0129992186202796e-05,
                0.00020342692356213902,
                6.144173136885882e-06,
                1.8925150487521332e-05
            ],
            [
                1.147877222879974e-05,
                1.4738976699106073e-05,
                8.9396941718352e-06,
                1.473898196763166e-05,
                1.0129992185539456e-05,
                1.8925150493166868e-05,
                2.5612828213352452e-06,
                1.1478772230198667e-05,
                0.00013982210630158876,
                7.889263525778283e-06
            ],
            [
                3.120191508185304e-05,
                1.1478773598329648e-05,
                2.430023783150746e-05,
                6.144174601410037e-06,
                1.0129992185981682e-05,
                5.144223202577919e-05,
                1.473898372822193e-05,
                1.8925143723620274e-05,
                1.4738980212296288e-05,
                1.8925145980181433e-05
            ],
            [
                0.9669140213729421,
                6.144176066264237e-06,
                6.60521524950855e-05,
                1.2098655372624967e-06,
                4.006367779199926e-05,
                0.015906391041210867,
                0.0007096703476670323,
                3.12019262340518e-05,
                1.0129993393945642e-05,
                7.484624501857396e-05
            ],
            [
                7.889262584508638e-06,
                7.889259763857458e-06,
                0.00013982212345967678,
                2.260325375615501e-06,
                1.3007130012980722e-05,
                2.7535704220525098e-05,
                4.7850927830148924e-06,
                4.0063692140011286e-05,
                1.3007123811229494e-05,
                1.4738987240824012e-05
            ],
            [
                1.4738980210687712e-05,
                0.9669140213729421,
                0.8175744739711883,
                0.8519528000888386,
                9.610242637576158e-05,
                0.8933094039240554,
                1.892515725376564e-05,
                6.962255418367598e-06,
                3.120190764467241e-05,
                7.48462272100267e-05
            ],
            [
                3.535626755929635e-05,
                0.9241418126663686,
                4.785094494463623e-06,
                1.0129989768911772e-05,
                4.785096776133645e-06,
                1.473898372822193e-05,
                8.939695237341456e-06,
                5.4222196154940574e-06,
                1.3007123803563812e-05,
                4.539786320660675e-05
            ],
            [
                2.1444953522913026e-05,
                4.5397863124032274e-05,
                3.1201918807538294e-05,
                6.605215250037168e-05,
                5.144221362431326e-05,
                4.5397863184146494e-05,
                4.006369216362198e-05,
                3.535626746270212e-05,
                9.61023917109201e-05,
                3.5356250660713247e-05
            ],
            [
                0.6224593312018546,
                1.6701425821573757e-05,
                5.422217676654099e-06,
                1.6701419849933667e-05,
                7.8892625849535e-06,
                2.43002436174814e-05,
                1.0129988564430787e-05,
                0.9525741251394714,
                2.7535681227157105e-05,
                1.67014198374782e-05
            ],
            [
                6.96225707894582e-06,
                5.422220908762902e-06,
                2.561282210562998e-06,
                0.994779874294351,
                0.9998415638037557,
                0.9986749777061796,
                9.610243770231598e-05,
                2.7535684518791692e-05,
                5.1442219781089866e-05,
                0.9999852610233104
            ],
            [
                0.00023050665225290986,
                4.0063682603624035e-05,
                3.1201907631845964e-05,
                9.610242636527403e-05,
                0.00013982204046248067,
                7.484623609796368e-05,
                6.60521445480501e-05,
                6.605215238984264e-05,
                7.484621826927065e-05,
                0.00013982214014578718
            ],
            [
                1.473897845457507e-05,
                6.962255418924822e-06,
                0.0002034269486658847,
                2.4300243616508983e-05,
                1.3007125362323574e-05,
                0.9968273174159751,
                1.147877222879974e-05,
                0.9465966728366374,
                6.605212101402784e-05,
                8.939695237341456e-06
            ],
            [
                7.484624490204296e-05,
                0.00020342689987606823,
                8.481107159890629e-05,
                9.610238050882334e-05,
                6.60521288207367e-05,
                6.605216026911993e-05,
                0.00020342702033085072,
                4.0063711246896956e-05,
                0.00010889693508045057,
                0.00037998447554048154
            ],
            [
                4.0063711256516126e-05,
                3.120190019784534e-05,
                1.012998977088337e-05,
                1.3007131561425676e-05,
                1.8925143725341476e-05,
                7.484625391903742e-05,
                2.430024362393472e-05,
                1.6701417860795016e-05,
                1.8925141467059383e-05,
                2.753569437686898e-05
            ],
            [
                3.1201926243586504e-05,
                5.8291286317783706e-05,
                6.9622562484666964e-06,
                0.0011695104868547142,
                1.8925152748558416e-05,
                4.539789016057757e-05,
                0.00010889694793538952,
                3.535625485066282e-05,
                0.0003353502230380636,
                1.8925141470949294e-05
            ],
            [
                0.00015843629205243188,
                1.4738978456049602e-05,
                9.610238039975287e-05,
                0.00015843617857507104,
                6.605212100874168e-05,
                0.00010889693508045057,
                4.006370647374544e-05,
                0.00010889687012128086,
                3.535626334323525e-05,
                9.610239178363376e-05
            ],
            [
                4.785093922776592e-06,
                2.144495607789177e-05,
                5.144220132947586e-05,
                3.120190392409636e-05,
                0.00023050674193329587,
                2.1444950965906214e-05,
                5.82912863042125e-05,
                1.4738976697229395e-05,
                6.605213673316984e-05,
                4.5397863181173815e-05
            ],
            [
                2.1444948403750736e-05,
                2.4300246519706854e-05,
                1.012998977108606e-05,
                2.1444945849006956e-05,
                4.5397852355660356e-05,
                1.8925141465200488e-05,
                2.753568124458694e-05,
                7.889261644760245e-06,
                2.7535697653779924e-05,
                4.222834954461155e-06
            ],
            [
                4.5397890254712545e-05,
                1.8925152742706337e-05,
                8.481106124762124e-05,
                2.144495862967221e-05,
                5.8291258521838744e-05,
                2.430023493564795e-05,
                5.8291244525692116e-05,
                1.670141785237998e-05,
                6.605212884908979e-05,
                5.829129330780371e-05
            ],
            [
                2.144495096457996e-05,
                4.785094492070025e-06,
                5.8291258534985854e-05,
                6.605213674902834e-05,
                2.4300249408672413e-05,
                4.5397868604005595e-05,
                4.006369214992195e-05,
                3.535624225509145e-05,
                1.3007126911974612e-05,
                5.144221359998557e-05
            ],
            [
                0.00012339463344461816,
                0.00010889694807323985,
                5.144219518243253e-05,
                0.00023050676632695716,
                0.00026119033820884815,
                9.610243764498401e-05,
                8.481101081535921e-05,
                2.1444958636771547e-05,
                9.610241483875839e-05,
                5.144221363404434e-05
            ],
            [
                1.1478768117434013e-05,
                3.7266401720529807e-06,
                8.939698431389304e-06,
                5.422219613846953e-06,
                6.9622562484666964e-06,
                7.889266345584138e-06,
                2.1444940733201126e-05,
                5.422221554670048e-06,
                4.222832940339353e-06,
                1.892514597563747e-05
            ],
            [
                3.535625068579429e-05,
                0.0002305067137769642,
                2.4300234934056724e-05,
                1.0129989770662257e-05,
                6.9622545892184106e-06,
                3.120190392795564e-05,
                7.484622713542509e-05,
                0.9984988174049108,
                6.605214462734262e-05,
                4.539787399744151e-05
            ],
            [
                1.892514822620912e-05,
                3.7266397282926013e-06,
                8.93969523617066e-06,
                3.288750241204353e-06,
                4.222833947820683e-06,
                6.962259568889411e-06,
                7.889264466344872e-06,
                4.7850950647493785e-06,
                5.422219616085833e-06,
                5.422220908314139e-06
            ],
            [
                5.1442219704738336e-05,
                8.939700565834043e-06,
                0.00017952790121781749,
                0.00010889688299997942,
                1.1478772227964558e-05,
                0.9989677688011864,
                3.1201918796982014e-05,
                0.9994472213233612,
                8.481108168178473e-05,
                9.610246072738731e-05
            ],
            [
                6.962254588724508e-06,
                1.670142781520948e-05,
                7.88926634755014e-06,
                8.939697369151141e-06,
                4.5397874023865346e-05,
                1.0129992186939844e-05,
                4.7850933535006355e-06,
                1.012999460150437e-05,
                1.8925148238291944e-05,
                3.726640616748873e-06
            ],
            [
                3.1201918788014855e-05,
                4.5397857775848465e-05,
                5.8291244621538684e-05,
                7.484620011059245e-05,
                0.9994472214580716,
                7.484620910307734e-05,
                2.4300249408672413e-05,
                8.48110714063931e-05,
                2.1444956079218013e-05,
                0.98901305643837
            ],
            [
                0.999704042868757,
                1.3007133109847152e-05,
                0.9999921107393,
                0.9998601779096136,
                0.9999646437535832,
                0.9995121428420225,
                0.9999687980775741,
                5.144221966244559e-05,
                0.999290329574646,
                0.9998911031300071
            ],
            [
                1.4738985485166298e-05,
                4.0063692132141055e-05,
                1.6701419843189485e-05,
                0.9241418189341296,
                1.6701419846834993e-05,
                0.9046505447409666,
                0.9975273766796957,
                0.9706877680296923,
                1.0129994600638342e-05,
                7.484623608435025e-05
            ],
            [
                3.120191879107958e-05,
                4.5397857748103446e-05,
                2.144495607789177e-05,
                6.605216035177641e-05,
                1.6701423831188846e-05,
                1.670142383167491e-05,
                4.539786859839053e-05,
                0.9796676465831374,
                5.829127247176183e-05,
                4.5397884797196873e-05
            ],
            [
                6.60521446167703e-05,
                2.7535704220525098e-05,
                2.753570094040789e-05,
                5.1442195212374294e-05,
                1.670141586150995e-05,
                6.962255419051463e-06,
                9.610242625969935e-05,
                1.8925157257965367e-05,
                4.539788484079622e-05,
                1.6701415864001047e-05
            ],
            [
                4.0063696922780274e-05,
                8.481104111148777e-05,
                0.00023050665896669716,
                3.1201922517673344e-05,
                2.7535697650273915e-05,
                4.539786318711917e-05,
                2.7535691079423274e-05,
                5.14422013436982e-05,
                9.610241472619204e-05,
                5.144222587386666e-05
            ],
            [
                5.8291286364010624e-05,
                4.539786320396437e-05,
                8.481101082523169e-05,
                6.962256249758443e-06,
                2.1444948395559206e-05,
                6.962253759043525e-06,
                5.144221362431326e-05,
                8.939700566289352e-06,
                4.5397857795336036e-05,
                1.8925145980181433e-05
            ],
            [
                1.8925150491445666e-05,
                3.7266388395620047e-06,
                1.892515049199645e-05,
                3.726637951170554e-06,
                1.0129992186202796e-05,
                6.962257908044647e-06,
                3.288750633488963e-06,
                6.962255419653012e-06,
                1.0129994601872894e-05,
                1.1478769493728398e-05
            ],
            [
                0.00012339454506575626,
                0.0002611902442391452,
                0.0001584362732789965,
                8.481106150677358e-05,
                4.5397863201321984e-05,
                0.00043055703643335056,
                0.00013982207385299317,
                0.9999038975737291,
                6.605212100345552e-05,
                6.605212102411961e-05
            ],
            [
                3.7266397280485686e-06,
                2.7535684522397864e-05,
                4.222833444168322e-06,
                1.3007123810638006e-05,
                1.8925141463066202e-05,
                6.9622545892184106e-06,
                1.892514822620912e-05,
                7.889261643727018e-06,
                8.939697368110433e-06,
                1.670142383167491e-05
            ],
            [
                4.5397874029150114e-05,
                6.605216824595201e-05,
                8.481102100559352e-05,
                0.00013982203907705838,
                7.484620040083068e-05,
                5.829127244377123e-05,
                2.7535691095550887e-05,
                3.535624641674347e-05,
                5.8291258453558646e-05,
                1.6701421843356024e-05
            ],
            [
                0.9579122735862823,
                7.889264466230069e-06,
                2.1444948409679848e-05,
                1.4738987238464762e-05,
                1.1478766755734576e-05,
                2.7535681241281285e-05,
                5.144220132161615e-05,
                2.1444950965282096e-05,
                5.422221554581283e-06,
                1.4738976699106073e-05
            ],
            [
                0.9933071487599494,
                8.481104129042625e-05,
                2.753568123767511e-05,
                4.222835457906302e-06,
                9.610242636527403e-05,
                3.288750241410738e-06,
                7.889266346603015e-06,
                6.144175332596544e-06,
                1.3007131564643372e-05,
                1.1478772229300848e-05
            ],
            [
                6.605215227306636e-05,
                7.484625387601897e-05,
                0.00010889688312673828,
                4.539788481371178e-05,
                3.1201918768604926e-05,
                7.484626290608339e-05,
                5.8291272374642915e-05,
                3.1201918798457626e-05,
                5.144221971634078e-05,
                0.00012339463353079768
            ],
            [
                1.8925150490826034e-05,
                7.48462271136436e-05,
                0.000335350146272333,
                0.00043055707816819775,
                1.1478769489719528e-05,
                1.6701429803316423e-05,
                2.7535704212311033e-05,
                2.1444953512849142e-05,
                0.0001233946033931049,
                5.1442219666936855e-05
            ],
            [
                0.00043055713517159254,
                0.00010889689621142153,
                0.0001088969351343231,
                6.605212885485651e-05,
                1.4738976695459959e-05,
                0.00010889689614645761,
                0.000230506659369122,
                0.00020342692397944955,
                9.610243743663133e-05,
                0.00023050674040408104
            ],
            [
                3.2887506333812835e-06,
                7.484624496248661e-05,
                8.939698434332555e-06,
                1.0129995809431767e-05,
                1.1478770861211786e-05,
                0.9947798753704149,
                1.6701419846834993e-05,
                1.4738983727256784e-05,
                5.422220908018252e-06,
                4.2228324370327694e-06
            ],
            [
                7.484626278192885e-05,
                1.4738987229134998e-05,
                5.829126545587422e-05,
                3.1201926212712214e-05,
                6.605212880872268e-05,
                5.14422258772351e-05,
                2.430023493052066e-05,
                7.889262582571338e-06,
                6.144172399334838e-06,
                2.7535684514885004e-05
            ],
            [
                1.1478766756653273e-05,
                2.9023123310580418e-06,
                8.48110715112881e-05,
                2.144494074076854e-05,
                1.0129987356706945e-05,
                2.7535697649071857e-05,
                0.9820137915183793,
                8.93969630362837e-06,
                6.144177530548804e-06,
                8.939693106182721e-06
            ],
            [
                2.1444953516281788e-05,
                4.006371126117997e-05,
                2.753568121183087e-05,
                2.1444953520182517e-05,
                4.5397874031792504e-05,
                1.3007131555463476e-05,
                0.9947798737744549,
                5.144221356106128e-05,
                7.484620040790966e-05,
                4.0063682591672956e-05
            ],
            [
                5.144220134032976e-05,
                5.8291293265817787e-05,
                1.6701415868193372e-05,
                1.4738988992031526e-05,
                3.5356259098234985e-05,
                3.120190020068305e-05,
                4.0063711278232147e-05,
                1.8925150490826034e-05,
                2.4300249416363357e-05,
                8.481108171572136e-05
            ],
            [
                3.535626334645077e-05,
                0.9968273170271802,
                7.889263524960312e-06,
                1.6701419850389357e-05,
                2.144495351940237e-05,
                1.8925152750692706e-05,
                1.8925152751174644e-05,
                1.89251527491092e-05,
                2.1444958631232504e-05,
                2.430024072285883e-05
            ],
            [
                0.00010889693482376376,
                3.535625491265802e-05,
                0.00037998442786112564,
                2.1444945850567248e-05,
                8.93969310675186e-06,
                1.892515048889829e-05,
                1.01299946023704e-05,
                2.1444948367551967e-05,
                7.889264465842609e-06,
                1.6701423834226767e-05
            ],
            [
                5.829124465589078e-05,
                4.5397852399094525e-05,
                5.144220136765162e-05,
                5.8291286317783706e-05,
                0.0001584361599676224,
                7.889261642134126e-06,
                0.00017952798700133205,
                3.535626755762428e-05,
                2.753570422373059e-05,
                0.0006263343066169153
            ],
            [
                4.5397852346412016e-05,
                3.535626755762428e-05,
                1.0129989769188164e-05,
                8.939694171331106e-06,
                3.120190018853766e-05,
                5.144220746454321e-05,
                2.7535687798506256e-05,
                3.5356238040705445e-05,
                2.4300249417247375e-05,
                7.88925976359915e-06
            ],
            [
                6.605216041280767e-05,
                0.00012339463351284362,
                5.8291251573808804e-05,
                0.0001233945599676219,
                7.484620933559467e-05,
                2.4300243620398656e-05,
                3.120190391558324e-05,
                0.9992903295499199,
                2.1444943296369872e-05,
                0.00020342692342007588
            ],
            [
                0.00015843621595594825,
                1.6701429805199933e-05,
                1.147877222702498e-05,
                7.889266347133978e-06,
                3.535626334490732e-05,
                1.3007134665674251e-05,
                7.484623611811155e-05,
                2.753569107391384e-05,
                1.4738983726184394e-05,
                6.962256248314727e-06
            ],
            [
                4.539788485433845e-05,
                2.753570422373059e-05,
                6.1441753335241615e-06,
                1.0129992185060374e-05,
                0.9959298618518454,
                1.3007123812554424e-05,
                2.1444945852673643e-05,
                3.5356238044435446e-05,
                7.889260704423598e-06,
                0.9924227572684318
            ],
            [
                3.535625491265802e-05,
                4.006369693006752e-05,
                7.4846209355198e-05,
                1.1478772229300848e-05,
                4.5397884856980825e-05,
                4.539785780309804e-05,
                0.9959298629768498,
                2.1444940736477737e-05,
                0.9975273768623164,
                2.4300243611116483e-05
            ],
            [
                7.484620927188383e-05,
                7.48462449330816e-05,
                4.5397857790051276e-05,
                4.006368735403649e-05,
                1.1478770859624945e-05,
                5.1442219525461983e-05,
                1.67014238214675e-05,
                8.939698434153684e-06,
                4.222831933795376e-06,
                0.00033535004054873987
            ],
            [
                5.8291279404102564e-05,
                0.00012339455987964702,
                4.5397874000744484e-05,
                2.7535697652678035e-05,
                8.481107159026786e-05,
                0.00010889692207498694,
                1.8925152750176348e-05,
                0.00023050674232230666,
                0.00015843627286175787,
                7.484620930782328e-05
            ],
            [
                2.1444958631232504e-05,
                9.61024034059329e-05,
                0.00012339455989760105,
                7.889264466115267e-06,
                1.1478768123823146e-05,
                1.6701417858577338e-05,
                3.7266410609160796e-06,
                2.1444953521586782e-05,
                4.785096776068365e-06,
                3.120191878131786e-05
            ],
            [
                2.144494583730477e-05,
                2.753569436294514e-05,
                9.610239168574998e-05,
                5.422218968822766e-06,
                1.3007128463069061e-05,
                5.144221967142812e-05,
                1.6701423828576233e-05,
                2.430023202476052e-05,
                5.14422197242005e-05,
                1.1478769491014062e-05
            ],
            [
                0.9964063976119969,
                0.9525741315347258,
                1.0129988563730593e-05,
                5.82912515784739e-05,
                0.9998766054402657,
                0.9996200155395052,
                5.422218968822766e-06,
                5.829128633093081e-05,
                0.9998415638422569,
                0.995929862195387
            ],
            [
                1.6701425819447213e-05,
                1.4738978457336465e-05,
                1.4738976699749503e-05,
                1.6701429804288556e-05,
                4.0063682618927264e-05,
                6.962256248314727e-06,
                3.120191879981973e-05,
                4.00636825989602e-05,
                2.1444958637356654e-05,
                1.0129993394129904e-05
            ],
            [
                4.0063687383622725e-05,
                0.00013982212343729845,
                9.61024377246894e-05,
                9.610243773517696e-05,
                0.00037998443303477214,
                4.539789026296999e-05,
                3.1201922514835635e-05,
                0.0001398221070929684,
                4.539786318711917e-05,
                0.00023050679451012358
            ],
            [
                0.00012339457454990706,
                2.753569434872079e-05,
                0.9995121428366298,
                3.535625912190121e-05,
                4.006367783266211e-05,
                4.0063687394553603e-05,
                0.9890130558817719,
                8.481103114893482e-05,
                6.60521445946645e-05,
                3.535624648041073e-05
            ],
            [
                4.7850950643402904e-06,
                1.1478770851648967e-05,
                1.6701415866188347e-05,
                3.2887502414436403e-06,
                6.1441738691562974e-06,
                4.2228319339950885e-06,
                1.1478764019328247e-05,
                1.67014178590634e-05,
                1.1478766755233466e-05,
                1.8925145981833788e-05
            ],
            [
                0.00012339460415256175,
                3.535625911829982e-05,
                1.8925152750176348e-05,
                0.00012339457479049144,
                3.5356246490314526e-05,
                3.535624226936835e-05,
                5.1442238173201186e-05,
                5.144221362094481e-05,
                2.753569109034197e-05,
                1.670142781560441e-05
            ],
            [
                5.829125158695591e-05,
                2.430024072091399e-05,
                2.4300237834601515e-05,
                3.535623804803683e-05,
                2.753569437145972e-05,
                9.610242630304791e-05,
                3.120190391853445e-05,
                5.144220131787343e-05,
                3.120192252175965e-05,
                1.6701417859944398e-05
            ],
            [
                6.962257909121104e-06,
                6.605212097654411e-05,
                1.1478764019787597e-05,
                3.1201926246083686e-05,
                3.5356267550807374e-05,
                2.430023203740195e-05,
                2.4300237829827827e-05,
                2.4300249415479343e-05,
                1.3007133115667397e-05,
                3.1201911361276113e-05
            ],
            [
                0.9997694932852572,
                5.1442195242316055e-05,
                0.00017952802968414412,
                9.610239197310875e-05,
                0.00017952800807500606,
                0.000158436253470535,
                0.00026119021265499714,
                4.539785238918559e-05,
                6.605216823537969e-05,
                0.9980732652511545
            ],
            [
                5.144221363404434e-05,
                1.0129993394129904e-05,
                8.939699500327152e-06,
                2.7535700938304286e-05,
                1.8925145978942173e-05,
                1.147877222879974e-05,
                0.00015843617887474504,
                0.00010889693494260025,
                1.0129993393742954e-05,
                0.0001795279008521367
            ],
            [
                0.00010889693514699898,
                1.1478764019328247e-05,
                2.4300249418927004e-05,
                1.4738978456398127e-05,
                8.481107158224648e-05,
                5.144220134032976e-05,
                1.4738976696371488e-05,
                8.939699500766203e-06,
                1.4738980213985297e-05,
                3.1201922520397544e-05
            ],
            [
                3.2887482811579057e-06,
                7.889261644982674e-06,
                0.9525741293468758,
                6.1441746016670885e-06,
                4.222831934248571e-06,
                3.2887494573232236e-06,
                1.0129995809044816e-05,
                1.9947306726213275e-06,
                0.6791787056691697,
                2.260324836651547e-06
            ],
            [
                0.00010889687024170175,
                4.785096776251149e-06,
                3.1201907642061724e-05,
                5.144220135417782e-05,
                2.4300234934056724e-05,
                6.605212875874436e-05,
                0.00010889690902832823,
                6.605213670529732e-05,
                3.5356242243001115e-05,
                2.430023203298187e-05
            ],
            [
                7.889262584350785e-06,
                0.00010889688291124823,
                4.5397874009662535e-05,
                1.6701421837705495e-05,
                3.726640172385136e-06,
                3.1201900204769344e-05,
                0.00013982214005220497,
                9.610240332972338e-05,
                5.144221969687863e-05,
                3.120190761845198e-05
            ],
            [
                2.1444948395559206e-05,
                9.610238047666152e-05,
                1.4738978455701077e-05,
                0.00020342690014243665,
                8.481103111438118e-05,
                4.539786317522845e-05,
                3.120191135560069e-05,
                5.829129329974581e-05,
                3.5356250691324983e-05,
                0.0003353500636330875
            ],
            [
                5.829128632668981e-05,
                9.610241473877709e-05,
                3.120191134288775e-05,
                5.8291258547708845e-05,
                2.144494329769612e-05,
                5.829126548301662e-05,
                2.7535704219423216e-05,
                8.481105136527973e-05,
                0.997817283631733,
                4.539787941498982e-05
            ],
            [
                4.539785779797843e-05,
                0.0013250221896835127,
                0.9997388095698354,
                0.00017952800835971484,
                0.00023050671441413696,
                0.00017952800792612165,
                3.535626333989112e-05,
                0.0001584362163363038,
                0.00023050676928478096,
                8.481102096980583e-05
            ]
        ]
    },
    {
        "q_id": "8068_mmlu_math",
        "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,
            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": [
            [
                0.9999999317440197,
                0.9999998874647574,
                0.999999953088334,
                0.9999999468421249,
                0.9999998555020306,
                0.9999999226557592,
                0.9999999226558238,
                0.9999999317440197,
                0.9999999317440197,
                0.9999999530883564
            ],
            [
                0.9999999317439464,
                0.9999999006881141,
                0.9999999530883452,
                0.9999999397642725,
                0.9999999468421059,
                0.9999999006880904,
                0.9999999226558238,
                0.9999999397643083,
                0.9999999397642437,
                0.999999939764215
            ],
            [
                0.9999999226557592,
                0.9999999226557131,
                0.9999999006880549,
                0.9999999468421883,
                0.9999999317439627,
                0.9999999468421249,
                0.9999999634651617,
                0.999999814460854,
                0.9999998555020135,
                0.9999999468421883
            ],
            [
                0.9999999317439221,
                0.9999998724809267,
                0.999999931743971,
                0.9999998555019962,
                0.9999998874648245,
                0.9999999123574942,
                0.9999999397642508,
                0.9999999317439464,
                0.9999999468421439,
                0.9999999397642365
            ],
            [
                0.9999999123574628,
                0.9999998874647306,
                0.9999998724809267,
                0.9999999317439383,
                0.9999999317439464,
                0.99999992265575,
                0.9999997617631469,
                0.9999999123574941,
                0.9999999530883396,
                0.9999999006881259
            ],
            [
                0.9999999317439953,
                0.9999998874648917,
                0.999999953088334,
                0.999999922655833,
                0.999999939764294,
                0.9999999123575778,
                0.999999931743922,
                0.999999939764251,
                0.9999999586005999,
                0.9999999468421187
            ],
            [
                0.9999999586006146,
                0.9999999397642437,
                0.9999999006879838,
                0.999999953088362,
                0.999999931743971,
                0.9999999317439384,
                0.9999999397642365,
                0.9999999530884012,
                0.9999999123575464,
                0.999999900687972
            ],
            [
                0.9999999006879957,
                0.999999931743971,
                0.9999999397643011,
                0.999999922655833,
                0.9999999468421312,
                0.9999998724809723,
                0.9999999317439058,
                0.9999999397642365,
                0.9999999006879838,
                0.9999999123575151
            ],
            [
                0.9999999586006294,
                0.9999999586005851,
                0.9999999634651748,
                0.9999999530883452,
                0.9999998555019791,
                0.9999999317440197,
                0.9999999006881259,
                0.999999939764215,
                0.9999999397642078,
                0.9999999586006443
            ],
            [
                0.9999999530883564,
                0.9999999397642725,
                0.9999998874647709,
                0.999999958600659,
                0.9999999677581298,
                0.9999999006881377,
                0.9999999226557131,
                0.9999998874649318,
                0.9999999317440116,
                0.9999999468421249
            ],
            [
                0.9999999006880075,
                0.9999999226558146,
                0.9999999226557408,
                0.999999939764215,
                0.9999999006881259,
                0.9999998724809875,
                0.9999998874648379,
                0.9999998144609202,
                0.9999998555019274,
                0.999999939764215
            ],
            [
                0.9999998555019963,
                0.9999999123574419,
                0.999999946842144,
                0.99999992265575,
                0.9999999226557778,
                0.9999998724809267,
                0.9999999468421883,
                0.9999998874649318,
                0.9999999530883172,
                0.9999999468420996
            ],
            [
                0.9999998724809571,
                0.9999999530884012,
                0.999999931743971,
                0.9999999468421502,
                0.9999999317439465,
                0.9999999530883396,
                0.9999999317439954,
                0.9999999468421947,
                0.9999999317439465,
                0.9999999317439546
            ],
            [
                0.9999999123575464,
                0.9999999123574419,
                0.999999939764215,
                0.999999814460876,
                0.9999999778405134,
                0.9999999006881496,
                0.999999922655833,
                0.9999999634651531,
                0.9999999677581259,
                0.9999999397642868
            ],
            [
                0.9999998724810027,
                0.9999998874648514,
                0.9999998724809115,
                0.9999999317439302,
                0.9999999397642078,
                0.9999999123575777,
                0.9999999123574836,
                0.999999730042126,
                0.9999999317439058,
                0.9999998874649184
            ],
            [
                0.9999998724809571,
                0.9999999634651879,
                0.9999999397642222,
                0.9999998874649184,
                0.9999999317439465,
                0.9999999397642293,
                0.999999931743979,
                0.9999999123575255,
                0.99999995860059,
                0.9999999123574419
            ],
            [
                0.999999922655833,
                0.9999999123575464,
                0.9999998724809571,
                0.999999974890009,
                0.9999999468421186,
                0.9999999586006098,
                0.9999999006880194,
                0.9999999123575987,
                0.9999999634651487,
                0.9999998724809874
            ],
            [
                0.9999999634651662,
                0.9999999634651444,
                0.99999995308839,
                0.999999953088334,
                0.9999999317439058,
                0.9999998724808964,
                0.9999998874648245,
                0.9999999006880785,
                0.9999999317439058,
                0.9999998874648514
            ],
            [
                0.9999999677581606,
                0.9999999123575359,
                0.999999946842163,
                0.999999939764215,
                0.9999999123575777,
                0.9999999226558515,
                0.9999999715466595,
                0.999999855502048,
                0.9999999468421947,
                0.9999999317439221
            ],
            [
                0.9999999006880904,
                0.9999999006880075,
                0.999999939764215,
                0.9999999317439954,
                0.9999998874647307,
                0.9999998362622942,
                0.9999999006879838,
                0.9999999226558238,
                0.9999998724809115,
                0.9999999123574732
            ],
            [
                0.9999999586006098,
                0.9999998874648782,
                0.9999998362623723,
                0.9999999123574419,
                0.9999998724809419,
                0.999999922655833,
                0.9999999397642078,
                0.9999999226557592,
                0.9999999006880904,
                0.9999999530883396
            ],
            [
                0.9999999317440279,
                0.9999999468421693,
                0.9999999123575882,
                0.9999999634651836,
                0.9999999397642222,
                0.9999999468421186,
                0.99999995860059,
                0.9999999397642365,
                0.9999999317440279,
                0.9999999317440278
            ],
            [
                0.9999999317440035,
                0.9999999530883172,
                0.9999999715466493,
                0.999999946842144,
                0.9999999634651705,
                0.9999999397642078,
                0.9999999778405292,
                0.9999999468421249,
                0.9999998874647843,
                0.9999999317439872
            ],
            [
                0.9999999397642508,
                0.9999998362622552,
                0.9999999226558146,
                0.999999931743971,
                0.9999999677581375,
                0.9999998724809267,
                0.9999999468421122,
                0.9999999226557961,
                0.9999998874649051,
                0.9999998874649184
            ],
            [
                0.9999999634652054,
                0.9999999317439954,
                0.9999998555019963,
                0.9999999778405134,
                0.9999999530883564,
                0.9999999468421629,
                0.9999999715466561,
                0.9999998874649184,
                0.9999999006881259,
                0.9999999468421947
            ],
            [
                0.999999946842163,
                0.999999855502048,
                0.999999946842182,
                0.9999999006879957,
                0.9999999123575986,
                0.9999999123575987,
                0.9999999317439302,
                0.999999939764215,
                0.9999998874649318,
                0.9999999006880194
            ],
            [
                0.9999999468421059,
                0.9999999586006542,
                0.9999999226557131,
                0.9999999468421756,
                0.9999999530883843,
                0.9999999586005999,
                0.9999999468421186,
                0.99999995860059,
                0.99999995860059,
                0.9999999468421187
            ],
            [
                0.9999999123574942,
                0.9999998362622747,
                0.9999999468421187,
                0.9999999317439302,
                0.9999999317439221,
                0.9999999397643156,
                0.9999999006880194,
                0.9999999468421503,
                0.9999999634651836,
                0.999999953088362
            ],
            [
                0.9999999397642437,
                0.9999999006879721,
                0.9999999586006196,
                0.9999999468421376,
                0.9999999317439546,
                0.9999999317440279,
                0.9999999006880194,
                0.9999999226558423,
                0.9999998362623528,
                0.9999999226557224
            ],
            [
                0.9999998555019446,
                0.9999999317439302,
                0.9999999123574732,
                0.9999999397642222,
                0.9999999317440279,
                0.9999999530883452,
                0.9999999468421249,
                0.9999999677581529,
                0.9999999530883955,
                0.999999939764258
            ],
            [
                0.9999999317439383,
                0.9999999317439465,
                0.99999995308839,
                0.9999998724809571,
                0.9999999530883564,
                0.9999999317439465,
                0.9999998724809267,
                0.999999931743971,
                0.9999999123575359,
                0.9999999226557778
            ],
            [
                0.9999999586005949,
                0.9999999634651531,
                0.99999995308839,
                0.9999999468421376,
                0.9999999317440116,
                0.9999999123575777,
                0.9999999317440197,
                0.999999939764258,
                0.9999999123574732,
                0.9999999634651836
            ],
            [
                0.9999998724809571,
                0.9999998555020307,
                0.9999999123574523,
                0.9999999006880785,
                0.9999999123574732,
                0.9999999226557131,
                0.9999998874649184,
                0.999999814460854,
                0.9999999317439058,
                0.9999999226557408
            ],
            [
                0.9999999226557776,
                0.9999999677581259,
                0.9999999586006196,
                0.9999999397642437,
                0.9999999634651617,
                0.9999999226558423,
                0.9999998874649184,
                0.9999999397642868,
                0.9999999317440197,
                0.9999999006879838
            ],
            [
                0.9999999397642365,
                0.9999999123575151,
                0.9999999715466731,
                0.9999999530884012,
                0.9999998724809723,
                0.9999999468421122,
                0.9999999226557131,
                0.9999999006880785,
                0.9999999530883732,
                0.9999999397642653
            ],
            [
                0.9999999530884012,
                0.9999999677581183,
                0.9999999530883228,
                0.9999998874647843,
                0.9999999468421122,
                0.9999999006881496,
                0.9999999586006146,
                0.9999999397642796,
                0.9999999634651662,
                0.9999999586006294
            ],
            [
                0.9999999530883172,
                0.9999999006880904,
                0.9999997300422225,
                0.9999999226557131,
                0.999999931743914,
                0.9999999715466426,
                0.999999953088334,
                0.9999999317439302,
                0.9999999226557316,
                0.9999999317440116
            ],
            [
                0.9999999468421313,
                0.9999998555020307,
                0.99999995860059,
                0.9999999317440116,
                0.9999999226557224,
                0.9999999586006294,
                0.9999999006880667,
                0.9999999468421377,
                0.9999999397642725,
                0.9999999586005949
            ],
            [
                0.9999999226557592,
                0.9999999468421883,
                0.9999999530883228,
                0.999999946842125,
                0.999999939764258,
                0.9999999397642078,
                0.9999998555019791,
                0.999999939764258,
                0.9999999317439221,
                0.9999999226557408
            ],
            [
                0.999999900687972,
                0.9999999123574419,
                0.9999999317440197,
                0.9999999226557316,
                0.999999946842125,
                0.9999999317439058,
                0.9999999530883452,
                0.9999999397643156,
                0.9999999677581028,
                0.9999999530883787
            ],
            [
                0.9999998362623528,
                0.9999999317439139,
                0.999999900687972,
                0.9999999317439546,
                0.9999999006881496,
                0.9999999586006048,
                0.999999939764258,
                0.9999999006880549,
                0.9999998724809419,
                0.9999999677581259
            ],
            [
                0.999999963465201,
                0.9999999530883396,
                0.9999999530883508,
                0.9999999397642222,
                0.9999999123575777,
                0.999999953088362,
                0.9999999530883228,
                0.9999998874648514,
                0.9999999317439139,
                0.9999999677581298
            ],
            [
                0.9999999226557776,
                0.999999855501979,
                0.999999922655833,
                0.9999999123575987,
                0.9999998555019446,
                0.999999939764215,
                0.9999999397642725,
                0.9999999397642293,
                0.999999887464744,
                0.9999999317439383
            ],
            [
                0.99999995308839,
                0.9999999317440035,
                0.9999999123574628,
                0.9999999397642508,
                0.9999999397642437,
                0.9999999123575672,
                0.9999999397643083,
                0.9999999317440279,
                0.9999999317439383,
                0.99999992265575
            ],
            [
                0.9999999715466629,
                0.999999974890006,
                0.9999999586006196,
                0.9999999397643156,
                0.9999999778405054,
                0.9999999317440278,
                0.9999999586006344,
                0.9999999317440035,
                0.9999999530883732,
                0.9999998724809571
            ],
            [
                0.9999999634651792,
                0.9999999715466561,
                0.99999992265575,
                0.9999999530883285,
                0.9999999586006048,
                0.9999999226557592,
                0.9999999468421756,
                0.9999999468421059,
                0.9999999397643011,
                0.99999997489
            ],
            [
                0.9999999006880075,
                0.9999999468421756,
                0.9999999317439302,
                0.9999999677581336,
                0.9999998144609202,
                0.9999999226558238,
                0.9999999586005851,
                0.9999999226557684,
                0.9999999317439383,
                0.9999999006879957
            ],
            [
                0.9999999468421186,
                0.9999999530883396,
                0.999999922655833,
                0.9999999634651836,
                0.9999999123575881,
                0.9999999634651748,
                0.999999953088334,
                0.9999999586005999,
                0.9999999468421122,
                0.9999999006880668
            ],
            [
                0.9999999123575151,
                0.9999998724810026,
                0.9999998874648648,
                0.9999998874647709,
                0.9999999715466493,
                0.9999998724809875,
                0.9999999006880785,
                0.9999999123575151,
                0.9999998555019791,
                0.9999998555019274
            ],
            [
                0.9999997897566589,
                0.99999992265575,
                0.9999997617629764,
                0.999999939764215,
                0.9999999677581375,
                0.9999999397642437,
                0.9999999317439954,
                0.9999999226558515,
                0.9999998144609423,
                0.9999999468421186
            ],
            [
                0.9999999006881378,
                0.9999999530883285,
                0.9999999397642294,
                0.9999999468421883,
                0.9999999530883843,
                0.9999999226558146,
                0.9999999006880311,
                0.9999999586005851,
                0.9999999006880194,
                0.9999999468421249
            ],
            [
                0.9999999397642222,
                0.9999999123575151,
                0.9999999123575672,
                0.9999999226558515,
                0.9999998724809267,
                0.9999999530883228,
                0.9999999634652097,
                0.9999998362623723,
                0.9999999317439954,
                0.9999998724809267
            ],
            [
                0.999999931743979,
                0.9999999226557316,
                0.9999999317440197,
                0.9999999397642078,
                0.9999999530883787,
                0.9999999677581259,
                0.9999999006879838,
                0.9999999397642222,
                0.9999999123575255,
                0.9999999468421312
            ],
            [
                0.9999998874647843,
                0.9999998724809419,
                0.9999998724809267,
                0.9999999586006048,
                0.9999999226558146,
                0.99999995860059,
                0.9999998724809723,
                0.9999999226558238,
                0.9999999397643156,
                0.9999998874647709
            ],
            [
                0.9999998724809571,
                0.9999999586006146,
                0.999999977840516,
                0.9999999677581259,
                0.9999999634651574,
                0.999999939764215,
                0.9999999123574732,
                0.9999999634651748,
                0.9999999397643156,
                0.9999999468421249
            ],
            [
                0.9999999468421947,
                0.9999999468421377,
                0.99999992265575,
                0.9999999006881141,
                0.999999958600659,
                0.9999999468421376,
                0.9999999123575778,
                0.9999999006880668,
                0.9999998144609202,
                0.9999999006880668
            ],
            [
                0.9999998874648648,
                0.999999939764215,
                0.9999999397642293,
                0.9999999715466459,
                0.9999999586006295,
                0.9999999397642293,
                0.999999974890027,
                0.9999999586006048,
                0.9999999317439058,
                0.9999999634651617
            ],
            [
                0.9999998874647574,
                0.9999999586006048,
                0.9999999226557684,
                0.9999999317439302,
                0.9999999468421377,
                0.9999999317439465,
                0.9999998874648648,
                0.9999999530884012,
                0.9999999468421313,
                0.9999999317440197
            ],
            [
                0.9999999586006048,
                0.9999999468420996,
                0.99999997489003,
                0.9999999778405028,
                0.9999999006881497,
                0.9999999677581259,
                0.9999999677581451,
                0.9999999468421502,
                0.9999999317439139,
                0.999999953088362
            ],
            [
                0.9999998724810027,
                0.999999939764294,
                0.9999999397642653,
                0.9999999226558238,
                0.999999939764258,
                0.9999999123575987,
                0.999999953088334,
                0.9999999468421312,
                0.9999998874649318,
                0.9999999123575672
            ],
            [
                0.9999999468421947,
                0.9999999586005851,
                0.9999998724809875,
                0.99999992265575,
                0.9999998724809874,
                0.9999999226557408,
                0.9999999468421947,
                0.9999998724810026,
                0.9999998555019963,
                0.9999998874649051
            ],
            [
                0.9999999226558053,
                0.9999999530883285,
                0.9999999123574628,
                0.9999999317439139,
                0.99999992265575,
                0.9999999226557684,
                0.9999999586006294,
                0.9999999317439954,
                0.9999999226557131,
                0.9999999226558423
            ],
            [
                0.999999922655833,
                0.999999931743979,
                0.9999999530883732,
                0.9999999634651617,
                0.9999999226557869,
                0.999999939764294,
                0.9999999006880075,
                0.9999999226557131,
                0.9999999226557131,
                0.9999999123575568
            ],
            [
                0.999999953088362,
                0.9999999397642293,
                0.9999999006880668,
                0.9999999226558423,
                0.9999999397643156,
                0.9999999715466358,
                0.9999999468421122,
                0.9999999397642868,
                0.9999999634651748,
                0.999999939764215
            ],
            [
                0.9999999006881141,
                0.9999999123575777,
                0.9999999468421186,
                0.9999999226557685,
                0.9999999397642365,
                0.9999999468421947,
                0.9999999586006146,
                0.9999999634651662,
                0.999999953088362,
                0.999999900688043
            ],
            [
                0.9999998555019962,
                0.9999998874648648,
                0.9999997617631752,
                0.999999887464744,
                0.9999999123574523,
                0.9999997617630616,
                0.9999998555020135,
                0.9999993524049702,
                0.9999998724808963,
                0.9999999317440035
            ],
            [
                0.9999991684722698,
                0.99999844650169,
                0.9999989322970028,
                0.9999991684721706,
                0.9999989322972572,
                0.9999986290421394,
                0.9999987901344608,
                0.9999994284996891,
                0.9999993524051246,
                0.9999987901343165
            ],
            [
                0.9999998724809571,
                0.9999999006881496,
                0.9999999317439221,
                0.9999999006879957,
                0.9999998724810026,
                0.9999999468421249,
                0.9999998874647843,
                0.9999999317439627,
                0.9999999226558515,
                0.9999999226557869
            ],
            [
                0.9999999677581259,
                0.9999999317439058,
                0.9999999226558423,
                0.9999999530883564,
                0.9999999468421249,
                0.9999999226558515,
                0.9999999715466731,
                0.9999999634652097,
                0.9999999677581298,
                0.9999999468421249
            ],
            [
                0.9999999317440035,
                0.9999999530883564,
                0.9999998555019962,
                0.9999998874647441,
                0.9999999226557684,
                0.9999999317440279,
                0.999999887464811,
                0.9999999317439708,
                0.9999999123574836,
                0.9999999006881377
            ],
            [
                0.9999999006880311,
                0.9999999397642868,
                0.9999999317440116,
                0.9999998555019963,
                0.9999999123575464,
                0.9999999317439302,
                0.9999999006880549,
                0.9999999317439954,
                0.9999998555019618,
                0.9999998724809875
            ],
            [
                0.999999887464905,
                0.9999999586005999,
                0.999999922655833,
                0.9999999317439384,
                0.999999958600659,
                0.9999999586006295,
                0.9999999397642293,
                0.9999999317439139,
                0.9999998362623137,
                0.9999999468420996
            ],
            [
                0.9999998874648112,
                0.9999999634651923,
                0.9999999006880194,
                0.9999997300420939,
                0.999999953088334,
                0.9999999468421502,
                0.9999999317440279,
                0.9999999226558423,
                0.9999998724809571,
                0.9999999634651966
            ],
            [
                0.9999999317439058,
                0.9999999586006196,
                0.999999958600659,
                0.9999997617630048,
                0.9999999123574733,
                0.9999999677581259,
                0.9999999530884012,
                0.9999999468421186,
                0.9999999317439627,
                0.9999999226557685
            ],
            [
                0.9999999317440279,
                0.9999999123575568,
                0.9999999317440035,
                0.9999999530883843,
                0.9999999226557961,
                0.9999999468421693,
                0.9999999226558238,
                0.9999998874648917,
                0.9999999317439954,
                0.999999855502048
            ],
            [
                0.9999998555019962,
                0.9999999634651748,
                0.9999998144608317,
                0.9999999634651836,
                0.9999999586006542,
                0.9999999317439302,
                0.9999998724809419,
                0.9999999397642508,
                0.9999999317439221,
                0.9999999468421502
            ],
            [
                0.9999999226558515,
                0.999999946842144,
                0.9999999317439302,
                0.9999999317440116,
                0.9999999397642653,
                0.9999999397643083,
                0.9999998724809115,
                0.9999999530883732,
                0.9999999226558053,
                0.9999999006881142
            ],
            [
                0.9999998874647709,
                0.9999998874648917,
                0.9999998874649184,
                0.9999999123575987,
                0.9999999317439302,
                0.9999999468421947,
                0.9999999123575359,
                0.9999999317439872,
                0.9999999530884012,
                0.9999999397642078
            ],
            [
                0.9999998874648514,
                0.9999999397643156,
                0.9999999397642508,
                0.9999999317439302,
                0.9999999123574523,
                0.9999999226557684,
                0.9999999123574419,
                0.9999999317440197,
                0.9999999226558515,
                0.9999999123575046
            ],
            [
                0.999999931743971,
                0.999999939764215,
                0.9999999586006344,
                0.9999999397642365,
                0.9999999123574419,
                0.9999999804443309,
                0.999999953088362,
                0.9999999634651662,
                0.9999999317440116,
                0.999999967758149
            ],
            [
                0.9999999123574419,
                0.9999999586005949,
                0.9999999226558515,
                0.9999999586006196,
                0.9999999468421187,
                0.9999999226557869,
                0.9999998724809571,
                0.999999887464905,
                0.9999999634651531,
                0.999999939764258
            ],
            [
                0.9999999586006344,
                0.9999999397642293,
                0.999999922655833,
                0.9999999530883285,
                0.9999999468421567,
                0.999999900687972,
                0.9999999586006146,
                0.9999999778404975,
                0.9999999317439302,
                0.9999999397642294
            ],
            [
                0.9999999586005999,
                0.9999998724808963,
                0.9999999397643156,
                0.9999998874648379,
                0.9999999530883508,
                0.999999953088334,
                0.9999999006881141,
                0.9999999468421377,
                0.99999992265575,
                0.9999999634651662
            ],
            [
                0.9999999530883396,
                0.9999999468421883,
                0.9999999468421186,
                0.9999998874648915,
                0.9999999634651748,
                0.9999999634651792,
                0.9999999397642294,
                0.9999999006880785,
                0.9999999226558515,
                0.9999999317439058
            ],
            [
                0.9999998724809267,
                0.999999958600659,
                0.9999999397642365,
                0.9999999226558238,
                0.9999999006880904,
                0.999999946842182,
                0.9999999468421187,
                0.9999999530883172,
                0.9999998724809419,
                0.9999999677581259
            ],
            [
                0.9999998724809419,
                0.9999999634651792,
                0.9999999397642796,
                0.9999999530883396,
                0.9999999677581222,
                0.9999996940978095,
                0.999999939764215,
                0.9999999123574419,
                0.9999999586006146,
                0.9999998724809115
            ],
            [
                0.9999999123575987,
                0.9999999530883396,
                0.9999999317439789,
                0.99999995860059,
                0.9999999317439954,
                0.9999999586006443,
                0.9999999226558423,
                0.9999998874649184,
                0.9999999530883396,
                0.9999999530883732
            ],
            [
                0.9999999226558238,
                0.9999999317440035,
                0.9999998555019446,
                0.9999999123575881,
                0.9999999715466629,
                0.9999999530884012,
                0.9999999468421377,
                0.9999999317439464,
                0.9999998724808963,
                0.9999999397642437
            ],
            [
                0.999999939764294,
                0.99999992265575,
                0.999999900688043,
                0.9999999468420996,
                0.9999999006880904,
                0.9999999123574523,
                0.9999999397642653,
                0.9999998555019446,
                0.9999999006880667,
                0.9999999634651836
            ],
            [
                0.999999974890015,
                0.999999953088362,
                0.9999998555020307,
                0.999999855502048,
                0.9999998874648782,
                0.999999974890021,
                0.9999999677581567,
                0.9999999317439302,
                0.9999999397642078,
                0.9999999226558515
            ],
            [
                0.9999999586006245,
                0.9999999530883508,
                0.9999998724810027,
                0.9999999397642868,
                0.9999999468421186,
                0.9999999586006393,
                0.9999998874647843,
                0.9999998874648379,
                0.9999999226557592,
                0.999999939764215
            ],
            [
                0.9999999468421693,
                0.9999999715466527,
                0.9999999778405134,
                0.9999999006880075,
                0.9999999317439302,
                0.9999998724809115,
                0.999999887464811,
                0.9999999317439302,
                0.9999999530883675,
                0.9999999397642222
            ],
            [
                0.9999998874648112,
                0.9999999317439954,
                0.9999999468421756,
                0.999999953088334,
                0.9999999634651966,
                0.9999999634651705,
                0.999999939764251,
                0.9999999586006098,
                0.9999999006879957,
                0.9999999397642437
            ],
            [
                0.9999999530883508,
                0.9999999123575672,
                0.9999999397642293,
                0.9999999317440197,
                0.9999999317440279,
                0.9999999317440197,
                0.9999998874649184,
                0.999999939764294,
                0.999999946842163,
                0.9999999397642437
            ],
            [
                0.9999998724808963,
                0.9999999006880667,
                0.9999998724810027,
                0.9999999123575359,
                0.9999999123575046,
                0.9999999123574419,
                0.9999999123575151,
                0.9999999317439465,
                0.9999999397643011,
                0.9999999123575359
            ],
            [
                0.9999999123574523,
                0.9999999634651967,
                0.9999999317439058,
                0.9999999123575255,
                0.9999999123575881,
                0.999999931743914,
                0.9999999634651574,
                0.9999999123575674,
                0.9999999226557316,
                0.99999995308839
            ],
            [
                0.9999999677581375,
                0.9999999468420996,
                0.9999999226557961,
                0.9999999586006048,
                0.9999999530883452,
                0.9999999530883396,
                0.9999998874649318,
                0.9999999530883508,
                0.9999999804443239,
                0.9999999530883508
            ],
            [
                0.999999855502048,
                0.9999999123575672,
                0.999999939764294,
                0.9999999317440116,
                0.9999999468421186,
                0.9999999530883396,
                0.9999999530883508,
                0.9999999317440279,
                0.9999999468421186,
                0.9999999468421376
            ],
            [
                0.9999998362623723,
                0.9999999226557316,
                0.99999995308839,
                0.9999998555019963,
                0.9999999006879838,
                0.9999999317439627,
                0.9999999123574523,
                0.9999999317440116,
                0.9999999317440035,
                0.9999999317440116
            ],
            [
                0.9999999468421312,
                0.9999999530883396,
                0.9999999226558515,
                0.9999999715466527,
                0.9999999397642653,
                0.9999998874649318,
                0.9999999317439546,
                0.9999999317439464,
                0.9999998555019618,
                0.9999999317440279
            ],
            [
                0.9999999468421565,
                0.9999998724809571,
                0.9999999634651617,
                0.9999999530883508,
                0.9999999123575046,
                0.9999999123575464,
                0.9999999226557869,
                0.9999999226557961,
                0.9999999123575151,
                0.999999946842163
            ],
            [
                0.9999999123575464,
                0.9999999530883732,
                0.9999999123574419,
                0.9999999123575672,
                0.9999999468421249,
                0.9999999586006098,
                0.9999998555019791,
                0.9999999226558053,
                0.999999946842182,
                0.9999999226558423
            ],
            [
                0.9999999397642078,
                0.9999999530883508,
                0.9999999397642222,
                0.999999931743914,
                0.999999953088362,
                0.9999999468421693,
                0.9999999530883732,
                0.9999999397642653,
                0.9999999530883285,
                0.9999999468421567
            ],
            [
                0.9999998724809723,
                0.9999998874647307,
                0.9999999226558053,
                0.9999999123575672,
                0.9999998555019274,
                0.9999999317440116,
                0.9999998555019274,
                0.9999999006881496,
                0.9999998724810026,
                0.9999999123575046
            ],
            [
                0.9999998874649051,
                0.9999999317439139,
                0.9999999586006146,
                0.9999999397642437,
                0.9999998362622552,
                0.9999999123574836,
                0.9999998555019274,
                0.9999998555019446,
                0.9999998362622357,
                0.9999998362622357
            ],
            [
                0.9999998874649318,
                0.9999998874648514,
                0.9999999317440197,
                0.9999999226557224,
                0.9999999634651792,
                0.9999999123574628,
                0.9999999006880312,
                0.999999953088362,
                0.9999999317439384,
                0.9999998555020306
            ],
            [
                0.9999999530883508,
                0.999999939764215,
                0.9999999468421249,
                0.9999999123574523,
                0.9999999634651748,
                0.999999939764258,
                0.999999939764215,
                0.9999999317439465,
                0.9999999006881496,
                0.9999999397642365
            ],
            [
                0.9999999397643156,
                0.9999999530883396,
                0.999999931743914,
                0.9999999006880668,
                0.9999998144609424,
                0.9999999586005851,
                0.9999999586005949,
                0.9999999226557501,
                0.9999999226557131,
                0.9999998724808963
            ],
            [
                0.9999999468421947,
                0.9999998874647441,
                0.9999999006880312,
                0.9999999397642437,
                0.9999999468421439,
                0.9999999123575672,
                0.9999998555019618,
                0.999999974890018,
                0.99999995860059,
                0.9999999006881377
            ],
            [
                0.999999900688043,
                0.9999998874647843,
                0.9999999468421883,
                0.9999999123575568,
                0.9999999397642222,
                0.999999931743979,
                0.9999999006879957,
                0.9999999397642222,
                0.999999855502048,
                0.9999999634651662
            ],
            [
                0.9999999468421059,
                0.999999967758149,
                0.9999998874649051,
                0.9999999123574419,
                0.9999999634651792,
                0.9999999317440279,
                0.9999999530883285,
                0.9999999586006048,
                0.9999999226558423,
                0.99999995308839
            ],
            [
                0.9999999123575568,
                0.9999999397643156,
                0.9999999226558515,
                0.9999999006881141,
                0.999999946842144,
                0.9999999317440279,
                0.9999999634651531,
                0.9999999468421249,
                0.9999999530883732,
                0.9999999468421124
            ],
            [
                0.999999939764251,
                0.9999999397643083,
                0.9999998874647977,
                0.999999946842144,
                0.999999974890018,
                0.9999999468421186,
                0.9999999006880785,
                0.9999999226557408,
                0.9999999006880549,
                0.9999999123575778
            ],
            [
                0.9999999317439546,
                0.999999953088362,
                0.9999999634651617,
                0.9999999123575255,
                0.9999999715466629,
                0.9999999634651444,
                0.9999999397642365,
                0.9999999530883228,
                0.9999998362622357,
                0.9999999530883508
            ],
            [
                0.9999999317439627,
                0.9999999317440035,
                0.9999999006879957,
                0.9999999677581414,
                0.99999992265575,
                0.9999998144609203,
                0.9999999586006146,
                0.9999999226557684,
                0.9999999715466561,
                0.9999999778405213
            ],
            [
                0.9999999317439383,
                0.9999999006879838,
                0.9999999123575151,
                0.9999999123574523,
                0.9999999123575359,
                0.9999998555019962,
                0.9999999468421186,
                0.9999999397642078,
                0.9999999123574628,
                0.9999999123575255
            ],
            [
                0.9999999586006492,
                0.9999998874647574,
                0.9999999006880312,
                0.9999999586006492,
                0.999999953088362,
                0.9999998362622747,
                0.9999999715466629,
                0.9999999677581144,
                0.9999999677581529,
                0.9999998874647306
            ],
            [
                0.9999999006880549,
                0.9999999317439465,
                0.9999999123575881,
                0.9999999006881141,
                0.9999999317440279,
                0.9999999468421947,
                0.9999999317439464,
                0.9999999006881377,
                0.999999931743914,
                0.9999999226557684
            ],
            [
                0.9999999123575359,
                0.9999999317439464,
                0.9999998874647843,
                0.999999946842163,
                0.9999999397643011,
                0.9999999006881022,
                0.9999999317439953,
                0.9999999586006098,
                0.999999939764258,
                0.9999999123575045
            ],
            [
                0.9999999397642365,
                0.9999999317439221,
                0.9999999226558423,
                0.9999998724809267,
                0.9999999006881377,
                0.9999999530883787,
                0.9999999317439139,
                0.9999999397643156,
                0.9999999715466696,
                0.9999999634651444
            ],
            [
                0.9999999634651792,
                0.9999999530883172,
                0.9999998724809722,
                0.9999999317439221,
                0.999999900688043,
                0.999999946842125,
                0.9999999123575777,
                0.9999999123575464,
                0.9999999586006492,
                0.9999999123575046
            ],
            [
                0.9999999634651574,
                0.9999999397642868,
                0.9999999586005949,
                0.9999999226557408,
                0.9999999226557592,
                0.999999958600659,
                0.9999999226558146,
                0.9999998724809571,
                0.9999999468421186,
                0.9999999586006146
            ],
            [
                0.9999999006881259,
                0.999999931743914,
                0.9999998874648915,
                0.9999999530883843,
                0.9999999226557224,
                0.9999999468421376,
                0.9999999468421883,
                0.999999953088334,
                0.9999999530883396,
                0.9999999317440197
            ],
            [
                0.9999998874649184,
                0.9999997300422869,
                0.9999999715466391,
                0.9999999530883396,
                0.9999999677581144,
                0.9999999397642725,
                0.9999999586005999,
                0.9999999468421947,
                0.9999997300422869,
                0.9999999468420996
            ],
            [
                0.999999958600659,
                0.9999998724808964,
                0.9999999226557316,
                0.999999931743971,
                0.9999999226557776,
                0.9999999468421059,
                0.9999999397642293,
                0.9999999317439546,
                0.9999999317440035,
                0.9999999530883732
            ],
            [
                0.9999998144609645,
                0.999999939764215,
                0.9999999468421376,
                0.9999998144609645,
                0.9999998874647976,
                0.9999999397642796,
                0.9999998724809875,
                0.9999999226558515,
                0.9999999123575882,
                0.999999855501979
            ]
        ]
    },
    {
        "q_id": "9040_mmlu_math",
        "cot_ids": [
            1,
            2,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            22,
            23,
            24,
            26,
            27,
            28,
            29,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            41,
            42,
            44,
            46,
            47,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            76,
            78,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            90,
            91,
            94,
            95,
            97,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            116,
            117,
            118,
            119,
            120,
            122,
            123,
            124,
            125
        ],
        "rewards": [
            [
                0.9999810748517849,
                NaN,
                0.9999485577744667,
                0.9999930377412715,
                NaN,
                0.9999885212277845,
                0.999992110733659,
                0.9999930377437568,
                0.9999945777823249,
                0.9999930377412687
            ],
            [
                0.9999724643039449,
                0.9999945777817094,
                0.9999945777797694,
                0.9999251537552875,
                0.9999832985803273,
                0.5926665999540698,
                0.9999921107357247,
                0.9999952149032767,
                0.9999952149060812,
                0.9968273167098115
            ],
            [
                1.4738988994015443e-05,
                7.889264465239894e-06,
                2.430024360271833e-05,
                5.422217029844958e-06,
                3.726640171517464e-06,
                6.144172401748879e-06,
                7.484620040790966e-05,
                1.0129987353537646e-05,
                2.4300249408672413e-05,
                6.962255416961874e-06
            ],
            [
                1.1478772228528306e-05,
                6.1441767990323395e-06,
                3.2887482809933958e-06,
                4.78509506499309e-06,
                6.9622562484666964e-06,
                5.4222183221120994e-06,
                1.0129995809247506e-05,
                1.4738985481091229e-05,
                2.1444950968441685e-05,
                1.8925145982866508e-05
            ],
            [
                0.9999998555019962,
                0.9999980052702816,
                0.9999997617629764,
                0.9999999226557316,
                0.9999997300422547,
                0.9999999123574419,
                0.999999730042126,
                0.9999999226558238,
                0.999999730042126,
                0.9999998144608319
            ],
            [
                6.144176797998549e-06,
                6.144176796780352e-06,
                2.753569437686898e-05,
                2.260325375354421e-06,
                2.1444953521586782e-05,
                5.422217676397663e-06,
                1.4738987240824012e-05,
                6.962259568889411e-06,
                0.0004878570269606992,
                6.9622554187981796e-06
            ],
            [
                2.260323758676741e-06,
                4.785092782501357e-06,
                2.1444956078515887e-05,
                3.7266397278791014e-06,
                1.3007126911974612e-05,
                2.4300252311252174e-05,
                5.422220908634683e-06,
                1.6701427811412077e-05,
                8.939700564890901e-06,
                2.4300232038197563e-05
            ],
            [
                2.4300234929636645e-05,
                1.994730434798734e-06,
                2.561282515783711e-06,
                1.6701417851711638e-05,
                1.3007134665413997e-05,
                8.93969310675186e-06,
                1.670142184171555e-05,
                8.93969523678858e-06,
                1.300713466420736e-05,
                2.144495607492721e-05
            ],
            [
                7.484620037305929e-05,
                0.00017952802850351664,
                1.1478768091084062e-05,
                4.539785229059168e-05,
                4.222834952460187e-06,
                6.9622554185195676e-06,
                5.8291279369750445e-05,
                2.9023116390104826e-06,
                1.8925141463066202e-05,
                3.2887490652810324e-06
            ],
            [
                0.9999998144608319,
                0.9999997617629764,
                0.9999997300421581,
                0.9999996072138934,
                0.9999998362622746,
                0.9999998144608317,
                0.9999996940978461,
                0.9999996533673375,
                0.9999997300422225,
                0.9999997617630616
            ],
            [
                0.9999885212277951,
                0.9999921107346018,
                0.9999938558261383,
                0.9999485577630051,
                0.9999967112521133,
                0.9999898700126502,
                0.9999756997577454,
                0.9999885212305096,
                0.9999990577549569,
                0.9999885212289471
            ],
            [
                0.9999546021098127,
                0.999996711250546,
                0.9999339478246739,
                0.9998601779749847,
                0.999948557768426,
                0.9999687980999882,
                0.9994472213149034,
                0.6224593382055109,
                0.999954602126061,
                0.4687906266262437
            ],
            [
                0.9999646437535655,
                0.4378234991142019,
                NaN,
                0.9999646437327449,
                0.9999852610215642,
                NaN,
                0.9999151889877557,
                0.9999982396559485,
                0.9999724642992381,
                0.9999339478242617
            ],
            [
                0.999997097686981,
                0.9999986290432843,
                0.9999984465024309,
                0.999996273361162,
                0.9999980052693292,
                0.9999977396754359,
                0.9999957771670639,
                0.9999982396565775,
                0.9999957771680675,
                0.9999945777784452
            ],
            [
                4.5397884803802836e-05,
                1.473898899664279e-05,
                3.1201922480102066e-05,
                1.0129995807699706e-05,
                4.222833444037741e-06,
                4.78509563535725e-06,
                NaN,
                9.610239194164611e-05,
                2.1444956078515887e-05,
                6.14417753110761e-06
            ],
            [
                NaN,
                0.9241418236349501,
                0.29421497216298875,
                0.34864514210180597,
                NaN,
                NaN,
                0.9999832985702228,
                0.9999898700066134,
                0.997199073658482,
                0.7549149813536518
            ],
            [
                0.999978555055139,
                0.999991060304765,
                0.9999810748450123,
                0.9999869928716397,
                0.9999945777797442,
                0.9999970976873251,
                0.939913343093499,
                0.9999987901344608,
                0.999994577782586,
                0.9999910603024856
            ],
            [
                0.9999962733589495,
                0.9999980052702789,
                NaN,
                0.9999930377462675,
                NaN,
                NaN,
                0.999998239655949,
                NaN,
                0.9999938558239386,
                0.7057850340255386
            ],
            [
                0.9999938558276156,
                0.9999957771665665,
                0.9999832985844037,
                0.9999910603069007,
                0.9999810748517927,
                0.9999687980738392,
                0.9999852610127773,
                0.9999938558239353,
                0.9999785550541608,
                0.9999938558239448
            ],
            [
                0.904650536386234,
                0.9999930377429291,
                0.8175744739711883,
                NaN,
                0.9999938558224725,
                0.5,
                0.9999957771680661,
                0.914900959053549,
                0.9999930377454161,
                0.9998415637838942
            ],
            [
                0.999996273361169,
                0.999975699750865,
                0.02595735545530691,
                0.817574478416099,
                0.9241418241572634,
                0.999915188989835,
                0.8670357649558007,
                NaN,
                0.9999930377405126,
                0.9999485577931384
            ],
            [
                3.1201918802543923e-05,
                6.144172404302622e-06,
                4.7850933535006355e-06,
                2.14449535222109e-05,
                1.3007130012980722e-05,
                4.222832941034507e-06,
                5.8291272448012225e-05,
                2.753568124348506e-05,
                1.012999459815081e-05,
                3.7266379512518984e-06
            ],
            [
                NaN,
                NaN,
                0.9999967112493675,
                0.9999852610110246,
                0.9999977396746249,
                0.9999945777791106,
                0.9999898700102415,
                0.9999810748540691,
                0.7772998560157665,
                0.9999945777803859
            ],
            [
                0.9999930377404577,
                0.9999869928746572,
                0.9999921107402443,
                0.9999646437368319,
                NaN,
                NaN,
                0.9999970976883629,
                0.9999898700126588,
                0.9999910603069173,
                0.999986992875341
            ],
            [
                8.939697368663308e-06,
                1.4738980211920955e-05,
                6.962254588724508e-06,
                6.144173868882483e-06,
                1.3007123808910861e-05,
                1.0129989768616954e-05,
                4.222831933795376e-06,
                7.889266346603015e-06,
                1.0129988561077228e-05,
                8.939697369151141e-06
            ],
            [
                7.338213304083124e-07,
                1.670142980608093e-05,
                5.043476486833397e-07,
                6.1441746017453204e-06,
                1.2098658277335738e-06,
                1.6701423831188846e-05,
                1.147877223059538e-05,
                1.0129989770662257e-05,
                1.3709576971160984e-06,
                2.2603251062013478e-06
            ],
            [
                0.9999967112521141,
                NaN,
                0.9999485577680651,
                0.9999991684717743,
                0.9999898700109018,
                0.9999546021169494,
                0.985936373757396,
                0.9859363703094722,
                0.9999962733593897,
                0.9999952149066473
            ],
            [
                3.120190388402792e-05,
                1.8925150481256165e-05,
                1.6701421837705495e-05,
                1.3007123808532309e-05,
                2.430023491549239e-05,
                2.1444948409679848e-05,
                8.939697364890742e-06,
                7.889261643899223e-06,
                4.5397868553139715e-05,
                2.4300252313020203e-05
            ],
            [
                0.9999151889564006,
                NaN,
                0.9999785550445309,
                0.29421497216298875,
                0.7057850154599562,
                NaN,
                0.9999485577987147,
                0.9999151889604793,
                0.6791787056691698,
                NaN
            ],
            [
                0.99999976176309,
                0.9999999468421439,
                0.9999998555020135,
                0.9999997617631752,
                0.9999998362622943,
                0.9999997617630616,
                0.9999998362622746,
                0.9999998362622943,
                0.9999998362623138,
                0.9999998724809875
            ],
            [
                NaN,
                NaN,
                0.9999832985821897,
                0.9999646437621322,
                NaN,
                NaN,
                0.9999724642992287,
                0.9999921107338442,
                0.9999852610110561,
                0.999996273358942
            ],
            [
                0.999999789756684,
                0.9999998362622357,
                0.9999998362622942,
                0.9999997300422869,
                0.9999994284996211,
                0.9999998555019618,
                0.9999999123575464,
                0.9999997617631183,
                0.9999998362622942,
                0.9999997617630332
            ],
            [
                0.9999930377421342,
                0.9999832985727468,
                0.9999982396572065,
                0.9999945777829743,
                0.8519528019683106,
                0.9999646437327541,
                0.9999852610198755,
                0.9999910603005673,
                0.9999869928670556,
                0.9999930377429231
            ],
            [
                2.7535697658087296e-05,
                1.0129988564578197e-05,
                1.553498310118888e-06,
                6.144173868558375e-06,
                2.1444958637941764e-05,
                6.605216814167028e-05,
                3.2887478889962107e-06,
                2.7535687816036267e-05,
                0.9999417087554069,
                3.7266397280960194e-06
            ],
            [
                0.9998911030944893,
                0.9999832985802002,
                0.9999885212332593,
                0.9997040428064051,
                0.9999785550541569,
                0.9999957771665713,
                0.999993855826132,
                NaN,
                0.9999898700114523,
                0.9999151889612357
            ],
            [
                5.829129321831856e-05,
                3.535623801292338e-05,
                0.00010889689599276248,
                4.006369695353247e-05,
                4.539789020847081e-05,
                1.3007133108948093e-05,
                3.5356250699942575e-05,
                4.006368262694324e-05,
                3.1201922520397544e-05,
                2.7535684522397864e-05
            ],
            [
                0.9999251537910755,
                0.9706877706265887,
                0.8175744850834648,
                0.9998766054426572,
                0.4378234991142019,
                0.9999885212346428,
                0.999986992865569,
                0.9999810748564414,
                0.9840936085505955,
                0.9999785550517464
            ],
            [
                0.9999998874648245,
                0.9999999123574941,
                0.9999998874647977,
                0.9999998874649318,
                0.9999998874648514,
                0.9999999226557869,
                0.9999999006880549,
                0.9999999006880668,
                0.9999999006880194,
                0.9999998362622552
            ],
            [
                1.4738976691331275e-05,
                2.75357009372024e-05,
                3.535626756251187e-05,
                5.422220262037209e-06,
                8.481103108723191e-05,
                4.539785237052376e-05,
                7.889261643727018e-06,
                0.0010322311876494695,
                5.422218968822766e-06,
                1.3007126911974612e-05
            ],
            [
                1.0129993394314164e-05,
                3.1201926235527406e-05,
                2.430023783667895e-05,
                1.1478773598538445e-05,
                6.962259568889411e-06,
                1.4738983727578497e-05,
                2.260324566939374e-06,
                4.006370173469883e-05,
                6.96225707640032e-06,
                9.61024260723218e-05
            ],
            [
                NaN,
                0.999972464306051,
                0.9999910603058411,
                NaN,
                NaN,
                0.9999339478465261,
                0.9999251537564756,
                0.9999869928747709,
                NaN,
                0.9149009613738741
            ],
            [
                NaN,
                0.9999967112501529,
                0.99999823965721,
                0.9999952149032257,
                0.999989870009103,
                0.999991060299457,
                0.9770226303408661,
                0.9999756997511581,
                0.946596665680527,
                0.9999938558232315
            ],
            [
                8.939695238333382e-06,
                1.1478770861859053e-05,
                3.288748279952497e-06,
                8.315278293687262e-07,
                1.7603425837062577e-06,
                2.5612828207295832e-06,
                1.4738983727578497e-05,
                8.939697368842181e-06,
                4.785094494716039e-06,
                1.2098656834613962e-06
            ],
            [
                0.9796676443199194,
                0.970687767658707,
                NaN,
                NaN,
                0.29421497216298875,
                0.9999810748518118,
                0.9998766054558517,
                NaN,
                0.9902915226768554,
                NaN
            ],
            [
                1.8925141461620395e-05,
                2.430024941804299e-05,
                0.9999930377445806,
                3.535624222267904e-05,
                1.8925150493717652e-05,
                4.785096203588998e-06,
                5.82912723593753e-05,
                2.753569434050672e-05,
                9.610244927358124e-05,
                8.481101090606248e-05
            ],
            [
                0.9999974387187074,
                0.9999885212305316,
                0.9999970976873234,
                0.9999898700126649,
                NaN,
                0.9999885212346381,
                0.9999930377420927,
                0.9999938558232571,
                0.9999151889819826,
                0.9999485577863967
            ],
            [
                5.422220908703723e-06,
                1.1478764017428212e-05,
                1.0677029973056687e-06,
                7.48462272410653e-05,
                1.8925150485318196e-05,
                3.120191507912884e-05,
                3.288749065077638e-06,
                0.0001398220233166092,
                4.006368740256958e-05,
                2.7535681241281285e-05
            ],
            [
                0.0017007227197746518,
                0.0007096705361053989,
                0.0001398221237119418,
                0.00013982204046248067,
                7.484624496248661e-05,
                0.00013982204039738008,
                0.0002611903393183976,
                8.481103100331595e-05,
                0.0008040858426577827,
                0.00017952802943077935
            ],
            [
                0.9999967112513312,
                0.9999921107395042,
                0.8354835350552603,
                0.9999724643089738,
                0.9999832985823763,
                0.9999970976887075,
                0.9999832985702259,
                0.9999869928715562,
                0.9999898700078209,
                0.9999910603051072
            ],
            [
                0.9999957771655493,
                0.9999980052700418,
                0.999994577781039,
                0.9999957771680693,
                0.9999970976873231,
                0.9999962733589466,
                0.9999987901346054,
                NaN,
                0.9999898700054077,
                0.9999974387165697
            ],
            [
                0.9999251537570397,
                0.9999724643035499,
                0.9999885212360565,
                0.9999957771665569,
                0.9999989322970039,
                0.9999938558239616,
                NaN,
                0.9999869928761923,
                0.9999974387184077,
                0.9999952149066574
            ],
            [
                0.9999785550592704,
                0.9820137913538826,
                0.9999910603047655,
                0.9999970976880815,
                0.9999910603047916,
                0.9999974387171789,
                0.9999962733620521,
                0.8933094167058151,
                NaN,
                0.9999982396569983
            ],
            [
                3.288749849114211e-06,
                4.785096205260165e-06,
                3.535625069312567e-05,
                3.7266388396975786e-06,
                6.962254588977791e-06,
                2.260324836696773e-06,
                9.422445938642879e-07,
                1.7603440524628877e-06,
                3.2887486732000038e-06,
                1.1478769492392108e-05
            ],
            [
                0.9999885212291516,
                NaN,
                0.7057850340255386,
                0.9999982396559479,
                NaN,
                0.9999945777797375,
                0.999978555056719,
                0.9999898700059082,
                0.9999982396559485,
                0.9999938558268656
            ],
            [
                0.9999898700136313,
                0.9999938558246729,
                NaN,
                NaN,
                0.999989870004203,
                0.9999957771645426,
                0.9999962733611618,
                0.9999938558224803,
                NaN,
                0.9999987901337398
            ],
            [
                NaN,
                0.9999810748517781,
                0.9999756997688868,
                NaN,
                0.9999756997565798,
                0.9999646437468485,
                0.999964643742003,
                0.651354857898194,
                0.9740426438382782,
                0.9999485577742627
            ],
            [
                0.9999546021372105,
                0.9999910603069027,
                0.9999038975626166,
                0.9999785550592852,
                0.6513548782017745,
                0.7057850402140659,
                0.957912276289704,
                0.9999869928731838,
                0.9999417087361303,
                0.9999417087206625
            ],
            [
                0.9999921107402423,
                0.9999599362984096,
                0.9999967112493688,
                0.9999930377429226,
                0.9999687980888137,
                0.9999810748473168,
                0.9996200154394812,
                NaN,
                0.9999898700042158,
                0.9999945777810337
            ],
            [
                1.47389819699641e-05,
                6.962256247098965e-06,
                3.288749065077638e-06,
                1.4738985483879434e-05,
                2.7535697653779924e-05,
                1.473898196677375e-05,
                1.1478769493331685e-05,
                6.144176066051891e-06,
                1.670142781520948e-05,
                2.56128159999123e-06
            ],
            [
                0.9999984465015048,
                0.9999962733607164,
                0.999991060302632,
                0.9999989322971302,
                0.9999982396561575,
                0.9999987901344609,
                0.9999898700066088,
                0.9999987901344607,
                0.9999980052698114,
                0.9999984465024307
            ],
            [
                0.999981074851773,
                0.9999646437408912,
                0.9999885212291407,
                0.9999646437578956,
                0.9999945777797393,
                0.9999967112497591,
                0.9999785550439309,
                0.9999967112509366,
                0.9999930377404467,
                0.999991060302632
            ],
            [
                0.9999599363176482,
                0.9999962733598343,
                NaN,
                0.999995214906089,
                0.9999957771665575,
                0.6791787121629466,
                0.9999485577987854,
                0.5312093733737563,
                0.9999724643056793,
                0.9998911030979784
            ],
            [
                0.999993855826869,
                0.9999885212291424,
                NaN,
                0.9999646437451443,
                0.9999832985722332,
                0.9999962733589403,
                0.8354835289107309,
                0.9999687980887109,
                0.9999898700126468,
                0.9999957771680679
            ],
            [
                2.1444950927991115e-05,
                1.3007128462785148e-05,
                0.00010889695901095134,
                2.26032402791394e-06,
                1.670141984792864e-05,
                2.5612812945260317e-06,
                2.1444958621558693e-05,
                3.2887494572514376e-06,
                6.1441760657054305e-06,
                5.4222176755001384e-06
            ],
            [
                3.535624645944555e-05,
                4.785093923916815e-06,
                5.144223807888457e-05,
                2.753568781222975e-05,
                1.6701423829123058e-05,
                1.4738978455325741e-05,
                3.5356242258821454e-05,
                2.753568781022632e-05,
                2.1444948411552198e-05,
                1.8925152752138513e-05
            ],
            [
                1.3007125362323574e-05,
                1.67014178590634e-05,
                2.7535694356133476e-05,
                1.3007123812057577e-05,
                1.892515274614874e-05,
                1.6701415869924985e-05,
                5.422217030555087e-06,
                5.8291265503797524e-05,
                1.147877086020957e-05,
                8.93969310662177e-06
            ],
            [
                0.9999832985841574,
                0.9999756997477216,
                0.999978555046523,
                NaN,
                0.9999921107345936,
                0.9890130548798951,
                0.9999546021439626,
                0.999993855825423,
                0.9999977396751738,
                0.999996711250152
            ],
            [
                5.82912863042125e-05,
                2.1444943298944354e-05,
                5.8291286375037224e-05,
                7.484620921906373e-05,
                6.60521444778882e-05,
                1.4738983726184394e-05,
                NaN,
                8.481101094863749e-05,
                0.00015843627176448936,
                8.481101068578313e-05
            ],
            [
                0.9999910603037124,
                NaN,
                NaN,
                NaN,
                0.9999151889699729,
                0.999986992866929,
                0.9999724643159803,
                0.6224593241981982,
                NaN,
                0.9999687980775139
            ],
            [
                0.999999266179107,
                0.999999495652712,
                0.9999986290431201,
                0.9999962733607167,
                0.9999992661787572,
                0.9999994284997573,
                0.9999996072136593,
                0.9999984465022455,
                0.999999653367503,
                0.9999990577556308
            ],
            [
                2.1444943298320236e-05,
                5.422217676299034e-06,
                1.3007125361448172e-05,
                6.9622587393661365e-06,
                4.222835457280279e-06,
                6.1441746016670885e-06,
                8.93969310647542e-06,
                8.939700566143004e-06,
                1.6701419849933667e-05,
                2.1444945848226808e-05
            ],
            [
                0.9999921107383599,
                0.9999910603005051,
                0.9999151889396038,
                0.9999869928761981,
                0.9999038976039318,
                0.9241418210233832,
                0.9999921107336545,
                0.9999898700090242,
                0.9999724643170979,
                0.999983298584174
            ],
            [
                2.430023203298187e-05,
                4.006367783266211e-05,
                1.4738987235622935e-05,
                2.430023489604404e-05,
                2.1444940740066406e-05,
                3.535625490931388e-05,
                7.484620025053846e-05,
                1.6701415853489846e-05,
                1.892514823488397e-05,
                4.539786862316288e-05
            ],
            [
                0.9999967112505427,
                0.9999952149032268,
                0.9999952149060765,
                0.9999952149032244,
                0.999997438716877,
                0.9999991684720716,
                0.9999852610215433,
                0.9999962733602734,
                0.9999982396567867,
                0.9999970976883612
            ],
            [
                0.9999852610145235,
                0.9999974387168757,
                0.9999987901340296,
                0.9999962733598319,
                0.9999910603005183,
                0.999997097688707,
                0.9999967112513269,
                0.9999962733593855,
                0.9999869928761911,
                0.9999930377437549
            ],
            [
                0.999993037742924,
                NaN,
                0.999978555049449,
                0.9999852610146068,
                0.9999785550556172,
                0.9999962733589393,
                0.9999852610162847,
                0.9999938558224711,
                0.9999810748427493,
                0.999954602138432
            ],
            [
                0.9999785550492726,
                NaN,
                0.9999952149032316,
                0.9999994956527722,
                0.9999974387165698,
                0.9999885212319,
                0.9999938558261318,
                0.9999832985743348,
                0.9999970976890544,
                0.999981074854065
            ],
            [
                0.9999957771650468,
                0.9626731169394882,
                0.9933071478962371,
                0.9999910603005032,
                0.9999921107336832,
                0.999948557762386,
                0.9999832985803346,
                0.9999832985845865,
                0.999995777168192,
                0.9999832985801657
            ],
            [
                0.9999962733611621,
                0.9999957771660535,
                0.9999885212318917,
                0.9999852610111337,
                0.9999952149072182,
                0.9999756997650809,
                0.9997694932305475,
                0.9999945777784462,
                0.9999910603015678,
                0.9999869928748566
            ],
            [
                NaN,
                0.9999945777810383,
                0.9999832985781659,
                0.9999852610227771,
                0.9999898700126806,
                0.9999938558246851,
                0.999986992876207,
                0.9999724643156039,
                NaN,
                NaN
            ],
            [
                0.9999599363080244,
                0.99999743871692,
                0.9999980052702788,
                0.7772998560157663,
                0.9999485577622317,
                0.999992110740239,
                0.9770226296718216,
                0.9999599362985877,
                0.9999921107383722,
                0.9241418257242034
            ],
            [
                0.7310585903489892,
                0.9999945777803908,
                0.9999967112497878,
                0.9999957771670606,
                0.9399133502467732,
                0.9999962733593866,
                0.731058584489497,
                0.8807970748488297,
                NaN,
                0.9999852610131681
            ],
            [
                0.5621765008857981,
                0.9399133477220883,
                NaN,
                1.0,
                0.999978555054784,
                NaN,
                0.8670357546485407,
                0.9999724643157619,
                NaN,
                0.924141814233309
            ],
            [
                0.9999898700090316,
                0.9999885212291643,
                0.9999852610181096,
                0.9999910603016114,
                0.9999980052693285,
                0.9999982396563674,
                0.9999921107355423,
                0.9999992661789323,
                0.9999952149072279,
                NaN
            ],
            [
                0.984093605751553,
                NaN,
                0.9999967112497616,
                0.999996711250543,
                0.9999987901347496,
                NaN,
                NaN,
                0.9999970976866348,
                0.9999938558275997,
                0.9999921107374627
            ],
            [
                0.9999974387168742,
                0.9999756997652249,
                NaN,
                0.9999756997659272,
                0.7981867777396212,
                0.9999810748563155,
                0.9999832985761884,
                0.9999898700078186,
                0.9999785550542851,
                0.9999785550516216
            ],
            [
                0.9999967112497598,
                2.144495864644536e-05,
                0.9999952149038162,
                0.9999984465028021,
                0.9999869928731567,
                0.9999952149032298,
                0.9999980052700408,
                0.9999952149055106,
                0.9999756997505924,
                0.9999785550525222
            ],
            [
                2.144494840687132e-05,
                1.0677033791291683e-06,
                6.962256249517824e-06,
                1.2098656834922064e-06,
                1.2098658277264215e-06,
                1.1478770861650256e-05,
                1.01299933928585e-05,
                1.8925143723000643e-05,
                2.2603251061232293e-06,
                1.370957533574467e-06
            ],
            [
                2.1444958620544503e-05,
                1.0129992182112188e-05,
                1.300712380408432e-05,
                3.535624226936835e-05,
                2.1444940724775554e-05,
                5.829125847391544e-05,
                1.6701415835201574e-05,
                1.6701419841852803e-05,
                8.939698430218506e-06,
                1.0129993389283824e-05
            ],
            [
                4.22283394762097e-06,
                1.1478773598538445e-05,
                4.7850933534310035e-06,
                8.939693106182721e-06,
                3.2887490653109436e-06,
                3.28874945711983e-06,
                1.4738976699106073e-05,
                1.8925141465200488e-05,
                1.01299946023704e-05,
                1.14787681240737e-05
            ],
            [
                0.9999785550593698,
                0.9999970976866313,
                0.9999984465022456,
                0.9999910603005051,
                0.9999962733598282,
                0.9999962733593835,
                0.999998629042957,
                0.9999952149037977,
                0.9999852610245447,
                0.9999977396754333
            ],
            [
                0.999991060301585,
                0.9999885212267646,
                0.9999546021206388,
                0.9999417087074849,
                0.9999151889808239,
                0.9999832985702168,
                0.999985261014535,
                0.999985261016291,
                NaN,
                NaN
            ],
            [
                0.999988521231895,
                0.9999646437538242,
                0.9999832985821797,
                0.9999810748472797,
                0.9999599362890327,
                0.9999756997593762,
                0.9999852610234251,
                0.9999982396572082,
                0.9999952149055086,
                0.9999599363082372
            ],
            [
                NaN,
                0.9999646437367182,
                0.9999938558275995,
                NaN,
                NaN,
                NaN,
                0.9999970976876725,
                0.9999898700102963,
                0.9999810748495466,
                NaN
            ],
            [
                NaN,
                0.999991060299436,
                0.9999982396561578,
                0.914900948612085,
                0.999975699767985,
                0.9999967112513277,
                0.9999832985761765,
                0.9999945777823249,
                0.9999990577557439,
                0.9149009567332237
            ],
            [
                0.9999952149055064,
                0.9999599363088733,
                0.9999599362887858,
                0.9999921107374165,
                0.9999852610165263,
                0.9999417087206391,
                0.9999417087345882,
                0.8354835289107309,
                0.9525741242979906,
                0.9999646437366961
            ],
            [
                0.8354835350552604,
                0.7549149978955811,
                0.5312093733737563,
                0.9999546021259963,
                0.9999810748518333,
                0.9999885212360128,
                0.9999852610145602,
                0.9999756997594321,
                0.9999785550413836,
                NaN
            ],
            [
                0.9999898700114523,
                NaN,
                0.9999930377454153,
                0.9999885212319903,
                0.9999251538007498,
                0.9999952149072279,
                0.9999910603047723,
                0.9999687980775326,
                0.9999898700042001,
                0.9999930377429248
            ],
            [
                0.9999974387177898,
                0.9999987901347493,
                0.9999967112517253,
                0.9999970976880163,
                0.999998239656997,
                0.9999992661789324,
                0.9999987901341731,
                0.9999921107402646,
                0.9999984465015049,
                0.9999957771660528
            ],
            [
                8.939698430836427e-06,
                1.0129992182112188e-05,
                8.481107162358746e-05,
                7.48462449913471e-05,
                2.753569108924008e-05,
                2.7535694331891973e-05,
                0.00026119024645824337,
                7.889264463446097e-06,
                2.144494838814782e-05,
                3.7266401719174067e-06
            ],
            [
                0.9999938558232021,
                0.9999945777823519,
                0.9999921107392973,
                0.999993855823206,
                0.9999974387180948,
                NaN,
                0.9999938558276176,
                0.9999970976869842,
                0.999994577780384,
                0.9999974387165685
            ]
        ]
    },
    {
        "q_id": "9041_mmlu_math",
        "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": [
            [
                0.9999990577552939,
                0.999997438718095,
                0.9999982396561572,
                0.9999995549148419,
                0.9999992661786696,
                0.9999989322972573,
                0.9999991684715759,
                0.9999996072137061,
                0.9999996533673375,
                0.9999994956524114
            ],
            [
                0.9999986290432837,
                0.9999980052707546,
                0.9999970976876695,
                0.999998005270041,
                0.9999970976876695,
                0.9999990577551816,
                0.9999989322970028,
                0.9999982396572067,
                0.9999977396751638,
                0.9999952149066473
            ],
            [
                0.999999168471675,
                0.9999992661789321,
                0.9999989322975119,
                0.9999991684721706,
                0.9999991684722698,
                0.9999989322970027,
                0.9999989322971301,
                0.9999990577556308,
                0.9999987901337397,
                0.999999352404893
            ],
            [
                0.9999995549150542,
                0.9999994956524716,
                0.9999994284994167,
                0.9999995549147889,
                0.9999996072136125,
                0.9999994956527721,
                0.9999994284994849,
                0.9999996533674615,
                0.9999992661787571,
                0.9999967112497588
            ],
            [
                0.9999991684716749,
                0.9999994284992805,
                0.9999982396559474,
                0.9999993524048931,
                0.9999986290429567,
                0.9999991684715758,
                0.9999991684718732,
                0.9999994956524716,
                0.9999994284996893,
                0.9999992661786696
            ],
            [
                0.9999994956525918,
                0.9999991684719723,
                0.9999993524054334,
                0.9999990577550691,
                0.9999994956527721,
                0.9999997617631469,
                0.9999993524048931,
                0.9999993524052018,
                0.9999997897565587,
                0.9999996533674615
            ],
            [
                0.9999982396565771,
                0.9999987901343167,
                0.9999980052707543,
                0.9999984465022456,
                0.999998790134605,
                0.9999992661789321,
                0.999999266178932,
                0.9999995549150011,
                0.9999990577556308,
                0.9999970976876699
            ],
            [
                0.9999990577550693,
                0.9999997300421581,
                0.999999495652712,
                0.9999984465018752,
                0.9999994284994167,
                0.9999993524049703,
                0.9999994284997574,
                0.9999990577557432,
                0.9999994956524716,
                0.9999992661790195
            ],
            [
                0.9999980052705165,
                0.9999993524051246,
                0.999999428499553,
                0.9999994284994849,
                0.9999991684717743,
                0.9999993524050474,
                0.9999990577552939,
                0.9999996940978825,
                0.9999990577557433,
                0.9999995549150011
            ],
            [
                0.9999986290423031,
                0.9999996533673375,
                0.9999997300421903,
                0.9999994284996211,
                0.9999962733607176,
                0.9999994284993486,
                0.9999989322967484,
                0.9999987901347493,
                0.9999993524050474,
                0.9999989322968755
            ],
            [
                0.9999996072138934,
                0.9999991684717742,
                0.999999168471576,
                0.9999992661792819,
                0.9999991684716749,
                0.9999992661791945,
                0.9999991684721706,
                0.9999996940978095,
                0.9999996072136592,
                0.9999996533672549
            ],
            [
                0.9999993524048931,
                0.9999989322975119,
                0.9999990577551815,
                0.999999428499553,
                0.9999994956524115,
                0.9999990577551815,
                0.999999266179107,
                0.9999987901347492,
                0.9999994956523514,
                0.9999986290427932
            ],
            [
                0.999999352404893,
                0.9999986290431201,
                0.9999984465020603,
                0.9999977396762416,
                0.9999962733593841,
                0.9999990577555185,
                0.9999980052693274,
                0.9999970976890532,
                0.999999266178757,
                0.9999997300420937
            ],
            [
                0.9999991684719723,
                0.9999991684720716,
                0.9999987901343165,
                0.999999554915001,
                0.9999991684715759,
                0.9999990577556308,
                0.999999554914842,
                0.9999992661789321,
                0.9999992661787571,
                0.9999994284997574
            ],
            [
                0.9999991684718732,
                0.9999996072136125,
                0.9999989322975119,
                0.9999994284996211,
                0.999998790134028,
                0.9999977396765107,
                0.9999987901337397,
                0.999999266178932,
                0.99999893229713,
                0.9999994284996211
            ],
            [
                0.9999996072137061,
                0.999999352405279,
                0.9999992661790196,
                0.9999990577554062,
                0.9999974387184006,
                0.9999990577549568,
                0.9999984465015048,
                0.9999987901347493,
                0.9999987901346051,
                0.9999990577554061
            ],
            [
                0.999999352404893,
                0.9999994956524115,
                0.999999428499553,
                0.9999990577555186,
                0.9999996533673375,
                0.9999993524050474,
                0.9999991684719725,
                0.9999993524050474,
                0.99999893229713,
                0.9999982396559476
            ],
            [
                0.9999994284997574,
                0.9999996072137061,
                0.9999996533674202,
                0.9999992661791944,
                0.9999989322967481,
                0.9999986290424663,
                0.9999986290421395,
                0.9999990577555185,
                0.9999996533673375,
                0.9999996072138465
            ],
            [
                0.9999993524054335,
                0.9999990577557432,
                0.9999991684722697,
                0.9999995549151073,
                0.9999994956524114,
                0.9999982396559475,
                0.9999991684719723,
                0.9999994284994849,
                0.9999987901346049,
                0.9999994956526519
            ],
            [
                0.9999996072138934,
                0.9999987901337397,
                0.9999991684719725,
                0.9999987901347493,
                0.9999987901347492,
                0.9999994956527122,
                0.9999992661790196,
                0.9999996072137061,
                0.99999844650169,
                0.9999980052705167
            ],
            [
                0.999998239656997,
                0.9999994284994167,
                0.9999992661790195,
                0.9999984465024307,
                0.9999995549148419,
                0.9999996533673375,
                0.9999991684722698,
                0.9999995549151073,
                0.9999993524054334,
                0.999999352405279
            ],
            [
                0.9999994284994849,
                0.9999987901341724,
                0.9999986290429568,
                0.9999994284994849,
                0.9999991684715759,
                0.9999996940977001,
                0.9999996072137529,
                0.9999994284994849,
                0.9999992661787571,
                0.9999992661786695
            ],
            [
                0.9999987901343165,
                0.9999984465028012,
                0.9999993524051246,
                0.9999994284992805,
                0.999999266178757,
                0.9999991684717742,
                0.9999996072137061,
                0.9999984465026158,
                0.9999996533672136,
                0.9999991684721706
            ],
            [
                0.9999996533674615,
                0.9999993524054334,
                0.9999991684720716,
                0.999999730042126,
                0.999999730042319,
                0.9999987901338839,
                0.9999986290431202,
                0.9999982396559476,
                0.9999994956523514,
                0.9999992661791071
            ],
            [
                0.9999995549147889,
                0.9999994956527721,
                0.9999990577557432,
                0.9999992661791945,
                0.9999991684715758,
                0.9999994284992805,
                0.99999893229713,
                0.9999991684720715,
                0.9999993524053562,
                0.9999974387165682
            ],
            [
                0.999998932296621,
                0.999999730042126,
                0.999999266179282,
                0.9999996533674202,
                0.9999984465020604,
                0.9999993524053562,
                0.9999987901340281,
                0.9999986290431201,
                0.9999997897567341,
                0.9999993524049703
            ],
            [
                0.999995777165046,
                0.9999994284997573,
                0.9999990577551815,
                0.9999986290427932,
                0.999999168471675,
                0.9999977396759718,
                0.999999266178932,
                0.999999266179282,
                0.9999994284994849,
                0.9999991684722698
            ],
            [
                0.9999994284993486,
                0.9999991684717742,
                0.9999994956525918,
                0.999999352405279,
                0.9999990577554062,
                0.9999991684718732,
                0.9999994956527722,
                0.9999993524053562,
                0.9999991684722698,
                0.9999992661792819
            ],
            [
                0.999999266178932,
                0.9999993524054335,
                0.99999893229713,
                0.999999352405279,
                0.999999266178757,
                0.9999992661791945,
                0.9999992661791944,
                0.999999554914895,
                0.9999977396751634,
                0.999999266179107
            ],
            [
                0.9999994956527721,
                0.9999994284993486,
                0.9999991684721706,
                0.9999994284996893,
                0.9999994284992805,
                0.999999352405279,
                0.9999994284994167,
                0.9999996533672549,
                0.9999994284992805,
                0.999999653367503
            ],
            [
                0.9999980052700409,
                0.9999991684722698,
                0.9999992661786696,
                0.9999970976866319,
                0.9999980052698033,
                0.9999991684722698,
                0.9999990577549568,
                0.999998239656577,
                0.9999984465018752,
                0.9999997300421903
            ],
            [
                0.999999554914789,
                0.9999997897566338,
                0.9999984465020604,
                0.999999428499553,
                0.9999990577557433,
                0.9999994284997574,
                0.9999993524051246,
                0.9999993524052018,
                0.9999993524050473,
                0.9999997897566089
            ],
            [
                0.9999986290421397,
                0.9999980052693277,
                0.9999967112509353,
                0.9999996533673788,
                0.9999974387165684,
                0.9999987901337396,
                0.9999987901338838,
                0.9999977396759723,
                0.9999980052702787,
                0.9999992661786696
            ],
            [
                0.9999995549150011,
                0.9999993524051247,
                0.9999996072136125,
                0.9999995549151073,
                0.9999991684721706,
                0.999999428499553,
                0.9999982396559477,
                0.9999994284992805,
                0.9999980052698032,
                0.9999970976890539
            ],
            [
                0.9999996940976272,
                0.9999990577549569,
                0.999999266178932,
                0.9999993524049702,
                0.9999970976890534,
                0.9999974387184005,
                0.9999990577554061,
                0.9999994284994848,
                0.9999989322968755,
                0.9999991684722698
            ],
            [
                0.9999992661786696,
                0.9999996533672136,
                0.9999990577557432,
                0.9999994284992805,
                0.9999996533674615,
                0.9999996533673375,
                0.9999990577552939,
                0.999999554914842,
                0.99999844650169,
                0.9999967112513272
            ],
            [
                0.9999994956523514,
                0.9999993524049703,
                0.9999994956523514,
                0.9999990577550693,
                0.9999986290421395,
                0.9999993524054335,
                0.9999996533672962,
                0.9999987901337397,
                0.9999996940978825,
                0.9999991684722698
            ],
            [
                0.9999996072136592,
                0.9999993524051246,
                0.9999977396748941,
                0.9999996940976636,
                0.9999994956523514,
                0.9999996072139402,
                0.9999991684722697,
                0.9999996072137529,
                0.9999993524049702,
                0.9999995549147358
            ],
            [
                0.9999989322967483,
                0.9999994284996211,
                0.9999980052709921,
                0.9999987901346049,
                0.9999990577552939,
                0.9999996533674615,
                0.9999994284992805,
                0.9999994956526519,
                0.9999993524052019,
                0.9999984465020604
            ],
            [
                0.9999990577552939,
                0.9999990577551815,
                0.9999990577554062,
                0.9999952149049374,
                0.9999992661790195,
                0.9999980052700409,
                0.9999990577556309,
                0.9999984465026159,
                0.999998790133884,
                0.9999974387187058
            ],
            [
                0.9999987901346049,
                0.9999997617631184,
                0.9999986290426298,
                0.9999990577551815,
                0.999999352404893,
                0.999996711252111,
                0.999998932296621,
                0.9999974387174843,
                0.9999987901347492,
                0.9999984465024307
            ],
            [
                0.9999997300421903,
                0.999998932297512,
                0.9999996533672549,
                0.9999991684720715,
                0.9999990577549568,
                0.9999996072136593,
                0.9999980052695654,
                0.9999980052693275,
                0.999999428499553,
                0.9999982396563671
            ],
            [
                0.9999994284995529,
                0.9999989322972573,
                0.9999991684719723,
                0.999999266178757,
                0.9999990577556308,
                0.9999970976887073,
                0.9999994956525317,
                0.999999266179282,
                0.9999996072139402,
                0.9999989322970028
            ],
            [
                0.9999996533674202,
                0.9999991684719725,
                0.9999982396572066,
                0.9999986290429568,
                0.999999352405279,
                0.9999977396748941,
                0.9999993524049703,
                0.9999992661791071,
                0.9999996533672962,
                0.999998790134605
            ],
            [
                0.9999991684716749,
                0.9999992661786695,
                0.9999994284995529,
                0.9999993524052019,
                0.9999994284993485,
                0.9999990577551815,
                0.9999984465016899,
                0.9999993524052018,
                0.9999992661788446,
                0.9999992661789321
            ],
            [
                0.9999995549149482,
                0.9999997897565838,
                0.9999994956524115,
                0.9999989322973847,
                0.9999987901341724,
                0.9999993524052018,
                0.9999994284997574,
                0.9999994956525917,
                0.9999993524052018,
                0.9999992661791945
            ],
            [
                0.9999991684722698,
                0.999998629042303,
                0.9999991684720715,
                0.9999992661791944,
                0.999999352404893,
                0.9999995549150542,
                0.9999986290426298,
                0.9999993524053563,
                0.9999984465026159,
                0.9999993524050474
            ],
            [
                0.9999989322975119,
                0.9999982396563671,
                0.9999992661791071,
                0.9999970976890534,
                0.9999986290432836,
                0.9999992661790196,
                0.9999991684722698,
                0.9999980052698032,
                0.9999991684715759,
                0.999998790133884
            ],
            [
                0.9999810748540172,
                0.9999756997650695,
                0.9999687980886374,
                0.9999724643187587,
                0.9999687980774823,
                0.9999898700041902,
                0.9999832985841309,
                0.9999869928668849,
                0.9999646437619449,
                0.999975699759271
            ],
            [
                0.9999991684717742,
                0.9999984465015048,
                0.9999994284997573,
                0.9999996072137529,
                0.9999996940977002,
                0.9999996940978825,
                0.9999993524052789,
                0.9999984465028011,
                0.9999996072136125,
                0.9999987901341724
            ],
            [
                0.9999984465026159,
                0.9999992661792819,
                0.9999989322967481,
                0.999998790133884,
                0.999999168471675,
                0.9999994284994167,
                0.9999995549151073,
                0.9999986290431201,
                0.9999986290424664,
                0.9999989322967482
            ],
            [
                0.9999991684718732,
                0.9999984465015047,
                0.9999990577556309,
                0.9999995549150542,
                0.9999992661791945,
                0.9999974387177899,
                0.9999987901340281,
                0.9999998144608097,
                0.999999428499553,
                0.9999994956523514
            ],
            [
                0.9999977396759722,
                0.9999993524051247,
                0.9999982396565771,
                0.9999991684718733,
                0.9999996940978461,
                0.9999994284995531,
                0.9999991684722698,
                0.9999989322975119,
                0.9999982396565772,
                0.999999428499553
            ],
            [
                0.9999993524051247,
                0.9999991684720716,
                0.9999994956525318,
                0.9999994956523514,
                0.999999266179282,
                0.9999994284997574,
                0.9999993524050474,
                0.9999996533674202,
                0.999999694097773,
                0.9999993524051246
            ],
            [
                0.9999986290427934,
                0.9999996072138934,
                0.9999991684721706,
                0.9999970976880154,
                0.9999977396751637,
                0.999999266179282,
                0.999997438718706,
                0.999999266179282,
                0.9999990577549569,
                0.9999996072137061
            ],
            [
                0.9999990577551815,
                0.9999994956527121,
                0.9999989322972573,
                0.9999993524052018,
                0.9999996072137998,
                0.9999982396572069,
                0.9999986290429568,
                0.9999994956527121,
                0.999998932296621,
                0.9999989322972574
            ],
            [
                0.9999990577554062,
                0.9999994284997574,
                0.9999994284997574,
                0.9999994956524716,
                0.9999994956527121,
                0.9999991684718732,
                0.999999495652652,
                0.9999994956527121,
                0.9999993524053562,
                0.999999554914895
            ],
            [
                0.9999996072137061,
                0.9999995549149481,
                0.99999709768767,
                0.9999991684722698,
                0.9999994284997574,
                0.9999987901343167,
                0.9999974387174845,
                0.9999992661788446,
                0.9999982396567869,
                0.9999957771655504
            ],
            [
                0.9999982396559474,
                0.9999989322975119,
                0.9999982396574164,
                0.9999986290432836,
                0.9999991684715759,
                0.9999989322973846,
                0.9999982396563671,
                0.9999980052705164,
                0.9999987901341723,
                0.9999995549150011
            ],
            [
                0.999999554914842,
                0.9999991684720715,
                0.9999994956525317,
                0.9999996940976636,
                0.999999554914895,
                0.999999352404893,
                0.9999992661788446,
                0.9999990577552939,
                0.999999554914789,
                0.9999993524054335
            ],
            [
                0.9999987901347493,
                0.9999997300422225,
                0.9999982396559474,
                0.9999989322970028,
                0.9999984465016901,
                0.9999991684720715,
                0.9999977396754328,
                0.999999428499553,
                0.9999970976876694,
                0.9999974387177897
            ],
            [
                0.9999992661786696,
                0.9999996533674615,
                0.9999984465028011,
                0.9999993524054335,
                0.9999986290432836,
                0.9999992661787571,
                0.999999495652652,
                0.9999994956524716,
                0.9999992661791944,
                0.9999987901344609
            ],
            [
                0.9999986290424665,
                0.99999844650169,
                0.9999993524053562,
                0.9999986290421397,
                0.9999996072139402,
                0.9999984465018753,
                0.9999989322972572,
                0.9999974387184002,
                0.9999994284994167,
                0.9999989322967482
            ],
            [
                0.9999989322968755,
                0.9999995549147359,
                0.9999990577557432,
                0.9999997300422547,
                0.9999984465018752,
                0.9999994956527121,
                0.9999991684717741,
                0.9999990577549569,
                0.9999992661787571,
                0.9999990577554062
            ],
            [
                0.9999974387168736,
                0.9999982396563671,
                0.9999977396746248,
                0.9999974387177898,
                0.9999994956524716,
                0.999996273361161,
                0.9999987901347492,
                0.9999984465024309,
                0.9999977396746246,
                0.9999980052693275
            ],
            [
                0.9999994956525918,
                0.9999994284994168,
                0.999999266179282,
                0.9999987901338839,
                0.9999994956525919,
                0.9999991684719725,
                0.999997739676511,
                0.9999989322973846,
                0.9999994284996893,
                0.9999970976869776
            ],
            [
                0.9999994956527721,
                0.9999991684715758,
                0.9999967112513274,
                0.9999997617631184,
                0.999998932296621,
                0.9999993524053562,
                0.9999974387174843,
                0.9999970976887071,
                0.9999996072137998,
                0.9999997617631468
            ],
            [
                0.9999994956524716,
                0.9999996940977001,
                0.9999990577551815,
                0.9999994956524115,
                0.9999993524049702,
                0.9999997897567091,
                0.9999996940977731,
                0.9999990577557432,
                0.9999987901344608,
                0.9999991684717742
            ],
            [
                0.999999495652652,
                0.9999991684721707,
                0.999998239656787,
                0.9999989322971301,
                0.9999984465024307,
                0.9999996533674615,
                0.9999987901341724,
                0.9999984465022457,
                0.9999995549148419,
                0.9999977396748945
            ],
            [
                0.9999987901344608,
                0.9999992661791945,
                0.9999991684720715,
                0.9999992661791944,
                0.9999987901338838,
                0.9999997300420937,
                0.9999994956524715,
                0.9999984465015048,
                0.99999893229713,
                0.999999057755743
            ],
            [
                0.9999994284994167,
                0.9999994956524716,
                0.9999977396762415,
                0.9999992661786695,
                0.9999992661789321,
                0.999998932297512,
                0.9999991684715759,
                0.9999994284997574,
                0.9999991684717742,
                0.9999996072137529
            ],
            [
                0.999999352405279,
                0.9999986290432835,
                0.9999995549151073,
                0.9999994284996893,
                0.9999995549151073,
                0.999999266179107,
                0.9999993524051246,
                0.9999995549149481,
                0.9999992661788446,
                0.9999996072137062
            ],
            [
                0.9999996072136592,
                0.9999989322975119,
                0.9999994284994167,
                0.9999984465015048,
                0.9999982396563671,
                0.9999980052705164,
                0.9999996940976272,
                0.9999989322975118,
                0.9999991684716749,
                0.9999994284993485
            ],
            [
                0.9999996072136125,
                0.9999992661786696,
                0.9999974387177898,
                0.9999989322973846,
                0.999997739675972,
                0.9999992661787571,
                0.9999986290424664,
                0.9999982396567869,
                0.9999982396561574,
                0.9999977396748944
            ],
            [
                0.9999989322967483,
                0.9999982396574163,
                0.999999266178757,
                0.999999428499553,
                0.9999974387184005,
                0.9999980052698032,
                0.9999992661788446,
                0.9999997300422547,
                0.9999989322971301,
                0.9999945777790928
            ],
            [
                0.999999352404893,
                0.9999990577552939,
                0.9999986290432835,
                0.9999995549150542,
                0.9999994956524114,
                0.9999995549150011,
                0.9999989322973846,
                0.9999993524052018,
                0.9999994284992805,
                0.9999995549147359
            ],
            [
                0.9999993524050474,
                0.999999352405279,
                0.9999996072136593,
                0.9999984465022456,
                0.9999989322970028,
                0.9999990577552939,
                0.9999994956527121,
                0.9999970976869772,
                0.9999984465018752,
                0.9999996072139402
            ],
            [
                0.9999994284994167,
                0.9999995549151073,
                0.9999992661791071,
                0.9999986290431202,
                0.9999994284992805,
                0.9999992661791944,
                0.9999991684719726,
                0.9999986290423031,
                0.9999995549151072,
                0.9999982396572066
            ],
            [
                0.9999980052705167,
                0.9999995549147358,
                0.9999995549149481,
                0.9999996940977366,
                0.9999987901340283,
                0.9999989322967482,
                0.9999991684719725,
                0.9999995549150011,
                0.9999996533672549,
                0.9999994284996893
            ],
            [
                0.999999428499553,
                0.9999992661789321,
                0.9999990577557432,
                0.9999986290426299,
                0.9999997617630049,
                0.9999995549150542,
                0.9999986290421395,
                0.9999996072136593,
                0.9999992661789321,
                0.9999984465022456
            ],
            [
                0.9999982396563672,
                0.9999996533672548,
                0.9999989322970028,
                0.9999993524052019,
                0.9999986290426298,
                0.9999962733598287,
                0.9999996533675028,
                0.9999994956527722,
                0.9999996940976636,
                0.9999995549147358
            ],
            [
                0.9999986290432835,
                0.9999989322975119,
                0.9999992661791071,
                0.9999996072138466,
                0.9999995549150542,
                0.9999967112493671,
                0.9999986290424664,
                0.9999977396746245,
                0.9999994956526519,
                0.999999266179107
            ],
            [
                0.9999992661791945,
                0.9999991684716749,
                0.9999977396751636,
                0.999999352405279,
                0.9999989322971301,
                0.9999994956526519,
                0.9999991684722698,
                0.9999992661790195,
                0.9999992661786695,
                0.9999991684719725
            ],
            [
                0.9999984465024307,
                0.9999987901344608,
                0.9999992661786695,
                0.9999990577552939,
                0.9999986290424664,
                0.9999980052700409,
                0.9999982396569966,
                0.9999990577555185,
                0.9999992661787571,
                0.9999991684721707
            ],
            [
                0.9999992661792819,
                0.9999990577557432,
                0.9999990577552939,
                0.999998932296621,
                0.999999352405279,
                0.9999986290427932,
                0.9999996072138934,
                0.9999984465024307,
                0.9999992661790195,
                0.9999991684720715
            ],
            [
                0.9999989322973847,
                0.9999986290429568,
                0.999999730042319,
                0.9999986290421399,
                0.9999994956527121,
                0.9999977396748941,
                0.9999997617630332,
                0.9999986290421395,
                0.9999986290432835,
                0.9999991684721707
            ],
            [
                0.999999352405279,
                0.999999266179282,
                0.9999990577555186,
                0.9999994956524716,
                0.9999994956527121,
                0.9999994956525918,
                0.9999980052707543,
                0.999999554914842,
                0.999999495652652,
                0.9999989322972573
            ],
            [
                0.9999982396561573,
                0.999999554914895,
                0.9999967112509354,
                0.999994577778446,
                0.9999990577556309,
                0.9999989322972573,
                0.9999986290432836,
                0.9999994284996211,
                0.9999995549151073,
                0.999999266178932
            ],
            [
                0.99999893229713,
                0.9999989322968754,
                0.9999990577552939,
                0.9999989322970028,
                0.9999989322973845,
                0.9999984465020604,
                0.9999984465028012,
                0.9999957771670596,
                0.9999993524049703,
                0.9999986290429566
            ],
            [
                0.999998005270041,
                0.9999990577551815,
                0.999999266178932,
                0.999998932296621,
                0.9999986290421395,
                0.9999992661790196,
                0.9999994284996211,
                0.99999844650169,
                0.9999991684721707,
                0.9999995549151073
            ],
            [
                0.9999990577550693,
                0.9999994956524114,
                0.9999989322970029,
                0.999998239656787,
                0.9999995549150011,
                0.9999992661792819,
                0.9999992661788445,
                0.9999996072138466,
                0.9999996533672962,
                0.9999991684721706
            ],
            [
                0.9999989322970029,
                0.9999989322973846,
                0.9999993524050474,
                0.999999266178932,
                0.9999980052702786,
                0.99999893229713,
                0.9999990577554061,
                0.9999995549147358,
                0.999999730042126,
                0.999999428499553
            ],
            [
                0.9999996072138934,
                0.9999990577549569,
                0.9999994284994167,
                0.9999996533673376,
                0.9999977396757025,
                0.9999982396569967,
                0.9999992661790195,
                0.999999266179282,
                0.9999990577556308,
                0.9999977396759718
            ],
            [
                0.9999996072137061,
                0.9999996533674615,
                0.9999994284993485,
                0.9999996533672136,
                0.9999993524052019,
                0.9999989322967482,
                0.9999994956525317,
                0.9999994284994168,
                0.9999984465018751,
                0.9999984465020604
            ],
            [
                0.9999991684718733,
                0.9999974387174843,
                0.9999990577551815,
                0.9999993524052018,
                0.9999996072137061,
                0.9999987901337397,
                0.9999994284997573,
                0.9999992661791944,
                0.9999992661791071,
                0.9999992661788445
            ],
            [
                0.99999893229713,
                0.999999266178932,
                0.9999987901343167,
                0.9999996940978825,
                0.9999994284994849,
                0.9999996072137998,
                0.9999996533672962,
                0.999999554914895,
                0.9999997617631752,
                0.9999997897565838
            ],
            [
                0.9999989322971301,
                0.9999980052705167,
                0.9999991684719725,
                0.9999984465022456,
                0.9999990577550691,
                0.9999984465024307,
                0.9999986290432835,
                0.9999984465022456,
                0.9999980052695653,
                0.9999974387171792
            ],
            [
                0.9999993524052019,
                0.9999989322971301,
                0.9999994956524115,
                0.999999352405279,
                0.999998790134028,
                0.9999994956523512,
                0.9999996533673375,
                0.9999986290426298,
                0.9999994284992805,
                0.9999997897565587
            ],
            [
                0.9999987901341723,
                0.9999984465024307,
                0.9999996072139402,
                0.9999984465028012,
                0.9999989322970029,
                0.9999996533674201,
                0.9999996533673375,
                0.999999352404893,
                0.9999970976876694,
                0.9999994956527121
            ],
            [
                0.9999991684716749,
                0.9999984465024309,
                0.9999994956527722,
                0.9999994284992805,
                0.9999995549150542,
                0.9999996072137529,
                0.999999266179282,
                0.9999995549151073,
                0.9999987901338838,
                0.9999995549149481
            ],
            [
                0.9999957771675626,
                0.9999869928730912,
                0.9999945777784449,
                0.9999785550515972,
                0.9999938558268636,
                0.9999251537372807,
                0.9999921107383558,
                0.9999898700114368,
                0.9999980052700408,
                0.9999982396559473
            ],
            [
                0.9999986290431203,
                0.9999993524052018,
                0.9999990577556308,
                0.9999996940976638,
                0.9999996940976272,
                0.9999996533674614,
                0.9999996072136593,
                0.9999994956523514,
                0.9999994956527121,
                0.9999991684720716
            ],
            [
                0.99999844650169,
                0.9999984465022456,
                0.9999995549150011,
                0.999998629042303,
                0.9999986290429567,
                0.9999994284996893,
                0.9999994956526519,
                0.9999991684722698,
                0.9999986290424665,
                0.9999991684716749
            ],
            [
                0.999999168471675,
                0.9999991684718733,
                0.9999970976873234,
                0.999999168471576,
                0.9999995549150542,
                0.9999993524049702,
                0.9999984465022456,
                0.9999992661787571,
                0.9999990577555186,
                0.9999989322973846
            ],
            [
                0.9999996072136125,
                0.99999743871779,
                0.9999990577551816,
                0.9999993524051246,
                0.9999989322973846,
                0.9999967112493667,
                0.9999990577552939,
                0.9999994284994167,
                0.9999993524050474,
                0.9999993524051247
            ],
            [
                0.9999995549147889,
                0.9999991684721706,
                0.9999980052707543,
                0.9999993524052019,
                0.9999989322973846,
                0.9999990577556308,
                0.999998790134605,
                0.9999986290432835,
                0.9999987901344608,
                0.9999982396561573
            ],
            [
                0.9999987901344608,
                0.9999993524049702,
                0.9999998555019274,
                0.999999694097846,
                0.999999352404893,
                0.999999057755743,
                0.9999986290429567,
                0.9999989322973847,
                0.9999994284992805,
                0.9999996533674614
            ],
            [
                0.9999977396748939,
                0.999999168471675,
                0.9999980052698031,
                0.9999989322972573,
                0.9999991684722698,
                0.9999991684722698,
                0.9999991684720716,
                0.9999967112521111,
                0.9999967112521111,
                0.9999991684720715
            ],
            [
                0.9999991684718733,
                0.9999994284994167,
                0.9999995549150542,
                0.9999994284993486,
                0.9999992661788446,
                0.9999989322975119,
                0.9999992661792819,
                0.9999990577549569,
                0.9999977396746246,
                0.9999992661791944
            ],
            [
                0.9999993524052019,
                0.9999984465020604,
                0.9999990577555185,
                0.9999987901337396,
                0.9999992661791944,
                0.999997739674894,
                0.9999991684719725,
                0.9999974387174841,
                0.9999990577552939,
                0.9999986290427932
            ],
            [
                0.9999991684717742,
                0.9999995549149481,
                0.9999994284997574,
                0.9999996072136125,
                0.9999991684721706,
                0.9999993524051246,
                0.9999996533673375,
                0.9999992661786696,
                0.9999996533673376,
                0.9999993524050474
            ],
            [
                0.9999991684721706,
                0.9999990577554061,
                0.9999991684720715,
                0.9999992661790196,
                0.9999987901343166,
                0.9999989322967483,
                0.9999980052702787,
                0.9999994284994167,
                0.9999994284992805,
                0.9999997300422869
            ],
            [
                0.9999994284992805,
                0.999999730042126,
                0.9999990577551816,
                0.9999993524049703,
                0.9999986290429568,
                0.9999993524049703,
                0.999999694097773,
                0.9999990577554062,
                0.9999994956523514,
                0.9999990577551816
            ],
            [
                0.9999977396746245,
                0.9999980052702786,
                0.9999991684722698,
                0.999999266179107,
                0.9999987901347492,
                0.9999974387177896,
                0.9999977396751634,
                0.9999974387171788,
                0.9999990577551815,
                0.9999989322975118
            ],
            [
                0.9999952149072178,
                0.9999990577554061,
                0.9999970976880151,
                0.999999428499553,
                0.999999168471675,
                0.9999995549149481,
                0.9999987901338838,
                0.9999989322973846,
                0.9999986290421395,
                0.999999168471675
            ],
            [
                0.9999996072136593,
                0.9999994284997574,
                0.9999991684722698,
                0.9999996072137061,
                0.9999982396563671,
                0.9999994956523514,
                0.999999789756634,
                0.999999554914895,
                0.9999996072139402,
                0.9999995549150542
            ],
            [
                0.9999994956524114,
                0.999999352404893,
                0.9999990577549569,
                0.9999991684718733,
                0.9999994284997574,
                0.9999996533673788,
                0.9999995549151073,
                0.9999996072138934,
                0.9999986290432836,
                0.9999996072136593
            ],
            [
                0.9999994956523514,
                0.9999991684718733,
                0.9999987901347491,
                0.9999995549150542,
                0.9999991684719723,
                0.9999995549150011,
                0.9999996940977366,
                0.9999995549147889,
                0.9999995549151073,
                0.9999994956526519
            ],
            [
                0.9999986290421397,
                0.9999996072137529,
                0.9999996940977731,
                0.9999989322967482,
                0.9999989322968755,
                0.999999266178932,
                0.9999986290423032,
                0.999999266178932,
                0.9999987901343166,
                0.9999987901341724
            ],
            [
                0.9999993524050474,
                0.9999991684717742,
                0.9999994956524115,
                0.9999989322972573,
                0.999999168471675,
                0.9999987901347492,
                0.9999967112493671,
                0.9999984465022456,
                0.999995777168067,
                0.9999989322967482
            ],
            [
                0.999999352404893,
                0.9999994284993486,
                0.9999997617630333,
                0.9999997897565838,
                0.9999997300422225,
                0.999999352405279,
                0.9999982396559477,
                0.9999993524052019,
                0.999998932296621,
                0.9999996533672136
            ],
            [
                0.999994577782325,
                0.9999980052700409,
                0.9999982396561573,
                0.9999990577552939,
                0.9999982396574163,
                0.9999990577555185,
                0.9999982396565769,
                0.9999994284994167,
                0.9999986290421397,
                0.9999957771655494
            ],
            [
                0.9999994284993486,
                0.9999989322966208,
                0.9999994284992805,
                0.999999266179107,
                0.9999987901344607,
                0.9999993524052018,
                0.9999986290432837,
                0.9999982396567868,
                0.999999266178757,
                0.9999986290427931
            ],
            [
                0.999999694097846,
                0.9999987901341723,
                0.9999994956524716,
                0.999999168471576,
                0.9999996072136593,
                0.9999993524049702,
                0.9999996072138934,
                0.9999995549149481,
                0.9999986290431201,
                0.9999994956527721
            ],
            [
                0.9999990577552939,
                0.99999893229713,
                0.9999991684718733,
                0.9999992661789321,
                0.9999991684722698,
                0.9999992661786696,
                0.999998932296621,
                0.9999986290424665,
                0.999999352405279,
                0.9999990577550693
            ],
            [
                0.9999984465022456,
                0.9999993524052018,
                0.9999990577556309,
                0.9999996072137061,
                0.9999993524050474,
                0.9999993524050474,
                0.9999996072136125,
                0.9999989322973847,
                0.9999989322967483,
                0.9999957771650466
            ],
            [
                0.9999984465028011,
                0.9999996072137529,
                0.9999990577554062,
                0.9999991684715759,
                0.9999986290421397,
                0.9999994284992805,
                0.9999987901344609,
                0.9999986290427934,
                0.9999989322968755,
                0.9999989322972573
            ],
            [
                0.9999987901347493,
                0.9999991684721706,
                0.9999996940977366,
                0.9999987901341724,
                0.9999994284997574,
                0.9999984465024307,
                0.9999994956527722,
                0.9999990577551815,
                0.999999495652652,
                0.9999984465015048
            ]
        ]
    },
    {
        "q_id": "8303_mmlu_math",
        "cot_ids": [
            2,
            3,
            4,
            6,
            7,
            8,
            13,
            14,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            27,
            28,
            29,
            30,
            31,
            33,
            34,
            35,
            36,
            37,
            38,
            40,
            41,
            42,
            44,
            45,
            46,
            48,
            49,
            50,
            51,
            52,
            54,
            55,
            57,
            58,
            59,
            60,
            61,
            63,
            64,
            66,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            78,
            79,
            80,
            82,
            83,
            85,
            88,
            89,
            90,
            92,
            94,
            95,
            96,
            97,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            119,
            120,
            121,
            123,
            125,
            126,
            127
        ],
        "rewards": [
            [
                3.726639283440905e-06,
                1.553498310118888e-06,
                1.5534975692866768e-06,
                1.4738978454950406e-05,
                1.9947301969471416e-06,
                1.8925157259824262e-05,
                1.7603434231097403e-06,
                5.422217030032353e-06,
                6.144173868882483e-06,
                4.785093923847183e-06
            ],
            [
                1.5534971989568904e-06,
                1.3709578605355551e-06,
                7.338210679755959e-07,
                1.2098658276862581e-06,
                2.902311293034278e-06,
                2.260324567227179e-06,
                3.927861534349064e-07,
                1.994729483630195e-06,
                2.902311292831027e-06,
                5.043472278195839e-07
            ],
            [
                3.72664017246987e-06,
                6.475945665441494e-07,
                1.2098655392464547e-06,
                1.2098659719441482e-06,
                8.31527829351332e-07,
                6.962257909323729e-06,
                6.475945665800774e-07,
                2.9023130227599746e-06,
                1.2098656834613962e-06,
                5.7150044702099e-07
            ],
            [
                1.3709570433661467e-06,
                9.422444815679433e-07,
                8.315284241257637e-07,
                3.9278634073312583e-07,
                3.0590229984892605e-07,
                3.4663253846316044e-07,
                4.4508521110762794e-07,
                5.715006513900631e-07,
                3.4663249714325014e-07,
                1.067702488159652e-06
            ],
            [
                0.320821300824607,
                0.5926665999540698,
                0.16451646289656316,
                0.5312093733737563,
                0.1329642316084462,
                0.7772998611746912,
                0.43782349911420193,
                0.20181322466072713,
                0.995390427354846,
                0.022977368362860108
            ],
            [
                7.338208930078229e-07,
                2.2603251061849014e-06,
                1.9947294836483373e-06,
                5.715003107689177e-07,
                1.2098653949842147e-06,
                1.7603434230088762e-06,
                3.7266379513162962e-06,
                9.422448185435711e-07,
                5.715002426410745e-07,
                6.475950297768503e-07
            ],
            [
                9.422450431569214e-07,
                1.3007134665674251e-05,
                1.5534973840377051e-06,
                1.9947290079889487e-06,
                3.2887478891128633e-06,
                3.7266397278791014e-06,
                3.288750633139005e-06,
                1.0677032518316716e-06,
                3.2887478889962107e-06,
                7.889262585211807e-06
            ],
            [
                6.605217603296344e-05,
                0.017986209797594792,
                0.0011695102575760821,
                0.020332353268454888,
                0.3775406687981454,
                0.34864512179822543,
                0.0013250223067603748,
                0.22270014398423355,
                0.0330859792229422,
                0.02297737220986642
            ],
            [
                7.338209804920378e-07,
                3.4663270374206273e-07,
                9.422447061876404e-07,
                5.715007194475252e-07,
                2.38236909984676e-07,
                2.382369099864094e-07,
                2.699578418172324e-07,
                2.1024334103247107e-07,
                9.422448184681581e-07,
                9.422450431012186e-07
            ],
            [
                2.2603251060142746e-06,
                9.422448184801556e-07,
                1.370957696715851e-06,
                1.3709572067356507e-06,
                1.3709570433075437e-06,
                1.067702742683591e-06,
                5.715002426202836e-07,
                3.726639726347116e-06,
                7.338207180661203e-07,
                3.4663274506641133e-07
            ],
            [
                0.9999038975513151,
                0.9999485577986821,
                0.9999785550439229,
                0.9999869928746372,
                0.9999339478632726,
                0.9999852610110026,
                0.9999417087067435,
                0.9998766053821879,
                0.9999151889284886,
                0.9999417087206486
            ],
            [
                2.260325105981383e-06,
                7.889263524788109e-06,
                4.785096775676685e-06,
                2.561281294558644e-06,
                3.726639727940109e-06,
                3.1201911346293e-05,
                6.144177530548804e-06,
                4.2228334437304904e-06,
                1.4738980207363312e-05,
                2.902313022952668e-06
            ],
            [
                6.475946437657736e-07,
                1.3709567164962755e-06,
                1.5534975693036317e-06,
                6.475945665800774e-07,
                6.475949525257309e-07,
                1.0677024881382882e-06,
                4.450852641596248e-07,
                1.7603430032374404e-06,
                1.209865394997419e-06,
                5.043475885606781e-07
            ],
            [
                4.222833444106873e-06,
                3.726640616477725e-06,
                2.260324836651547e-06,
                9.422449308566668e-07,
                1.994729959224386e-06,
                3.7266410605974813e-06,
                1.209866116149238e-06,
                1.7603425836005905e-06,
                2.5612834318257725e-06,
                1.994729721436347e-06
            ],
            [
                0.9999251537549613,
                0.9997694933400741,
                0.999925153737218,
                0.9999724643056468,
                0.999964643736671,
                0.9999724643187674,
                0.9994472212745128,
                0.9999885212305081,
                0.9996646498915447,
                0.9999151889183183
            ],
            [
                1.5534983100425914e-06,
                8.315283250260307e-07,
                1.5534973840984598e-06,
                8.315277302444853e-07,
                3.927863406961518e-07,
                7.338211554464836e-07,
                2.3823688158658173e-07,
                9.422450427515764e-07,
                4.222831933864508e-06,
                1.3709578604981489e-06
            ],
            [
                1.994730672468935e-06,
                2.9023112926779284e-06,
                2.260323758746637e-06,
                1.1478769490700865e-05,
                1.7603438427852151e-06,
                2.2603234891147668e-06,
                2.5612815998491325e-06,
                1.76034279349265e-06,
                7.88926164421493e-06,
                5.422220906065395e-06
            ],
            [
                1.5534973841895917e-06,
                2.902312331081799e-06,
                6.144176798870286e-06,
                3.2887486732000038e-06,
                1.2098653950315304e-06,
                2.9023123310290063e-06,
                2.9023130230133794e-06,
                4.785092783149804e-06,
                2.260324028351814e-06,
                5.422220908762902e-06
            ],
            [
                1.067702488159652e-06,
                1.209865394997419e-06,
                1.0677024881140118e-06,
                6.475948753847607e-07,
                1.2098652507285942e-06,
                8.3152792848466e-07,
                3.726639727940109e-06,
                1.9947306726213275e-06,
                2.5612825159421147e-06,
                2.260324836651547e-06
            ],
            [
                1.2098662604192665e-06,
                5.715007195353674e-07,
                1.3709570432888404e-06,
                9.422445938861406e-07,
                3.059021539909339e-07,
                6.475947209826952e-07,
                9.422450431860582e-07,
                1.5534973841705173e-06,
                1.8553910183269882e-07,
                9.422445938797133e-07
            ],
            [
                2.902311292920774e-06,
                6.144173136019732e-06,
                4.222833444283541e-06,
                2.9023130230133794e-06,
                1.2098662603862553e-06,
                2.5612816000145246e-06,
                4.785096776394765e-06,
                3.726640616477725e-06,
                1.2098656834613962e-06,
                1.9947297213746646e-06
            ],
            [
                2.9023116389365734e-06,
                1.5534981249397663e-06,
                5.715004470243685e-07,
                4.2228319339950885e-06,
                1.8925148230890784e-05,
                6.962258738435319e-06,
                1.0677028700130727e-06,
                2.561281905293402e-06,
                1.2098655392811161e-06,
                1.0677027427413698e-06
            ],
            [
                5.42222090821551e-06,
                1.994729721396435e-06,
                1.4738983725406915e-05,
                4.7850967757637256e-06,
                3.2887490649221017e-06,
                6.9622579086271995e-06,
                5.422218968595919e-06,
                1.7603438427852151e-06,
                1.9947304347570075e-06,
                3.7266388391247794e-06
            ],
            [
                7.338208055489796e-07,
                1.9947301969707264e-06,
                1.9947299591826594e-06,
                4.450849458179853e-07,
                3.0590215398829087e-07,
                5.043473480607e-07,
                1.209865395009523e-06,
                9.422448185388577e-07,
                1.7603436329394601e-06,
                4.222835457449267e-06
            ],
            [
                9.42244256886598e-07,
                1.0677028699858827e-06,
                8.315283250082584e-07,
                5.422219616026655e-06,
                7.33820805514942e-07,
                1.5534981245618166e-06,
                1.3709573700365957e-06,
                1.3709575335121232e-06,
                2.5612815999423112e-06,
                8.315278293604072e-07
            ],
            [
                1.20986611609532e-06,
                5.04347588554027e-07,
                4.4508526416286326e-07,
                8.315278293899016e-07,
                5.715005832676369e-07,
                5.715003107525447e-07,
                1.3709572068079696e-06,
                6.475947981860793e-07,
                1.2098656834349874e-06,
                5.715005832676369e-07
            ],
            [
                5.043476486833397e-07,
                2.2603253754921562e-06,
                1.7603427935678977e-06,
                1.9947294835866542e-06,
                2.5612815999679353e-06,
                8.315281267800897e-07,
                1.2098656834349874e-06,
                5.715006514074756e-07,
                4.222835457852533e-06,
                4.222832437497486e-06
            ],
            [
                5.715003788933905e-07,
                3.0590222691880844e-07,
                3.4663262110630603e-07,
                1.2098658277264215e-06,
                3.466326211105621e-07,
                5.715004470272272e-07,
                5.715005832762133e-07,
                8.315279285205827e-07,
                1.9947299591826594e-06,
                9.4224425692559e-07
            ],
            [
                1.9947304346826253e-06,
                5.043474081831035e-07,
                9.422447061576466e-07,
                4.4508499884930563e-07,
                6.475947981754775e-07,
                9.422447061782138e-07,
                5.715003107525447e-07,
                8.315277301945715e-07,
                1.3709570431803621e-06,
                5.715005151400212e-07
            ],
            [
                2.9023112930949896e-06,
                8.315278293899016e-07,
                5.043474081931949e-07,
                1.0677026154376365e-06,
                1.0677032518501217e-06,
                1.994729245842213e-06,
                4.4508489275752546e-07,
                1.0677028700203557e-06,
                1.3709578605455302e-06,
                1.5534979396645902e-06
            ],
            [
                4.222834450820197e-06,
                5.422217029844958e-06,
                4.785094494019719e-06,
                1.760344052650207e-06,
                2.260324028045508e-06,
                9.422443691773458e-07,
                5.422221554926484e-06,
                6.47594566594213e-07,
                2.2603251060738913e-06,
                1.2098659719232413e-06
            ],
            [
                1.0677031245851707e-06,
                4.450851049917114e-07,
                1.067702488159652e-06,
                9.422445938797133e-07,
                3.0590211752206485e-07,
                1.9947290078746543e-06,
                2.5612812946681295e-06,
                5.715005832676369e-07,
                1.5534975693347152e-06,
                6.475949525919915e-07
            ],
            [
                3.4663257978039603e-07,
                1.0677028700266676e-06,
                2.38237023581637e-07,
                3.466326210962177e-07,
                6.47594720987407e-07,
                2.3823682478845333e-07,
                4.4508515804389805e-07,
                1.2751904288617538e-07,
                2.699579061812927e-07,
                3.05902226922147e-07
            ],
            [
                0.005911068626395828,
                0.0001398221237119418,
                0.13296424363358259,
                0.015906390137353562,
                3.2887486729876365e-06,
                0.042087731520181665,
                0.022977370286363187,
                0.01798620923830578,
                0.033085980653064666,
                0.11920293297380237
            ],
            [
                8.315283249522945e-07,
                9.422442568763144e-07,
                1.370957370236096e-06,
                5.043474683050556e-07,
                3.9278610660884725e-07,
                3.0590211750759763e-07,
                7.33820893021171e-07,
                9.422448184561605e-07,
                1.994729245878497e-06,
                1.0677031245429291e-06
            ],
            [
                3.288748280837859e-06,
                6.962258738574625e-06,
                1.0677031245186523e-06,
                4.222832940423847e-06,
                1.2098652507439992e-06,
                1.994730196992497e-06,
                1.1478764019787597e-05,
                2.5612831265909735e-06,
                1.7603438427660027e-06,
                7.88926540454376e-06
            ],
            [
                9.610241451644106e-05,
                4.785096205260165e-06,
                4.222832436272325e-06,
                2.4300243615448162e-05,
                1.6701419845073e-05,
                6.962257906765564e-06,
                2.2603253751858496e-06,
                2.5612822103393692e-06,
                5.422217673754406e-06,
                8.9397005654763e-06
            ],
            [
                4.2228354571957855e-06,
                4.222831934052698e-06,
                2.260325105693578e-06,
                8.939698433974813e-06,
                1.9947294836483373e-06,
                2.561282515853595e-06,
                3.2887478890769702e-06,
                4.785092782396909e-06,
                4.222832437443716e-06,
                5.422220262037209e-06
            ],
            [
                1.0677028699858827e-06,
                4.785096775998733e-06,
                6.14417753110761e-06,
                1.9947299592407137e-06,
                4.222832940500659e-06,
                1.2098659719232413e-06,
                1.0677026153784014e-06,
                7.338210679816025e-07,
                2.2603253755949437e-06,
                3.2887478889034873e-06
            ],
            [
                1.7603436329714805e-06,
                3.927861065988446e-07,
                4.450852110742317e-07,
                5.715003107577426e-07,
                7.338207180534397e-07,
                4.450851580362069e-07,
                9.422449308335287e-07,
                7.338212429167144e-07,
                3.92786106602417e-07,
                7.338209804920378e-07
            ],
            [
                3.2887502407138142e-06,
                9.422443691996268e-07,
                8.315281267339571e-07,
                3.927863407225873e-07,
                8.315280276399315e-07,
                3.927862002491823e-07,
                1.2098659718539182e-06,
                9.422447061576466e-07,
                8.315279284544091e-07,
                5.043472879383035e-07
            ],
            [
                3.726641060956752e-06,
                2.5612822106421996e-06,
                1.3709568799592562e-06,
                5.715005151446993e-07,
                9.42244930862237e-07,
                2.3823702358748722e-07,
                1.5534979397267575e-06,
                5.715004470272272e-07,
                1.2098655392222467e-06,
                2.902311985079115e-06
            ],
            [
                0.9978172830658162,
                0.014063629845490687,
                0.9947798740670476,
                3.2887494572514376e-06,
                0.017986211936052907,
                0.06008664365190536,
                0.04742587065312426,
                0.005911067696058906,
                0.09534946875514018,
                0.06008664449346691
            ],
            [
                3.726639727092773e-06,
                NaN,
                1.0129987350921133e-05,
                8.31528325021115e-07,
                6.475948753276293e-07,
                1.2098662603961589e-06,
                3.726640172290235e-06,
                6.475950297821511e-07,
                1.0129988556912918e-05,
                7.338209805133949e-07
            ],
            [
                0.7057850340255385,
                0.24508502416032488,
                0.09534946040040722,
                0.9997388096926838,
                0.4378234991142019,
                0.9992903295067421,
                0.24508501313237172,
                0.5621765008857981,
                0.32082130731838393,
                0.9997694932268587
            ],
            [
                1.2098661157971212e-06,
                1.7603425834564988e-06,
                5.715005832510042e-07,
                1.3709572066334069e-06,
                9.422448184801556e-07,
                9.422449308420983e-07,
                1.9947299590810645e-06,
                6.475947209638476e-07,
                8.31528325021115e-07,
                1.994729721396435e-06
            ],
            [
                2.260323758835034e-06,
                3.7266388391247794e-06,
                2.260324836624822e-06,
                2.5612815999679353e-06,
                1.7603440526806268e-06,
                9.422448185264317e-07,
                1.553498495295912e-06,
                8.315278293838516e-07,
                1.9947306725669014e-06,
                4.450851049890802e-07
            ],
            [
                0.939913356558485,
                0.9971990724137791,
                0.7057850154599563,
                0.348645142101806,
                0.9988304895072978,
                0.9997388097411012,
                0.9989677687315613,
                0.880797068590724,
                0.0850990519679964,
                0.033085978865411605
            ],
            [
                7.338211554591642e-07,
                7.338208929998139e-07,
                1.5534971989258068e-06,
                2.561282210562998e-06,
                7.338208055302923e-07,
                5.71500310747347e-07,
                4.4508505192495825e-07,
                1.5534975693707442e-06,
                9.422447062202052e-07,
                4.450848927437622e-07
            ],
            [
                5.422217030121119e-06,
                0.00012339455199243045,
                1.8925152748558416e-05,
                6.962257908348587e-06,
                1.4738976698006875e-05,
                1.4738988994980593e-05,
                1.1478768122069266e-05,
                6.9622570777680525e-06,
                4.222833946645451e-06,
                5.4222215537823875e-06
            ],
            [
                2.260324836624822e-06,
                7.338211554531576e-07,
                1.5534977545243671e-06,
                3.927862002606139e-07,
                6.475946437966953e-07,
                7.338213304196583e-07,
                9.422447061679302e-07,
                5.715004470243685e-07,
                4.450849988798682e-07,
                1.209865683500459e-06
            ],
            [
                3.726641060773727e-06,
                2.9023116389761676e-06,
                6.144173869240119e-06,
                1.5534983098744568e-06,
                2.5612831264675113e-06,
                1.0129990977520359e-05,
                5.422218969029887e-06,
                8.315278292643609e-07,
                3.28874867308036e-06,
                5.422218322664422e-06
            ],
            [
                5.422218969720291e-06,
                1.5534975691524517e-06,
                9.422450431260706e-07,
                1.7603432131375548e-06,
                1.2098655392222467e-06,
                1.994729483666479e-06,
                2.9023112930949896e-06,
                1.7603427935518875e-06,
                2.561281599881745e-06,
                3.726641061058432e-06
            ],
            [
                9.422449307512599e-07,
                3.4663249713205845e-07,
                1.0677032518413822e-06,
                3.466327863850901e-07,
                5.715005151296257e-07,
                2.699578096253257e-07,
                4.4508489270328195e-07,
                6.475947981295368e-07,
                5.043475885228353e-07,
                1.2098658276444443e-06
            ],
            [
                1.5534973840984598e-06,
                2.902311984952413e-06,
                1.9947292458004866e-06,
                6.475947209918244e-07,
                5.043475885292571e-07,
                1.209865539274514e-06,
                1.7603438428188364e-06,
                7.338213304143191e-07,
                1.994729483535857e-06,
                1.2098652507583041e-06
            ],
            [
                6.475946437928669e-07,
                2.56128159999123e-06,
                8.31528424146183e-07,
                5.422221555069497e-06,
                4.222833947282995e-06,
                1.994729008074216e-06,
                4.785095064148803e-06,
                5.715003107655392e-07,
                1.0677032518413822e-06,
                9.422448185101494e-07
            ],
            [
                3.726639284017094e-06,
                1.370957696865476e-06,
                2.561282515886208e-06,
                1.7603440526133836e-06,
                1.994730672468935e-06,
                1.994730434778778e-06,
                6.144173136556186e-06,
                6.144176797283277e-06,
                1.0677028699742299e-06,
                2.260324028281919e-06
            ],
            [
                3.059023727728012e-07,
                4.4508489275469177e-07,
                2.699577452733192e-07,
                1.9947306726049992e-06,
                5.715005832798517e-07,
                1.3709570433661467e-06,
                1.553497198826904e-06,
                9.422444815563743e-07,
                6.475945665741875e-07,
                2.6995768090929735e-07
            ],
            [
                1.9947294835630703e-06,
                4.785093922115089e-06,
                2.9023133677438847e-06,
                3.288747889038086e-06,
                5.422218969532895e-06,
                1.0677026154279257e-06,
                4.222833945815874e-06,
                5.422218961139563e-06,
                4.222834953520201e-06,
                1.994730672265745e-06
            ],
            [
                6.144173135896795e-06,
                6.144172403201774e-06,
                1.7603432132464244e-06,
                2.4300240711101413e-05,
                7.889261643382609e-06,
                1.4738988989189704e-05,
                6.962255419051463e-06,
                1.9947290080125335e-06,
                4.222835456581284e-06,
                3.7266379504926854e-06
            ],
            [
                1.9947294834796172e-06,
                3.726640172385136e-06,
                6.1441738691562974e-06,
                4.2228324370327694e-06,
                1.1478769491598686e-05,
                2.2603248364644736e-06,
                8.93970056152486e-06,
                3.288748280520804e-06,
                1.2098659719122375e-06,
                2.5612834317116285e-06
            ],
            [
                1.5534971989427613e-06,
                7.338207180864763e-07,
                7.338208055579897e-07,
                2.260323489266892e-06,
                1.209865539274514e-06,
                7.338208055536515e-07,
                7.338208930355202e-07,
                1.209865539274514e-06,
                1.2098655392871682e-06,
                2.2603253755949437e-06
            ],
            [
                0.26894141551050293,
                0.05340332810495602,
                0.4073334000459302,
                0.18242551491653522,
                0.2018132270610754,
                0.9525741288419873,
                0.9999852610151317,
                0.09534946361376596,
                0.16451646494473962,
                0.9999599363228239
            ],
            [
                8.315278293687262e-07,
                1.5534981248881956e-06,
                1.0677028700203557e-06,
                1.9947297214182054e-06,
                3.466326624205564e-07,
                8.315281267581578e-07,
                3.9278620025275473e-07,
                9.422447061876404e-07,
                2.260325375520937e-06,
                8.315283250260307e-07
            ],
            [
                1.5534983100228109e-06,
                4.450851580402549e-07,
                1.067702615417244e-06,
                5.043472278227948e-07,
                1.5534979397500702e-06,
                2.3823696679040834e-07,
                8.315279285012978e-07,
                8.315282258956806e-07,
                5.715003788853339e-07,
                1.3709573702111586e-06
            ],
            [
                1.855390354791913e-07,
                8.315277301688584e-07,
                1.8553912395262116e-07,
                3.059022633747535e-07,
                1.8553903547666011e-07,
                6.475947209985977e-07,
                3.466326210854988e-07,
                2.102433159670327e-07,
                1.444980209556342e-07,
                1.0677024881683915e-06
            ],
            [
                1.3709573702566696e-06,
                8.31528325021115e-07,
                9.422448184133123e-07,
                8.315277302649045e-07,
                1.3709576970824327e-06,
                1.0677026154279257e-06,
                3.726639727750306e-06,
                3.4663270374947136e-07,
                2.561283431916622e-06,
                3.0590222691672177e-07
            ],
            [
                3.535625070315809e-05,
                3.7266383951544193e-06,
                0.00048785705767128226,
                0.004070137194920931,
                0.00010889690926520891,
                0.06008665311947338,
                0.0003799845722257878,
                0.0007096702857073526,
                0.0019267345943757425,
                0.0002959570266115192
            ],
            [
                8.315280276096808e-07,
                1.3709570433075437e-06,
                1.2098662603752517e-06,
                4.4508499887035535e-07,
                3.4663274507287414e-07,
                2.5612825160096693e-06,
                2.902310946944611e-06,
                1.2098658276598493e-06,
                6.475950297709604e-07,
                8.315281267649641e-07
            ],
            [
                0.9999687980849252,
                0.9999852610215512,
                0.9999785550490375,
                0.9999785550592685,
                0.999915188948979,
                0.9999921107374159,
                0.9999038975515724,
                0.9999251537996711,
                0.9999785550592651,
                0.999981074856277
            ],
            [
                1.370957533534567e-06,
                1.3709578604495207e-06,
                1.9947301970287804e-06,
                5.422218969306048e-06,
                3.2887478891128633e-06,
                1.067702488159652e-06,
                6.14417460073947e-06,
                1.0677027427068966e-06,
                2.260324567054496e-06,
                1.370957860466977e-06
            ],
            [
                0.9997965730292492,
                0.9996200155199823,
                0.9988304894844514,
                0.9914225157821906,
                0.9924227576606213,
                0.9995121427745558,
                0.7549149813536518,
                0.9924227583189394,
                0.9890130561853708,
                0.998967768943438
            ],
            [
                5.715002426140462e-07,
                1.5534979396448094e-06,
                2.9023130228444433e-06,
                3.72664061671159e-06,
                4.785092782858221e-06,
                2.2603251061232293e-06,
                3.726640616423495e-06,
                2.260324297702111e-06,
                1.5534973841450852e-06,
                3.7266410609940346e-06
            ],
            [
                1.9947301969471416e-06,
                2.260324028331257e-06,
                1.760343213227212e-06,
                3.726639284050988e-06,
                1.553497754476329e-06,
                9.422444815323792e-07,
                2.260324836651547e-06,
                2.902311984952413e-06,
                2.260323489410794e-06,
                4.222835457664342e-06
            ],
            [
                8.315281267581578e-07,
                2.3823693839057394e-07,
                5.043472879419732e-07,
                4.4508521110499674e-07,
                3.927862002556126e-07,
                1.3709568798220997e-06,
                6.475949525781504e-07,
                4.450849458153541e-07,
                3.9278605979011705e-07,
                5.043476486764593e-07
            ],
            [
                8.315279285012978e-07,
                3.059022633413675e-07,
                6.475947981389606e-07,
                2.6995777744140237e-07,
                9.422449308241022e-07,
                2.1024336609083744e-07,
                2.1024326583998928e-07,
                8.315281267430323e-07,
                6.475947980989097e-07,
                3.059022998436399e-07
            ],
            [
                6.475947209918244e-07,
                1.2098662604049616e-06,
                5.715004470025379e-07,
                1.5534979397677313e-06,
                1.5534983100228109e-06,
                1.3709570433979422e-06,
                9.422445938728576e-07,
                1.553497754476329e-06,
                7.338208930265102e-07,
                9.422450431732037e-07
            ],
            [
                6.96225375863827e-06,
                4.53978902461248e-05,
                1.6701419845680582e-05,
                6.144175333837093e-06,
                7.889265404113251e-06,
                4.785096204972935e-06,
                7.889263525103816e-06,
                2.902311292155282e-06,
                8.315276404541325e-07,
                7.889265405677441e-06
            ],
            [
                1.7603434229000067e-06,
                1.5534981247426673e-06,
                7.338208930144969e-07,
                1.9947297213746646e-06,
                5.4222170304318e-06,
                1.4738985480179701e-05,
                1.553498495230919e-06,
                1.0677024881382882e-06,
                2.260324297702111e-06,
                1.7603425837062577e-06
            ],
            [
                8.315280276263186e-07,
                1.855390575969964e-07,
                3.4663257978465195e-07,
                7.338208930315157e-07,
                1.0677033791291683e-06,
                1.7603438427243761e-06,
                2.699577130905084e-07,
                3.0590237278114764e-07,
                3.4663270374490014e-07,
                3.927862002606139e-07
            ],
            [
                7.338209804920378e-07,
                1.0677032518209896e-06,
                1.7603436329554703e-06,
                3.0590233631503464e-07,
                3.726637950973972e-06,
                9.422447061876404e-07,
                7.3382106794623e-07,
                6.9622554187981796e-06,
                3.2887482812506295e-06,
                1.5534971989696065e-06
            ],
            [
                7.338211554591642e-07,
                4.4508505193123265e-07,
                3.9278610661366994e-07,
                3.059023727786437e-07,
                1.2098655391947376e-06,
                4.4508489275752546e-07,
                2.102432658363562e-07,
                1.2751910369020252e-07,
                3.059021539664509e-07,
                9.42244481511812e-07
            ],
            [
                1.0677028699489821e-06,
                4.4508521110175827e-07,
                5.043472278195839e-07,
                1.2098652507439992e-06,
                3.2887502412970765e-06,
                1.0677026154473471e-06,
                4.450851049941403e-07,
                1.6373774480479287e-07,
                2.3823693838927385e-07,
                5.715003107416295e-07
            ],
            [
                5.422221553072258e-06,
                4.78509449306228e-06,
                5.422219614951598e-06,
                4.2228319341064674e-06,
                3.7266383946527958e-06,
                6.02357849981697e-08,
                1.6701415864001047e-05,
                4.222834953197588e-06,
                1.1253518883234654e-07,
                1.8553907969759193e-07
            ],
            [
                1.5534983100765009e-06,
                6.475951069808602e-07,
                2.260324028281919e-06,
                1.2098658276862581e-06,
                2.902313022952668e-06,
                2.561282210590951e-06,
                9.422444815323792e-07,
                2.260325375615501e-06,
                9.422448184912962e-07,
                2.902311292960369e-06
            ],
            [
                7.338208930078229e-07,
                5.715002426301592e-07,
                1.2098662603202336e-06,
                3.2887494572514376e-06,
                1.9947292456281383e-06,
                1.2098652507583041e-06,
                1.3709570432501875e-06,
                3.7266401722360055e-06,
                5.42221767672807e-06,
                1.9947290080343035e-06
            ],
            [
                0.0006263341707886652,
                2.753569437476538e-05,
                0.002182715986932243,
                0.014063626552529782,
                1.0677031245186523e-06,
                0.00029595720318738257,
                0.0059110681612273485,
                0.0001795279864214665,
                0.00026119027700124324,
                0.000552778741694912
            ],
            [
                3.2887494572095624e-06,
                5.715003107525447e-07,
                1.7603430034439723e-06,
                3.927862002606139e-07,
                1.2098661161602417e-06,
                2.5612831265909735e-06,
                1.067703379136937e-06,
                1.0677032518209896e-06,
                3.288749064802458e-06,
                2.2603245672025095e-06
            ],
            [
                1.99472995920443e-06,
                9.422448184133123e-07,
                1.1478768122987964e-05,
                1.4738980212296288e-05,
                1.4738978456049602e-05,
                2.561281599734989e-06,
                1.9947301968382903e-06,
                1.4738978456049602e-05,
                1.7603430033158905e-06,
                2.5612831266165976e-06
            ],
            [
                1.3007128458384476e-05,
                3.7266388392671313e-06,
                5.422217673931937e-06,
                6.962257077932685e-06,
                1.3007131554942966e-05,
                2.430024072188641e-05,
                1.0129989769464556e-05,
                8.939697367703906e-06,
                1.8925143720384422e-05,
                1.3007133109847152e-05
            ],
            [
                1.0677033791204289e-06,
                2.699578418198104e-07,
                1.0677024881829577e-06,
                5.715006513999389e-07,
                1.2098662603499435e-06,
                1.994729721396435e-06,
                1.760342793515064e-06,
                1.3709570433786157e-06,
                9.422448185101494e-07,
                1.0677028700130727e-06
            ],
            [
                4.222835457664342e-06,
                7.338208055369664e-07,
                1.5534979395798164e-06,
                4.222833444283541e-06,
                1.5534971989258068e-06,
                9.422442569097361e-07,
                9.422443692261927e-07,
                1.3709578605243332e-06,
                3.726640616477725e-06,
                1.0677026154279257e-06
            ],
            [
                4.450848927599543e-07,
                4.4508505193791187e-07,
                1.5534975693707442e-06,
                7.338210679979539e-07,
                1.5534984952492866e-06,
                8.315279285251204e-07,
                1.0677027427413698e-06,
                1.3709575337078829e-06,
                1.0677028700203557e-06,
                1.7603432132464244e-06
            ],
            [
                2.3823696678412476e-07,
                8.315278294001114e-07,
                8.315280276456036e-07,
                7.338213304243302e-07,
                4.450852641681257e-07,
                4.45084945809282e-07,
                5.04347528438253e-07,
                5.043474081867732e-07,
                5.715005151296257e-07,
                3.059021904506262e-07
            ],
            [
                3.7266392838544054e-06,
                3.72664061671159e-06,
                2.561282210530385e-06,
                1.370957860466977e-06,
                9.422443692090534e-07,
                1.0129993393742954e-05,
                1.670142582254589e-05,
                3.2887486731252264e-06,
                8.939699499823059e-06,
                1.3007131562514014e-05
            ],
            [
                5.422218967797024e-06,
                1.4449803570314595e-07,
                4.222834450420771e-06,
                5.422220906864292e-06,
                3.2887502401335425e-06,
                1.892515499389843e-05,
                4.785093352595421e-06,
                5.422217676101776e-06,
                4.222831933649433e-06,
                5.422218322851817e-06
            ]
        ]
    },
    {
        "q_id": "8014_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            9,
            10,
            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,
            8,
            11
        ],
        "rewards": [
            [
                0.9998601779134524,
                0.9995694428945262,
                0.9999832985821548,
                0.9999687980961541,
                0.9994472212691102,
                0.9999485577866964,
                0.9999756997535904,
                0.9999599363174594,
                0.9998911030662648,
                0.9999724642958515
            ],
            [
                0.9999832985801554,
                0.9999646437367106,
                0.9991959141513562,
                0.9984988176237317,
                0.9986749774285844,
                0.9999869928653372,
                0.9999646437451345,
                0.9999485577987062,
                0.9995121429587626,
                0.9999151889287737
            ],
            [
                2.430024940080467e-05,
                1.670142383167491e-05,
                3.535624645944555e-05,
                2.1444940712293222e-05,
                1.0129993389652346e-05,
                2.1444945844014022e-05,
                1.147877222485351e-05,
                4.006369685690351e-05,
                1.6701423831188846e-05,
                5.1442219756013625e-05
            ],
            [
                0.9999785550439516,
                0.9999898700090272,
                0.9999810748517763,
                0.999948557780452,
                0.9999869928730905,
                0.9999930377437511,
                0.9999930377454128,
                0.999959936312681,
                0.9997694932971086,
                0.9995121428738686
            ],
            [
                1.300713311155064e-05,
                3.535625067794842e-05,
                1.8925145977014425e-05,
                4.006368739659403e-05,
                7.889263522779056e-06,
                3.535625491265802e-05,
                2.144495096387783e-05,
                1.6701427809710842e-05,
                4.006370647870077e-05,
                3.535624222010662e-05
            ],
            [
                1.1478766754941153e-05,
                1.1478765385746131e-05,
                6.962255418658875e-06,
                2.4300240711101413e-05,
                8.939695237666677e-06,
                1.4738976696371488e-05,
                1.3007128453415979e-05,
                8.939698433974813e-06,
                1.1478765387416494e-05,
                1.6701419849933667e-05
            ],
            [
                1.3007131559816827e-05,
                1.4738985481520185e-05,
                3.120192624233791e-05,
                1.0129995809763438e-05,
                2.430024362393472e-05,
                1.8925148227861472e-05,
                1.4738987239698005e-05,
                1.0129990976156825e-05,
                2.7535694373763664e-05,
                1.1478772227338172e-05
            ],
            [
                0.9998204719997218,
                0.9999957771655511,
                0.9999930377462417,
                0.9999869928730944,
                0.9997040429919795,
                0.9998911030669905,
                0.9999852610110213,
                0.9999986290432835,
                0.9999910603036991,
                0.999986992876213
            ],
            [
                1.892514597343433e-05,
                1.0129987355785634e-05,
                1.3007125356952865e-05,
                4.785093353626844e-06,
                7.889259762307618e-06,
                7.889262585211807e-06,
                4.785093924103951e-06,
                6.14417313680765e-06,
                1.670142781560441e-05,
                1.6701429805655623e-05
            ],
            [
                5.1442225851784594e-05,
                1.892514822538295e-05,
                1.1478773595970265e-05,
                5.144223201941656e-05,
                4.0063682616886836e-05,
                1.3007133108948093e-05,
                1.4738983724146862e-05,
                4.5397884856980825e-05,
                2.1444948408977715e-05,
                1.4738980212296288e-05
            ],
            [
                0.9999151889387117,
                0.9995121428940773,
                0.9999756997680053,
                0.9995121427903653,
                0.9998601779606158,
                0.9982992778514438,
                0.9971990729763016,
                0.9840936076467381,
                0.9940889324161287,
                0.9940889308974905
            ],
            [
                0.9998204719735339,
                0.9999724643056397,
                0.9999485577926327,
                0.9999485577864644,
                0.9999251537373908,
                0.9997694933196578,
                0.9999898700090211,
                0.9999485577865307,
                0.9999417087555146,
                0.9999646437325401
            ],
            [
                2.144494073796001e-05,
                7.889260704308795e-06,
                1.8925143720384422e-05,
                3.535626331905454e-05,
                1.0129992186387057e-05,
                1.8925143718318983e-05,
                1.6701419850845044e-05,
                2.430025231213619e-05,
                3.120191508321514e-05,
                2.7535681245588654e-05
            ],
            [
                0.9770226285009934,
                0.9997388097906812,
                0.9998766054559217,
                0.9986749776964746,
                0.999373665764467,
                0.9978172835566832,
                0.9999485577927724,
                0.998498817587785,
                0.9998415638222387,
                0.9996200154609055
            ],
            [
                0.9996646499159949,
                0.9999869928762016,
                0.9999852610110318,
                0.999983298578181,
                0.9999785550567739,
                0.9999832985742202,
                0.9999687980776816,
                0.9999910603026332,
                0.9999485577805405,
                0.9999921107392975
            ],
            [
                1.6701421840318107e-05,
                6.1441767990323395e-06,
                NaN,
                1.892515500663531e-05,
                2.753570092878799e-05,
                2.753569108573408e-05,
                2.1444953506061874e-05,
                8.939697367264857e-06,
                5.422218323231539e-06,
                1.4738988996240646e-05
            ],
            [
                5.144219521911119e-05,
                1.1478765385746131e-05,
                1.89251572481201e-05,
                2.1444943278894603e-05,
                1.6701419845680582e-05,
                8.481105128568296e-05,
                1.6701421812976822e-05,
                5.144220131413071e-05,
                4.0063687383622725e-05,
                6.96225541916544e-06
            ],
            [
                1.473898196677375e-05,
                1.0129989769962063e-05,
                7.889266345584138e-06,
                3.7266397278180926e-06,
                1.1478772230198667e-05,
                3.288749456964293e-06,
                2.5612828209811664e-06,
                4.539787399116584e-05,
                1.8925154999337424e-05,
                1.1478769492642663e-05
            ],
            [
                4.2228324372555256e-06,
                1.8925141459279565e-05,
                2.1444950963097686e-05,
                1.6701417850314193e-05,
                2.144495603607593e-05,
                2.1444945848226808e-05,
                1.473898020838208e-05,
                3.535624219412524e-05,
                2.430025231213619e-05,
                1.89251482270353e-05
            ],
            [
                0.9986749775835572,
                0.9996646498790951,
                0.9999910603058298,
                0.9999980052702787,
                0.9998204719546908,
                0.9999038975397494,
                0.9998766054705328,
                0.9999832985801618,
                0.9999724643056813,
                0.99989110305373
            ],
            [
                0.9999599362984326,
                0.999738809696894,
                0.9986749778454396,
                0.9999756997563937,
                0.999933947871323,
                0.9999485577622176,
                0.9997694932112311,
                0.9999810748450078,
                0.9993736657351371,
                0.9997388096671109
            ],
            [
                2.1444950963097686e-05,
                8.939693105076969e-06,
                8.939697368305565e-06,
                1.670141586150995e-05,
                8.939693104637921e-06,
                1.012999218369684e-05,
                3.2887482811579057e-06,
                6.144177530671741e-06,
                4.2228324377164004e-06,
                1.3007125362323574e-05
            ],
            [
                0.9999810748540298,
                0.9999785550515963,
                0.9999151889792269,
                0.99997855504393,
                0.9999599363221838,
                0.9997694932070929,
                0.9999756997505882,
                0.9999724642990725,
                0.9999251537906992,
                0.9994472213443282
            ],
            [
                0.9999898700078178,
                0.9998766053682664,
                0.9999038975405786,
                0.9999724643187715,
                0.9999810748495156,
                0.999820471996812,
                0.9999910603036981,
                0.9999869928699978,
                0.9999885212346179,
                0.999876605382565
            ],
            [
                0.9998204719527318,
                0.9999962733602722,
                0.9999038975519067,
                0.99997246431224,
                0.9997965730085849,
                0.9998766054599434,
                0.9999974387184003,
                0.9999898700090245,
                0.9999485577926825,
                0.9998766054266548
            ],
            [
                0.9999724642991131,
                0.9997388097349986,
                0.9999038975869141,
                0.9999599363030588,
                0.9998766054255973,
                0.9999599362983224,
                0.9998415637095612,
                0.9999546021209916,
                0.9999869928715435,
                0.9999687980738009
            ],
            [
                0.9999546021205734,
                0.9999151889286763,
                0.9999852610233245,
                0.9999151889790857,
                0.9999339478634874,
                0.9999599362935213,
                0.9999756997650883,
                0.9999885212346196,
                0.9999646437536056,
                0.9999970976869772
            ],
            [
                0.9999930377412631,
                0.9999898700078194,
                0.9999485577742059,
                0.99997246431879,
                0.999994577781677,
                0.999933947847887,
                0.9999251537998436,
                0.9999151889591908,
                0.9999810748540305,
                0.9998415637663771
            ],
            [
                0.9999810748517651,
                0.9993736657266479,
                0.9998204720386982,
                0.9999982396561572,
                0.9999485577680203,
                0.9999785550439346,
                0.9999885212277727,
                0.999986992866886,
                0.9999546021476909,
                0.9999646437535491
            ],
            [
                7.889261642794245e-06,
                1.300712380555121e-05,
                8.939696301839653e-06,
                1.3007134664822509e-05,
                6.1441724044534996e-06,
                8.93969310418261e-06,
                3.7266388396975786e-06,
                1.4738983726184394e-05,
                4.785094493932679e-06,
                3.288750241374845e-06
            ],
            [
                1.670142383167491e-05,
                2.430023782010365e-05,
                6.962257908196617e-06,
                2.7535684513582775e-05,
                1.3007130012341915e-05,
                1.0129990977262395e-05,
                1.4738987232298539e-05,
                1.892515499555078e-05,
                6.144177530425867e-06,
                1.3007123809644304e-05
            ],
            [
                7.889265406904397e-06,
                6.962257909007124e-06,
                6.144173136645595e-06,
                1.6701415866735174e-05,
                2.4300243620398656e-05,
                8.939700566289352e-06,
                8.939694172542558e-06,
                4.785092782936557e-06,
                7.889265406151004e-06,
                1.0129994601688632e-05
            ],
            [
                2.4300232036606334e-05,
                7.484624491729e-05,
                1.4738987241172537e-05,
                1.8925150490826034e-05,
                3.53562506877236e-05,
                3.535625488822007e-05,
                3.120191506210258e-05,
                5.8291251560237615e-05,
                0.00015843615755870482,
                3.535625067177463e-05
            ],
            [
                4.539786857692116e-05,
                5.144223197188398e-05,
                2.7535687806920664e-05,
                2.1444953517842076e-05,
                1.670142781086525e-05,
                1.3007130010117919e-05,
                5.144221971259806e-05,
                1.8925148236674017e-05,
                3.535626333641835e-05,
                9.610240337377108e-05
            ],
            [
                0.9999952149049406,
                0.9999417087209703,
                0.9998911030940805,
                0.9999599362984134,
                0.9999151889896499,
                0.9998415637283369,
                0.9999646437325463,
                0.9978172835779812,
                0.9999038976204043,
                0.9991959142231892
            ],
            [
                0.9999810748562817,
                0.9999417087276105,
                0.9999417087067719,
                0.9999417087068075,
                0.9999339478554764,
                0.9999646437324624,
                0.999989870004201,
                0.9999687980738113,
                0.9999785550464785,
                0.9999599363078678
            ],
            [
                0.9999910603037004,
                0.9999756997592771,
                0.9999251537819165,
                0.9999869928715381,
                0.999975699756396,
                0.9999546021097657,
                0.9989677687350426,
                0.9959298632014731,
                0.999941708706802,
                0.9999417087207414
            ],
            [
                2.4300232031037035e-05,
                1.6701419846288166e-05,
                0.00010889694687853696,
                3.535624219978455e-05,
                7.889264457390238e-06,
                1.8925148232267744e-05,
                3.120191133221797e-05,
                1.8925150479534963e-05,
                1.4738976696371488e-05,
                1.3007130007515371e-05
            ],
            [
                4.5397852346412016e-05,
                4.5397879034816765e-05,
                4.0063691975610905e-05,
                7.48462358997521e-05,
                6.605216026239207e-05,
                3.5356246402852425e-05,
                2.4300237821252875e-05,
                3.535625063627531e-05,
                6.605213649000608e-05,
                4.539788476879124e-05
            ],
            [
                0.9999938558224701,
                0.9999885212346176,
                0.9999646437536087,
                0.9999982396561572,
                0.9999967112521116,
                0.9999952149037951,
                0.9999962733616047,
                0.9999832985781935,
                0.9999910602994376,
                0.9999756997506213
            ],
            [
                2.4300246519706854e-05,
                1.1478772229050293e-05,
                3.5356259116499136e-05,
                3.1201922514835635e-05,
                1.3007130012980722e-05,
                1.4738978431545582e-05,
                3.120190390775116e-05,
                6.605212101883346e-05,
                3.53562633082504e-05,
                3.1201926209079954e-05
            ],
            [
                2.7535684513582775e-05,
                0.00015843621325196613,
                1.6701419829944157e-05,
                2.4300246513165137e-05,
                3.5356263316996617e-05,
                3.5356242204929376e-05,
                0.00017952794218190895,
                3.12019262070368e-05,
                2.7535681242383173e-05,
                1.6701429802769596e-05
            ],
            [
                1.1478773597390071e-05,
                1.4738980210258757e-05,
                1.0129988562422337e-05,
                1.4738980213020151e-05,
                1.0129989769962063e-05,
                1.0129987353242826e-05,
                1.147876812238246e-05,
                1.0129989770441144e-05,
                7.889265406294507e-06,
                8.939698434966738e-06
            ],
            [
                0.9999417087067435,
                0.9971990732539862,
                0.9999251537549879,
                0.99966464985724,
                0.9999756997563937,
                0.9959298631995857,
                0.9997388097282729,
                0.9999339478713302,
                0.9940889314611653,
                0.9999417087279332
            ],
            [
                4.006370172318498e-05,
                4.539785774447017e-05,
                3.5356263294359356e-05,
                4.006368253424943e-05,
                4.006370643585172e-05,
                5.829127933751884e-05,
                4.539786857361818e-05,
                5.829128635171172e-05,
                3.120190760732817e-05,
                4.5397868549836734e-05
            ],
            [
                0.9999339478400403,
                0.9999832985822078,
                0.9992903294447825,
                0.999992110737422,
                0.999512142984279,
                0.9999599363080509,
                0.9999339478401787,
                0.9999485577682291,
                0.999968798081254,
                0.9999251537917595
            ],
            [
                7.4846253614641e-05,
                4.006368258642613e-05,
                5.829126542194621e-05,
                3.1201922520397544e-05,
                1.8925148236674017e-05,
                4.006367781356952e-05,
                4.006368261047406e-05,
                2.7535697651475977e-05,
                5.82912446122085e-05,
                5.8291265478351516e-05
            ],
            [
                1.3007131562514014e-05,
                4.785093923916815e-06,
                5.422217675628357e-06,
                1.4738988997044936e-05,
                2.260325375354421e-06,
                1.147876402018431e-05,
                6.144173136019732e-06,
                1.1478764014985311e-05,
                6.144176798255599e-06,
                6.144176797998549e-06
            ],
            [
                0.9999869928668885,
                0.9999646437493104,
                0.9997040428781085,
                0.9997388097941087,
                0.9997694931802645,
                0.9999485578048138,
                0.9997388097917604,
                0.9999869928668892,
                0.9997694933462111,
                0.9999957771670628
            ],
            [
                2.7535697654881812e-05,
                4.006367783499403e-05,
                4.006368739659403e-05,
                6.605213673845602e-05,
                3.535623806128476e-05,
                2.7535700941409604e-05,
                6.605214465281235e-05,
                3.120190019330501e-05,
                7.484620927188383e-05,
                1.8925152744771773e-05
            ],
            [
                4.539785775768208e-05,
                2.1444958627955892e-05,
                3.1201903930339314e-05,
                2.753569764256071e-05,
                5.144221359998557e-05,
                4.006367784548767e-05,
                2.1444953517061932e-05,
                5.82912653460323e-05,
                2.4300237821252875e-05,
                3.12019187588432e-05
            ],
            [
                2.430023492769181e-05,
                4.539788482296012e-05,
                1.8925152742706337e-05,
                2.1444945854624007e-05,
                3.5356254903911806e-05,
                3.120190391705884e-05,
                2.4300234907624647e-05,
                3.120191876292951e-05,
                0.00013982202274901334,
                6.60521524840326e-05
            ],
            [
                0.9999038976197933,
                0.9994472214472986,
                0.9999339478399482,
                0.9986749778482124,
                0.9998204720996493,
                0.9996646499024917,
                0.9996200155706243,
                0.9999646437620285,
                0.9999038975755232,
                0.9999646437624038
            ],
            [
                5.144219521574275e-05,
                1.6701417860795016e-05,
                4.785092782936557e-06,
                3.120192622962497e-05,
                1.1478773597870298e-05,
                1.30071346612026e-05,
                1.0129994602057158e-05,
                2.4300237828059798e-05,
                1.1478766756444477e-05,
                6.962258737092915e-06
            ],
            [
                1.8925150493717652e-05,
                1.6701417854810315e-05,
                3.120191135560069e-05,
                3.535625912717466e-05,
                4.539785233683338e-05,
                4.539786860697828e-05,
                2.144494329769612e-05,
                2.4300237832303074e-05,
                9.610242532560827e-05,
                2.753568124458694e-05
            ],
            [
                7.889266346287306e-06,
                7.88926070293116e-06,
                3.7266379509129646e-06,
                1.147877086073156e-05,
                1.3007133113703658e-05,
                4.222831934052698e-06,
                1.0129990977262395e-05,
                4.785093353100252e-06,
                1.0129994600398803e-05,
                1.4738978448810996e-05
            ],
            [
                0.9999869928715388,
                0.9999930377462404,
                0.9988304899405609,
                0.999981074854025,
                0.9999869928715435,
                0.9999852610215463,
                0.9999957771680666,
                0.9999785550541578,
                0.9999832985741811,
                0.999925153737418
            ],
            [
                0.9890130566711292,
                0.9993736657205269,
                0.9998204720571469,
                0.9997965729793377,
                0.9959298620424921,
                0.9999417087553878,
                0.9999810748495058,
                0.9953904284039189,
                0.9999417087553785,
                0.9968273168651822
            ],
            [
                0.9999546021098239,
                0.9999832985781602,
                0.9999546021098896,
                0.9996200155529036,
                0.9999885212359889,
                0.9999832985841349,
                0.999948557804886,
                0.9999832985761902,
                0.9998766053675968,
                0.9999599363222681
            ],
            [
                0.18242551936144574,
                0.2450850021044189,
                0.022977369742764476,
                0.06008665227791172,
                0.08509904268669496,
                0.13296423676207597,
                1.1478769492141554e-05,
                0.03732688734412946,
                0.0953494616857507,
                0.10669060388702056
            ],
            [
                9.610246036941213e-05,
                3.1201915058697335e-05,
                3.120191134947124e-05,
                1.670142383167491e-05,
                1.147876949187012e-05,
                4.5397852378781204e-05,
                1.3007134665674251e-05,
                1.300712846411008e-05,
                7.889261644982674e-06,
                4.0063687383622725e-05
            ],
            [
                0.999991060299447,
                0.9995694429123876,
                0.9999885212305086,
                0.9999832985701977,
                0.9999945777829703,
                0.9999687980924642,
                0.9980732653389113,
                0.999948557780625,
                0.9999810748450472,
                0.9999417087420795
            ],
            [
                0.9999832985722096,
                0.9999938558239347,
                0.9999339478794839,
                0.9999646437536778,
                0.9998415637377076,
                0.9999599362889321,
                0.9999930377420932,
                0.9999646437410246,
                0.999925153801033,
                0.9999898700090254
            ],
            [
                0.9986749776163695,
                0.9999724643056662,
                0.9998911030657862,
                0.9999885212277838,
                0.9999952149072173,
                0.999841563708895,
                0.9999977396765108,
                0.999959936303167,
                0.9997040429970858,
                0.9999785550541627
            ],
            [
                0.9999724642958047,
                0.9998766054693604,
                0.9998204719728286,
                0.9999869928699907,
                0.9999852610180443,
                0.9997694932701864,
                0.9999687980737704,
                0.9999687980849346,
                0.9999546021097478,
                0.99996879809982
            ],
            [
                0.9999945777810308,
                0.9999885212291395,
                0.9999938558224694,
                0.9997388096536823,
                0.9999038975514479,
                0.999569442937614,
                0.9997040428096774,
                0.9999869928761911,
                0.9997694933037822,
                0.9999485577742104
            ],
            [
                0.9999810748495187,
                0.9994472214152691,
                0.99919591423923,
                0.9988304895399353,
                0.9988304898691662,
                0.9989677687864212,
                0.9986749777243573,
                0.9978172839846705,
                0.9992903297395553,
                0.998967769200091
            ],
            [
                2.4300240713399853e-05,
                4.006368738595465e-05,
                1.30071346612026e-05,
                2.7535697639856078e-05,
                2.4300252299759956e-05,
                4.539785234971499e-05,
                1.6701425819994037e-05,
                3.120190389923804e-05,
                4.0063682546783496e-05,
                1.6701425822059825e-05
            ],
            [
                0.999988521227774,
                0.9999251537729397,
                0.9999038975738913,
                0.9998766053970073,
                0.9992903295305189,
                0.9999869928746431,
                0.9997040427682932,
                0.9999251537998088,
                0.9998766053967362,
                0.9993736657746323
            ],
            [
                1.4738983726559732e-05,
                1.8925157250667477e-05,
                1.3007130012341915e-05,
                1.89251482286188e-05,
                1.8925143714394646e-05,
                1.147876675466972e-05,
                5.422220907554695e-06,
                1.8925157247225074e-05,
                6.144173136019732e-06,
                1.892514597770291e-05
            ],
            [
                0.9998204719726039,
                0.9997965729313854,
                0.9998601779106286,
                0.9997388097869575,
                0.9998204719518542,
                0.9980732650460902,
                0.9997040429863308,
                0.9998204720369168,
                0.9988304895294641,
                0.9994472214774951
            ],
            [
                1.1478772229050293e-05,
                3.1201911358551906e-05,
                2.430023203572232e-05,
                1.6701421841259862e-05,
                2.7535681242383173e-05,
                1.8925141463066202e-05,
                1.1478770856158943e-05,
                2.1444956072586775e-05,
                2.1444953513707305e-05,
                1.4738988995409548e-05
            ],
            [
                1.3007128460797749e-05,
                7.889260703906985e-06,
                1.8925143721072897e-05,
                1.8925141467059383e-05,
                2.7535687788789623e-05,
                2.1444948400318094e-05,
                1.8925150482908516e-05,
                6.144176798132662e-06,
                5.422217676397663e-06,
                1.1478770858372173e-05
            ],
            [
                0.9999151889490012,
                0.9999852610180436,
                0.9998911031304412,
                0.9999417087137823,
                0.9999599363126486,
                0.9984988180091984,
                0.9986749778831815,
                0.9999687980812105,
                0.9999485577618926,
                0.9975273765550773
            ],
            [
                0.9999687980812073,
                0.9998766054706261,
                0.9999687980849506,
                0.9999038976084988,
                0.9999687980812332,
                0.9998911030528268,
                0.9997040427793669,
                0.9999724643189002,
                0.9999687980962252,
                0.9999898700078145
            ],
            [
                0.9997965731011569,
                0.9999546021208918,
                0.9999151889393237,
                0.9999810748540273,
                0.9998204720801143,
                0.9994472214338564,
                0.9980732652950328,
                0.99994855776199,
                0.9998766054559685,
                0.998967768805508
            ],
            [
                0.9999339478240872,
                0.9999938558254007,
                0.9999687980961026,
                0.9999756997507266,
                0.999820472068637,
                0.9998601779473616,
                0.9998204720413467,
                0.9999785550490627,
                0.9999930377437575,
                0.9999885212318887
            ],
            [
                0.9999599363127625,
                0.9999151889892723,
                0.9999910603005062,
                0.000804085976596539,
                0.9999251537371887,
                0.9999417087346145,
                0.9999251537370873,
                0.9999251537906992,
                0.9995694430195555,
                0.9999151889790765
            ],
            [
                0.9998204720806836,
                0.9999785550413764,
                0.9999339478478042,
                0.9999785550592795,
                0.9999785550439432,
                0.9999930377454109,
                0.9999810748495503,
                0.9999970976890532,
                0.999997097688707,
                0.9999810748562864
            ],
            [
                7.889266347356409e-06,
                1.0129992185060374e-05,
                6.962259569117366e-06,
                5.422218323290717e-06,
                1.3007134665130082e-05,
                1.4738981970312625e-05,
                4.2228319339950885e-06,
                4.2228319341064674e-06,
                8.939694170729447e-06,
                2.260324028281919e-06
            ],
            [
                0.9992903295825716,
                0.9998601778632761,
                0.9995121428244819,
                0.9999945777810317,
                0.999903897609068,
                0.9999339478241241,
                0.9999646437619673,
                0.9996646497631855,
                0.9999785550490408,
                0.9999485577620417
            ],
            [
                0.999983298580161,
                0.9999724643023602,
                0.9999599362983397,
                0.9999785550464837,
                0.9999687980812043,
                0.9999687980849379,
                0.9999251538001324,
                0.9998766053965656,
                0.9999599363221864,
                0.999948557768061
            ],
            [
                0.9998415637085216,
                0.9988304896137776,
                0.9995694428475057,
                0.999796572936914,
                0.9999785550516096,
                0.9999339478556297,
                0.9999038975513012,
                0.9998911031320985,
                0.9994472214396128,
                0.9999810748427427
            ],
            [
                0.9999485577805097,
                0.9995121427723703,
                0.9999785550413814,
                0.9999599363079568,
                0.999978555051619,
                0.9999810748585477,
                0.9999810748540359,
                0.9999921107374153,
                0.9998911031053034,
                0.9999910603015664
            ],
            [
                2.753570419688461e-05,
                2.4300249402042293e-05,
                2.430023782328611e-05,
                1.4738983723664288e-05,
                3.120192250723057e-05,
                1.3007130010922344e-05,
                2.4300237821252875e-05,
                7.88926164421493e-06,
                3.535626333989112e-05,
                4.006368255581968e-05
            ],
            [
                1.892515500450102e-05,
                1.3007128457958606e-05,
                1.1478765387416494e-05,
                4.785096776068365e-06,
                1.4738988994498018e-05,
                7.889265405505236e-06,
                4.7850956342431385e-06,
                1.4738988996240646e-05,
                1.3007123808910861e-05,
                1.892514372479069e-05
            ],
            [
                4.7850967744320136e-06,
                6.144174598593655e-06,
                1.4738983725809062e-05,
                6.144175332283612e-06,
                6.962256249517824e-06,
                1.3007134664822509e-05,
                1.3007131563507714e-05,
                2.9023119835956434e-06,
                7.88925976080083e-06,
                1.473898020682712e-05
            ],
            [
                0.999975699747833,
                0.9998911030784938,
                0.9997965730603195,
                0.9999417087207354,
                0.9999724643154878,
                0.9999898700041907,
                0.9997388097709373,
                0.9998601779621069,
                0.9999151889791752,
                0.9999151889495899
            ],
            [
                0.9999687980812186,
                0.9999417087137878,
                0.999738809601275,
                0.9999756997621879,
                0.9999785550413702,
                0.9999832985801625,
                0.9997965731027078,
                0.9999910602994357,
                0.999959936322208,
                0.9999832985781602
            ],
            [
                0.9999646437577749,
                0.9999485577986598,
                0.9986749774318193,
                0.999993037742092,
                0.9999485577864269,
                0.9992903294363615,
                0.9988304900032521,
                0.999088948914742,
                0.999860177877938,
                0.9999756997650743
            ],
            [
                1.012998856312253e-05,
                1.892515500450102e-05,
                1.012999339031569e-05,
                1.6701417858577338e-05,
                4.222834450236421e-06,
                1.6701415862785876e-05,
                2.144495860837422e-05,
                1.3007134665130082e-05,
                8.93969523617066e-06,
                5.422218322664422e-06
            ],
            [
                0.9999251537376357,
                0.99998107485629,
                0.9999885212318825,
                0.999941708727773,
                0.9999832985841333,
                0.9999832985702337,
                0.99477987327874,
                0.99807326494714,
                0.9999251537732246,
                0.9999339478240049
            ],
            [
                0.9999251537373908,
                0.9924227596635892,
                0.9959298624653127,
                0.9999485577803072,
                0.9999756997535343,
                0.9999599363079912,
                0.9999251537821657,
                0.9998601778608084,
                0.9999599363033326,
                0.9982992771849564
            ],
            [
                0.9998766053822795,
                0.9999599362935554,
                0.9998911031174975,
                0.9999921107355383,
                0.9980732652726458,
                0.9999038976086108,
                0.9999546021152467,
                0.998299277415025,
                0.9990889489772605,
                0.9999485577679911
            ],
            [
                8.939698432446272e-06,
                1.1478768123280277e-05,
                1.67014178590634e-05,
                1.1478765386330758e-05,
                5.422221554758815e-06,
                2.144495605799804e-05,
                2.4300237812059105e-05,
                1.670142979997471e-05,
                1.670141586949968e-05,
                1.6701419844465412e-05
            ],
            [
                1.1478773596283455e-05,
                1.0129988563546333e-05,
                1.1478773596575768e-05,
                1.0129994598777299e-05,
                1.6701423831188846e-05,
                2.753568781022632e-05,
                4.53978686205205e-05,
                1.8925143723000643e-05,
                1.0129990979215566e-05,
                2.1444948408977715e-05
            ],
            [
                0.9997388095755275,
                0.999988521226404,
                0.999820472104876,
                0.9995121429459618,
                0.9998415637172605,
                0.999373665833802,
                0.9997040430055589,
                0.9997040427838273,
                0.9999869928699907,
                0.999993037746244
            ],
            [
                0.99991518893894,
                0.9999832985722068,
                0.9999869928746505,
                0.9999724643056629,
                0.9999938558232027,
                0.9999785550413814,
                0.9999832985801729,
                0.9999910603015705,
                0.9995121427797216,
                0.9999339478478042
            ],
            [
                0.9999687980998683,
                0.9999724643122069,
                0.9999724643122256,
                0.9999962733593835,
                0.9997694933745821,
                0.9999832985761709,
                0.9999930377462429,
                0.9999485577803285,
                0.999954602109809,
                0.9999251537998535
            ],
            [
                2.144494072867628e-05,
                1.4738987241494252e-05,
                2.753569108693614e-05,
                1.670142781244497e-05,
                3.535626334490732e-05,
                2.753568780802255e-05,
                1.6701415868193372e-05,
                2.7535704207102113e-05,
                6.605217613916744e-05,
                1.1478773595343877e-05
            ],
            [
                2.4300243624818735e-05,
                7.484620927188383e-05,
                5.1442231983486416e-05,
                4.006370648788271e-05,
                1.670142581762446e-05,
                2.1444948409679848e-05,
                4.5397852367551086e-05,
                4.0063696945516495e-05,
                5.144223190750916e-05,
                1.0129989770441144e-05
            ],
            [
                3.120191135412508e-05,
                2.1444953504969666e-05,
                4.006371127619171e-05,
                2.753568124769226e-05,
                2.4300232030064617e-05,
                1.670142781478417e-05,
                8.93969630333567e-06,
                1.012999097799944e-05,
                2.9023112927307205e-06,
                2.144495095279976e-05
            ],
            [
                0.9991959141159072,
                0.9998911031051132,
                0.9999938558261332,
                0.9999957771645424,
                0.9998911030916133,
                0.999986992873089,
                0.9999251537375127,
                0.9999687980998273,
                0.9999546021206461,
                0.9999785550541526
            ],
            [
                0.9999687980998521,
                0.9999852610180342,
                0.9998911031175514,
                0.9999151889184082,
                0.9984988179545804,
                0.9999957771660527,
                0.9999599362985282,
                0.9999251537641438,
                0.9999832985701989,
                0.9999724643089233
            ],
            [
                5.422220908018252e-06,
                8.939700566289352e-06,
                4.785096776068365e-06,
                1.670142781478417e-05,
                5.422218969306048e-06,
                4.22283545795623e-06,
                6.962254588977791e-06,
                6.962257908044647e-06,
                8.939695237959376e-06,
                1.89251482355036e-05
            ],
            [
                0.9999546021098513,
                0.9999852610145241,
                0.9971990733755951,
                0.9999921107355346,
                0.9999852610215536,
                0.998674977341855,
                0.9986749775703089,
                0.9999251537645294,
                0.9999599363031396,
                0.9999646437451547
            ],
            [
                1.6701423830702777e-05,
                1.4738988974605243e-05,
                1.14787708580381e-05,
                2.4300249408672413e-05,
                NaN,
                4.5397874031792504e-05,
                0.0004878571813367457,
                2.7535681224252135e-05,
                4.539786860136322e-05,
                1.3007134663876127e-05
            ],
            [
                1.4738988993532872e-05,
                6.144174601208867e-06,
                1.3007134663521234e-05,
                1.3007123810306773e-05,
                3.7266410609160796e-06,
                1.0129988563546333e-05,
                6.144172401145369e-06,
                1.3007126910649678e-05,
                6.962256248871951e-06,
                1.012999339309804e-05
            ],
            [
                1.4738981970956057e-05,
                1.1478764018012839e-05,
                8.93969950000193e-06,
                1.012998735462479e-05,
                3.7266388396128453e-06,
                1.670142382681424e-05,
                1.147877086020957e-05,
                1.0129993393742954e-05,
                4.785096205882502e-06,
                1.3007128462785148e-05
            ],
            [
                0.9999038975755442,
                0.9999151889285838,
                0.9999599362888627,
                0.9999485577746635,
                0.9989677691811241,
                0.9999485577681363,
                0.9999599362888137,
                0.9993736658820415,
                0.9999724643089352,
                0.9999921107374196
            ],
            [
                1.6701417860795016e-05,
                9.610246055259474e-05,
                5.1442207317454294e-05,
                0.00012339455826198656,
                2.4300243620398656e-05,
                3.1201918796982014e-05,
                2.753569109254574e-05,
                6.605216822432677e-05,
                5.1442238087492836e-05,
                3.5356246476937965e-05
            ],
            [
                0.9998415637894682,
                0.9997694932192662,
                0.9999810748585536,
                0.9999687980924453,
                0.999903897562755,
                0.999989870010234,
                0.999986992871546,
                0.9999852610197972,
                0.9999546021152204,
                0.9999785550516015
            ],
            [
                0.9990889488959864,
                0.9999646437451318,
                0.9998415637843208,
                0.9982992773586937,
                0.9999599363222021,
                0.9999687980737909,
                0.9999785550464939,
                0.9999546021368614,
                0.9989677687493277,
                0.999933947855464
            ],
            [
                1.1478766754064213e-05,
                3.1201907631845964e-05,
                1.1478766741849697e-05,
                8.481103099344347e-05,
                2.4300232027942982e-05,
                1.6701417858577338e-05,
                2.1444943287710254e-05,
                4.5397873994468824e-05,
                3.120190019784534e-05,
                2.7535684479824982e-05
            ],
            [
                0.9999724643056611,
                0.9992903295100858,
                0.9999599363031364,
                0.9992903295897542,
                0.9999038975403494,
                0.9999810748517677,
                0.9992903297591628,
                0.9999756997535193,
                0.999981074842751,
                0.9999885212291455
            ],
            [
                0.26894141551050293,
                0.9986749773386199,
                0.8933093954028816,
                NaN,
                0.5,
                0.9993736659085295,
                0.9994472213322367,
                0.9994472214169734,
                0.9984988180275206,
                0.4378234991142019
            ],
            [
                1.6701427809710842e-05,
                6.14417606400666e-06,
                1.47389819549775e-05,
                1.3007134661628471e-05,
                6.962257907348116e-06,
                6.9622562489985925e-06,
                1.4738981962698681e-05,
                1.4738988998117324e-05,
                1.0129992185299915e-05,
                8.939693105467234e-06
            ],
            [
                0.9999756997651039,
                0.9998911030786903,
                0.9999339478634014,
                0.9999885212305113,
                0.9999810748450095,
                0.9997694931807676,
                0.9999687980998887,
                0.9997040427543952,
                0.9999832985761793,
                0.999948557768061
            ],
            [
                0.9999832985802247,
                0.9995121429435776,
                0.9995121429554134,
                0.9999417087209059,
                0.9999869928669113,
                0.9999938558224692,
                0.9999869928684382,
                0.9999930377437511,
                0.9998601779620052,
                0.9994472213172833
            ],
            [
                1.3007130009313495e-05,
                1.8925143725341476e-05,
                1.8925145979561802e-05,
                5.144219520863158e-05,
                4.539786836949404e-05,
                1.1478768122987964e-05,
                2.753570094040789e-05,
                5.829129325648758e-05,
                2.144494585197151e-05,
                4.539786860136322e-05
            ],
            [
                1.670142383015595e-05,
                7.889264465555602e-06,
                1.1478766751997141e-05,
                5.422218322763051e-06,
                1.4738985478678359e-05,
                4.7850927830845245e-06,
                8.939693104637921e-06,
                4.5397873950208886e-05,
                4.222835457449267e-06,
                1.0129994599624903e-05
            ],
            [
                0.0010322309038667092,
                4.539787939913551e-05,
                0.02033235423310517,
                0.00017952790114468135,
                0.29421498454004374,
                0.16451645470385745,
                0.320821300824607,
                9.610239162282471e-05,
                0.16451645880021024,
                0.0035936022679511474
            ],
            [
                0.9968273164712327,
                0.9988304897406561,
                0.9999151889590107,
                0.9992903296824254,
                0.9996200155209993,
                0.9992903296022203,
                0.9992903295058753,
                0.9998415638243041,
                0.9999599363173963,
                0.9997965729322378
            ],
            [
                7.889264466344872e-06,
                5.422218968714274e-06,
                1.3007133107008012e-05,
                6.9622562484666964e-06,
                1.1478764019328247e-05,
                8.939693106020111e-06,
                1.4738981966291175e-05,
                7.889261644358435e-06,
                1.6701419848961534e-05,
                1.147876538789672e-05
            ],
            [
                1.3007130009739366e-05,
                4.22283394786293e-06,
                2.4300231991521528e-05,
                8.939694172542558e-06,
                6.144173868983067e-06,
                5.422217029943586e-06,
                1.3007126906036072e-05,
                7.88926070328992e-06,
                1.0129992185299915e-05,
                3.726641060658489e-06
            ],
            [
                0.9986749776353174,
                0.9999724643089759,
                0.9999885212264112,
                0.9999756997681591,
                0.99951214287753,
                0.9995694428922717,
                0.9999785550490868,
                0.999891103130389,
                0.9998204720663698,
                0.999978555056715
            ],
            [
                6.962259568078904e-06,
                2.1444940732342966e-05,
                1.892515500450102e-05,
                3.535625069312567e-05,
                4.785096204537733e-06,
                6.962257078249291e-06,
                7.889263524615903e-06,
                2.753569764115831e-05,
                2.144494072867628e-05,
                2.430023781904283e-05
            ],
            [
                6.962256244819412e-06,
                4.0063706481032684e-05,
                1.1478766753082876e-05,
                2.4300234928664224e-05,
                3.5356246340085515e-05,
                1.8925150490206403e-05,
                1.3007133105966991e-05,
                1.0129994599901296e-05,
                2.1444950959977102e-05,
                1.892514146884943e-05
            ]
        ]
    },
    {
        "q_id": "8023_mmlu_math",
        "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": [
            [
                0.9999996072139402,
                0.9999996940977731,
                0.9999997617631752,
                0.9999998362622552,
                0.9999994956527121,
                0.9999995549149481,
                0.9999996940978825,
                0.9999996533672135,
                0.999999554914842,
                0.9999998144608317
            ],
            [
                0.9999991684717742,
                0.9999992661790195,
                0.9999993524050474,
                0.9999996940978825,
                0.9999996533674202,
                0.9999997300422869,
                0.999999168471675,
                0.9999992661786695,
                0.9999996072138934,
                0.999999352405279
            ],
            [
                0.9999997300420937,
                0.9999991684717742,
                0.9999991684717742,
                0.9999989322967482,
                0.9999993524051246,
                0.9999987901341724,
                0.9999977396762412,
                0.9999997300422547,
                0.9999992661791944,
                0.9999974387187054
            ],
            [
                0.9999996072137061,
                0.9999984465026158,
                0.9999997300421903,
                0.9999997300422868,
                0.9999996940976272,
                0.9999995549151072,
                0.9999997300421581,
                0.9999996072136593,
                0.9999992661791944,
                0.9999996533675028
            ],
            [
                0.9999992661788446,
                0.9999995549148419,
                0.9999997300422869,
                0.9999995549151073,
                0.9999994956526519,
                0.9999997300422547,
                0.9999996940977731,
                0.9999996533672549,
                0.9999993524050474,
                0.9999994284996211
            ],
            [
                0.9999992661788445,
                0.999999495652712,
                0.9999994284997574,
                0.9999995549150011,
                0.999998932296621,
                0.9999996072137998,
                0.9999997300422869,
                0.9999997617630048,
                0.9999996940976272,
                0.9999998144608097
            ],
            [
                0.9999996533673788,
                0.9999998362623528,
                0.9999994956524716,
                0.9999989322972572,
                0.9999995549151072,
                0.9999997897566589,
                0.9999996533674201,
                0.9999996940978825,
                0.9999992661786695,
                0.9999996072136592
            ],
            [
                0.9999996072139402,
                0.9999997300422869,
                0.9999994956526519,
                0.9999992661788445,
                0.999999352405279,
                0.9999996072137529,
                0.9999996072136125,
                0.9999990577551815,
                0.9999991684718733,
                0.9999990577555186
            ],
            [
                0.999999352404893,
                0.999999428499553,
                0.9999996940977366,
                0.999999554914842,
                0.9999994284996212,
                0.9999989322975118,
                0.9999996940978825,
                0.9999996072137061,
                0.9999994284996211,
                0.9999996940977366
            ],
            [
                0.9999989322972573,
                0.9999996940976272,
                0.999999694097773,
                0.9999996940977366,
                0.9999996072137061,
                0.9999995549150542,
                0.999999730042319,
                0.9999996940978825,
                0.9999995549147358,
                0.9999994956525918
            ],
            [
                0.9999991684718732,
                0.9999991684719723,
                0.9999990577555185,
                0.9999997617629764,
                0.9999993524049702,
                0.9999997300422869,
                0.9999996072139402,
                0.9999990577554062,
                0.9999996533673788,
                0.999999266178932
            ],
            [
                0.999999352405279,
                0.9999987901344607,
                0.9999989322970027,
                0.9999996072137998,
                0.999999495652712,
                0.9999996533674614,
                0.999999554914895,
                0.9999989322971299,
                0.9999995549151072,
                0.9999994956524114
            ],
            [
                0.9999996072137529,
                0.9999994284994167,
                0.9999994956524114,
                0.9999997897565838,
                0.9999982396574163,
                0.9999994956527121,
                0.9999996072139402,
                0.9999986290421395,
                0.999999814460876,
                0.9999994956525918
            ],
            [
                0.9999994284994849,
                0.9999992661791944,
                0.9999945777810311,
                0.9999996072138466,
                0.9999974387184002,
                0.9999993524052019,
                0.9999993524050474,
                0.9999990577551815,
                0.99999862904312,
                0.9999992661788446
            ],
            [
                0.9999997897566089,
                0.9999994956525318,
                0.999999554914895,
                0.9999990577557432,
                0.9999996533673788,
                0.9999996940978461,
                0.9999998362623137,
                0.9999991684719723,
                0.9999991684720715,
                0.9999996072138465
            ],
            [
                6.475948753930064e-07,
                5.715003107715166e-07,
                2.902311984952413e-06,
                8.315278294072958e-07,
                9.422445938964242e-07,
                1.5534981249496567e-06,
                1.5534983100920427e-06,
                1.3709572068422585e-06,
                1.3709572068354007e-06,
                1.7603434231097403e-06
            ],
            [
                0.9999984465015048,
                0.9999990577552939,
                0.999999789756634,
                0.9999990577550693,
                0.9999991684717742,
                0.999999694097773,
                0.9999991684722698,
                0.999999057755743,
                0.9999996533672962,
                0.9999994956525917
            ],
            [
                0.9999996072136593,
                0.9999996072137061,
                0.9999992661790195,
                0.9999994956526519,
                0.9999991684718732,
                0.9999994284993486,
                0.9999997897565587,
                0.9999996940978825,
                0.9999996533673375,
                0.9999990577550691
            ],
            [
                0.9999989322972573,
                0.9999997617631752,
                0.9999997300421581,
                0.999999428499553,
                0.9999996940978095,
                0.9999996533674614,
                0.9999997617631752,
                0.9999994284997574,
                0.999999554914895,
                0.9999996533672962
            ],
            [
                0.9999996533672135,
                0.999999428499553,
                0.9999993524050474,
                0.9999996940976636,
                0.9999996533674615,
                0.9999994956524716,
                0.9999982396559475,
                0.9999995549148419,
                0.9999995549150541,
                0.9999991684721706
            ],
            [
                1.0677033791495609e-06,
                4.7850933538313875e-06,
                1.209865827740176e-06,
                6.475946438022905e-07,
                0.9988304896140496,
                6.144177531599359e-06,
                9.422443692489024e-07,
                5.043474683220276e-07,
                3.9278610661822475e-07,
                7.338208930421943e-07
            ],
            [
                0.999998932296621,
                0.9999994956525318,
                0.9999990577551815,
                0.9999996072136592,
                0.999999168471675,
                0.9999993524052018,
                0.9999989322973846,
                0.9999992661790195,
                0.999999266178757,
                0.9999989322973846
            ],
            [
                0.9999993524051246,
                0.9999992661789321,
                0.9999994284996893,
                0.9999994284993486,
                0.9999994284992804,
                0.9999982396574164,
                0.9999989322973846,
                0.999999352405279,
                0.9999993524054334,
                0.999998790134028
            ],
            [
                0.9999998362623332,
                0.9999995549150011,
                0.9999995549148419,
                0.9999994284997573,
                0.9999992661790195,
                0.9999996533672136,
                0.9999997300420937,
                0.9999996940977366,
                0.9999987901343166,
                0.9999994956524114
            ],
            [
                0.9999996533674615,
                0.9999997897567091,
                0.9999996533672136,
                0.9999995549148419,
                0.9999996072138465,
                0.9999990577554062,
                0.9999996940978825,
                0.999999352405279,
                0.9999997300420937,
                0.9999996533672962
            ],
            [
                0.9999993524049703,
                0.9999990577551815,
                0.9999996940976272,
                0.9999996072139402,
                0.9999993524052019,
                0.9999991684715759,
                0.9999994956527722,
                0.9999996533673788,
                0.9999995549147358,
                0.9999994956527721
            ],
            [
                0.9999986290426297,
                0.999999554914895,
                0.9999996533672549,
                0.9999998362623723,
                0.9999993524051247,
                0.9999993524051247,
                0.9999991684721706,
                0.999999352404893,
                0.9999991684720715,
                0.999999814460876
            ],
            [
                0.999999428499553,
                0.9999986290432835,
                0.9999991684715759,
                0.9999970976866313,
                0.9999987901344607,
                0.9999970976887074,
                0.9999970976876693,
                0.9999998144608317,
                0.9999982396569966,
                0.9999982396565771
            ],
            [
                0.9999994956524716,
                0.999999352405279,
                0.9999995549150542,
                0.9999991684720715,
                0.9999994284994168,
                0.9999992661790195,
                0.9999987901347492,
                0.9999996533674201,
                0.9999996940977002,
                0.9999994956525317
            ],
            [
                1.4738985483504099e-05,
                2.260324567302214e-06,
                2.1444953521586782e-05,
                3.288748673295719e-06,
                1.012998856015592e-05,
                1.670142781520948e-05,
                3.535623802218407e-05,
                4.785092783371756e-06,
                3.288748673295719e-06,
                5.422217030614265e-06
            ],
            [
                0.9999994284992805,
                0.9999977396759718,
                0.9999996940976271,
                0.9999991684718733,
                0.9999996072138934,
                0.9999996072136592,
                0.9999992661786696,
                0.9999991684718733,
                0.9999992661790195,
                0.9999980052698031
            ],
            [
                0.9999984465022456,
                0.9999977396748939,
                0.9999995549149481,
                0.9999994956523514,
                0.9999996072138934,
                0.9999994284994167,
                0.9999994956524716,
                0.9999984465024306,
                0.9999996940976636,
                0.9999998555020307
            ],
            [
                0.9999994284994849,
                0.999999554914895,
                0.9999997897567091,
                0.9999998144609424,
                0.9999997300422869,
                0.9999994284996891,
                0.9999998362623528,
                0.9999998362623137,
                0.9999995549150011,
                0.9999995549147358
            ],
            [
                0.9999994284994848,
                0.9999987901341723,
                0.9999994284994167,
                0.9999977396748939,
                0.9999996940978825,
                0.99999893229713,
                0.9999994284995529,
                0.9999967112505429,
                0.9999994284996211,
                0.9999991684717742
            ],
            [
                0.9999994284994849,
                0.9999977396765107,
                0.9999991684718732,
                0.9999962733598284,
                0.999999495652652,
                0.9999992661792819,
                0.9999994284997574,
                0.9999987901337396,
                0.9999994284997573,
                0.9999990577556308
            ],
            [
                0.9999992661790195,
                0.9999993524049702,
                0.9999952149037948,
                0.9999998724808963,
                0.9999992661789321,
                0.9999996072138934,
                0.9999957771670592,
                0.9999990577552939,
                0.9999952149072177,
                0.9999986290421395
            ],
            [
                0.9999989322972574,
                0.999999266178757,
                0.9999996940978461,
                0.9999994956524114,
                0.9999996940977366,
                0.999999428499553,
                0.9999995549147359,
                0.9999997897566338,
                0.999999730042126,
                0.9999993524054335
            ],
            [
                0.9999996940976272,
                0.9999994284994167,
                0.9999994956525317,
                0.9999996072137998,
                0.9999993524054334,
                0.9999996533672962,
                0.9999993524051246,
                0.999999495652712,
                0.9999987901338838,
                0.9999996072136592
            ],
            [
                0.9999995549147359,
                0.999999730042319,
                0.9999990577554061,
                0.9999977396765106,
                0.999999814460854,
                0.9999991684720715,
                0.9999977396751634,
                0.9999989322968754,
                0.9999996940978825,
                0.999999266179107
            ],
            [
                0.999999554914895,
                0.9999991684715759,
                0.999999428499553,
                0.9999986290424664,
                0.9999996940976636,
                0.9999994956527121,
                0.9999996533673788,
                0.9999994284994849,
                0.9999996072136592,
                0.999999694097846
            ],
            [
                0.9999993524054334,
                0.9999996072138466,
                0.9999998724809723,
                0.9999993524051246,
                0.9999997300420937,
                0.9999996940976271,
                0.9999992661786695,
                0.9999998362623332,
                0.9999993524052019,
                0.9999996940976636
            ],
            [
                0.9999996940978825,
                0.9999984465026159,
                0.9999996072136125,
                0.9999995549150542,
                0.9999996072136125,
                0.9999996072137529,
                0.9999989322975118,
                0.9999996072137529,
                0.9999997300422869,
                0.9999993524054335
            ],
            [
                0.9999993524051246,
                0.9999994284994848,
                0.9999995549150542,
                0.9999994956524115,
                0.9999997897567342,
                0.9999991684722698,
                0.999999352405279,
                0.9999995549147889,
                0.9999993524049703,
                0.9999993524054334
            ],
            [
                0.9999997300422869,
                0.9999994284994848,
                0.9999996072136125,
                0.9999994284996211,
                0.9999994284994167,
                0.9999995549147889,
                0.9999995549147889,
                0.9999997300422225,
                0.9999997300423191,
                0.9999997300422225
            ],
            [
                0.9999994956525918,
                0.9999957771645424,
                0.9999996533672962,
                0.9999977396754328,
                0.9999993524053562,
                0.9999995549147358,
                0.999999554914895,
                0.9999921107374156,
                0.9999967112521111,
                0.9999989322968755
            ],
            [
                0.999999855501979,
                0.999999428499553,
                0.9999997897566089,
                0.9999997300421581,
                0.9999996072137529,
                0.9999996533672548,
                0.9999994956527721,
                0.999999266179107,
                0.999999730042319,
                0.9999996940976636
            ],
            [
                0.9999996533672548,
                0.9999996072137061,
                0.9999996533672135,
                0.99999976176309,
                0.9999996533673375,
                0.9999998362623722,
                0.9999997617631752,
                0.9999994956523514,
                0.999999789756684,
                0.9999998144609423
            ],
            [
                0.9999996072137529,
                0.99999976176309,
                0.9999995549150541,
                0.9999987901338838,
                0.999999495652652,
                0.9999996533673375,
                0.9999996072137998,
                0.99999976176309,
                0.9999992661789321,
                0.9999989322967482
            ],
            [
                0.999999057755743,
                0.9999996072138934,
                0.9999994284997574,
                0.999999266179282,
                0.9999997300422868,
                0.9999990577549569,
                0.9999995549151072,
                0.999999495652652,
                0.9999997617630332,
                0.9999994956525918
            ],
            [
                0.9999989322968754,
                0.9999930377404322,
                0.9999989322972572,
                0.9999980052702787,
                0.9999992661790195,
                0.9999977396759717,
                0.9999984465028012,
                0.9999996533673788,
                0.99999893229713,
                0.999999495652712
            ],
            [
                0.9999930377420916,
                0.9999995549149481,
                0.9999962733607163,
                0.9999991684721706,
                0.9999980052705164,
                0.9999984465026159,
                0.9999996533672962,
                0.9999921107402369,
                0.9999938558224707,
                0.999998790134028
            ],
            [
                0.999999789756634,
                0.9999997617631469,
                0.9999996533674615,
                0.9999993524054335,
                0.9999996940977366,
                0.9999995549147358,
                0.9999996940978825,
                0.9999996533673375,
                0.9999996940977001,
                0.999999352405279
            ],
            [
                0.9999993524052019,
                0.9999995549148419,
                0.9999996072138934,
                0.9999996940977366,
                0.9999994284996893,
                0.9999996940978461,
                0.9999995549148419,
                0.999999789756684,
                0.9999995549151073,
                0.9999998724809116
            ],
            [
                4.222833444467892e-06,
                6.962256247998122e-06,
                1.670142980380249e-05,
                3.726637950973972e-06,
                1.0129993394129904e-05,
                4.785094494185095e-06,
                5.422218969384951e-06,
                1.3007128458810347e-05,
                2.1444956069076118e-05,
                3.288750241374845e-06
            ],
            [
                0.9999996940978825,
                0.9999996533672136,
                0.9999997617631752,
                0.9999996533672962,
                0.9999993524051246,
                0.9999992661792819,
                0.9999996072137061,
                0.9999994284993486,
                0.9999994956524716,
                0.9999994284996211
            ],
            [
                0.9999994284994849,
                0.9999996940976636,
                0.9999997897566089,
                0.9999993524053562,
                0.9999997897566338,
                0.9999987901344607,
                0.9999986290426298,
                0.999998790134028,
                0.999999057755743,
                0.9999990577555185
            ],
            [
                0.9999996940976271,
                0.9999994284997574,
                0.9999996533674202,
                0.9999996533673788,
                0.9999992661790196,
                0.9999997617631183,
                0.9999996533674202,
                0.999999495652652,
                0.9999994956523514,
                0.9999995549149481
            ],
            [
                0.9999996533673788,
                0.9999996533674202,
                0.999999694097846,
                0.9999996533673375,
                0.9999996940976636,
                0.999999352405279,
                0.9999997300422869,
                0.9999996072139402,
                0.9999995549151073,
                0.9999994284996893
            ],
            [
                0.9999982396559474,
                0.9999990577552937,
                0.9999992661788446,
                0.9999995549147889,
                0.9999987901347491,
                0.9999994284996211,
                0.999999168471675,
                0.9999987901338838,
                0.9999997300422869,
                0.9999987901341723
            ],
            [
                0.9999995549149481,
                0.9999997617631468,
                0.9999994956524716,
                0.9999997300421903,
                0.9999987901344607,
                0.9999994956524715,
                0.999999653367379,
                0.9999987901343167,
                0.9999994284996212,
                0.9999994284992805
            ],
            [
                0.9999998144609644,
                0.9999996072137998,
                0.9999997897567342,
                0.9999998144608981,
                0.999999789756684,
                0.9999996533672549,
                0.9999997897567091,
                0.9999995549147889,
                0.9999996940977002,
                0.9999996533672549
            ],
            [
                0.9999998362622357,
                0.9999996072137998,
                0.9999997617631184,
                0.9999996533674615,
                0.9999993524052018,
                0.9999994956525318,
                0.9999997617629763,
                0.9999997300422225,
                0.9999996072138466,
                0.9999993524049703
            ],
            [
                0.9999993524052789,
                0.9999989322966208,
                0.9999993524051246,
                0.9999997300422547,
                0.9999994284993485,
                0.9999990577550691,
                0.9999987901338839,
                0.9999991684718733,
                0.9999995549149481,
                0.9999990577552939
            ],
            [
                0.9999996533674615,
                0.9999997300420937,
                0.9999996072137998,
                0.9999997617630333,
                0.9999996533674615,
                0.9999997617631184,
                0.9999995549148419,
                0.9999996533672962,
                0.9999996533672549,
                0.9999995549149481
            ],
            [
                0.9999996533672136,
                0.9999987901340281,
                0.9999994284993485,
                0.9999998144608981,
                0.9999998724809115,
                0.9999995549149481,
                0.9999994956526519,
                0.9999994956525918,
                0.9999991684719723,
                0.9999994956525317
            ],
            [
                0.999998790134605,
                0.9999992661788445,
                0.9999996940976636,
                0.999999057755743,
                0.9999994956524114,
                0.9999990577557432,
                0.9999992661789321,
                0.9999990577556308,
                0.9999996940976272,
                0.9999991684721706
            ],
            [
                0.9999993524053562,
                0.9999995549148419,
                0.9999987901344607,
                0.9999992661792819,
                0.9999930377420916,
                0.999999554914895,
                0.9999991684722698,
                0.9999996072137529,
                0.9999995549147359,
                0.9999974387180948
            ],
            [
                0.9999992661789321,
                0.9999991684719723,
                0.9999995549150542,
                0.9999994956527121,
                0.9999996072137998,
                0.9999997300422225,
                0.9999990577549569,
                0.9999995549149481,
                0.9999998144609423,
                0.9999994284994849
            ],
            [
                0.9999997617630332,
                0.9999994284994168,
                0.9999995549148419,
                0.9999996940977002,
                0.9999995549150011,
                0.9999993524054335,
                0.9999997300422225,
                0.9999994284992805,
                0.9999994956525918,
                0.9999996940978095
            ],
            [
                0.9999997300422868,
                0.9999994284996893,
                0.9999995549147358,
                0.9999996072139402,
                0.999999428499553,
                0.9999996072139402,
                0.9999995549151072,
                0.9999993524053562,
                0.9999996533672548,
                0.999999730042126
            ],
            [
                0.9999977396762412,
                0.9999984465026158,
                0.9999991684718732,
                0.9999993524054334,
                0.9999957771670593,
                0.9999994956523514,
                0.9999992661790195,
                0.9999994284996893,
                0.9999986290432835,
                0.9999990577552937
            ],
            [
                0.9999997300422547,
                0.9999987901347492,
                0.9999998362623332,
                0.9999994284992805,
                0.9999995549151073,
                0.9999977396751635,
                0.9999991684720715,
                0.9999996940976272,
                0.9999982396569966,
                0.9999982396569966
            ],
            [
                0.9999994956524115,
                0.9999997617630332,
                0.999999855501979,
                0.9999990577556308,
                0.99999976176309,
                0.999999789756684,
                0.9999997617630616,
                0.9999996940977731,
                0.999999789756684,
                0.9999997300422869
            ],
            [
                0.9999993524052018,
                0.9999996940976272,
                0.999999694097846,
                0.9999997617631752,
                0.999999694097846,
                0.9999996940977366,
                0.9999995549151073,
                0.9999996533673375,
                0.9999996072138934,
                0.9999996533674615
            ],
            [
                0.9999996533674202,
                0.9999995549149481,
                0.9999990577552939,
                0.9999990577555185,
                0.9999994284997574,
                0.9999989322968755,
                0.9999997300422869,
                0.9999993524052018,
                0.9999997300422869,
                0.9999995549148419
            ],
            [
                0.9999998362622747,
                0.9999984465022455,
                0.9999997300420937,
                0.9999986290429567,
                0.9999989322972573,
                0.9999990577555185,
                0.9999938558239352,
                0.9999987901341723,
                0.9999994956524114,
                0.9999990577555185
            ],
            [
                0.9999993524054335,
                0.9999996072136125,
                0.9999987901343166,
                0.9999987901347495,
                0.999999352405279,
                0.9999994956527721,
                0.9999990577555186,
                0.9999994956524115,
                0.9999997617631184,
                0.9999992661791944
            ],
            [
                0.9999996533674202,
                0.9999996533672962,
                0.9999996533672962,
                0.9999996072137529,
                0.9999998555019618,
                0.999999266179282,
                0.9999996533675028,
                0.9999996072138466,
                0.9999996072138934,
                0.9999996940977366
            ],
            [
                0.9999991684719725,
                0.999999814460876,
                0.9999992661792819,
                0.9999993524053562,
                0.9999996072136592,
                0.9999993524050474,
                0.9999996072139402,
                0.9999995549151073,
                0.9999993524050474,
                0.9999996940977731
            ],
            [
                0.9999996072139402,
                0.9999990577557432,
                0.9999995549150011,
                0.9999997300422225,
                0.9999996533672135,
                0.9999997617630616,
                0.9999996940978095,
                0.9999997617630616,
                0.9999997617630049,
                0.9999996072136125
            ],
            [
                0.9999995549151073,
                0.9999995549148419,
                0.9999996533673788,
                0.9999995549147359,
                0.9999994284992805,
                0.9999997300422225,
                0.9999994956524115,
                0.9999990577555185,
                0.999999730042126,
                0.9999997300422869
            ],
            [
                0.9999994956525317,
                0.9999991684719723,
                0.9999994956526519,
                0.9999994284993485,
                0.9999994956524115,
                0.9999997897565587,
                0.9999994284993485,
                0.9999990577554061,
                0.9999994284996211,
                0.9999994956524716
            ],
            [
                0.9999987901341723,
                0.9999994956526519,
                0.9999984465022456,
                0.9999977396757023,
                0.9999992661789321,
                0.9999994956523512,
                0.9999998144609423,
                0.9999996533673375,
                0.9999987901343166,
                0.9999992661788445
            ],
            [
                0.9999996072137998,
                0.9999998362622942,
                0.9999996072137998,
                0.9999993524053562,
                0.9999991684717742,
                0.999999789756634,
                0.9999996940977366,
                0.9999993524050473,
                0.9999997300421903,
                0.9999997300421581
            ],
            [
                0.9999995549148419,
                0.9999997300421581,
                0.9999994284995529,
                0.9999992661790196,
                0.9999991684715759,
                0.9999993524053563,
                0.9999984465015047,
                0.9999993524054334,
                0.9999982396561573,
                0.9999967112509348
            ],
            [
                0.999999730042126,
                0.9999996072137998,
                0.9999994956527722,
                0.9999992661786695,
                0.9999995549148419,
                0.9999996072139402,
                0.9999995549150011,
                0.9999996533675028,
                0.9999994956525918,
                0.9999997617630049
            ],
            [
                0.9999995549149481,
                0.9999996533672962,
                0.9999993524054335,
                0.9999996940976636,
                0.9999997617630616,
                0.9999996533673375,
                0.9999994284997574,
                0.9999994956525918,
                0.9999995549150011,
                0.9999997300422869
            ],
            [
                0.9999994284994848,
                0.9999986290429566,
                0.9999995549150011,
                0.9999996072137529,
                0.9999986290426297,
                0.9999984465022455,
                0.99999976176309,
                0.9999995549147358,
                0.9999998555019274,
                0.9999996072138465
            ],
            [
                0.9999995549147358,
                0.9999997300422225,
                0.9999992661789321,
                0.9999996533672548,
                0.9999996072137998,
                0.9999997617630333,
                0.999999789756634,
                0.9999990577554062,
                0.9999995549150011,
                0.9999997300422225
            ],
            [
                0.9999986290432835,
                0.9999996072136125,
                0.9999992661790195,
                0.9999970976869773,
                0.9999996072137061,
                0.9999994284992805,
                0.9999993524049702,
                0.9999996072137529,
                0.9999996940977366,
                0.999999266179107
            ],
            [
                0.999999730042319,
                0.999998932296621,
                0.9999987901343166,
                0.9999994956527721,
                0.9999994284997574,
                0.9999995549150542,
                0.9999996072138465,
                0.9999996072136125,
                0.999999057755743,
                0.9999994284995529
            ],
            [
                0.9999995549148419,
                0.9999991684715759,
                0.9999996940977366,
                0.9999992661792819,
                0.9999994284997573,
                0.9999996072136125,
                0.99999844650169,
                0.9999997300421903,
                0.9999991684720715,
                0.9999994956524114
            ],
            [
                0.9999991684719723,
                0.9999996940978461,
                0.9999996533673788,
                0.9999997897566338,
                0.9999994956524114,
                0.9999994284993485,
                0.9999996940977731,
                0.999999730042126,
                0.9999996940978095,
                0.9999996533674615
            ],
            [
                0.9999998362622552,
                0.9999987901346049,
                0.9999992661792819,
                0.9999996533672136,
                0.9999997300421903,
                0.9999995549151073,
                0.999999554914789,
                0.9999996533675028,
                0.9999990577551816,
                0.9999994284996891
            ],
            [
                0.9999994956525918,
                0.9999996940976636,
                0.9999992661786695,
                0.9999996940978095,
                0.9999992661789321,
                0.9999990577551815,
                0.999999653367379,
                0.9999993524050474,
                0.9999990577552939,
                0.9999998144609202
            ],
            [
                0.9999995549149481,
                0.9999990577549569,
                0.9999993524054335,
                0.9999995549147359,
                0.9999995549148419,
                0.9999996940977366,
                0.9999997300423191,
                0.999999653367503,
                0.999999057755743,
                0.9999991684717742
            ],
            [
                0.9999996072137529,
                0.9999989322966208,
                0.9999993524052018,
                0.9999982396569969,
                0.9999997300421581,
                0.9999994956524114,
                0.9999991684717741,
                0.9999980052707544,
                0.999999694097846,
                0.99999893229713
            ],
            [
                0.999999814460876,
                0.9999994956524715,
                0.9999986290421394,
                0.9999998362622943,
                0.9999996533672135,
                0.9999998144608097,
                0.9999993524049702,
                0.9999990577551814,
                0.9999989322972572,
                0.9999977396748938
            ],
            [
                0.999999495652712,
                0.9999997300421581,
                0.9999996533675028,
                0.9999996072137061,
                0.9999994284992805,
                0.9999997897565838,
                0.9999996072136592,
                0.9999990577552937,
                0.999999352404893,
                0.9999994284994167
            ],
            [
                0.9999998362623723,
                0.9999996072137529,
                0.9999997617631469,
                0.9999994284993486,
                0.999999554914842,
                0.9999992661792819,
                0.9999996940976272,
                0.9999996072139402,
                0.9999992661788446,
                0.9999994284997574
            ],
            [
                0.9999994284994849,
                0.9999997300420939,
                0.9999989322975119,
                0.9999994956523514,
                0.9999991684721706,
                0.9999990577552939,
                0.9999980052700409,
                0.9999991684719723,
                0.9999996072138465,
                0.9999994284993485
            ],
            [
                0.999999495652652,
                0.9999995549149481,
                0.9999994956527722,
                0.9999997617630332,
                0.9999996072138466,
                0.9999997300422869,
                0.9999994284994848,
                0.9999994956527722,
                0.9999996940976271,
                0.9999990577549569
            ],
            [
                0.9999995549150541,
                0.999999789756684,
                0.9999996940978825,
                0.9999993524051246,
                0.9999990577550691,
                0.999999352405279,
                0.999999352404893,
                0.999999554914842,
                0.9999990577550691,
                0.9999994956525918
            ],
            [
                0.9999997897566338,
                0.999999554914789,
                0.9999986290426298,
                0.9999996533673375,
                0.9999996940977731,
                0.9999995549149481,
                0.9999997617630332,
                0.9999997617630332,
                0.9999987901347492,
                0.9999994956527722
            ],
            [
                0.999999352404893,
                0.9999994284996212,
                0.9999994956525918,
                0.9999996533673375,
                0.9999996072137998,
                0.9999990577552937,
                0.999999266179107,
                0.9999994956525317,
                0.999999266178932,
                0.9999996072137529
            ],
            [
                0.9999996072136592,
                0.9999996072136125,
                0.9999995549147359,
                0.9999996533672962,
                0.9999991684718732,
                0.9999994284994167,
                0.999999730042126,
                0.9999996533672549,
                0.9999999006880668,
                0.9999994284994848
            ],
            [
                0.999999352405279,
                0.9999994956523514,
                0.999999352405279,
                0.9999980052705164,
                0.9999996533673375,
                0.9999994956526519,
                0.9999967112509351,
                0.9999994956527121,
                0.9999974387180952,
                0.9999982396572065
            ],
            [
                0.9999991684716749,
                0.9999997300421581,
                0.9999994284996211,
                0.9999994284997574,
                0.9999994956525918,
                0.9999998144609424,
                0.999999428499553,
                0.9999996533672963,
                0.9999989322972573,
                0.9999996533672963
            ],
            [
                0.9999997617631752,
                0.9999996533673375,
                0.9999993524052018,
                0.9999996533674201,
                0.999998932296621,
                0.9999986290423029,
                0.9999995549148419,
                0.9999993524054334,
                0.9999997300422869,
                0.9999994284994167
            ],
            [
                0.9999991684718733,
                0.999999554914895,
                0.9999992661791944,
                0.9999993524051247,
                0.9999994284994168,
                0.9999993524053563,
                0.9999996940978825,
                0.999999266179107,
                0.9999994284996211,
                0.9999996072137529
            ],
            [
                0.9999990577556307,
                0.9999995549151073,
                0.9999987901344607,
                0.9999996940977366,
                0.9999987901338839,
                0.9999998144608317,
                0.9999986290426297,
                0.9999996533674614,
                0.9999994284992805,
                0.9999996940976636
            ],
            [
                0.9999996533673376,
                0.9999997617630332,
                0.9999995549147358,
                0.9999996940978095,
                0.9999995549150011,
                0.9999994956526519,
                0.9999996940978461,
                0.9999997617629764,
                0.9999996940978095,
                0.9999998362623722
            ],
            [
                2.902310947190096e-06,
                3.927860597945825e-07,
                6.144176066795103e-06,
                5.043472879525233e-07,
                3.466325797888292e-07,
                1.3709567165386693e-06,
                1.370957860567974e-06,
                1.55349775456958e-06,
                6.475947209985977e-07,
                1.994729721482609e-06
            ],
            [
                0.9999997300422869,
                0.9999992661786696,
                0.9999997617631752,
                0.9999995549147359,
                0.9999995549148419,
                0.999999694097773,
                0.9999996940978825,
                0.9999994284996211,
                0.999998629042303,
                0.9999996072136125
            ],
            [
                0.9999996533672136,
                0.9999997897565838,
                0.9999990577550691,
                0.9999996072138934,
                0.9999998144609424,
                0.9999991684719723,
                0.999999168471675,
                0.9999993524054334,
                0.9999992661786696,
                0.9999993524051246
            ],
            [
                0.9999996072137529,
                0.9999993524052018,
                0.9999996072139402,
                0.9999995549147889,
                0.9999996940977731,
                0.9999993524053562,
                0.9999991684720716,
                0.9999996072137061,
                0.9999991684717742,
                0.9999996940978825
            ],
            [
                0.9999986290429567,
                0.9999994956527721,
                0.9999996072136592,
                0.9999996533674202,
                0.9999997300422869,
                0.9999996072138466,
                0.9999991684717742,
                0.9999996533673375,
                0.9999998362623528,
                0.999999694097773
            ],
            [
                0.9999994956523512,
                0.9999996940977002,
                0.9999996940977366,
                0.9999995549147359,
                0.9999996940976636,
                0.999999730042126,
                0.9999997897567091,
                0.9999993524052019,
                0.9999998874647709,
                0.9999987901337397
            ],
            [
                0.9999994284994848,
                0.9999996072138466,
                0.9999994956525918,
                0.9999992661786696,
                0.999999266178757,
                0.9999997617631468,
                0.9999998144609424,
                0.9999993524054334,
                0.9999994956525918,
                0.999999266179107
            ],
            [
                0.9999992661787571,
                0.9999995549147358,
                0.9999997617630616,
                0.9999994956523512,
                0.9999995549147889,
                0.9999994284994849,
                0.9999996533673375,
                0.9999990577550693,
                0.9999994284993486,
                0.9999991684721706
            ],
            [
                0.9999994956524715,
                0.9999990577552939,
                0.9999998874647574,
                0.9999994956524716,
                0.9999994284993485,
                0.9999995549151073,
                0.9999995549147889,
                0.9999993524053563,
                0.9999996533674615,
                0.9999996533672549
            ],
            [
                0.9999996940977366,
                0.99999893229713,
                0.9999992661786696,
                0.9999994284995529,
                0.999998790134605,
                0.9999997897566338,
                0.9999998555019962,
                0.9999994956527722,
                0.9999990577550691,
                0.999999554914895
            ],
            [
                0.9999997300422225,
                0.9999991684717742,
                0.9999994284996211,
                0.9999996072136593,
                0.9999994284996893,
                0.9999995549150011,
                0.999999266179282,
                0.9999989322973847,
                0.9999995549151073,
                0.9999987901346051
            ],
            [
                0.9999994284994848,
                0.9999996940978825,
                0.9999997300420937,
                0.9999994956524716,
                0.999999352405279,
                0.9999995549147358,
                0.9999992661788445,
                0.9999996072137998,
                0.9999996940978825,
                0.9999996072136125
            ],
            [
                0.9999989322968755,
                0.9999994284996893,
                0.9999989322972572,
                0.9999994284994848,
                0.9999989322970028,
                0.9999991684719725,
                0.9999994956523514,
                0.9999987901337396,
                0.9999997897566589,
                0.9999977396754333
            ],
            [
                0.9999992661790195,
                0.9999993524051246,
                0.9999992661790195,
                0.9999996533675028,
                0.9999998874649051,
                0.9999996533672135,
                0.9999991684720715,
                0.9999982396563671,
                0.9999994956526519,
                0.9999996533673375
            ],
            [
                0.9999995549150542,
                0.9999989322971301,
                0.9999993524053563,
                0.9999998362622552,
                0.9999996533672962,
                0.9999996940977366,
                0.9999994284997573,
                0.9999993524050474,
                0.9999994956524114,
                0.9999984465028012
            ],
            [
                0.9999994956527722,
                0.9999994284992805,
                0.9999986290421397,
                0.999999554914895,
                0.9999994956527721,
                0.9999990577550693,
                0.9999989322970028,
                0.9999991684715759,
                0.9999992661786695,
                0.999999266179282
            ]
        ]
    },
    {
        "q_id": "8567_mmlu_math",
        "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,
            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": [
            [
                9.422442568951678e-07,
                3.927863875459951e-07,
                1.5534983101393749e-06,
                1.9947299592570416e-06,
                1.0677029972993568e-06,
                1.9947299592824403e-06,
                3.059021904571643e-07,
                8.315278294001114e-07,
                2.260323758713745e-06,
                NaN
            ],
            [
                0.9998911030907593,
                0.0075772403994412004,
                0.9999810748472494,
                0.9999151889182126,
                0.01243164857783098,
                0.9996200154242477,
                0.0006263342272623171,
                0.00048785716694647787,
                0.004609571730687207,
                0.9999546021097292
            ],
            [
                0.9964063971251197,
                0.9997388097528578,
                0.0006263342477385715,
                0.00012339455994966783,
                0.9999810748427351,
                0.0015011824608999788,
                0.9990889487712671,
                0.999983298574177,
                0.9990889489929962,
                0.9980732653912966
            ],
            [
                7.338209805200689e-07,
                6.475948753991907e-07,
                9.422442569097361e-07,
                1.0129992185539456e-05,
                5.04347348075149e-07,
                1.2098662604192665e-06,
                5.715002426439334e-07,
                1.7603438427852151e-06,
                2.2603251061664e-06,
                7.338213304283347e-07
            ],
            [
                2.699578096393206e-07,
                1.0677032518501217e-06,
                4.450852641717689e-07,
                1.275190124842887e-07,
                5.043472879504592e-07,
                9.422445938917108e-07,
                1.0677033791107183e-06,
                3.2887498492936755e-06,
                1.0677031245429291e-06,
                1.2098652507957165e-06
            ],
            [
                7.338207180838067e-07,
                5.715005832827105e-07,
                1.2098656834922064e-06,
                3.927862002654366e-07,
                5.043472879504592e-07,
                8.315280276456036e-07,
                5.715003107655392e-07,
                3.4663262110189246e-07,
                1.553498495295912e-06,
                1.0677029972920738e-06
            ],
            [
                0.00037998448124475914,
                0.007577240784627306,
                0.047425872840974444,
                0.9989677691868861,
                0.9940889320823021,
                0.9940889303310794,
                0.04742587738497126,
                0.9986749775245566,
                0.0059110695156886104,
                0.9986749778859543
            ],
            [
                0.0066928516889333284,
                0.9999910603004999,
                0.03308597898458847,
                0.008577483758456102,
                0.014063627456479755,
                0.999704042831067,
                0.9995694428584153,
                0.002800926612699306,
                0.0031726834823769963,
                0.997817283534371
            ],
            [
                3.9278610661545617e-07,
                5.715004470272272e-07,
                5.715002426475718e-07,
                6.475947209953583e-07,
                6.475949525981759e-07,
                7.338207180864763e-07,
                8.315278294001114e-07,
                9.422444815679433e-07,
                8.31528325021115e-07,
                1.3709576970949014e-06
            ],
            [
                0.9999980052700408,
                0.9989677690645619,
                0.9999938558253986,
                0.9999952149037948,
                0.042087728366189174,
                0.9999977396759716,
                0.0015011823956376192,
                0.9999967112501509,
                0.9998766054252419,
                0.05340333017646162
            ],
            [
                5.144223194755629e-05,
                0.9902915235453877,
                0.0850990490675896,
                0.9999910603058294,
                0.0031726828365943563,
                0.9980732654289066,
                0.00048785709894040515,
                0.9999910603036963,
                0.9999724643023452,
                0.9999957771675627
            ],
            [
                0.0001584361782846178,
                0.9933071501685122,
                0.999860177975949,
                0.0004305570811242075,
                0.012431647971832022,
                0.9978172836504956,
                0.00020342697236675942,
                0.0004878570452394564,
                0.07585818211049715,
                0.000911051118265736
            ],
            [
                1.5534979397267575e-06,
                1.5534973841705173e-06,
                2.3823682478975334e-07,
                2.5612831266165976e-06,
                7.338213304243302e-07,
                5.422221555133606e-06,
                2.2603242978665707e-06,
                1.0677027427413698e-06,
                8.315280276580819e-07,
                1.0677027427340866e-06
            ],
            [
                9.931193325852072e-08,
                1.0677028700266676e-06,
                9.422444815495185e-07,
                2.2603242978007868e-06,
                3.92786340734912e-07,
                8.315281267581578e-07,
                8.31528424151477e-07,
                1.2751908849167202e-07,
                1.2098661161861e-06,
                1.7603432132784448e-06
            ],
            [
                0.9999417087275401,
                0.9999898700090272,
                0.9999599363030446,
                0.26894142722948733,
                0.9975273763558024,
                0.012431650887487653,
                0.999796573003438,
                0.9997388097216687,
                0.9999485577740842,
                0.9998911030649053
            ],
            [
                5.043475885606781e-07,
                1.3709576971160984e-06,
                1.7603425837366772e-06,
                5.715006514105942e-07,
                2.699578739999358e-07,
                1.2098656834834034e-06,
                6.47594720987407e-07,
                5.422217676654099e-06,
                6.47594566594213e-07,
                5.715006514105942e-07
            ],
            [
                0.9996646498906275,
                0.9997694933402955,
                0.000430556981521721,
                0.9998415637841339,
                0.008577484376207065,
                0.9991959142454031,
                0.999373665975387,
                0.9998204719698353,
                0.0017007227583170762,
                0.012431653608766854
            ],
            [
                1.0677024881941248e-06,
                1.7603425837366772e-06,
                2.902313023063532e-06,
                1.9947304348595095e-06,
                4.2228319339950885e-06,
                7.338207180801359e-07,
                1.209865683500459e-06,
                1.7603430034439723e-06,
                1.2098656835076114e-06,
                2.2603237589542675e-06
            ],
            [
                0.9999810748540198,
                0.9999485577863506,
                0.9992903294538638,
                0.001032231157518555,
                0.999664649850791,
                0.009708477976782488,
                0.9991959139601754,
                0.00020342699696737054,
                0.0003353501863431056,
                0.9999646437408781
            ],
            [
                0.999991060302632,
                0.9999957771660523,
                0.9996646500115032,
                0.9995121428825537,
                0.9991959140587587,
                6.60521445480501e-05,
                0.9999910602994336,
                0.9999852610233023,
                0.9999952149060758,
                0.0008040858348478069
            ],
            [
                0.9982992775010042,
                0.9978172837955245,
                0.0004878571715445516,
                0.989013057622406,
                0.001325022203085732,
                0.9996200155154941,
                0.00010889686955878851,
                0.9997040428317042,
                0.004609571380284056,
                0.000552778599395022
            ],
            [
                0.9986749773840642,
                0.9993736658208678,
                0.9890130559222517,
                0.009708476508335893,
                0.9998204720557494,
                0.9999646437535306,
                0.9990889489983472,
                0.9994472213894782,
                0.9999989322975118,
                0.9998601779758696
            ],
            [
                0.9997388096289302,
                0.9998415637647267,
                0.9997040428657001,
                0.0005527785391306276,
                0.9999852610180329,
                4.0063706471413514e-05,
                0.00048785717191353274,
                0.9998766054254141,
                0.9999485577925665,
                0.9997965729784852
            ],
            [
                8.31528424151477e-07,
                4.4508505193386385e-07,
                1.5534984953298217e-06,
                2.1024326584505647e-07,
                1.444980381819277e-07,
                8.315279285251204e-07,
                4.450849988780466e-07,
                3.927862002654366e-07,
                3.4663278639738526e-07,
                1.6373770576616226e-07
            ],
            [
                0.999997097687323,
                0.9998204720340175,
                0.9999921107374146,
                0.9996200154238939,
                0.9999339478711562,
                0.9999852610233015,
                0.9999910602994351,
                0.007577239496004776,
                0.9999038975393139,
                0.015906392265791817
            ],
            [
                0.999620015518302,
                0.999954602131396,
                0.9998204719696734,
                0.9997694932577313,
                0.005220125347767061,
                0.9940889318606629,
                0.999981074844992,
                0.9999982396574163,
                0.9999151889687629,
                0.999933947847516
            ],
            [
                0.9999982396565769,
                0.9993736659014247,
                0.999996273360272,
                0.0066928500915301396,
                0.9999938558253988,
                0.0021827164220188564,
                0.0006263342375733134,
                0.9999984465016899,
                0.9995694429631032,
                0.9999974387180947
            ],
            [
                1.0677028700320085e-06,
                1.0677027427525368e-06,
                NaN,
                1.553497384180408e-06,
                5.422217030209884e-06,
                5.422218968714274e-06,
                5.422218322940583e-06,
                1.9947301970287804e-06,
                5.422220908560712e-06,
                4.222834954607099e-06
            ],
            [
                0.0004305571226336006,
                0.9971990734972039,
                0.0059110686811215335,
                0.9991959139579774,
                0.998830489727737,
                0.0007096704400080176,
                0.9990889488764361,
                0.0006263342224165133,
                0.9988304898668545,
                0.0013250225866665466
            ],
            [
                2.2603242978213447e-06,
                3.4663253846473677e-07,
                6.475948753847607e-07,
                1.3709567165461505e-06,
                2.5612834318583854e-06,
                2.9023123311055552e-06,
                5.043474081957179e-07,
                1.2098662604247682e-06,
                1.3709567165386693e-06,
                6.475946437996402e-07
            ],
            [
                0.9998911030517746,
                0.9999546021422047,
                0.9999251537907204,
                0.9988304896215291,
                0.010986940475040835,
                0.9997965729787044,
                0.999933947855328,
                0.9991959140860235,
                0.9998601779429186,
                0.002800926612699306
            ],
            [
                0.9994472213920831,
                0.999996273358939,
                0.9998204720555091,
                0.9998415637642472,
                0.9999952149043652,
                0.0021827159483931062,
                0.9999945777790913,
                0.9999832985761732,
                0.9999646437577258,
                0.9978172830460394
            ],
            [
                0.46879062662624377,
                0.00048785717032407517,
                0.0009110511861354775,
                0.9990889489860555,
                0.9996646499306886,
                7.4846209355198e-05,
                6.605216819020694e-05,
                0.1329642436335826,
                0.9998911031297852,
                0.9992903297045509
            ],
            [
                9.61024148597335e-05,
                0.033085978150350394,
                0.00026119030826621373,
                0.0005527787423059172,
                0.008577485088996691,
                0.007577241428938652,
                0.9984988177099339,
                0.9933071505926289,
                0.9995694430171256,
                0.004609573166485764
            ],
            [
                2.2603234893594005e-06,
                9.422447062150634e-07,
                1.5534971989907999e-06,
                5.04347348075149e-07,
                3.927861066170637e-07,
                7.338208055489796e-07,
                1.6373764720990908e-07,
                3.4663262110803996e-07,
                4.450851049917114e-07,
                2.5612834318583854e-06
            ],
            [
                3.4663274507098256e-07,
                6.47594720987407e-07,
                6.47594720987407e-07,
                3.2887506332945414e-06,
                3.927863875584984e-07,
                1.0677028699742299e-06,
                2.699579061812927e-07,
                5.715007195431641e-07,
                7.338211554641698e-07,
                4.4508489275752546e-07
            ],
            [
                5.715007195410849e-07,
                3.4663249712133957e-07,
                4.7850950648799385e-06,
                2.9023112931688987e-06,
                1.76034363298589e-06,
                4.222833444467892e-06,
                1.0677028700130727e-06,
                7.338212429504183e-07,
                3.288750241473551e-06,
                2.5612816000145246e-06
            ],
            [
                0.9953904285107491,
                0.9820137924724606,
                0.003172682149576024,
                0.9988304895774684,
                0.9975273774044356,
                0.060086652067521305,
                0.9999599363030446,
                0.002800926608147101,
                0.004070138406754643,
                0.0001584362730899713
            ],
            [
                0.9991959139656471,
                0.9947798736946569,
                0.9994472213250333,
                0.5,
                0.0009110509812547046,
                0.9992903295448425,
                0.9986749773857587,
                0.9988304900006683,
                0.0008040857727421348,
                0.9994472213259659
            ],
            [
                8.315282259089153e-07,
                5.422219616140078e-06,
                2.260325375634003e-06,
                1.9947299592933255e-06,
                2.902312331125353e-06,
                1.2098656834613962e-06,
                5.422220262505697e-06,
                6.962257907702715e-06,
                1.4449795205429202e-07,
                1.2098656834922064e-06
            ],
            [
                1.209866116149238e-06,
                2.6995790618350237e-07,
                1.6373774480535133e-07,
                6.475950297768503e-07,
                8.315279285251204e-07,
                3.466327863945479e-07,
                5.715002426410745e-07,
                1.1253516205427619e-07,
                2.6995780963846126e-07,
                5.715004470272272e-07
            ],
            [
                5.043472879525233e-07,
                4.450851580497677e-07,
                1.5534984953298217e-06,
                9.422442569208767e-07,
                1.9947292458004866e-06,
                5.715005151574337e-07,
                2.260325375615501e-06,
                6.475945666009864e-07,
                5.715002426439334e-07,
                5.043472278280699e-07
            ],
            [
                0.9999785550567057,
                0.9999251537729549,
                0.9992903296214977,
                0.999996273359384,
                0.9999970976869772,
                0.9999251537817373,
                0.9999930377429216,
                0.9995121427682832,
                0.9997694932298903,
                0.9999151889182053
            ],
            [
                0.020332355160653563,
                0.9997965730266685,
                0.9998766054545571,
                0.9998601778765159,
                0.9990889489946385,
                0.9971990731083156,
                0.001169510118458642,
                0.9990889489995659,
                0.9971990727649492,
                0.9953904288056005
            ],
            [
                0.00522012596196987,
                0.9999485578047809,
                0.9999898700114378,
                0.999876605425161,
                0.999820472098231,
                0.002182716092407777,
                0.9996646497706592,
                0.9997040429363959,
                0.9999485577741123,
                0.00037998452845982005
            ],
            [
                5.144220744957233e-05,
                8.93969630362837e-06,
                8.481108167314633e-05,
                9.610241487022105e-05,
                0.0003799845302064789,
                0.0005527786692103984,
                0.00280092751598691,
                4.539786860697828e-05,
                1.0129992186202796e-05,
                1.8925145983348442e-05
            ],
            [
                5.422220262333096e-06,
                7.338211554688417e-07,
                2.5612831266608576e-06,
                2.902312331125353e-06,
                2.260323489435463e-06,
                2.2603240283888175e-06,
                6.962257909323729e-06,
                1.9947306726213275e-06,
                3.7266406167827664e-06,
                3.288747889229516e-06
            ],
            [
                0.9999251537459726,
                0.9998766053958977,
                0.9999724643154672,
                0.9999756997650643,
                0.16451645880021026,
                0.9998911030777682,
                0.9999687980923492,
                0.9999952149043653,
                0.0373268854700467,
                0.9994472213362243
            ],
            [
                1.3709570433885908e-06,
                5.7150044702099e-07,
                1.5534973841592143e-06,
                1.2098656834834034e-06,
                4.4508526417014975e-07,
                2.902313368860448e-06,
                1.2098655392574583e-06,
                1.5534973841705173e-06,
                1.99472924590571e-06,
                6.475951069932288e-07
            ],
            [
                0.9999151889688017,
                0.99995460211518,
                0.9999785550439259,
                0.9999921107345936,
                0.9995121428294205,
                0.9998766054692149,
                0.9998601778925734,
                0.9999646437577242,
                0.00015843625426351888,
                0.0019267346821324938
            ],
            [
                1.0677024881382882e-06,
                2.382368815916736e-07,
                5.715007195384861e-07,
                2.260323489435463e-06,
                2.2603248366762157e-06,
                7.338208055536515e-07,
                3.9278610661545617e-07,
                2.699578739984626e-07,
                3.059023727869902e-07,
                3.9278638755671223e-07
            ],
            [
                0.9995121428798573,
                0.9998601779260209,
                0.029312233295254998,
                0.0001398220564670591,
                0.999903897619401,
                0.99996879808864,
                0.9995121428245953,
                0.9999930377462409,
                0.0006263343037021457,
                0.9999724643187576
            ],
            [
                5.715003788933905e-07,
                3.9278634073312583e-07,
                9.422450431800595e-07,
                5.043473480643696e-07,
                1.067703379136937e-06,
                5.04347648686092e-07,
                5.715005832762133e-07,
                2.260323758923431e-06,
                4.450851049890802e-07,
                3.4663262110425684e-07
            ],
            [
                8.315280276399315e-07,
                2.902311984915459e-06,
                1.0677033791291683e-06,
                1.0129992184544441e-05,
                9.422450431912e-07,
                2.561281294616881e-06,
                1.7603432132464244e-06,
                1.3709573702566696e-06,
                7.338209805090567e-07,
                1.5534977545384963e-06
            ],
            [
                5.715003107738556e-07,
                1.5534975693601474e-06,
                1.0677024881941248e-06,
                1.0677029973056687e-06,
                2.2603240281935217e-06,
                3.9278638755456876e-07,
                1.9947306726049992e-06,
                1.2098652508144226e-06,
                4.4508526417014975e-07,
                4.450848927637999e-07
            ],
            [
                0.9999962733616047,
                0.006692851757039674,
                0.9999995549151073,
                0.9999980052693275,
                0.00591107024901322,
                0.9999785550592574,
                0.999373665972873,
                0.999988521230513,
                0.999998239656367,
                0.9999986290424663
            ],
            [
                0.00023050673939131153,
                0.00170072218650571,
                0.10669059536584677,
                0.0009110512001756666,
                0.9971990736890468,
                0.0019267349301796595,
                0.9980732656111363,
                0.009708474753363424,
                0.0002611904303242687,
                7.48462357636178e-05
            ],
            [
                0.037326884399142314,
                0.9998415637458471,
                0.9999251537816741,
                0.002800926562625055,
                0.0002305067137769642,
                0.0003799845711534717,
                0.0009110510317463932,
                0.001325022716221377,
                0.9999546021476133,
                0.006692851054306047
            ],
            [
                0.999820471970005,
                0.00048785710410614153,
                0.0007096705286339096,
                0.008577487116487505,
                0.9984988177717062,
                NaN,
                0.0002959572030926622,
                0.002800927483471153,
                0.9998766054105196,
                0.9984988180788231
            ],
            [
                0.06754668926255561,
                0.9998911030908227,
                0.00170072229402916,
                0.02033235248931431,
                0.0021827160249642858,
                0.0019267343320009892,
                0.002472623628692113,
                0.0003799844299504829,
                0.002472622946448689,
                0.0035936020787026234
            ],
            [
                0.00012339458927403105,
                0.0015011823631809389,
                0.9995694430125411,
                0.0003353500221280951,
                0.014063628967367705,
                0.0009110511967848284,
                0.00026119027481254345,
                0.0005527786018068841,
                0.0002034269229820478,
                0.004070137506373486
            ],
            [
                0.9999687980997854,
                0.9998766054546704,
                0.9999810748517685,
                0.9995121428887697,
                0.9999957771675629,
                0.999841563802036,
                0.9996200155619243,
                0.9999810748449955,
                0.9999938558268634,
                0.10669058755477132
            ],
            [
                0.05340332471521976,
                0.9998415638400048,
                0.9995121428301584,
                0.0007096703594315292,
                0.9999785550592586,
                0.9999832985741761,
                0.09534945847239201,
                0.9999151889283764,
                0.9988304899326734,
                0.9999785550413712
            ],
            [
                1.9947301970287804e-06,
                1.760344052693435e-06,
                1.994729008105057e-06,
                9.422450431860582e-07,
                1.0677032518700286e-06,
                7.33820893021171e-07,
                8.315283250260307e-07,
                2.5612825160271407e-06,
                1.3709578605617394e-06,
                2.2603237589028734e-06
            ],
            [
                1.3709567165461505e-06,
                1.0677027427166074e-06,
                2.2603253755949437e-06,
                3.466325384661554e-07,
                6.475949526003845e-07,
                1.209866116149238e-06,
                6.475945666033422e-07,
                1.7603425837062577e-06,
                1.209865250822125e-06,
                3.0590229985449037e-07
            ],
            [
                3.9278634073312583e-07,
                9.422450431800595e-07,
                6.475950297942253e-07,
                7.338212429420757e-07,
                3.9278634073098236e-07,
                5.715003788933905e-07,
                8.764240137829087e-08,
                7.338211554398095e-07,
                1.3709572067955008e-06,
                1.0677027427471959e-06
            ],
            [
                0.006692851834433249,
                0.999903897608017,
                0.009708477735026021,
                0.008577484890999567,
                0.002800926867622776,
                0.025957358328060655,
                0.0003353500256990463,
                0.0004878570432526349,
                0.0009110511793538013,
                0.0004305571321028532
            ],
            [
                3.7266397283231055e-06,
                1.76034300345598e-06,
                1.3709575337016483e-06,
                6.47594566597747e-07,
                3.0590229985296015e-07,
                9.422450431732037e-07,
                8.315279285149107e-07,
                1.275189972820578e-07,
                3.2887490652810324e-06,
                2.3823685319076597e-07
            ],
            [
                5.043472278255469e-07,
                2.260325375615501e-06,
                1.6373770576683237e-07,
                6.962257079275089e-06,
                1.5534973841895917e-06,
                1.3709570433885908e-06,
                1.7603436329714805e-06,
                3.288750633488963e-06,
                1.2098661161927025e-06,
                1.5534983101301911e-06
            ],
            [
                0.9997040427958052,
                0.1824255304737224,
                0.9999038976081016,
                0.9978172832564836,
                0.9999952149066464,
                0.9999885212332446,
                0.9999251537906317,
                0.999915188978871,
                0.9999910602994343,
                0.9999687980774743
            ],
            [
                0.01798621101487092,
                0.9999546021097243,
                0.9999938558239334,
                0.00970847506675134,
                0.9999417087206002,
                0.9997388097536861,
                0.07585817740967664,
                0.9999417087344652,
                0.9959298624124601,
                0.9999038975623424
            ],
            [
                0.9980732649063958,
                0.9995121427643663,
                0.001700722243627542,
                5.8291258453558646e-05,
                0.9988304897471836,
                0.005911068002522816,
                0.00017952800846419514,
                0.0004878571030559644,
                0.16451646289656316,
                0.0002034270441797163
            ],
            [
                0.9997388096595644,
                0.999796573075402,
                0.9999724643121931,
                0.9999646437577242,
                0.9992903297052939,
                0.9997388095659975,
                0.0011695105128287496,
                0.9996646497710006,
                0.9999885212264026,
                0.9999417087066808
            ],
            [
                0.9999945777810304,
                0.9996200154241814,
                0.999998446502801,
                0.999997097686631,
                0.9999957771675625,
                0.0013250225322874124,
                0.9999967112513268,
                0.9999974387177893,
                0.9999546021367759,
                0.9991959142444211
            ],
            [
                3.0590237278838124e-07,
                3.927862470861484e-07,
                4.450851580540182e-07,
                5.715003788993679e-07,
                7.338210679949506e-07,
                6.475949525981759e-07,
                4.450851580540182e-07,
                5.715003107689177e-07,
                5.71500719517695e-07,
                3.466326624322211e-07
            ],
            [
                2.26032402841657e-06,
                6.1441753337365085e-06,
                6.962256249429175e-06,
                8.315278294001114e-07,
                1.370956879949281e-06,
                3.7266379512857925e-06,
                8.315280276580819e-07,
                2.382370235922541e-07,
                7.88926258532661e-06,
                2.430023492663099e-05
            ],
            [
                3.7266397282926013e-06,
                6.962255419380732e-06,
                2.902311984989368e-06,
                1.473898372822193e-05,
                1.994729483608425e-06,
                6.475950297868629e-07,
                1.553498495295912e-06,
                2.9023130227599746e-06,
                5.422218323349895e-06,
                5.422219615967477e-06
            ],
            [
                2.382368815916736e-07,
                0.9997388096284439,
                1.855391681883394e-07,
                1.012998977108606e-05,
                0.004609571348234988,
                7.338209805170655e-07,
                1.553498495230919e-06,
                1.5534975693347152e-06,
                0.9993736658241105,
                8.315280276580819e-07
            ],
            [
                9.422447061782138e-07,
                3.4663266242969896e-07,
                2.9023112932045342e-06,
                2.5612816000145246e-06,
                1.2098658277335738e-06,
                1.7603432132079998e-06,
                3.726639728348526e-06,
                1.2098655392871682e-06,
                1.7603425837702984e-06,
                3.4663249714325014e-07
            ],
            [
                0.01798621062007865,
                0.9999852610127589,
                0.025957359929267797,
                0.9998601778762229,
                0.006692850942859311,
                0.999860177909463,
                0.014063629716354952,
                0.9999599362982811,
                0.012431650029941812,
                0.9999546021097102
            ],
            [
                1.7603432132784448e-06,
                2.260324028372372e-06,
                1.0129989771657269e-05,
                1.370956716529941e-06,
                2.2603245672867952e-06,
                2.902312331081799e-06,
                3.2887498494282754e-06,
                8.31527730252048e-07,
                1.067702615468225e-06,
                4.785092783267308e-06
            ],
            [
                2.561282515988704e-06,
                1.9947301969471416e-06,
                1.1478772222347966e-05,
                7.338207180761315e-07,
                1.5534981249291695e-06,
                9.422449308716635e-07,
                1.9947294836483373e-06,
                5.04347348075149e-07,
                4.22283344433731e-06,
                4.4508505193386385e-07
            ],
            [
                1.0129994601872894e-05,
                1.7603427936079236e-06,
                4.006368262111344e-05,
                1.1478769494083349e-05,
                2.9023123311055552e-06,
                3.7266401725935817e-06,
                1.0677029973158649e-06,
                1.3709578605542582e-06,
                2.260324567302214e-06,
                6.96225956837018e-06
            ],
            [
                0.9999599363125974,
                0.0021827162977808286,
                0.9999599363030484,
                0.999891103103726,
                0.999738809691521,
                9.610241478352397e-05,
                0.9999251537905773,
                0.00012339455978987673,
                0.9999151889891205,
                0.9999599363221565
            ],
            [
                1.9947292458930106e-06,
                5.043474081957179e-07,
                6.475945666033422e-07,
                2.1024339115914997e-07,
                7.889264465239894e-06,
                1.7603438428460541e-06,
                3.2887502414436403e-06,
                5.043472278280699e-07,
                1.067702488159652e-06,
                3.9278615343901467e-07
            ],
            [
                8.315280276505193e-07,
                9.422447061953531e-07,
                1.0677027427471959e-06,
                5.043476486915964e-07,
                1.0677031245851707e-06,
                3.0590237278838124e-07,
                1.760342793583908e-06,
                3.9278634073098236e-07,
                2.699576809121209e-07,
                3.4663266242969896e-07
            ],
            [
                0.9995121428985335,
                0.9986749775348778,
                0.9997388095659975,
                0.9989677689476395,
                0.999373665824912,
                0.9984988178741366,
                0.0075772401123024805,
                0.9996200154708106,
                0.9999599363221504,
                0.00023050671371660047
            ],
            [
                0.9997694933131117,
                0.9996646499320739,
                0.9998415637076294,
                0.9997694931749592,
                0.22270014914315833,
                0.9995694428586032,
                0.0015011819440361278,
                0.9999151889687783,
                0.0035936021395622806,
                0.9998415638209408
            ],
            [
                0.999996273358939,
                0.9999151889182596,
                0.06008664407268613,
                0.9999974387171787,
                0.9999970976890528,
                9.610240321366119e-05,
                0.0005527786099107413,
                0.9999251537638204,
                0.9999992661788446,
                0.9998911031045918
            ],
            [
                0.9988304898801814,
                0.9998415638020107,
                0.9998601779427253,
                0.0010322310294321678,
                0.9999546021475986,
                0.9998204720127897,
                0.9999417087066884,
                0.9999785550592568,
                0.9984988180711453,
                0.40733340004593027
            ],
            [
                0.9986749774575454,
                0.00029595702780843905,
                0.9997388097848751,
                0.004070138476595538,
                0.999704042865614,
                0.0024726231853487222,
                0.9999251537906851,
                0.9994472213900893,
                0.9999038975966157,
                0.9999546021476057
            ],
            [
                1.2751908849167202e-07,
                1.3709570434054234e-06,
                1.637376276909393e-07,
                2.699576809121209e-07,
                4.450849988798682e-07,
                1.7603432133136672e-06,
                4.450849988798682e-07,
                7.338212429420757e-07,
                5.043472879504592e-07,
                5.715007195384861e-07
            ],
            [
                0.998674977570925,
                0.999664650010469,
                0.9997965730025117,
                0.04208773061904093,
                0.9999251537638378,
                0.9991959140533339,
                0.9995694429126631,
                0.9999151889485854,
                0.999796572930536,
                0.9996646498915447
            ],
            [
                0.9999687980923468,
                0.9994472214729608,
                0.9999687980997854,
                0.010986945059385056,
                0.9999546021205543,
                0.0021827162435217734,
                0.0004305570161922016,
                0.9999898700126439,
                0.0017007220534849805,
                0.020332352044091135
            ],
            [
                0.9998601779425421,
                0.9999945777797379,
                0.9999151889687703,
                0.9999785550439201,
                0.9999485577924884,
                0.9994472214536338,
                0.05340332829327471,
                0.0009110512786417841,
                0.9999810748472546,
                0.9991959140464125
            ],
            [
                3.726638395527247e-06,
                1.9947297214544894e-06,
                1.7603425837366772e-06,
                3.726640172503764e-06,
                1.0677031245429291e-06,
                2.260325375615501e-06,
                0.9999485577741333,
                2.561283431888668e-06,
                4.222833947820683e-06,
                1.5534971989992774e-06
            ],
            [
                0.9992903294570835,
                0.9999724643154813,
                0.9992903294538638,
                0.9999546021367883,
                0.9995121428826957,
                0.9999869928746379,
                0.002800926885181281,
                0.9997965730761567,
                0.9999977396759716,
                0.9998911030648022
            ],
            [
                0.9998766053957163,
                0.9999151889890853,
                0.9999885212332469,
                0.9997965730752333,
                0.9999485577924795,
                0.998674977856685,
                0.9997694931751738,
                0.9999930377437511,
                0.0005527787395403144,
                0.9997965730265855
            ],
            [
                0.9997694933675934,
                0.001169510359432361,
                0.0007096704418242909,
                0.9984988179212513,
                0.0010322312770818698,
                0.9999810748562764,
                0.9975273773447106,
                0.9999546021368217,
                0.00033535002532829176,
                0.999796572929876
            ],
            [
                6.475945666009864e-07,
                1.3709578605455302e-06,
                3.059023363221292e-07,
                7.338212429537553e-07,
                4.450849458218309e-07,
                5.043475885657239e-07,
                4.450848927637999e-07,
                5.043476486902204e-07,
                5.715005832872586e-07,
                1.760344052693435e-06
            ],
            [
                7.338208055579897e-07,
                7.338207180714596e-07,
                7.8892607025437e-06,
                8.31527730252048e-07,
                1.2098662603961589e-06,
                1.3709576971242028e-06,
                2.561282210530385e-06,
                3.2887498491620677e-06,
                4.450851580497677e-07,
                9.422442568951678e-07
            ],
            [
                2.2603251060738913e-06,
                1.209865971934245e-06,
                9.422447062030659e-07,
                4.222834451254188e-06,
                1.3709568799243436e-06,
                5.422220908314139e-06,
                5.043474683156057e-07,
                1.0677028700203557e-06,
                4.4508499887035535e-07,
                1.5534983101061718e-06
            ],
            [
                2.9023123311055552e-06,
                2.260325375520937e-06,
                1.7603436329554703e-06,
                2.5612828213818346e-06,
                2.902312331081799e-06,
                1.7603432132784448e-06,
                5.043472278312808e-07,
                1.067703251864202e-06,
                3.7266401725681614e-06,
                2.3823685319174098e-07
            ],
            [
                9.610238034242095e-05,
                1.1478764017428212e-05,
                4.539788473741292e-05,
                0.0035936032200297747,
                0.0035936030808028496,
                0.006692849580732689,
                0.0017007221384759358,
                0.00010889688314099864,
                0.0002611902708379255,
                0.0005527785399345815
            ],
            [
                1.994729483666479e-06,
                2.260324567302214e-06,
                1.3007130013572209e-05,
                7.338211554758494e-07,
                1.5534975693707442e-06,
                0.9978172837863968,
                1.5534971989992774e-06,
                0.9997694931757305,
                0.998498817601047,
                9.422445939002803e-07
            ],
            [
                0.9968273178231789,
                7.88926164299515e-06,
                0.0015011824322822595,
                6.605216825123819e-05,
                0.0004878572231451593,
                0.0007096703635594228,
                0.9986749776898506,
                0.9740426402591096,
                0.002800927036704682,
                0.9984988177209272
            ],
            [
                0.9999687980737616,
                0.9999832985741774,
                0.9999832985741766,
                0.002182716624856468,
                0.999796573050908,
                0.9999921107345933,
                0.9999898700126446,
                0.0021827162551849347,
                0.9999910603058282,
                0.9999952149032237
            ],
            [
                0.9999938558268638,
                0.0009110510756153549,
                0.9999910603047628,
                0.9997040430068247,
                0.014063627572701902,
                0.9999952149072175,
                0.9995694428596054,
                0.999620015514278,
                0.9997040427945652,
                0.9994472212581443
            ],
            [
                4.4508505193123265e-07,
                1.3709576970949014e-06,
                5.715005832827105e-07,
                1.0677028700130727e-06,
                3.288750241500471e-06,
                1.7603440527046419e-06,
                2.260323758835034e-06,
                2.2603234893861252e-06,
                8.315280276546789e-07,
                7.338210679816025e-07
            ],
            [
                0.9997040428317042,
                0.0008040859974543222,
                0.010986942822872518,
                0.005911068878134079,
                0.9995121428304139,
                0.9999930377437515,
                0.9997388097538306,
                0.999993037746241,
                0.9995121428832917,
                0.9998204719701069
            ],
            [
                4.4508505193791187e-07,
                2.902311639073834e-06,
                5.715005151485975e-07,
                1.9947301968673173e-06,
                5.715005832853093e-07,
                3.288748673295719e-06,
                9.422443692446175e-07,
                1.2098661161861e-06,
                8.315281267800897e-07,
                3.288750633139005e-06
            ],
            [
                3.059021175247079e-07,
                5.043474683009273e-07,
                9.422443691996268e-07,
                1.6373774480404828e-07,
                1.7603434231241496e-06,
                1.9947290080905435e-06,
                9.42244818532859e-07,
                0.9579122687801985,
                1.0677031245851707e-06,
                8.315282259051341e-07
            ],
            [
                0.9997040428664148,
                0.9988304897632303,
                0.9999885212318742,
                0.9998601779092757,
                0.9997388097531315,
                0.10669059252545562,
                0.9990889487856253,
                0.9988304895310959,
                0.007577242297358379,
                0.9999852610215422
            ],
            [
                0.9998601778592663,
                0.012431652888428185,
                0.9999756997534923,
                0.012431650830317928,
                0.9999417087414205,
                0.9997965729783551,
                0.9998415637456558,
                0.9999885212359839,
                0.9999339478317334,
                0.004070138367115217
            ],
            [
                5.8291258539226846e-05,
                0.0002611902138101439,
                0.9947798731481613,
                4.5397879426550244e-05,
                1.3709572068179446e-06,
                0.0007096704488004321,
                3.12019262340518e-05,
                0.01590639241157527,
                0.00669284936093501,
                0.00970847709034214
            ],
            [
                0.9995121428239993,
                0.9999646437450735,
                0.9999339478474506,
                0.008577487282805133,
                0.999664649970408,
                0.9999038975736865,
                0.9999724643121848,
                0.9999756997534786,
                0.9994472213914721,
                0.9968273175566187
            ],
            [
                0.0004878572277999999,
                1.855391681883394e-07,
                6.023569884692295e-08,
                0.9947798744442745,
                1.3709578605542582e-06,
                3.4663249714325014e-07,
                3.9278634073312583e-07,
                9.422444815679433e-07,
                8.315279284937352e-07,
                1.3709576970949014e-06
            ],
            [
                0.9953904280171935,
                0.0009110513743270114,
                5.8291293265817787e-05,
                0.9997694932298365,
                0.0024726228442270475,
                0.0010322310907743815,
                0.9989677691711605,
                0.987568349787115,
                NaN,
                0.9991959139519445
            ],
            [
                0.9999756997679721,
                0.9989677690609606,
                0.9999898700114384,
                0.01406362591976483,
                0.010986944664706339,
                0.006692851233859125,
                0.13296425050508956,
                0.9999646437492865,
                0.9982992772976188,
                0.06754669583231303
            ],
            [
                1.994729483694599e-06,
                2.5612822106841303e-06,
                5.715002426343175e-07,
                1.994729245878497e-06,
                8.939699500896292e-06,
                7.338210679949506e-07,
                2.5612831266608576e-06,
                1.5534975693869924e-06,
                3.726640616748873e-06,
                1.760344052714248e-06
            ],
            [
                2.26032537546132e-06,
                2.5612825160096693e-06,
                8.315280276546789e-07,
                1.3709570434054234e-06,
                1.760342793515064e-06,
                1.0677033791291683e-06,
                8.315282258900085e-07,
                2.260323758923431e-06,
                2.2603251062147097e-06,
                1.3709567165386693e-06
            ],
            [
                9.422448185015797e-07,
                5.043472879481655e-07,
                2.3823685318968256e-07,
                3.9278610661545617e-07,
                2.1024336609724313e-07,
                1.855391681891831e-07,
                7.338207180761315e-07,
                1.6373774480404828e-07,
                2.3823690999160957e-07,
                1.209865394997419e-06
            ],
            [
                0.012431651001827105,
                0.05340332753999997,
                0.9999756997592703,
                0.9999910603047621,
                0.003593601864443294,
                0.06008664512463807,
                0.9999417087206043,
                0.9999599363078162,
                0.0009110512751449818,
                0.002472623259430708
            ],
            [
                1.0677029972745947e-06,
                1.994729008074216e-06,
                4.4508505193791187e-07,
                8.315277302588544e-07,
                2.2603251061458426e-06,
                7.338211554725124e-07,
                4.785095634843714e-06,
                5.7150044702099e-07,
                2.260323489435463e-06,
                3.2887490652451393e-06
            ],
            [
                0.999512142829165,
                0.999664649850108,
                0.9996200154274757,
                0.9998204719913294,
                0.9999339478711289,
                0.9999599362887106,
                0.999933947863251,
                0.025957358987381236,
                0.9993736659031736,
                0.999876605410331
            ],
            [
                0.9999724643187647,
                0.9999251537907886,
                0.9999687980886276,
                0.9999982396572065,
                0.9984988176043623,
                0.9999756997505828,
                0.9995121429397175,
                0.9999962733611605,
                0.9999945777790913,
                0.9953904286282623
            ]
        ]
    },
    {
        "q_id": "8359_mmlu_math",
        "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": [
            [
                0.9999599363030898,
                0.9998415637091554,
                0.9996646499323082,
                0.9998204719507311,
                0.9999687980774912,
                0.9999151889386722,
                0.9999687980886445,
                0.999925153755067,
                0.999860177943238,
                0.9998766054408529
            ],
            [
                0.9999687980998114,
                0.9999417087554018,
                0.9999546021368043,
                0.9999417087137005,
                0.9998766053818595,
                0.9997694931764818,
                0.9998415638024049,
                0.9999910603015658,
                0.9995694429663222,
                0.9999151889692632
            ],
            [
                0.9993736659819088,
                0.9999599363221695,
                0.9999546021368043,
                0.9997040429736727,
                0.999915188948652,
                0.9996646499743009,
                0.999876605440246,
                0.9999151889183892,
                0.9997694932867596,
                0.9999038975852501
            ],
            [
                0.9999038975509124,
                0.9999339478553727,
                0.9998204720565147,
                0.9997040428332111,
                0.9998204719919982,
                0.9999756997534849,
                0.9997965730034855,
                0.9998766053965853,
                0.9999599363221864,
                0.9997040429427336
            ],
            [
                0.9999417087414922,
                0.9999646437493162,
                0.9999832985701949,
                0.9999546021368043,
                0.9999756997679721,
                0.9999687980923623,
                0.9999724643121931,
                0.9998766054257517,
                0.9999599363173919,
                0.9999546021422182
            ],
            [
                0.9998415637274033,
                0.9999339478712945,
                0.9994472213985147,
                0.9999339478554337,
                0.9999485578047809,
                0.9999852610162783,
                0.9999251537639728,
                0.9999251537462421,
                0.9997694932586367,
                0.9999599363030772
            ],
            [
                0.9999687980849687,
                0.9998911030650874,
                0.9996200154317428,
                0.999941708734578,
                0.9999417087485492,
                0.9999785550413738,
                0.9998415637268824,
                0.999948557792583,
                0.9999038975510327,
                0.9971990727512926
            ],
            [
                0.9998415638405372,
                0.9993736659816902,
                0.9997388097583524,
                0.999704042973578,
                0.9997965730766273,
                0.9992903295532635,
                0.9980732653062263,
                0.9997694933699542,
                0.9997694932063417,
                0.9997965730282903
            ],
            [
                0.999903897562685,
                0.9998415637457918,
                0.9999038976196939,
                0.9999724643155093,
                0.9995694428690245,
                0.9999724642958001,
                0.9999151889387943,
                0.9998911031168874,
                0.999820472013615,
                0.9994472213293746
            ],
            [
                0.9999251537461773,
                0.9999151889688683,
                0.999933947871162,
                0.9999599363030722,
                0.9999646437577323,
                0.9999898700078157,
                0.9999952149072171,
                0.9999756997621821,
                0.9999251537639298,
                0.9999646437493069
            ],
            [
                0.9998415638216555,
                0.9997388097856731,
                0.9999151889688949,
                0.9984988180071043,
                0.9999038975738438,
                0.9997965729794797,
                0.9991959138773989,
                0.9997388096327985,
                0.9999417087136822,
                0.9998601779428737
            ],
            [
                0.999964643761987,
                0.999860177859604,
                0.9999599363078577,
                0.9999785550541617,
                0.999933947831781,
                0.9999724643154864,
                0.999986992869992,
                0.9999687980961044,
                0.9999485577680401,
                0.9999810748540267
            ],
            [
                0.9996200154278516,
                0.9999687980812239,
                0.9998911030519949,
                0.9999898700090217,
                0.9999852610110069,
                0.9999251537372724,
                0.9999869928730917,
                0.9999038975966262,
                0.9999785550567123,
                0.9999546021259963
            ],
            [
                0.9999599362887435,
                0.999933947839654,
                0.9998766053664693,
                0.9997965729548229,
                0.9999417087067342,
                0.9992903297145403,
                0.999991060300501,
                0.9999646437450979,
                0.9997965730296695,
                0.9999151889891026
            ],
            [
                0.9999852610110069,
                0.9999646437325065,
                0.9999646437450943,
                0.9999038975395914,
                0.9999339478634082,
                0.9999724642990605,
                0.9999687980923747,
                0.9999885212332466,
                0.9999810748517677,
                0.999981074856284
            ],
            [
                0.9999151889487513,
                0.999941708741521,
                0.9999546021368281,
                0.9997694932051076,
                0.9996646499336252,
                0.9999810748562783,
                0.9997965730278168,
                0.9999151889893241,
                0.9998766053667367,
                0.999841563764616
            ],
            [
                0.9999417087553356,
                0.999925153746088,
                0.9999485577802407,
                0.9999038976197429,
                0.9998766053963412,
                0.9999417087414875,
                0.9995694429158196,
                0.9998415637834425,
                0.9999151889183805,
                0.9990889490049171
            ],
            [
                0.9999485577864644,
                0.9999599362983168,
                0.999972464318766,
                0.9999687980849237,
                0.9999251537552591,
                0.9999832985741806,
                0.9999599363126515,
                0.9999646437450908,
                0.9998601778929518,
                0.9994472213375428
            ],
            [
                0.999891103078169,
                0.9999756997563815,
                0.9999485577802911,
                0.9999151889588132,
                0.9999724643089085,
                0.9999599362887661,
                0.999933947847691,
                0.999985261023302,
                0.99994855779869,
                0.999985261023302
            ],
            [
                0.99719907355118,
                0.9998911031170444,
                0.9984988176301882,
                0.9991959139653197,
                0.9997388097863419,
                0.9998601778762229,
                0.9997040427617402,
                0.9998415638028936,
                0.9998911030909717,
                0.9993736659773544
            ],
            [
                0.9999599363030588,
                0.9999339478239488,
                0.9999546021205913,
                0.9998766054253961,
                0.9999646437366568,
                0.9999646437535196,
                0.9997965730763432,
                0.9998601779597389,
                0.9999599363126035,
                0.9999910603026325
            ],
            [
                0.9999832985801554,
                0.9999930377437518,
                0.999968798092389,
                0.9999724643089097,
                0.9999485578048216,
                0.9999869928684378,
                0.9998415637653166,
                0.9999810748472558,
                0.9999151889187124,
                0.9999599362982967
            ],
            [
                0.9998204720130666,
                0.9998766053963017,
                0.9997040429054999,
                0.9997965730527251,
                0.9997694933407449,
                0.9999485577925108,
                0.9997694932034241,
                0.9999038975393677,
                0.9999038975509236,
                0.9997694933406912
            ],
            [
                0.9999417087555388,
                0.9994472212681454,
                0.9998601779595375,
                0.9997040427975704,
                0.9998911031170444,
                0.9996646499778719,
                0.9995121427679141,
                0.9997040428692477,
                0.9984988174026423,
                0.9997040430108719
            ],
            [
                0.9997388097247923,
                0.9959298614818775,
                0.9994472214036921,
                0.9984988174036893,
                0.9999417087206578,
                0.9993736658379921,
                0.9997388097235763,
                0.9991959140032004,
                0.9995121427741869,
                0.999796572929876
            ],
            [
                0.9999785550464855,
                0.9999687980960991,
                0.9999785550490391,
                0.9998601779429858,
                0.9999898700041931,
                0.9999810748449972,
                0.999991060299436,
                0.9999251537818761,
                0.9999832985761765,
                0.9999832985821429
            ],
            [
                0.9999832985841419,
                0.9999546021259874,
                0.9999724643056438,
                0.9999785550464881,
                0.9999898700078138,
                0.9999485578048216,
                0.999988521234614,
                0.999933947863362,
                0.9999885212264068,
                0.9999646437535807
            ],
            [
                0.9999921107345944,
                0.9999910603068951,
                0.9999885212318768,
                0.9999038975737626,
                0.9999869928653345,
                0.9999599362935263,
                0.9998911030650004,
                0.9999785550490452,
                0.9997965730523404,
                0.9999921107345945
            ],
            [
                0.9999687980960773,
                0.9999038975741934,
                0.999373665921646,
                0.9999485577925582,
                0.9999339478396944,
                0.9999646437324774,
                0.9999251537728298,
                0.9999151889688855,
                0.9999485577802578,
                0.9998601778929295
            ],
            [
                0.9999832985761674,
                0.9999485577925504,
                0.9999038975737402,
                0.9999921107364745,
                0.9999810748562789,
                0.999954602142314,
                0.9999810748472596,
                0.9999756997506067,
                0.9999687980849237,
                0.9999852610215482
            ],
            [
                0.9997694933134538,
                0.9999251537461169,
                0.999903897539223,
                0.9999485577986859,
                0.9999417087067041,
                0.9998911030651763,
                0.9999417087067719,
                0.9999724643154826,
                0.9999832985741811,
                0.9999546021314167
            ],
            [
                0.9999724643154851,
                0.9999417087415464,
                0.9999151889183183,
                0.9999785550516006,
                0.9999832985781628,
                0.9999038975738676,
                0.999841563708404,
                0.9999599362934934,
                0.9999038975394585,
                0.9999038975737291
            ],
            [
                0.999968798096083,
                0.9999339478632836,
                0.9999869928746427,
                0.9999921107383568,
                0.9999546021205791,
                0.9999930377429218,
                0.9999151889488717,
                0.9999869928684394,
                0.9995121427865051,
                0.9999724643089085
            ],
            [
                0.9999810748472532,
                0.9997694933682104,
                0.9999852610162828,
                0.9999885212277727,
                0.9999832985841371,
                0.9999546021097568,
                0.9999417087276202,
                0.9999038975853815,
                0.9999898700078147,
                0.9999930377462418
            ],
            [
                0.9998911030392651,
                0.9998601778931552,
                0.9999785550567089,
                0.9999687980812015,
                0.999941708706721,
                0.9999756997650798,
                0.9998911031041102,
                0.9999546021098202,
                0.9999251537729164,
                0.9999151889891562
            ],
            [
                0.9999151889385013,
                0.9999785550515897,
                0.9999038975394349,
                0.9996200155631845,
                0.9995121427689927,
                0.9988304894871712,
                0.999569442914279,
                0.9997965730277251,
                0.9999724643154851,
                0.9998204719703889
            ],
            [
                0.999968798077481,
                0.9998766053960377,
                0.9997388096921669,
                0.9997965730037667,
                0.9998415637457365,
                0.999968798096083,
                0.9999339478554764,
                0.9999339478318973,
                0.9999151889587867,
                0.9998911031169287
            ],
            [
                0.999903897585194,
                0.9999151889184268,
                0.9991959140707778,
                0.999941708706721,
                0.9999485577679911,
                0.9999546021205883,
                0.9999785550592627,
                0.9999646437450979,
                0.9999756997534912,
                0.9999038975508887
            ],
            [
                0.9999898700066082,
                0.9999756997621821,
                0.9999832985781653,
                0.999903897573855,
                0.9998766053814608,
                0.9999724642957817,
                0.9999832985801516,
                0.9999724643121942,
                0.9999546021097816,
                0.9999852610197907
            ],
            [
                0.999959936298325,
                0.999925153781771,
                0.9999724642958047,
                0.9999756997679652,
                0.9999785550439327,
                0.999988521231877,
                0.9999646437493283,
                0.9999417087345988,
                0.9999417087555761,
                0.9998204720353939
            ],
            [
                0.9999646437408817,
                0.9999599362887743,
                0.9999485577680203,
                0.9999546021368376,
                0.9999810748449967,
                0.9999339478317867,
                0.9999756997621986,
                0.9999151889488396,
                0.9999898700114376,
                0.9999852610110029
            ],
            [
                0.9999687980774995,
                0.9999417087206578,
                0.9999832985741811,
                0.9999151889590218,
                0.9999417087206578,
                0.9999485577619005,
                0.999948557767984,
                0.9999646437366851,
                0.9999339478239545,
                0.9999599363126231
            ],
            [
                0.9999785550515963,
                0.9999485577864038,
                0.9999417087207189,
                0.9999810748472645,
                0.9999417087275961,
                0.9999869928730909,
                0.9999687980774881,
                0.9999599363078874,
                0.9999038975511235,
                0.9999785550439266
            ],
            [
                0.9999852610162793,
                0.9999339478790701,
                0.99997569976798,
                0.9999038975507998,
                0.9996646497750594,
                0.9999687980774927,
                0.999948557786501,
                0.9998911031039645,
                0.99990389758532,
                0.9999485577925209
            ],
            [
                0.9998204720347489,
                0.999985261014518,
                0.9998204719488896,
                0.9999756997534868,
                0.9997694931765422,
                0.9999546021098057,
                0.9990889488053345,
                0.9996646499324252,
                0.9999687980849298,
                0.9999724643056345
            ],
            [
                0.9999724643023429,
                0.9998204720771078,
                0.9994472214632169,
                0.9997694932592338,
                0.9999485577618926,
                0.9992903295443473,
                0.998967769109098,
                0.9998601779429633,
                0.9997694932587575,
                0.9999417087137246
            ],
            [
                0.999860177926322,
                0.9999646437324528,
                0.9999810748585477,
                0.999925153746234,
                0.9999646437366584,
                0.9998766054696206,
                0.9999756997563768,
                0.9999756997563877,
                0.9998204720776067,
                0.9996646498554546
            ],
            [
                0.9980732654906945,
                0.9995121428898766,
                0.9999599363079055,
                0.9999885212346137,
                0.9998911030910874,
                0.9997040429027788,
                0.9997694933134538,
                0.9999724643056384,
                0.9999339478317647,
                0.9999485577925747
            ],
            [
                0.9999599363030699,
                0.9998911031173439,
                0.9999646437408817,
                0.9999724642957987,
                0.999820471949822,
                0.9999485577679982,
                0.9998601778770367,
                0.9996200154776425,
                0.9998415637837214,
                0.9999417087206391
            ],
            [
                0.9999869928761894,
                0.9998766054701557,
                0.9999485577986598,
                0.9998766054112485,
                0.9999756997621748,
                0.9999485577864516,
                0.9999852610145241,
                0.9997965730029439,
                0.9999599363174413,
                0.999986992874644
            ],
            [
                0.9999785550567132,
                0.999941708748494,
                0.9999885212305142,
                0.9999832985701967,
                0.9999852610197877,
                0.9999724642990765,
                0.9999938558232023,
                0.9999832985741806,
                0.9999599363127246,
                0.9999646437324962
            ],
            [
                0.999891103116943,
                0.9997388095989572,
                0.999925153763988,
                0.996827317675908,
                0.9998415638215978,
                0.9998601778929741,
                0.9999485577802684,
                0.9999151889386154,
                0.998498817386065,
                0.9997388097232875
            ],
            [
                0.9999151889284702,
                0.9999151889689127,
                0.999860177860143,
                0.9999038975508887,
                0.9999038975737187,
                0.9999546021476443,
                0.9999810748517651,
                0.9999756997650677,
                0.999933947871197,
                0.9999646437493283
            ],
            [
                0.9998601778600699,
                0.9999646437366768,
                0.9999151889891291,
                0.9999687980998022,
                0.9999646437535248,
                0.9999251537996269,
                0.9999251537371533,
                0.9999756997621821,
                0.9999852610233055,
                0.9999485577803285
            ],
            [
                0.9999724643155011,
                0.9999832985761721,
                0.9999910603015691,
                0.9999898700090227,
                0.9999885212291413,
                0.9999724643089434,
                0.9999832985841359,
                0.9999485577619005,
                0.9999756997650755,
                0.9998601778601187
            ],
            [
                0.99997246431548,
                0.999988521226404,
                0.9999251537906715,
                0.9999945777810308,
                0.9999724643122028,
                0.9999852610127677,
                0.999988521234616,
                0.9998911030779377,
                0.9998204719918179,
                0.9999756997621767
            ],
            [
                0.9996646499735692,
                0.9998415637081136,
                0.9999485577741227,
                0.9999599362887888,
                0.9999339478554163,
                0.9998601778929295,
                0.999796572955921,
                0.9999599363126077,
                0.9998766053958636,
                0.9998601779428107
            ],
            [
                0.9999785550516107,
                0.9999417087137501,
                0.9999546021151928,
                0.9999832985801532,
                0.999993037742092,
                0.9999810748585362,
                0.9999810748517658,
                0.9999724643187772,
                0.9999921107336547,
                0.9999930377445827
            ],
            [
                0.9999417087345488,
                0.9999832985721865,
                0.999933947831754,
                0.9999687980997979,
                0.9998415637082864,
                0.999925153746088,
                0.9999546021205761,
                0.999933947823881,
                0.9999756997563761,
                0.9999546021097423
            ],
            [
                0.9999485577618736,
                0.9999687980997966,
                0.9999417087137051,
                0.9999151889283845,
                0.9996646498141448,
                0.9999485577925624,
                0.9997965730043467,
                0.9999756997563923,
                0.9988304899692546,
                0.9997965729309534
            ],
            [
                0.9999417087136958,
                0.9999646437493034,
                0.9999599362935362,
                0.9999646437451019,
                0.9998204719490672,
                0.9999339478318275,
                0.9999756997621788,
                0.9993736657708431,
                0.9999921107336548,
                0.9999869928653483
            ],
            [
                0.9997965729799119,
                0.99979657307584,
                0.9993736658325634,
                0.9999417087345395,
                0.9999546021260286,
                0.9993736657608235,
                0.9995121428278311,
                0.9995694430196557,
                0.9999417087206302,
                0.9997040428702467
            ],
            [
                0.9999810748562891,
                0.9999687980998254,
                0.9999546021476909,
                0.9999251537818369,
                0.9998415637459325,
                0.9999852610145189,
                0.9999724642990933,
                0.9999599363174135,
                0.999981074845,
                0.9999832985702045
            ],
            [
                0.9994472213262553,
                0.999738809568893,
                0.9998601779594948,
                0.9998601779264806,
                0.9999869928653401,
                0.9999251537550745,
                0.9990889487973342,
                0.9997965730771127,
                0.9999599363221485,
                0.9998601778761578
            ],
            [
                0.9999832985721903,
                0.9998204719487146,
                0.9999546021260286,
                0.9999151889791444,
                0.9998911031039217,
                0.9999724643089399,
                0.999933947847538,
                0.9999151889486347,
                0.9991959139721476,
                0.9999151889486693
            ],
            [
                0.999994577779092,
                0.9999910602994351,
                0.999992110735535,
                0.9999785550541551,
                0.9999417087345128,
                0.9998204720998897,
                0.9999785550413738,
                0.9999885212291397,
                0.9999646437324866,
                0.999985261011009
            ],
            [
                0.9999417087276151,
                0.9999546021259992,
                0.9999251537996416,
                0.9999885212318786,
                0.999941708706721,
                0.999860177893495,
                0.9999485578049051,
                0.999903897562355,
                0.9999599362983224,
                0.9999599362888236
            ],
            [
                0.9998204720987822,
                0.9998911030392968,
                0.9997965731008195,
                0.9994472214648249,
                0.9997694932324457,
                0.9998766053813334,
                0.9998601779429633,
                0.9996200154293108,
                0.9997040428686622,
                0.9999724642990713
            ],
            [
                0.9953904287842344,
                0.9997965731000796,
                0.9998204720772462,
                0.9997965730034855,
                0.9998204720138449,
                0.9997965730761567,
                0.9997040428671468,
                0.9997388095673958,
                0.9999151889185779,
                0.9997965730762514
            ],
            [
                0.9999832985841359,
                0.9999599362935362,
                0.999983298574178,
                0.9999151889487236,
                0.9997965729319299,
                0.9998766053960377,
                0.9999810748472612,
                0.9999756997505873,
                0.9999869928730878,
                0.999796573003956
            ],
            [
                0.9999251537907504,
                0.9999339478634014,
                0.9998766053963214,
                0.9999546021099609,
                0.9999756997505913,
                0.9998766054254681,
                0.9999251537818293,
                0.9999038975969373,
                0.9999546021313986,
                0.9999339478554053
            ],
            [
                0.9999687980886571,
                0.9999339478792026,
                0.9998766053812616,
                0.9999038976197681,
                0.9999646437535384,
                0.999972464305637,
                0.9999417087067435,
                0.9999251537995921,
                0.9999687980737751,
                0.9999038975394349
            ],
            [
                0.9999869928715466,
                0.9999852610233055,
                0.9999952149032243,
                0.9999952149066466,
                0.9999910603015663,
                0.9999546021476836,
                0.999954602131393,
                0.9997694932588178,
                0.9999151889790031,
                0.9999599363030631
            ],
            [
                0.9999339478319313,
                0.9999938558224696,
                0.9999832985702152,
                0.9999756997679775,
                0.9999810748517772,
                0.9999646437619653,
                0.999989870007816,
                0.999986992868442,
                0.9999646437409081,
                0.9999832985841371
            ],
            [
                0.9999417087206625,
                0.9998415638404197,
                0.9999921107355375,
                0.9999485577742429,
                0.999989870005405,
                0.9999417087068402,
                0.9999251537728939,
                0.9999785550592659,
                0.9999038975621907,
                0.9999151889187952
            ],
            [
                0.9998766053963807,
                0.9999417087484445,
                0.9999852610197902,
                0.9999885212332457,
                0.9999724643122055,
                0.9999417087136822,
                0.9999885212359817,
                0.9999038975622536,
                0.9999485577925665,
                0.9999251537372883
            ],
            [
                0.9997388097251114,
                0.9999339478554053,
                0.9998601778762229,
                0.9999038975853941,
                0.9999546021206174,
                0.9999251537371739,
                0.9999599362983143,
                0.9999756997506042,
                0.9999852610233041,
                0.9999756997476946
            ],
            [
                0.9999646437619633,
                0.9999687980812105,
                0.9999151889588225,
                0.99995993630786,
                0.9998766054402837,
                0.999954602120621,
                0.9999832985721903,
                0.9999869928668896,
                0.9999898700126456,
                0.9999832985821464
            ],
            [
                0.9959298618839345,
                0.9999810748540198,
                0.9997965730277251,
                0.9997965729786599,
                0.9999756997621777,
                0.9999785550567105,
                0.9999810748540267,
                0.9998415637658954,
                0.9997388095676162,
                0.9999756997650764
            ],
            [
                0.999968798092365,
                0.9999251537460739,
                0.999972464315472,
                0.9999756997563761,
                0.9999417087416309,
                0.9999251537818369,
                0.9999339478790124,
                0.9997965731020684,
                0.9999038975394012,
                0.9999852610162773
            ],
            [
                0.9998766053963609,
                0.9998415637645353,
                0.9997694933691493,
                0.9999251537371957,
                0.999876605439966,
                0.9999646437535286,
                0.9995694429146548,
                0.9999852610215486,
                0.9998766054253442,
                0.9999417087207138
            ],
            [
                0.999876605425486,
                0.9999339478789758,
                0.9998601779765166,
                0.9999038976196352,
                0.9999599362982833,
                0.9999756997592791,
                0.9999151889386338,
                0.9998911030391304,
                0.9999038976196352,
                0.999915188968851
            ],
            [
                0.9989677687380436,
                0.9997694933136886,
                0.9993736659873375,
                0.9996646498555815,
                0.9998911030782783,
                0.9997965729306721,
                0.9998204719712562,
                0.9999251537461931,
                0.9991959142505008,
                0.9998766054697518
            ],
            [
                0.9999417087067766,
                0.9999832985761693,
                0.9999756997650686,
                0.9999599363030923,
                0.9999785550541692,
                0.9999885212359829,
                0.9999151889589898,
                0.9999251537908882,
                0.9999151889287973,
                0.9999724643154692
            ],
            [
                0.9999724642957943,
                0.9999852610180324,
                0.9999417087415015,
                0.9999756997621891,
                0.9999646437408835,
                0.9999869928746418,
                0.9999339478475212,
                0.9999832985821541,
                0.9999646437408835,
                0.9997388096925318
            ],
            [
                0.9999599363126256,
                0.999290329484534,
                0.9999687980960907,
                0.9999852610110029,
                0.9999417087275736,
                0.999704043008745,
                0.9999339478239136,
                0.9999546021422155,
                0.9999646437535405,
                0.9997694932315871
            ],
            [
                0.9999756997592842,
                0.9999832985761709,
                0.999972464312229,
                0.9999724643155059,
                0.9999646437408817,
                0.9999756997621958,
                0.9999724643121964,
                0.9999646437366672,
                0.9999417087345831,
                0.9999687980960875
            ],
            [
                0.9996646498519421,
                0.9998204720993386,
                0.9999251537550087,
                0.9997388096294927,
                0.9999038975625634,
                0.9999485577987836,
                0.999820471992147,
                0.9999852610162767,
                0.9997694932317078,
                0.9999151889689584
            ],
            [
                0.9997694933143458,
                0.9998911030651018,
                0.9998601779266231,
                0.9999921107345964,
                0.9999151889488297,
                0.999903897619545,
                0.9998601779440924,
                0.9999038975740969,
                0.9998415637646713,
                0.9999417087206722
            ],
            [
                0.9999485578049003,
                0.9999151889184854,
                0.9999417087554314,
                0.9999724643023473,
                0.999981074854021,
                0.9999724643089193,
                0.9999810748472546,
                0.9999417087276304,
                0.9999869928653375,
                0.9999417087137551
            ],
            [
                0.999841563746405,
                0.9999339478318334,
                0.9999852610110085,
                0.9999810748585416,
                0.9999810748585369,
                0.9999785550592668,
                0.9999038975625899,
                0.9999724643056384,
                0.9999546021097478,
                0.9999724643154864
            ],
            [
                0.9999546021368069,
                0.9999546021368871,
                0.9999810748562789,
                0.999972464312199,
                0.9999646437451019,
                0.9999646437408835,
                0.9999251537728504,
                0.9999339478396881,
                0.9998766054256153,
                0.9999756997592761
            ],
            [
                0.9999038975622865,
                0.9998415637271659,
                0.9998911030917227,
                0.9999852610215458,
                0.9999339478396944,
                0.9991959141612239,
                0.999964643732451,
                0.9999546021476734,
                0.9996200155622891,
                0.9998204720779462
            ],
            [
                0.9997965730277251,
                0.9999339478475492,
                0.9999869928699877,
                0.9999646437324686,
                0.999941708748413,
                0.9999546021205821,
                0.9999810748495163,
                0.9999687980812153,
                0.9999646437619848,
                0.9999251537373471
            ],
            [
                0.9999724643122083,
                0.9999417087414693,
                0.9998911031170887,
                0.9996200155625101,
                0.9998911030520091,
                0.9999251537372409,
                0.9992903297260984,
                0.9999339478238973,
                0.9999852610110042,
                0.9999485577741598
            ],
            [
                0.9999687980998099,
                0.9998601778606415,
                0.9997965730763432,
                0.999891103039666,
                0.9997388097547729,
                0.9999599362983339,
                0.9999339478239136,
                0.9990889489508755,
                0.9999687980998521,
                0.9999251537461092
            ],
            [
                0.9994472214590042,
                0.9998911031169287,
                0.9995121428939354,
                0.9994472213286029,
                0.9996646498528886,
                0.9999646437366894,
                0.9999151889386529,
                0.9998766054107618,
                0.9999251537996416,
                0.9998911030394758
            ],
            [
                0.9999599362935857,
                0.9999646437619757,
                0.9999687980849412,
                0.9999687980886429,
                0.9999687980849181,
                0.9999646437451037,
                0.9999646437619757,
                0.9998204719709062,
                0.9999417087554069,
                0.9999599363174162
            ],
            [
                0.9999417087276508,
                0.9999038975741654,
                0.9998601779430528,
                0.9999599362887323,
                0.9999724643122055,
                0.9999832985721947,
                0.9999724642958217,
                0.999986992869995,
                0.9999646437493261,
                0.9992903295501676
            ],
            [
                0.9998415637842584,
                0.9999546021314575,
                0.9999038975851828,
                0.9999599363030846,
                0.9998204720985366,
                0.999933947847567,
                0.9999810748517677,
                0.9998601779096359,
                0.99998329857418,
                0.999933947839643
            ],
            [
                0.9998204720774604,
                0.9995121429515248,
                0.999620015519905,
                0.9996646498131788,
                0.999820472077907,
                0.9997965729311901,
                0.9990889486104142,
                0.9999546021151456,
                0.9999599363174084,
                0.9997965729550982
            ],
            [
                0.9999852610127649,
                0.9999151889890767,
                0.9999599363126231,
                0.9998204719497045,
                0.9999687980997993,
                0.999959936298279,
                0.9999546021098278,
                0.999985261016273,
                0.9999869928653392,
                0.9999546021476665
            ],
            [
                0.999915188928435,
                0.99990389759675,
                0.9997965730520119,
                0.9996646498124666,
                0.9997694932853645,
                0.9999339478475554,
                0.9999417087553831,
                0.9998911030778062,
                0.9996200155165111,
                0.9999546021422182
            ],
            [
                0.999891103103726,
                0.9998415637463428,
                0.9998911030910002,
                0.999964643757745,
                0.9999785550541551,
                0.999925153772803,
                0.9999038975966046,
                0.999933947823881,
                0.9996200155624438,
                0.9999251537906513
            ],
            [
                0.9999756997621788,
                0.9999921107355351,
                0.999915188948705,
                0.9999885212346156,
                0.99997569976797,
                0.9999339478554163,
                0.9999910603068951,
                0.9999785550490391,
                0.9999910602994342,
                0.9999646437577393
            ],
            [
                0.9999485578048176,
                0.9999756997476946,
                0.9999810748427519,
                0.9998601779442042,
                0.9999810748517691,
                0.9999646437409151,
                0.9999869928684382,
                0.999992110733655,
                0.9999930377437508,
                0.9999785550413756
            ],
            [
                0.9999339478790759,
                0.9999921107374162,
                0.9997694932313523,
                0.9999646437619735,
                0.9999646437535268,
                0.9999038975854193,
                0.9998911031306947,
                0.9999038975508663,
                0.9999687980849181,
                0.999992110738356
            ],
            [
                0.9999485577925467,
                0.9999885212305142,
                0.999997739674894,
                0.9999810748517663,
                0.9999930377445817,
                0.9999852610110046,
                0.9999832985701977,
                0.9999957771670593,
                0.9999885212332523,
                0.9999724642958094
            ],
            [
                0.999988521231877,
                0.9999810748517691,
                0.9999898700054001,
                0.9999756997679721,
                0.9999885212318773,
                0.9998911030650431,
                0.9999938558232021,
                0.999983298574178,
                0.9999885212305113,
                0.9999869928715388
            ],
            [
                0.9998911030650004,
                0.9998911030780216,
                0.9999756997592822,
                0.9999785550515972,
                0.9999251537463025,
                0.9999038975396054,
                0.9999599363078904,
                0.9999852610215618,
                0.9999339478790581,
                0.9999599362935121
            ],
            [
                0.999975699767971,
                0.9999938558239343,
                0.999988521234614,
                0.9999646437324913,
                0.999925153790781,
                0.9999910602994346,
                0.9999921107383564,
                0.9999885212264031,
                0.9999921107345944,
                0.9999957771675629
            ],
            [
                0.9999910603036973,
                0.9999646437451205,
                0.9999785550439292,
                0.9999339478711234,
                0.9999756997621798,
                0.9999785550516107,
                0.9999832985702053,
                0.9999599363126541,
                0.9999251537550375,
                0.9999151889387425
            ],
            [
                0.9997388097550692,
                0.9999485577741519,
                0.9995694428692249,
                0.9998415637838366,
                0.9996646498127008,
                0.999941708713745,
                0.9998601778764243,
                0.999841563764616,
                0.9999756997505854,
                0.9996646497385888
            ],
            [
                0.9998766054109881,
                0.9999832985841328,
                0.9999038975737402,
                0.9998601778595816,
                0.999860177943712,
                0.9999417087275871,
                0.9998911030520361,
                0.9999485577618847,
                0.9998204719915698,
                0.9999810748517651
            ],
            [
                0.9999485577619706,
                0.9998766054696584,
                0.9999251537995992,
                0.9997965730763906,
                0.9997694933130513,
                0.9986749777677991,
                0.9999546021205518,
                0.9996200154760506,
                0.9999785550439266,
                0.999968798081212
            ],
            [
                0.9999599362982944,
                0.9999151889587689,
                0.9999810748540267,
                0.9999756997505934,
                0.9999938558253997,
                0.9999251537907204,
                0.9999599362983168,
                0.9999785550515979,
                0.9999810748495163,
                0.9998601779432623
            ],
            [
                0.9999785550515996,
                0.9998601778596691,
                0.9984988173970584,
                0.999903897562355,
                0.9999810748585355,
                0.9999832985761725,
                0.9999785550592643,
                0.9998415637083141,
                0.9991959142508281,
                0.9999151889184656
            ],
            [
                0.9999251537371668,
                0.9999151889185681,
                0.9998766053665553,
                0.9999417087206302,
                0.9999646437324408,
                0.9999810748450007,
                0.999986992874641,
                0.9999339478396377,
                0.9999852610162793,
                0.9999251537552057
            ],
            [
                0.9999251537371739,
                0.9999417087206722,
                0.999925153781778,
                0.9998911030391304,
                0.9999151889487612,
                0.9999810748562803,
                0.9999599363221789,
                0.9999756997621867,
                0.999948557786415,
                0.9999339478790523
            ],
            [
                0.999954602136907,
                0.9998766054400665,
                0.9999687980960875,
                0.9999251537375028,
                0.9998766053960197,
                0.9998766053812275,
                0.9999810748472558,
                0.9999646437577374,
                0.9999810748449992,
                0.9999646437324844
            ],
            [
                0.9999724643122014,
                0.9997694932865181,
                0.9999485577987062,
                0.9999646437619502,
                0.9998766053667009,
                0.9997965730774678,
                0.9999724643187715,
                0.9999832985841314,
                0.9999151889488926,
                0.9999339478317925
            ],
            [
                0.9997040427639705,
                0.9999687980960875,
                0.9999485577986458,
                0.9998911030651763,
                0.9999339478712945,
                0.9999339478712879,
                0.999972464318766,
                0.9999810748472558,
                0.9999687980737751,
                0.999959936312657
            ],
            [
                0.9996646498923643,
                0.9999546021097598,
                0.9999038976195339,
                0.9997388096610463,
                0.9982992776085278,
                0.9999687980960844,
                0.9998766054254321,
                0.9999339478239425,
                0.999964643736671,
                0.9999756997679626
            ],
            [
                0.9999869928699903,
                0.999995214905506,
                0.999891103039086,
                0.9998415638030457,
                0.9999885212359829,
                0.9999251537996269,
                0.9999546021151962,
                0.9999687980923763,
                0.9999785550515939,
                0.9999251537641612
            ],
            [
                0.9999151889287404,
                0.9999599362982967,
                0.9999687980960923,
                0.9999646437408855,
                0.9999646437493181,
                0.9999151889386246,
                0.9996646499326595,
                0.9999810748540359,
                0.9999339478711851,
                0.9999546021476836
            ],
            [
                0.9999599363078874,
                0.999981074854034,
                0.999978555054151,
                0.9999687980923682,
                0.9999599363174084,
                0.9999810748562783,
                0.9999724643154891,
                0.9999646437577528,
                0.9999930377445818,
                0.9999599363078454
            ],
            [
                0.9995121429466146,
                0.9997694932037662,
                0.9995121428847109,
                0.9997694932867596,
                0.9978172836134778,
                0.9988304898969083,
                0.9859363733570753,
                0.9990889490003606,
                0.9999339478239727,
                0.9999151889790302
            ],
            [
                0.9999599363173941,
                0.9999485577680053,
                0.9999339478633364,
                0.9999417087206391,
                0.9999151889285541,
                0.9997040428342875,
                0.999664649813052,
                0.9999546021314046,
                0.9999724643023462,
                0.9999646437619673
            ]
        ]
    },
    {
        "q_id": "7740_mmlu_math",
        "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": [
            [
                0.9999984465026158,
                0.9999994284994849,
                0.9999986290431201,
                0.9999984465018751,
                0.999999057755743,
                0.9999921107383561,
                0.9999990577556308,
                0.9999910603068939,
                0.9999957771675625,
                0.9999991684721706
            ],
            [
                0.999995214906076,
                0.9999994284995529,
                0.9999986290423029,
                0.9999962733593835,
                0.9999974387168733,
                0.9999982396572065,
                0.999988521227772,
                0.9999994284992805,
                0.9999987901344607,
                0.9999986290421395
            ],
            [
                0.9999986290426298,
                0.9999967112513267,
                0.9999994284993485,
                0.9999980052709919,
                0.9999987901346049,
                0.999998790134028,
                0.9999989322967481,
                0.9999974387187053,
                0.999998239656367,
                0.9999980052707542
            ],
            [
                0.999998790134028,
                0.9999869928761919,
                0.999992110737415,
                0.9999945777823236,
                0.9999938558232014,
                0.9999945777803841,
                0.9999986290424663,
                0.9999962733616049,
                0.9999980052693274,
                0.9999984465026159
            ],
            [
                0.999998239656367,
                0.9999980052702786,
                0.9999910603068951,
                0.999997097689053,
                0.9999869928668885,
                0.9999957771655491,
                0.9999910603026321,
                0.9999994284996211,
                0.9999984465024306,
                0.9999987901337396
            ],
            [
                0.9999921107355338,
                0.9999724643089085,
                0.999941708706721,
                0.9999251537549482,
                0.9999810748495038,
                0.9999417087345085,
                0.9999646437492953,
                0.9999921107336528,
                0.9999945777797374,
                0.9999974387184
            ],
            [
                0.9999992661791944,
                0.9999982396569966,
                0.9999945777829697,
                0.9999989322966208,
                0.9999974387184,
                0.999959936293519,
                0.9999986290424664,
                0.9999990577552937,
                0.9999852610233032,
                0.9999980052702786
            ],
            [
                0.9999982396561572,
                0.9999967112505429,
                0.9999984465020603,
                0.9999952149049353,
                0.9999910603015675,
                0.9999921107364745,
                0.9999989322967482,
                0.9999921107345946,
                0.9999945777797381,
                0.9999986290426297
            ],
            [
                0.9999992661791944,
                0.9999974387168734,
                0.9999980052707541,
                0.9999982396561572,
                0.9999991684718733,
                0.9999989322967482,
                0.9999994284997573,
                0.9999986290429566,
                0.9999967112517189,
                0.9999995549151073
            ],
            [
                0.999998239656367,
                0.9999991684722697,
                0.9999993524049703,
                0.9999984465020603,
                0.9999994956527722,
                0.9999986290421394,
                0.9999994956525317,
                0.9999970976880149,
                0.9999990577556307,
                0.9999989322966208
            ],
            [
                0.999992110737415,
                0.9999251537639091,
                0.9999962733611601,
                0.9999930377454105,
                0.9998911030390022,
                0.9999852610145148,
                0.9999485577679982,
                0.9999869928746385,
                0.9999339478474896,
                0.9999785550413652
            ],
            [
                0.9999945777784464,
                0.9999756997505873,
                0.9999986290429567,
                0.9999938558239336,
                0.999997097688361,
                0.9999952149072168,
                0.9999987901337396,
                0.999998005270992,
                0.9999987901343166,
                0.9999898700078136
            ],
            [
                0.9999990577551814,
                0.9999996072138465,
                0.9999945777803838,
                0.9999982396574162,
                0.999997438717484,
                0.999998239656367,
                0.9999962733598274,
                0.9999986290423029,
                0.9999992661787571,
                0.9999982396572065
            ],
            [
                0.9999957771650455,
                0.9999945777784449,
                0.9999982396572065,
                0.9999991684719723,
                0.9999984465020603,
                0.9999974387177893,
                0.9999993524052019,
                0.9999921107336528,
                0.9999984465015047,
                0.9999980052702786
            ],
            [
                0.9999977396751633,
                0.999997097687323,
                0.9999995549150011,
                0.9999995549151073,
                0.999997097689053,
                0.9999967112509347,
                0.9999984465016899,
                0.9999992661789321,
                0.9999991684718732,
                0.9999991684715759
            ],
            [
                0.9999992661792819,
                0.999998790134605,
                0.9999974387180947,
                0.9999989322973846,
                0.9999938558275958,
                0.9999930377462406,
                0.9999987901341724,
                0.9999992661792819,
                0.9999869928746399,
                0.9999898700066094
            ],
            [
                0.9999885212359839,
                0.9999945777829697,
                0.9999991684722698,
                0.999993855823934,
                0.9999910603005013,
                0.9999977396757023,
                0.9999852610197898,
                0.9999989322972572,
                0.9999756997505957,
                0.9999810748472558
            ],
            [
                0.99999457778297,
                0.9999986290431201,
                0.9999991684721706,
                0.9999869928715396,
                0.9999962733611603,
                0.9999952149066467,
                0.99999862904312,
                0.99997569975349,
                0.9999990577555185,
                0.9999970976869773
            ],
            [
                0.9999756997476936,
                0.9999993524054334,
                0.9999962733620489,
                0.9999962733593835,
                0.9999930377420916,
                0.9999994956527722,
                0.9999986290427932,
                0.9999992661791945,
                0.9999938558268642,
                0.9999898700078143
            ],
            [
                0.9999984465022455,
                0.9999967112501505,
                0.9999977396765106,
                0.9999977396746244,
                0.9999974387187054,
                0.9999991684719723,
                0.9999980052693274,
                0.9999987901341723,
                0.9999992661790196,
                0.9999986290427931
            ],
            [
                0.9999970976866309,
                0.9999984465018751,
                0.9999984465026158,
                0.9999984465026159,
                0.9999930377429213,
                0.9999967112517191,
                0.9999984465015046,
                0.9999974387184,
                0.9999991684720715,
                0.9999986290431201
            ],
            [
                0.9999990577549568,
                0.9999938558246663,
                0.9999990577554061,
                0.9999991684719723,
                0.9999957771655487,
                0.9999962733598274,
                0.9999974387187053,
                0.9999930377429208,
                0.9999993524053562,
                0.99999862904312
            ],
            [
                0.9999987901341723,
                0.9999952149072168,
                0.9999982396569966,
                0.999999266179107,
                0.9999869928684385,
                0.9999930377412614,
                0.9999967112509349,
                0.9999687980774995,
                0.999996711251327,
                0.9999987901343165
            ],
            [
                0.9999982396563672,
                0.9999967112501508,
                0.9999945777823233,
                0.9999646437493181,
                0.999993855827596,
                0.9999987901338838,
                0.9999982396561572,
                0.999993037745411,
                0.9999974387177893,
                0.9999986290432835
            ],
            [
                0.9999986290426298,
                0.9999994956525318,
                0.9999945777803841,
                0.9999980052702786,
                0.9999832985781634,
                0.999992110735535,
                0.9999986290424664,
                0.9999832985701977,
                0.9999885212332469,
                0.9999938558232014
            ],
            [
                0.9999992661790195,
                0.9999991684721706,
                0.9999977396754328,
                0.9999984465024306,
                0.999996711249367,
                0.9999980052709919,
                0.9999832985781607,
                0.9999980052702785,
                0.999995777166556,
                0.9999952149060758
            ],
            [
                0.999986992869988,
                0.9999984465022455,
                0.9999885212359858,
                0.999985261011005,
                0.9999980052700408,
                0.9999898700078157,
                0.9999977396765107,
                0.9999832985801511,
                0.9999910603026309,
                0.9999974387171787
            ],
            [
                0.999985261021549,
                0.9999980052702785,
                0.9999151889488297,
                0.99997246431548,
                0.9999980052707541,
                0.9999910603068943,
                0.99999862904312,
                0.999997097687323,
                0.999998790134028,
                0.999988521227772
            ],
            [
                0.9999898700090213,
                0.9999991684721706,
                0.9999974387184001,
                0.9999982396569966,
                0.9999962733593833,
                0.9999994284997573,
                0.9999991684720715,
                0.9999938558275967,
                0.9999974387168734,
                0.9999982396572065
            ],
            [
                0.9999962733598275,
                0.9999986290429567,
                0.999998629042303,
                0.9999974387180949,
                0.9999938558232012,
                0.9999957771660524,
                0.9999982396572065,
                0.9999962733589393,
                0.9999977396751634,
                0.9999962733620489
            ],
            [
                0.9999967112521109,
                0.9999962733611603,
                0.999988521227776,
                0.9999417087345395,
                0.9999967112501508,
                0.9999987901338838,
                0.9999977396754328,
                0.9999970976880149,
                0.9999957771650457,
                0.9999930377420914
            ],
            [
                0.9999756997650677,
                0.9999810748449961,
                0.9999869928668871,
                0.9999977396757022,
                0.9999993524049702,
                0.9999952149037948,
                0.9999938558253986,
                0.9999869928699859,
                0.9999910603058282,
                0.9999938558261311
            ],
            [
                0.999948557792528,
                0.9999974387171787,
                0.9999986290424663,
                0.9999987901340281,
                0.9999546021151707,
                0.9999977396759717,
                0.9999930377429213,
                0.9999910602994353,
                0.9999993524049703,
                0.9999938558239342
            ],
            [
                0.9999982396574163,
                0.999997097687323,
                0.9999986290426297,
                0.999998446502801,
                0.9999984465020604,
                0.9999989322970028,
                0.9999993524050474,
                0.9999974387165681,
                0.9999993524054334,
                0.9999970976883609
            ],
            [
                0.9999957771670593,
                0.999978555041368,
                0.9999945777829697,
                0.9999989322966208,
                0.9999921107355342,
                0.9999970976873229,
                0.9999938558239337,
                0.9999962733593833,
                0.999991060305829,
                0.9999938558253988
            ],
            [
                0.9999987901343165,
                0.9999990577550691,
                0.9999974387180947,
                0.9999986290431201,
                0.99999893229713,
                0.9999977396754328,
                0.9999996533672549,
                0.999997438717484,
                0.9999992661790196,
                0.999997097686631
            ],
            [
                0.999999266178757,
                0.9999970976887069,
                0.999999266179107,
                0.999998005269803,
                0.9999993524050473,
                0.9999990577554061,
                0.9999995549149481,
                0.9999994284996211,
                0.9999992661792819,
                0.9999991684718732
            ],
            [
                0.9999991684719723,
                0.9999994284996211,
                0.999993855825399,
                0.9999987901337396,
                0.9999970976883611,
                0.9999977396759717,
                0.9999996072137998,
                0.999954602109754,
                0.9999952149072168,
                0.9999869928746395
            ],
            [
                0.9999991684715759,
                0.9999986290426297,
                0.9999957771660523,
                0.9999986290427931,
                0.9999977396754327,
                0.9999991684716749,
                0.9999997300420937,
                0.9999980052700408,
                0.9999952149043646,
                0.9999938558224688
            ],
            [
                0.9999869928653368,
                0.9999991684720715,
                0.999998446502801,
                0.9999984465022455,
                0.9999852610180333,
                0.999993855827596,
                0.9999938558246664,
                0.9999974387180947,
                0.99998699287154,
                0.9999952149049355
            ],
            [
                0.9999938558246669,
                0.999989870004192,
                0.9999930377437515,
                0.9999646437619594,
                0.9999987901347491,
                0.999998790134028,
                0.999998005269803,
                0.9999995549150542,
                0.9999957771660524,
                0.9999970976876689
            ],
            [
                0.9999989322967481,
                0.9999898700114376,
                0.9999599363030746,
                0.9999599363126306,
                0.9999852610180336,
                0.9999987901340281,
                0.9999990577555185,
                0.9999977396746245,
                0.9999832985721903,
                0.9999945777797377
            ],
            [
                0.999997438717484,
                0.9992903294573313,
                0.9999151889889952,
                0.9999687980997938,
                0.9999038975621306,
                0.9995694430145703,
                0.9998204720556789,
                0.9998204719487485,
                0.9999687980849155,
                0.9999785550490315
            ],
            [
                0.999999168471675,
                0.9999885212305091,
                0.9999980052700407,
                0.9999930377429215,
                0.999997097688361,
                0.9999984465016899,
                0.9999945777797379,
                0.9999980052700408,
                0.9999982396572065,
                0.9999921107336535
            ],
            [
                0.9999967112505427,
                0.9999977396762411,
                0.9999992661791944,
                0.9999977396765107,
                0.9999957771675624,
                0.9999977396759717,
                0.9999990577554062,
                0.9999982396561572,
                0.9999756997534859,
                0.9999984465022455
            ],
            [
                0.9999994956524114,
                0.9999991684722698,
                0.9999898700090227,
                0.9999989322968754,
                0.999998446502801,
                0.9999984465026159,
                0.9999938558224692,
                0.9999952149060761,
                0.9999991684721706,
                0.9999993524051246
            ],
            [
                0.9999984465020603,
                0.9999898700041916,
                0.9999945777803843,
                0.9999986290427932,
                0.9999984465015047,
                0.9999852610197894,
                0.999988521234614,
                0.999995777166556,
                0.999995214906076,
                0.9999852610127625
            ],
            [
                0.9999986290423029,
                0.9999992661787571,
                0.9999989322970027,
                0.9999962733611605,
                0.9999962733607162,
                0.9999984465018752,
                0.999996273360272,
                0.9999910603068932,
                0.9999974387165681,
                0.9999977396765105
            ],
            [
                0.999997438717484,
                0.9999962733616046,
                0.9999989322973845,
                0.9999930377420916,
                0.9999987901337396,
                0.9999993524054335,
                0.9999986290423029,
                0.9999910603015656,
                0.9999962733607161,
                0.9999989322975118
            ],
            [
                0.9999957771680658,
                0.9999984465016899,
                0.9999967112497586,
                0.9999967112493665,
                0.9999982396567868,
                0.9999984465016899,
                0.9999986290426297,
                0.9999991684717742,
                0.9999980052709919,
                0.9999991684720715
            ],
            [
                0.9999974387187055,
                0.9999995549150011,
                0.9999984465016899,
                0.9999991684718732,
                0.9999687980774881,
                0.9999984465018751,
                0.9999967112497586,
                0.9999980052709919,
                0.9999957771665557,
                0.9999977396765105
            ],
            [
                0.9999869928684365,
                0.9999987901344607,
                0.9999970976883609,
                0.9999987901337396,
                0.9999921107364745,
                0.9999984465016898,
                0.9999977396748939,
                0.9999967112521109,
                0.9999930377412614,
                0.9999987901337396
            ],
            [
                0.9999991684721706,
                0.9999996072137998,
                0.999998790134605,
                0.9999938558232012,
                0.9999980052702786,
                0.9999982396561572,
                0.9999992661788445,
                0.9999980052695652,
                0.9999952149055057,
                0.9999990577556308
            ],
            [
                0.9999996072136592,
                0.9999996533674202,
                0.9999996533674202,
                0.999993855827596,
                0.9999986290421394,
                0.9999993524054334,
                0.9999989322975119,
                0.999997097686631,
                0.9999986290426297,
                0.9999984465015047
            ],
            [
                0.9999967112517189,
                0.9999982396572065,
                0.9999982396565769,
                0.9999996940977731,
                0.9999986290431201,
                0.9999990577549568,
                0.9999986290421394,
                0.9999994284993485,
                0.999997438717484,
                0.9999977396759717
            ],
            [
                0.9999987901337396,
                0.999999352404893,
                0.9999986290426297,
                0.9999974387187053,
                0.9999991684720715,
                0.9999992661791071,
                0.9999970976866309,
                0.9999980052707541,
                0.999998005270992,
                0.9999984465026159
            ],
            [
                0.9999898700126462,
                0.9999974387177893,
                0.9999930377437513,
                0.9999987901337396,
                0.9999984465018751,
                0.9999756997477014,
                0.9999970976866309,
                0.9999938558253983,
                0.9999987901344608,
                0.9999980052693275
            ],
            [
                0.9999952149043645,
                0.9999962733616048,
                0.999997438716568,
                0.9999898700126442,
                0.9999982396561572,
                0.9999967112517189,
                0.999996273358939,
                0.9999987901347491,
                0.9999967112493665,
                0.9999974387187054
            ],
            [
                0.9999945777810306,
                0.9999982396565769,
                0.9999930377437515,
                0.9999982396572065,
                0.9999970976866309,
                0.9999967112501508,
                0.9999910603036978,
                0.9999989322972572,
                0.9999982396565769,
                0.9999977396757023
            ],
            [
                0.999998239656367,
                0.9999982396559474,
                0.9999977396762411,
                0.9999984465022455,
                0.9999977396751633,
                0.9999992661789321,
                0.9999986290429566,
                0.9999957771645421,
                0.9999986290421394,
                0.9999996533675028
            ],
            [
                0.9999989322975119,
                0.9999987901341723,
                0.9999930377404309,
                0.9999989322972572,
                0.9999987901337396,
                0.9999599363078407,
                0.9999945777829701,
                0.9999974387187054,
                0.999999352404893,
                0.999997097687323
            ],
            [
                0.9999910603036981,
                0.9999991684717742,
                0.9999974387187058,
                0.9999898700114368,
                0.9999993524050474,
                0.9999986290421394,
                0.9999930377412624,
                0.9999785550439309,
                0.9999995549147358,
                0.9999984465022455
            ],
            [
                0.999993855826131,
                0.9999869928653358,
                0.9999984465024306,
                0.9999977396748938,
                0.9999952149043648,
                0.9999989322973845,
                0.9999986290423029,
                0.9999989322967482,
                0.9999987901347491,
                0.9999967112517189
            ],
            [
                0.9999977396746245,
                0.9999945777790915,
                0.9999910603015668,
                0.9999970976873229,
                0.9999982396565771,
                0.9999987901338838,
                0.9999898700066077,
                0.9999957771645422,
                0.9999967112521111,
                0.9999967112497585
            ],
            [
                0.9999952149049355,
                0.9999952149037944,
                0.9999990577551815,
                0.9999991684715759,
                0.9999970976880151,
                0.9999687980998022,
                0.9999930377454109,
                0.999997097688707,
                0.9999962733616048,
                0.9999991684719723
            ],
            [
                0.9999990577549569,
                0.9999989322966208,
                0.9999987901343166,
                0.9999967112509347,
                0.9999945777790916,
                0.999998790134028,
                0.999999266178932,
                0.999993037741261,
                0.9999977396748939,
                0.9999910603047633
            ],
            [
                0.9999980052700409,
                0.9999989322970027,
                0.9999967112517189,
                0.9999984465015047,
                0.9999984465020603,
                0.999998790134028,
                0.9999996533674202,
                0.9999986290426297,
                0.9999987901347491,
                0.9999984465020603
            ],
            [
                0.9999991684717741,
                0.999998446502801,
                0.9999967112505427,
                0.9999987901338838,
                0.9999984465024306,
                0.9999980052705163,
                0.9999989322968754,
                0.9999989322973846,
                0.9999989322967482,
                0.9999990577555185
            ],
            [
                0.9999990577552937,
                0.9999982396572065,
                0.9999989322967481,
                0.9999993524053563,
                0.9999980052695652,
                0.9999984465022455,
                0.9999977396765105,
                0.9999989322970027,
                0.9999989322972572,
                0.9999984465020603
            ],
            [
                0.9999987901346049,
                0.9999986290427931,
                0.9999982396559474,
                0.9999967112505427,
                0.9999952149072167,
                0.9999984465024306,
                0.9999910603015651,
                0.9999980052698031,
                0.9999967112497585,
                0.9999938558239333
            ],
            [
                0.999993855823934,
                0.9999852610162749,
                0.9999980052693275,
                0.9999984465015047,
                0.9999982396567867,
                0.9999989322968754,
                0.9999952149055055,
                0.9999990577552937,
                0.9999869928653358,
                0.9999974387184
            ],
            [
                0.9999852610145195,
                0.999998790134028,
                0.9999938558268638,
                0.9999982396561572,
                0.9999952149043647,
                0.9999980052707542,
                0.999998629042303,
                0.9999485577803159,
                0.9999967112517189,
                0.9999485578047951
            ],
            [
                0.9999921107364762,
                0.9999986290424664,
                0.9999977396754327,
                0.9999885212305073,
                0.99999862904312,
                0.9999852610110042,
                0.9999785550413666,
                0.9999977396757022,
                0.9999945777823234,
                0.9999977396765105
            ],
            [
                0.9999977396754329,
                0.9999977396746244,
                0.9999967112497585,
                0.9999982396572065,
                0.9999982396569966,
                0.9999980052705163,
                0.9999898700078143,
                0.999996273362049,
                0.9999930377429215,
                0.9999921107345942
            ],
            [
                0.9999982396574163,
                0.9999991684722698,
                0.9999869928699887,
                0.9999977396762411,
                0.9999756997534859,
                0.9999992661788446,
                0.999996273362049,
                0.9999980052700408,
                0.9999957771680661,
                0.9999991684722698
            ],
            [
                0.9999938558268646,
                0.9999989322968754,
                0.9999921107392962,
                0.9999995549147889,
                0.999997438717484,
                0.9999980052709919,
                0.9999930377445811,
                0.9999910603036963,
                0.9999977396748939,
                0.9999974387171787
            ],
            [
                0.9999852610162767,
                0.9999945777829699,
                0.9999989322972572,
                0.9999984465015047,
                0.999995214903224,
                0.9999974387187053,
                0.9999991684722698,
                0.9999989322973845,
                0.9999982396565769,
                0.9999869928699899
            ],
            [
                0.9999938558239335,
                0.9999967112513267,
                0.999989870009021,
                0.9999898700114366,
                0.9999974387171787,
                0.999998239656367,
                0.9999977396762411,
                0.9999974387184,
                0.9999957771660521,
                0.9999852610162754
            ],
            [
                0.9999910603026316,
                0.9999785550592677,
                0.9999962733607161,
                0.9999832985761721,
                0.9999977396765105,
                0.9999957771675627,
                0.9999980052693275,
                0.9999974387177893,
                0.9999974387187053,
                0.9999982396567867
            ],
            [
                0.9999885212359819,
                0.9999938558246659,
                0.9999687980849312,
                0.9999992661791945,
                0.9999967112505427,
                0.9999810748517645,
                0.9999417087275915,
                0.999998239656367,
                0.9999546021314167,
                0.9999724643187576
            ],
            [
                0.999996711251327,
                0.9999982396565769,
                0.9999930377420911,
                0.9999970976887068,
                0.9999994284996891,
                0.9999962733593833,
                0.999989870006606,
                0.9999974387187054,
                0.9999967112517189,
                0.9999977396748939
            ],
            [
                0.9999910603026315,
                0.9999980052695653,
                0.9999980052700408,
                0.999999266178932,
                0.9999984465018751,
                0.999998005269803,
                0.9999992661790196,
                0.9999980052698032,
                0.9999967112497586,
                0.9999982396572065
            ],
            [
                0.9999967112501507,
                0.9999869928761888,
                0.9999930377429213,
                0.9999852610215463,
                0.9999952149072169,
                0.9999967112517189,
                0.9999724642990699,
                0.9999974387171787,
                0.9999885212291397,
                0.999991060306894
            ],
            [
                0.9999992661792819,
                0.999999495652652,
                0.9999993524050474,
                0.9999974387180947,
                0.9999992661792819,
                0.9999974387187054,
                0.9999994284992805,
                0.9999991684722698,
                0.9999986290432834,
                0.9999980052695652
            ],
            [
                0.9999910603047633,
                0.9999869928668873,
                0.9999984465016899,
                0.9999485577618773,
                0.9999852610233055,
                0.9999970976876689,
                0.9999930377429215,
                0.9999977396748941,
                0.9999724643056358,
                0.9999980052700408
            ],
            [
                0.9999989322967482,
                0.9999984465016899,
                0.999997097686977,
                0.9999974387180947,
                0.9999990577550691,
                0.9999962733598275,
                0.9999987901338838,
                0.9999990577551815,
                0.9999982396561572,
                0.9999987901337396
            ],
            [
                0.9999986290424663,
                0.9999987901341723,
                0.9999938558275957,
                0.9999996072138465,
                0.999997438717484,
                0.999999352405279,
                0.999999352405279,
                0.999997438717484,
                0.9999967112505427,
                0.9999930377454107
            ],
            [
                0.999999266178757,
                0.9999984465015047,
                0.9999957771680659,
                0.9999987901347492,
                0.9999990577555185,
                0.9999967112501509,
                0.999999789756684,
                0.9999987901344607,
                0.9999989322967482,
                0.999998005269803
            ],
            [
                0.9999724643023675,
                0.9999898700114384,
                0.9999938558268636,
                0.9999930377454114,
                0.9999945777803843,
                0.9999945777823239,
                0.9999930377462414,
                0.9999869928746427,
                0.9999991684722697,
                0.9999980052693275
            ],
            [
                0.9999995549148419,
                0.9999982396565769,
                0.999998446502801,
                0.9999996940978095,
                0.999999266179107,
                0.9999997617630616,
                0.9999938558239335,
                0.9999989322973845,
                0.999999554914842,
                0.9999990577551815
            ],
            [
                0.9999977396748938,
                0.9999984465016899,
                0.9999945777810304,
                0.999997438717484,
                0.9999974387177893,
                0.9999869928761888,
                0.9999967112509347,
                0.999993037740431,
                0.9999986290429567,
                0.9999967112517189
            ],
            [
                0.9999952149066464,
                0.9999930377420911,
                0.9999930377437507,
                0.999933947879035,
                0.9999646437408933,
                0.9999984465016899,
                0.9999991684721706,
                0.999997097688361,
                0.9999980052702786,
                0.9999974387177893
            ],
            [
                0.9999957771675627,
                0.9999869928684382,
                0.9999785550413688,
                0.9999967112509347,
                0.9999945777829702,
                0.9999938558239335,
                0.999995777168066,
                0.9999952149037944,
                0.9999991684718732,
                0.9999970976876689
            ],
            [
                0.9999945777816769,
                0.9999970976883608,
                0.9999992661788445,
                0.9999832985701973,
                0.9999984465022456,
                0.9999986290432835,
                0.9999945777784454,
                0.9999991684717742,
                0.9999989322972572,
                0.9999952149032242
            ],
            [
                0.999998446502801,
                0.9999962733620487,
                0.9999957771660521,
                0.999998446502801,
                0.9999982396565769,
                0.9999970976876691,
                0.9999930377437506,
                0.9999945777790915,
                0.9999980052705163,
                0.9999957771680658
            ],
            [
                0.9999910603068934,
                0.9999938558275963,
                0.9999417087136822,
                0.9999945777790921,
                0.999997097688361,
                0.999997097686977,
                0.9999957771665557,
                0.9999151889285072,
                0.9999852610180312,
                0.9999967112509348
            ],
            [
                0.9999885212264029,
                0.9999974387177893,
                0.9999930377404309,
                0.9999980052695652,
                0.999996273362049,
                0.9999957771670592,
                0.9999970976866309,
                0.9999832985781628,
                0.9999885212359809,
                0.9999885212332442
            ],
            [
                0.9999980052705163,
                0.9999832985781612,
                0.9999977396754327,
                0.9999921107336532,
                0.9999898700126442,
                0.9999974387184,
                0.9999869928684375,
                0.9999938558239339,
                0.9999967112501507,
                0.9999785550413688
            ],
            [
                0.9999957771645421,
                0.9999995549147889,
                0.9999989322970028,
                0.9999967112493666,
                0.9999982396572065,
                0.9999977396751633,
                0.9999980052695653,
                0.9999980052700408,
                0.9999962733616046,
                0.9999986290421395
            ],
            [
                0.9999977396762411,
                0.9999962733598275,
                0.9999980052700408,
                0.999997097686631,
                0.9999974387171787,
                0.9999785550439274,
                0.9999987901337396,
                0.9999995549147889,
                0.9999989322968754,
                0.9999852610215454
            ],
            [
                0.999995214904365,
                0.999993855827596,
                0.9999832985701962,
                0.9999952149037944,
                0.9999930377412616,
                0.9999987901341724,
                0.9999984465028011,
                0.9999996072136592,
                0.9999967112505429,
                0.999996273358939
            ],
            [
                0.9999910603005002,
                0.9999485577802758,
                0.999988521229141,
                0.9999646437324645,
                0.999985261018032,
                0.9999982396559474,
                0.9999990577550691,
                0.9999785550490427,
                0.9999994284996893,
                0.9999987901337396
            ],
            [
                0.9999989322970027,
                0.9999994284994167,
                0.9999977396757023,
                0.9999994284996891,
                0.9999974387187053,
                0.9999986290421395,
                0.9999984465020603,
                0.9999992661791944,
                0.9999991684720715,
                0.999997097689053
            ],
            [
                0.999991060299436,
                0.9999910603036972,
                0.9999724643187611,
                0.9999151889183183,
                0.999993037740431,
                0.9999974387180948,
                0.999998239656577,
                0.9999852610162737,
                0.9999810748495068,
                0.9999952149037942
            ],
            [
                0.9999885212346137,
                0.9999967112505429,
                0.9999898700041953,
                0.9999832985841333,
                0.9999938558246667,
                0.999994577781031,
                0.9999952149043648,
                0.9999938558232011,
                0.9999151889487236,
                0.9999957771645421
            ],
            [
                0.9999930377454106,
                0.999997097686977,
                0.9999952149037942,
                0.9999962733616045,
                0.9999970976880151,
                0.999995214903224,
                0.9999945777797377,
                0.9999967112497585,
                0.9999957771655488,
                0.9999910602994336
            ],
            [
                0.9998766054400504,
                0.9999687980923553,
                0.9999151889688683,
                0.9999417087067125,
                0.9999930377412608,
                0.9999967112517187,
                0.9998766054253101,
                0.9999038975622432,
                0.9999898700102287,
                0.9999417087345216
            ],
            [
                0.9999756997621694,
                0.9999869928715392,
                0.9999930377404305,
                0.9999485577802613,
                0.9999599362935033,
                0.999992110738355,
                0.9999921107374147,
                0.9999952149032237,
                0.9999810748562752,
                0.999995214904935
            ],
            [
                0.9999994284994167,
                0.9999952149037944,
                0.999999266179107,
                0.9999991684715759,
                0.9999977396748939,
                0.999997097686977,
                0.999997097686977,
                0.9999952149032239,
                0.9999987901344607,
                0.999997097687323
            ],
            [
                0.9998911030648799,
                0.9999930377462402,
                0.9999785550464837,
                0.9999485577802474,
                0.9998766054399318,
                0.9999810748540229,
                0.999996273358939,
                0.9999546021097292,
                0.9999251537371668,
                0.9998766053662896
            ],
            [
                0.9999982396572065,
                0.9999980052695652,
                0.9999852610233051,
                0.9999930377429213,
                0.9999991684721706,
                0.9999982396561572,
                0.9999957771645422,
                0.9999982396567867,
                0.9999980052695652,
                0.9999910603015664
            ],
            [
                0.9999994956527121,
                0.9999989322966208,
                0.9999967112505427,
                0.9999885212359813,
                0.9999984465015047,
                0.9999990577551815,
                0.9999967112513268,
                0.9999990577549568,
                0.999997097687323,
                0.9999987901338839
            ],
            [
                0.9999974387168733,
                0.9999599363174034,
                0.9999977396765105,
                0.999998005269803,
                0.9999984465016899,
                0.9999984465020603,
                0.9999987901344607,
                0.9999982396565769,
                0.9999984465024306,
                0.9999986290432835
            ],
            [
                0.9999952149032237,
                0.9999992661786696,
                0.9999945777784456,
                0.9999980052705164,
                0.999999266178757,
                0.9999982396559474,
                0.9999938558224696,
                0.9999987901346049,
                0.9999962733616047,
                0.9999967112497589
            ],
            [
                0.9999930377437511,
                0.9999970976866311,
                0.9999832985761679,
                0.9999984465015046,
                0.9999930377420908,
                0.9999957771675625,
                0.9999910603047624,
                0.9999930377429213,
                0.9999938558275957,
                0.9999957771660521
            ],
            [
                0.9999980052705164,
                0.9999852610162764,
                0.9999984465022455,
                0.9999885212359833,
                0.9999977396765106,
                0.9999938558246657,
                0.9999417087206438,
                0.9999982396572065,
                0.9999977396754328,
                0.9999952149043648
            ],
            [
                0.9999991684719723,
                0.9999991684720715,
                0.9999982396567867,
                0.9999957771655491,
                0.9999984465015047,
                0.9999962733602719,
                0.9999974387177893,
                0.9999991684722698,
                0.999986992873088,
                0.9999982396561571
            ],
            [
                0.9999984465015047,
                0.9999938558239339,
                0.9999977396757023,
                0.9999984465020604,
                0.9999986290421395,
                0.9999982396565769,
                0.9999980052705164,
                0.9999977396748939,
                0.9999992661792819,
                0.999999168471675
            ],
            [
                0.9999986290429566,
                0.9999970976883609,
                0.9999885212277717,
                0.9999962733620488,
                0.9999984465020603,
                0.9999957771655488,
                0.9999977396765106,
                0.9999989322973845,
                0.9999967112505427,
                0.9999991684720715
            ],
            [
                0.9999984465018751,
                0.9999991684715758,
                0.9999599362983067,
                0.9999984465016899,
                0.9999977396746244,
                0.9999974387168734,
                0.9999993524049703,
                0.9999980052709919,
                0.9999990577549568,
                0.9999989322968754
            ],
            [
                0.999993855822469,
                0.9999986290423029,
                0.9999982396574163,
                0.9999970976890529,
                0.9999984465020603,
                0.9999970976890528,
                0.9999970976890529,
                0.9999756997505969,
                0.9999990577556308,
                0.9999986290429566
            ],
            [
                0.9999986290431201,
                0.9999980052695652,
                0.9999984465020603,
                0.9999970976869773,
                0.9999990577554061,
                0.9999977396765106,
                0.9999832985761721,
                0.9999974387187054,
                0.9999970976873229,
                0.9999852610215472
            ],
            [
                0.999998446502801,
                0.9999982396561572,
                0.9999990577549569,
                0.9999977396748939,
                0.999998239656367,
                0.9999987901337396,
                0.9999987901343166,
                0.999998239656367,
                0.9999980052693275,
                0.9999986290424663
            ],
            [
                0.9999980052707542,
                0.9999994284997573,
                0.9999992661792819,
                0.9999989322967481,
                0.9999984465015047,
                0.9999987901343165,
                0.9999987901344607,
                0.999995777168066,
                0.9999986290427931,
                0.9999994284996211
            ],
            [
                0.9999989322975119,
                0.9999992661786696,
                0.9999992661787571,
                0.9999977396748938,
                0.9999991684717742,
                0.9999996072136592,
                0.9999990577549568,
                0.9999991684719723,
                0.999999057755743,
                0.9999984465020603
            ],
            [
                0.9999984465026159,
                0.9999982396567867,
                0.999993855824666,
                0.999981074844998,
                0.9999869928761911,
                0.9999982396565769,
                0.9999989322970028,
                0.9999151889689214,
                0.9999930377412616,
                0.9999982396559474
            ],
            [
                0.9999962733616046,
                0.9999974387177893,
                0.999993855823934,
                0.9999910603047634,
                0.999997097686631,
                0.9999930377412611,
                0.9999974387184,
                0.9999974387184003,
                0.9999646437366672,
                0.9999982396574163
            ],
            [
                0.9999485577680127,
                0.9999687980997979,
                0.9999599362887237,
                0.9999785550592722,
                0.9999599362887345,
                0.9999885212291416,
                0.9999810748449955,
                0.9999921107402361,
                0.9999724642957865,
                0.9999151889385525
            ]
        ]
    },
    {
        "q_id": "8246_mmlu_math",
        "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,
            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": [
            [
                1.1478769492642663e-05,
                8.939697368663308e-06,
                7.889265405849647e-06,
                3.7266406165319545e-06,
                3.72664017246987e-06,
                6.144176065582494e-06,
                6.962253758916883e-06,
                4.222835457852533e-06,
                3.7266397282926013e-06,
                4.785093353187292e-06
            ],
            [
                0.9999962733616047,
                0.9999930377412621,
                0.9999898700114359,
                0.9999869928746481,
                0.9999810748427463,
                0.9999810748472581,
                0.9999930377454118,
                0.9999957771645422,
                0.9999945777790923,
                0.9999785550567378
            ],
            [
                0.9999977396759717,
                0.9999885212318759,
                0.9999945777829703,
                0.9999977396751636,
                0.9999962733616052,
                0.9999977396757023,
                0.9999991684717741,
                0.9999938558253989,
                0.9999967112513268,
                0.999993855825399
            ],
            [
                0.9999982396574163,
                0.9999938558268652,
                0.9999987901341723,
                0.9999970976890534,
                0.9999967112493667,
                0.9999952149037962,
                0.9999974387174841,
                0.9999970976890532,
                0.9999974387168735,
                0.9999957771655494
            ],
            [
                4.222832940577472e-06,
                4.222833444283541e-06,
                6.144176066051891e-06,
                1.4738978434119307e-05,
                5.4222196154940574e-06,
                6.962257908753841e-06,
                3.726638839656906e-06,
                1.0129989771288745e-05,
                3.7266388394569345e-06,
                6.144174601410037e-06
            ],
            [
                6.962258738283349e-06,
                5.4222215550004564e-06,
                4.222834954134701e-06,
                5.422218322851817e-06,
                4.222833444168322e-06,
                5.422220262264056e-06,
                5.422217030288788e-06,
                6.144176798870286e-06,
                4.7850950647493785e-06,
                4.7850956351657615e-06
            ],
            [
                0.9999151889586856,
                0.999997097686631,
                0.9999982396574163,
                0.9999970976880153,
                0.9999984465026159,
                0.9999982396574163,
                0.999998790134028,
                0.99999862904312,
                0.9999987901347492,
                0.9999957771665555
            ],
            [
                6.144176066443055e-06,
                3.726641061027928e-06,
                6.962257908487893e-06,
                2.902311985079115e-06,
                2.7535681238877168e-05,
                2.260324028404236e-06,
                7.88926634644516e-06,
                6.14417313680765e-06,
                2.5612812946681295e-06,
                8.9396994983433e-06
            ],
            [
                0.9999977396751637,
                0.9999938558232011,
                0.9999970976887068,
                0.9999990577550691,
                0.9999832985701967,
                0.9999962733602717,
                0.9999982396561572,
                0.9999974387177893,
                0.9999546021476502,
                0.9999952149055057
            ],
            [
                6.962254589433702e-06,
                4.22283344433731e-06,
                5.422220261948442e-06,
                5.422221554670048e-06,
                1.1478764018305152e-05,
                6.962257908196617e-06,
                5.422221555133606e-06,
                2.2603245672497918e-06,
                4.785093924047376e-06,
                1.1478772225981004e-05
            ],
            [
                2.5612819053166966e-06,
                1.1478766754064213e-05,
                8.939696303010449e-06,
                4.222834451065997e-06,
                7.889264464508026e-06,
                8.939697367037201e-06,
                1.3007131562845248e-05,
                6.144173869072478e-06,
                3.2887506334560605e-06,
                6.9622579075254155e-06
            ],
            [
                4.222835457906302e-06,
                6.144172403928222e-06,
                3.2887498493325602e-06,
                4.222835457906302e-06,
                7.889264465986113e-06,
                4.785096775998733e-06,
                4.222834954607099e-06,
                5.422221554926484e-06,
                2.5612822106654943e-06,
                1.892514823364471e-05
            ],
            [
                0.9999921107364753,
                0.9999910603058275,
                0.9999938558224686,
                0.9999910603036979,
                0.9999885212332513,
                0.9999869928653464,
                0.9999810748472673,
                0.9999724642990738,
                0.9999952149037948,
                0.9999852610215495
            ],
            [
                2.902311985079115e-06,
                7.88926634687567e-06,
                6.962258738701267e-06,
                2.9023112930949896e-06,
                5.422218969029887e-06,
                4.785094494463623e-06,
                3.2887494573232236e-06,
                3.726640616670918e-06,
                2.1444940736477737e-05,
                4.785096205512581e-06
            ],
            [
                1.4738978452886064e-05,
                7.8892654060075e-06,
                1.4738976696800444e-05,
                1.4738988993050295e-05,
                0.9626731089077047,
                3.535625067177463e-05,
                6.962253759157502e-06,
                4.222834954461155e-06,
                3.2887494572095624e-06,
                4.785095635296322e-06
            ],
            [
                0.9999982396559474,
                0.9999970976890531,
                0.9999986290423029,
                0.9999974387177895,
                0.9999938558246669,
                0.9999977396759717,
                0.9999991684722698,
                0.9999986290432835,
                0.9999982396563671,
                0.9999992661789321
            ],
            [
                8.939696302051047e-06,
                3.2887486728201357e-06,
                7.338211554688417e-07,
                6.475947981975644e-07,
                3.726640172120768e-06,
                8.31528126775552e-07,
                5.42221961567159e-06,
                1.2098662604049616e-06,
                9.422447061953531e-07,
                1.553498310118888e-06
            ],
            [
                4.785093353687772e-06,
                6.962258738701267e-06,
                8.939698433974813e-06,
                5.422217030362759e-06,
                3.288750633545794e-06,
                1.1478770861211786e-05,
                7.88926070328992e-06,
                5.422221555069497e-06,
                7.889266346603015e-06,
                8.93969843377968e-06
            ],
            [
                0.9999785550592659,
                0.9999930377404334,
                0.9999898700054003,
                0.9999984465015047,
                0.9999885212305103,
                0.9999970976880149,
                0.9999599363126355,
                0.9999898700126474,
                0.9999785550515878,
                0.9999974387174841
            ],
            [
                0.9999869928730897,
                0.99999844650169,
                0.9999967112505428,
                0.9999980052702787,
                0.999996711251719,
                0.9999974387168735,
                0.9999952149037953,
                0.9999957771650455,
                0.9999962733593839,
                0.9999957771660526
            ],
            [
                0.999997097687323,
                0.9995694430122656,
                0.9999921107374158,
                0.9999938558268645,
                0.999978555046496,
                0.9999921107374165,
                0.9999962733593833,
                0.9999921107336539,
                0.9999832985741823,
                0.9999938558232021
            ],
            [
                0.9999756997505892,
                0.9999910603004999,
                0.9999646437450908,
                0.999989870011436,
                0.9999810748562764,
                0.9999910603058291,
                0.999972464315498,
                0.999959936322189,
                0.9999921107374157,
                0.9999930377454113
            ],
            [
                4.222831934248571e-06,
                6.9622562489985925e-06,
                3.726638839656906e-06,
                5.422217676575195e-06,
                3.2887486731252264e-06,
                6.9622537587775775e-06,
                8.939697368842181e-06,
                2.9023126769762986e-06,
                6.9622537587775775e-06,
                7.889263525261671e-06
            ],
            [
                3.2887506334201674e-06,
                3.2887502412970765e-06,
                6.9622537584863015e-06,
                4.785094494402695e-06,
                6.144175334094145e-06,
                1.4738983722270186e-05,
                3.726638395320497e-06,
                1.1478766756214804e-05,
                2.4300249391876106e-05,
                3.2887498492936755e-06
            ],
            [
                0.9999885212277764,
                0.9999952149037942,
                0.999991060304764,
                0.9999910603036997,
                0.9999898700041926,
                0.9999810748450013,
                0.9999938558261315,
                0.9999898700090262,
                0.999996273358939,
                0.999998239656577
            ],
            [
                2.5612812944538183e-06,
                7.88925976283858e-06,
                6.144173136556186e-06,
                2.1444940740066406e-05,
                3.2887506332945414e-06,
                8.939700566289352e-06,
                2.902311985079115e-06,
                1.994729721469003e-06,
                1.6701419850389357e-05,
                2.9023130230133794e-06
            ],
            [
                4.7850933534310035e-06,
                4.785094494576774e-06,
                4.222834451215781e-06,
                3.7266397281434697e-06,
                5.4222183231674305e-06,
                6.962258738283349e-06,
                6.962259569003389e-06,
                4.785095635017795e-06,
                8.939694170518055e-06,
                1.4738976697229395e-05
            ],
            [
                0.9999938558275968,
                0.9999990577550691,
                0.9999938558253989,
                0.9999832985821424,
                0.9999957771665566,
                0.9999967112513267,
                0.99998107485853,
                0.9999921107345946,
                0.9999974387180949,
                0.999996711252111
            ],
            [
                0.9999980052707542,
                0.9999945777790917,
                0.999997097689053,
                0.9999977396751634,
                0.9999962733598279,
                0.9999938558253995,
                0.9999970976869772,
                0.9999957771680661,
                0.9999962733607166,
                0.9999967112493667
            ],
            [
                0.9999994284993485,
                0.999995777166053,
                0.999997438718095,
                0.9999869928684351,
                0.9999957771675625,
                0.9999962733620495,
                0.9999945777803845,
                0.9999991684718732,
                0.9999980052693275,
                0.9999977396765106
            ],
            [
                0.9999970976869771,
                0.9999967112509351,
                0.9999967112517192,
                0.999996711249367,
                0.9999970976876693,
                0.9999898700053977,
                0.9999957771645431,
                0.9999967112501513,
                0.9999982396569966,
                0.9999970976880151
            ],
            [
                6.962253759043525e-06,
                6.962257909007124e-06,
                2.9023109469842055e-06,
                6.144175333926503e-06,
                2.5612812945260317e-06,
                1.553498495338299e-06,
                5.422218322940583e-06,
                3.7266383953679482e-06,
                2.902313368897403e-06,
                6.962253758017727e-06
            ],
            [
                0.9999910603026337,
                0.9999974387171788,
                0.9999930377404322,
                0.9999898700078149,
                0.9999962733593841,
                0.9999977396748939,
                0.9999921107374177,
                0.9999852610127582,
                0.9999989322975119,
                0.9999938558246677
            ],
            [
                3.7266406163624873e-06,
                6.144172404028807e-06,
                8.939700565102295e-06,
                3.726640616630245e-06,
                4.785096205651846e-06,
                1.4738985475943776e-05,
                6.144177530794679e-06,
                6.962257079173776e-06,
                6.144173869240119e-06,
                6.144173136645595e-06
            ],
            [
                1.4738983725406915e-05,
                5.829129321322935e-05,
                1.9947297214544894e-06,
                1.6701415866188347e-05,
                1.2098653950480359e-06,
                1.7603432132784448e-06,
                4.222833947498071e-06,
                3.7266388395111645e-06,
                1.30071315602427e-05,
                6.962258738283349e-06
            ],
            [
                0.99973880959746,
                0.9998601779759694,
                0.9999921107345966,
                0.9999687980849105,
                0.9999885212332504,
                0.9999970976883609,
                0.9999921107345933,
                0.9999756997534802,
                0.9999952149066471,
                0.9999930377437514
            ],
            [
                0.9999974387187054,
                0.9999952149049356,
                0.9999970976876693,
                0.9999869928746372,
                0.9999970976866313,
                0.9999962733620488,
                0.999996273361605,
                0.9999995549149481,
                0.9999930377429204,
                0.9999970976880149
            ],
            [
                0.9999930377412614,
                0.9999989322975118,
                0.9999974387168735,
                0.9999982396559474,
                0.9999957771675634,
                0.999996273361161,
                0.9999989322972572,
                0.999995777165046,
                0.9999980052695654,
                0.999983298582142
            ],
            [
                6.9622579086271995e-06,
                2.260323758835034e-06,
                2.7535700933696396e-05,
                4.222835457906302e-06,
                5.422218969306048e-06,
                4.785094494185095e-06,
                5.422218323093458e-06,
                4.785092783149804e-06,
                3.7266397280960194e-06,
                7.889264465986113e-06
            ],
            [
                0.9999977396757024,
                0.9999982396561572,
                0.9999967112521112,
                0.9999957771670593,
                0.9999910603026332,
                0.9999980052707544,
                0.9999962733611617,
                0.999989870005401,
                0.9999921107336557,
                0.9999970976880158
            ],
            [
                0.999997097687323,
                0.9999952149037944,
                0.999994577779739,
                0.9999974387174843,
                0.9999974387168734,
                0.9999921107336559,
                0.9999930377462434,
                0.9999967112501511,
                0.9999957771680659,
                0.9999982396559474
            ],
            [
                0.9999930377437514,
                0.9999417087136911,
                0.999989870007814,
                0.9999910603026321,
                0.999991060300501,
                0.9999485577679615,
                0.9999810748540331,
                0.9999898700078145,
                0.9999898700066077,
                0.9999724642990628
            ],
            [
                4.222833444283541e-06,
                2.5612815998491325e-06,
                3.288749065209246e-06,
                4.7850933534310035e-06,
                5.422218969463855e-06,
                4.785096776133645e-06,
                6.962256248871951e-06,
                6.144173868983067e-06,
                5.422220908402905e-06,
                6.962258738435319e-06
            ],
            [
                0.999996273359828,
                0.9999724642957877,
                0.9999898700126435,
                0.9999962733593837,
                0.9999982396567868,
                0.9999938558246666,
                0.9999885212277724,
                0.9999962733607165,
                0.9999957771650457,
                0.9999957771670592
            ],
            [
                0.9999921107392981,
                0.99997855505672,
                0.9999952149037954,
                0.9999952149072172,
                0.9999910603058331,
                0.9999898700090254,
                0.9999930377429226,
                0.9999957771650457,
                0.9999921107364748,
                0.9999930377445817
            ],
            [
                2.2603242978213447e-06,
                2.902311292920774e-06,
                6.962254589104433e-06,
                6.1441775312976045e-06,
                4.785093923768848e-06,
                4.785092783267308e-06,
                4.785096776133645e-06,
                1.3007126910649678e-05,
                2.5612831265630198e-06,
                8.939699498099386e-06
            ],
            [
                2.144494329496561e-05,
                8.939700564468113e-06,
                4.222833444168322e-06,
                3.7266397281434697e-06,
                2.902311293034278e-06,
                5.422220262264056e-06,
                7.889266346603015e-06,
                4.222834451215781e-06,
                1.0129995808418327e-05,
                6.144173868670137e-06
            ],
            [
                2.9023112930949896e-06,
                5.4222202621161125e-06,
                7.889260703462123e-06,
                3.7266397280960194e-06,
                3.2887494573561262e-06,
                8.93969310584124e-06,
                7.8892654060075e-06,
                1.5534971989696065e-06,
                8.939696301384342e-06,
                6.962257909007124e-06
            ],
            [
                0.9999967112505432,
                0.9999945777797382,
                0.9999921107336528,
                0.9999930377404336,
                0.9999885212332477,
                0.9999957771670598,
                0.9999832985701994,
                0.9999982396561572,
                0.9999930377429207,
                0.999997097688015
            ],
            [
                1.4738980210258757e-05,
                6.144176798255599e-06,
                6.144176798132662e-06,
                6.962257908880483e-06,
                2.9023119851266288e-06,
                2.1444958621558693e-05,
                3.7266401722360055e-06,
                3.7266397281434697e-06,
                2.9023123310290063e-06,
                5.422217676200406e-06
            ],
            [
                0.9999930377454113,
                0.9999957771660528,
                0.9999986290429566,
                0.9999930377462414,
                0.9999832985721934,
                0.9999938558246662,
                0.999997097689053,
                0.9999910603058334,
                0.999996273358939,
                0.999992110733654
            ],
            [
                0.9999921107345945,
                0.9999930377437524,
                0.9999417087414969,
                0.9999977396759716,
                0.9999986290429567,
                0.9999980052707542,
                0.9999970976883611,
                0.9999938558239339,
                0.9999687980849431,
                0.9999982396569966
            ],
            [
                1.1478765384054893e-05,
                1.9947306726358406e-06,
                7.889261643382609e-06,
                4.222834451012227e-06,
                6.144175333926503e-06,
                4.785093924047376e-06,
                4.78509563466093e-06,
                6.144174600862407e-06,
                3.7266397281434697e-06,
                3.726639727994339e-06
            ],
            [
                2.902312677084523e-06,
                1.6701429799367125e-05,
                7.889261644760245e-06,
                3.7266401724291984e-06,
                1.0129992185060374e-05,
                6.962259568509485e-06,
                3.7266383954560706e-06,
                4.785096776251149e-06,
                2.561283126639892e-06,
                8.93970056529743e-06
            ],
            [
                0.999997097687323,
                0.9999962733611605,
                0.9999962733620493,
                0.999996273361605,
                0.9999952149060767,
                0.9999921107364788,
                0.9999977396746245,
                0.9999974387174841,
                0.9999921107336567,
                0.9999910603036993
            ],
            [
                1.3007130010922344e-05,
                2.5612825159677387e-06,
                4.785096205717126e-06,
                6.962257908753841e-06,
                1.0129987354108855e-05,
                8.93969523678858e-06,
                7.889262584350785e-06,
                4.7850944945245504e-06,
                5.422220262264056e-06,
                3.726639283806955e-06
            ],
            [
                1.994730434735237e-06,
                1.5534975693205863e-06,
                3.2887490649759413e-06,
                2.5612822106654943e-06,
                1.5534975693347152e-06,
                2.5612828211442287e-06,
                3.2887498492518007e-06,
                4.222832940834793e-06,
                2.5612825157464395e-06,
                3.7266388394569345e-06
            ],
            [
                0.999994577779092,
                0.9999869928761884,
                0.9999921107345956,
                0.9999938558275977,
                0.9999962733607163,
                0.999993855823202,
                0.9999938558246669,
                0.9999970976876691,
                0.9999970976890533,
                0.9999930377437526
            ],
            [
                1.3007131559816827e-05,
                7.88926446430712e-06,
                4.785093924103951e-06,
                3.1201922508819695e-05,
                8.939700564468113e-06,
                7.889263524960312e-06,
                1.0129993391808207e-05,
                2.9023126768680736e-06,
                4.785095064819011e-06,
                5.144220129803702e-05
            ],
            [
                3.7266388396128453e-06,
                5.422218969217281e-06,
                5.422221554374162e-06,
                1.473898196677375e-05,
                7.889260703117714e-06,
                7.889262584006375e-06,
                6.144174601208867e-06,
                6.9622579092224155e-06,
                5.422221555069497e-06,
                5.422220908402905e-06
            ],
            [
                8.939696301839653e-06,
                4.222832437443716e-06,
                3.2887494573232236e-06,
                1.4738976697229395e-05,
                3.7266379512112265e-06,
                6.144173868670137e-06,
                5.422218969306048e-06,
                5.422220908703723e-06,
                6.144176066264237e-06,
                7.889264465699106e-06
            ],
            [
                6.962258738827909e-06,
                6.962257908753841e-06,
                1.0129995809247506e-05,
                6.962255418658875e-06,
                6.144176066264237e-06,
                1.012999459934851e-05,
                5.422220908560712e-06,
                6.962258739169842e-06,
                1.0677029973114952e-06,
                6.9622562487453084e-06
            ],
            [
                3.7266379512112265e-06,
                3.7266392838544054e-06,
                2.5612825160096693e-06,
                8.939700565102295e-06,
                3.726639283806955e-06,
                2.9023112930659533e-06,
                6.962255419380732e-06,
                2.9023109471452223e-06,
                2.5612812943280275e-06,
                7.889263524960312e-06
            ],
            [
                4.222834954403545e-06,
                5.422220908314139e-06,
                6.144177530794679e-06,
                7.889266347133978e-06,
                4.222835458044565e-06,
                5.422220262195015e-06,
                6.9622570784012604e-06,
                7.889263524443698e-06,
                5.4222202617511845e-06,
                4.785096775998733e-06
            ],
            [
                5.422217030032353e-06,
                8.939695237504067e-06,
                6.962258738701267e-06,
                2.7535681236473055e-05,
                6.144177531532303e-06,
                4.785094494402695e-06,
                3.7266406167827664e-06,
                5.4222183231674305e-06,
                1.0129995807441742e-05,
                6.144176066353646e-06
            ],
            [
                0.9999974387165682,
                0.9999810748495063,
                0.999997097689053,
                0.999996273360272,
                0.999997739674894,
                0.9999938558246665,
                0.9999984465022455,
                0.999978555043919,
                0.9999957771670592,
                0.9999962733593835
            ],
            [
                0.9999977396748941,
                0.9999974387168736,
                0.9999962733620497,
                0.9999991684720715,
                0.9999967112501514,
                0.9999984465028011,
                0.9999974387165683,
                0.9999984465028011,
                0.99999844650169,
                0.9999984465020604
            ],
            [
                0.9999967112493668,
                0.9999970976876694,
                0.9999984465020603,
                0.9999832985821381,
                0.9999967112521106,
                0.9999962733607161,
                0.9999945777829707,
                0.999995777166556,
                0.9999417087553398,
                0.9999687980997913
            ],
            [
                1.994730196992497e-06,
                4.7850950649408664e-06,
                2.5612825159421147e-06,
                8.939696301611998e-06,
                1.1478773596847203e-05,
                4.222831933864508e-06,
                7.889264465699106e-06,
                4.785092783149804e-06,
                1.3007131562845248e-05,
                3.726638395320497e-06
            ],
            [
                0.9999945777816776,
                0.9999977396751634,
                0.9999938558224701,
                0.9999957771675629,
                0.9999885212305081,
                0.9999938558239342,
                0.9999921107392983,
                0.9999938558232018,
                0.9999945777803843,
                0.9999885212346129
            ],
            [
                0.9999962733598278,
                0.9999898700102298,
                0.9999885212318786,
                0.999991060302634,
                0.9999485577986705,
                0.9999938558261329,
                0.9999945777790924,
                0.9999952149055064,
                0.9999970976869776,
                0.9999967112497591
            ],
            [
                3.7266383954560706e-06,
                2.5612822106654943e-06,
                6.1441767989541075e-06,
                4.785095635296322e-06,
                1.1478766754377407e-05,
                4.7850950649408664e-06,
                6.9622537584863015e-06,
                6.962257078249291e-06,
                3.7266410608720178e-06,
                5.422218969463855e-06
            ],
            [
                0.9999898700078153,
                0.9999970976869773,
                0.9999957771675635,
                0.9999756997592842,
                0.9999977396746246,
                0.9999938558239347,
                0.9999962733593838,
                0.9999910603005021,
                0.9999993524050474,
                0.9999885212264057
            ],
            [
                4.2228319341064674e-06,
                6.144174601410037e-06,
                4.7850944942634305e-06,
                2.9023133689317184e-06,
                1.9947297214544894e-06,
                8.939695237959376e-06,
                6.962257908880483e-06,
                2.2603251061664e-06,
                6.144176066353646e-06,
                1.370957370247318e-06
            ],
            [
                4.2228319339950885e-06,
                2.9023109470871505e-06,
                6.962258739169842e-06,
                8.939693105467234e-06,
                5.422220908402905e-06,
                1.473898372275276e-05,
                1.99472995920443e-06,
                2.7535691080725503e-05,
                1.0129993393540266e-05,
                5.422220261652556e-06
            ],
            [
                1.3007125360146898e-05,
                8.939700564468113e-06,
                6.144172403470001e-06,
                8.939698432917844e-06,
                8.939697368305565e-06,
                7.889266346129453e-06,
                7.8892625849535e-06,
                1.6701423829123058e-05,
                1.4738978452886064e-05,
                1.8925155000025902e-05
            ],
            [
                7.889263524788109e-06,
                1.147877222879974e-05,
                7.889266346746518e-06,
                1.3007130011655787e-05,
                6.1441760654483806e-06,
                5.422218322851817e-06,
                6.144176066521288e-06,
                4.785096205260165e-06,
                1.6701419850389357e-05,
                5.422220908634683e-06
            ],
            [
                0.9999974387168734,
                0.9999986290421395,
                0.9999991684720715,
                0.9999921107345949,
                0.9999930377462403,
                0.9999987901346049,
                0.9999952149043656,
                0.999998005270992,
                0.9999974387187054,
                0.9999938558275973
            ],
            [
                0.9999974387180948,
                0.999995777165549,
                0.9999938558224686,
                0.9999987901343166,
                0.9999930377454109,
                0.9999977396746244,
                0.9999990577556308,
                0.9999945777803844,
                0.9999687980960708,
                0.9999977396746244
            ],
            [
                0.9999970976873231,
                0.9999938558232021,
                0.999998239656367,
                0.9999967112505428,
                0.999999057755069,
                0.9999898700066084,
                0.9999980052702786,
                0.9999990577551815,
                0.9999952149037946,
                0.999995214903795
            ],
            [
                0.9999987901338838,
                0.9999785550490299,
                0.9999990577549568,
                0.999876605454541,
                0.9999938558253993,
                0.9999952149043648,
                0.9999994284994848,
                0.9999921107355368,
                0.9999930377437515,
                0.9999930377420918
            ],
            [
                7.889263525261671e-06,
                4.222835457664342e-06,
                6.962258738701267e-06,
                1.3007133112662637e-05,
                4.222832437443716e-06,
                6.144173869072478e-06,
                1.012999460150437e-05,
                7.889264465239894e-06,
                6.962259567914269e-06,
                6.962257079059797e-06
            ],
            [
                0.9999957771670596,
                0.9999724643122083,
                0.9999952149072174,
                0.9999869928684385,
                0.9999952149032242,
                0.9999977396746247,
                0.9999885212291469,
                0.9999970976876692,
                0.999981074845,
                0.9999938558275968
            ],
            [
                3.7266392839425286e-06,
                5.422217029736466e-06,
                2.260323758882316e-06,
                3.2887490653109436e-06,
                6.144174601097106e-06,
                8.939696302831578e-06,
                4.7850944943330625e-06,
                4.222833947674739e-06,
                3.7266410608720178e-06,
                4.7850927830845245e-06
            ],
            [
                0.9999869928653392,
                0.9999910603005011,
                0.9999832985841355,
                0.9999910603015666,
                0.9999885212264054,
                0.9999898700102291,
                0.9999885212305117,
                0.9999832985702067,
                0.9999852610110074,
                0.9999898700102304
            ],
            [
                1.0129992184544441e-05,
                1.0129995807441742e-05,
                5.4222202621161125e-06,
                5.422220908481809e-06,
                7.889263524788109e-06,
                7.88926164421493e-06,
                4.222833444168322e-06,
                1.9947301970287804e-06,
                2.9023133689317184e-06,
                6.962253757840428e-06
            ],
            [
                0.9999957771655492,
                0.9999984465026158,
                0.9999982396567868,
                0.9999982396574163,
                0.9999930377404328,
                0.9999974387177897,
                0.9999987901337396,
                0.9999921107392964,
                0.9999957771665559,
                0.999994577782324
            ],
            [
                0.9999930377445807,
                0.999975699765066,
                0.9999957771650467,
                0.999998790134028,
                0.9999930377412649,
                0.9999962733598294,
                0.999996711250935,
                0.9999962733589396,
                0.9999980052702787,
                0.999997438717179
            ],
            [
                0.9999970976873234,
                0.9999970976876692,
                0.9999952149043653,
                0.9999974387187053,
                0.9999970976869772,
                0.004070137266649395,
                0.9999957771670596,
                0.9999930377454136,
                0.999996711249759,
                0.9999967112501509
            ],
            [
                5.422221554670048e-06,
                3.7266397281434697e-06,
                3.2887502412970765e-06,
                6.962258739169842e-06,
                2.902313023039776e-06,
                4.222831934156396e-06,
                3.7266406165827946e-06,
                3.7266410609940346e-06,
                3.726641060773727e-06,
                4.222833444283541e-06
            ],
            [
                0.9999992661790195,
                0.9999987901338838,
                0.9999967112521109,
                0.9999989322972572,
                0.9999982396561572,
                0.9999974387180951,
                0.9999952149037944,
                0.9999974387171788,
                0.9999980052693276,
                0.9999989322973846
            ],
            [
                4.22283394762097e-06,
                6.962256249112569e-06,
                7.889261644875049e-06,
                6.144176798255599e-06,
                1.5534975693488444e-06,
                5.422220262037209e-06,
                3.2887486732000038e-06,
                4.2228319341064674e-06,
                1.3007130010543792e-05,
                4.785093353687772e-06
            ],
            [
                3.2887486729876365e-06,
                1.994730434847717e-06,
                4.785096205582214e-06,
                5.422218322457301e-06,
                7.889259763728304e-06,
                7.889264465986113e-06,
                2.56128159999123e-06,
                1.1478768120315386e-05,
                6.96225873895455e-06,
                4.7850944945245504e-06
            ],
            [
                0.9999810748562764,
                0.99999893229713,
                0.9999980052707542,
                0.9999756997650677,
                0.999994577782324,
                0.9999810748540158,
                0.9999852610110022,
                0.9999980052705165,
                0.9999869928715378,
                0.9999485577618628
            ],
            [
                7.88926258381982e-06,
                6.144173135483279e-06,
                1.4738976696800444e-05,
                1.4738980202752053e-05,
                4.222833947428939e-06,
                1.0129988561906404e-05,
                1.0129994596087078e-05,
                7.88926634687567e-06,
                8.939695235959266e-06,
                1.1478772227338172e-05
            ],
            [
                0.9999974387174841,
                0.9999852610180304,
                0.9999930377462408,
                0.9999967112517189,
                0.9999980052700408,
                0.9999977396765105,
                0.9999785550515988,
                0.9999921107402364,
                0.999996273360272,
                0.9999832985781612
            ],
            [
                0.9999930377429218,
                0.9999756997476946,
                0.999998005269803,
                0.9999885212264035,
                0.9999945777803856,
                0.9999885212305086,
                0.9999869928715392,
                0.999993855824667,
                0.9999921107392973,
                0.9999910603047645
            ],
            [
                3.726637950851956e-06,
                8.9396941702904e-06,
                4.222834954514924e-06,
                2.9023116390104826e-06,
                4.222834954461155e-06,
                8.939696302831578e-06,
                2.5612825159677387e-06,
                2.2603242978007868e-06,
                1.0129988562164371e-05,
                2.1444953521586782e-05
            ],
            [
                1.760342583722268e-06,
                1.0129993393945642e-05,
                6.962254588585202e-06,
                4.785096775676685e-06,
                1.1478768120315386e-05,
                6.962257909121104e-06,
                8.939699499627926e-06,
                3.7266379512112265e-06,
                4.222831933864508e-06,
                8.939697368110433e-06
            ],
            [
                1.4738976696371488e-05,
                7.88925976283858e-06,
                5.422218322851817e-06,
                6.962253759043525e-06,
                5.422220262195015e-06,
                7.889262584350785e-06,
                3.2887498493325602e-06,
                2.5612812945260317e-06,
                5.422217676397663e-06,
                6.144174601309452e-06
            ],
            [
                6.9622562492265485e-06,
                6.962258738701267e-06,
                1.1478770859917257e-05,
                6.9622562492265485e-06,
                1.3007131562845248e-05,
                2.561283126639892e-06,
                4.22283545795623e-06,
                3.726640616670918e-06,
                3.726641060956752e-06,
                2.561282515988704e-06
            ],
            [
                0.9999898700066103,
                0.999996273362049,
                0.9999852610127629,
                0.9999885212305122,
                0.9999921107383554,
                0.9999832985702084,
                0.9999756997505835,
                0.9999930377404321,
                0.9999952149055062,
                0.9999952149032246
            ],
            [
                3.2887502413389517e-06,
                3.726640616630245e-06,
                4.222833444429485e-06,
                8.939693106182721e-06,
                3.7266401724291984e-06,
                6.144175333289463e-06,
                4.7850950643402904e-06,
                7.889260701467423e-06,
                5.422220908481809e-06,
                2.561283126639892e-06
            ],
            [
                0.9999952149066469,
                0.9999945777829703,
                0.9999970976887068,
                0.9999945777803847,
                0.9999945777823237,
                0.9999962733598281,
                0.9999898700078153,
                0.9999967112505428,
                0.9999967112513272,
                0.9999962733589393
            ],
            [
                0.999998005270992,
                0.9999962733589393,
                0.9999967112497591,
                0.9999945777829701,
                0.9999938558268644,
                0.999993855826132,
                0.9999945777810308,
                0.9999832985781659,
                0.999986992876195,
                0.9999885212359899
            ],
            [
                6.144176066051891e-06,
                8.939694171331106e-06,
                4.7850927830845245e-06,
                1.670142781244497e-05,
                1.300713156215912e-05,
                7.889265406151004e-06,
                7.889263524615903e-06,
                8.939699498814873e-06,
                5.422218322940583e-06,
                5.422221554374162e-06
            ],
            [
                1.670142979997471e-05,
                4.7850950647493785e-06,
                4.222833947674739e-06,
                3.2887490652810324e-06,
                4.222832437443716e-06,
                2.9023119846303784e-06,
                1.892514821904893e-05,
                2.5612819051373276e-06,
                2.2603234894560207e-06,
                6.1441753335241615e-06
            ],
            [
                4.222833947774596e-06,
                1.7603430034311638e-06,
                1.7603432132784448e-06,
                1.76034363298589e-06,
                5.422220908560712e-06,
                1.9947290080343035e-06,
                4.2228319341064674e-06,
                7.889260703763482e-06,
                5.422219614705025e-06,
                6.9622545892184106e-06
            ],
            [
                0.9999970976866313,
                0.999996273361605,
                0.9999982396572065,
                0.9999962733589393,
                0.9999970976890531,
                0.9999962733602723,
                0.9999974387174843,
                0.9999952149060768,
                0.9999989322967482,
                0.9999952149060767
            ],
            [
                0.999995214906647,
                0.9999832985701949,
                0.999999057755743,
                0.999989870006605,
                0.9999938558224697,
                0.9999967112501508,
                0.9999990577550691,
                0.9999974387168735,
                0.9999938558239337,
                0.9999952149049355
            ],
            [
                0.9999938558261329,
                0.9999952149066472,
                0.9999952149049366,
                0.9999967112505429,
                0.999995777165549,
                0.9999970976876692,
                0.9999980052695653,
                0.9999962733598287,
                0.9999938558232011,
                0.9999974387171788
            ],
            [
                0.9999957771665562,
                0.9999970976869772,
                0.9999869928730875,
                0.9999984465024306,
                0.9997694933129977,
                0.9999910603015684,
                0.9999974387171787,
                0.9999921107364741,
                0.9999898700054024,
                0.9999952149060763
            ],
            [
                0.9999957771670596,
                0.999998005269803,
                0.9999980052702786,
                0.9999980052707541,
                0.9999869928761884,
                0.9999952149049358,
                0.9999869928684382,
                0.9999957771660528,
                0.9999970976869772,
                0.9999991684718732
            ],
            [
                2.5612822106421996e-06,
                5.422221554847581e-06,
                3.7266379512112265e-06,
                1.3007134662432895e-05,
                1.473898899664279e-05,
                2.260324567268294e-06,
                6.962257908487893e-06,
                6.962253759043525e-06,
                6.962259568775433e-06,
                4.2228319339950885e-06
            ],
            [
                0.9999967112517191,
                0.9999991684720715,
                0.9999852610145185,
                0.9999957771670596,
                0.9999991684722698,
                0.9999967112501509,
                0.9999921107392978,
                0.9999977396746244,
                0.9999885212359833,
                0.9999898700066088
            ],
            [
                0.9999646437619467,
                0.9999957771655492,
                0.9999967112509348,
                0.999994577779738,
                0.9999952149032248,
                0.999996711250151,
                0.9999921107364764,
                0.9999990577549568,
                0.9999938558268644,
                0.9999945777816776
            ],
            [
                0.9999974387171789,
                0.9999974387177895,
                0.9999986290426298,
                0.9999984465020604,
                0.9999986290421395,
                0.9999984465026159,
                0.9999982396563671,
                0.9999967112493666,
                0.9999984465026159,
                0.9999977396762412
            ],
            [
                1.8925143721072897e-05,
                3.2887494573561262e-06,
                1.4738983726559732e-05,
                5.422218323231539e-06,
                3.7266383953679482e-06,
                1.3007130010922344e-05,
                5.422218323019487e-06,
                4.222833947728508e-06,
                4.7850944942634305e-06,
                3.726639728184142e-06
            ],
            [
                0.9999938558268634,
                0.9999957771680663,
                0.9999945777797384,
                0.9999980052707543,
                0.9999898700102311,
                0.9999989322973846,
                0.9999930377404321,
                0.9999982396559474,
                0.9999930377429225,
                0.9999952149032243
            ],
            [
                4.222835457794923e-06,
                1.300712535865635e-05,
                4.2228344508893285e-06,
                6.962257908348587e-06,
                5.422220261948442e-06,
                6.9622570786798724e-06,
                5.422218968083048e-06,
                3.120190020204515e-05,
                2.5612819052654485e-06,
                4.222834954514924e-06
            ],
            [
                5.422218322851817e-06,
                4.785092782936557e-06,
                1.9947304348332037e-06,
                2.902312330965655e-06,
                3.288750241374845e-06,
                1.1478773597640625e-05,
                1.012999339309804e-05,
                7.889265406151004e-06,
                1.1478764017428212e-05,
                2.5612831265630198e-06
            ],
            [
                5.422218969384951e-06,
                3.7266392835764795e-06,
                5.422221554926484e-06,
                8.939696301384342e-06,
                4.785094494402695e-06,
                1.3007131561804229e-05,
                8.939693103938694e-06,
                3.2887482811220126e-06,
                5.422220908314139e-06,
                7.889263525778283e-06
            ],
            [
                0.9999251537460401,
                0.9999921107392967,
                0.9999921107383567,
                0.9999852610197967,
                0.9999980052707542,
                0.9999970976869769,
                0.9999957771650466,
                0.9999984465020603,
                0.9999938558275969,
                0.9999938558239333
            ],
            [
                5.422217676654099e-06,
                5.422219615898437e-06,
                4.2228319341064674e-06,
                6.962258739068529e-06,
                2.2603248367173307e-06,
                4.2228339475595195e-06,
                3.726638395415398e-06,
                4.222831934052698e-06,
                4.785096775998733e-06,
                8.939693106182721e-06
            ],
            [
                0.9999952149032248,
                0.9999952149060765,
                0.9999952149066473,
                0.999997438718095,
                0.9999485577986525,
                0.9999756997592695,
                0.9999984465020603,
                0.9999957771670596,
                0.9999810748540244,
                0.999985261016281
            ],
            [
                0.9999991684717742,
                0.9999974387174844,
                0.9999970976869771,
                0.9999967112521111,
                0.9999986290429567,
                0.9999970976866313,
                0.9999921107374168,
                0.9999957771680662,
                0.9999930377412624,
                0.9999986290427932
            ],
            [
                0.9999938558253989,
                0.9999898700066073,
                0.9999952149037942,
                0.9999952149043652,
                0.999995214904935,
                0.9999945777823238,
                0.999998005269803,
                0.9999977396746245,
                0.999998239656367,
                0.9999970976873229
            ]
        ]
    },
    {
        "q_id": "8976_mmlu_math",
        "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,
            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,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                7.889266346129453e-06,
                2.753568451618723e-05,
                1.300712846217e-05,
                4.222833947774596e-06,
                1.670141586949968e-05,
                3.53562591336057e-05,
                1.6701425819994037e-05,
                1.4738981965326028e-05,
                7.889265406151004e-06,
                2.430023783150746e-05
            ],
            [
                2.902312677007974e-06,
                1.1478768123823146e-05,
                7.889266346746518e-06,
                3.726637951170554e-06,
                7.889262584350785e-06,
                7.889261643899223e-06,
                1.1478764018827141e-05,
                1.4738988998787566e-05,
                5.422218322664422e-06,
                7.88926352407059e-06
            ],
            [
                5.422217676797111e-06,
                1.3007123811229494e-05,
                1.1478768124324254e-05,
                3.2887478891128633e-06,
                5.422218969029887e-06,
                1.3007131564903626e-05,
                7.889259763469998e-06,
                5.422217030362759e-06,
                1.1478769491598686e-05,
                7.889264464895484e-06
            ],
            [
                0.9999898700042591,
                0.9999038975510843,
                0.999986992869995,
                0.9999687980961398,
                0.999996273360719,
                0.9999485577987409,
                0.9999756997623095,
                0.999992110733686,
                0.9999910603037417,
                0.9999885212318786
            ],
            [
                1.3007130009739366e-05,
                3.7266401721817755e-06,
                4.78509563466093e-06,
                1.8925157257965367e-05,
                1.3007134665413997e-05,
                1.8925143707303306e-05,
                1.8925152750176348e-05,
                3.1201903922734266e-05,
                1.3007125359413455e-05,
                1.670142781432848e-05
            ],
            [
                1.147876675466972e-05,
                8.93969416907082e-06,
                7.889265406151004e-06,
                2.2603248365343694e-06,
                1.1478770860982112e-05,
                1.012999097799944e-05,
                1.4738980209347228e-05,
                8.93969417167259e-06,
                1.0129995804364571e-05,
                7.889260703619978e-06
            ],
            [
                7.889259759767604e-06,
                8.939696302652706e-06,
                3.2887498493983645e-06,
                8.939697368110433e-06,
                5.422220261849814e-06,
                2.1444950954750122e-05,
                5.422218322763051e-06,
                1.6701427813872793e-05,
                2.430023203572232e-05,
                2.4300232031037035e-05
            ],
            [
                8.939698431942181e-06,
                2.9023130224326608e-06,
                1.670141785237998e-05,
                2.1444953507076064e-05,
                1.3007134661628471e-05,
                1.6701429801675944e-05,
                7.889263525405172e-06,
                2.430023781904283e-05,
                1.147876812106705e-05,
                1.892515725376564e-05
            ],
            [
                5.829127933242964e-05,
                2.430024941459533e-05,
                5.8291244578280495e-05,
                6.144174601410037e-06,
                1.473898899256772e-05,
                2.4300234929636645e-05,
                1.6701425822059825e-05,
                3.1201903922734266e-05,
                3.12019076377484e-05,
                5.144221969687863e-05
            ],
            [
                2.902312676941983e-06,
                5.422217676101776e-06,
                6.962257909121104e-06,
                3.726637950973972e-06,
                7.8892625849535e-06,
                1.012998735462479e-05,
                1.8925141466439755e-05,
                6.9622537593854575e-06,
                6.9622537593854575e-06,
                3.2887506330851655e-06
            ],
            [
                1.6701417857058377e-05,
                4.539789021177379e-05,
                1.670142781086525e-05,
                3.535625068579429e-05,
                2.4300240730549767e-05,
                1.4738976690741464e-05,
                2.7535691054881254e-05,
                1.147876675162131e-05,
                8.939698434495167e-06,
                7.484624495540762e-05
            ],
            [
                2.2603234893594005e-06,
                3.2887482811220126e-06,
                4.222833947359807e-06,
                6.1441731363550164e-06,
                1.760343213227212e-06,
                3.7266379512112265e-06,
                1.1478773598538445e-05,
                7.889266346746518e-06,
                3.288749064802458e-06,
                1.147877222879974e-05
            ],
            [
                4.785094493932679e-06,
                1.3007134663876127e-05,
                6.144173136645595e-06,
                6.144177530671741e-06,
                6.144173135896795e-06,
                1.670141586454787e-05,
                3.726637950973972e-06,
                4.785096775920397e-06,
                1.2098653950205268e-06,
                4.222833444037741e-06
            ],
            [
                4.78509563509613e-06,
                1.0129992184544441e-05,
                6.962253757840428e-06,
                7.889264466230069e-06,
                1.473898196677375e-05,
                2.902312330891746e-06,
                1.1478764019077695e-05,
                3.535626331056557e-05,
                7.889263524960312e-06,
                1.8925152741191683e-05
            ],
            [
                6.144177530794679e-06,
                6.962257908196617e-06,
                8.93969310584124e-06,
                7.889264464106214e-06,
                4.785096205512581e-06,
                8.939694170729447e-06,
                5.422219615829396e-06,
                6.144173868558375e-06,
                1.0129987355988324e-05,
                7.889264465842609e-06
            ],
            [
                1.0129992185981682e-05,
                1.8925141467059383e-05,
                1.1478772229300848e-05,
                1.012999218340202e-05,
                6.962256248606003e-06,
                6.9622545892184106e-06,
                1.1478766754064213e-05,
                1.473898196677375e-05,
                7.889263525261671e-06,
                1.6701417857058377e-05
            ],
            [
                2.144495863045236e-05,
                1.4738978452886064e-05,
                6.1441760657054305e-06,
                2.1444940740066406e-05,
                1.4738981970312625e-05,
                1.0129990978644356e-05,
                6.962257078819179e-06,
                1.3007125359413455e-05,
                1.8925157260443894e-05,
                1.0129994601872894e-05
            ],
            [
                1.0129992186939844e-05,
                3.7266392839832006e-06,
                4.785096205830278e-06,
                1.8925157263094544e-05,
                3.726640616630245e-06,
                4.222833947774596e-06,
                4.785095064819011e-06,
                2.5612812946681295e-06,
                1.1478769492893215e-05,
                1.0129988562901417e-05
            ],
            [
                4.785093353352668e-06,
                1.3007125357804606e-05,
                2.561281905100056e-06,
                3.288748280891699e-06,
                8.93969843377968e-06,
                4.785095063713602e-06,
                1.99472900790731e-06,
                2.5612834318583854e-06,
                1.1478764015736973e-05,
                6.144176064856046e-06
            ],
            [
                7.889259763728304e-06,
                1.30071346612026e-05,
                6.144177531459659e-06,
                8.939693105467234e-06,
                8.939697368305565e-06,
                2.144494073796001e-05,
                1.0129990977004428e-05,
                3.7266383950256237e-06,
                8.939695236983711e-06,
                1.6701415866735174e-05
            ],
            [
                2.1444958631232504e-05,
                1.4738987239698005e-05,
                1.892514145232592e-05,
                6.14417386791016e-06,
                7.889265405677441e-06,
                3.5356250681935664e-05,
                8.93969949923766e-06,
                1.1478773596575768e-05,
                6.144173865552e-06,
                6.144177531007026e-06
            ],
            [
                8.939699499627926e-06,
                8.939698434966738e-06,
                4.7850950649408664e-06,
                4.222833444229772e-06,
                4.222832437497486e-06,
                1.0129990979215566e-05,
                2.9023119850210436e-06,
                3.2887506334201674e-06,
                1.0129988564264954e-05,
                1.1478773597870298e-05
            ],
            [
                2.90231198483099e-06,
                2.1444945848226808e-05,
                1.0129988563343644e-05,
                4.785096205778054e-06,
                7.889266341939142e-06,
                1.3007126910294786e-05,
                1.147876812238246e-05,
                4.785096204868486e-06,
                1.8925157258585e-05,
                1.1478772229050293e-05
            ],
            [
                0.9999485577742286,
                0.9998911030654314,
                0.9999687980774881,
                0.9998415637097733,
                0.9999339478795214,
                0.9998204719963315,
                0.9999251537731004,
                0.9999599363179712,
                0.9999485577926986,
                0.9999417087561071
            ],
            [
                2.9023126769050284e-06,
                6.144173136455602e-06,
                8.939698434332555e-06,
                5.422218322348809e-06,
                7.889264466115267e-06,
                8.939695236593446e-06,
                7.889259763326495e-06,
                1.6701425824307884e-05,
                4.7850944937411915e-06,
                1.4738987239295859e-05
            ],
            [
                1.0129987355122296e-05,
                6.144172404129392e-06,
                6.144176065314267e-06,
                3.7266401724291984e-06,
                1.3007123806876143e-05,
                7.889265406567165e-06,
                1.670141586949968e-05,
                1.0129987356375273e-05,
                8.939695237666677e-06,
                8.93969630317306e-06
            ],
            [
                3.1201926241089315e-05,
                7.8892654060075e-06,
                1.3007128460040644e-05,
                0.00013982205683325005,
                3.12019113570763e-05,
                2.144494839938192e-05,
                2.1444940734059286e-05,
                2.4300243613326524e-05,
                3.5356250689524286e-05,
                1.8925157232078512e-05
            ],
            [
                1.1478766755233466e-05,
                6.962257079173776e-06,
                2.4300243614475748e-05,
                6.144175334094145e-06,
                4.785093923916815e-06,
                1.473897845240349e-05,
                6.144172403592939e-06,
                3.7266397280960194e-06,
                6.962254589617333e-06,
                6.9622579086271995e-06
            ],
            [
                1.4738976691867467e-05,
                6.1441767989541075e-06,
                1.1478768124783601e-05,
                8.939699500164542e-06,
                7.889264466230069e-06,
                1.4738983726184394e-05,
                6.962256249327861e-06,
                7.88926634644516e-06,
                8.939699498587217e-06,
                1.0129993393742954e-05
            ],
            [
                6.9622562487453084e-06,
                7.889262584508638e-06,
                7.889260704050487e-06,
                6.1441767990323395e-06,
                1.3007125359792008e-05,
                8.939696303010449e-06,
                1.0129995809044816e-05,
                6.962257909121104e-06,
                6.144175333401224e-06,
                1.147877222879974e-05
            ],
            [
                1.4738988998787566e-05,
                1.6701423830702777e-05,
                5.422217030288788e-06,
                2.4300243625614346e-05,
                4.222831934202483e-06,
                4.539786857989385e-05,
                6.605216823009351e-05,
                1.473898899664279e-05,
                1.1478770861211786e-05,
                1.6701417859944398e-05
            ],
            [
                7.889266346746518e-06,
                1.4738978450419574e-05,
                1.4738983725809062e-05,
                1.6701427811412077e-05,
                1.4738976699106073e-05,
                2.4300243625614346e-05,
                7.88925976359915e-06,
                6.96225707894582e-06,
                3.7266388395111645e-06,
                8.93969950101825e-06
            ],
            [
                8.939697368500698e-06,
                1.1478766754941153e-05,
                6.962255418367598e-06,
                1.0129995806317745e-05,
                4.222834451012227e-06,
                6.144175333021237e-06,
                3.726641060773727e-06,
                6.144177530425867e-06,
                3.7266383946527958e-06,
                6.962259568775433e-06
            ],
            [
                4.222834451065997e-06,
                1.473898899664279e-05,
                6.962257908348587e-06,
                8.939700565102295e-06,
                2.9023119851055122e-06,
                4.785095064436034e-06,
                6.144173133963328e-06,
                1.0129992185981682e-05,
                3.726638837999516e-06,
                2.9023133686835932e-06
            ],
            [
                2.1444953517061932e-05,
                2.2603242976733308e-06,
                3.726640616748873e-06,
                3.28875024125221e-06,
                6.144175331590693e-06,
                1.8925157259824262e-05,
                1.67014178554179e-05,
                5.422217676797111e-06,
                7.889259763469998e-06,
                1.0129992185760567e-05
            ],
            [
                8.939695237504067e-06,
                5.422221554758815e-06,
                6.144176066353646e-06,
                1.4738983726184394e-05,
                4.222834451169694e-06,
                1.0129995809247506e-05,
                5.422221554758815e-06,
                6.14417313680765e-06,
                2.144495863482118e-05,
                6.1441760661636525e-06
            ],
            [
                1.0129990977004428e-05,
                7.8892625849535e-06,
                1.0129989769722525e-05,
                1.1478766756444477e-05,
                1.8925148223661747e-05,
                1.892515499864894e-05,
                5.422217030032353e-06,
                4.222833444106873e-06,
                3.7266406165827946e-06,
                2.1444948406091176e-05
            ],
            [
                1.1478766755233466e-05,
                2.4300240725599276e-05,
                6.962254588724508e-06,
                1.1478770861211786e-05,
                1.8925150489517924e-05,
                1.4738978456719842e-05,
                7.889264465555602e-06,
                1.1478768122695653e-05,
                4.785096205347206e-06,
                1.1478764016780948e-05
            ],
            [
                1.1478773597870298e-05,
                1.3007134660350856e-05,
                1.1478768124324254e-05,
                1.8925145971093502e-05,
                5.422221554926484e-06,
                1.6701419846288166e-05,
                1.1478766755985128e-05,
                1.1478772229300848e-05,
                1.4738980204575109e-05,
                1.1478772226356834e-05
            ],
            [
                1.3007131563507714e-05,
                1.4738988995409548e-05,
                6.144174601410037e-06,
                5.422221554847581e-06,
                2.7535684513582775e-05,
                7.88926070328992e-06,
                1.1478765385098868e-05,
                1.670142582102693e-05,
                6.144176066353646e-06,
                1.4738988994498018e-05
            ],
            [
                1.012999460150437e-05,
                1.012999460108057e-05,
                8.93969417150998e-06,
                4.785093353187292e-06,
                6.962253757840428e-06,
                5.4222209070122355e-06,
                1.0129989770662257e-05,
                6.1441760661636525e-06,
                2.5612825159677387e-06,
                3.2887486732000038e-06
            ],
            [
                5.422220907554695e-06,
                7.88926070328992e-06,
                8.939698432690187e-06,
                6.962254589433702e-06,
                1.012998856312253e-05,
                1.6701423828576233e-05,
                8.939695236398313e-06,
                2.1444940738662144e-05,
                2.1444940731484803e-05,
                4.78509449410676e-06
            ],
            [
                4.785093353274332e-06,
                3.7266392836374875e-06,
                5.422221554581283e-06,
                4.785093353013212e-06,
                1.994729008074216e-06,
                4.785096775920397e-06,
                1.760344052650207e-06,
                5.422218322664422e-06,
                6.962255416961874e-06,
                7.889265404328504e-06
            ],
            [
                1.3007133114318805e-05,
                8.939693105272102e-06,
                4.785092782597101e-06,
                6.144173868882483e-06,
                5.422220908481809e-06,
                1.0129987355785634e-05,
                7.889259761704902e-06,
                8.939695237813028e-06,
                6.96225707894582e-06,
                1.6701421840318107e-05
            ],
            [
                4.222833947359807e-06,
                7.889266346603015e-06,
                7.88926446470893e-06,
                3.726639284050988e-06,
                1.3007126911643378e-05,
                7.889264464508026e-06,
                1.7603436327425345e-06,
                7.889263525103816e-06,
                2.5612822106654943e-06,
                3.2887506334201674e-06
            ],
            [
                8.93969630226244e-06,
                1.4738985482351282e-05,
                1.9947299590520376e-06,
                2.260324028281919e-06,
                6.144172403928222e-06,
                2.4300234897635273e-05,
                8.939696300376156e-06,
                3.288750241042834e-06,
                6.962253759271479e-06,
                6.144177530794679e-06
            ],
            [
                2.4300237824258528e-05,
                1.0129987355343409e-05,
                1.6701427809710842e-05,
                2.144495096083526e-05,
                1.6701415868649062e-05,
                1.8925141469400216e-05,
                8.939693106329072e-06,
                8.939693105272102e-06,
                2.75357042110088e-05,
                1.3007133114011233e-05
            ],
            [
                2.5612831264302397e-06,
                2.902311984915459e-06,
                5.422217030614265e-06,
                3.2887482811579057e-06,
                1.7603427932316836e-06,
                3.726640172120768e-06,
                5.422218969661113e-06,
                7.889264464508026e-06,
                2.260323758806253e-06,
                2.902311293034278e-06
            ],
            [
                7.889260704308795e-06,
                5.422218323093458e-06,
                4.22283394786293e-06,
                8.93969310675186e-06,
                6.144173869072478e-06,
                4.222831934156396e-06,
                1.1478764019557924e-05,
                2.902313022984344e-06,
                1.1478770861441461e-05,
                4.2228319341064674e-06
            ],
            [
                8.93969310367852e-06,
                0.9994472213741388,
                3.535624645738762e-05,
                5.144220745705777e-05,
                2.4300240708626165e-05,
                1.8925150473958278e-05,
                0.04742587418734382,
                0.009708476123316396,
                0.01798621387711511,
                2.4300246488324276e-05
            ],
            [
                7.889259763857458e-06,
                8.939694170062744e-06,
                5.4222170296279735e-06,
                1.6701423830702777e-05,
                5.422219615750493e-06,
                1.1478765388105516e-05,
                1.4738980210258757e-05,
                7.88926070328992e-06,
                1.3007133112662637e-05,
                3.288749065077638e-06
            ],
            [
                2.9023133690425823e-06,
                3.288750241473551e-06,
                4.222835457906302e-06,
                3.72664017246987e-06,
                5.422217030495909e-06,
                6.144174601588856e-06,
                7.889260704423598e-06,
                6.144176065940129e-06,
                7.889266347248781e-06,
                3.2887478890769702e-06
            ],
            [
                5.422218322664422e-06,
                6.144176066051891e-06,
                1.0129995807939249e-05,
                2.9023133689317184e-06,
                1.0129992184802409e-05,
                4.7850933534310035e-06,
                8.9396973679153e-06,
                7.889260703763482e-06,
                7.889266345584138e-06,
                2.2603253755949437e-06
            ],
            [
                5.422220908560712e-06,
                7.889260704050487e-06,
                2.5612828212909852e-06,
                1.4738987237124277e-05,
                1.3007126909916233e-05,
                1.3007123810638006e-05,
                6.96225375833433e-06,
                1.3007126909537681e-05,
                1.3007134665130082e-05,
                1.3007126911335805e-05
            ],
            [
                6.962253758916883e-06,
                5.422220908116881e-06,
                3.7266410608720178e-06,
                1.4738988995409548e-05,
                5.422219615967477e-06,
                6.14417606659952e-06,
                5.422220908481809e-06,
                5.422217676299034e-06,
                4.78509506499309e-06,
                5.422220262333096e-06
            ],
            [
                4.7850950646797465e-06,
                6.144174601410037e-06,
                4.222832437497486e-06,
                5.4222202617511845e-06,
                2.260323489410794e-06,
                5.422217676797111e-06,
                6.962259569003389e-06,
                6.144175333635923e-06,
                6.962257908880483e-06,
                1.0677026153638352e-06
            ],
            [
                1.0129988559160908e-05,
                2.7535691082027735e-05,
                1.1478765384430723e-05,
                1.6701421840804172e-05,
                1.892514145845339e-05,
                2.4300234912928744e-05,
                2.1444940733201126e-05,
                3.1201911351060354e-05,
                2.7535684529910724e-05,
                1.3007126900026555e-05
            ],
            [
                8.939694170062744e-06,
                1.3007126909537681e-05,
                3.120190013870751e-05,
                7.484622751061124e-05,
                1.1478769487046951e-05,
                1.3007125360146898e-05,
                1.670141586454787e-05,
                5.422221555069497e-06,
                7.889260704050487e-06,
                4.006371126117997e-05
            ],
            [
                8.939699499823059e-06,
                4.222835458044565e-06,
                1.0129988563546333e-05,
                1.1478764018827141e-05,
                4.785095064819011e-06,
                1.4738985479697128e-05,
                8.93969950101825e-06,
                1.1478772228256871e-05,
                6.962257909323729e-06,
                6.1441738691562974e-06
            ],
            [
                5.422217676486429e-06,
                6.962254589104433e-06,
                3.288749065209246e-06,
                1.1478765387416494e-05,
                2.5612834317535587e-06,
                1.670142980380249e-05,
                2.9023116390104826e-06,
                5.422221554374162e-06,
                4.785093353739995e-06,
                4.7850950649408664e-06
            ],
            [
                3.2887506329595395e-06,
                4.785094494185095e-06,
                3.2887498492518007e-06,
                2.561281904871769e-06,
                3.2887502413389517e-06,
                5.4222202609325635e-06,
                4.222831934248571e-06,
                3.726637951079042e-06,
                3.726637951170554e-06,
                6.144176065314267e-06
            ],
            [
                7.889266346287306e-06,
                7.889260703906985e-06,
                8.939700564679507e-06,
                1.0129988562164371e-05,
                1.012999580884213e-05,
                1.8925157259824262e-05,
                6.144173868312501e-06,
                6.1441753335241615e-06,
                1.8925155003330605e-05,
                1.1478764018576587e-05
            ],
            [
                4.2228324372555256e-06,
                6.962257909323729e-06,
                5.422217676797111e-06,
                5.422218323019487e-06,
                1.1478770860982112e-05,
                2.902313022984344e-06,
                6.96225541916544e-06,
                3.726641060956752e-06,
                4.222833947728508e-06,
                7.889265406681968e-06
            ],
            [
                1.1478764019557924e-05,
                1.6701429805199933e-05,
                5.422217030121119e-06,
                1.4738987237553233e-05,
                1.4738976697229395e-05,
                4.222833444037741e-06,
                1.1478772229781076e-05,
                2.43002320236113e-05,
                6.144177530291754e-06,
                6.144175329690753e-06
            ],
            [
                5.829125154581821e-05,
                1.4738980213020151e-05,
                2.7535704222728874e-05,
                1.6701425824307884e-05,
                3.120191508446373e-05,
                4.006369694347607e-05,
                2.4300240728958537e-05,
                4.006371128012683e-05,
                1.3007125361448172e-05,
                2.7535704226635563e-05
            ],
            [
                6.9622587393661365e-06,
                1.012998977022003e-05,
                2.561282210530385e-06,
                2.5612816000145246e-06,
                8.939693106329072e-06,
                3.726639727940109e-06,
                1.0129994600638342e-05,
                1.4738980212644815e-05,
                5.422218323231539e-06,
                6.144176066521288e-06
            ],
            [
                1.147876538716594e-05,
                6.9622545892184106e-06,
                4.7850956352353935e-06,
                1.1478773593172406e-05,
                2.144495606626759e-05,
                4.785094494185095e-06,
                4.785092783267308e-06,
                6.144175333401224e-06,
                4.222832436164788e-06,
                1.0129989770441144e-05
            ],
            [
                1.4738988994498018e-05,
                1.012999339309804e-05,
                1.1478766752372975e-05,
                1.3007130010922344e-05,
                1.3007131558444574e-05,
                2.1444948403750736e-05,
                1.4738988995838502e-05,
                1.1478772229050293e-05,
                3.2887478884069663e-06,
                1.473898722977843e-05
            ],
            [
                5.422220907909759e-06,
                3.726641060773727e-06,
                1.012999339309804e-05,
                8.939693105272102e-06,
                6.962258739068529e-06,
                3.120191508060445e-05,
                4.222835457852533e-06,
                1.0129995801232122e-05,
                8.939698432690187e-06,
                1.0129989770662257e-05
            ],
            [
                4.785093923982095e-06,
                2.9023133686835932e-06,
                3.726639283752725e-06,
                8.93969630348202e-06,
                5.4222196154940574e-06,
                4.222832437186393e-06,
                4.222832940942332e-06,
                2.9023119850210436e-06,
                1.300713466420736e-05,
                1.670142780594382e-05
            ],
            [
                0.9998204720155245,
                0.9998766054274915,
                0.9998204719725152,
                0.9998415638408991,
                0.9998766053680097,
                0.9998601779262772,
                0.9999038975739906,
                0.9998766054132485,
                0.9996646500195525,
                0.9999485577804199
            ],
            [
                5.422219615750493e-06,
                2.9023126768258393e-06,
                6.144177529855884e-06,
                3.28874867308036e-06,
                2.5612834317116285e-06,
                2.5612819052374947e-06,
                2.9023116390104826e-06,
                4.785094494402695e-06,
                2.9023112928785396e-06,
                1.9947304347570075e-06
            ],
            [
                1.670141587031992e-05,
                1.4738980209347228e-05,
                1.8925157257345735e-05,
                1.6701423826206655e-05,
                1.3007134662054344e-05,
                3.5356254894393866e-05,
                1.7603434229576435e-06,
                6.962258738827909e-06,
                1.0129987355564522e-05,
                1.300713466281145e-05
            ],
            [
                1.7603432133032607e-06,
                3.7266388396975786e-06,
                4.7850950647493785e-06,
                1.4738983723664288e-05,
                7.889262584809997e-06,
                1.670141586454787e-05,
                6.962257908753841e-06,
                4.785093353187292e-06,
                1.3007133110746217e-05,
                2.260324297702111e-06
            ],
            [
                3.7266379512518984e-06,
                8.93969630348202e-06,
                6.962255419051463e-06,
                4.222835457733473e-06,
                6.144172403470001e-06,
                3.2887482811220126e-06,
                4.785095065045315e-06,
                4.222832437386106e-06,
                1.0129987355122296e-05,
                4.222835457852533e-06
            ],
            [
                6.144173136729416e-06,
                4.785096205260165e-06,
                1.8925141468298646e-05,
                1.1478764019787597e-05,
                6.962253759581752e-06,
                5.42221767672807e-06,
                1.892514823426434e-05,
                1.0129993394314164e-05,
                1.3007125361448172e-05,
                7.88925976397226e-06
            ],
            [
                1.0129987355122296e-05,
                6.144173136556186e-06,
                8.939698433974813e-06,
                5.422219615829396e-06,
                1.0129993391808207e-05,
                1.0129995809044816e-05,
                2.902313022659669e-06,
                2.9023130230133794e-06,
                2.144495607640949e-05,
                7.88926352407059e-06
            ],
            [
                8.939695235243779e-06,
                1.4738987238464762e-05,
                1.0129990977759901e-05,
                1.8925148232956223e-05,
                1.473898197063434e-05,
                4.222833947121688e-06,
                8.939696302652706e-06,
                1.3007123811797321e-05,
                6.962257909007124e-06,
                1.1478766755734576e-05
            ],
            [
                6.962257907702715e-06,
                2.144495607336692e-05,
                1.0129992185299915e-05,
                1.6701429797422853e-05,
                7.889265405677441e-06,
                7.889261644631091e-06,
                2.430024362393472e-05,
                6.144175333155351e-06,
                1.300713156215912e-05,
                7.889263524788109e-06
            ],
            [
                5.42221767672807e-06,
                1.1478773593548236e-05,
                8.93969310584124e-06,
                6.144177531532303e-06,
                2.260324836624822e-06,
                3.7266392836374875e-06,
                6.96225541916544e-06,
                1.6701427809710842e-05,
                7.889261644501938e-06,
                1.1478768123823146e-05
            ],
            [
                1.8925141461620395e-05,
                3.2887502412970765e-06,
                1.8925157255280296e-05,
                1.3007134658978603e-05,
                1.012998856078241e-05,
                1.8925157262061825e-05,
                1.3007128461838766e-05,
                1.8925152746768368e-05,
                3.2887506330851655e-06,
                1.3007134662054344e-05
            ],
            [
                1.4738985481091229e-05,
                6.962259569003389e-06,
                4.7850967763512445e-06,
                5.422217029844958e-06,
                8.93969950000193e-06,
                1.4738988995838502e-05,
                1.1478764019787597e-05,
                1.8925141468298646e-05,
                4.222834451169694e-06,
                7.88925976283858e-06
            ],
            [
                1.6701421837705495e-05,
                7.88926258343236e-06,
                1.670142183934597e-05,
                1.3007126911643378e-05,
                1.3007126909159127e-05,
                1.1478764018576587e-05,
                1.4738988995409548e-05,
                2.1444950954750122e-05,
                5.42221767672807e-06,
                1.1478765387416494e-05
            ],
            [
                1.14787681240737e-05,
                6.962253758017727e-06,
                8.939697368842181e-06,
                7.889260701926633e-06,
                1.0129992183991656e-05,
                1.4738981969615573e-05,
                8.939697368110433e-06,
                7.889262584809997e-06,
                1.1478768124324254e-05,
                1.3007126911974612e-05
            ],
            [
                0.9999724643056793,
                0.9999339478823125,
                0.9999810748495693,
                0.9999687980739378,
                0.9999810748474713,
                0.9999151889403023,
                0.9999885212360079,
                0.9999852610233527,
                0.9999599362890641,
                0.9999756997478274
            ],
            [
                7.889266345957247e-06,
                3.7266383953679482e-06,
                1.8925150486075525e-05,
                2.9023123308072772e-06,
                1.3007134656423374e-05,
                4.785096205077381e-06,
                5.422221554482653e-06,
                7.88926164421493e-06,
                5.422218969384951e-06,
                6.962256248871951e-06
            ],
            [
                1.3007126910649678e-05,
                1.4738976695942536e-05,
                1.1478769491306371e-05,
                5.422219615582823e-06,
                1.6701417850314193e-05,
                1.012999459934851e-05,
                2.1444958623509054e-05,
                1.0129990978220553e-05,
                1.3007126912258525e-05,
                2.144494072376136e-05
            ],
            [
                3.7266410607194972e-06,
                1.3007134663521234e-05,
                1.0129993393742954e-05,
                6.144173136645595e-06,
                7.889262584809997e-06,
                1.6701417857058377e-05,
                7.88926258381982e-06,
                2.1444956070012293e-05,
                1.6701425823457267e-05,
                8.939695237341456e-06
            ],
            [
                1.1478768122069266e-05,
                1.3007133112662637e-05,
                5.4222183222304545e-06,
                1.1478769492893215e-05,
                1.0129990978847043e-05,
                1.6701429795417824e-05,
                1.6701427812931038e-05,
                1.0129987353537646e-05,
                1.8925145980732218e-05,
                8.939695236398313e-06
            ],
            [
                7.889260704050487e-06,
                2.902312677060767e-06,
                4.2228324372555256e-06,
                1.0129990977262395e-05,
                1.0129987352616339e-05,
                4.222835457595211e-06,
                6.9622587393661365e-06,
                1.0129995808418327e-05,
                7.889261644875049e-06,
                8.93969630317306e-06
            ],
            [
                1.5534981248881956e-06,
                7.889261644358435e-06,
                6.9622579092224155e-06,
                1.1478766755233466e-05,
                4.222834954514924e-06,
                5.422219615898437e-06,
                4.222835457364773e-06,
                1.7603430034311638e-06,
                1.994730672496148e-06,
                4.222834450420771e-06
            ],
            [
                1.300713311112477e-05,
                6.9622579075254155e-06,
                3.7266410608245674e-06,
                6.962258738827909e-06,
                2.9023109470871505e-06,
                4.222834954514924e-06,
                2.9023126769050284e-06,
                4.222832436871463e-06,
                6.962257077590752e-06,
                1.3007126908733257e-05
            ],
            [
                3.7266410609160796e-06,
                4.222831934052698e-06,
                1.1478766754941153e-05,
                1.0129989768322136e-05,
                5.422218322664422e-06,
                7.889264465239894e-06,
                2.260323489410794e-06,
                2.2603248364644736e-06,
                2.9023130229209922e-06,
                6.144176798691468e-06
            ],
            [
                6.1441746016670885e-06,
                1.1478765384764794e-05,
                6.962257908880483e-06,
                4.539787938592359e-05,
                5.8291244568526206e-05,
                1.0129990978644356e-05,
                0.0259573580454947,
                1.300712845923622e-05,
                1.4738981968060613e-05,
                1.6701419835959236e-05
            ],
            [
                5.422220907909759e-06,
                1.3007128458384476e-05,
                4.222834954134701e-06,
                2.9023126769762986e-06,
                8.939697368305565e-06,
                2.4300234931404677e-05,
                1.4738988989779516e-05,
                1.8925143725892257e-05,
                2.260323758835034e-06,
                6.96225541788636e-06
            ],
            [
                4.785093924156175e-06,
                4.222833947428939e-06,
                6.144174601208867e-06,
                4.22283394762097e-06,
                5.422220908703723e-06,
                6.962257908753841e-06,
                1.9947304348332037e-06,
                3.7266410609940346e-06,
                6.144172404218801e-06,
                3.7266397280960194e-06
            ],
            [
                1.147877222702498e-05,
                2.1444948392516633e-05,
                2.1444953513707305e-05,
                2.4300234928664224e-05,
                1.8925145961179394e-05,
                7.88926070097951e-06,
                1.012998735462479e-05,
                6.962255418924822e-06,
                1.147876401711502e-05,
                2.7535684498857565e-05
            ],
            [
                2.561283126639892e-06,
                1.0129993390610508e-05,
                1.0129995808639442e-05,
                7.889263525663481e-06,
                8.9396941718352e-06,
                5.422220908481809e-06,
                5.422219615069953e-06,
                6.144172403715875e-06,
                4.7850950643402904e-06,
                6.962254587951994e-06
            ],
            [
                1.1478772229551402e-05,
                4.22283394762097e-06,
                5.422220908762902e-06,
                1.0129992185760567e-05,
                5.422221554847581e-06,
                6.962257909121104e-06,
                6.144173868670137e-06,
                6.1441767987808774e-06,
                6.144172404129392e-06,
                7.889263525893087e-06
            ],
            [
                3.726639284050988e-06,
                5.422219615898437e-06,
                4.2228324375512536e-06,
                4.2228324375512536e-06,
                8.939696302051047e-06,
                5.4222215552470286e-06,
                5.42222090882208e-06,
                3.726641061085547e-06,
                2.5612822106421996e-06,
                1.0129990978441666e-05
            ],
            [
                1.6701429800582296e-05,
                6.962254586824882e-06,
                7.88926634644516e-06,
                2.9023126767836054e-06,
                1.300712845966209e-05,
                4.2228349527213495e-06,
                2.1444945850567248e-05,
                1.6701427806612162e-05,
                1.6701423829669885e-05,
                1.1478764019557924e-05
            ],
            [
                1.1478773597870298e-05,
                0.9978172838320353,
                0.5,
                0.9994472212994675,
                0.9999646437494898,
                0.9988304898535275,
                7.889264463890957e-06,
                7.889262582571338e-06,
                0.9986749775974215,
                0.9999599363035162
            ],
            [
                4.2228339475595195e-06,
                6.144175333926503e-06,
                5.422218323231539e-06,
                2.9023133687311063e-06,
                1.994729721469003e-06,
                1.4738981966291175e-05,
                3.726639283901856e-06,
                4.7850927830845245e-06,
                1.2098658276598493e-06,
                1.0129989769464556e-05
            ],
            [
                1.4738976695942536e-05,
                2.7535700934898458e-05,
                2.430025231213619e-05,
                1.3007131564383116e-05,
                1.892514146884943e-05,
                1.670142582102693e-05,
                8.9396941718352e-06,
                2.144494073796001e-05,
                6.962257908044647e-06,
                1.4738983724146862e-05
            ],
            [
                5.422220261849814e-06,
                7.889263525663481e-06,
                8.939697368842181e-06,
                1.670142781244497e-05,
                1.6701425823882575e-05,
                4.2228349543420954e-06,
                7.889259763728304e-06,
                5.422221554670048e-06,
                8.93969417199781e-06,
                5.422218969306048e-06
            ],
            [
                8.939698434657777e-06,
                6.1441760661636525e-06,
                1.1478773597390071e-05,
                6.144176066051891e-06,
                3.288750241410738e-06,
                4.785096205434246e-06,
                1.1478770859019436e-05,
                1.1478768122987964e-05,
                1.012999460150437e-05,
                1.670142183825232e-05
            ],
            [
                2.1444950963097686e-05,
                9.610244921065592e-05,
                2.1444940741392653e-05,
                7.889264463675704e-06,
                3.5356259116499136e-05,
                2.1444956078515887e-05,
                2.7535687806920664e-05,
                3.120190392795564e-05,
                1.3007126910649678e-05,
                6.605212099816935e-05
            ],
            [
                8.939693105662367e-06,
                5.422218322763051e-06,
                1.473898723610551e-05,
                8.939696301839653e-06,
                1.0129992185760567e-05,
                6.962257909007124e-06,
                1.0129988562901417e-05,
                6.962253759581752e-06,
                1.4738983723235332e-05,
                1.300712846115264e-05
            ],
            [
                5.422220262264056e-06,
                1.0129988563730593e-05,
                1.6701423832586287e-05,
                1.1478765386894505e-05,
                6.144176066521288e-06,
                2.430024072091399e-05,
                1.6701419850389357e-05,
                1.3007126911974612e-05,
                6.1441767987808774e-06,
                4.222834954461155e-06
            ],
            [
                6.14417606659952e-06,
                1.892515048889829e-05,
                6.962259568230874e-06,
                1.0129988563343644e-05,
                1.012999460108057e-05,
                2.1444956071728615e-05,
                1.8925148237775583e-05,
                1.0129992185760567e-05,
                8.93970056565517e-06,
                1.1478770861211786e-05
            ],
            [
                6.96225458885115e-06,
                5.422218969601935e-06,
                8.939697368110433e-06,
                6.144177531381426e-06,
                7.889259763857458e-06,
                6.962253759157502e-06,
                7.889263525405172e-06,
                6.1441753337365085e-06,
                7.889262585441413e-06,
                1.0129990979215566e-05
            ],
            [
                2.753570419688461e-05,
                1.3007123811513407e-05,
                1.3007123811797321e-05,
                8.939700564890901e-06,
                1.4738981968864903e-05,
                1.4738978453743973e-05,
                2.7535681242383173e-05,
                1.1478772228528306e-05,
                2.1444948406091176e-05,
                1.892515274614874e-05
            ],
            [
                1.8925157254522964e-05,
                6.1441738691562974e-06,
                6.962257077033528e-06,
                2.2603234893594005e-06,
                7.889260703906985e-06,
                8.939700565102295e-06,
                1.0129993393945642e-05,
                1.3007134663876127e-05,
                1.3007134665413997e-05,
                6.962258739169842e-06
            ],
            [
                6.9622562492265485e-06,
                8.939693106329072e-06,
                6.9622562481627565e-06,
                1.3007128462477575e-05,
                1.4738987239295859e-05,
                6.962259569003389e-06,
                8.939699500489763e-06,
                1.1478766754064213e-05,
                1.147876949187012e-05,
                4.222832940942332e-06
            ],
            [
                1.4738985484227961e-05,
                1.4738976692993472e-05,
                5.4222209070122355e-06,
                8.939695237666677e-06,
                6.1441775291964935e-06,
                1.1478772229551402e-05,
                7.889265405505236e-06,
                1.0129990978441666e-05,
                5.422219612012453e-06,
                1.4738983724146862e-05
            ],
            [
                1.3007128460419196e-05,
                1.4738981968060613e-05,
                6.1441746016670885e-06,
                1.1478773597640625e-05,
                7.889260703763482e-06,
                7.889260703462123e-06,
                4.785096776068365e-06,
                1.0129994599072117e-05,
                6.9622545892184106e-06,
                1.994729483608425e-06
            ],
            [
                1.012999218369684e-05,
                3.7266383950256237e-06,
                7.889264466115267e-06,
                6.962255418367598e-06,
                1.4738981970312625e-05,
                4.78509563509613e-06,
                5.422219615286937e-06,
                8.93969950000193e-06,
                4.222834450820197e-06,
                1.8925141467679015e-05
            ],
            [
                1.8925157255968775e-05,
                1.670142979608617e-05,
                1.0129993390610508e-05,
                5.422220262037209e-06,
                1.14787735942999e-05,
                4.785093353100252e-06,
                6.9622537584863015e-06,
                8.93969843377968e-06,
                7.889262584508638e-06,
                4.222835457906302e-06
            ],
            [
                1.1478770860481005e-05,
                1.3007131564383116e-05,
                1.8925152746768368e-05,
                1.3007130012010681e-05,
                6.962258738701267e-06,
                8.939696302051047e-06,
                6.96225956837018e-06,
                1.8925152746768368e-05,
                1.1478766756444477e-05,
                1.0129994600159262e-05
            ],
            [
                4.5397890268254766e-05,
                4.539785769789816e-05,
                8.481105128568296e-05,
                4.539785771672514e-05,
                3.120192248396136e-05,
                0.0001398220738753715,
                6.605212884380361e-05,
                0.00010889689573290682,
                4.006368736190672e-05,
                0.00013982208974161491
            ],
            [
                3.2887490649759413e-06,
                7.889261643181705e-06,
                1.4738983726184394e-05,
                1.012999217990105e-05,
                1.6701427811412077e-05,
                4.785092783149804e-06,
                3.7266397274452643e-06,
                6.9622579092224155e-06,
                3.120192622315499e-05,
                8.939695236983711e-06
            ],
            [
                5.829128633093081e-05,
                3.5356242243001115e-05,
                1.6701427811412077e-05,
                2.1444943294263477e-05,
                6.144176065828368e-06,
                2.144494328685209e-05,
                1.4738983723664288e-05,
                3.2887498491620677e-06,
                8.93970056565517e-06,
                8.939699497855469e-06
            ],
            [
                6.9622570780973205e-06,
                6.962257078819179e-06,
                6.144174600862407e-06,
                4.7850944937411915e-06,
                1.0129994600859455e-05,
                1.1478764018576587e-05,
                4.006368257039418e-05,
                7.889259762666377e-06,
                6.96225873895455e-06,
                1.1478766751997141e-05
            ],
            [
                1.1478764019328247e-05,
                4.785093923916815e-06,
                6.962257909007124e-06,
                7.889262585211807e-06,
                4.785093353274332e-06,
                3.7266388392671313e-06,
                1.3007125358230479e-05,
                1.473898899256772e-05,
                8.939695237504067e-06,
                3.288747889178668e-06
            ],
            [
                4.785096776068365e-06,
                4.222835457595211e-06,
                8.939695237666677e-06,
                7.889264466115267e-06,
                8.939695237504067e-06,
                1.0129989771473008e-05,
                5.422218322664422e-06,
                1.0129987355122296e-05,
                4.785096775842062e-06,
                5.422220908314139e-06
            ],
            [
                0.9999151889287515,
                0.9999687980738009,
                0.9999832985841393,
                0.9999885212318956,
                0.9999785550490868,
                0.999997097688711,
                0.9999910603047831,
                0.9999852610180473,
                0.9999646437451295,
                0.9999038976085548
            ]
        ]
    },
    {
        "q_id": "8530_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            9,
            11,
            12,
            13,
            15,
            16,
            19,
            20,
            21,
            22,
            23,
            25,
            26,
            28,
            30,
            31,
            32,
            34,
            35,
            36,
            38,
            39,
            40,
            43,
            44,
            46,
            48,
            49,
            50,
            51,
            53,
            54,
            57,
            58,
            61,
            62,
            63,
            64,
            65,
            66,
            70,
            71,
            73,
            74,
            75,
            76,
            77,
            78,
            80,
            83,
            84,
            85,
            88,
            89,
            90,
            91,
            93,
            94,
            96,
            97,
            98,
            99,
            101,
            102,
            103,
            104,
            106,
            107,
            108,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            120,
            122,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                0.0019267346203445767,
                1.6701415866188347e-05,
                3.120192243129346e-05,
                1.6701415859504925e-05,
                6.962257077932685e-06,
                0.7981867729389246,
                4.222833444168322e-06,
                1.5534983100920427e-06,
                4.785094493932679e-06,
                NaN
            ],
            [
                0.9999810748533594,
                NaN,
                0.9999869928757166,
                0.9999832985762465,
                NaN,
                0.9999852610197894,
                0.9999869928699961,
                0.9669140224455338,
                NaN,
                0.8519528038477825
            ],
            [
                7.484620933559467e-05,
                NaN,
                3.726640616630245e-06,
                NaN,
                0.0001584362693878427,
                2.7535681238877168e-05,
                7.484624501857396e-05,
                NaN,
                7.484626273564317e-05,
                4.5397857734561226e-05
            ],
            [
                NaN,
                0.9999339478263636,
                0.970687770467595,
                0.9999599362887508,
                0.999769493315969,
                0.9999957771645459,
                0.904650527388829,
                0.9993736659008418,
                NaN,
                0.9999251537818369
            ],
            [
                4.222834954514924e-06,
                1.892515500808112e-05,
                1.8925152744083297e-05,
                1.3007134662432895e-05,
                2.7535697651475977e-05,
                1.0129990979031306e-05,
                3.120191878949046e-05,
                1.994729008056074e-06,
                NaN,
                3.28874867308036e-06
            ],
            [
                0.00010889694813820381,
                9.610242591710606e-05,
                1.6701417861189946e-05,
                3.120190392670705e-05,
                8.93969417199781e-06,
                8.939697368842181e-06,
                1.6701415866735174e-05,
                0.00012339460411844904,
                3.1201903906162046e-05,
                2.753569109034197e-05
            ],
            [
                5.144219519403497e-05,
                8.939694169835089e-06,
                5.829127932776453e-05,
                3.120190762537599e-05,
                0.0002959571304594004,
                9.610240339544534e-05,
                1.8925157249015125e-05,
                0.0010322308062713872,
                0.001700722771955165,
                0.0024726225990099808
            ],
            [
                0.00012339460337156002,
                3.120190391410763e-05,
                1.892514372640862e-05,
                0.00037998443223882653,
                8.93969630362837e-06,
                NaN,
                0.00012339460415256175,
                NaN,
                0.00013982207370041356,
                0.0001795279426886382
            ],
            [
                7.889263525778283e-06,
                1.892514822276672e-05,
                1.3007125359413455e-05,
                NaN,
                3.5356254905712496e-05,
                1.892515048820981e-05,
                0.3775406687981454,
                6.962255419653012e-06,
                1.012999580884213e-05,
                2.144494073054863e-05
            ],
            [
                NaN,
                1.6701417840046025e-05,
                1.012998856015592e-05,
                NaN,
                4.00636969128696e-05,
                2.7535694375867267e-05,
                NaN,
                0.00012339463011772965,
                NaN,
                9.610244927358124e-05
            ],
            [
                1.300713001414004e-05,
                2.1444948410303962e-05,
                1.89251527491092e-05,
                1.01299933928585e-05,
                8.481108168178473e-05,
                1.4738978454950406e-05,
                2.4300234933172706e-05,
                NaN,
                6.144175332887123e-06,
                3.120190391705884e-05
            ],
            [
                0.000379984469836204,
                0.00015843625380709215,
                8.481105136527973e-05,
                0.0005527785450155708,
                0.9993736658437486,
                9.610237997885274e-05,
                0.0003353499821841792,
                0.0004878571051563188,
                0.00033535018729926236,
                0.5621765008857981
            ],
            [
                3.12019225022362e-05,
                2.7535694136958206e-05,
                1.3007125357804606e-05,
                4.0063682616886836e-05,
                2.7535684528909006e-05,
                7.889264465555602e-06,
                NaN,
                2.144494328404357e-05,
                7.8892625849535e-06,
                1.1478769491598686e-05
            ],
            [
                7.889264461637948e-06,
                4.006369681871831e-05,
                3.1201911339482505e-05,
                1.892514597632595e-05,
                NaN,
                NaN,
                2.144494070714426e-05,
                1.892515273885085e-05,
                1.3007134658505415e-05,
                9.610243765756909e-05
            ],
            [
                8.939698435096828e-06,
                4.785096776303374e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9996646497744642,
                1.3007125342804474e-05,
                NaN,
                7.889260704531226e-06
            ],
            [
                1.473898196677375e-05,
                1.5534971989427613e-06,
                1.6701421837158667e-05,
                5.144219521574275e-05,
                0.18242552602881168,
                NaN,
                NaN,
                4.006370170554982e-05,
                0.37754066879814546,
                6.1441760654483806e-06
            ],
            [
                6.962255418063657e-06,
                4.785096205717126e-06,
                2.144495349217527e-05,
                1.3007131543917626e-05,
                7.484620019989652e-05,
                2.4300252308334918e-05,
                1.4738980142323096e-05,
                1.147876675124548e-05,
                4.006369693691754e-05,
                3.726640168236576e-06
            ],
            [
                1.8925150491445666e-05,
                1.4738978450419574e-05,
                4.0063692152253866e-05,
                NaN,
                NaN,
                NaN,
                4.006368731905769e-05,
                0.0001584362535028076,
                NaN,
                3.535626332702904e-05
            ],
            [
                0.5,
                3.120190764058611e-05,
                1.3007131563176482e-05,
                5.422217030288788e-06,
                2.7535697592675292e-05,
                0.29421497835151617,
                3.1201900207380036e-05,
                0.02033235542036712,
                1.4738985430260109e-05,
                1.0
            ],
            [
                6.144176797439742e-06,
                5.144223802948063e-05,
                1.1478764019328247e-05,
                6.962257078553231e-06,
                3.120190387585532e-05,
                1.0129993391531815e-05,
                1.3007134661628471e-05,
                0.7310585786300048,
                3.7266383953679482e-06,
                1.553497198801472e-06
            ],
            [
                2.5612831264302397e-06,
                1.3007130013856124e-05,
                2.4300237829827827e-05,
                NaN,
                1.3007126912542439e-05,
                4.0063696941289896e-05,
                5.1442238137271045e-05,
                7.889263525261671e-06,
                9.610244819685922e-05,
                6.60521524840326e-05
            ],
            [
                3.2887498491620677e-06,
                1.3709573702722555e-06,
                2.9023109469842055e-06,
                1.0129987355785634e-05,
                2.4300243606431198e-05,
                1.1478766756653273e-05,
                1.2098661161861e-06,
                3.7266383948154845e-06,
                1.370957370236096e-06,
                1.6701425823882575e-05
            ],
            [
                2.7535687805818776e-05,
                6.144174599867732e-06,
                1.3007131560621253e-05,
                NaN,
                NaN,
                NaN,
                4.0063692129517645e-05,
                0.00013982203671716138,
                2.1444943246206497e-05,
                NaN
            ],
            [
                3.726640616630245e-06,
                0.00020342699560593142,
                NaN,
                0.0008040860994984622,
                0.00033535026141117883,
                0.00020342697294685079,
                2.5612815999679353e-06,
                6.605212877796679e-05,
                0.0013250221841377668,
                2.4300252313020203e-05
            ],
            [
                4.5397884856980825e-05,
                5.422217027024168e-06,
                1.147876948575242e-05,
                5.144221976237626e-05,
                4.2228344501365644e-06,
                3.5356259104666025e-05,
                4.006369689654616e-05,
                1.0129989764415789e-05,
                7.889262585082652e-06,
                8.93969736929749e-06
            ],
            [
                1.3007130008887624e-05,
                5.422220908402905e-06,
                6.96225707894582e-06,
                0.0002034269971893443,
                4.785094493836935e-06,
                3.1201903930339314e-05,
                8.939694170940841e-06,
                0.000487857011520259,
                1.3007128460419196e-05,
                3.288750633518874e-06
            ],
            [
                0.09534945847239201,
                0.000179528005914876,
                2.4300240719941574e-05,
                NaN,
                NaN,
                NaN,
                0.9995694429550493,
                0.0006263341357385689,
                0.9999687980924505,
                7.889263525405172e-06
            ],
            [
                NaN,
                0.0002611902128145898,
                0.00023050671205324414,
                0.0002611904286903425,
                0.037326888013444755,
                5.8291264734055934e-05,
                0.00029595702201328064,
                0.00037998456841188027,
                0.00017952789965322604,
                0.0001233946033931049
            ],
            [
                0.00033535005868644144,
                2.4300240731964193e-05,
                7.88926634687567e-06,
                NaN,
                2.1444950940863522e-05,
                0.9996200155237962,
                1.1478773595343877e-05,
                6.962255418063657e-06,
                0.0005527786782790016,
                NaN
            ],
            [
                0.9999952149060776,
                0.9999687980998182,
                0.9999339478711341,
                0.99998526102158,
                NaN,
                0.9999930377420979,
                0.9999810748495156,
                0.9999869928715429,
                0.9995694429506905,
                0.0017007226901266336
            ],
            [
                0.9993736659303538,
                6.9622570786798724e-06,
                0.9998601779435574,
                0.9997694933152848,
                0.9933071493202787,
                NaN,
                NaN,
                0.9995121429663693,
                0.9996646500190159,
                0.9992903295364217
            ],
            [
                2.1444945852673643e-05,
                1.1478768118310953e-05,
                NaN,
                3.12019225022362e-05,
                3.1201900209877224e-05,
                5.422218969029887e-06,
                0.00012339461870253485,
                NaN,
                1.8925143710057227e-05,
                0.00012339455973421916
            ],
            [
                0.46879062662624377,
                5.8291244593124e-05,
                0.000626334135920742,
                0.9999038975872973,
                0.9999646437496492,
                0.9999546021381029,
                0.9999724643089384,
                0.9999251538063291,
                8.481104106212545e-05,
                0.9999546021261888
            ],
            [
                0.679178699175393,
                1.0129987354366822e-05,
                3.726638395415398e-06,
                1.0129988548731703e-05,
                3.1201903922734266e-05,
                7.889264447947691e-06,
                3.7266392836374875e-06,
                4.006369691549301e-05,
                0.0,
                4.006370169826257e-05
            ],
            [
                0.9999810748450335,
                0.9998601778941887,
                0.999373665839413,
                0.9999930377420924,
                0.9994472212703323,
                0.999876605394842,
                0.9579122681794381,
                0.9149009631141181,
                0.5621765008857982,
                0.9999251537639511
            ],
            [
                9.610243744921641e-05,
                NaN,
                0.00013982214009899607,
                6.60521682190406e-05,
                NaN,
                0.7057850340255386,
                2.4300237770687153e-05,
                1.892515724164839e-05,
                7.889263525534328e-06,
                3.120192622803585e-05
            ],
            [
                0.9859363759397891,
                4.539785781515392e-05,
                1.892514147143123e-05,
                1.6701415867707307e-05,
                0.0003353500701017786,
                NaN,
                1.4738981967202704e-05,
                3.5356250694926364e-05,
                2.9023123310580418e-06,
                0.7981867777396212
            ],
            [
                NaN,
                0.00043055698402681345,
                4.53978847572308e-05,
                0.0011695103116999782,
                0.000295957021694676,
                5.829125844846945e-05,
                NaN,
                4.5397879059919406e-05,
                NaN,
                0.0005527785814186091
            ],
            [
                1.4738983716586539e-05,
                3.7266401720529807e-06,
                2.5612819052374947e-06,
                4.785093924103951e-06,
                7.338208055536515e-07,
                1.5534984953298217e-06,
                2.1444943298320236e-05,
                3.1201907574637766e-05,
                3.2887486731641103e-06,
                2.5612812946890944e-06
            ],
            [
                NaN,
                0.9998766053671119,
                0.9999599363174188,
                0.9999756997476992,
                NaN,
                0.9999832985822078,
                0.8933094067644466,
                NaN,
                0.9995121429594154,
                0.817574471748733
            ],
            [
                0.005911068618186972,
                0.0009110510862647044,
                4.539787387721303e-05,
                2.1444948408275583e-05,
                8.481103101257137e-05,
                5.829127939986156e-05,
                4.006368736453013e-05,
                4.539788484641129e-05,
                0.9998766054701126,
                0.00037998443974503594
            ],
            [
                NaN,
                NaN,
                0.9740426404474869,
                0.9999599363152073,
                0.13296424706933604,
                0.8175744695262775,
                NaN,
                NaN,
                0.9999832985702178,
                0.9999810748443244
            ],
            [
                8.481105099876433e-05,
                0.000108896909056849,
                6.144176798870286e-06,
                7.88926164299515e-06,
                2.430024072188641e-05,
                0.00013982210653147538,
                NaN,
                8.481107145513842e-05,
                1.892514371900746e-05,
                3.120191506210258e-05
            ],
            [
                0.9992903296553464,
                2.1444940721576954e-05,
                1.4738981963234875e-05,
                0.9998766054253783,
                1.3007125341337584e-05,
                1.1478765388105516e-05,
                0.29421496597446134,
                0.22270013882530884,
                8.939697368305565e-06,
                NaN
            ],
            [
                NaN,
                5.144221962539264e-05,
                6.605214441493472e-05,
                1.0129993391531815e-05,
                4.539788974902612e-05,
                2.1444953508090254e-05,
                4.222832437109582e-06,
                1.6701425813006818e-05,
                4.539785768997102e-05,
                4.006369690762278e-05
            ],
            [
                8.315279284937352e-07,
                1.1478773596847203e-05,
                7.889265407004852e-06,
                1.670142979997471e-05,
                0.012431652934163972,
                1.067703379136937e-06,
                1.300712690556288e-05,
                2.430024358875087e-05,
                6.1441738691562974e-06,
                7.484620923485531e-05
            ],
            [
                NaN,
                8.939693106329072e-06,
                8.939698433373153e-06,
                4.785095635413826e-06,
                2.9023126770343703e-06,
                1.8925155000714377e-05,
                2.144494074201677e-05,
                5.144220749598207e-05,
                2.7535694354731078e-05,
                1.3007126906036072e-05
            ],
            [
                0.992422757765672,
                0.0005527787168044878,
                0.2689414213699951,
                0.9989677690858095,
                NaN,
                3.120190390775116e-05,
                2.430024647418002e-05,
                NaN,
                3.1201903922734266e-05,
                0.999941708748449
            ],
            [
                NaN,
                0.00023050663048172873,
                0.00013982201524616948,
                5.8291272379732106e-05,
                0.000203426899085842,
                3.120190387358516e-05,
                0.0001233945450100987,
                0.0001398220739160594,
                NaN,
                NaN
            ],
            [
                1.4738978457041559e-05,
                1.670142382493073e-05,
                6.9622554171645e-06,
                3.7266383950934104e-06,
                4.00636873158513e-05,
                5.8291244291588967e-05,
                1.1478772223642496e-05,
                2.1444956079218013e-05,
                2.1444958622572883e-05,
                1.0129990973503458e-05
            ],
            [
                1.6701421840318107e-05,
                0.00029595698170550237,
                1.4738985482351282e-05,
                0.9999945777803876,
                2.144495607789177e-05,
                4.0063687374440786e-05,
                0.0002034268981920281,
                3.5356246487099006e-05,
                1.6701415864001047e-05,
                0.9999910603058294
            ],
            [
                4.222832437386106e-06,
                1.892515049571424e-05,
                6.9622537570932415e-06,
                1.1478764018576587e-05,
                1.8925150482908516e-05,
                1.4738976692993472e-05,
                6.96225707894582e-06,
                2.5612819052072116e-06,
                4.006368735403649e-05,
                7.889262584809997e-06
            ],
            [
                7.889261643554814e-06,
                0.0,
                NaN,
                NaN,
                NaN,
                2.1444945853375776e-05,
                NaN,
                2.1444953522913026e-05,
                NaN,
                1.6701423833436905e-05
            ],
            [
                0.9975273771546244,
                2.753568450356562e-05,
                1.7603434228679863e-06,
                5.829129323782717e-05,
                6.605212087995142e-05,
                0.9525741308615412,
                NaN,
                0.000158436272776466,
                0.9991959141740379,
                1.3007128460419196e-05
            ],
            [
                0.9324533027598817,
                0.9999687980945938,
                0.5926665999540698,
                NaN,
                0.9999945777832369,
                0.9579122731357119,
                0.9999869928717005,
                NaN,
                0.8670357512127873,
                NaN
            ],
            [
                1.5534983100595462e-06,
                2.4300240711101413e-05,
                1.0129993393540266e-05,
                7.889266347248781e-06,
                5.422220908703723e-06,
                9.610244905264348e-05,
                1.4738985484549675e-05,
                0.00017952803026139778,
                1.147876948232818e-05,
                1.012999460108057e-05
            ],
            [
                4.5397879405741464e-05,
                0.9993736659771723,
                1.8925157250667477e-05,
                5.829124461687359e-05,
                NaN,
                3.726639727994339e-06,
                1.3007131564383116e-05,
                4.222831934156396e-06,
                0.9989677689621648,
                NaN
            ],
            [
                6.605212872606623e-05,
                0.9999885212318881,
                0.0003353501847430065,
                0.9999952149066532,
                0.00043055698034432754,
                0.0011695104655043297,
                6.605216016003259e-05,
                0.9999599362938282,
                0.00020342692402384427,
                0.9999930377404449
            ],
            [
                0.9999962733607445,
                0.7310585844894971,
                0.9999982396563669,
                0.9999910603015749,
                0.9999852610145252,
                0.9999417087324761,
                0.9770226313026176,
                0.999989870006606,
                0.9999785550439222,
                0.9999910603058544
            ],
            [
                1.8925148238808306e-05,
                0.00023050679563691373,
                0.0005527787406336923,
                0.00013982210702583335,
                6.605217604545803e-05,
                0.0004305571817538054,
                4.00636873566599e-05,
                0.00017952800867054373,
                6.1441775312976045e-06,
                2.7535704212311033e-05
            ],
            [
                3.1201907623673364e-05,
                0.1329642419157059,
                6.605214449759119e-05,
                1.3007123806876143e-05,
                1.3007131561804229e-05,
                2.144495096083526e-05,
                1.1478773596283455e-05,
                1.8925143724239906e-05,
                5.422220908560712e-06,
                3.726640616748873e-06
            ],
            [
                7.484622709131757e-05,
                0.00010889690882234504,
                1.1478770838077277e-05,
                6.605217598875182e-05,
                NaN,
                5.8291293208140155e-05,
                4.006369218184011e-05,
                5.829125847900465e-05,
                3.120192250723057e-05,
                8.481107121387991e-05
            ],
            [
                6.962256243730292e-06,
                2.144494838463716e-05,
                8.939695213811695e-06,
                1.4738983721733992e-05,
                8.481102098831671e-05,
                5.422220259157241e-06,
                8.481108073217634e-05,
                5.1442201196235026e-05,
                2.7535687762043832e-05,
                1.3007134656943884e-05
            ],
            [
                1.3007128456539035e-05,
                0.00012339455978987673,
                3.535625490931388e-05,
                4.222833946077037e-06,
                3.5356250696598434e-05,
                2.4300232032009452e-05,
                4.006369693691754e-05,
                2.7535681236473055e-05,
                2.430023781683279e-05,
                0.0001088969343420799
            ],
            [
                8.939697304789829e-06,
                0.00010889686928784151,
                NaN,
                6.962257078553231e-06,
                1.4738981968462759e-05,
                1.6701417853595148e-05,
                4.006371125884805e-05,
                2.1444955999565088e-05,
                4.2228344501365644e-06,
                4.785096775998733e-06
            ],
            [
                6.60521445480501e-05,
                0.00023050671395134835,
                0.0001795279655384715,
                3.5356238062828204e-05,
                0.000261190368789857,
                5.829127241747701e-05,
                2.7535684505068197e-05,
                0.0005527785852454304,
                0.01098694374378939,
                7.484624501857396e-05
            ],
            [
                1.8925150486075525e-05,
                1.8925157262061825e-05,
                0.9998911031175879,
                3.120192622644674e-05,
                6.9622562481627565e-06,
                1.6701423831188846e-05,
                1.300713311517055e-05,
                2.4300237817893614e-05,
                5.829128626561938e-05,
                NaN
            ],
            [
                5.144220746828593e-05,
                0.00020342689824530177,
                1.0129995804364571e-05,
                1.892515500450102e-05,
                4.5397890190965e-05,
                0.9993736659824918,
                0.9902915220321715,
                0.0001233945731710354,
                NaN,
                NaN
            ],
            [
                0.0009110513739031566,
                2.753570413007019e-05,
                NaN,
                0.7057850154599562,
                NaN,
                0.0007096704518550738,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                7.8892607025437e-06,
                1.4738978453743973e-05,
                7.484620927950735e-05,
                0.37754066879814546,
                1.892514146382353e-05,
                4.006369695353247e-05,
                1.1478765374158004e-05,
                4.5397890197901266e-05,
                0.00023050676444897375,
                0.00017952805001862485
            ],
            [
                4.785096204972935e-06,
                6.962253759043525e-06,
                1.892515726357648e-05,
                1.892515274614874e-05,
                1.8925141470949294e-05,
                4.0063692165808155e-05,
                1.4738981968462759e-05,
                2.430025231469984e-05,
                1.1478764020560142e-05,
                6.60521682190406e-05
            ],
            [
                4.539788482626311e-05,
                4.00636825989602e-05,
                2.5612819052374947e-06,
                7.889266346287306e-06,
                7.889264465397747e-06,
                8.939695237162584e-06,
                1.147877086020957e-05,
                7.889259763469998e-06,
                3.120192621634449e-05,
                2.4300252313904224e-05
            ],
            [
                0.9999869928700009,
                NaN,
                0.00013982205654233167,
                6.605212801483632e-05,
                0.9999952149066473,
                0.999989870005398,
                0.11920292828022307,
                0.9999756997650652,
                0.8354835391516133,
                0.00010889690892692112
            ],
            [
                NaN,
                NaN,
                NaN,
                6.962253742174839e-06,
                4.785095630030404e-06,
                7.889265394555899e-06,
                6.144177516858052e-06,
                5.829129319244845e-05,
                2.5612812941789413e-06,
                2.7535691060090174e-05
            ],
            [
                1.3007126908307386e-05,
                7.338210679695891e-07,
                4.222831934156396e-06,
                0.9980732654692032,
                6.962255416759247e-06,
                1.3709578605355551e-06,
                1.5534973841309562e-06,
                0.9992903295246159,
                3.726639727994339e-06,
                2.1444943287710254e-05
            ],
            [
                1.1478765387416494e-05,
                1.3007130011655787e-05,
                1.4738987242137685e-05,
                4.7850933534310035e-06,
                1.4738985446345907e-05,
                0.9999938558246672,
                8.939695234723424e-06,
                1.6701427813872793e-05,
                3.535626294065219e-05,
                5.14422197242005e-05
            ],
            [
                0.00023050673977361526,
                0.001032230855969373,
                8.481101084374256e-05,
                0.00026119024515110337,
                0.00013982202373365993,
                0.0008040858149253544,
                0.0009110512928409201,
                0.00037998456008761283,
                0.00012339455890115095,
                0.00023050662805376595
            ],
            [
                2.7535684518791692e-05,
                2.430024072471526e-05,
                7.889259762666377e-06,
                0.9999885212332705,
                6.962258738701267e-06,
                3.5356267531385634e-05,
                2.1444958628814052e-05,
                0.9999546021476268,
                1.6701419845680582e-05,
                4.539785232329117e-05
            ],
            [
                3.120190761663585e-05,
                2.4300240707388545e-05,
                3.120191879981973e-05,
                2.7535704202894907e-05,
                NaN,
                5.4222183222304545e-06,
                4.785096774693134e-06,
                3.120190749381984e-05,
                1.4738983726908257e-05,
                3.5356250638847714e-05
            ],
            [
                3.12019186816575e-05,
                NaN,
                NaN,
                1.4738988973747334e-05,
                NaN,
                2.144494073483943e-05,
                9.610244890302106e-05,
                5.1442231983486416e-05,
                NaN,
                1.3007131543917626e-05
            ],
            [
                1.67014158650947e-05,
                4.0063692129517645e-05,
                NaN,
                NaN,
                NaN,
                3.1201903906162046e-05,
                NaN,
                3.120190763922401e-05,
                NaN,
                4.006368260595596e-05
            ],
            [
                3.1201907623673364e-05,
                NaN,
                0.0010322309815348257,
                8.481104109174285e-05,
                0.0001088968684306349,
                0.0001795279436002284,
                1.0129993393540266e-05,
                5.1442219536690144e-05,
                NaN,
                5.144220132535887e-05
            ],
            [
                3.726640172503764e-06,
                0.0031726826009610427,
                6.962255418215627e-06,
                2.1444950959196957e-05,
                7.889259763469998e-06,
                7.338211554464836e-07,
                2.1444953507076064e-05,
                4.006368263612517e-05,
                2.144494073054863e-05,
                3.1201926224857616e-05
            ],
            [
                6.9622562472889285e-06,
                9.610243761002552e-05,
                1.3007131557025005e-05,
                2.430024072188641e-05,
                4.539786858947248e-05,
                4.5397890187331725e-05,
                0.00010889690836918206,
                4.785096203588998e-06,
                3.1201911358551906e-05,
                1.0129995808418327e-05
            ],
            [
                NaN,
                NaN,
                1.3007125351889727e-05,
                NaN,
                NaN,
                5.144220750533887e-05,
                4.785095632885315e-06,
                NaN,
                2.902312328257395e-06,
                NaN
            ],
            [
                5.8291285700717914e-05,
                NaN,
                2.902313368860448e-06,
                0.0008040861137154286,
                4.0063677742154484e-05,
                NaN,
                1.892515726099468e-05,
                1.8925152639778576e-05,
                2.4300243601392304e-05,
                8.939698434657777e-06
            ],
            [
                NaN,
                4.006370637667922e-05,
                0.00017952804691817145,
                0.0001795279646059851,
                1.300712843988273e-05,
                1.5534979396815448e-06,
                4.222833443645997e-06,
                1.8925154962572585e-05,
                6.605212873904136e-05,
                3.120190392670705e-05
            ],
            [
                7.889259763010786e-06,
                5.82912515996789e-05,
                0.9999785550593413,
                0.9999785550413756,
                0.5621765008857982,
                0.18242552158390102,
                0.9999339478715565,
                0.9982992775191883,
                2.1444943294263477e-05,
                NaN
            ],
            [
                0.999993037742107,
                NaN,
                0.9999885212307351,
                NaN,
                NaN,
                0.9998204720812269,
                0.9999930377412616,
                1.8925152706698834e-05,
                5.1442225844299154e-05,
                0.0002959570953956673
            ],
            [
                1.8925154994724604e-05,
                NaN,
                0.10669058542447808,
                0.9999339478508856,
                0.2942149597859341,
                NaN,
                0.999968798092416,
                0.7310585903489892,
                NaN,
                0.9998766054130727
            ]
        ]
    },
    {
        "q_id": "8983_mmlu_math",
        "cot_ids": [
            0,
            2,
            4,
            5,
            9,
            10,
            11,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            24,
            26,
            27,
            28,
            29,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            48,
            49,
            50,
            51,
            52,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            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,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            107,
            108,
            109,
            110,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.4300252316291068e-05,
                1.473898021366358e-05,
                0.9998601779594297,
                5.8291286393273546e-05,
                5.422220908762902e-06,
                2.2603245672867952e-06,
                0.9999869928668841,
                NaN,
                3.535624228441698e-05,
                3.120190021453107e-05
            ],
            [
                4.222833444506298e-06,
                1.994729483666479e-06,
                1.5534979397677313e-06,
                3.72664017246987e-06,
                4.785092783371756e-06,
                6.962255419279419e-06,
                3.7266397282926013e-06,
                2.1444948410303962e-05,
                1.370957370247318e-06,
                1.0677027427471959e-06
            ],
            [
                5.422217030555087e-06,
                5.715004470295662e-07,
                6.475951069932288e-07,
                1.5534981249397663e-06,
                1.0129990979842057e-05,
                9.422444815679433e-07,
                1.2098662604192665e-06,
                1.2098662604049616e-06,
                2.561282515988704e-06,
                7.338211554758494e-07
            ],
            [
                1.1478769493540482e-05,
                4.78509278348926e-06,
                6.144172404693786e-06,
                4.222832437747125e-06,
                3.2887486733420804e-06,
                1.3007123812980299e-05,
                5.422217676979575e-06,
                1.0677027427525368e-06,
                3.1201903931474406e-05,
                1.7603427936263351e-06
            ],
            [
                1.0677029972993568e-06,
                7.889260704818233e-06,
                8.315277302649045e-07,
                1.0677024881829577e-06,
                6.1441760667392215e-06,
                7.338210679949506e-07,
                5.144221978689107e-05,
                8.939697369671496e-06,
                8.939694172290508e-06,
                4.785096776394765e-06
            ],
            [
                5.14422381608502e-05,
                1.553497384180408e-06,
                6.1441724044534996e-06,
                6.144173869240119e-06,
                6.962253759581752e-06,
                4.222832437747125e-06,
                1.2098661161982042e-06,
                5.422219616085833e-06,
                2.1444950970119003e-05,
                5.4222215552470286e-06
            ],
            [
                9.422445938964242e-07,
                6.475947210031623e-07,
                1.8925141472773765e-05,
                1.3709567165461505e-06,
                1.300712691308661e-05,
                3.7266392840781026e-06,
                6.144172404520556e-06,
                3.288750241473551e-06,
                8.939695237959376e-06,
                1.1478772230407462e-05
            ],
            [
                4.450849458218309e-07,
                8.315282258956806e-07,
                3.288750633545794e-06,
                3.288748281295496e-06,
                1.3709570434122812e-06,
                2.1444943292703185e-05,
                7.338208055613267e-07,
                6.475948753965404e-07,
                1.5534973841592143e-06,
                4.7850933538313875e-06
            ],
            [
                1.0677031245623505e-06,
                1.6701421842961097e-05,
                1.892514823488397e-05,
                3.535624649468763e-05,
                2.4300240730549767e-05,
                1.147876538716594e-05,
                2.260323758939877e-06,
                8.939693106329072e-06,
                4.539787405573911e-05,
                0.9995694429648818
            ],
            [
                1.9947299590810645e-06,
                2.2603234894560207e-06,
                2.902311985079115e-06,
                7.88926070328992e-06,
                6.47594566597747e-07,
                1.0129987356706945e-05,
                2.2603251061664e-06,
                8.939700566801578e-06,
                5.422220908560712e-06,
                3.288748673265808e-06
            ],
            [
                1.4738981971813965e-05,
                2.2603242978377903e-06,
                1.370957533676711e-06,
                7.48462628538078e-05,
                4.785092783415276e-06,
                3.120192625278069e-05,
                1.5534981249496567e-06,
                8.939694172770212e-06,
                1.7603432133032607e-06,
                4.222834954514924e-06
            ],
            [
                3.120190765307203e-05,
                1.670141786325573e-05,
                2.7535700947019215e-05,
                3.120191509274984e-05,
                2.260324028427877e-06,
                5.144219525429276e-05,
                8.481108177187105e-05,
                5.1442213646395314e-05,
                6.1441760667392215e-06,
                1.9947304348703948e-06
            ],
            [
                7.484624508881928e-05,
                0.0001795280087698,
                4.539785780557527e-05,
                2.4300249423965898e-05,
                6.144176066672166e-06,
                1.8925155008528632e-05,
                0.9999852610145148,
                0.00012339453078510262,
                0.0001398221236224284,
                2.7535700944314574e-05
            ],
            [
                5.144223203551027e-05,
                0.9999339478631828,
                3.120191137012976e-05,
                0.9999038975392328,
                6.96225873895455e-06,
                0.9992903296235616,
                3.535626755762428e-05,
                2.4300246527309398e-05,
                0.00015843621644695267,
                2.1444945856418342e-05
            ],
            [
                2.5612812946890944e-06,
                9.422442569097361e-07,
                1.5534973841450852e-06,
                6.475945665900901e-07,
                8.315278293899016e-07,
                7.889263526266196e-06,
                5.043476486833397e-07,
                1.2098659719524008e-06,
                7.338210679755959e-07,
                4.785093924047376e-06
            ],
            [
                0.9999962733589389,
                0.9999962733589389,
                0.9999977396751633,
                0.999975699759268,
                0.9999967112493664,
                0.9999930377462403,
                0.99999303774624,
                0.9999967112501504,
                0.9999945777803838,
                0.9999930377445801
            ],
            [
                4.222834451169694e-06,
                6.962256249606473e-06,
                4.78509563546605e-06,
                1.9947290081177566e-06,
                3.7266379512112265e-06,
                9.42244818532859e-07,
                1.5534975693792215e-06,
                8.315282258832022e-07,
                4.222832941111319e-06,
                1.1478772230198667e-05
            ],
            [
                7.338207180714596e-07,
                1.3709576971316842e-06,
                4.450849458218309e-07,
                1.3709578605542582e-06,
                9.422448185264317e-07,
                1.7603440524628877e-06,
                9.422443692261927e-07,
                1.0677026154730804e-06,
                9.422443692390473e-07,
                8.315277302788957e-07
            ],
            [
                7.889264466545779e-06,
                7.889265406681968e-06,
                1.8925143727854426e-05,
                4.22283394786293e-06,
                NaN,
                1.6701423835320418e-05,
                3.726638395215427e-06,
                NaN,
                4.006368260129212e-05,
                2.2603251062147097e-06
            ],
            [
                4.785096205582214e-06,
                2.260324028372372e-06,
                6.144177531599359e-06,
                1.2098661161789477e-06,
                4.222832437747125e-06,
                2.9023126768258393e-06,
                4.785093353909723e-06,
                1.0677027427340866e-06,
                7.889261645090304e-06,
                3.726640616670918e-06
            ],
            [
                1.9947290080905435e-06,
                7.33820893021171e-07,
                3.726640616670918e-06,
                1.3709567165461505e-06,
                9.422442569028803e-07,
                1.3709568799106278e-06,
                4.4508489275752546e-07,
                2.2603251062013478e-06,
                5.715002426439334e-07,
                2.9023133690821773e-06
            ],
            [
                2.753568781693781e-05,
                0.9999832985721836,
                0.0002959570988658745,
                0.00026119024673183083,
                6.14417606659952e-06,
                3.535626755929635e-05,
                0.99995460213681,
                0.9998911031167544,
                2.1444945855248125e-05,
                3.1201922520397544e-05
            ],
            [
                5.71500242637956e-07,
                3.7266379512857925e-06,
                1.0129988564099116e-05,
                5.043473480730849e-07,
                5.043475885674441e-07,
                1.7603438428660665e-06,
                5.715002426410745e-07,
                3.0590229985449037e-07,
                8.315278293951957e-07,
                5.043475885634304e-07
            ],
            [
                1.670142581883963e-05,
                1.1478768124992398e-05,
                1.6701421834728333e-05,
                4.78509563535725e-06,
                6.962254589617333e-06,
                6.144176798132662e-06,
                2.2603237589028734e-06,
                2.9023109471188266e-06,
                3.288748673265808e-06,
                4.222831934248571e-06
            ],
            [
                3.7266379512112265e-06,
                6.144175334094145e-06,
                0.998674977716347,
                3.7266392838544054e-06,
                7.889261644875049e-06,
                8.939700566801578e-06,
                1.994730434816876e-06,
                3.726640616630245e-06,
                1.892514147046736e-05,
                5.422217676925328e-06
            ],
            [
                0.9999869928715358,
                0.9999982396565769,
                0.9999898700090201,
                0.9999921107364738,
                0.9999785550515873,
                0.9999957771650453,
                0.9999910603015649,
                0.9999970976873229,
                0.9999930377454102,
                0.9999962733593831
            ],
            [
                3.726638839806038e-06,
                1.0677026154551157e-06,
                1.9947301970106386e-06,
                3.726639284125553e-06,
                1.553497199007048e-06,
                4.78509563550957e-06,
                5.422217676797111e-06,
                6.962257079775324e-06,
                3.7266388398585725e-06,
                5.04347408197782e-07
            ],
            [
                2.1444945850567248e-05,
                1.0129988562901417e-05,
                1.0129988561648438e-05,
                8.939698433974813e-06,
                1.1478772227338172e-05,
                1.4738985485166298e-05,
                1.300712846361323e-05,
                1.300713001414004e-05,
                1.8925154997891613e-05,
                4.0063687388140825e-05
            ],
            [
                0.9999910603004997,
                3.5356254894393866e-05,
                0.999997438717484,
                5.144220748924517e-05,
                8.481104113061569e-05,
                0.9999930377412606,
                0.9999952149032236,
                0.9999970976890528,
                0.9999970976883609,
                5.144220136428317e-05
            ],
            [
                6.144177530794679e-06,
                4.222833947674739e-06,
                6.962254589104433e-06,
                7.889262584350785e-06,
                1.3007134663876127e-05,
                1.670142383495587e-05,
                1.670142781636389e-05,
                7.889265406567165e-06,
                1.3007125361755747e-05,
                6.9622570786798724e-06
            ],
            [
                7.484624508881928e-05,
                0.00013982205735608936,
                5.829129331162062e-05,
                0.9999646437492881,
                0.00026119027671245645,
                0.9999967112513266,
                9.610239201366058e-05,
                0.0010322309385592675,
                0.9997388096285122,
                8.481107168590743e-05
            ],
            [
                3.535625071344775e-05,
                2.5612812947077304e-06,
                1.8925145981833788e-05,
                9.610243785962923e-05,
                7.88926540679677e-06,
                5.422218969661113e-06,
                1.6701417861584877e-05,
                2.2603251062013478e-06,
                2.2603242978213447e-06,
                3.535625913514915e-05
            ],
            [
                1.2098658277451275e-06,
                3.120190765307203e-05,
                1.2098661161982042e-06,
                5.422220262505697e-06,
                1.4738988998117324e-05,
                NaN,
                1.1478773598914277e-05,
                3.726638395527247e-06,
                1.0677028700320085e-06,
                1.3709578605617394e-06
            ],
            [
                3.726639284050988e-06,
                7.48462093682669e-05,
                2.1444956079218013e-05,
                1.4738983728784933e-05,
                1.147876675686207e-05,
                1.1478765387667046e-05,
                1.670142980687079e-05,
                2.430023493485234e-05,
                2.144494329952946e-05,
                1.3007126913820052e-05
            ],
            [
                7.3382080556433e-07,
                3.4663249714451116e-07,
                1.3709572068422585e-06,
                1.5534984953298217e-06,
                1.76034300345598e-06,
                7.338213304316717e-07,
                6.1441731370702875e-06,
                1.67014238321306e-05,
                2.2603251061849014e-06,
                7.338213304316717e-07
            ],
            [
                0.9998415637454438,
                0.9999756997650714,
                4.539789028526512e-05,
                0.0001398221073676117,
                3.7266397283231055e-06,
                0.9997388096592225,
                1.6701419853184244e-05,
                1.6701427815999337e-05,
                2.1444950968441685e-05,
                1.4738983728490028e-05
            ],
            [
                4.222835457852533e-06,
                4.0063692185483734e-05,
                1.3709576970537545e-06,
                1.370957370196196e-06,
                1.7603434231385591e-06,
                2.5612834317535587e-06,
                6.475951069808602e-07,
                3.288749849114211e-06,
                2.9023123307122503e-06,
                1.9947299591100915e-06
            ],
            [
                2.144494074201677e-05,
                1.892514598427789e-05,
                1.012999460108057e-05,
                1.0129993393742954e-05,
                8.93969310675186e-06,
                5.1442219784084046e-05,
                1.1478770861441461e-05,
                2.430024072285883e-05,
                6.962256249517824e-06,
                2.561283126535066e-06
            ],
            [
                2.561282821176841e-06,
                2.561283126639892e-06,
                6.962255418658875e-06,
                5.4222196143006464e-06,
                4.785096775920397e-06,
                1.3007134663876127e-05,
                3.7266406163624873e-06,
                3.7266388395620047e-06,
                8.939695237341456e-06,
                1.892515725920463e-05
            ],
            [
                1.0129993391236997e-05,
                1.7603434231705793e-06,
                1.4738978458140753e-05,
                1.994730434847717e-06,
                9.422448185264317e-07,
                8.315277302701984e-07,
                3.726639283440905e-06,
                3.726640172537657e-06,
                1.3709578605617394e-06,
                9.422442569290178e-07
            ],
            [
                5.82912515827149e-05,
                1.473898724181597e-05,
                3.535623806861614e-05,
                9.610242633451056e-05,
                3.1201907654207106e-05,
                2.75356812513986e-05,
                8.939695238211425e-06,
                0.00010889687022902587,
                2.1444950970119003e-05,
                2.4300246522270504e-05
            ],
            [
                7.889265407004852e-06,
                NaN,
                1.4738976694494812e-05,
                2.2603234895176927e-06,
                3.7266410609160796e-06,
                3.288750241500471e-06,
                1.0129994602222992e-05,
                7.88926634687567e-06,
                1.0677024881887838e-06,
                3.7266388397721442e-06
            ],
            [
                1.2098661161789477e-06,
                5.04347648686092e-07,
                2.9023119851055122e-06,
                2.260324836696773e-06,
                5.715003107619008e-07,
                1.7603425836005905e-06,
                7.338210679909462e-07,
                7.338211554464836e-07,
                6.144173136455602e-06,
                6.475945666009864e-07
            ],
            [
                1.300713001414004e-05,
                6.962258739530771e-06,
                2.5612812947240366e-06,
                1.147876402018431e-05,
                6.1441767989541075e-06,
                1.3007133115903994e-05,
                6.144176066443055e-06,
                7.338210679909462e-07,
                1.5534971989809095e-06,
                1.7603436329714805e-06
            ],
            [
                6.962257079275089e-06,
                9.422443692390473e-07,
                5.043475284430694e-07,
                1.553497384180408e-06,
                6.9622595694023114e-06,
                1.3709568799368123e-06,
                1.0677033791437343e-06,
                1.7603438428460541e-06,
                1.5534973841592143e-06,
                4.785092783319532e-06
            ],
            [
                4.785095064819011e-06,
                8.93969310662177e-06,
                1.1478769491014062e-05,
                5.422217676797111e-06,
                6.14417313680765e-06,
                2.144495863482118e-05,
                1.1478764019077695e-05,
                7.889260704308795e-06,
                1.0129994600398803e-05,
                1.3007131559816827e-05
            ],
            [
                2.4300240732671408e-05,
                0.9996646499298982,
                7.484620934866355e-05,
                5.1442232038504445e-05,
                3.535625492783527e-05,
                2.4300246520590875e-05,
                5.1442195245310235e-05,
                2.7535694380675497e-05,
                0.00015843621647461487,
                9.610244926309368e-05
            ],
            [
                0.9998911030699139,
                0.2689414330889797,
                0.9998766054556021,
                0.9840936085797521,
                0.9999852610163138,
                0.9999852610180751,
                2.561282515886208e-06,
                0.9989677687960247,
                0.4378234991142019,
                0.9999251537406317
            ],
            [
                0.9999952149072165,
                0.9999417087344652,
                0.9999994956525918,
                0.9999986290421394,
                0.9999885212291376,
                0.9999980052707541,
                0.9999967112505425,
                0.9999970976887068,
                0.9999952149037941,
                0.9999910603047617
            ],
            [
                1.8925141472773765e-05,
                0.9999756997505781,
                5.829129334130764e-05,
                2.1444948414321717e-05,
                1.1478770861650256e-05,
                4.785094494750855e-06,
                8.481105144611057e-05,
                1.300713466685723e-05,
                6.605212096501064e-05,
                4.5397857812676685e-05
            ],
            [
                0.9999038975507166,
                3.5356238062828204e-05,
                0.0001233945745678611,
                2.1444945854624007e-05,
                4.539786864000808e-05,
                2.7535691097454142e-05,
                6.144175334367959e-06,
                3.535626756842843e-05,
                6.605217613436184e-05,
                2.7535684534618784e-05
            ],
            [
                0.9999417087275358,
                0.999841563745317,
                0.9998766054692957,
                0.9998415638021374,
                0.9990889486543891,
                0.9998601778592275,
                0.9982992774676008,
                0.9971990728592448,
                0.9998415638406848,
                0.5
            ],
            [
                0.9999832985721853,
                0.9999810748449944,
                2.7535694378772238e-05,
                0.9997388095978781,
                2.7535697664698622e-05,
                1.3007133116353526e-05,
                0.00017952796598251267,
                1.1478772230929451e-05,
                0.9999485577618125,
                0.0001233946042513091
            ],
            [
                5.8291251631486394e-05,
                0.00023050674248327666,
                0.00033535018646018593,
                7.48462272350754e-05,
                0.9997388097541118,
                1.892514147143123e-05,
                3.120190020862863e-05,
                4.006367785525258e-05,
                6.605215250517728e-05,
                4.0063711285810896e-05
            ],
            [
                3.1201907642061724e-05,
                1.1478772230407462e-05,
                2.561282821352716e-06,
                4.785093353626844e-06,
                0.00010889687022902587,
                6.962255419570695e-06,
                5.829126554578343e-05,
                0.0002305066315012048,
                6.9622579095833456e-06,
                8.939698435226916e-06
            ],
            [
                1.2098653950403334e-06,
                9.422445938917108e-07,
                6.14417753171671e-06,
                8.31528126775552e-07,
                3.288747889229516e-06,
                1.994729008105057e-06,
                9.422444815220956e-07,
                7.338207180601138e-07,
                7.33820893021171e-07,
                7.338210679949506e-07
            ],
            [
                1.1478764019996392e-05,
                6.1441746017453204e-06,
                4.7850967763512445e-06,
                7.88925976397226e-06,
                7.889266347456862e-06,
                2.9023109471689794e-06,
                3.7266410608720178e-06,
                7.889260704531226e-06,
                1.6701427813872793e-05,
                1.0129987356191011e-05
            ],
            [
                1.8925143726890553e-05,
                1.0129989772412744e-05,
                1.3007123812767362e-05,
                0.9978172832265649,
                8.939694172542558e-06,
                2.561283432035425e-06,
                2.7535704227537108e-05,
                4.5397890268254766e-05,
                1.6701419852819694e-05,
                6.9622595694023114e-06
            ],
            [
                1.3007130014376633e-05,
                7.88926634755014e-06,
                4.006370650653807e-05,
                2.753568453191415e-05,
                2.144494330062167e-05,
                5.1442213657997754e-05,
                0.00010889689621142153,
                1.6701423834591316e-05,
                0.00013982210734726777,
                2.430025231469984e-05
            ],
            [
                7.889261645090304e-06,
                1.7603438428740716e-06,
                NaN,
                4.450849988811838e-07,
                1.0677027427471959e-06,
                7.338208930421943e-07,
                2.2603251062013478e-06,
                1.0677029973158649e-06,
                2.9023112931873767e-06,
                7.88926634755014e-06
            ],
            [
                5.04347648686092e-07,
                8.315284241597959e-07,
                2.2603251062147097e-06,
                0.9999724643056167,
                1.3709572068079696e-06,
                3.7266397282926013e-06,
                0.9999251537459666,
                0.9999724643154654,
                0.9999810748449911,
                0.9999869928684348
            ],
            [
                1.147876538330323e-05,
                1.4738981969240237e-05,
                8.939699499627926e-06,
                2.4300246508833455e-05,
                3.7266388396975786e-06,
                7.88926164421493e-06,
                8.939699500636112e-06,
                6.962256249112569e-06,
                4.785092782692845e-06,
                2.9023116390421582e-06
            ],
            [
                5.1442219778095686e-05,
                5.144223816721283e-05,
                1.8925157264471508e-05,
                2.7535700945316292e-05,
                1.3007125363293615e-05,
                3.1201918809808464e-05,
                2.7535684534618784e-05,
                2.7535704229340197e-05,
                1.8925152752138513e-05,
                0.9999785550541436
            ],
            [
                0.00010889694808591575,
                4.7850950648799385e-06,
                2.4300246524568948e-05,
                2.5612815999679353e-06,
                1.3007126913820052e-05,
                1.3007125360809367e-05,
                0.9993736657599855,
                2.4300243625614346e-05,
                2.1444943298944354e-05,
                2.430023783601594e-05
            ],
            [
                6.962257079629686e-06,
                1.4738981971813965e-05,
                2.1444948410303962e-05,
                7.88926258532661e-06,
                6.605216041761327e-05,
                1.8925157264919016e-05,
                1.0129994602656007e-05,
                6.605216829977486e-05,
                1.0129994602656007e-05,
                8.481104136817193e-05
            ],
            [
                2.430024362932722e-05,
                1.300712691308661e-05,
                0.0001088968960910006,
                2.1444945854624007e-05,
                3.120191136263821e-05,
                2.753568781423318e-05,
                2.260324028404236e-06,
                2.1444950968441685e-05,
                6.962255419475714e-06,
                6.605213678458984e-05
            ],
            [
                2.1444940744864302e-05,
                1.0129992186774007e-05,
                1.012998977108606e-05,
                4.222832437677995e-06,
                3.1201903931474406e-05,
                7.889259764273619e-06,
                5.422219615750493e-06,
                1.6701423833831836e-05,
                1.670142781709299e-05,
                4.450848927621807e-07
            ],
            [
                0.00026119033967558135,
                0.00013982209049434095,
                0.00012339454545895,
                8.481102110555223e-05,
                0.0001088969221019232,
                0.0002305067410680822,
                9.610239172350516e-05,
                9.610242625969935e-05,
                5.144220137064579e-05,
                0.00023050663267494372
            ],
            [
                6.47594952595231e-07,
                7.338212429504183e-07,
                5.043474683204221e-07,
                3.288749849498565e-06,
                8.315277302701984e-07,
                2.9023126770343703e-06,
                5.043472278299047e-07,
                8.315282259089153e-07,
                4.450849988811838e-07,
                8.315278294072958e-07
            ],
            [
                6.144177531208195e-06,
                6.475947981975644e-07,
                1.0677032518578904e-06,
                7.338208055579897e-07,
                7.889259764079887e-06,
                4.222833947774596e-06,
                9.422450431954847e-07,
                1.2098662604126641e-06,
                1.3709572068272963e-06,
                4.450849988780466e-07
            ],
            [
                0.9999756997563694,
                1.3007134665130082e-05,
                0.9999952149055052,
                1.1478773598914277e-05,
                4.539787405573911e-05,
                1.300713156582635e-05,
                8.939695238536645e-06,
                3.535624224711697e-05,
                2.753569437145972e-05,
                0.00043055708771260213
            ],
            [
                5.043476486902204e-07,
                9.422448185435711e-07,
                1.2098659719661556e-06,
                NaN,
                3.2887502415438413e-06,
                2.5612812947380135e-06,
                1.7603438428188364e-06,
                3.535626755428014e-05,
                4.785095065132354e-06,
                4.785093924251918e-06
            ],
            [
                3.120190020204515e-05,
                4.00636826148464e-05,
                6.605213674374218e-05,
                2.4300232036606334e-05,
                3.1201926243586504e-05,
                5.144223815074485e-05,
                5.144223202577919e-05,
                4.5397890270732005e-05,
                6.605216828103296e-05,
                0.00017952798611586167
            ],
            [
                0.9999957771645419,
                0.9999945777797374,
                0.9999869928746369,
                0.9999967112493664,
                0.9999910603047617,
                0.9999898700102277,
                0.9999599363173639,
                0.9999910603036959,
                0.9999810748495044,
                0.9999724642990513
            ],
            [
                9.422444815563743e-07,
                4.785092783454444e-06,
                2.6995787400208416e-07,
                2.9023119851635836e-06,
                1.4738980213020151e-05,
                6.144175334015912e-06,
                4.78509563546605e-06,
                1.5534975693601474e-06,
                4.450849458179853e-07,
                1.0677027427471959e-06
            ],
            [
                2.260323758923431e-06,
                6.9622579095833456e-06,
                1.2098662604049616e-06,
                1.012999460278499e-05,
                7.889259763857458e-06,
                8.939699501229642e-06,
                4.785094494750855e-06,
                6.962257909412379e-06,
                1.76034300345598e-06,
                1.0129989772412744e-05
            ],
            [
                2.9023126769050284e-06,
                5.422217030362759e-06,
                6.47594643788744e-07,
                1.760344052632596e-06,
                6.962254589104433e-06,
                2.902311292960369e-06,
                8.939695237504067e-06,
                1.2098659718847284e-06,
                1.3709576970949014e-06,
                1.3709576970824327e-06
            ],
            [
                2.561281905100056e-06,
                1.6701421841259862e-05,
                1.7603436328994344e-06,
                1.994729958830706e-06,
                2.5612812947508257e-06,
                5.4222183234485234e-06,
                1.3709576971160984e-06,
                3.7266401724291984e-06,
                4.2228349546493465e-06,
                6.962256249517824e-06
            ],
            [
                8.939694172290508e-06,
                1.5534975693601474e-06,
                1.7603432132784448e-06,
                1.5534979397677313e-06,
                1.9947306726049992e-06,
                1.1478765388898939e-05,
                2.9023109471452223e-06,
                8.939699500489763e-06,
                1.994729245878497e-06,
                1.553498310118888e-06
            ],
            [
                1.1478765387667046e-05,
                2.144495863045236e-05,
                NaN,
                NaN,
                3.12019262448351e-05,
                2.753570422573402e-05,
                NaN,
                1.670141587068447e-05,
                NaN,
                NaN
            ],
            [
                0.9999957771670589,
                0.999992110736474,
                0.9999995549151073,
                0.9999992661790195,
                0.999995214903794,
                0.9999987901343165,
                0.9999986290421394,
                0.9999995549151073,
                0.9999952149066461,
                0.9999987901341723
            ],
            [
                4.539788486936701e-05,
                0.001325022710983726,
                0.9998415637077608,
                3.1201903929204235e-05,
                0.00037998443974503594,
                1.892515500663531e-05,
                6.1441767990323395e-06,
                3.535626757125808e-05,
                3.5356246488642456e-05,
                1.300712536203966e-05
            ],
            [
                1.2098656833865714e-06,
                1.5534984953298217e-06,
                2.561283431888668e-06,
                3.726639284017094e-06,
                1.3709570433979422e-06,
                3.4663249713741784e-07,
                4.222832941072913e-06,
                4.785093924103951e-06,
                1.7603434231097403e-06,
                1.994729483694599e-06
            ],
            [
                0.9999599363221466,
                NaN,
                0.9999546021205307,
                8.481103122174425e-05,
                NaN,
                3.535623805498234e-05,
                NaN,
                2.4300237834601515e-05,
                NaN,
                5.422220908560712e-06
            ],
            [
                3.7266406168403854e-06,
                6.1441724044534996e-06,
                1.7603425837606927e-06,
                1.7603427936079236e-06,
                5.422218969818919e-06,
                2.561282515988704e-06,
                1.0677027427525368e-06,
                1.3007126912258525e-05,
                1.0129992187400498e-05,
                1.0677026154551157e-06
            ],
            [
                8.939694172542558e-06,
                1.892515500808112e-05,
                4.006371128945452e-05,
                4.5397890270732005e-05,
                5.8291279378656556e-05,
                8.939698435226916e-06,
                8.939695237813028e-06,
                3.120191879561992e-05,
                1.6701417861189946e-05,
                6.962255419475714e-06
            ],
            [
                1.3007130013572209e-05,
                1.3007128464559612e-05,
                5.422220908402905e-06,
                3.2887482811220126e-06,
                6.962257079059797e-06,
                4.22283394786293e-06,
                8.939700566289352e-06,
                1.0129988563343644e-05,
                2.7535697663897248e-05,
                1.0129988564578197e-05
            ],
            [
                1.3709578604981489e-06,
                1.2098652508347793e-06,
                3.9278634073312583e-07,
                6.47594952595231e-07,
                9.422450431912e-07,
                7.338211554725124e-07,
                5.422221555192784e-06,
                9.422449308673789e-07,
                1.0677024881829577e-06,
                1.994729483694599e-06
            ],
            [
                NaN,
                3.5356250704701545e-05,
                5.829127941597736e-05,
                0.9999417087206086,
                0.00015843617900614056,
                2.7535697660090726e-05,
                0.00023050666014043624,
                3.535625492359079e-05,
                9.610246076724e-05,
                0.9999785550567073
            ],
            [
                1.0677028700203557e-06,
                1.2098659719441482e-06,
                1.670142383015595e-05,
                1.2098658277335738e-06,
                6.475949525919915e-07,
                8.315278293899016e-07,
                1.209866116149238e-06,
                7.889263526093993e-06,
                1.2098662603752517e-06,
                6.475945666009864e-07
            ],
            [
                2.753570422373059e-05,
                2.7535700943413033e-05,
                0.0001584362543718626,
                2.1444945855248125e-05,
                2.7535700944314574e-05,
                5.14422075023447e-05,
                2.4300232042706045e-05,
                6.962254589781966e-06,
                5.144223815748175e-05,
                8.481108169906156e-05
            ],
            [
                6.962256249821764e-06,
                1.4738985485997396e-05,
                2.4300243627117176e-05,
                3.1201911372399926e-05,
                1.012998977198894e-05,
                7.484620940529543e-05,
                0.9999251537638503,
                4.5397890289724144e-05,
                1.6701429803316423e-05,
                0.9999724642990531
            ],
            [
                1.7603427936263351e-06,
                5.422220262333096e-06,
                1.6701427816728442e-05,
                2.9023112931873767e-06,
                1.6701423835320418e-05,
                3.2887482812506295e-06,
                2.2603240283888175e-06,
                1.5534981249397663e-06,
                1.0129987357287368e-05,
                1.0677032518501217e-06
            ],
            [
                0.9999938558232007,
                0.9999869928746368,
                0.9999967112513267,
                NaN,
                0.9999986290427932,
                0.9999921107392972,
                0.9999921107355335,
                0.999992110734593,
                0.0006263342496696063,
                0.9999687980737492
            ],
            [
                9.610238060880459e-05,
                0.9999339478790124,
                0.00010889687024170175,
                1.6701429808298613e-05,
                2.7535704221626983e-05,
                0.9999038975508214,
                0.0002959569911689175,
                0.9999339478474842,
                3.535626335686906e-05,
                0.9999785550515867
            ],
            [
                1.370956879949281e-06,
                2.260324028351814e-06,
                3.726639728262097e-06,
                4.785094494576774e-06,
                1.0677024881829577e-06,
                4.222834954514924e-06,
                6.962257909501028e-06,
                1.2098662603862553e-06,
                1.1478770862589836e-05,
                1.4738980214843206e-05
            ],
            [
                1.1478769493916314e-05,
                3.726638839806038e-06,
                2.2603251061664e-06,
                1.0129995809247506e-05,
                9.422443692330485e-07,
                3.7266379512857925e-06,
                7.889263525663481e-06,
                4.785095635592258e-06,
                3.288748673265808e-06,
                2.2603237589028734e-06
            ],
            [
                2.260325375615501e-06,
                2.561283432005142e-06,
                5.043476486902204e-07,
                4.7850967763512445e-06,
                8.315280276580819e-07,
                8.93969736955767e-06,
                9.422445938964242e-07,
                3.2887506334560605e-06,
                8.31528126775552e-07,
                4.222835458175145e-06
            ],
            [
                4.785095065093186e-06,
                2.2603234895176927e-06,
                0.9994472213184087,
                1.6701425826191394e-05,
                4.785095065093186e-06,
                6.605217615887045e-05,
                0.00015843623564914578,
                0.00033535010811387836,
                1.300713001508642e-05,
                2.753569438157704e-05
            ],
            [
                2.260324028281919e-06,
                1.670141587031992e-05,
                1.9947306725868575e-06,
                5.422218969769604e-06,
                1.1478764017428212e-05,
                3.2887490653408545e-06,
                5.422218323019487e-06,
                6.9622587396067566e-06,
                7.889262584508638e-06,
                1.8925157261545463e-05
            ],
            [
                1.5534981249496567e-06,
                0.999996273360716,
                0.9999810748562722,
                0.9999938558275955,
                0.999986992876188,
                0.9998415637076825,
                0.9999687980960651,
                0.9999930377429205,
                0.9999599362934974,
                0.9999987901341723
            ],
            [
                1.0129993392600532e-05,
                2.4300240725599276e-05,
                3.2887498493983645e-06,
                7.889265405333033e-06,
                1.012999459535003e-05,
                1.1478772227338172e-05,
                6.144177531381426e-06,
                1.4738985482753428e-05,
                6.1441775312976045e-06,
                3.7266388393349185e-06
            ],
            [
                2.902311984915459e-06,
                0.9997694933672178,
                3.535626334953767e-05,
                1.892514824021969e-05,
                8.481101095665886e-05,
                4.006367783047594e-05,
                5.829127939986156e-05,
                2.1444953524161264e-05,
                1.4738976699749503e-05,
                1.892515500450102e-05
            ],
            [
                4.222835458117536e-06,
                4.222833947932061e-06,
                1.4738987242968784e-05,
                1.5534975693792215e-06,
                7.889260704050487e-06,
                1.4738981970956057e-05,
                6.96225873895455e-06,
                6.962254589528684e-06,
                1.670141985166528e-05,
                6.144176799166453e-06
            ],
            [
                9.422447061953531e-07,
                3.72664017246987e-06,
                2.2603245672867952e-06,
                1.473897670007122e-05,
                1.7603440527046419e-06,
                1.370957370247318e-06,
                4.222833444429485e-06,
                6.962255419804982e-06,
                3.535624649751729e-05,
                1.0677024881829577e-06
            ],
            [
                4.450848927599543e-07,
                8.315278294001114e-07,
                4.222832437677995e-06,
                8.315282259089153e-07,
                1.7603425836678333e-06,
                1.5534971989568904e-06,
                3.0590229985449037e-07,
                3.2887482811908074e-06,
                6.475947209918244e-07,
                3.288750633545794e-06
            ],
            [
                0.9999885212318748,
                4.006368740256958e-05,
                0.0001088969092026217,
                5.1442232038504445e-05,
                4.5397879462552736e-05,
                4.539786861523573e-05,
                6.605214466722918e-05,
                4.539789026032761e-05,
                2.4300246525276163e-05,
                0.9998766054252095
            ],
            [
                0.9999967112509346,
                0.9999962733589388,
                0.9999930377454102,
                0.9999962733602715,
                0.9999646437577183,
                0.9999869928699852,
                0.9999885212264008,
                0.9999952149060757,
                0.9999984465026158,
                0.9999687980923481
            ],
            [
                3.2887490653109436e-06,
                1.0129989771823107e-05,
                2.1444950965906214e-05,
                6.144172404302622e-06,
                2.7535704218321328e-05,
                7.889261644982674e-06,
                6.144175334094145e-06,
                8.93969310647542e-06,
                6.962253759828703e-06,
                3.7266392839425286e-06
            ],
            [
                8.481107163963022e-05,
                0.0002611903706517724,
                4.006368740446426e-05,
                8.481107167850307e-05,
                9.610243787850682e-05,
                6.605217617761233e-05,
                0.9995694429609864,
                0.00010889689615913351,
                0.0002611902158240513,
                0.0002034269970117653
            ]
        ]
    },
    {
        "q_id": "8019_mmlu_math",
        "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,
            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": [
            [
                0.9999952149049356,
                0.9999974387180947,
                0.9999984465015047,
                0.999997097687323,
                0.9999970976887069,
                0.9999967112517189,
                0.9999980052709919,
                0.9999977396765106,
                0.999996273361605,
                0.9999991684721706
            ],
            [
                1.4738985481091229e-05,
                2.753568450937557e-05,
                1.67014158650947e-05,
                2.4300240727367308e-05,
                5.144221359998557e-05,
                1.0129995809044816e-05,
                1.6701421841259862e-05,
                2.1444950957402623e-05,
                4.539788485433845e-05,
                2.430024072091399e-05
            ],
            [
                0.9999869928699903,
                0.999993037740431,
                0.9999977396751635,
                0.999993037745413,
                0.999993855826132,
                0.9999977396748939,
                0.9999930377462408,
                0.9999967112513268,
                0.9999967112505427,
                0.9999945777823254
            ],
            [
                0.9999974387171787,
                0.9999945777797382,
                0.9999977396759717,
                0.999993037746241,
                0.9999977396765106,
                0.999995214903224,
                0.9999967112517189,
                0.9999852610215463,
                0.9999921107383561,
                0.9999970976866313
            ],
            [
                0.9999984465018751,
                0.9999995549151073,
                0.9999952149072168,
                0.9999810748427379,
                0.9999885212264044,
                0.9999987901343165,
                0.9999930377462405,
                0.9999982396561572,
                0.9999984465026158,
                0.9999962733598278
            ],
            [
                0.9999832985721891,
                0.9999990577550691,
                0.9999977396751634,
                0.9999996072136592,
                0.9999986290429566,
                0.9999982396565769,
                0.9999938558232017,
                0.9999945777790916,
                0.9999995549150011,
                0.9999945777816768
            ],
            [
                0.9999938558253987,
                0.9999989322968754,
                0.9999967112497589,
                0.9999938558239335,
                0.9999952149043647,
                0.9999957771660528,
                0.9999974387177897,
                0.9999962733616047,
                0.9999970976883612,
                0.9999982396565769
            ],
            [
                0.9999992661787571,
                0.9999992661791944,
                0.9999930377437508,
                0.9999992661786696,
                0.9999984465022455,
                0.9999982396561572,
                0.9999989322972572,
                0.9999962733620488,
                0.9999990577556308,
                0.9999957771665557
            ],
            [
                6.144172404302622e-06,
                3.120192252437034e-05,
                6.962258739068529e-06,
                2.9023123310580418e-06,
                6.962254589104433e-06,
                4.006371128012683e-05,
                8.939696303010449e-06,
                6.962253757840428e-06,
                4.785093923982095e-06,
                5.82912653104079e-05
            ],
            [
                0.9999910603068948,
                0.9999987901341723,
                0.9999984465015047,
                0.999997097687323,
                0.9999910603047633,
                0.9999952149049351,
                0.9999869928653358,
                0.9999967112497586,
                0.9999970976866311,
                0.9999984465016899
            ],
            [
                0.999998239656367,
                0.999998005270992,
                0.9999977396748939,
                0.9999967112521109,
                0.9999990577552939,
                0.9999989322970028,
                0.9999996072138465,
                0.9999987901344607,
                0.9999930377429208,
                0.9999977396746245
            ],
            [
                0.9999984465016899,
                0.9999898700054003,
                0.9999974387165681,
                0.999992110736476,
                0.9999987901343165,
                0.9999832985781584,
                0.9999990577556308,
                0.9999970976887069,
                0.9999970976883609,
                0.9999910602994343
            ],
            [
                0.999997097686631,
                0.9999974387180947,
                0.9999967112505427,
                0.9999984465018751,
                0.9999938558239341,
                0.9999967112501505,
                0.9999930377429209,
                0.999997097687323,
                0.9999992661787571,
                0.9999982396574163
            ],
            [
                0.9999957771675625,
                0.999998790134028,
                0.9999957771660524,
                0.999996711251719,
                0.9999986290424663,
                0.999998239656577,
                0.9999930377437511,
                0.999991060304763,
                0.999995777165549,
                0.9999974387184002
            ],
            [
                0.9999910602994379,
                0.9999945777797385,
                0.9999957771650463,
                0.9999962733607172,
                0.9999970976869772,
                0.9999945777829704,
                0.9999930377454136,
                0.9999970976869775,
                0.9999990577549569,
                0.999995777167563
            ],
            [
                0.999997438717484,
                0.9999938558246659,
                0.9999869928684368,
                0.9999962733589393,
                0.999997097688707,
                0.9999952149072169,
                0.9999930377429213,
                0.999997438717484,
                0.9999945777810305,
                0.9999930377454107
            ],
            [
                0.9999984465016899,
                0.9999993524049702,
                0.9999980052693274,
                0.9999980052698031,
                0.999996273362049,
                0.9999724643122099,
                0.9999977396751634,
                0.9999967112501512,
                0.9999993524053562,
                0.9999921107402364
            ],
            [
                0.9999991684715758,
                0.9999980052707541,
                0.9999986290423029,
                0.999999554914895,
                0.9999986290421394,
                0.9999962733611608,
                0.9999974387187054,
                0.9999996940978095,
                0.9999994956524716,
                0.9999989322970027
            ],
            [
                0.9999957771660528,
                0.9999984465022456,
                0.9999970976876693,
                0.9999982396559476,
                0.9999977396751634,
                0.9999957771665573,
                0.9999930377412619,
                0.9999952149055056,
                0.9999898700114427,
                0.9999967112517191
            ],
            [
                0.9999967112521111,
                0.999998446502801,
                0.9999898700102303,
                0.999995777166556,
                0.9999962733611605,
                0.999996711252111,
                0.9999921107374175,
                0.9999962733620488,
                0.9999980052709921,
                0.9999970976883609
            ],
            [
                0.9999991684721706,
                0.9999982396567868,
                0.9999945777790915,
                0.9999974387177893,
                0.9999984465018751,
                0.9999938558232019,
                0.9999957771665561,
                0.9999921107345937,
                0.9999910603036967,
                0.999998239656367
            ],
            [
                2.4300243615448162e-05,
                6.962256249606473e-06,
                8.939695237162584e-06,
                0.9999810748562764,
                4.785096776303374e-06,
                6.144172404520556e-06,
                4.222832941072913e-06,
                1.3007126913346863e-05,
                1.012998735687278e-05,
                2.7535694375867267e-05
            ],
            [
                0.9999987901347491,
                0.9999952149049358,
                0.999996711252111,
                0.9999962733611605,
                0.9999952149037952,
                0.9999945777810312,
                0.9999938558232014,
                0.9999980052705164,
                0.9999980052693275,
                0.9999977396746245
            ],
            [
                0.9999993524050474,
                0.9999974387177895,
                0.9999980052700408,
                0.9999967112509349,
                0.9999970976876695,
                0.9999987901337396,
                0.9999982396572065,
                0.9999984465028011,
                0.9999957771665561,
                0.9999980052702786
            ],
            [
                0.9999977396754329,
                0.9999957771665562,
                0.9999974387174844,
                0.9999962733607166,
                0.999998239656577,
                0.9999952149043654,
                0.9999974387168735,
                0.9999967112509347,
                0.9999990577556308,
                0.9999977396746244
            ],
            [
                0.9999967112505428,
                0.999997097687323,
                0.9999980052702786,
                0.9999832985701967,
                0.9999984465026158,
                0.9999957771660523,
                0.9999982396574163,
                0.9999898700053991,
                0.9999986290424664,
                0.999997097687669
            ],
            [
                0.9999756997477232,
                0.999993855827596,
                0.9999970976887069,
                0.9999785550439318,
                0.9999938558275963,
                0.9999339478239027,
                0.999993855826131,
                0.9999546021206279,
                0.9999938558268635,
                0.9999967112493666
            ],
            [
                0.9999992661786696,
                0.9999984465024307,
                0.9999987901338838,
                0.9999980052702786,
                0.9999986290421394,
                0.9999980052709919,
                0.999996711251719,
                0.999997097686631,
                0.9999982396574163,
                0.999998239656367
            ],
            [
                0.9999993524049702,
                0.9999980052702786,
                0.9999984465018751,
                0.9999991684715758,
                0.999998446502801,
                0.9999970976880149,
                0.9999990577550691,
                0.9999977396751633,
                0.9999990577551815,
                0.9999992661790196
            ],
            [
                0.9999952149055056,
                0.9999930377429208,
                0.9999957771660523,
                0.9999921107355342,
                0.9999921107402394,
                0.9999982396565769,
                0.9999962733598275,
                0.9999957771655489,
                0.9999984465015047,
                0.9999957771645422
            ],
            [
                0.9999952149037942,
                0.9999945777790916,
                0.9999977396762411,
                0.9999977396757023,
                0.9999982396569966,
                0.9999982396572065,
                0.9999910603068949,
                0.9999982396574163,
                0.9999982396572065,
                0.9999982396559474
            ],
            [
                0.9999974387174844,
                0.9999952149043658,
                0.9999970976869772,
                0.9999982396567868,
                0.9999938558268644,
                0.999996273362049,
                0.9999970976890529,
                0.9999967112509347,
                0.9999921107355363,
                0.9999952149043654
            ],
            [
                0.9999921107402377,
                0.9999952149055061,
                0.9999945777829699,
                0.9999938558239343,
                0.999994577778446,
                0.9999921107383568,
                0.9999957771645421,
                0.9999957771675634,
                0.9999962733607165,
                0.9999977396759717
            ],
            [
                0.9999967112509347,
                0.999994577779739,
                0.9999957771670592,
                0.999997097687669,
                0.9999984465022455,
                0.9999938558224688,
                0.9999987901341723,
                0.9999938558261313,
                0.9999974387171788,
                0.9999898700066067
            ],
            [
                0.9999977396754328,
                0.9999992661789321,
                0.9999974387184,
                0.9999986290427932,
                0.9999952149049356,
                0.9999993524053562,
                0.9999990577551815,
                0.9999990577555185,
                0.9999987901347492,
                0.9999984465026158
            ],
            [
                0.9999945777829696,
                0.9999990577556308,
                0.9999938558261312,
                0.9999599362982898,
                0.9999967112521109,
                0.9999898700078138,
                0.9999921107364745,
                0.9999810748585355,
                0.9999962733616046,
                0.9999987901338838
            ],
            [
                0.9999921107402364,
                0.999975699762171,
                0.999997097686977,
                0.999997097686631,
                0.9999992661788446,
                0.9999977396746244,
                0.999994577778445,
                0.9999957771675625,
                0.9999869928653345,
                0.9999910603068939
            ],
            [
                0.9999957771645419,
                0.9999945777816769,
                0.999997438716568,
                0.9999967112513267,
                0.9999989322968754,
                0.9999982396572065,
                0.9999952149043647,
                0.9999945777790913,
                0.9999980052693274,
                0.9999980052693276
            ],
            [
                0.9999977396765106,
                0.99999893229713,
                0.9999987901340281,
                0.9999962733602719,
                0.9999984465022455,
                0.9999957771665559,
                0.9999995549150011,
                0.9999986290424663,
                0.9999993524051246,
                0.9999970976876689
            ],
            [
                0.9999986290429567,
                0.9999967112521111,
                0.9999930377454118,
                0.9999898700054015,
                0.9999952149032245,
                0.9999984465024307,
                0.9999982396567868,
                0.9999970976873231,
                0.9999984465028012,
                0.9999974387177895
            ],
            [
                0.9999987901347492,
                0.9999967112513272,
                0.999999266179107,
                0.9999967112521118,
                0.9999987901346049,
                0.9999982396574163,
                0.9999982396569966,
                0.9999980052693274,
                0.9999986290429566,
                0.9999982396574163
            ],
            [
                0.9999952149066468,
                0.9999990577551815,
                0.9999980052707544,
                0.9999945777810315,
                0.9999980052705164,
                0.9999938558253989,
                0.9999952149066464,
                0.9999962733589395,
                0.9999991684717741,
                0.9999984465024307
            ],
            [
                0.999997097689053,
                0.9999957771675626,
                0.9999990577555185,
                0.9999967112501507,
                0.9999962733602726,
                0.9999991684720715,
                0.9999980052707542,
                0.9999869928653372,
                0.9999991684719723,
                0.9999982396572065
            ],
            [
                0.9999957771650454,
                0.9999957771675629,
                0.9999967112493665,
                0.9999982396567867,
                0.9999970976880149,
                0.999996711251327,
                0.9999957771670593,
                0.9999974387174843,
                0.999996711250935,
                0.9999977396762413
            ],
            [
                0.9999869928746402,
                0.9999930377462407,
                0.9999930377429213,
                0.9999910603026337,
                0.9999945777816779,
                0.9999982396561572,
                0.9999974387171787,
                0.9999952149072182,
                0.999996711250935,
                0.9999996072139402
            ],
            [
                0.999997438717484,
                0.9999977396762411,
                0.999997438717484,
                0.9999974387171787,
                0.9999938558253987,
                0.9999952149055057,
                0.9999982396565769,
                0.999998239656577,
                0.9999990577551815,
                0.9999974387168734
            ],
            [
                0.9999992661790196,
                0.9999967112501505,
                0.9999898700066069,
                0.9999987901338839,
                0.9999991684720715,
                0.9999982396561572,
                0.9999982396567867,
                0.9999910602994343,
                0.9999952149066468,
                0.999995777166556
            ],
            [
                0.9999980052693275,
                0.9999930377412636,
                0.9999989322972572,
                0.9999980052709921,
                0.9999967112501507,
                0.9999962733607165,
                0.9999945777803844,
                0.9999930377429219,
                0.9999952149060765,
                0.9999980052705165
            ],
            [
                0.9999898700114376,
                0.9999967112513268,
                0.9999982396572065,
                0.9999938558246663,
                0.9999967112501508,
                0.9999982396572065,
                0.9999724643089319,
                0.9999885212264029,
                0.9999957771650456,
                0.9999885212318762
            ],
            [
                0.9999952149060763,
                0.9999952149043652,
                0.9999910603004994,
                0.9999970976887069,
                0.999996273358939,
                0.9999980052705165,
                0.9999898700102304,
                0.9999957771675627,
                0.9999982396572065,
                0.9999967112513272
            ],
            [
                0.9999974387180948,
                0.9999957771680665,
                0.9999962733620492,
                0.9999974387187056,
                0.9999974387168734,
                0.9999938558275967,
                0.9999986290432834,
                0.9999974387184003,
                0.9999952149049351,
                0.9999974387165682
            ],
            [
                0.9999967112501507,
                0.9999967112493665,
                0.9999974387187053,
                0.9999991684720715,
                0.9999993524049702,
                0.9999977396759717,
                0.9999992661791944,
                0.9999910603068948,
                0.9999980052693274,
                0.9999994956526519
            ],
            [
                0.9999990577556308,
                0.9999982396567868,
                0.9999974387168734,
                0.999972464305641,
                0.999997097687669,
                0.9999832985821476,
                0.9999967112505428,
                0.9999977396751634,
                0.9999885212359824,
                0.9999910603058294
            ],
            [
                0.9999945777797382,
                0.9999989322973846,
                0.9999952149032243,
                0.999997438717484,
                0.9999982396567867,
                0.9999938558239342,
                0.9999957771655497,
                0.999996273360272,
                0.9999984465018752,
                0.999997438716568
            ],
            [
                0.9999952149055056,
                0.9999974387180947,
                0.9999898700102304,
                0.9999938558275963,
                0.9999974387187054,
                0.9999938558268635,
                0.9999967112513267,
                0.999997097687669,
                0.9999930377412609,
                0.9999952149072168
            ],
            [
                0.9999945777816772,
                0.999997438717484,
                0.999996273360272,
                0.9999967112517192,
                0.9999687980960773,
                0.9999898700114368,
                0.9999832985841314,
                0.9999974387177893,
                0.9999967112513269,
                0.9999952149072169
            ],
            [
                0.9999962733607166,
                0.999997097688707,
                0.9999974387187054,
                0.9999970976873231,
                0.9999977396757023,
                0.9999977396754328,
                0.9999957771665557,
                0.9999977396748941,
                0.9999852610110065,
                0.9999980052705164
            ],
            [
                0.9999974387168734,
                0.9999945777784456,
                0.9999986290424663,
                0.9999984465022455,
                0.9999910603005008,
                0.9999962733602722,
                0.9999967112517191,
                0.9999980052702786,
                0.9999970976869772,
                0.9999832985781617
            ],
            [
                0.9999990577557432,
                0.9999898700041912,
                0.9999885212359813,
                0.9999994284996893,
                0.9999980052695653,
                0.9999852610180346,
                0.9999994956524114,
                0.9999992661790195,
                0.9999832985841317,
                0.9999921107374158
            ],
            [
                0.9999952149066468,
                0.9999980052693275,
                0.999998239656577,
                0.9999957771660526,
                0.999993855823934,
                0.999996711250151,
                0.9999974387174845,
                0.9999984465026158,
                0.9999974387187056,
                0.9999970976876692
            ],
            [
                0.999998239656367,
                0.999997097689053,
                0.9999977396748938,
                0.9999989322975118,
                0.9999967112517191,
                0.9999982396572065,
                0.9999724643187565,
                0.9999977396751634,
                0.9999980052705164,
                0.9999987901337396
            ],
            [
                0.9999986290421394,
                0.9999967112521111,
                0.999998790134028,
                0.9999921107402366,
                0.9999785550490408,
                0.9999990577550693,
                0.999998005269803,
                0.9999984465024306,
                0.99999457778297,
                0.999994577778445
            ],
            [
                0.9999970976890529,
                0.9999921107355343,
                0.9999967112517191,
                0.9999898700078143,
                0.9999982396572065,
                0.9999987901347492,
                0.999999168471675,
                0.999998239656367,
                0.9999957771665561,
                0.9999990577554061
            ],
            [
                0.9999898700078154,
                0.9999984465020603,
                0.9999945777823233,
                0.9999990577554062,
                0.9999982396561572,
                0.9999982396569966,
                0.9999910603036976,
                0.9999967112521109,
                0.9999970976887068,
                0.999998446502801
            ],
            [
                0.9999970976876692,
                0.9999417087415413,
                0.9999962733616048,
                0.9999930377420919,
                0.9999921107374152,
                0.9999980052693275,
                0.9999921107392973,
                0.9999945777829696,
                0.9999938558253986,
                0.999993855826131
            ],
            [
                0.9999977396762413,
                0.9999962733611607,
                0.9999992661786696,
                0.99999844650169,
                0.9999974387177895,
                0.9999984465024306,
                0.9999974387165681,
                0.9999977396762412,
                0.9999910602994351,
                0.9999930377462422
            ],
            [
                0.9999992661788446,
                0.999997097686631,
                0.9999990577552937,
                0.9999990577550691,
                0.9999990577555185,
                0.9999974387184,
                0.9999995549151073,
                0.999998005269803,
                0.9999990577557432,
                0.999997097688361
            ],
            [
                0.9999785550592643,
                0.9999724643023452,
                0.9999938558268648,
                0.9999038975966373,
                0.9999852610215518,
                0.9999885212359813,
                0.999972464299064,
                0.9999724643089352,
                0.9999898700090235,
                0.9999646437535583
            ],
            [
                0.9999930377429215,
                0.9999957771650458,
                0.999997438717179,
                0.999986992874644,
                0.99999893229713,
                0.9999977396765107,
                0.9999974387168734,
                0.999997097687669,
                0.9999986290424663,
                0.9999962733607163
            ],
            [
                0.9999980052700408,
                0.999998932296621,
                0.99999893229713,
                0.9999992661788445,
                0.999999495652652,
                0.9999989322975118,
                0.9999991684719723,
                0.9999994956526519,
                0.9999991684715758,
                0.9999991684720715
            ],
            [
                0.9999869928699895,
                0.9999970976876693,
                0.9999970976869775,
                0.999998790134605,
                0.999998239656577,
                0.9999938558261313,
                0.9999967112517189,
                0.9999977396754329,
                0.9999992661791945,
                0.9999994956525317
            ],
            [
                5.1442213603354026e-05,
                4.539785238406597e-05,
                5.8291258547708845e-05,
                2.144494074076854e-05,
                0.9998601779430752,
                8.481107158224648e-05,
                1.670142383495587e-05,
                7.4846209355198e-05,
                4.222832437386106e-06,
                5.1442225840182154e-05
            ],
            [
                0.999997438716568,
                0.9999921107392962,
                0.9999938558253998,
                0.9999974387187055,
                0.9999974387165682,
                0.999991060301566,
                0.9999967112505428,
                0.9999938558268646,
                0.9999952149032242,
                0.9999984465024309
            ],
            [
                0.9999957771680659,
                0.9999952149043647,
                0.999995777164542,
                0.9999995549151073,
                0.9999898700114362,
                0.999997097687669,
                0.9999977396765105,
                0.9999962733598278,
                0.9999967112509348,
                0.999997097686631
            ],
            [
                0.9999977396746244,
                0.9999984465015047,
                0.9999984465026159,
                0.999998005269803,
                0.9999984465026158,
                0.9999984465022456,
                0.9999970976873231,
                0.9999974387168736,
                0.9999945777810304,
                0.999997097686977
            ],
            [
                0.999998005270992,
                0.9999982396565769,
                0.9999910603004999,
                0.9999945777810305,
                0.9999977396765105,
                0.9999852610162734,
                0.9999974387184,
                0.9999967112517189,
                0.999997097687323,
                0.9999810748427413
            ],
            [
                0.9999898700102313,
                0.9999945777810315,
                0.9999962733593839,
                0.9999967112513274,
                0.9999910603058302,
                0.9999952149037952,
                0.9999986290424664,
                0.9999938558268634,
                0.9999852610233037,
                0.9999989322973846
            ],
            [
                0.99999862904312,
                0.9999970976890532,
                0.9999990577552939,
                0.999995777166556,
                0.9999990577551815,
                0.9999987901344608,
                0.9999957771670593,
                0.9999898700066122,
                0.9999974387187053,
                0.9999967112517189
            ],
            [
                0.9999921107392962,
                0.9999962733607161,
                0.999998446502801,
                0.9999982396569966,
                0.9999992661786696,
                0.9999980052693275,
                0.9999974387168734,
                0.999999266178757,
                0.9999970976890529,
                0.999997097686631
            ],
            [
                0.999996273360272,
                0.9999930377429209,
                0.9999990577555185,
                0.9999832985801561,
                0.9999957771660521,
                0.9999957771650454,
                0.9999995549147359,
                0.99998329857418,
                0.9999977396757022,
                0.999996273358939
            ],
            [
                1.1478766754377407e-05,
                4.006368258904954e-05,
                1.4738976699106073e-05,
                4.0063706492255065e-05,
                3.1201907650801864e-05,
                1.0129992185060374e-05,
                0.9999785550541495,
                1.30071346612026e-05,
                1.4738976698006875e-05,
                3.1201926243586504e-05
            ],
            [
                0.9999970976883611,
                0.9999957771680663,
                0.9999974387168733,
                0.9999984465018751,
                0.999995214904935,
                0.9999970976866316,
                0.9999994284994849,
                0.9999957771645422,
                0.9999970976876693,
                0.9999987901347492
            ],
            [
                0.9999832985821464,
                0.99999862904312,
                0.9999984465022455,
                0.9999980052700408,
                0.9999984465026158,
                0.999981074842744,
                0.9999967112493665,
                0.9999977396754328,
                0.9999990577550691,
                0.9999992661791944
            ],
            [
                0.9999992661790195,
                0.9999989322967481,
                0.9999977396746245,
                0.9999945777790917,
                0.9999957771645427,
                0.9999852610145177,
                0.9999962733616051,
                0.9999993524052789,
                0.9999982396572065,
                0.9999974387180949
            ],
            [
                0.9999984465022455,
                0.9999982396561572,
                0.9999994284995529,
                0.9999974387171787,
                0.9999995549151073,
                0.9999989322973845,
                0.9999982396574163,
                0.9999990577550691,
                0.9999974387168735,
                0.9999987901346049
            ],
            [
                0.9999986290431201,
                0.9999980052702786,
                0.9999987901337396,
                0.999996711252111,
                0.9999945777816769,
                0.9999980052693274,
                0.9999987901347491,
                0.9999991684722698,
                0.9999989322975118,
                0.9999994284992805
            ],
            [
                0.999991060299434,
                0.9999974387180948,
                0.9999921107355342,
                0.9999945777816769,
                0.9999898700078134,
                0.9999938558224688,
                0.9999989322972573,
                0.9999992661787571,
                0.9999986290429566,
                0.9999921107355343
            ],
            [
                0.9999962733593833,
                0.9999898700126462,
                0.999992110737415,
                0.9999970976883612,
                0.9999974387184,
                0.9999339478317925,
                0.9999869928653365,
                0.9999832985761683,
                0.9999970976887071,
                0.9999962733607165
            ],
            [
                0.9999990577557432,
                0.9999986290426298,
                0.9999984465018751,
                0.9999994284997573,
                0.9999990577554061,
                0.999999352404893,
                0.9999980052700408,
                0.9999996533674202,
                0.999999168471675,
                0.9999990577549569
            ],
            [
                0.9999987901337396,
                0.9999991684718732,
                0.9999974387184002,
                0.9999990577552939,
                0.9999938558246664,
                0.9999945777784456,
                0.9999982396572065,
                0.9999970976869773,
                0.9999986290429566,
                0.9999938558275967
            ],
            [
                0.999997097686631,
                0.9999977396765106,
                0.9999977396748938,
                0.9999810748540237,
                0.9999984465022455,
                0.9999993524049703,
                0.9999967112509347,
                0.9999986290432834,
                0.9999967112517187,
                0.9999987901344608
            ],
            [
                0.9999967112505431,
                0.999998239656367,
                0.9999974387187053,
                0.9999982396561572,
                0.9999957771645424,
                0.9999977396746245,
                0.9999938558232014,
                0.9999977396765106,
                0.9999962733589393,
                0.9999980052702788
            ],
            [
                0.9999990577554062,
                0.9999984465018751,
                0.9999930377454106,
                0.9999921107383567,
                0.99999862904312,
                0.9999977396751634,
                0.9999974387168734,
                0.9999974387177896,
                0.9999980052693275,
                0.9999952149066473
            ],
            [
                0.9999989322971301,
                0.9999991684722698,
                0.9999986290432835,
                0.9999974387174841,
                0.9999974387184002,
                0.9999990577551816,
                0.9999974387177895,
                0.999999168471675,
                0.999998239656367,
                0.9999982396559474
            ],
            [
                0.9999990577552939,
                0.9999957771655489,
                0.9999992661789321,
                0.9999977396759717,
                0.9999980052693275,
                0.9999957771680662,
                0.9999921107383563,
                0.999993037740431,
                0.999996273358939,
                0.9999962733611604
            ],
            [
                0.9999986290427931,
                0.9999974387174841,
                0.9999957771680663,
                0.9999938558253993,
                0.9999987901340281,
                0.9999962733607163,
                0.9999984465020604,
                0.9999986290427932,
                0.9999967112521113,
                0.9999987901347492
            ],
            [
                0.9999984465022456,
                0.9999967112497589,
                0.9999974387184002,
                0.9999970976866313,
                0.9999962733598278,
                0.9999930377445819,
                0.9999967112501509,
                0.9999977396757024,
                0.9999982396559474,
                0.9999967112517191
            ],
            [
                0.9999962733620492,
                0.9999967112505431,
                0.9999962733593839,
                0.999996711252111,
                0.9999945777810307,
                0.9999869928668892,
                0.9999986290421395,
                0.9999986290424664,
                0.9999982396572065,
                0.9999974387165683
            ],
            [
                2.144495863201265e-05,
                1.3007125361448172e-05,
                8.939696303010449e-06,
                2.430024072648329e-05,
                1.300712536258383e-05,
                1.4738985484227961e-05,
                6.144173136556186e-06,
                1.670142582300158e-05,
                6.1441775312976045e-06,
                1.670142183983204e-05
            ],
            [
                0.9999990577551815,
                0.9999987901338839,
                0.999996711251327,
                0.9999952149055056,
                0.9999984465020603,
                0.9999982396559474,
                0.9999984465026158,
                0.9999984465026159,
                0.9999945777803848,
                0.9999938558275967
            ],
            [
                0.9999952149032253,
                0.9999962733602722,
                0.9999952149072168,
                0.9999977396757025,
                0.9999938558275985,
                0.999994577782971,
                0.9999974387180949,
                0.9999945777823247,
                0.999998239656367,
                0.9999938558224692
            ],
            [
                0.999999352405279,
                0.9999938558275973,
                0.9999984465022456,
                0.9999989322967482,
                0.9999980052709921,
                0.9999990577556308,
                0.9999977396757023,
                0.9999977396762412,
                0.9999930377454143,
                0.999998005269803
            ],
            [
                0.9999832985721857,
                0.9999974387187054,
                0.9999977396759717,
                0.9999977396757023,
                0.9999980052695652,
                0.9999986290421394,
                0.999996711252111,
                0.9999977396748939,
                0.9999945777790913,
                0.9999546021097568
            ],
            [
                0.9999962733616047,
                0.9999945777823238,
                0.9999952149043646,
                0.9999974387171787,
                0.9999986290429566,
                0.999986992869988,
                0.9999980052695653,
                0.9999938558268635,
                0.9999977396765106,
                0.9999977396757023
            ],
            [
                0.9999930377429209,
                0.9999967112497585,
                0.9999992661786696,
                0.9999984465022455,
                0.9999980052695653,
                0.9999986290426297,
                0.9999967112505427,
                0.9999984465016899,
                0.9999974387165681,
                0.9999938558268635
            ],
            [
                0.9999970976890528,
                0.9999974387171788,
                0.9999962733593835,
                0.9999970976880151,
                0.9999967112497586,
                0.9999977396748938,
                0.9999962733607164,
                0.9999984465016899,
                0.9999990577557432,
                0.9999982396567868
            ],
            [
                0.9999832985721908,
                0.999996273360272,
                0.9999910603005002,
                0.9999810748495139,
                0.9999994956526519,
                0.999981074847252,
                0.9999945777803843,
                0.9999945777816768,
                0.9999869928653397,
                0.9999977396762411
            ],
            [
                0.9999984465016899,
                0.9999974387180947,
                0.9999962733620489,
                0.999995777168066,
                0.9999938558232014,
                0.9999938558261311,
                0.9999967112493666,
                0.9999921107345939,
                0.9999967112513272,
                0.9999945777790914
            ],
            [
                0.9999952149066464,
                0.9999967112521111,
                0.9999984465022456,
                0.999989870004192,
                0.9999970976880151,
                0.9999982396559474,
                0.9999984465018751,
                0.9999957771650456,
                0.999998239656367,
                0.9999910603036973
            ],
            [
                0.9999687980886605,
                0.9999952149066469,
                0.9999967112497588,
                0.9999977396757024,
                0.999995214906647,
                0.999998239656367,
                0.9999982396565769,
                0.9999938558232019,
                0.9999989322970028,
                0.9999957771665561
            ],
            [
                6.962257909121104e-06,
                6.144173136243255e-06,
                2.9023109472244114e-06,
                1.0129992186589747e-05,
                6.962257909501028e-06,
                4.785096205778054e-06,
                2.5612819053399912e-06,
                0.9997965729794325,
                5.422217676797111e-06,
                4.222835457852533e-06
            ],
            [
                1.8925145981833788e-05,
                2.4300243618542217e-05,
                1.8925145982866508e-05,
                1.473898723508674e-05,
                1.0129987355564522e-05,
                8.939700566143004e-06,
                1.0129989768911772e-05,
                1.0129990979031306e-05,
                1.3007131560621253e-05,
                1.14787735942999e-05
            ],
            [
                0.9999982396561572,
                0.9999986290429567,
                0.9999989322972573,
                0.999989870007814,
                0.9999885212277733,
                0.9999977396757024,
                0.9999930377445819,
                0.999985261012762,
                0.9999852610215575,
                0.9999977396765106
            ],
            [
                0.9999970976880149,
                0.9999987901340281,
                0.9999980052700408,
                0.9999986290432835,
                0.9999987901344608,
                0.99999893229713,
                0.9999986290421395,
                0.999997097689053,
                0.9999977396759716,
                0.9999910603015656
            ],
            [
                0.9999546021097478,
                0.9999938558232012,
                0.9999974387184,
                0.9999952149043648,
                0.9999962733607162,
                0.9999938558232014,
                0.999997097686631,
                0.9999993524050474,
                0.9999962733611603,
                0.9999970976866311
            ],
            [
                0.9999984465022455,
                0.9999869928684368,
                0.999994577779738,
                0.9999785550413659,
                0.999997438717484,
                0.9999962733620489,
                0.999995214904935,
                0.9999957771655488,
                0.9999970976866309,
                0.9999974387171787
            ],
            [
                0.9999980052705163,
                0.999992110734595,
                0.9999987901344608,
                0.9999991684717742,
                0.999996273362049,
                0.9999921107364745,
                0.9999990577556308,
                0.9999962733593835,
                0.9999987901347492,
                0.9999970976883609
            ],
            [
                0.999998446502801,
                0.9999938558232014,
                0.999991060302632,
                0.9999910603047628,
                0.9999945777803841,
                0.9999852610162746,
                0.9999974387184,
                0.9999945777784451,
                0.9999945777803843,
                0.9999974387171787
            ],
            [
                0.9998204719486806,
                1.8925150486075525e-05,
                1.3007128462785148e-05,
                5.144219518243253e-05,
                1.1478766754377407e-05,
                5.144223199097187e-05,
                4.5397857734561226e-05,
                2.7535704207102113e-05,
                4.00636778083227e-05,
                3.1201900178208404e-05
            ],
            [
                0.9999986290423029,
                0.999995777166556,
                0.999995777166556,
                0.9999991684715759,
                0.9999967112493665,
                0.9999980052709919,
                0.9999992661791944,
                0.9999990577552939,
                0.9999970976876689,
                0.9999957771665559
            ],
            [
                0.9999910603036972,
                0.999998239656367,
                0.9999990577550691,
                0.9999980052705164,
                0.9999986290427931,
                0.9999984465018751,
                0.9999994284994848,
                0.9999982396561572,
                0.9999952149049351,
                0.9999986290423029
            ],
            [
                0.9999991684719723,
                0.9999974387180948,
                0.9999980052709919,
                0.9999982396563674,
                0.9999986290421394,
                0.9999984465018752,
                0.9999982396559474,
                0.9999982396572065,
                0.9999977396751634,
                0.9999974387168735
            ],
            [
                0.9999989322968754,
                0.9999962733611604,
                0.9999977396759718,
                0.9999898700078167,
                0.9999967112505427,
                0.9999952149060768,
                0.9999970976890532,
                0.9999986290432836,
                0.9999974387187056,
                0.9999970976876693
            ],
            [
                0.9999967112521114,
                0.9999967112505435,
                0.9999977396762413,
                0.9999980052705166,
                0.9999977396754328,
                0.9999996072138934,
                0.9999974387180954,
                0.9999986290421395,
                0.999996711250543,
                0.9999977396751634
            ],
            [
                0.9999977396757023,
                0.999998239656367,
                0.9999977396762412,
                0.9999957771665564,
                0.9999967112493667,
                0.9999986290431201,
                0.9999967112513269,
                0.9999982396561572,
                0.9999977396765107,
                0.9999984465020604
            ],
            [
                0.9999980052700408,
                0.9999967112497586,
                0.9999962733611608,
                0.9999910603047624,
                0.9999980052707542,
                0.9999957771680665,
                0.9999930377412629,
                0.9999974387165681,
                0.9999898700066069,
                0.9999957771675627
            ],
            [
                0.999997739674894,
                0.9999986290431201,
                0.9999980052705163,
                0.9999982396559474,
                0.9999962733607166,
                0.9999977396754328,
                0.9999977396746245,
                0.999996711249367,
                0.9999952149049361,
                0.9999986290426298
            ]
        ]
    },
    {
        "q_id": "8000_mmlu_math",
        "cot_ids": [
            0,
            2,
            3,
            4,
            6,
            9,
            10,
            12,
            14,
            15,
            17,
            19,
            20,
            23,
            24,
            25,
            26,
            27,
            28,
            31,
            32,
            33,
            34,
            35,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            51,
            52,
            53,
            55,
            56,
            58,
            60,
            61,
            63,
            64,
            66,
            68,
            69,
            70,
            73,
            75,
            76,
            77,
            78,
            79,
            81,
            82,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            110,
            111,
            112,
            113,
            114,
            115,
            117,
            118,
            119,
            120,
            121,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                3.5356267555952205e-05,
                3.5356238044435446e-05,
                6.962253759271479e-06,
                7.889265406904397e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                0.0001398220732548812,
                0.18242552602881168
            ],
            [
                NaN,
                4.222832436379863e-06,
                0.00020342699555265777,
                1.0677033787407408e-06,
                NaN,
                1.300713155082621e-05,
                NaN,
                NaN,
                3.7266401721817755e-06,
                NaN
            ],
            [
                NaN,
                NaN,
                1.4738987238464762e-05,
                NaN,
                3.535624643449313e-05,
                6.962257078249291e-06,
                6.475945665900901e-07,
                NaN,
                NaN,
                NaN
            ],
            [
                1.5534971989696065e-06,
                8.939694171331106e-06,
                2.9023133689924295e-06,
                4.222834450505264e-06,
                3.288749849209925e-06,
                2.9023130229209922e-06,
                5.422218322763051e-06,
                4.222835457664342e-06,
                9.422448185388577e-07,
                1.4738987240824012e-05
            ],
            [
                6.962257907348116e-06,
                2.7535700939406174e-05,
                2.144494072867628e-05,
                NaN,
                5.422220908703723e-06,
                1.5534973841450852e-06,
                6.144173868178388e-06,
                9.610246057636654e-05,
                2.2603240281935217e-06,
                0.00017952790121781749
            ],
            [
                NaN,
                5.4222176759932836e-06,
                3.288749456838667e-06,
                NaN,
                1.01299933920846e-05,
                3.4663274506641133e-07,
                NaN,
                NaN,
                4.0063677800452475e-05,
                1.9947290080343035e-06
            ],
            [
                1.5534973841154145e-06,
                1.99472900790731e-06,
                1.0129990976156825e-05,
                4.4508499887035535e-07,
                1.5534971988707037e-06,
                5.71500583272315e-07,
                6.475949525351545e-07,
                8.315283250006957e-07,
                1.3007126888669986e-05,
                1.994729245842213e-06
            ],
            [
                2.430024067255831e-05,
                3.12019261530068e-05,
                NaN,
                9.422450431912e-07,
                1.3007126910649678e-05,
                4.539789023423405e-05,
                NaN,
                NaN,
                6.144176797864436e-06,
                1.1478766755734576e-05
            ],
            [
                7.338209804853638e-07,
                7.889263524960312e-06,
                NaN,
                5.144222580312921e-05,
                2.4300246512104316e-05,
                1.3007131561425676e-05,
                9.610238053958679e-05,
                0.00010889692189118655,
                0.00020342702008815938,
                NaN
            ],
            [
                2.9023112925037123e-06,
                5.715007195353674e-07,
                5.422218969384951e-06,
                NaN,
                2.902311293034278e-06,
                1.2098653950315304e-06,
                2.2603240281935217e-06,
                5.715005832442471e-07,
                6.475947209709154e-07,
                1.1253514863806946e-07
            ],
            [
                NaN,
                2.4300246486733047e-05,
                2.7535687785784475e-05,
                9.422448185101494e-07,
                4.006368260595596e-05,
                1.76034258364702e-06,
                NaN,
                NaN,
                6.605216022346663e-05,
                4.222831933795376e-06
            ],
            [
                7.338208055436404e-07,
                8.481103112301959e-05,
                0.00017952805096939573,
                4.006367784344724e-05,
                NaN,
                1.8925145954914227e-05,
                1.0129992183991656e-05,
                1.4738985482753428e-05,
                1.4738985472887472e-05,
                0.00013982207367803525
            ],
            [
                1.1478764009640154e-05,
                NaN,
                0.0013250221272938733,
                NaN,
                0.0009110511064507856,
                NaN,
                NaN,
                0.0001088969086131929,
                0.00048785709150401553,
                0.00037998447115172537
            ],
            [
                7.889265401501483e-06,
                3.535625068000635e-05,
                3.5356267524954594e-05,
                NaN,
                8.93969417167259e-06,
                NaN,
                4.0063692165808155e-05,
                6.475948753676801e-07,
                3.2887478891128633e-06,
                1.8925148202663113e-05
            ],
            [
                8.315283250006957e-07,
                2.9023126768258393e-06,
                9.42244256886598e-07,
                9.42244930849811e-07,
                8.315283250082584e-07,
                3.2887482811579057e-06,
                1.5534979397140412e-06,
                1.0677027426709671e-06,
                7.33821067986608e-07,
                1.5534975693347152e-06
            ],
            [
                6.962253756232077e-06,
                2.2603245668941476e-06,
                0.8354835391516133,
                8.939699497855469e-06,
                2.9023116388547446e-06,
                4.222835456903897e-06,
                1.4738980203395485e-05,
                1.4738988995409548e-05,
                4.785096775676685e-06,
                2.9023116387069255e-06
            ],
            [
                2.5612831264302397e-06,
                2.382368531882742e-07,
                1.0677033791000363e-06,
                7.8892654060075e-06,
                4.4508489275469177e-07,
                4.222835457852533e-06,
                1.7603425836678333e-06,
                6.962255413213276e-06,
                2.9023130230133794e-06,
                4.785092782501357e-06
            ],
            [
                5.1442225836439433e-05,
                NaN,
                2.2603237589028734e-06,
                NaN,
                7.889262584350785e-06,
                1.99472995920443e-06,
                2.7535697622726747e-05,
                2.1444945825992654e-05,
                2.1444940739364273e-05,
                NaN
            ],
            [
                8.315278293762888e-07,
                NaN,
                2.9023112930949896e-06,
                4.7850933534310035e-06,
                2.2603234893594005e-06,
                NaN,
                2.7535694295229195e-05,
                1.4738985474174337e-05,
                NaN,
                2.260323758835034e-06
            ],
            [
                3.288748672413347e-06,
                4.7850933534310035e-06,
                1.4738988993050295e-05,
                4.785096204868486e-06,
                2.260325105693578e-06,
                6.144172402452975e-06,
                0.00013982212283104867,
                9.422450431372112e-07,
                6.475950297574138e-07,
                1.7603427934702357e-06
            ],
            [
                0.20181322706107543,
                NaN,
                0.00013982203965075748,
                NaN,
                NaN,
                NaN,
                NaN,
                8.481106119455672e-05,
                NaN,
                1.9947299591354906e-06
            ],
            [
                NaN,
                3.28875024092319e-06,
                1.892515274546026e-05,
                1.3007125359792008e-05,
                NaN,
                6.1441724013465395e-06,
                3.120191878131786e-05,
                5.144221974927673e-05,
                3.120191124912986e-05,
                1.3709573702111586e-06
            ],
            [
                1.6373770576526875e-07,
                1.5534975690337685e-06,
                8.9396941718352e-06,
                1.7603425836870455e-06,
                3.059021539845349e-07,
                9.422449308138184e-07,
                3.7266392819902646e-06,
                7.889265406904397e-06,
                2.561282209165318e-06,
                7.889262581337206e-06
            ],
            [
                1.1478773597118638e-05,
                4.5397863149134916e-05,
                4.5397879405741464e-05,
                7.484621812387922e-05,
                8.481103109648735e-05,
                8.9396941702904e-06,
                1.9947299591354906e-06,
                1.99472995920443e-06,
                8.939694171135975e-06,
                8.48110410719979e-05
            ],
            [
                4.22283344433731e-06,
                4.785093923916815e-06,
                1.8925143721761383e-05,
                4.222835457595211e-06,
                1.0129993392600532e-05,
                2.7535694366751658e-05,
                3.726641060773727e-06,
                2.5612831263929686e-06,
                6.605215238359538e-05,
                1.012999339309804e-05
            ],
            [
                6.96225458885115e-06,
                1.892515725920463e-05,
                6.962259569003389e-06,
                0.0006263342426012905,
                3.535624226936835e-05,
                0.7310585844894971,
                1.7603438428188364e-06,
                1.1478773597640625e-05,
                3.53562633126235e-05,
                1.1478764019077695e-05
            ],
            [
                2.9023109469023766e-06,
                7.889260701926633e-06,
                3.2887506332466845e-06,
                1.7603440525701563e-06,
                4.2228344508893285e-06,
                6.9622570761976915e-06,
                1.3709578604308174e-06,
                3.1201903922734266e-05,
                0.00020342704326222456,
                1.3007133107008012e-05
            ],
            [
                1.4738976695459959e-05,
                8.93970056399654e-06,
                1.7603432132784448e-06,
                1.7603440526133836e-06,
                1.4738981968060613e-05,
                1.3007126909159127e-05,
                5.8291258398425644e-05,
                5.4222209070122355e-06,
                1.0129989769722525e-05,
                4.222834951876411e-06
            ],
            [
                NaN,
                NaN,
                2.7535691079423274e-05,
                1.2098656834723998e-06,
                3.2887494572095624e-06,
                6.605216041280767e-05,
                2.9023116390104826e-06,
                2.4300232033865884e-05,
                0.0004305571805263095,
                7.889260703619978e-06
            ],
            [
                5.422218967333467e-06,
                9.422442568300383e-07,
                1.3709573701637772e-06,
                NaN,
                1.553498495230919e-06,
                1.3709568799106278e-06,
                1.5534981248712412e-06,
                1.5534971988495103e-06,
                1.9947297214182054e-06,
                1.9947299591826594e-06
            ],
            [
                1.7603436328770204e-06,
                NaN,
                1.0677028699955933e-06,
                1.7603427934462202e-06,
                1.2098658276730537e-06,
                NaN,
                1.3007133114602719e-05,
                3.2887494573232236e-06,
                5.422218322763051e-06,
                1.0129987354366822e-05
            ],
            [
                2.561281599881745e-06,
                1.5534981247907057e-06,
                1.760343632774555e-06,
                2.2603245670174926e-06,
                4.2228349543420954e-06,
                1.8925141465200488e-05,
                3.2887506333812835e-06,
                2.1444958619530313e-05,
                6.962256249517824e-06,
                5.043475284350422e-07
            ],
            [
                6.1441760661636525e-06,
                1.670142781478417e-05,
                6.9622570786798724e-06,
                5.422221554038823e-06,
                5.422220261544064e-06,
                5.422217675362059e-06,
                3.7266410603195545e-06,
                2.26032429753354e-06,
                2.561281599881745e-06,
                2.5612834314274337e-06
            ],
            [
                2.5612831264675113e-06,
                2.5612831262578596e-06,
                4.222833947498071e-06,
                4.222835456903897e-06,
                2.7535700927485757e-05,
                2.56128343152993e-06,
                1.7603430033158905e-06,
                1.3709572065835317e-06,
                3.7266379506485954e-06,
                1.1478766753751021e-05
            ],
            [
                1.3709575336530204e-06,
                2.260323758806253e-06,
                3.28874867308036e-06,
                2.9023130227124616e-06,
                1.5534973841309562e-06,
                1.5534973839896667e-06,
                1.370957206753107e-06,
                2.5612834315811786e-06,
                1.7603425836678333e-06,
                1.2098655392464547e-06
            ],
            [
                1.4738980212296288e-05,
                8.939699500164542e-06,
                8.93969950000193e-06,
                1.6701427808495672e-05,
                2.260325375615501e-06,
                8.93969417199781e-06,
                1.4738987238893715e-05,
                2.4300252313020203e-05,
                2.7535681245588654e-05,
                2.4300246513165137e-05
            ],
            [
                NaN,
                7.338212429367364e-07,
                8.315283250082584e-07,
                4.539786836949404e-05,
                2.9023109467598367e-06,
                NaN,
                NaN,
                4.539785235863304e-05,
                NaN,
                NaN
            ],
            [
                3.466325384532298e-07,
                0.00015843625423585665,
                4.006369694755693e-05,
                6.144174600471243e-06,
                6.144177525664837e-06,
                NaN,
                1.5534973840786793e-06,
                3.2887482809455384e-06,
                0.651354857898194,
                0.00017952798724424872
            ],
            [
                3.7266392836374875e-06,
                4.222833947498071e-06,
                2.902313368897403e-06,
                8.939699498814873e-06,
                1.473898547706978e-05,
                4.2228319339950885e-06,
                2.9023130224960116e-06,
                5.144219523595344e-05,
                3.2887498494282754e-06,
                6.962257076628275e-06
            ],
            [
                4.222835455260108e-06,
                2.1024329090685577e-07,
                8.939693105076969e-06,
                8.315278293899016e-07,
                4.45084945805234e-07,
                1.1478768116515313e-05,
                1.012998855521771e-05,
                3.7266383953679482e-06,
                1.1478765381674627e-05,
                3.0590222691672177e-07
            ],
            [
                2.902313368860448e-06,
                1.994729245842213e-06,
                1.0677031245783732e-06,
                1.3709567165087443e-06,
                4.222834954211514e-06,
                1.0677028699489821e-06,
                3.2887498491620677e-06,
                4.222835457364773e-06,
                4.539785777882115e-05,
                2.2603245671202796e-06
            ],
            [
                NaN,
                2.753569107251144e-05,
                1.8925154999337424e-05,
                9.422450431732037e-07,
                NaN,
                NaN,
                2.7535681240079227e-05,
                1.3007125360146898e-05,
                1.4738976695459959e-05,
                NaN
            ],
            [
                NaN,
                5.422220261070644e-06,
                NaN,
                3.2887490653109436e-06,
                NaN,
                4.78509563466093e-06,
                2.26032429753354e-06,
                8.939700562110258e-06,
                8.93969417167259e-06,
                8.939694169835089e-06
            ],
            [
                3.726639727526609e-06,
                3.2887482810801374e-06,
                5.422219615395428e-06,
                7.338213303355652e-07,
                5.4222183221120994e-06,
                2.902310946400847e-06,
                5.422218969384951e-06,
                NaN,
                2.5612819052374947e-06,
                1.209866116137134e-06
            ],
            [
                2.260325105911487e-06,
                1.0677031245186523e-06,
                1.1478768123280277e-05,
                5.4222170296279735e-06,
                5.715003107689177e-07,
                4.222834450328596e-06,
                NaN,
                6.962259567407701e-06,
                8.315280276338815e-07,
                1.473898547706978e-05
            ],
            [
                NaN,
                1.994729721323867e-06,
                2.260324836624822e-06,
                5.043474683126242e-07,
                2.9023130227124616e-06,
                2.9023123309287002e-06,
                5.4222209070122355e-06,
                3.7266397280485686e-06,
                4.785095063591747e-06,
                2.5612825157045092e-06
            ],
            [
                6.144176797864436e-06,
                1.6701415868649062e-05,
                2.902313022554084e-06,
                7.889261640899994e-06,
                4.7850956351657615e-06,
                NaN,
                4.785096773840142e-06,
                8.939695229812583e-06,
                6.962254586824882e-06,
                3.288749456563487e-06
            ],
            [
                1.2098652507715085e-06,
                7.338208930265102e-07,
                3.059023727869902e-07,
                4.450851049890802e-07,
                5.715003788801361e-07,
                9.422443691996268e-07,
                3.2887494544577595e-06,
                6.9622570777680525e-06,
                3.288747888478753e-06,
                1.4738988997044936e-05
            ],
            [
                NaN,
                9.610239119353451e-05,
                NaN,
                2.1444943275617995e-05,
                NaN,
                6.144173134868593e-06,
                NaN,
                NaN,
                8.93969310367852e-06,
                6.962254577757329e-06
            ],
            [
                1.1478764013816059e-05,
                2.260324836624822e-06,
                2.5612828209345766e-06,
                1.7603432131855856e-06,
                1.4738988967205773e-05,
                1.76034279349265e-06,
                3.535624639436346e-05,
                3.535626333281696e-05,
                4.450852641681257e-07,
                5.422219615750493e-06
            ],
            [
                NaN,
                1.4449798650476187e-07,
                NaN,
                1.2098662603499435e-06,
                NaN,
                4.0063682527545155e-05,
                0.18242551713899047,
                2.9023133687311063e-06,
                7.338209805133949e-07,
                NaN
            ],
            [
                8.939699499627926e-06,
                0.0002959572042809718,
                2.7535697653779924e-05,
                NaN,
                3.2887482810382622e-06,
                6.9622562478334885e-06,
                2.4300249397180202e-05,
                0.000123394589256077,
                7.484625401596508e-05,
                8.481107159890629e-05
            ],
            [
                5.144223809160982e-05,
                4.785093353100252e-06,
                8.93969842784439e-06,
                1.012998977088337e-05,
                5.04347528438253e-07,
                5.422217676575195e-06,
                8.31528324914481e-07,
                3.927862470257753e-07,
                8.315284241257637e-07,
                4.222835457003754e-06
            ],
            [
                3.288749849368453e-06,
                NaN,
                1.1478773586115126e-05,
                3.4663278639044955e-07,
                7.88926352599354e-06,
                2.260324028372372e-06,
                NaN,
                9.422442568428928e-07,
                1.9947301970287804e-06,
                2.5612828212676906e-06
            ],
            [
                NaN,
                0.00010889686974417332,
                NaN,
                NaN,
                NaN,
                5.422217029736466e-06,
                NaN,
                1.4738988982594524e-05,
                8.93969416295666e-06,
                2.144494838924002e-05
            ],
            [
                6.9622562487453084e-06,
                5.829127243062412e-05,
                NaN,
                4.222831932781451e-06,
                6.96225541916544e-06,
                5.422218969029887e-06,
                2.902311639126627e-06,
                5.829126539607611e-05,
                1.5534971989258068e-06,
                3.7266401721817755e-06
            ],
            [
                1.621222490544928e-08,
                NaN,
                NaN,
                NaN,
                2.561281905058126e-06,
                7.889261642794245e-06,
                1.1478772219925941e-05,
                NaN,
                1.994729721396435e-06,
                4.450848927437622e-07
            ],
            [
                6.962254589332388e-06,
                1.9947297213492663e-06,
                0.0,
                4.539786858616951e-05,
                2.260324566803695e-06,
                6.962255419051463e-06,
                1.9947290080905435e-06,
                1.3007126912826352e-05,
                6.144173868312501e-06,
                NaN
            ],
            [
                4.785095634930755e-06,
                4.2228344508893285e-06,
                2.561282210530385e-06,
                4.222831933564939e-06,
                6.144172404129392e-06,
                1.553497198826904e-06,
                1.4738988990369329e-05,
                2.561282821176841e-06,
                2.561282515820982e-06,
                3.28874867308036e-06
            ],
            [
                1.553497754476329e-06,
                9.422443691524936e-07,
                8.3152773023541e-07,
                4.006368253424943e-05,
                4.5397852343109035e-05,
                7.338211553937586e-07,
                2.102432658340616e-07,
                5.043476486512307e-07,
                5.04347408156499e-07,
                6.9622562484666964e-06
            ],
            [
                6.144172402765906e-06,
                1.9947292458004866e-06,
                2.902311292960369e-06,
                1.5534981249164537e-06,
                1.370957206783032e-06,
                1.6701425820540864e-05,
                4.222831933649433e-06,
                1.2098653950205268e-06,
                8.315282258956806e-07,
                1.7603440524340693e-06
            ],
            [
                4.4508505192819656e-07,
                7.889260702141888e-06,
                8.939698432446272e-06,
                2.699577130905084e-07,
                1.9947301968056346e-06,
                4.7850962029623105e-06,
                3.4663270374206273e-07,
                5.04347348051526e-07,
                2.9023109470554753e-06,
                NaN
            ],
            [
                1.2098656833865714e-06,
                6.144173135483279e-06,
                4.222833443891798e-06,
                6.475947209638476e-07,
                0.0004305570106559469,
                6.9622595668378125e-06,
                5.715006512996219e-07,
                3.2887486729337966e-06,
                2.5612812944538183e-06,
                2.7535704190573806e-05
            ],
            [
                NaN,
                6.96225624580722e-06,
                3.120191878131786e-05,
                NaN,
                1.4738981968462759e-05,
                3.535623794449717e-05,
                4.539786860136322e-05,
                3.2887490645272776e-06,
                6.962255416759247e-06,
                2.9023126754426735e-06
            ],
            [
                3.726639727940109e-06,
                0.0002959569908847567,
                NaN,
                1.0129989770441144e-05,
                6.96225541788636e-06,
                0.5312093733737563,
                2.2603234893861252e-06,
                1.994730672496148e-06,
                7.484626270351544e-05,
                4.450852641519336e-07
            ],
            [
                5.715003107655392e-07,
                2.561282821106957e-06,
                1.0677033790145821e-06,
                NaN,
                NaN,
                NaN,
                3.2887482810382622e-06,
                2.102433159684668e-07,
                1.4738983723664288e-05,
                3.2887494570181325e-06
            ],
            [
                8.939699497335115e-06,
                2.4300234786072458e-05,
                7.889262578323629e-06,
                NaN,
                0.00010889693488397425,
                2.260324028306588e-06,
                3.4663270374490014e-07,
                NaN,
                0.00013982210684477224,
                1.3007131552624333e-05
            ],
            [
                NaN,
                1.760344052632596e-06,
                1.209865394997419e-06,
                7.338212429307298e-07,
                1.3709567163940317e-06,
                3.7266388386231563e-06,
                6.475950297332654e-07,
                3.9278634072580244e-07,
                1.2098652507957165e-06,
                2.5612831265630198e-06
            ],
            [
                2.2603245666515692e-06,
                9.422449307512599e-07,
                2.699576809009495e-07,
                3.2887502408573863e-06,
                5.715003788853339e-07,
                1.0677028699489821e-06,
                1.9947290078746543e-06,
                5.715004470077356e-07,
                9.422450431372112e-07,
                2.5612828208367393e-06
            ],
            [
                0.0003799844753746595,
                2.26032537546132e-06,
                7.889265404328504e-06,
                6.962258738701267e-06,
                1.670141785809127e-05,
                NaN,
                2.7535700904947163e-05,
                5.4222202621161125e-06,
                3.2887490649221017e-06,
                1.012999460108057e-05
            ],
            [
                NaN,
                1.7603438427660027e-06,
                1.7603432128813917e-06,
                2.9023130228840374e-06,
                5.043474081684252e-07,
                9.931201612754015e-08,
                3.059023727758615e-07,
                1.125351218064284e-07,
                3.059023727694626e-07,
                1.1478770861859053e-05
            ],
            [
                2.1444956063303036e-05,
                NaN,
                8.939700561817559e-06,
                1.1478764014985311e-05,
                2.2603240274740096e-06,
                1.209865971934245e-06,
                NaN,
                NaN,
                1.670142183825232e-05,
                3.7266379505740294e-06
            ],
            [
                5.422221554758815e-06,
                2.7535684521195802e-05,
                2.7535694373763664e-05,
                0.00033535010948957305,
                7.484623609088468e-05,
                0.0002959570274467799,
                5.14422258772351e-05,
                NaN,
                6.144176066672166e-06,
                1.1478768122695653e-05
            ],
            [
                8.481105123878872e-05,
                7.889263519392366e-06,
                1.0129987351621326e-05,
                3.2887478889962107e-06,
                5.422218968595919e-06,
                1.0129995807165349e-05,
                1.6701423809741124e-05,
                7.889261643181705e-06,
                5.422218966820596e-06,
                3.726640171686931e-06
            ],
            [
                2.5612815998141903e-06,
                2.5612834317535587e-06,
                2.9023130228444433e-06,
                6.962255419051463e-06,
                6.9622579086271995e-06,
                6.144177530146464e-06,
                2.4300237830711845e-05,
                3.2887498491620677e-06,
                1.994730434778778e-06,
                2.9023133684671433e-06
            ],
            [
                8.939694171331106e-06,
                1.994729483608425e-06,
                2.561281905293402e-06,
                2.9023126766832993e-06,
                2.7535694369155778e-05,
                1.4738981965326028e-05,
                2.902311292960369e-06,
                1.9947294834143063e-06,
                4.7850939232204965e-06,
                1.3709578603185986e-06
            ],
            [
                0.0001398221213032179,
                NaN,
                1.5534983101301911e-06,
                1.0129992185539456e-05,
                1.473898196763166e-05,
                3.12019038250036e-05,
                3.726637950973972e-06,
                NaN,
                2.9023130228444433e-06,
                4.006368258642613e-05
            ],
            [
                6.144172403827636e-06,
                1.553498495091042e-06,
                8.315278293407441e-07,
                7.889264465986113e-06,
                7.338213304083124e-07,
                1.3007123808910861e-05,
                2.260324297570543e-06,
                6.144177531007026e-06,
                5.715003107130418e-07,
                8.939696301384342e-06
            ],
            [
                0.0001795280499376526,
                NaN,
                1.892515726357648e-05,
                NaN,
                NaN,
                NaN,
                2.2603245671202796e-06,
                1.0129992185760567e-05,
                0.00012339454520938868,
                1.1478766751997141e-05
            ],
            [
                8.481105141464207e-05,
                9.422443692090534e-07,
                7.889263523008662e-06,
                5.1442213464124794e-05,
                2.9023116388547446e-06,
                NaN,
                NaN,
                5.422218321589366e-06,
                1.4738978435781506e-05,
                2.144494840687132e-05
            ],
            [
                7.33820893021171e-07,
                0.6791787121629465,
                1.892514371900746e-05,
                1.3007130012980722e-05,
                8.939697368305565e-06,
                8.939698433373153e-06,
                1.9947306725215466e-06,
                6.962259567914269e-06,
                6.144174601097106e-06,
                4.5397868256532134e-05
            ],
            [
                0.924141819456443,
                1.994729958743625e-06,
                8.939697367037201e-06,
                4.222834450328596e-06,
                2.260325105981383e-06,
                8.939700565102295e-06,
                0.3208213138121609,
                9.610241472619204e-05,
                0.4378234991142019,
                4.222833945416449e-06
            ],
            [
                6.144176797283277e-06,
                4.00636823517767e-05,
                1.370957206783032e-06,
                1.9947299591100915e-06,
                7.33820893021171e-07,
                1.7603430033799313e-06,
                3.288749065077638e-06,
                5.422218969217281e-06,
                1.3709575335919232e-06,
                2.9023112931213857e-06
            ],
            [
                6.962257078819179e-06,
                5.829129323316207e-05,
                1.3007134661628471e-05,
                4.0063696922780274e-05,
                6.1441731306999e-06,
                7.88926164421493e-06,
                1.3007125360478133e-05,
                1.7603436328770204e-06,
                NaN,
                2.5612834318583854e-06
            ],
            [
                1.670142181698688e-05,
                7.484625390487944e-05,
                4.539787397828422e-05,
                NaN,
                NaN,
                2.2603245661540776e-06,
                NaN,
                NaN,
                NaN,
                4.006370160119636e-05
            ],
            [
                1.7603427934702357e-06,
                NaN,
                2.2603237586397375e-06,
                3.2887498493325602e-06,
                6.144173868983067e-06,
                7.889261642363733e-06,
                3.927862470816829e-07,
                NaN,
                2.144494073483943e-05,
                NaN
            ],
            [
                1.5534975692683091e-06,
                4.0063711254184204e-05,
                NaN,
                0.00012339455989760105,
                NaN,
                NaN,
                2.7535681240079227e-05,
                NaN,
                2.561282819029073e-06,
                5.043472878915159e-07
            ],
            [
                1.7603436329714805e-06,
                NaN,
                NaN,
                4.222832940942332e-06,
                5.8291244514241416e-05,
                3.535624632233585e-05,
                NaN,
                1.994730434798734e-06,
                5.422221553072258e-06,
                1.3007130012341915e-05
            ],
            [
                4.4508510498604413e-07,
                1.067702742726318e-06,
                1.1478772229050293e-05,
                9.422445938642879e-07,
                5.043475885606781e-07,
                5.715003107525447e-07,
                1.3709572066782945e-06,
                2.9023126767360923e-06,
                6.475949525781504e-07,
                1.0677029972920738e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.0129992182112188e-05,
                3.1201915058697335e-05,
                NaN,
                NaN
            ],
            [
                6.144174601309452e-06,
                3.726638394957837e-06,
                3.2887478890769702e-06,
                6.9622579086271995e-06,
                2.902312330891746e-06,
                0.0007096704157772796,
                6.605212886590941e-05,
                2.7535681199409607e-05,
                1.370957697068717e-06,
                2.144495607336692e-05
            ],
            [
                1.8925145974191664e-05,
                2.260323758557508e-06,
                1.3007130002168321e-05,
                1.1478773597118638e-05,
                4.222833946315156e-06,
                1.0129987352948008e-05,
                3.288749849114211e-06,
                1.8925145968614975e-05,
                1.1478769467545481e-05,
                1.0129995805691255e-05
            ],
            [
                0.8670357546485408,
                NaN,
                0.7772998611746912,
                NaN,
                4.539787936841779e-05,
                0.00020342689983167352,
                0.7057850340255386,
                0.9902915213785336,
                0.5,
                0.9971990725054735
            ],
            [
                0.00012339461834524895,
                0.7310585903489891,
                2.7535684519993744e-05,
                8.315283250082584e-07,
                6.9622545863942985e-06,
                3.288748280658394e-06,
                1.3709568798956654e-06,
                0.000230506736104841,
                1.0129995801637498e-05,
                6.144176797585032e-06
            ]
        ]
    },
    {
        "q_id": "8895_mmlu_math",
        "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": [
            [
                0.9990889489954332,
                0.9999785550515878,
                0.9999417087344962,
                0.9980732655625566,
                0.9999339478632105,
                0.9995121428256455,
                0.999704043008745,
                0.9986749778576094,
                0.999903897573676,
                0.9993736658293936
            ],
            [
                0.9999417087275438,
                0.9997694931760726,
                0.999891103038896,
                0.9998601778596691,
                0.999948557761846,
                0.9992903295460809,
                0.9996200155624438,
                0.9999646437408679,
                0.9999038976194303,
                0.9996646500113862
            ],
            [
                0.9993736659051411,
                0.9998204719702819,
                0.9993736659069263,
                0.999933947878961,
                0.9990889487931486,
                0.9998601779261898,
                0.9999485577863858,
                0.9998204720557833,
                0.9998911031039359,
                0.9984988175733016
            ],
            [
                0.9999599363030631,
                0.9998911030389086,
                0.9992903295481449,
                0.999954602147616,
                0.999373665976553,
                0.9999646437408649,
                0.9997040428307913,
                0.9998601779428311,
                0.9999151889586547,
                0.9999485577679644
            ],
            [
                0.9999339478396165,
                0.9999339478238761,
                0.9998911030907348,
                0.9990889487724858,
                0.9999038976194708,
                0.9995121428307829,
                0.9982992777579537,
                0.9996200155614821,
                0.9999599362934953,
                0.9999485577618392
            ],
            [
                0.9999599362982768,
                0.9999038975736445,
                0.9999417087553565,
                0.9997694932300513,
                0.9998601779261043,
                0.9998766054547565,
                0.999820471970005,
                0.9989677690561588,
                0.9999417087275694,
                0.9999852610145143
            ],
            [
                0.9995694429122874,
                0.9999599362982599,
                0.9993736658990929,
                0.999290329533656,
                0.9989677690536378,
                0.993307150146842,
                0.999891103078169,
                0.9997965731004437,
                0.9996200155621453,
                0.9995694429617128
            ],
            [
                0.9999038975735285,
                0.9999785550464736,
                0.9999885212305064,
                0.9999485578047429,
                0.9999417087344838,
                0.9998204720767708,
                0.9998204720768701,
                0.9998204720767369,
                0.999769493367875,
                0.9998766054397721
            ],
            [
                0.9999485577986525,
                0.999569442965934,
                0.9997388095676162,
                0.9996200155161462,
                0.9999339478711289,
                0.9998204720774969,
                0.9998601779428311,
                0.9990889486747871,
                0.9995694430182779,
                0.9984988177727532
            ],
            [
                0.9999546021097102,
                0.9997694932303799,
                0.999704042936749,
                0.9998766054692634,
                0.9997388097845256,
                0.9997694932303799,
                0.9995694429660341,
                0.9992903297145403,
                0.9999339478474747,
                0.9999339478317487
            ],
            [
                0.9999869928668845,
                0.9999038975851828,
                0.9999546021313694,
                0.9999930377412605,
                0.9999967112521109,
                0.9998601779594093,
                0.9999687980849142,
                0.9999546021421896,
                0.9999251537461169,
                0.9999724643023379
            ],
            [
                0.9999038975392727,
                0.9997388095674719,
                0.9998766054693442,
                0.9988304898922845,
                0.9998204719699032,
                0.9998766054401024,
                0.9998911030648276,
                0.9996646498504494,
                0.9997694931756702,
                0.9999339478474694
            ],
            [
                0.9999151889384766,
                0.999620015471916,
                0.9993736659777552,
                0.9992903295373299,
                0.9994472212632575,
                0.9993736659740389,
                0.999959936303039,
                0.9993736659047402,
                0.9998766054251933,
                0.9998766054694789
            ],
            [
                0.9999151889687783,
                0.9999339478396064,
                0.9998601779426847,
                0.9997965729540741,
                0.9999151889788488,
                0.9995121428280865,
                0.9999485577924884,
                0.9998766053957486,
                0.9999417087066731,
                0.9998766054546542
            ],
            [
                0.9984988179589429,
                0.9989677691858058,
                0.9980732657823962,
                0.9998911030519949,
                0.9995121428248224,
                0.9995121429431802,
                0.9997694932585831,
                0.9999546021259557,
                0.9995694430143824,
                0.999290329627029
            ],
            [
                0.9999921107402355,
                0.9999869928684342,
                0.9999038976079275,
                0.9999339478238224,
                0.9999756997476807,
                0.9999251537995654,
                0.9999724643023399,
                0.9999485577863506,
                0.9996646498518251,
                0.9999810748562717
            ],
            [
                0.9998601779093775,
                0.9998204720770059,
                0.9999852610110009,
                0.9999151889587429,
                0.999968798077481,
                0.9999599363173749,
                0.9999251537727715,
                0.9999546021151381,
                0.9998911030389624,
                0.9999599362887508
            ],
            [
                0.9993736657632283,
                0.9999546021422073,
                0.9998415637269676,
                0.9999038976194506,
                0.9999724642957734,
                0.9999687980886374,
                0.9998204719701774,
                0.9999485577986358,
                0.9999151889486347,
                0.9997694933135142
            ],
            [
                0.9995694429110724,
                0.9995694429126631,
                0.9993736659035743,
                0.9997388096601193,
                0.9993736657516785,
                0.9997965730029439,
                0.9999038975850787,
                0.9998204719698691,
                0.9993736659004411,
                0.9999921107392954
            ],
            [
                0.9999546021476212,
                0.9999151889688598,
                0.9995121428224666,
                0.9991959141567343,
                0.9999251537638759,
                0.9996646497719275,
                0.9988304894864913,
                0.9999038975621809,
                0.9999417087136402,
                0.9995694430172133
            ],
            [
                0.9998766053664693,
                0.9998601778928846,
                0.9998766054692957,
                0.9994472213296962,
                0.999876605454525,
                0.9999756997621647,
                0.999933947847516,
                0.999820472055543,
                0.9999038975851088,
                0.9995121427693617
            ],
            [
                0.9996200155601113,
                0.9999251537370999,
                0.9999898700102277,
                0.9991959142485832,
                0.9997965730025117,
                0.999373665899275,
                0.9999339478395968,
                0.9996646498505665,
                0.9997694933674324,
                0.9998911031167671
            ],
            [
                0.9997388095982276,
                0.999903897596573,
                0.9998415638026308,
                0.9997965730272278,
                0.9999756997679594,
                0.9999599362934879,
                0.9997965730511625,
                0.9997965730512038,
                0.999948557780225,
                0.9998204720129281
            ],
            [
                0.9996200154720597,
                0.9997694932307689,
                0.9996200155160689,
                0.9998766054546057,
                0.999948557780225,
                0.9998601778593883,
                0.9992903297097933,
                0.9998911031167418,
                0.9995694430155974,
                0.9995694430141946
            ],
            [
                0.9999756997679619,
                0.9999938558246658,
                0.9975273763747536,
                0.9988304896000427,
                0.9998911030519141,
                0.9993736657499297,
                0.9968273166074583,
                0.9994472213907003,
                0.9980732649117686,
                0.9997040429712185
            ],
            [
                0.9996646498115299,
                0.9996646497304907,
                0.9993736658231632,
                0.9984988176947525,
                0.9999251537371326,
                0.9997965729297902,
                0.9996646497317494,
                0.9999785550592557,
                0.9999646437577242,
                0.9997040429008672
            ],
            [
                0.9999417087483837,
                0.9999417087066884,
                0.99937366583781,
                0.999569442914855,
                0.9996646497712348,
                0.9990889488845953,
                0.9998204720554438,
                0.9999546021421944,
                0.9999417087553089,
                0.9999756997621694
            ],
            [
                0.9998766053811916,
                0.9999599363173711,
                0.9995694428617596,
                0.999948557774109,
                0.999738809660902,
                0.9998601779267939,
                0.9999417087553479,
                0.9997694933404632,
                0.999964643732436,
                0.9998204720768701
            ],
            [
                0.9991959142530729,
                0.9997040429714769,
                0.999903897539346,
                0.9999869928746372,
                0.9999898700066069,
                0.999941708713625,
                0.9999339478711133,
                0.9999151889283524,
                0.9982992779303075,
                0.9999869928715357
            ],
            [
                0.9999546021097292,
                0.9997965729782722,
                0.9999339478632154,
                0.9999852610145148,
                0.9999921107374146,
                0.9999910603068937,
                0.9997388095668258,
                0.9997040429728288,
                0.9998766054693604,
                0.9998601779094832
            ],
            [
                0.9997388097230672,
                0.9999038975507166,
                0.9994472213262553,
                0.9997694933421802,
                0.9999151889486094,
                0.9990889488932313,
                0.9993736659037565,
                0.998830489873518,
                0.9992903294578266,
                0.999891103116832
            ],
            [
                0.9997694931752275,
                0.9999599363078219,
                0.999664649972496,
                0.9995121427645933,
                0.9997965730999907,
                0.9998601778596243,
                0.9990889486681644,
                0.9995121427738178,
                0.9982992773326036,
                0.9991959142537276
            ],
            [
                0.9993736659740389,
                0.9995694428602566,
                0.9999724642957734,
                0.9999038975966262,
                0.9999832985821387,
                0.999991060300499,
                0.9999339478553524,
                0.9999810748585295,
                0.9999151889485539,
                0.9999724643121942
            ],
            [
                0.9996200154744918,
                0.9990889488944499,
                0.9999485578047577,
                0.9993736658353688,
                0.9988304896167695,
                0.9997694931750665,
                0.9975273773332252,
                0.9998766054399983,
                0.9989677690577193,
                0.9997388096285806
            ],
            [
                0.9997388095991016,
                0.9999251537995464,
                0.9999945777797374,
                0.9997694932305475,
                0.9998415637833363,
                0.9986749777215846,
                0.9999646437577258,
                0.9998601779766589,
                0.9991959140707778,
                0.9992903297160676
            ],
            [
                5.422221555192784e-06,
                3.5356267555952205e-05,
                7.889262585211807e-06,
                1.3007131563176482e-05,
                1.0129988562422337e-05,
                1.300713311112477e-05,
                2.260324836776948e-06,
                6.144176799166453e-06,
                5.422218969601935e-06,
                3.726641061058432e-06
            ],
            [
                0.9999546021097193,
                0.9999885212332436,
                0.9999546021313795,
                0.9998415637456005,
                0.9995694428613839,
                0.9999339478317286,
                0.9996646499728472,
                0.9999038975622222,
                0.9998415637833893,
                0.9999251537996058
            ],
            [
                0.999933947871098,
                0.9999687980811913,
                0.9997965730997274,
                0.9999417087205882,
                0.9992903297175949,
                0.9992903294546068,
                0.9999251537906513,
                0.9999546021151239,
                0.9999599363173749,
                0.9998911030389356
            ],
            [
                0.9999251537906066,
                0.9999339478474747,
                0.9999599363030609,
                0.9999339478318583,
                0.9998911030907348,
                0.9999546021259487,
                0.999704042973199,
                0.9999785550541426,
                0.9999852610197857,
                0.9999151889891026
            ],
            [
                0.9992903297117747,
                0.9998911030388207,
                0.9997040428654331,
                0.9998766054251933,
                0.9994472212599773,
                0.999447221256472,
                0.9980732656326277,
                0.9998415637831543,
                0.9989677691691197,
                0.997199073602555
            ],
            [
                0.997527377236172,
                0.9999546021151307,
                0.9994472214542448,
                0.9992903296235616,
                0.9971990729984124,
                0.9999038975392628,
                0.994779874572435,
                0.9990889489958571,
                0.9947798731457432,
                0.9986749775926459
            ],
            [
                0.9999151889384297,
                0.9999417087483837,
                0.9997388096598381,
                0.9995694429683765,
                0.9997388095667575,
                0.9975273768324538,
                0.998674977570925,
                0.9995694428609079,
                0.999290329542077,
                0.9993736657501482
            ],
            [
                0.9991959141560794,
                0.9964063979229647,
                0.9998911031167798,
                0.9996646497712348,
                0.9999885212305059,
                0.9999038976080066,
                0.9999785550439183,
                0.9996646497316323,
                0.9999930377412604,
                0.9999485578047429
            ],
            [
                0.9997388095991016,
                0.9986749776940099,
                0.9988304897458237,
                0.9986749776821482,
                0.9982992773326036,
                0.9984988177275582,
                0.998830489595283,
                0.9999599362935014,
                0.999290329624057,
                0.9993736658994573
            ],
            [
                0.999704042759312,
                0.9997388096908217,
                0.9999339478789245,
                0.9989677689308334,
                0.9992903294568359,
                0.9982992776877867,
                0.9997965729297074,
                0.9998766054398044,
                0.9989677688069486,
                0.9999151889890027
            ],
            [
                0.9999646437450943,
                0.9997694932856999,
                0.9993736659757878,
                0.9999852610233032,
                0.999903897573697,
                0.9998415637456005,
                0.9998911030908624,
                0.99997246431547,
                0.9999038976194913,
                0.999948557774137
            ],
            [
                0.9997965730511625,
                0.9999339478474747,
                0.999915188989068,
                0.9999485578047611,
                0.999933947878971,
                0.9999852610110012,
                0.9998601779260209,
                0.9999599362934974,
                0.9999724642990565,
                0.9999546021422182
            ],
            [
                0.9986749778773276,
                0.9995694429165961,
                0.9990889487757706,
                0.99956944296403,
                0.9990889487831881,
                0.9990889489974996,
                0.9999038976080269,
                0.9993736659781195,
                0.9982992779415737,
                0.9999485577618493
            ],
            [
                0.9999417087483685,
                0.9997965729784409,
                0.9998415637645076,
                0.99896776881115,
                0.9998766054105375,
                0.9996200154733421,
                0.9998766054399156,
                0.9998204720343571,
                0.9998911030779662,
                0.9997388095669703
            ],
            [
                0.9998204720985706,
                0.9991959142520909,
                0.9990889487786315,
                0.9999485577802159,
                0.9999852610127579,
                0.9988304900066518,
                0.9997388097527894,
                0.9997388096593592,
                0.9986749773551031,
                0.9999339478474458
            ],
            [
                0.9999151889283604,
                0.9890130556894925,
                0.9999832985761665,
                0.9999974387174839,
                0.9999687980960641,
                0.999941708734492,
                0.9993736657501482,
                0.9999756997534811,
                0.9999599363126097,
                0.9989677688169122
            ],
            [
                0.999876605410392,
                0.9998766054252921,
                0.9999339478632154,
                0.9996200155625101,
                0.9999785550541442,
                0.9999546021313743,
                0.9999151889384845,
                0.9992903297077707,
                0.9999599363030446,
                0.9980732655838241
            ],
            [
                0.9995694430144701,
                0.9999339478789658,
                0.9992903294600969,
                0.9964063970542556,
                0.9997388096601876,
                0.9998601779760528,
                0.9997040430074533,
                0.9999417087275205,
                0.999941708741432,
                0.9999810748495038
            ],
            [
                0.9999417087553695,
                0.9996200155139906,
                0.9999339478474597,
                0.9998204720772828,
                0.9996200154254085,
                0.9999957771665555,
                0.999941708741432,
                0.9999930377412604,
                0.996827317696526,
                0.9995694429616252
            ],
            [
                0.9999339478789658,
                0.9999251537816801,
                0.9997694933122868,
                0.9999910603026303,
                0.9998911030778981,
                0.9968273164358876,
                0.9999251537549951,
                0.9999339478553327,
                0.9997040427952713,
                0.9999756997679586
            ],
            [
                0.9999756997476845,
                0.9996646498123495,
                0.9999646437535178,
                0.9996200155169533,
                0.9984988180744607,
                0.9998204720340488,
                0.9997965729301778,
                0.9999339478395777,
                0.9998415637268294,
                0.9999151889283604
            ],
            [
                0.9990889490086787,
                0.9996646499320739,
                0.9994472212592055,
                0.999841563764616,
                0.9986749775613741,
                0.9996646497714592,
                0.9999251537549112,
                0.998967768808029,
                0.9999339478711341,
                0.9996646498112958
            ],
            [
                0.9991959142447484,
                0.9999251537460276,
                0.9996200154713965,
                0.9997040427599234,
                0.9997694933408053,
                0.9995694430144701,
                0.999841563783553,
                0.999948557780225,
                0.9999646437450763,
                0.9998204720342526
            ],
            [
                0.9995121429386673,
                0.9990889489893404,
                0.9999898700053974,
                0.9992903295370822,
                0.9971990736591323,
                0.9996646497310566,
                0.9998766054400665,
                0.9993736658252764,
                0.9986749775545959,
                0.9996646497703273
            ],
            [
                0.9998766054253442,
                0.9999546021421873,
                0.9999546021313743,
                0.996827317461629,
                0.9998601779096583,
                0.9998911031168874,
                0.9999546021151405,
                0.9996646498914276,
                0.9998204719702453,
                0.9998415638401131
            ],
            [
                0.9996200155151292,
                0.9999599363030408,
                0.9997040427606381,
                0.9999810748495038,
                0.9999687980849142,
                0.9999151889384149,
                0.9984988180788231,
                0.9998911030777436,
                0.9999852610145143,
                0.999925153737113
            ],
            [
                0.9999646437408605,
                0.9999646437450763,
                0.9997694933131654,
                0.9996646498905104,
                0.9999646437366521,
                0.9999724643023389,
                0.9999687980923541,
                0.999290329716563,
                0.9999785550464871,
                0.9998415637456558
            ],
            [
                0.9999151889486347,
                0.9999485577802578,
                0.9999687980923553,
                0.9997965729301778,
                0.9997694933402955,
                0.9998766054399983,
                0.9999417087136521,
                0.9999599363078239,
                0.9996200154263591,
                0.9997965730278641
            ],
            [
                0.9971990727538939,
                0.99979657309939,
                0.9998911030388706,
                0.9997388095979464,
                0.9989677688248351,
                0.999447221455306,
                0.9999038975621508,
                0.9999151889485773,
                0.998830489464325,
                0.9984988179224726
            ],
            [
                0.9980732651589204,
                0.9984988179311975,
                0.9997965729784852,
                0.999447221453473,
                0.9998204720554098,
                0.9992903295400543,
                0.999620015561261,
                0.9998601779759897,
                0.9990889489795917,
                0.9999938558224682
            ],
            [
                0.9968273178614693,
                0.9999810748495034,
                0.9992903296343766,
                0.9999339478474645,
                0.9999785550464765,
                0.9999646437366505,
                0.9996200155619243,
                0.9994472213242616,
                0.9999485577679873,
                0.9996646499304641
            ],
            [
                0.999860177909463,
                0.9999832985821387,
                0.9998204720342866,
                0.9986749776111318,
                0.9994472214585218,
                0.9999885212359795,
                0.9997388096607576,
                0.9998415637078393,
                0.9998766054546218,
                0.9999785550567023
            ],
            [
                0.9975273764855894,
                0.9999485577740872,
                0.9995121428235167,
                0.9999038975850886,
                0.9999546021097243,
                0.9940889325009535,
                0.9978172834172323,
                0.9996646499698518,
                0.999820472055577,
                0.9997040427609998
            ],
            [
                0.9986749774273519,
                0.9914225133824653,
                0.999373665902372,
                0.9999546021151431,
                0.9998911030519014,
                0.9997694931759586,
                0.9986749775874083,
                0.9959298618669461,
                0.9999339478238412,
                0.9998911030518618
            ],
            [
                0.9999339478632105,
                0.9999756997650621,
                0.9999945777797375,
                0.9999921107392993,
                0.9999898700102277,
                0.999954602109706,
                0.9999977396762428,
                0.9999974387165688,
                0.9999251537548878,
                0.9999910603026306
            ],
            [
                0.9999687980849129,
                0.9999038975965423,
                0.9996200155158589,
                0.9996646498913104,
                0.9994472213193091,
                0.9995694428614715,
                0.9998601778928643,
                0.9996646500109276,
                0.9995121429430667,
                0.9997965729783995
            ],
            [
                0.9999251537995654,
                0.9995121428836323,
                0.9998204719487146,
                0.9993736658260779,
                0.9996200155622891,
                0.9994472212584338,
                0.99997246431547,
                0.9992903294543592,
                0.9996646497302664,
                0.9984988173960114
            ],
            [
                0.9991959142422231,
                0.999664649773713,
                0.9998766054104872,
                0.9999785550464785,
                0.9999930377437505,
                0.9995694429117238,
                0.9996646498533667,
                0.9999339478395871,
                0.9998766053958474,
                0.9999485577802376
            ],
            [
                0.9995121428251914,
                0.9999599362934934,
                0.999447221388417,
                0.9999417087483646,
                0.9997040427599234,
                0.9999251537460085,
                0.9997388096908217,
                0.999860177859431,
                0.9999756997534754,
                0.9990889486612768
            ],
            [
                0.9998766054397721,
                0.9998911031038947,
                0.9999485577802376,
                0.9953904268249678,
                0.999841563840279,
                0.9999832985781555,
                0.9999546021097292,
                0.9971990736136103,
                0.9999756997505845,
                0.9999810748517594
            ],
            [
                0.9993736659816902,
                0.9997694932857603,
                0.9999810748517607,
                0.9996646497711177,
                0.9999151889485385,
                0.9988304894953307,
                0.9993736657534638,
                0.9999151889890594,
                0.9988304896126897,
                0.9996646498922374
            ],
            [
                0.9998766054252598,
                0.9997388095979464,
                0.9988304895993628,
                0.9998601778927789,
                0.9997965729295415,
                0.9999038975621907,
                0.9999251537638503,
                0.999860177943122,
                0.9999251537906513,
                0.998299277510887
            ],
            [
                0.9998204719485422,
                0.999975699753477,
                0.9998204720557154,
                0.9996200154271773,
                0.9999038976194807,
                0.9997388095976653,
                0.9999687980737538,
                0.9999852610145148,
                0.9993736658317618,
                0.999915188958804
            ],
            [
                0.9989677690503967,
                0.9998911031298519,
                0.9998601779593483,
                0.9997965729539883,
                0.9999038975850585,
                0.9991959139569953,
                0.9998766054399156,
                0.9999485577802578,
                0.999948557798614,
                0.9998601779093998
            ],
            [
                0.9999832985801471,
                0.9999852610197867,
                0.999972464302344,
                0.9997694932031357,
                0.9990889486685883,
                0.9997040430096922,
                0.999664649972135,
                0.9999832985701949,
                0.9989677688316775,
                0.9998204719489601
            ],
            [
                0.9997694932859883,
                0.9996200154701583,
                0.9989677689308334,
                0.9999151889384686,
                0.9999038976194708,
                0.9999687980923481,
                0.9997965730270088,
                0.9999251537549232,
                0.999891103103726,
                0.9999546021259682
            ],
            [
                0.9994472213914721,
                0.9989677688038274,
                0.9999151889385092,
                0.9999646437492881,
                0.9999646437535052,
                0.9999885212264011,
                0.9986749777077202,
                0.9990889486677935,
                0.9999151889182442,
                0.9997965730024703
            ],
            [
                0.9999151889485854,
                0.9999251537460145,
                0.9997040428314286,
                0.999989870005398,
                0.9999646437366568,
                0.9999756997650613,
                0.9994472214632169,
                0.9996200154720597,
                0.9989677691969698,
                0.9997040427973809
            ],
            [
                0.9999546021313743,
                0.999769493258013,
                0.9991959139643376,
                0.9999646437619342,
                0.9991959141576695,
                0.9993736657507312,
                0.9978172837311235,
                0.9999151889890939,
                0.9980732654306975,
                0.9997694932301049
            ],
            [
                0.9999251537727589,
                0.9999417087136483,
                0.9993736659059426,
                0.9998204720128236,
                0.9999485577802343,
                0.9995694428620352,
                0.9991959141713721,
                0.9999251537906513,
                0.999088948786049,
                0.9997040428313339
            ],
            [
                0.9998601778761356,
                0.9999687980849168,
                0.9999756997476829,
                0.997817283458307,
                0.9999485577802313,
                0.9993736657513141,
                0.9998766054545571,
                0.9998204719487824,
                0.9996646499321911,
                0.9999251537370814
            ],
            [
                0.9999930377412606,
                0.9999687980886254,
                0.9999977396751633,
                0.9999885212277696,
                0.9999885212264009,
                0.9999485577740787,
                0.9999885212332428,
                0.9999724643121858,
                0.9999945777816766,
                0.9999885212318741
            ],
            [
                0.9991959139763565,
                0.9999832985721839,
                0.997199073557033,
                0.9991959142520909,
                0.999915188968877,
                0.9995121427678006,
                0.9998415637078393,
                0.9995121428286825,
                0.998967769189527,
                0.998967769189527
            ],
            [
                0.998967768816432,
                0.9991959140546434,
                0.9997694931749592,
                0.9982992779514563,
                0.995929862565355,
                0.9988304896188093,
                0.999933947863201,
                0.9982992773341848,
                0.9999151889384377,
                0.9999485578047547
            ],
            [
                0.9995694429651699,
                0.999664649931147,
                0.9998415638211505,
                0.9995694428592421,
                0.9999251537906317,
                0.9991959139637295,
                0.9988304894616051,
                0.9998911031038139,
                0.998299277480053,
                0.9998766054252095
            ],
            [
                0.9999852610145143,
                0.9996646497703273,
                0.9998911031167291,
                0.9999251537995039,
                0.9999756997679573,
                0.9999962733593831,
                0.9998204719487485,
                0.999903897585194,
                0.9999756997592822,
                0.9999785550566999
            ],
            [
                0.9982992773256857,
                0.9999485577925007,
                0.9997694932310572,
                0.9999151889283524,
                0.9999339478317487,
                0.9999485577740995,
                0.9993736659025906,
                0.9998911030648404,
                0.9989677687980654,
                0.9999417087066731
            ],
            [
                0.999876605439851,
                0.9975273766498333,
                0.9998415637455751,
                0.9933071487135132,
                0.9990889489995659,
                0.9993736658994573,
                0.9999151889283604,
                0.9999646437535082,
                0.9995694429625396,
                0.9986749777215846
            ],
            [
                0.999933947878971,
                0.9999417087136776,
                0.9998766053957809,
                0.9984988174026423,
                0.9998911030388207,
                0.998967768927112,
                0.9999485577740872,
                0.9984988175755701,
                0.9984988173949644,
                0.9998911030388833
            ],
            [
                0.99979657309939,
                0.9996200155617031,
                0.9997388096918022,
                0.9999485577679526,
                0.9999251537371462,
                0.9999810748472499,
                0.9998911030389624,
                0.9999724643187635,
                0.9998766053663866,
                0.9999832985761657
            ],
            [
                0.9999810748449924,
                0.9996200154248226,
                0.9997388096294927,
                0.9999599362934974,
                0.999569442965746,
                0.9994472213913113,
                0.9999339478238508,
                0.9999417087414243,
                0.9999646437619387,
                0.9998766054694268
            ],
            [
                0.9999724643187476,
                0.9999885212277698,
                0.9999646437450794,
                0.9999251537995278,
                0.9998415638023241,
                0.9997388095669703,
                0.999373665827426,
                0.9999417087136441,
                0.9988304896276486,
                0.999954602125951
            ],
            [
                0.9999151889788945,
                0.9999151889687629,
                0.9998911030908227,
                0.9998766053810586,
                0.9998911031037759,
                0.9999485577618328,
                0.9999785550413632,
                0.9999724643121858,
                0.9999339478396218,
                0.9994472213962958
            ],
            [
                0.9999646437577213,
                0.9995121429435492,
                0.9999339478632202,
                0.9995694430160734,
                0.9996200154713965,
                0.9999485578047674,
                0.9999151889384377,
                0.9984988179769162,
                0.9995694430150338,
                0.9998204719698691
            ],
            [
                0.9998415637832834,
                0.9999687980737492,
                0.9980732649189324,
                0.9999724643154663,
                0.9999546021313986,
                0.999915188968877,
                0.9989677687980654,
                0.999959936298269,
                0.9999251537638258,
                0.9995121428226936
            ],
            [
                0.9998601778927362,
                0.9997040429016766,
                0.9998911030520091,
                0.999903897573676,
                0.9990889486657272,
                0.998967768940797,
                0.9997965730028107,
                0.9991959141596338,
                0.9989677691664788,
                0.9991959141622059
            ],
            [
                0.9996646499323082,
                0.9998415638399263,
                0.9998766053958151,
                0.9999485577741191,
                0.9999485577986323,
                0.9995121428241128,
                0.9999251537639369,
                0.9998601778928643,
                0.9982992777494546,
                0.9998601778926324
            ],
            [
                0.9999151889586244,
                0.9999599363125866,
                0.9999810748562722,
                0.9999756997534747,
                0.9998766054545571,
                0.9998601779592263,
                0.9999756997534747,
                0.999972464318746,
                0.9999339478474549,
                0.9999339478789471
            ],
            [
                0.9999546021313719,
                0.9998601778593883,
                0.9988304898895648,
                0.9999339478238508,
                0.9999151889283684,
                0.9993736657554313,
                0.9994472212598166,
                0.9997040427609998,
                0.9993736657542289,
                0.9978172832727105
            ],
            [
                0.99992515377279,
                0.9998911030389624,
                0.9997694932305475,
                0.9999038976079864,
                0.9999485577618298,
                0.9998911030777935,
                0.9998415637645353,
                0.9998766053957648,
                0.9984988175666708,
                0.9999599363221565
            ],
            [
                0.9986749775476639,
                0.9999485577924947,
                0.999512142828569,
                0.9999339478474842,
                0.999891103090875,
                0.9991959141503273,
                0.9999687980886323,
                0.9998204719486441,
                0.9997965730513785,
                0.9999151889687863
            ],
            [
                0.9995694428597932,
                0.9996646498931935,
                0.9993736659055419,
                0.9998911031039502,
                0.9997040427950904,
                0.9995694428618473,
                0.9997040427951766,
                0.9999251537638258,
                0.9999417087553398,
                0.9998766053957486
            ],
            [
                0.9997040428306192,
                0.9998601779593259,
                0.9997388096599065,
                0.999915188928401,
                0.9971990732663422,
                0.999373665753646,
                0.9996200155188326,
                0.996406398186412,
                0.9940889322327977,
                0.9999151889586775
            ],
            [
                0.9997040429032524,
                0.9989677689193093,
                0.9997694932030217,
                0.9998601779429858,
                0.9998415638024603,
                0.9994472214572999,
                0.9999038975852962,
                0.9992903295425724,
                0.9997694932037662,
                0.9998911030389894
            ],
            [
                0.9999151889789598,
                0.9988304898675344,
                0.9996200154250436,
                0.9975273772976199,
                0.999841563783417,
                0.9997694933132795,
                0.9968273169837353,
                0.9994472213262553,
                0.9998204720557833,
                0.9998601778927992
            ],
            [
                0.9993736657557956,
                0.9998415638210446,
                0.9999687980960721,
                0.9997694933685592,
                0.9999724642990586,
                0.9995694429153311,
                0.9997040429023138,
                0.9999038975622977,
                0.9999810748562717,
                0.9999038975393677
            ],
            [
                0.9997694933123403,
                0.9999251537727589,
                0.9994472214545342,
                0.9975273767020927,
                0.99919591417039,
                0.9999687980960733,
                0.9998601779092168,
                0.9975273770489571,
                0.9998766053958636,
                0.9991959139605028
            ],
            [
                0.9997388096908217,
                0.9999599363173711,
                0.9999151889284097,
                0.9998204720127558,
                0.9997040429374809,
                0.9998911030518491,
                0.9980732651423541,
                0.9999646437535052,
                0.9996200155631071,
                0.9997388097222843
            ],
            [
                0.9999485577741262,
                0.9999546021367934,
                0.9999599363221673,
                0.9996200155606861,
                0.9990889488809396,
                0.9999417087205764,
                0.9999339478553573,
                0.999664649850225,
                0.9999546021422212,
                0.9999339478711399
            ],
            [
                0.9999982396569966,
                0.9999785550464736,
                0.999954602147594,
                0.9999898700090206,
                0.9999810748517589,
                0.9999485577618964,
                0.9998601779594297,
                0.9999785550567016,
                0.9999967112497585,
                0.999993037742097
            ],
            [
                0.9998204720341847,
                0.9999485577618096,
                0.9994472213215281,
                0.9999251537906132,
                0.9991959139666291,
                0.9890130557502123,
                0.9998911031038535,
                0.99944722132275,
                0.9989677690693637,
                0.9999417087483762
            ],
            [
                0.999903897550667,
                0.9993736659797227,
                0.9997965729786156,
                0.9998415637457365,
                0.9999151889688949,
                0.9999885212318742,
                0.999925153772803,
                0.9999485577986293,
                0.9995694428604445,
                0.9999785550515867
            ],
            [
                0.9999417087066922,
                0.9993736657556134,
                0.9993736657557956,
                0.9991959141615512,
                0.9990889486822047,
                0.999796573051423,
                0.9999417087275358,
                0.9947798745893618,
                0.9999151889586775,
                0.9990889487910293
            ],
            [
                0.9999546021097171,
                0.9997040429015819,
                0.997527376332257,
                0.9933071488218642,
                0.9999151889688344,
                0.9999485577986358,
                0.9998911030647897,
                0.9999151889789345,
                0.9999417087066808,
                0.9999038975850585
            ],
            [
                0.9996646498510153,
                0.9999724642990537,
                0.9998911030908227,
                0.9997040430073586,
                0.9999756997476829,
                0.9991959141535074,
                0.9998766054105033,
                0.9997040428332111,
                0.9999599363221586,
                0.9998204719916742
            ],
            [
                0.9999038975621809,
                0.9998415637081712,
                0.9997694932854182,
                0.9999724643154645,
                0.9997694932575167,
                0.9996200155608962,
                0.9996646499324252,
                0.9992903297085136,
                0.9999546021367712,
                0.9999339478710831
            ],
            [
                0.9998601778927362,
                0.999933947823871,
                0.998498817742914,
                0.9999546021367712,
                0.9998204720553759,
                0.9999485577924913,
                0.9999810748427375,
                0.99919591415318,
                0.9988304896019465,
                0.9996200155636378
            ],
            [
                0.9992903295425724,
                0.9999646437619434,
                0.9968273170853521,
                0.9997694932849822,
                0.998674977881641,
                0.9997388097850879,
                0.9999151889385698,
                0.9996200155160025,
                0.9999785550464758,
                0.9992903297120224
            ],
            [
                0.9999756997563714,
                0.999876605410471,
                0.9999151889384605,
                0.9999646437492907,
                0.9998204719698353,
                0.99994170874838,
                0.999738809722634,
                0.9999417087483685,
                0.9998415637458471,
                0.9999339478710692
            ],
            [
                0.9997965730027248,
                0.9999151889688598,
                0.9999151889789185,
                0.9993736657572165,
                0.9989677688173924,
                0.9999251537906579,
                0.9933071500168208,
                0.9999724643089007,
                0.9986749778670063,
                0.9999546021313577
            ],
            [
                0.9982992779346558,
                0.9997965730515561,
                0.9998911030910287,
                0.9999810748472515,
                0.9993736659029914,
                0.9997388096604688,
                0.9998415637457918,
                0.9999898700102283,
                0.9999646437366521,
                0.9998204719487824
            ],
            [
                0.9997694933679286,
                0.999933947823881,
                0.9999339478790019,
                0.9998766054399983,
                0.9999339478632352,
                0.9993736659000402,
                0.9999724643121868,
                0.9995121427683967,
                0.9989677688190729,
                0.9998766054547045
            ],
            [
                0.9994472213248725,
                0.9997965731000796,
                0.9996200155173292,
                0.9999038976194708,
                0.9964063978796126,
                0.9999417087067002,
                0.9982992775290711,
                0.9989677689333544,
                0.9990889486698069,
                0.9998911030389086
            ]
        ]
    },
    {
        "q_id": "8382_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            19,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            29,
            30,
            32,
            33,
            34,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            100,
            101,
            102,
            103,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.1444956079842134e-05,
                3.120190392795564e-05,
                3.288747889178668e-06,
                1.3007131560621253e-05,
                2.7535700931292276e-05,
                1.6701419845680582e-05,
                2.7535684488840414e-05,
                1.3007126910294786e-05,
                7.889261641674914e-06,
                1.4738976698757546e-05
            ],
            [
                0.9999945777784498,
                0.9999885212264112,
                0.9999977396754328,
                0.9999898700054032,
                0.9999687980998082,
                0.9999952149049361,
                0.9999967112497589,
                0.9999945777823273,
                0.9998911030908354,
                0.9999852610127611
            ],
            [
                2.430024072648329e-05,
                2.7535681235270997e-05,
                6.605216039358521e-05,
                4.785094494402695e-06,
                2.753568452790729e-05,
                5.4222183231674305e-06,
                1.1478769493540482e-05,
                1.6701419852090592e-05,
                5.144220744545534e-05,
                6.962257079059797e-06
            ],
            [
                1.147876812574406e-05,
                1.2098652508287273e-06,
                1.892515500388139e-05,
                1.06770312455264e-06,
                2.561283431986506e-06,
                4.0063701736593515e-05,
                1.892514597770291e-05,
                4.0063706490068886e-05,
                1.0129995806888955e-05,
                2.1444958635523312e-05
            ],
            [
                0.00017952803016475351,
                0.9999646437577657,
                0.9999599363221466,
                2.144495095654446e-05,
                3.1201918806289706e-05,
                0.9999599362982855,
                0.0008040860362703776,
                0.9997965730509908,
                3.5356267560968415e-05,
                0.9999910603005003
            ],
            [
                0.0001088969089855471,
                8.481105138193951e-05,
                4.0063706492255065e-05,
                2.144495863614743e-05,
                0.00010889696091391995,
                4.0063687388140825e-05,
                3.1201918806289706e-05,
                2.4300243628620005e-05,
                0.9978172834304169,
                4.0063692167994334e-05
            ],
            [
                4.78509506499309e-06,
                9.610240339544534e-05,
                3.726639728262097e-06,
                5.422217030555087e-06,
                1.8925157249015125e-05,
                3.726638839806038e-06,
                1.8925145983348442e-05,
                8.939698433974813e-06,
                2.7535681245588654e-05,
                2.5612822106841303e-06
            ],
            [
                2.1444943291142893e-05,
                3.535623804983752e-05,
                2.4300243624818735e-05,
                3.535626332895835e-05,
                7.889262585441413e-06,
                1.553498495281783e-06,
                3.120191135991401e-05,
                2.4300243616508983e-05,
                5.8291286270284484e-05,
                8.93969417150998e-06
            ],
            [
                8.939696302652706e-06,
                0.00010889692162340838,
                3.5356246311274475e-05,
                2.4300234934056724e-05,
                8.93969736955767e-06,
                2.753568781022632e-05,
                2.430023782328611e-05,
                4.539785774116719e-05,
                3.7266383955611403e-06,
                1.9947306725669014e-06
            ],
            [
                5.1442207429361644e-05,
                5.82912515784739e-05,
                4.006369218184011e-05,
                9.610241491147206e-05,
                3.535623804983752e-05,
                5.144221963025818e-05,
                7.889261643899223e-06,
                7.889260704308795e-06,
                4.539786860697828e-05,
                8.481107162358746e-05
            ],
            [
                1.6701419850845044e-05,
                6.962254588433232e-06,
                1.8925141442067574e-05,
                8.939695237504067e-06,
                5.422220262505697e-06,
                6.962255419728997e-06,
                5.422220908762902e-06,
                3.535626332895835e-05,
                8.939696301611998e-06,
                1.3007130014636887e-05
            ],
            [
                1.8925150493717652e-05,
                0.00012339455975396863,
                9.610244928336962e-05,
                0.00029595723816501897,
                4.539789021837975e-05,
                6.9622595694023114e-06,
                4.7850956342431385e-06,
                6.962258739530771e-06,
                1.3007131562514014e-05,
                1.4738978457872657e-05
            ],
            [
                3.1201911358551906e-05,
                1.4738981971250963e-05,
                1.6701419845680582e-05,
                4.5397890237206746e-05,
                2.144494584573034e-05,
                1.8925154994724604e-05,
                4.78509563546605e-06,
                2.1444948412137308e-05,
                4.006370650260296e-05,
                4.006369217003476e-05
            ],
            [
                1.1478769494083349e-05,
                6.144177531532303e-06,
                8.939693106329072e-06,
                1.8925152744083297e-05,
                3.288750241500471e-06,
                7.484625391195843e-05,
                8.939698433974813e-06,
                1.0677028700203557e-06,
                1.0129988559492579e-05,
                4.006368262694324e-05
            ],
            [
                2.144495863045236e-05,
                2.430024072188641e-05,
                5.422220907554695e-06,
                3.1201926243586504e-05,
                6.1441753337365085e-06,
                1.0129994599901296e-05,
                1.3007128462785148e-05,
                7.889264465842609e-06,
                1.1478770861650256e-05,
                8.481101090606248e-05
            ],
            [
                2.1444956077189637e-05,
                3.120192252175965e-05,
                1.4738978456719842e-05,
                8.939695237813028e-06,
                6.9622545892184106e-06,
                3.5356267564055315e-05,
                0.00010889692214311985,
                2.4300232040584407e-05,
                4.539785780045566e-05,
                4.539789028526512e-05
            ],
            [
                3.12019076377484e-05,
                0.00013982208928794488,
                1.8925152750692706e-05,
                1.6701421842566163e-05,
                1.6701427812931038e-05,
                1.8925141469950998e-05,
                6.962258739068529e-06,
                2.1444943290362748e-05,
                1.8925150493717652e-05,
                1.1478766749115769e-05
            ],
            [
                2.7535691095550887e-05,
                4.785092783415276e-06,
                4.222834451254188e-06,
                1.30071315640992e-05,
                3.1201900186835035e-05,
                3.1201907645920996e-05,
                1.4738987237124277e-05,
                1.0129993394314164e-05,
                1.4738980213341866e-05,
                1.6701415867707307e-05
            ],
            [
                1.0129992186387057e-05,
                7.889261643181705e-06,
                4.539788484641129e-05,
                0.00010889694820079102,
                1.5534983100425914e-06,
                1.0129988563730593e-05,
                8.939697369671496e-06,
                0.00015843621595594825,
                4.539786861787811e-05,
                4.5397873964411704e-05
            ],
            [
                6.605216820750714e-05,
                0.00012339461889105253,
                1.6701419852090592e-05,
                1.670141785651155e-05,
                0.0001398220565667444,
                2.2603253755476615e-06,
                8.481108169042316e-05,
                4.222833947820683e-06,
                6.605216827622735e-05,
                2.7535687801010546e-05
            ],
            [
                6.962257909501028e-06,
                3.53562422342549e-05,
                6.144173869240119e-06,
                8.4811051160426e-05,
                5.829127245607013e-05,
                1.147877222879974e-05,
                1.0129993393945642e-05,
                1.209865827740176e-06,
                2.753569106650115e-05,
                3.1201900204769344e-05
            ],
            [
                1.1478772228528306e-05,
                1.8925143725341476e-05,
                1.3007126911974612e-05,
                1.892515047684989e-05,
                1.4738987241494252e-05,
                3.120190389378964e-05,
                1.7603427936079236e-06,
                1.3007128458384476e-05,
                1.147876538789672e-05,
                4.539789021177379e-05
            ],
            [
                6.605215251574962e-05,
                1.994730434798734e-06,
                3.7266388397382506e-06,
                3.288748281295496e-06,
                5.422217030209884e-06,
                7.88925976283858e-06,
                8.939700566289352e-06,
                2.902311985079115e-06,
                8.939693105076969e-06,
                3.535626334156318e-05
            ],
            [
                1.7603438427852151e-06,
                7.889261643899223e-06,
                6.962258737472841e-06,
                2.260324297853209e-06,
                2.5612834319655406e-06,
                3.9278638755992735e-07,
                5.715005832798517e-07,
                8.315282259009745e-07,
                1.2098653950315304e-06,
                9.422447062202052e-07
            ],
            [
                4.539789027320923e-05,
                0.0005527787342342163,
                2.1444943292703185e-05,
                5.8291251603919903e-05,
                1.5534977545243671e-06,
                2.7535694373763664e-05,
                1.4738987226400411e-05,
                9.422450431732037e-07,
                3.535623802218407e-05,
                6.962253759904688e-06
            ],
            [
                1.3007130013288297e-05,
                4.006370171458602e-05,
                2.5612812946890944e-06,
                1.067703251864202e-06,
                1.1478764018576587e-05,
                8.939700564890901e-06,
                3.726641061027928e-06,
                2.5612812947077304e-06,
                6.14417606659952e-06,
                7.484624510079911e-05
            ],
            [
                7.484623605603429e-05,
                0.00013982207335253211,
                7.484621780369138e-05,
                0.00012339454489698813,
                2.753569437266178e-05,
                0.00017952790149991412,
                8.93969630362837e-06,
                7.48462626866348e-05,
                2.4300232039788792e-05,
                4.006371126336615e-05
            ],
            [
                4.222834451215781e-06,
                6.9622587393661365e-06,
                4.006369693691754e-05,
                2.430023783601594e-05,
                2.1444948404530884e-05,
                4.785094494716039e-06,
                5.144221975264518e-05,
                1.670141985245514e-05,
                5.144222592139923e-05,
                8.939699500327152e-06
            ],
            [
                4.785096776194573e-06,
                1.6701417861189946e-05,
                2.753568451618723e-05,
                0.00029595723844056906,
                6.60521524950855e-05,
                4.006371128770557e-05,
                7.484620048414485e-05,
                2.7535684526905577e-05,
                2.144495863958007e-05,
                0.0002959569928222166
            ],
            [
                1.3709576971242028e-06,
                4.006369216362198e-05,
                2.561282821352716e-06,
                2.6995787400282076e-07,
                3.120190763491069e-05,
                1.2098659719601033e-06,
                6.605213671058347e-05,
                4.006368258117931e-05,
                1.2098653950551882e-06,
                4.785093353787868e-06
            ],
            [
                6.144176066672166e-06,
                6.605217586044201e-05,
                5.422217675362059e-06,
                7.484623592480082e-05,
                5.144223199471459e-05,
                7.889261644631091e-06,
                1.4738987238464762e-05,
                4.222834954561012e-06,
                6.962257078249291e-06,
                1.670142979875954e-05
            ],
            [
                1.6701419850389357e-05,
                8.939697369671496e-06,
                3.288747889178668e-06,
                2.7535704222728874e-05,
                3.1201911372399926e-05,
                0.00857748715608694,
                0.00010889696086955431,
                2.4300232041998833e-05,
                9.610239196262121e-05,
                0.0002611902135821544
            ],
            [
                7.889261641904523e-06,
                1.4738976695942536e-05,
                2.4300232030064617e-05,
                1.670142980608093e-05,
                5.8291286034908874e-05,
                4.5397879429522924e-05,
                4.7850950649408664e-06,
                1.473898724181597e-05,
                1.0129988561077228e-05,
                1.300712536350655e-05
            ],
            [
                2.7535684513582775e-05,
                1.4738987232298539e-05,
                1.4738981968462759e-05,
                2.430025228711852e-05,
                2.4300237824258528e-05,
                1.3007131564383116e-05,
                1.4738988983291576e-05,
                1.1478768124783601e-05,
                5.1442195197777694e-05,
                8.939693101694668e-06
            ],
            [
                6.962259565976648e-06,
                2.4300249418927004e-05,
                3.7266379512112265e-06,
                5.8291251531398806e-05,
                1.4738988998787566e-05,
                3.5356267555952205e-05,
                5.1442219692761636e-05,
                1.8925155000025902e-05,
                1.0129995809929273e-05,
                4.006371126992468e-05
            ],
            [
                2.4300240730549767e-05,
                4.0063696945516495e-05,
                5.422219615829396e-06,
                1.6701423834591316e-05,
                5.829124466818968e-05,
                1.8925148220012804e-05,
                7.484623606311329e-05,
                1.4738978455701077e-05,
                4.222833946937338e-06,
                1.0129995809431767e-05
            ],
            [
                4.006370643876662e-05,
                4.006371126117997e-05,
                4.539786316234683e-05,
                2.4300246507772637e-05,
                1.0129987355122296e-05,
                1.994729245917502e-06,
                4.5397852361605714e-05,
                5.144221364340114e-05,
                0.00010889692164083773,
                4.2228319341064674e-06
            ],
            [
                4.0063711217164954e-05,
                2.430023782328611e-05,
                1.3007125355533295e-05,
                5.829127920604779e-05,
                4.0063677818524845e-05,
                2.1444953509026425e-05,
                3.5356267488169044e-05,
                1.0129990974903845e-05,
                3.5356254910985954e-05,
                5.422217676654099e-06
            ],
            [
                0.00010889686967920941,
                5.144221361046519e-05,
                1.892515272680245e-05,
                8.939698433373153e-06,
                4.006369217003476e-05,
                1.8925152740434357e-05,
                1.3007126906036072e-05,
                1.8925148237775583e-05,
                1.6701423831188846e-05,
                3.535623804803683e-05
            ],
            [
                7.484620043459196e-05,
                0.9995694429663222,
                0.0005527787286065363,
                9.61024489421746e-05,
                5.144222588771473e-05,
                3.120190392670705e-05,
                1.892514372737249e-05,
                5.144223816384438e-05,
                7.484623614370479e-05,
                2.430025231469984e-05
            ],
            [
                4.222834954134701e-06,
                2.5612825160271407e-06,
                1.670142581762446e-05,
                2.902310947208574e-06,
                2.2603234893861252e-06,
                5.043473480643696e-07,
                6.475946438022905e-07,
                3.0590211752206485e-07,
                1.0677028700320085e-06,
                1.370957533676711e-06
            ],
            [
                7.484622722255103e-05,
                4.785093924156175e-06,
                1.5534973841154145e-06,
                2.9023109469842055e-06,
                1.300713311112477e-05,
                6.962257909323729e-06,
                8.939699499823059e-06,
                9.422443692390473e-07,
                3.120191508820951e-05,
                6.962253759670401e-06
            ],
            [
                0.00013982209029700466,
                6.144174601410037e-06,
                9.610238028229237e-05,
                7.484624500496053e-05,
                2.7535681241281285e-05,
                8.481103109648735e-05,
                5.829127243528923e-05,
                1.1478768122695653e-05,
                1.4738976694012237e-05,
                8.481108155405963e-05
            ],
            [
                0.00017952798518076319,
                1.3007131564903626e-05,
                5.4222183222304545e-06,
                0.0758581727088564,
                1.5534979397500702e-06,
                2.430023493228869e-05,
                2.7535700936100516e-05,
                1.300712845966209e-05,
                1.1478769483831504e-05,
                8.315283250150648e-07
            ],
            [
                0.00033535014794072883,
                2.753570093009022e-05,
                5.8291244639350886e-05,
                1.4738976697631541e-05,
                5.829127240390582e-05,
                5.144220134032976e-05,
                1.6701421842961097e-05,
                4.222834451065997e-06,
                7.48462094167307e-05,
                6.605215250037168e-05
            ],
            [
                8.939698435226916e-06,
                1.4738983727578497e-05,
                2.4300249409733237e-05,
                8.939694172542558e-06,
                1.8925157262578186e-05,
                1.994729959270648e-06,
                2.7535704228438656e-05,
                2.2603234894560207e-06,
                6.962259569313662e-06,
                4.006367784548767e-05
            ],
            [
                5.144221973879711e-05,
                8.481103109648735e-05,
                3.1201918772464205e-05,
                2.56128159999123e-06,
                4.539786860697828e-05,
                2.1444950953735936e-05,
                0.0004305571373886001,
                7.889266347356409e-06,
                3.1201922511884416e-05,
                1.1478773598538445e-05
            ],
            [
                0.9770226290027769,
                3.120192623836512e-05,
                7.48462093285157e-05,
                3.5356246490314526e-05,
                0.00020342702047291395,
                0.00023050679593873252,
                1.4738983727578497e-05,
                0.00012339463324353262,
                1.6701421837705495e-05,
                0.9993736656927638
            ],
            [
                2.5612825160271407e-06,
                9.610241479471069e-05,
                8.939694170518055e-06,
                1.670142781520948e-05,
                4.0063692165808155e-05,
                1.6701421843720577e-05,
                5.1442207479139826e-05,
                1.994729721469003e-06,
                4.006369218184011e-05,
                0.00020342701912923257
            ],
            [
                1.4738983726184394e-05,
                3.120191136263821e-05,
                1.3007134665413997e-05,
                1.4738987242432592e-05,
                3.5356254916002164e-05,
                1.8925148236674017e-05,
                1.7603434231385591e-06,
                1.4738983726184394e-05,
                3.120190020068305e-05,
                1.3709576971379186e-06
            ],
            [
                8.481107149277722e-05,
                3.53562633126235e-05,
                2.4300234929636645e-05,
                4.539786861787811e-05,
                0.0002034270212542617,
                3.535626334323525e-05,
                5.829125851250855e-05,
                1.1478770861650256e-05,
                6.605214462205646e-05,
                3.535625068386498e-05
            ],
            [
                1.3007131563176482e-05,
                6.475945666033422e-07,
                5.144222590680261e-05,
                2.260325375650449e-06,
                4.006371126117997e-05,
                2.2603248367512505e-06,
                6.962254589332388e-06,
                4.222834954561012e-06,
                7.484620015633356e-05,
                1.0677028700266676e-06
            ],
            [
                0.0031726821473669624,
                0.00012339460410229036,
                3.1201926241089315e-05,
                0.9989677689524412,
                0.9890130561550109,
                0.0001398220233410219,
                0.9991959141767034,
                3.535625490931388e-05,
                0.9999599363126054,
                2.7535687813231466e-05
            ],
            [
                4.539786321436876e-05,
                2.144495863201265e-05,
                3.7266397280485686e-06,
                3.1201915067096954e-05,
                7.484620018247132e-05,
                4.5397874031792504e-05,
                0.00010889686928784151,
                5.1442238170207006e-05,
                6.6052121039017e-05,
                2.4300243628620005e-05
            ],
            [
                1.0129988564430787e-05,
                9.61023919304594e-05,
                4.0063696945516495e-05,
                3.5356242260622145e-05,
                1.6701419850389357e-05,
                5.422220908634683e-06,
                8.93969417199781e-06,
                2.260325375664839e-06,
                7.484624500496053e-05,
                0.9999945777784447
            ],
            [
                0.9840936053725161,
                5.1442238137271045e-05,
                9.61024490987887e-05,
                0.0003353502281896029,
                0.00010889688312673828,
                5.8291251611977796e-05,
                3.12019076377484e-05,
                7.484624507683945e-05,
                5.1442225848041874e-05,
                0.8670357615200474
            ],
            [
                0.9990889486977284,
                0.9997965729556724,
                0.0007096703640547701,
                0.9990889486839001,
                0.999569442970155,
                0.992422759859684,
                0.9995694429147549,
                0.999841563822271,
                0.9998204720777556,
                0.9999339478556528
            ],
            [
                7.889263525778283e-06,
                4.7850944937411915e-06,
                6.962258737979408e-06,
                4.006367777742476e-05,
                1.6701427811412077e-05,
                7.484620032132827e-05,
                2.144494329496561e-05,
                1.1478770858706246e-05,
                2.430025231213619e-05,
                3.120190390934028e-05
            ],
            [
                4.2228324375973415e-06,
                4.222832941034507e-06,
                0.00010889690906952487,
                1.6701421840804172e-05,
                2.4300237829827827e-05,
                3.7266388391993445e-06,
                7.889266345397582e-06,
                3.120190390775116e-05,
                4.5397884708016386e-05,
                4.7850933534310035e-06
            ],
            [
                1.1478764019787597e-05,
                1.1478764019996392e-05,
                4.785096205830278e-06,
                1.892515266277381e-05,
                6.605212881496996e-05,
                2.144495863614743e-05,
                6.605212884908979e-05,
                6.9622579092224155e-06,
                2.9023123310580418e-06,
                2.1444948408275583e-05
            ],
            [
                6.144173137014406e-06,
                1.4738987232298539e-05,
                6.605215250037168e-05,
                4.222831929916343e-06,
                9.610240337377108e-05,
                1.0129987356541108e-05,
                5.1442232038504445e-05,
                7.889265406294507e-06,
                1.5534981249574276e-06,
                1.6701429805199933e-05
            ],
            [
                0.00020342702093757907,
                0.9968273174513201,
                0.9999810748540229,
                0.9999898700078136,
                2.4300246513165137e-05,
                0.9998601779771431,
                0.0003353501066894002,
                0.9999417087414281,
                6.605217612907568e-05,
                0.9999852610145198
            ],
            [
                2.4300246517938825e-05,
                3.535624227579939e-05,
                2.902312331081799e-06,
                1.2098659719601033e-06,
                8.315282258956806e-07,
                2.4300243624818735e-05,
                3.535623806128476e-05,
                2.4300252288444548e-05,
                3.535626333989112e-05,
                1.4738988995838502e-05
            ],
            [
                0.9999151889790666,
                1.3007123809644304e-05,
                0.00023050679713930062,
                0.9999910603058283,
                0.9914225153069975,
                0.9999546021476057,
                0.9995121427726825,
                0.99999457778297,
                0.9947798754236135,
                8.481107136566915e-05
            ],
            [
                1.1478766753082876e-05,
                7.484625388309796e-05,
                1.1478773598914277e-05,
                1.1478773597390071e-05,
                3.120190758848578e-05,
                6.9622562489985925e-06,
                1.892515044118663e-05,
                1.670141586907437e-05,
                2.430023202688216e-05,
                1.147876675466972e-05
            ],
            [
                5.715005151485975e-07,
                6.144177531532303e-06,
                1.1478765388105516e-05,
                7.889263525893087e-06,
                4.785092783371756e-06,
                9.422442569097361e-07,
                2.9023133679075416e-06,
                8.939694172290508e-06,
                1.1478768124992398e-05,
                7.889259764359722e-06
            ],
            [
                0.0006263341688211962,
                0.9997965730027693,
                0.9971990726849604,
                0.9998911031307691,
                0.999620015426724,
                0.9997694933132795,
                0.9999599362982599,
                1.892515726357648e-05,
                0.5312093733737563,
                0.0001584361977565129
            ],
            [
                3.7266392836374875e-06,
                4.539785777882115e-05,
                0.9998911030909859,
                0.9988304894926109,
                1.0129994601688632e-05,
                8.481103119829716e-05,
                0.9980732652820484,
                0.9999546021260356,
                3.5356259116499136e-05,
                2.7535687815134722e-05
            ],
            [
                2.7535684518791692e-05,
                1.1478772229551402e-05,
                2.26032537546132e-06,
                2.2603237589028734e-06,
                6.962256247998122e-06,
                4.785096775998733e-06,
                5.144222590043998e-05,
                1.1478766753751021e-05,
                1.012999580884213e-05,
                8.939695236398313e-06
            ],
            [
                0.9999599362983067,
                0.999915188928337,
                0.9999417087345395,
                0.9978172840120535,
                0.00020342692442339695,
                0.00037998452852614883,
                0.0001398220571262028,
                0.0015011826034650902,
                0.00012339461900416312,
                0.00010889687020208962
            ],
            [
                1.8925155005051806e-05,
                2.1444948412137308e-05,
                0.0001233946182231613,
                2.7535684532815695e-05,
                3.7266397280485686e-06,
                1.4738980212296288e-05,
                2.561283126639892e-06,
                1.67014158650947e-05,
                4.5397852343109035e-05,
                2.430023493228869e-05
            ],
            [
                1.8925157259824262e-05,
                1.4738981960929243e-05,
                5.829125851250855e-05,
                1.147876812069122e-05,
                1.4738985472244041e-05,
                2.1444956069076118e-05,
                5.144223198722914e-05,
                4.785095065093186e-06,
                2.1444958637356654e-05,
                5.422217676979575e-06
            ],
            [
                8.481101095665886e-05,
                0.9998911031038679,
                0.9993736659897786,
                0.9980732651983213,
                0.9999038976082164,
                0.997527377190804,
                0.9820137932620449,
                0.99944722139025,
                2.7535691088138193e-05,
                0.9975273770753739
            ],
            [
                2.902313023101807e-06,
                1.2098658277264215e-06,
                1.5534983101393749e-06,
                8.939695238211425e-06,
                0.00012339454529556814,
                1.0677028700203557e-06,
                3.2887506333394084e-06,
                1.994729721482609e-06,
                3.288749457383046e-06,
                2.902312330601386e-06
            ],
            [
                1.9947301969707264e-06,
                7.88926352599354e-06,
                8.939693105467234e-06,
                1.7603440521330776e-06,
                1.9947297214182054e-06,
                6.1441760654483806e-06,
                2.9023112931213857e-06,
                1.2098661161789477e-06,
                0.00012339457430752727,
                1.9947306726358406e-06
            ],
            [
                1.0129990978220553e-05,
                0.9914225146892466,
                0.9770226302154202,
                9.610241489119613e-05,
                0.9902915238229599,
                0.00017952798700133205,
                0.9940889325283164,
                0.9975273772826886,
                0.9669140224455339,
                0.0001233946336474991
            ],
            [
                1.4738983727578497e-05,
                4.0063692144966625e-05,
                5.1442195212374294e-05,
                4.5397879462552736e-05,
                1.89251482270353e-05,
                4.006370650464339e-05,
                1.6701425786941456e-05,
                4.5397879462552736e-05,
                1.4738976699427788e-05,
                4.006369693473136e-05
            ],
            [
                4.539787401825028e-05,
                7.484626289355904e-05,
                9.610242638554995e-05,
                3.1201907650801864e-05,
                9.610246055259474e-05,
                0.00012339461900416312,
                9.610246073717569e-05,
                5.829127245988703e-05,
                3.5356242271040426e-05,
                6.605217609735863e-05
            ],
            [
                4.785093924156175e-06,
                1.4738978451438343e-05,
                1.5534981249291695e-06,
                1.1478768123280277e-05,
                1.0129990977262395e-05,
                1.2098662604192665e-06,
                3.1201926224857616e-05,
                1.209865683500459e-06,
                1.3007125354586914e-05,
                1.670142383495587e-05
            ],
            [
                0.9875683465398744,
                2.1444945848226808e-05,
                3.5356242264223526e-05,
                0.9999646437366584,
                0.9997040427979493,
                0.9992903295493833,
                2.4300237834601515e-05,
                8.481106153947614e-05,
                0.9947798751745471,
                0.9999646437493
            ],
            [
                5.144223194755629e-05,
                1.2098661161861e-06,
                2.9023119850527192e-06,
                3.53562633231704e-05,
                9.61024490638302e-05,
                2.753570422373059e-05,
                2.902311984952413e-06,
                1.8925150486075525e-05,
                1.6701421840318107e-05,
                6.605215238359538e-05
            ],
            [
                0.9999952149043646,
                3.5356267547205986e-05,
                1.8925152750176348e-05,
                3.120191508185304e-05,
                2.1444945848226808e-05,
                5.82912445630129e-05,
                0.00010889693512006272,
                0.00015843625380709215,
                2.430024361951464e-05,
                8.481108166450792e-05
            ],
            [
                0.0001233945451573219,
                1.473898899256772e-05,
                5.144220136428317e-05,
                0.9859363730084089,
                8.481101087089185e-05,
                1.8925141457627214e-05,
                4.0063692187232674e-05,
                3.5356238038776134e-05,
                8.481108169906156e-05,
                0.00010889690869558618
            ],
            [
                2.430023493564795e-05,
                3.535625489632318e-05,
                3.1201900203407254e-05,
                2.260323758835034e-06,
                1.8925145978942173e-05,
                1.1478769489719528e-05,
                5.829126551185543e-05,
                2.430024072091399e-05,
                4.0063682616886836e-05,
                4.006370648569653e-05
            ],
            [
                3.5356238044435446e-05,
                4.5397879429522924e-05,
                0.000203426946771709,
                0.00012339460418487908,
                4.539786862811735e-05,
                3.120191507481552e-05,
                4.785092783319532e-06,
                3.120191508321514e-05,
                8.939697369151141e-06,
                2.430024941804299e-05
            ],
            [
                5.144219497096888e-05,
                3.535625487947387e-05,
                1.4738980213985297e-05,
                3.535625912190121e-05,
                2.1444948375821515e-05,
                2.5612828207295832e-06,
                1.0129995809247506e-05,
                5.8291272354286105e-05,
                3.120190754943891e-05,
                8.481108138869572e-05
            ],
            [
                7.889261644760245e-06,
                4.222834451169694e-06,
                1.892514597343433e-05,
                8.315282259051341e-07,
                2.1444948400318094e-05,
                1.0677027427525368e-06,
                8.93969950101825e-06,
                6.962256249429175e-06,
                1.8925143726890553e-05,
                3.726639283806955e-06
            ],
            [
                5.144222590979679e-05,
                0.9999485577926522,
                6.605216811571998e-05,
                0.9999546021205518,
                0.9998766053964813,
                0.9999646437366552,
                0.96267311131724,
                0.9770226292118533,
                7.484624503218738e-05,
                0.00010889694792112913
            ],
            [
                0.9997388095660659,
                5.829127939986156e-05,
                0.9998204720344249,
                0.9998766054252095,
                2.7535684521195802e-05,
                0.9999952149032237,
                0.979667646212118,
                0.0004305570319241836,
                0.9993736658278268,
                0.9999687980960721
            ],
            [
                4.006370646616669e-05,
                2.4300232029003796e-05,
                4.785093353787868e-06,
                1.3007123812317831e-05,
                2.1444958616409722e-05,
                1.8925148227861472e-05,
                2.4300246519706854e-05,
                6.144176066672166e-06,
                2.430024071781994e-05,
                5.14422381608502e-05
            ],
            [
                2.1444940725789744e-05,
                5.144221974927673e-05,
                1.3007131565140219e-05,
                1.0677024881829577e-06,
                1.5534971989809095e-06,
                1.1478772230762415e-05,
                3.120190761300358e-05,
                2.260323489490968e-06,
                3.1201922480102066e-05,
                4.539787943513799e-05
            ],
            [
                5.1442213617576366e-05,
                1.3007123811229494e-05,
                8.481102092352864e-05,
                5.144223816721283e-05,
                0.00017952802809081942,
                4.0063711246896956e-05,
                4.0063711246896956e-05,
                2.430025230532926e-05,
                3.5356267550807374e-05,
                5.8291293265817787e-05
            ],
            [
                0.00012339453058940345,
                3.5356259128846735e-05,
                2.5612822106841303e-06,
                7.889265406294507e-06,
                3.7266401719851935e-06,
                4.006370171458602e-05,
                1.0129992185760567e-05,
                9.610242625969935e-05,
                8.93969310584124e-06,
                6.605216033495677e-05
            ],
            [
                1.7603432131855856e-06,
                1.0129990979694647e-05,
                1.0129994600859455e-05,
                2.5612812944538183e-06,
                4.5397879445707534e-05,
                3.2887498494551953e-06,
                7.48462449913471e-05,
                6.144172403827636e-06,
                1.670142781560441e-05,
                2.7535700938304286e-05
            ],
            [
                4.785095065045315e-06,
                4.539786319306454e-05,
                3.5356250696598434e-05,
                4.006369694959736e-05,
                7.48462180835835e-05,
                8.481107143601051e-05,
                4.785096774153486e-06,
                3.120192252437034e-05,
                1.892514147046736e-05,
                1.4738988998117324e-05
            ],
            [
                0.9971990725763579,
                8.481101087953025e-05,
                0.00012339458954513738,
                0.0001795279860766816,
                0.00012339455994966783,
                2.753568452349975e-05,
                0.00029595706214884565,
                0.04742587688008271,
                0.9924227590332847,
                3.5356242272712497e-05
            ],
            [
                2.2603245672867952e-06,
                1.0677024881980089e-06,
                1.6701427815999337e-05,
                7.889263526093993e-06,
                6.144176066850984e-06,
                4.0063701740091395e-05,
                1.4738987242700688e-05,
                3.120191879561992e-05,
                6.605214465281235e-05,
                4.785093924251918e-06
            ],
            [
                2.4300246516082393e-05,
                2.753568123266654e-05,
                1.3007134649798706e-05,
                6.962257908880483e-06,
                3.5356250704701545e-05,
                1.147876812106705e-05,
                2.902313368583287e-06,
                2.4300249362084747e-05,
                3.2887498492936755e-06,
                2.4300249402042293e-05
            ],
            [
                1.8925148236674017e-05,
                8.481105142266346e-05,
                2.4300240723831244e-05,
                4.5397890240179425e-05,
                2.1444943296369872e-05,
                4.006370648569653e-05,
                1.8925157255968775e-05,
                8.481104132251176e-05,
                4.006368262694324e-05,
                1.670141984792864e-05
            ],
            [
                3.2887498494282754e-06,
                5.829129329168791e-05,
                3.288749457383046e-06,
                2.561283126679493e-06,
                3.5356267531385634e-05,
                6.962254589781966e-06,
                4.785094494576774e-06,
                5.829125855619084e-05,
                1.5534971989907999e-06,
                1.370956716529941e-06
            ],
            [
                0.00010889689565051356,
                0.9875683493297573,
                0.9241418241572634,
                0.0001233946031291802,
                0.9990889490041224,
                0.0008040859360501325,
                0.9999546021151355,
                0.9999756997621702,
                0.9996200154723582,
                0.9770226318462163
            ],
            [
                1.1478765388314311e-05,
                3.1201922514835635e-05,
                6.962256248871951e-06,
                4.785093924251918e-06,
                7.889266344981421e-06,
                1.99472972129484e-06,
                1.5534984953298217e-06,
                4.222834954561012e-06,
                9.4224425692559e-07,
                8.939695237959376e-06
            ],
            [
                3.1201926219749737e-05,
                4.539787398158721e-05,
                3.1201922403597413e-05,
                1.6701429803316423e-05,
                0.003172682518489387,
                5.144223815074485e-05,
                4.006368262300812e-05,
                3.535623803273096e-05,
                0.0006263342950307061,
                6.605213661879638e-05
            ],
            [
                2.7535704229340197e-05,
                1.670142781560441e-05,
                6.605213645060008e-05,
                1.3007123812057577e-05,
                7.889261644875049e-06,
                6.605213660534067e-05,
                1.0129988561077228e-05,
                1.1478769489009626e-05,
                1.4738976695942536e-05,
                2.260323758939877e-06
            ],
            [
                6.605216033495677e-05,
                1.6701419850845044e-05,
                5.829129317633263e-05,
                1.3709568799760888e-06,
                1.6701425824733193e-05,
                7.889265406294507e-06,
                0.00010889694772465279,
                4.0063682618927264e-05,
                1.4738987242137685e-05,
                2.4300240725599276e-05
            ],
            [
                4.785094494185095e-06,
                7.88926258532661e-06,
                1.1478764019077695e-05,
                3.120192251903545e-05,
                1.6701429805199933e-05,
                3.120191507912884e-05,
                1.4738987242137685e-05,
                4.006367783499403e-05,
                1.4738988997044936e-05,
                1.0677029973114952e-06
            ],
            [
                0.00012339461892516522,
                2.753569765708558e-05,
                1.473898195567455e-05,
                0.00026119027685684985,
                8.93969630317306e-06,
                4.53978848619353e-05,
                3.5356259112640515e-05,
                1.6701419838268058e-05,
                0.00012339454541047406,
                NaN
            ],
            [
                0.9914225148397243,
                3.535625070778844e-05,
                0.00026119024574387616,
                0.9999646437493,
                0.9999151889789512,
                0.9998911030389356,
                0.999088949007831,
                0.9999417087483837,
                0.0024726233203042794,
                0.9999417087206773
            ],
            [
                1.14787681240737e-05,
                2.561282515914161e-06,
                5.829125851250855e-05,
                3.120191508321514e-05,
                6.605212080450339e-05,
                3.288748672760313e-06,
                1.3007133114602719e-05,
                2.753570420970657e-05,
                1.6701415862785876e-05,
                2.144494581132591e-05
            ],
            [
                6.144172403335888e-06,
                5.144222588771473e-05,
                1.3007130014376633e-05,
                3.72663839489005e-06,
                1.8925150491445666e-05,
                1.6701415866188347e-05,
                2.144495351940237e-05,
                3.120192252175965e-05,
                8.939698434495167e-06,
                1.6701417857058377e-05
            ],
            [
                5.1442231976000976e-05,
                7.484621824966732e-05,
                0.9984988180591049,
                0.00020342697194648913,
                7.484626278192885e-05,
                4.0063677816192936e-05,
                0.9998766054104082,
                9.610243758625373e-05,
                0.00013982207330370664,
                9.61024033409101e-05
            ],
            [
                2.7535684522397864e-05,
                4.222833444168322e-06,
                1.892515049199645e-05,
                1.147876401160283e-05,
                5.144222589744581e-05,
                0.00010889692159013416,
                3.535626755762428e-05,
                2.144494074201677e-05,
                3.535626333088765e-05,
                3.5356250681935664e-05
            ],
            [
                6.962256249112569e-06,
                4.2228324375512536e-06,
                5.829127244377123e-05,
                7.484620930782328e-05,
                4.539789027320923e-05,
                1.6701417861189946e-05,
                1.4738983728490028e-05,
                5.8291265441454815e-05,
                4.539785237052376e-05,
                5.144221363404434e-05
            ],
            [
                0.9525741278322102,
                0.9940889323094136,
                8.48110109406161e-05,
                5.829126547411052e-05,
                3.120190393260949e-05,
                2.753569764776963e-05,
                1.4738985483128763e-05,
                0.9971990734295713,
                0.00026119033967558135,
                0.00012339455993350918
            ],
            [
                9.422448185388577e-07,
                2.7535700943413033e-05,
                4.5397879429522924e-05,
                0.00020342704250455392,
                9.61023918311773e-05,
                5.144219525429276e-05,
                5.422218968477564e-06,
                2.4300249418927004e-05,
                0.00013982204065167932,
                3.535623805665442e-05
            ],
            [
                5.422219616085833e-06,
                2.753568781693781e-05,
                8.31528424151477e-07,
                1.0129993394129904e-05,
                4.222834954753043e-06,
                1.6701421842566163e-05,
                1.670142781709299e-05,
                2.2603245673155757e-06,
                1.6701425826191394e-05,
                2.561283126679493e-06
            ]
        ]
    },
    {
        "q_id": "8829_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            10,
            11,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            50,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            70,
            71,
            73,
            74,
            75,
            76,
            77,
            79,
            80,
            81,
            82,
            83,
            84,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            94,
            96,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            112,
            113,
            115,
            116,
            118,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.1478768122695653e-05,
                4.450852641596248e-07,
                2.902311639073834e-06,
                6.1441767987808774e-06,
                2.902312330759764e-06,
                2.144495863411905e-05,
                3.7266406165319545e-06,
                6.96225375833433e-06,
                2.260324836295902e-06,
                3.7266410609160796e-06
            ],
            [
                1.012999339449843e-05,
                NaN,
                1.4738983726559732e-05,
                1.8925143702277406e-05,
                2.7535687806920664e-05,
                NaN,
                2.4300234934056724e-05,
                1.7603427935967163e-06,
                8.93969736654937e-06,
                NaN
            ],
            [
                6.962257909121104e-06,
                8.939695237162584e-06,
                6.962257909501028e-06,
                2.902313368897403e-06,
                6.144173869240119e-06,
                7.88926258381982e-06,
                1.553498495295912e-06,
                4.7850927830845245e-06,
                6.475948753991907e-07,
                1.5534979397500702e-06
            ],
            [
                6.47594643784032e-07,
                6.475947981472062e-07,
                6.475950297942253e-07,
                1.7603430034311638e-06,
                7.338207180601138e-07,
                2.5612828211442287e-06,
                1.0677027427340866e-06,
                6.475948753741589e-07,
                8.315279285251204e-07,
                1.2098652507715085e-06
            ],
            [
                0.002182716391086122,
                0.9997040428743972,
                0.9999724643089467,
                0.8519527963298947,
                NaN,
                0.5312093733737563,
                0.1480472055495773,
                0.14804720179063333,
                0.9999546021178781,
                0.16451646289656316
            ],
            [
                1.4738983722270186e-05,
                5.422220907298259e-06,
                3.726641057519953e-06,
                3.5356246482211416e-05,
                8.939698426315848e-06,
                7.889259762106714e-06,
                1.670142183059676e-05,
                7.88926164421493e-06,
                3.2887486728201357e-06,
                6.962255415872755e-06
            ],
            [
                3.726638839806038e-06,
                4.222834451292594e-06,
                3.2887498492518007e-06,
                7.889264465699106e-06,
                7.889261645090304e-06,
                5.422219615188307e-06,
                4.222834451327159e-06,
                4.2228324377164004e-06,
                0.0019267345294536587,
                4.22283294098842e-06
            ],
            [
                4.785095635413826e-06,
                2.260324027054637e-06,
                6.962259568889411e-06,
                6.962253759581752e-06,
                1.3709572067955008e-06,
                4.006371127619171e-05,
                5.422219614951598e-06,
                3.7266392835764795e-06,
                2.2603251060142746e-06,
                6.1441738671166565e-06
            ],
            [
                2.2603234893861252e-06,
                3.0590229985449037e-07,
                1.553497939625029e-06,
                2.9023126770343703e-06,
                1.994730434735237e-06,
                1.5534975693792215e-06,
                1.5534977545102382e-06,
                7.889263525534328e-06,
                2.1024334103122815e-07,
                3.2887490653647836e-06
            ],
            [
                4.785095061816132e-06,
                1.7603434230921292e-06,
                1.3709578605355551e-06,
                3.288749064802458e-06,
                2.561282210087786e-06,
                2.5612819052072116e-06,
                1.7603432132079998e-06,
                3.2887486729876365e-06,
                1.5534977543406908e-06,
                1.0677028700130727e-06
            ],
            [
                4.7850950646797465e-06,
                0.020332351413358315,
                2.7535687794499397e-05,
                0.0002959570571631143,
                4.785094491408521e-06,
                5.422220261198862e-06,
                7.889262584006375e-06,
                6.962253757295868e-06,
                1.0129987350921133e-05,
                8.939693103158165e-06
            ],
            [
                3.927862470861484e-07,
                2.9023112931213857e-06,
                4.7850933535006355e-06,
                4.785094494576774e-06,
                6.144173868882483e-06,
                9.422445938917108e-07,
                5.4222183231674305e-06,
                1.0129993393945642e-05,
                2.4300243623139103e-05,
                4.222832940777184e-06
            ],
            [
                1.5534971989568904e-06,
                1.8925152752138513e-05,
                4.5397890257685224e-05,
                1.8925148239290237e-05,
                1.3007126911974612e-05,
                2.9023116390421582e-06,
                1.0677026154473471e-06,
                6.9622545892184106e-06,
                5.422218969463855e-06,
                3.1201918802543923e-05
            ],
            [
                1.209866116170145e-06,
                7.338211554641698e-07,
                1.994730196992497e-06,
                1.0677031244603883e-06,
                6.144175333289463e-06,
                5.715005151446993e-07,
                3.927861534257969e-07,
                1.3709572068079696e-06,
                2.260324027765926e-06,
                1.0677027427166074e-06
            ],
            [
                8.939698430218506e-06,
                0.9998601778931329,
                0.9999869928653375,
                0.9999984465015047,
                0.6791786861878392,
                1.0129992186589747e-05,
                0.9999938558268662,
                0.9999832985781686,
                3.1201911346293e-05,
                0.9999945777784468
            ],
            [
                0.9999646437324375,
                0.9998766054253622,
                0.9525741301883565,
                6.9622537587775775e-06,
                0.9890130577337255,
                6.605212860977054e-05,
                9.610239191997185e-05,
                7.48462182289749e-05,
                1.8925148230890784e-05,
                0.9890130560538113
            ],
            [
                2.4300237832303074e-05,
                5.829125857188255e-05,
                1.6701429806475863e-05,
                3.535623805665442e-05,
                1.9947299592570416e-06,
                4.0063696951637786e-05,
                8.48110108616364e-05,
                4.785096776303374e-06,
                2.4300246522270504e-05,
                0.00010889692218114752
            ],
            [
                3.726639728184142e-06,
                5.144222589407736e-05,
                8.481106153145476e-05,
                6.9622537593854575e-06,
                6.96225873967641e-06,
                1.473897670007122e-05,
                1.3007128462785148e-05,
                1.7603427935342762e-06,
                2.753568453191415e-05,
                3.120190392670705e-05
            ],
            [
                3.2887482811220126e-06,
                1.7603438428740716e-06,
                6.475945665671197e-07,
                9.422445938728576e-07,
                6.144172404129392e-06,
                6.962254589705982e-06,
                1.3007123812057577e-05,
                1.0677029972920738e-06,
                1.1478773598914277e-05,
                8.939695237162584e-06
            ],
            [
                5.422218968595919e-06,
                1.7603430034655858e-06,
                8.939698435340743e-06,
                8.3152792852928e-07,
                6.962255419653012e-06,
                1.9947306726358406e-06,
                1.0677033791000363e-06,
                1.1478764019787597e-05,
                3.7266401724291984e-06,
                3.92786340734912e-07
            ],
            [
                4.222831934202483e-06,
                3.535624219978455e-05,
                1.994729483608425e-06,
                2.902311985146426e-06,
                3.288748673035494e-06,
                2.2603251061849014e-06,
                3.726640172337686e-06,
                6.144173869312763e-06,
                3.7266383950934104e-06,
                2.9023133690188264e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                1.0129987344914205e-05,
                3.7266379512857925e-06,
                NaN,
                NaN,
                1.553498495281783e-06,
                1.3709578605542582e-06,
                6.144173867608406e-06
            ],
            [
                5.422219615829396e-06,
                6.144173868882483e-06,
                1.6701421840804172e-05,
                8.93969630317306e-06,
                1.3007123811797321e-05,
                4.222832941072913e-06,
                5.422219616026655e-06,
                6.9622570784012604e-06,
                1.2098659718539182e-06,
                1.147876949310201e-05
            ],
            [
                5.422220262505697e-06,
                4.785095064148803e-06,
                5.42221861652966e-06,
                1.1478766754941153e-05,
                4.222832437677995e-06,
                1.370956716529941e-06,
                6.1441731370702875e-06,
                4.539787397134796e-05,
                5.422218969769604e-06,
                5.42222090882208e-06
            ],
            [
                7.88926540679677e-06,
                4.785096205930373e-06,
                1.9947306725669014e-06,
                1.7603438427243761e-06,
                2.7535681241281285e-05,
                1.1478770861650256e-05,
                2.260323758806253e-06,
                2.902310946944611e-06,
                1.3709567164962755e-06,
                3.1201907648418184e-05
            ],
            [
                1.2098662603862553e-06,
                1.067703251784089e-06,
                9.42244481511812e-07,
                6.475947209567798e-07,
                1.0677033790757595e-06,
                1.5534981245957261e-06,
                9.422447061062286e-07,
                2.2603245668941476e-06,
                2.260324836341129e-06,
                1.0677031245623505e-06
            ],
            [
                3.9278634072866033e-07,
                1.8553905759893702e-07,
                1.5534979397500702e-06,
                2.2603234890695403e-06,
                9.422443692090534e-07,
                9.422445938557184e-07,
                1.5534971989696065e-06,
                6.47594720987407e-07,
                1.9947301966967833e-06,
                4.45084998867117e-07
            ],
            [
                1.209865827698362e-06,
                1.7603427935967163e-06,
                4.0063677837180203e-05,
                7.889262585441413e-06,
                5.422220908560712e-06,
                6.962255419653012e-06,
                2.9023116380522973e-06,
                0.0001795280072339397,
                2.2603248367358324e-06,
                8.939699500327152e-06
            ],
            [
                4.785093352238557e-06,
                2.5612834318257725e-06,
                8.939700561817559e-06,
                1.0129995809247506e-05,
                1.5534981248133121e-06,
                1.3709572067181944e-06,
                8.939696302831578e-06,
                1.4738983721251418e-05,
                1.553497754284175e-06,
                1.5534975692866768e-06
            ],
            [
                8.481103062816224e-05,
                7.889261644875049e-06,
                1.300713311517055e-05,
                1.5534984952662413e-06,
                5.422217676486429e-06,
                4.53978848619353e-05,
                2.5612831263929686e-06,
                7.889261643181705e-06,
                1.6701417851711638e-05,
                1.3007125361755747e-05
            ],
            [
                3.288747889178668e-06,
                3.726638839656906e-06,
                1.2098658277264215e-06,
                9.422450431372112e-07,
                8.31528126775552e-07,
                3.2887494571676872e-06,
                4.222833444283541e-06,
                4.7850956351657615e-06,
                2.699577774560111e-07,
                2.5612825157464395e-06
            ],
            [
                8.939696302652706e-06,
                7.889261644982674e-06,
                3.7266397278791014e-06,
                1.994729483608425e-06,
                6.1441760657054305e-06,
                2.56128159999123e-06,
                2.56128159999123e-06,
                3.288749065125496e-06,
                5.42222090767305e-06,
                4.006369693691754e-05
            ],
            [
                1.2098661161602417e-06,
                3.92786293909545e-07,
                8.939700566565793e-06,
                2.4300252319959737e-05,
                2.2603251061664e-06,
                5.422220259157241e-06,
                1.9947297209610287e-06,
                5.422218322763051e-06,
                1.3709578604981489e-06,
                1.9947306726049992e-06
            ],
            [
                3.2887482810382622e-06,
                4.222834449583514e-06,
                4.22283193393364e-06,
                2.902313022984344e-06,
                6.9622587393661365e-06,
                7.88926164421493e-06,
                2.902310946944611e-06,
                3.120192624733229e-05,
                1.0129988563343644e-05,
                6.96225375863827e-06
            ],
            [
                1.0129989770441144e-05,
                1.4738978451920916e-05,
                2.1444948412137308e-05,
                2.902313022984344e-06,
                3.2887494570719725e-06,
                3.7266388396128453e-06,
                7.889264466639056e-06,
                4.222834451065997e-06,
                3.726641061027928e-06,
                3.28875024125221e-06
            ],
            [
                1.0677024881382882e-06,
                9.422450431654909e-07,
                6.144175332440078e-06,
                3.2887498491620677e-06,
                4.78509563546605e-06,
                2.561281599776919e-06,
                3.288750241473551e-06,
                4.539785238670836e-05,
                3.726638395527247e-06,
                2.5612831266165976e-06
            ],
            [
                1.3007123810306773e-05,
                1.3007130013856124e-05,
                3.5356246478738656e-05,
                8.93969630348202e-06,
                1.1478768124783601e-05,
                1.3007123812554424e-05,
                1.0677027426952437e-06,
                1.6701425824307884e-05,
                5.829129330780371e-05,
                0.9991959138735174
            ],
            [
                3.7266383954560706e-06,
                4.785096203884934e-06,
                6.144176066672166e-06,
                1.3709575336530204e-06,
                2.9023126770343703e-06,
                1.47389819699641e-05,
                3.726639283040963e-06,
                4.222832437443716e-06,
                1.9947297214182054e-06,
                2.56128282131428e-06
            ],
            [
                3.5356237867839234e-05,
                0.00015843629177119916,
                2.430023781683279e-05,
                5.144220743347863e-05,
                9.610244918898165e-05,
                0.00020342697111186785,
                0.00017952794435509826,
                7.484626283964982e-05,
                1.6701419848475466e-05,
                0.00015843615985927873
            ],
            [
                6.475951069484661e-07,
                2.5612812940112203e-06,
                2.9023116387069255e-06,
                3.2887486725569194e-06,
                3.726639283291774e-06,
                2.2603237586397375e-06,
                1.4738980205754734e-05,
                4.222833946645451e-06,
                2.56128129423019e-06,
                6.475947209567798e-07
            ],
            [
                1.9947301970587145e-06,
                8.939693106987645e-06,
                2.902313022984344e-06,
                6.475950297906914e-07,
                8.939699500766203e-06,
                1.0677027427471959e-06,
                7.88926352599354e-06,
                6.144176799099397e-06,
                7.338210679816025e-07,
                7.88925976283858e-06
            ],
            [
                0.9999885212305079,
                4.539786321436876e-05,
                6.144173136952939e-06,
                6.605214465761795e-05,
                9.610242495085316e-05,
                1.4738978457041559e-05,
                1.892515049423401e-05,
                0.00012339463329919025,
                3.7266397282926013e-06,
                7.889264465986113e-06
            ],
            [
                3.466327863850901e-07,
                1.4449796927932878e-07,
                1.9947306726213275e-06,
                2.699578096324459e-07,
                1.9947306725868575e-06,
                1.994730196992497e-06,
                2.382369099864094e-07,
                1.5534983100595462e-06,
                2.699578418090074e-07,
                1.3709575335919232e-06
            ],
            [
                3.5356259128846735e-05,
                6.962257909412379e-06,
                2.7535694377870696e-05,
                1.5534977545102382e-06,
                7.88926163685319e-06,
                6.144176798691468e-06,
                8.939700565834043e-06,
                2.9023126765777146e-06,
                6.962253757840428e-06,
                2.1444945856418342e-05
            ],
            [
                1.370956879949281e-06,
                4.222833947428939e-06,
                3.4663257978039603e-07,
                9.422443692176231e-07,
                8.315280276505193e-07,
                6.14417533430649e-06,
                2.1024329090781183e-07,
                1.7603438427660027e-06,
                1.99472995920443e-06,
                3.2887482811908074e-06
            ],
            [
                1.0677024881499412e-06,
                6.962254588585202e-06,
                3.288748673295719e-06,
                1.0129993394314164e-05,
                3.2887490653408545e-06,
                6.14417313680765e-06,
                7.889263524257144e-06,
                6.1441738684354385e-06,
                1.1478770860982112e-05,
                2.561281599914358e-06
            ],
            [
                2.2603234893861252e-06,
                3.1201926246083686e-05,
                3.7266410608720178e-06,
                3.726641061085547e-06,
                1.1478769492392108e-05,
                8.93969630348202e-06,
                7.88926634687567e-06,
                2.902312677007974e-06,
                1.6701429807630274e-05,
                2.7535684532815695e-05
            ],
            [
                1.7603427929819248e-06,
                1.4738981963771067e-05,
                3.1201911358551906e-05,
                3.5356238040705445e-05,
                8.939693104865575e-06,
                1.6701415866188347e-05,
                2.144495095654446e-05,
                2.1444953514565465e-05,
                2.7535684276476884e-05,
                0.000158436190472129
            ],
            [
                8.939697369004791e-06,
                2.5612825159677387e-06,
                1.6701415868649062e-05,
                4.785095065171522e-06,
                1.6701429804288556e-05,
                3.7266401721817755e-06,
                7.889264465699106e-06,
                1.4738985484871391e-05,
                7.33820805514942e-07,
                1.2098662603631479e-06
            ],
            [
                0.007577240812640842,
                1.0129989768027317e-05,
                0.11920291263495983,
                0.9997694933317641,
                0.3775406617944891,
                3.5356242249174894e-05,
                6.962253759486771e-06,
                1.4738988995838502e-05,
                0.13296422989056964,
                0.9992903295881029
            ],
            [
                4.450849458200093e-07,
                3.9278629390507954e-07,
                9.422445938454347e-07,
                3.726638394957837e-06,
                1.3709575336093795e-06,
                3.2887482810801374e-06,
                1.067702742683591e-06,
                1.0677029971978802e-06,
                8.939700563248534e-06,
                1.5534983099790112e-06
            ],
            [
                6.144173868670137e-06,
                1.0677026154774503e-06,
                1.3709573702722555e-06,
                5.422219616184461e-06,
                4.222832940942332e-06,
                4.22283344433731e-06,
                6.1441760667392215e-06,
                5.71500719517695e-07,
                1.1478769489343698e-05,
                8.315283250343497e-07
            ],
            [
                4.006370643293681e-05,
                1.3007131562845248e-05,
                1.1478765386894505e-05,
                6.144176066353646e-06,
                1.8925150490206403e-05,
                1.1478765387416494e-05,
                4.5397890257685224e-05,
                2.1444945851269378e-05,
                0.0010322310486391229,
                5.144221360709674e-05
            ],
            [
                1.2098659719524008e-06,
                6.47594643788744e-07,
                8.315282259009745e-07,
                2.1024334103352274e-07,
                5.715005832213768e-07,
                3.2887486732000038e-06,
                9.931187406289015e-08,
                1.0677033791437343e-06,
                1.067702742683591e-06,
                1.6373774480479287e-07
            ],
            [
                2.260323758923431e-06,
                6.1441753335241615e-06,
                1.0129989769188164e-05,
                1.9947306726049992e-06,
                1.2098662604049616e-06,
                4.222831933649433e-06,
                9.422444815679433e-07,
                1.209866116170145e-06,
                6.9622595694023114e-06,
                4.785095635413826e-06
            ],
            [
                7.88925976283858e-06,
                5.829127939562056e-05,
                7.484624505179073e-05,
                6.962254588977791e-06,
                0.00020342699565328585,
                1.3007130012673148e-05,
                1.1478769492642663e-05,
                1.8925141470949294e-05,
                1.4738985480179701e-05,
                5.829126549573962e-05
            ],
            [
                9.422442569208767e-07,
                8.31528424151477e-07,
                2.2603242978665707e-06,
                1.7603432132912532e-06,
                3.059021904543821e-07,
                1.7603430033399058e-06,
                1.7603425835749741e-06,
                5.04347528440776e-07,
                7.338209805133949e-07,
                6.475946437928669e-07
            ],
            [
                1.9947301970451086e-06,
                1.760343632920248e-06,
                1.1478770862067849e-05,
                1.1478772230407462e-05,
                3.2887498489407274e-06,
                2.5612819053166966e-06,
                3.2887478891128633e-06,
                1.01299946023704e-05,
                6.9622587393661365e-06,
                1.0129988564578197e-05
            ],
            [
                6.1441753337365085e-06,
                0.999664649970408,
                1.7603425837702984e-06,
                8.939695237341456e-06,
                7.88926634687567e-06,
                3.2887506333812835e-06,
                2.144494330062167e-05,
                6.962254589104433e-06,
                7.889263525778283e-06,
                1.3007126912826352e-05
            ],
            [
                1.4738981970956057e-05,
                2.561282515886208e-06,
                1.9947294836483373e-06,
                6.1441760661636525e-06,
                1.0129992183991656e-05,
                3.7266401721817755e-06,
                6.144173136556186e-06,
                4.7850956342431385e-06,
                1.4738978454172926e-05,
                2.561281599502042e-06
            ],
            [
                1.3007130014636887e-05,
                5.42221767672807e-06,
                4.222833947774596e-06,
                1.370957206783032e-06,
                1.3007130014873483e-05,
                2.902312677007974e-06,
                3.7266406167827664e-06,
                7.484626265287347e-05,
                7.889265407004852e-06,
                1.5534977545384963e-06
            ],
            [
                0.9999885212346126,
                0.9999957771680668,
                0.9999546021422182,
                0.9999921107392967,
                0.9999869928730875,
                0.9999898700041916,
                0.999972464295789,
                0.9999967112497585,
                0.9999952149064409,
                0.9999756997506015
            ],
            [
                2.144494585197151e-05,
                4.785093353739995e-06,
                7.889264465986113e-06,
                1.0129995809044816e-05,
                2.1444943298320236e-05,
                6.962258739271155e-06,
                8.939697369004791e-06,
                4.006369693910372e-05,
                6.962256249429175e-06,
                7.889263525534328e-06
            ],
            [
                8.315281267430323e-07,
                2.7535697662094155e-05,
                6.144175334172377e-06,
                3.726640616670918e-06,
                6.96225873895455e-06,
                2.260323758939877e-06,
                6.144175334418252e-06,
                1.0677031244603883e-06,
                6.1441731363550164e-06,
                2.561282210590951e-06
            ],
            [
                1.0677033791107183e-06,
                1.0677027426709671e-06,
                3.7266397280485686e-06,
                3.466327863784696e-07,
                5.715003107655392e-07,
                1.0677026153784014e-06,
                5.422220262505697e-06,
                1.3709572067181944e-06,
                4.7850956351657615e-06,
                1.067702488159652e-06
            ],
            [
                0.9996200154415154,
                0.8175744806385542,
                0.20181321986003056,
                0.8670357546485407,
                0.20181322706107543,
                8.93969310662177e-06,
                0.14804719427274568,
                0.9980732649072912,
                0.999915188928498,
                0.9999251537728863
            ],
            [
                1.9947297214182054e-06,
                1.8925145983348442e-05,
                5.422218322565793e-06,
                4.0063687392367425e-05,
                2.7535700941409604e-05,
                4.222831934052698e-06,
                1.3709576969627325e-06,
                6.96225707894582e-06,
                1.0677028699625768e-06,
                9.422444815220956e-07
            ],
            [
                1.1478764019557924e-05,
                6.962258738827909e-06,
                4.785093923690512e-06,
                3.2887482810382622e-06,
                3.726640616670918e-06,
                1.012999460150437e-05,
                1.7603436325696244e-06,
                3.2887498494282754e-06,
                4.785093923516432e-06,
                3.2887506330851655e-06
            ],
            [
                2.7535681242383173e-05,
                4.222833443553821e-06,
                6.605213679900668e-05,
                1.892514372737249e-05,
                0.006692849726232566,
                0.4378234991142019,
                0.00015843625468306267,
                2.7535694369155778e-05,
                0.9953904280535157,
                0.004609571482841073
            ],
            [
                2.561281294558644e-06,
                1.370956716481313e-06,
                6.9622562487453084e-06,
                2.2603240282243575e-06,
                2.9023112925037123e-06,
                1.5534975693205863e-06,
                2.561283126304449e-06,
                2.260325375572331e-06,
                3.0590211751371835e-07,
                1.5534983100595462e-06
            ],
            [
                1.0129995809763438e-05,
                3.726639728262097e-06,
                4.222832437324657e-06,
                6.144176799166453e-06,
                9.42244818532859e-07,
                1.0129988564430787e-05,
                4.222834954280646e-06,
                2.5612822106654943e-06,
                6.144173136556186e-06,
                1.3709578604831862e-06
            ],
            [
                4.222834449698732e-06,
                9.42244256915735e-07,
                3.288750633545794e-06,
                5.422220262505697e-06,
                7.889260694177436e-06,
                1.3709575337078829e-06,
                1.5534975693601474e-06,
                1.6701421837705495e-05,
                4.222833444429485e-06,
                3.7266406168403854e-06
            ],
            [
                7.338213304283347e-07,
                5.043472879240838e-07,
                3.2887498494551953e-06,
                5.043475885606781e-07,
                1.067703251864202e-06,
                2.5612834319655406e-06,
                3.4663278639044955e-07,
                1.5534977545384963e-06,
                7.338210679816025e-07,
                9.422448185264317e-07
            ],
            [
                6.144172404129392e-06,
                1.370956879949281e-06,
                2.9023123309287002e-06,
                2.902312330965655e-06,
                3.7266388397721442e-06,
                8.315282259009745e-07,
                3.927862470861484e-07,
                7.338209804506587e-07,
                6.962259569003389e-06,
                1.0129987356706945e-05
            ],
            [
                4.006370638746435e-05,
                1.6701417844299117e-05,
                2.4300246507772637e-05,
                4.222832940423847e-06,
                1.3007134663876127e-05,
                8.481108167314633e-05,
                0.005911070005483769,
                2.2603237582655916e-06,
                2.2603240281935217e-06,
                2.902311984783477e-06
            ],
            [
                6.1441731363550164e-06,
                7.889265405677441e-06,
                5.422218969384951e-06,
                5.14422075023447e-05,
                8.939694171135975e-06,
                4.539785781036459e-05,
                2.75356812513986e-05,
                1.8925145981283003e-05,
                3.12019187926687e-05,
                1.0129995803259e-05
            ],
            [
                7.484625353622762e-05,
                8.481101093197769e-05,
                0.0006263341426975795,
                0.00023050663251397382,
                9.610240345767146e-05,
                0.0002959569928222166,
                8.481108174040254e-05,
                0.00020342697294685079,
                0.000261190307757037,
                0.0008040861087114307
            ],
            [
                2.430023493052066e-05,
                6.962257909121104e-06,
                7.889264466445326e-06,
                1.4738981970956057e-05,
                1.8925150492616083e-05,
                2.1444950969026795e-05,
                5.1442195248304415e-05,
                0.0001584362539523188,
                7.889261642578988e-06,
                2.7535681240079227e-05
            ],
            [
                5.4222215552470286e-06,
                3.726640616670918e-06,
                2.144495096083526e-05,
                8.315284241333265e-07,
                2.5612825156159896e-06,
                1.300712691308661e-05,
                8.939700566435704e-06,
                5.422218969720291e-06,
                7.889263522779056e-06,
                7.889266347356409e-06
            ],
            [
                2.902313022952668e-06,
                3.5356254919217684e-05,
                7.484621828233953e-05,
                6.605212880295596e-05,
                1.3007131552056503e-05,
                1.1478770859624945e-05,
                1.8925150490826034e-05,
                1.1478763997446522e-05,
                3.7266388394569345e-06,
                2.1444950959977102e-05
            ],
            [
                2.260325375634003e-06,
                2.2603251061458426e-06,
                1.0129988563730593e-05,
                1.3709572067955008e-06,
                1.147876812574406e-05,
                2.5612828208367393e-06,
                1.067702488159652e-06,
                3.2887478890769702e-06,
                1.0677027427068966e-06,
                2.2603251060142746e-06
            ],
            [
                3.535624227734284e-05,
                2.9023130227124616e-06,
                6.962257908753841e-06,
                2.4300234937946394e-05,
                7.484620047815493e-05,
                8.939697369004791e-06,
                5.4222183231674305e-06,
                4.006370171895837e-05,
                0.002182716069081457,
                6.605216822432677e-05
            ],
            [
                2.9023126767360923e-06,
                3.7266401724291984e-06,
                2.561281294558644e-06,
                1.9947301970451086e-06,
                7.889263525405172e-06,
                2.5612825160096693e-06,
                7.889260704631679e-06,
                2.9023123310290063e-06,
                2.9023116390104826e-06,
                1.994729008056074e-06
            ],
            [
                8.315277302701984e-07,
                1.994729959224386e-06,
                2.5612822106421996e-06,
                4.785092782936557e-06,
                1.3709568799243436e-06,
                2.561281905293402e-06,
                4.222835457595211e-06,
                6.962257079465052e-06,
                4.22283294098842e-06,
                1.2098662604049616e-06
            ],
            [
                6.144173136885882e-06,
                2.561282821352716e-06,
                2.902310946944611e-06,
                1.30071253611406e-05,
                1.994730672439908e-06,
                2.9023119845723063e-06,
                1.5534975691778837e-06,
                1.0129987354108855e-05,
                1.994730434816876e-06,
                1.994730434778778e-06
            ],
            [
                3.2887494569044713e-06,
                1.0129990970260453e-05,
                1.8925145981833788e-05,
                1.7603430033799313e-06,
                4.785096775058701e-06,
                1.8925148210787172e-05,
                2.430025227049901e-05,
                7.889264464106214e-06,
                6.962253759043525e-06,
                6.144175328953129e-06
            ],
            [
                1.4738985483879434e-05,
                0.9999945777784457,
                3.726638395415398e-06,
                4.539786320924914e-05,
                0.00023050668595599,
                1.670142781025767e-05,
                2.7535694373763664e-05,
                0.9999832985781701,
                3.535623801986889e-05,
                0.00010889690925332526
            ],
            [
                3.288748280293481e-06,
                2.260325375615501e-06,
                6.475947981813674e-07,
                5.715005832762133e-07,
                3.726638839833152e-06,
                1.994729008056074e-06,
                1.0129990979215566e-05,
                2.2603242976733308e-06,
                1.7603440526133836e-06,
                6.475951069855719e-07
            ],
            [
                1.1478766757049986e-05,
                8.939700566565793e-06,
                1.0129995807699706e-05,
                2.260324028404236e-06,
                1.3709568799760888e-06,
                6.9622562492265485e-06,
                1.760343213227212e-06,
                8.939694172420599e-06,
                1.2098659719441482e-06,
                2.144494585197151e-05
            ],
            [
                3.7266388386231563e-06,
                6.962258736902953e-06,
                1.1478766753751021e-05,
                6.475947981860793e-07,
                1.3709573700615334e-06,
                2.260323758676741e-06,
                2.561282821239737e-06,
                6.96225707894582e-06,
                1.6701427813417103e-05,
                2.561283126679493e-06
            ],
            [
                3.2887498493325602e-06,
                9.422443691996268e-07,
                1.3709573702722555e-06,
                4.222835457364773e-06,
                2.2603253755949437e-06,
                3.4663270374206273e-07,
                5.715005151353432e-07,
                1.5534975687737956e-06,
                3.4663262110189246e-07,
                6.475950297709604e-07
            ],
            [
                1.994730434735237e-06,
                6.144173869502757e-06,
                1.8553914607043678e-07,
                3.9278624706864377e-07,
                2.2603251061849014e-06,
                1.3709575336405514e-06,
                2.2603251061458426e-06,
                2.5612815999679353e-06,
                5.715003788933905e-07,
                2.5612812947240366e-06
            ],
            [
                3.7266388393349185e-06,
                8.93970056529743e-06,
                4.222832940646604e-06,
                1.8925141463066202e-05,
                4.222835457595211e-06,
                1.4738983719589221e-05,
                1.2751899728141993e-07,
                3.7266397281434697e-06,
                1.0677027427471959e-06,
                1.9947301970451086e-06
            ],
            [
                0.9997388096294242,
                0.00037998452634835264,
                0.9999646437535384,
                0.9999251537560793,
                0.9999417087358656,
                0.14804719803168948,
                0.9999251537907204,
                0.43782349911420193,
                0.0006263341599675854,
                8.93969629982328e-06
            ],
            [
                4.222835457526079e-06,
                3.726641060658489e-06,
                1.9947299591354906e-06,
                6.9622562481627565e-06,
                2.260323758882316e-06,
                2.9023116388969785e-06,
                2.9023126766832993e-06,
                2.2603242976404388e-06,
                1.1478769492141554e-05,
                3.2887502412970765e-06
            ],
            [
                3.7266401724291984e-06,
                7.338213303682682e-07,
                8.31528324914481e-07,
                4.222831934156396e-06,
                2.9023116391477434e-06,
                6.475948753847607e-07,
                6.962253759670401e-06,
                1.0129988542651073e-05,
                4.222833444283541e-06,
                1.3007133111929193e-05
            ],
            [
                1.2098661159797817e-06,
                6.144172404129392e-06,
                2.2603251061664e-06,
                3.46632621089282e-07,
                2.9023126767360923e-06,
                7.889262584666493e-06,
                2.2603240282243575e-06,
                1.01299946023704e-05,
                1.0677033791204289e-06,
                4.222834953712232e-06
            ],
            [
                2.7535684534618784e-05,
                1.670142582254589e-05,
                2.753569109454917e-05,
                2.4300232040584407e-05,
                4.785095064436034e-06,
                6.144176798255599e-06,
                7.889262584508638e-06,
                1.2098653950205268e-06,
                5.422218969306048e-06,
                3.726640616630245e-06
            ],
            [
                0.003172682565616047,
                2.9023119851266288e-06,
                1.3709575337016483e-06,
                6.144176799099397e-06,
                0.0009110512862711707,
                6.144172404028807e-06,
                6.962257909412379e-06,
                2.561282821239737e-06,
                8.939696304002375e-06,
                8.939696304002375e-06
            ],
            [
                2.902311984952413e-06,
                3.2887478891128633e-06,
                1.7603425837702984e-06,
                3.2887490653408545e-06,
                3.927863875584984e-07,
                6.47594798194325e-07,
                3.7266379512857925e-06,
                6.47594566597747e-07,
                9.422442568951678e-07,
                4.785092783415276e-06
            ],
            [
                8.939696302831578e-06,
                2.5612819052654485e-06,
                4.785094492661896e-06,
                8.939694170062744e-06,
                6.962259568648793e-06,
                1.5534979396645902e-06,
                6.605215250037168e-05,
                6.144172404218801e-06,
                2.2603248367512505e-06,
                2.430024072648329e-05
            ],
            [
                1.0129988562661878e-05,
                2.2603234893861252e-06,
                2.144495351940237e-05,
                2.430023782717578e-05,
                7.889266347004826e-06,
                6.144172403827636e-06,
                3.2887486732000038e-06,
                1.7603430034311638e-06,
                1.994730197071414e-06,
                2.4300234937946394e-05
            ]
        ]
    },
    {
        "q_id": "8267_mmlu_math",
        "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,
            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,
            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": [
            [
                0.9999038976199246,
                0.9999485577864112,
                0.9999485577865059,
                0.9999485577680053,
                0.9999599363221673,
                0.9999546021313795,
                0.9999687980886359,
                0.9999038975852738,
                0.9998766054404185,
                0.9997694933123941
            ],
            [
                0.9999151889586936,
                0.9999038975392727,
                0.9999038975965836,
                0.9998911031298249,
                0.9997388096301462,
                0.9998415637077608,
                0.9999687980960814,
                0.9993736659017891,
                0.9999151889587182,
                0.9995121429391215
            ],
            [
                0.9993736659726908,
                0.9999546021421849,
                0.999796573003077,
                0.9995694428599811,
                0.9996200154270225,
                0.9995694429119116,
                0.9997965730268786,
                0.9996646498514739,
                0.9998415637643762,
                0.9998204719489601
            ],
            [
                0.9998911030518745,
                0.9996200154268787,
                0.9999151889183534,
                0.9999038976194913,
                0.9998766053663525,
                0.9998415637266403,
                0.999925153790678,
                0.9999251537906257,
                0.9990889489983472,
                0.9997694932853645
            ],
            [
                0.9999910603004994,
                0.9999885212346123,
                0.9999785550490333,
                0.9999852610145168,
                0.9999910602994336,
                0.9999962733607161,
                0.9999646437450925,
                0.999992110733653,
                0.9999485577864075,
                0.9994472213925655
            ],
            [
                0.9999646437324408,
                0.9999546021097423,
                0.9992903295398066,
                0.9999810748517607,
                0.999975699750582,
                0.9999417087553831,
                0.9999724643187803,
                0.999964643757734,
                0.9999785550515911,
                0.9999756997505781
            ],
            [
                0.9998601778927565,
                0.9984988175195562,
                0.9984988177209272,
                0.9999417087483762,
                0.999620015471695,
                0.999512142828938,
                0.999876605410604,
                0.9998911031037886,
                0.999738809753405,
                0.9991959140616583
            ],
            [
                0.9998911030647778,
                0.9998911031167671,
                0.9991959141567343,
                0.9994472213891888,
                0.9989677691805238,
                0.99989110309081,
                0.9998766054547727,
                0.9999151889385013,
                0.9998911030389482,
                0.999964643736649
            ],
            [
                0.999841563821455,
                0.9995694428616595,
                0.9991959139685466,
                0.9988304894616051,
                0.9995121429447696,
                0.9994472213233612,
                0.9997694932858139,
                0.9998415638402491,
                0.9991959139585853,
                0.999915188989068
            ],
            [
                0.9997965730512038,
                0.9998766053665913,
                0.9998415637646713,
                0.9997965731007721,
                0.999891103116859,
                0.9997388096936793,
                0.9997965729549146,
                0.9998601779093775,
                0.9998415637651623,
                0.999373665694221
            ],
            [
                0.9999546021205791,
                0.9998601778593477,
                0.9999724643187494,
                0.9997388097230672,
                0.9999687980960708,
                0.9989677690458352,
                0.9998204720778312,
                0.9993736658982914,
                0.9997388095671831,
                0.9990889486637139
            ],
            [
                0.9706877673407197,
                0.9940889297537231,
                0.9989677691842451,
                0.9959298620141782,
                0.9993736658967611,
                0.998830489582772,
                0.9984988177495449,
                0.9959298616083461,
                0.9975273769570725,
                0.9999687980811902
            ],
            [
                8.939694172542558e-06,
                1.4738981970956057e-05,
                7.889266347456862e-06,
                4.539785776395774e-05,
                2.4300243624818735e-05,
                5.1442213614207906e-05,
                2.1444958636771547e-05,
                1.30071315640992e-05,
                7.889266347456862e-06,
                6.962255419653012e-06
            ],
            [
                0.9999151889788945,
                0.999954602136796,
                0.9997694931759586,
                0.999891103129683,
                0.9995121428861868,
                0.9986749777034069,
                0.9875683511363205,
                0.9997388095675478,
                0.9971990734744429,
                0.9998415638211253
            ],
            [
                0.9999724642990565,
                0.9998911030778711,
                0.9993736659016069,
                0.9998911030648276,
                0.9999339478238459,
                0.9997965730755767,
                0.9998601779260615,
                0.9999251537549172,
                0.9994472213885778,
                0.999964643732433
            ],
            [
                0.9999599363221545,
                0.9999485578047641,
                0.9998911030390163,
                0.9995121428840013,
                0.9999810748562746,
                0.9998766053957486,
                0.9999151889284097,
                0.9999151889183355,
                0.9997040428662339,
                0.9996646498927155
            ],
            [
                0.999769493287437,
                0.9998911031038012,
                0.998498817583248,
                0.9998204720770059,
                0.9991959142488639,
                0.9999417087205921,
                0.9999251537727775,
                0.9992903295433153,
                0.9995121428841148,
                0.9997965730270532
            ],
            [
                0.99973880966303,
                0.9997965729787044,
                0.9968273165257229,
                0.9998911030909162,
                0.9968273174417475,
                0.9997694933680964,
                0.9997694932851969,
                0.999447221325194,
                0.9992903296369359,
                0.9989677688259154
            ],
            [
                0.9999546021151483,
                0.9998601778760948,
                0.9999038976081129,
                0.9999339478474896,
                0.9998911030778569,
                0.9997965730759288,
                0.9998204720127244,
                0.9999151889688097,
                0.999860177859368,
                0.9996200154262044
            ],
            [
                0.9998911031038409,
                0.9971990730289771,
                0.999860177942705,
                0.9990889487901816,
                0.9997040427960807,
                0.9995694429138906,
                0.9995694428612838,
                0.9998766053958474,
                0.999704042831067,
                0.9996200155611172
            ],
            [
                0.9999151889384845,
                0.999841563745628,
                0.9996646497721616,
                0.999891103129893,
                0.9999151889587429,
                0.9982992772059076,
                0.9992903294682701,
                0.9999546021097508,
                0.9990889488805157,
                0.9998911030389086
            ],
            [
                0.9992903296243045,
                0.9999546021421827,
                0.9997694933135142,
                0.9998415638023241,
                0.9999339478395914,
                0.9994472214574606,
                0.9998766054695147,
                0.9997694932856999,
                0.999876605425276,
                0.99990389756239
            ],
            [
                0.9995121429432937,
                0.9999546021313795,
                0.9995694430166496,
                0.9999151889182516,
                0.9993736659021899,
                0.9997694933677074,
                0.9996200155162901,
                0.9998766053958636,
                0.9998415638400854,
                0.9997388097848751
            ],
            [
                0.9995694428624236,
                0.9998911031038947,
                0.9991959140717599,
                0.9986749776915451,
                0.9998766053811251,
                0.9997040427599234,
                0.9997694932300513,
                0.9998766053664531,
                0.9997388096913766,
                0.9997388095669703
            ],
            [
                8.93969630388855e-06,
                6.9622579095833456e-06,
                1.3007126911335805e-05,
                4.785092783371756e-06,
                1.4738976698757546e-05,
                1.892515500663531e-05,
                1.3007125363057018e-05,
                8.939694172542558e-06,
                4.222834451254188e-06,
                3.288750241500471e-06
            ],
            [
                0.9998601779594948,
                0.9999251537906383,
                0.9998204720123639,
                0.9995694430141946,
                0.9996200155624438,
                0.999569442964694,
                0.9993736658258594,
                0.9998601778927362,
                0.9998911031038139,
                0.9998204720343205
            ],
            [
                0.9995121429478634,
                0.9998204719918544,
                0.9998204719487485,
                0.9989677688586873,
                0.9997694933684385,
                0.9997694932577917,
                0.9997388097231431,
                0.9999339478553375,
                0.999925153746154,
                0.9999038975737515
            ],
            [
                0.9999151889486434,
                0.9999151889687863,
                0.9999417087136483,
                0.999903897608017,
                0.9999599363221628,
                0.9995121428835189,
                0.9997965730274498,
                0.9997965730766746,
                0.9992903295476083,
                0.9997965729793377
            ],
            [
                0.9999756997476845,
                0.9998766054693442,
                0.9997965729544619,
                0.9992903296285564,
                0.9971990734035585,
                0.9999417087067041,
                0.9998766054253961,
                0.9902915249153408,
                0.9968273179019688,
                0.9996646498119885
            ],
            [
                4.785093353787868e-06,
                2.561282821352716e-06,
                2.561283126679493e-06,
                3.726640616748873e-06,
                4.22283294098842e-06,
                2.5612834319655406e-06,
                2.5612812946890944e-06,
                2.5612831266165976e-06,
                2.902311293147782e-06,
                4.222832941034507e-06
            ],
            [
                0.999978555043919,
                0.9999038975736144,
                0.9999546021097148,
                0.9999785550439201,
                0.9998911030389356,
                0.9999151889689035,
                0.9999038975966926,
                0.9999546021367807,
                0.9998766054547565,
                0.9999546021313719
            ],
            [
                0.9999546021259655,
                0.9999885212277699,
                0.9998204720986411,
                0.9996646497721616,
                0.9998415637080029,
                0.9998601779761361,
                0.999959936317381,
                0.9999810748562764,
                0.9999810748449924,
                0.9999151889789432
            ],
            [
                0.9998415638400323,
                0.9993736659178931,
                0.9999546021476133,
                0.999876605410604,
                0.999891103090875,
                0.9999151889688598,
                0.9998415637078946,
                0.9982992777283057,
                0.9993736657572165,
                0.9997965730999907
            ],
            [
                0.9999151889791752,
                0.9999646437451037,
                0.999933947855464,
                0.9999756997621694,
                0.9998766054253622,
                0.999941708734578,
                0.9998911030778838,
                0.9999646437450824,
                0.9988304896722533,
                0.9999485577740962
            ],
            [
                0.9990889486739395,
                0.999841563745628,
                0.999925153790854,
                0.9998766054399156,
                0.9998204719491404,
                0.9997388097850879,
                0.9997388097229227,
                0.9998415638214249,
                0.9991959138909612,
                0.9997965729308113
            ],
            [
                0.9997694931752811,
                0.9975273766888842,
                0.9999038975967038,
                0.9996646498550839,
                0.9998601778608084,
                0.9975273774193669,
                0.9998204720342866,
                0.9975273767279351,
                0.9996200155659482,
                0.9988304897552069
            ],
            [
                0.9997388097539673,
                0.9980732653742825,
                0.999664649890969,
                0.999954602115126,
                0.9993736657554313,
                0.9996646497317494,
                0.9988304897898843,
                0.9993736659031736,
                0.9997965730759761,
                0.9999251537549482
            ],
            [
                2.902311985079115e-06,
                1.1478764019328247e-05,
                2.2603251061849014e-06,
                2.9023116390104826e-06,
                0.00013982205731540148,
                2.4300249419722622e-05,
                7.889265406904397e-06,
                8.939695236983711e-06,
                3.726638395493353e-06,
                1.8925145981833788e-05
            ],
            [
                0.9999151889182762,
                0.9999038975622536,
                0.9989677688290366,
                0.9997965730270088,
                0.9991959142463385,
                0.9953904284039189,
                0.9994472213959742,
                0.9989677691800437,
                0.9996200154265803,
                0.9999038975392522
            ],
            [
                0.9998766054693442,
                0.9999038975621907,
                0.9999785550439318,
                0.9991959139567147,
                0.9999646437619372,
                0.999373665830778,
                0.9999852610145151,
                0.9998911030520503,
                0.9999885212346117,
                0.9997040429011341
            ],
            [
                0.999088948695662,
                0.9999151889182682,
                0.9999038975736865,
                0.9978172831631782,
                0.9991959141654796,
                0.9992903296303314,
                0.9988304894595653,
                0.9994472214638601,
                0.9998204719701408,
                0.9997965729549146
            ],
            [
                0.9999339478711082,
                0.9995121429405406,
                0.999941708748413,
                0.9998415637098816,
                0.9998766054399156,
                0.9999810748540167,
                0.9998766054398994,
                0.9996200154283822,
                0.9999599363173896,
                0.9996646500119716
            ],
            [
                0.9999151889586936,
                0.9997965729542871,
                0.9998766053665034,
                0.9992903294560929,
                0.9998204719912641,
                0.9999038975507067,
                0.9996200154716175,
                0.9998601779427456,
                0.9998601779266231,
                0.9999339478397121
            ],
            [
                0.999796573076722,
                0.9999038975392831,
                0.9999485577802278,
                0.9999852610162713,
                0.9998601778761578,
                0.9999599363030652,
                0.9996646497721616,
                0.9999485577679776,
                0.999796572954595,
                0.9999546021313769
            ],
            [
                0.9997388097848067,
                0.9997040429721915,
                0.999876605439948,
                0.9999038975621705,
                0.99962001542511,
                0.9999251537638628,
                0.998073265686804,
                0.9998911030519267,
                0.9999339478474997,
                0.999796573075618
            ],
            [
                0.9993736658260779,
                0.999876605410708,
                0.9990889487006953,
                0.998073264899232,
                0.9996200154722146,
                0.9998204720351616,
                0.9999339478317487,
                0.9999038975507685,
                0.999796572954376,
                0.999925153737113
            ],
            [
                1.0129988563343644e-05,
                3.7266379512857925e-06,
                4.006369218184011e-05,
                1.012998977108606e-05,
                6.962257909501028e-06,
                6.144173136645595e-06,
                6.962254589528684e-06,
                1.1478772229989872e-05,
                2.2603245672867952e-06,
                1.473898899908247e-05
            ],
            [
                0.9999339478475102,
                0.9999417087205654,
                0.9991959138735174,
                0.9999546021098166,
                0.9988304896201693,
                0.999860177943238,
                0.9997388097848751,
                0.9999417087136648,
                0.9998204720985001,
                0.9998601779763111
            ],
            [
                0.999941708741465,
                0.9988304896181294,
                0.9998415637274033,
                0.9999546021097344,
                0.9998601778760724,
                0.9980732648849043,
                0.999860177892673,
                0.9999546021259581,
                0.99829927797557,
                0.9997694933402955
            ],
            [
                0.9988304899009879,
                0.9995694429105213,
                0.9996646498920032,
                0.9999485577618298,
                0.9998415637643255,
                0.9997965730027693,
                0.9982992777423391,
                0.9997388095983036,
                0.9999251537817373,
                0.9995121428823267
            ],
            [
                0.9990889489019203,
                0.9998204720348951,
                0.9999599363221545,
                0.9996200155625875,
                0.9998766054106218,
                0.99956944296403,
                0.9998415637644823,
                0.999891103064853,
                0.9994472212687887,
                0.9998601778594514
            ],
            [
                4.0063696922780274e-05,
                1.4738988998787566e-05,
                1.4738987241494252e-05,
                1.0129987356375273e-05,
                5.42222090882208e-06,
                2.1444943291142893e-05,
                1.4738976699106073e-05,
                2.1444943296369872e-05,
                1.1478766754941153e-05,
                1.0129994601688632e-05
            ],
            [
                0.9999417087345085,
                0.9999151889284795,
                0.9978172832889376,
                0.9998766054400162,
                0.9998204719701069,
                0.9995121427688792,
                0.9996646499712081,
                0.9989677691884468,
                0.9998601778594738,
                0.998967769208614
            ],
            [
                0.9995694429643182,
                0.9999599362934879,
                0.9997040429370244,
                0.9995121427683967,
                0.9978172830511105,
                0.9990889490162022,
                0.9999251537639511,
                0.9999038975393034,
                0.9998601778763776,
                0.9998415638028936
            ],
            [
                0.9999038975621907,
                0.9982992772794348,
                0.99951214282627,
                0.9996200154744144,
                0.9998911030778838,
                0.9994472213293746,
                0.9997040429366628,
                0.9993736659793219,
                0.9996200154262819,
                0.9968273171295333
            ],
            [
                0.9997040427622138,
                0.9989677690698437,
                0.9997694932031357,
                0.9999251537460145,
                0.9995694428616595,
                0.9998601779595151,
                0.9990889488923836,
                0.9996646498103884,
                0.9999646437450763,
                0.999796573075618
            ],
            [
                0.9999038975853325,
                0.9998601779261674,
                0.9996646498107299,
                0.9996200155173954,
                0.9999485577863724,
                0.9990889486706546,
                0.9991959138823094,
                0.9999251537728095,
                0.9999599362887323,
                0.9998415638400323
            ],
            [
                5.422219616026655e-06,
                4.785093353626844e-06,
                2.1444945853375776e-05,
                4.222832437639588e-06,
                2.902313023063532e-06,
                5.4222215552470286e-06,
                3.726640616748873e-06,
                0.9940889325009536,
                1.4738981969615573e-05,
                2.4300234937239182e-05
            ],
            [
                0.9999485577802103,
                0.999948557767984,
                0.9999785550490375,
                0.9999646437450873,
                0.999986992871595,
                0.999992110740236,
                0.9997040430062134,
                0.999995214906089,
                0.9999417087414608,
                0.9999852610233009
            ],
            [
                0.9999339478238761,
                0.9994472212633861,
                0.9997040427967179,
                0.9997694932312318,
                0.9994472213261267,
                0.9999546021205622,
                0.9997965730753162,
                0.9999756997679619,
                0.9997694933408053,
                0.9984988180964475
            ],
            [
                0.9980732651333992,
                0.999088948902768,
                0.9994472213373821,
                0.9997694932028607,
                0.9995694428622356,
                0.99992515377279,
                0.9933071493729064,
                0.9997388097848067,
                0.9998766053665213,
                0.9997965729784409
            ],
            [
                0.9997965730513342,
                0.999290329547856,
                0.9998911030389086,
                0.9999724643187565,
                0.9998204720987116,
                0.9996200155175502,
                0.9998601778599254,
                0.9995694429123752,
                0.9994472214560778,
                0.9995694430174136
            ],
            [
                0.9999646437493,
                0.9999038975393139,
                0.9997965730758843,
                0.9999251537996416,
                0.9991959141753473,
                0.9999038976081016,
                0.9997965730753162,
                0.9999724642957851,
                0.9975273768864361,
                0.9999151889284177
            ],
            [
                3.726641061027928e-06,
                8.93969950000193e-06,
                1.7603427936183298e-06,
                1.0129989771657269e-05,
                4.2228349546493465e-06,
                3.7266410609940346e-06,
                1.8925152747938785e-05,
                1.4738988996240646e-05,
                3.7266379512112265e-06,
                2.2603248367656408e-06
            ],
            [
                0.999569442913327,
                0.9999151889587602,
                0.9999832985801465,
                0.9999756997476821,
                0.9997965729298345,
                0.9999151889486094,
                0.9998415637833893,
                0.9994472212573725,
                0.9999038975965423,
                0.9999339478238556
            ],
            [
                0.999860177909463,
                0.9997040427602764,
                0.9999151889586856,
                0.9997965729303111,
                0.9992903295375776,
                0.9975273764591727,
                0.9999646437535161,
                0.9999038976194913,
                0.9998601778595368,
                0.9999339478474694
            ],
            [
                0.9999832985701931,
                0.9984988177329676,
                0.999512142770724,
                0.99995993630782,
                0.9998601778926955,
                0.9933071477909818,
                0.9998601779093165,
                0.9988304894689486,
                0.9999251537817111,
                0.9999417087275562
            ],
            [
                0.9999485577863596,
                0.9999810748585312,
                0.9992903296233139,
                0.9989677689684071,
                0.9999546021205518,
                0.9980732654235338,
                0.9999756997476862,
                0.9999339478553942,
                0.9997040429375756,
                0.9994472214599368
            ],
            [
                0.9998415637834701,
                0.9995121428250495,
                0.9998415637833618,
                0.9986749775493583,
                0.9978172840085039,
                0.9999485578047674,
                0.9999038975508887,
                0.9999251537728095,
                0.9994472214608694,
                0.9991959141538348
            ],
            [
                0.9993736658979271,
                0.9995121429387809,
                0.9978172834618566,
                0.9980732651750389,
                0.9984988175218247,
                0.9999038976080479,
                0.9964063980438504,
                0.9993736658382106,
                0.9982992775942966,
                0.9953904275642331
            ],
            [
                0.9999038975851828,
                0.9995121427663813,
                0.9998204720128943,
                0.9998766054252419,
                0.9998601778930413,
                0.9997040429728288,
                0.999664649773108,
                0.9995121427689927,
                0.9999546021367908,
                0.9999417087067125
            ],
            [
                7.889260704050487e-06,
                5.422221555133606e-06,
                2.144494328685209e-05,
                2.4300237824258528e-05,
                1.3007133111929193e-05,
                1.1478773598099973e-05,
                2.7535700932494338e-05,
                1.892515049199645e-05,
                4.222833947774596e-06,
                1.4738980210258757e-05
            ],
            [
                0.9991959141462119,
                0.9999151889283524,
                0.9996646497714592,
                0.9998911031298519,
                0.9998911030517746,
                0.9999151889485773,
                0.9997388095989572,
                0.9999724643056231,
                0.9996200154711754,
                0.9994472213229109
            ],
            [
                5.422221555192784e-06,
                1.6701425824307884e-05,
                8.93969630333567e-06,
                1.0129994601688632e-05,
                4.7850927830845245e-06,
                7.889260704423598e-06,
                2.7535697660090726e-05,
                8.939698434966738e-06,
                1.4738983724575818e-05,
                1.8925152752138513e-05
            ],
            [
                0.9980732656850131,
                0.9996200154721371,
                0.9992903295473606,
                0.9994472213894782,
                0.9998204719914313,
                0.9984988180105943,
                0.999373665976553,
                0.9997040430067387,
                0.9991959139630748,
                0.9999038975851403
            ],
            [
                5.144222589407736e-05,
                6.144176066353646e-06,
                2.430023493228869e-05,
                5.8291286335171815e-05,
                7.484625398547097e-05,
                8.481101097331865e-05,
                0.00010889694803204319,
                1.0129988563730593e-05,
                0.00020342697341447548,
                4.006370648788271e-05
            ],
            [
                0.9998204719524341,
                0.9999251537997914,
                0.999769493231292,
                0.9999251537371668,
                0.9999151889486094,
                0.9996646497714592,
                0.9999646437366602,
                0.9998204720134662,
                0.9998204720133931,
                0.9996646498928325
            ],
            [
                0.996827316846037,
                0.9997694932852572,
                0.9997694932576776,
                0.9995121428825537,
                0.9999417087067002,
                0.9997388097221476,
                0.999769493176247,
                0.9997388096919465,
                0.9999785550541495,
                0.9998415637841962
            ],
            [
                0.99995460211518,
                0.9998911031168733,
                0.9999038975393573,
                0.9998415637646436,
                0.9998204720129621,
                0.9995694428603443,
                0.9998766053958151,
                0.9998415637092224,
                0.9999417087275778,
                0.9992903295413339
            ],
            [
                0.9996646498927155,
                0.9998601778765628,
                0.9998204720126225,
                0.9997965731000796,
                0.9998204720984661,
                0.9999151889790666,
                0.9998911030518871,
                0.9999151889688017,
                0.9999687980923682,
                0.9998911030389086
            ],
            [
                0.9968273169837353,
                0.9991959141538348,
                0.9986749777112633,
                0.9999687980923503,
                0.999891103039281,
                0.9996646498110714,
                0.9999485577863757,
                0.9999417087066884,
                0.9978172838259501,
                0.9999151889586547
            ],
            [
                0.9998911030517628,
                0.9997694932035918,
                0.9996200155619243,
                0.9998911031037886,
                0.9999339478396271,
                0.9999810748495125,
                0.9997388095980908,
                0.9998601779092757,
                0.9999485578047876,
                0.9997965729305833
            ],
            [
                0.9984988174181727,
                0.9992903295398066,
                0.9980732656344187,
                0.9999417087344614,
                0.9953904275428671,
                0.9984988179191573,
                0.9988304894898911,
                0.9998415637078393,
                0.9998911030389624,
                0.9982992774828201
            ],
            [
                0.9989677691842451,
                0.9999646437324344,
                0.999290329627318,
                0.9999251537460211,
                0.9999251537638759,
                0.999290329713302,
                0.9999646437493142,
                0.9998204720127558,
                0.9990889488928075,
                0.9999251537816801
            ],
            [
                0.9999756997621677,
                0.9998911030389086,
                0.9994472213235218,
                0.9998415637078946,
                0.999738809754332,
                0.9999546021313821,
                0.9996200155166548,
                0.9999038976194206,
                0.9999151889182596,
                0.9998601779595151
            ],
            [
                0.9999038976196002,
                0.999903897608017,
                0.9998601778927565,
                0.9998204720988187,
                0.9998601778596466,
                0.9998911031038409,
                0.9999599363173987,
                0.9994472214633777,
                0.9999251537460276,
                0.9992903295440996
            ],
            [
                1.3007123812317831e-05,
                7.889260704732132e-06,
                3.535626334323525e-05,
                8.93969950101825e-06,
                5.144223201604811e-05,
                1.8925141471913163e-05,
                3.535625911829982e-05,
                2.1444948409679848e-05,
                8.481103114029641e-05,
                6.962257079376403e-06
            ],
            [
                0.9999151889182516,
                0.9989677690556786,
                0.9997965730752747,
                0.9995694429132268,
                0.9999251537460537,
                0.9998415638400577,
                0.9995694429623517,
                0.9988304894817316,
                0.9996200155172518,
                0.9999038975507474
            ],
            [
                0.9999151889689775,
                0.9999339478553833,
                0.9997388096606132,
                0.9999038976080269,
                0.999941708706721,
                0.9999339478711028,
                0.9998204720125233,
                0.9997388096910954,
                0.9998415638400854,
                0.9999646437535097
            ],
            [
                5.144221363703851e-05,
                6.144173869312763e-06,
                1.0129987356375273e-05,
                3.726638839806038e-06,
                6.962257079465052e-06,
                1.4738976698006875e-05,
                6.962259569313662e-06,
                1.892515049199645e-05,
                1.012998735687278e-05,
                1.4738985485166298e-05
            ],
            [
                0.9959298632146864,
                0.9999151889789345,
                0.9995121427660125,
                0.9998204720126564,
                0.9993736658973441,
                0.9995121429464726,
                0.9997965729299204,
                0.9998204719913973,
                0.9999599362887198,
                0.9996200154700147
            ],
            [
                4.0063711285810896e-05,
                3.535624227425594e-05,
                5.82912445982132e-05,
                1.012998977198894e-05,
                2.4300252313020203e-05,
                5.144220136428317e-05,
                2.7535704224732304e-05,
                3.5356246490314526e-05,
                4.785095065093186e-06,
                3.1201922520397544e-05
            ],
            [
                0.9991959138764168,
                0.9997694932582344,
                0.999860177942768,
                0.9996646500107031,
                0.9999151889587016,
                0.9999756997650636,
                0.9997965731001239,
                0.9998911030389752,
                0.9968273172075869,
                0.9980732651477269
            ],
            [
                0.9994472212569223,
                0.999796573027139,
                0.9997388095980149,
                0.9998415637271659,
                0.9997694931755025,
                0.9996646499723789,
                0.9997694931758446,
                0.9999151889385346,
                0.9999038975392831,
                0.9997965730999463
            ],
            [
                0.9999485577863896,
                0.999964643736673,
                0.9998911030910144,
                0.9999785550541467,
                0.9999339478238862,
                0.9994472212651226,
                0.9999810748540167,
                0.9999339478397121,
                0.9999785550464798,
                0.9999599363125938
            ],
            [
                0.9999485577618527,
                0.9999417087553242,
                0.9999724643089025,
                0.9992903294551022,
                0.99956944285943,
                0.9982992772808182,
                0.9997694932307689,
                0.9999417087414523,
                0.999738809754849,
                0.9998766053810425
            ],
            [
                0.9999852610180304,
                0.9999339478474747,
                0.999933947839665,
                0.999978555059262,
                0.9996646499327863,
                0.999933947855328,
                0.9999251537639657,
                0.9999687980737526,
                0.999941708748494,
                0.9999417087067083
            ],
            [
                0.9986749774116389,
                0.9996200154697935,
                0.9997694933408053,
                0.9998911030389229,
                0.9997965730028551,
                0.9996646499716764,
                0.999569443019067,
                0.9997388097848067,
                0.9996200155154941,
                0.9993736658221795
            ],
            [
                0.9999546021313719,
                0.9998415638022435,
                0.9978172836200699,
                0.9997694932307689,
                0.9993736659033557,
                0.9999251537370515,
                0.9998415637644547,
                0.9999251537371533,
                0.9998911030780644,
                0.9999339478317237
            ],
            [
                0.9997965730029882,
                0.9991959139663017,
                0.9999339478475102,
                0.9995694428620352,
                0.9999339478553573,
                0.999512142940796,
                0.9999339478238608,
                0.9999599363173769,
                0.9998911031298249,
                0.9998601778760724
            ],
            [
                0.99986017797601,
                0.9998766054692957,
                0.9999151889689214,
                0.9996646498944132,
                0.9997965730515561,
                0.9998204720556789,
                0.9995121428845974,
                0.9999339478317867,
                0.9997388097549249,
                0.9995121429421017
            ],
            [
                0.9998911030389894,
                0.9999151889890187,
                0.9997040430063856,
                0.9997965729544204,
                0.9999251537906921,
                0.9997388096923874,
                0.9998766053957325,
                0.9998766054402837,
                0.9999038975850983,
                0.9989677691889268
            ],
            [
                0.9998766054399821,
                0.9999599363125995,
                0.999941708741432,
                0.9999038975736242,
                0.9999810748472489,
                0.9999756997534794,
                0.9999485577986525,
                0.9999869928699852,
                0.9999417087345,
                0.9999151889384932
            ],
            [
                0.9999151889183009,
                0.9998415637646436,
                0.9996200155151292,
                0.999841563764616,
                0.9996646498942863,
                0.9999687980997889,
                0.9997694932582947,
                0.9998415637458196,
                0.9999646437577213,
                0.9992903296310743
            ],
            [
                0.9999339478475554,
                0.9991959141512626,
                0.999569443013919,
                0.9999251537818069,
                0.9999151889283524,
                0.999738809566689,
                0.9997694932027467,
                0.9968273170124531,
                0.9997965729784852,
                0.9991959142553177
            ],
            [
                0.999903897596573,
                0.9999646437577374,
                0.9999810748449939,
                0.9999646437450961,
                0.9997694933678146,
                0.9997694933674324,
                0.9999546021476212,
                0.9999151889485612,
                0.999933947863225,
                0.9998415637834978
            ],
            [
                0.9999546021097396,
                0.9988304897465036,
                0.9998415637278391,
                0.9998204720126904,
                0.9996200155651633,
                0.999769493312555,
                0.9995121428823267,
                0.99982047196977,
                0.9902915215217967,
                0.9994472214568174
            ],
            [
                0.9997040427608189,
                0.9998911030518871,
                0.9997388096292115,
                0.9991959142511087,
                0.9997965729789262,
                0.9998204720129281,
                0.999664650012918,
                0.9997040429721915,
                0.9986749778808707,
                0.9997388096913081
            ],
            [
                0.9991959139813138,
                0.999569442911348,
                0.9999417087484003,
                0.999841563821342,
                0.9999251537995338,
                0.9996200155659482,
                0.9996646498918861,
                0.9999251537549356,
                0.999738809691027,
                0.9998766054399156
            ],
            [
                0.9999599363126209,
                0.9999546021259655,
                0.9978172835642896,
                0.999704042831153,
                0.9998415638213696,
                0.9999485577925007,
                0.9998601778596466,
                0.9998415638213143,
                0.999972464308929,
                0.9999251537728716
            ],
            [
                0.9998415637644292,
                0.999903897573676,
                0.9999339478396017,
                0.9997965729304916,
                0.9998766054550456,
                0.9997388097230672,
                0.9999724642957784,
                0.9998415637838066,
                0.9996646498594939,
                0.9999485577986458
            ],
            [
                0.9998766054695308,
                0.9999151889586856,
                0.9999151889486261,
                0.9998911031039089,
                0.9998204719697047,
                0.9980732657454577,
                0.99986017797601,
                0.999796573099902,
                0.9993736659775366,
                0.999620015425917
            ],
            [
                0.9998911030649195,
                0.9997965730027693,
                0.9984988179257882,
                0.9999687980923503,
                0.9999038976082164,
                0.9996200154284596,
                0.9959298629919506,
                0.9995694428600688,
                0.9998204719920347,
                0.9998601779594521
            ],
            [
                0.9997388097219424,
                0.9998204719914993,
                0.9999485577740962,
                0.999447221256472,
                0.9995121428872653,
                0.9998204719485422,
                0.9999251537638956,
                0.9998415637644016,
                0.9999151889789512,
                0.99994170874144
            ],
            [
                0.999959936312614,
                0.9997040429721055,
                0.9999485577618361,
                0.9978172833822428,
                0.9999151889385265,
                0.9998766054548085,
                0.9984988179268351,
                0.9999339478317593,
                0.9998601779594724,
                0.9999756997476854
            ],
            [
                0.9997694931767165,
                0.9997694932303262,
                0.9998415637079753,
                0.9995694429709817,
                0.9990889489812341,
                0.9995694430147581,
                0.9998415638401937,
                0.9984988180920851,
                0.9982992774021775,
                0.9991959141716995
            ],
            [
                0.9995694428617596,
                0.9998911030649195,
                0.9999687980886387,
                0.9995121429390079,
                0.9999038975393788,
                0.9995694429168968,
                0.9997694933128837,
                0.9999417087344762,
                0.9995694430163614,
                0.999959936288716
            ],
            [
                0.9997388097846623,
                0.9997694932576776,
                0.9998204720997304,
                0.9998766054547045,
                0.999948557786366,
                0.9998204720129621,
                0.9998415637080029,
                0.9997388095673958,
                0.9968273167149659,
                0.9997694932298903
            ],
            [
                0.9998766054398833,
                0.9998601778929518,
                0.9998766053957971,
                0.9998911030910429,
                0.9999151889385265,
                0.9990889489360406,
                0.9990889488780785,
                0.9999724643023473,
                0.9998911031168067,
                0.9999151889286035
            ],
            [
                0.9975273765602456,
                0.9971990732188691,
                0.999195914061331,
                0.9579122713334306,
                0.9997040430111733,
                0.9993736658410526,
                0.9982992777453038,
                0.9978172839400462,
                0.9978172840556636,
                0.9996200155641684
            ],
            [
                0.9999339478239027,
                0.9997388097571895,
                0.9986749775348778,
                0.9998911030909432,
                0.9999687980811962,
                0.9998415637644823,
                0.9999546021476081,
                0.9997965730518255,
                0.9988304899064275,
                0.999512142828938
            ],
            [
                0.99986017797601,
                0.9999546021368017,
                0.9994472213271879,
                0.9998415637454691,
                0.9997388096607576,
                0.9993736659855158,
                0.9999038976194807,
                0.9996200155676838,
                0.9990889486797145,
                0.9999546021097453
            ],
            [
                0.9959298623331813,
                0.9996200155610399,
                0.9999417087275438,
                0.9991959139640569,
                0.9999485577802343,
                0.999664649970408,
                0.9997965729793851,
                0.9986749773996231,
                0.9997965730513785,
                0.9991959139620928
            ],
            [
                0.9998766054400324,
                0.9993736659752047,
                0.9999038975393901,
                0.9999038975965836,
                0.9999687980849095,
                0.999933947823881,
                0.9996646500118544,
                0.999915188958804,
                0.999941708755344,
                0.998299277748071
            ],
            [
                0.999796573051423,
                0.9995121428296759,
                0.9997694933681567,
                0.999891103116832,
                0.9998766054694268,
                0.9988304897611905,
                0.999841563840362,
                0.9990889487943672,
                0.9986749772706844,
                0.9998601778762006
            ]
        ]
    },
    {
        "q_id": "7930_mmlu_math",
        "cot_ids": [
            0,
            1,
            3,
            4,
            5,
            6,
            9,
            10,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            30,
            31,
            32,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            49,
            50,
            55,
            56,
            57,
            58,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            72,
            73,
            75,
            76,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            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": [
            [
                0.9999251537906645,
                0.9993736658285919,
                0.999860177942705,
                0.9999546021097218,
                0.99539042744031,
                0.9995694429643182,
                0.9992903296321063,
                0.9999599363078162,
                0.9997388096912398,
                0.9999687980774782
            ],
            [
                1.553497384196656e-06,
                1.7603438428564603e-06,
                3.288750633569722e-06,
                6.9622587393661365e-06,
                1.0677027427471959e-06,
                1.553497384196656e-06,
                7.889266347248781e-06,
                2.260323489490968e-06,
                3.726640172537657e-06,
                1.7603427936183298e-06
            ],
            [
                7.889262585541864e-06,
                2.753569109254574e-05,
                1.6701423833436905e-05,
                1.3007131565140219e-05,
                1.3007130014873483e-05,
                1.4738981971250963e-05,
                8.93969950101825e-06,
                1.6701425824733193e-05,
                3.53562675670136e-05,
                8.939698435340743e-06
            ],
            [
                2.9023109471689794e-06,
                1.9947297214944016e-06,
                2.9023109472244114e-06,
                3.2887486732358968e-06,
                4.222834954607099e-06,
                1.9947301970813926e-06,
                4.222834954687752e-06,
                5.422217676979575e-06,
                3.2887486733420804e-06,
                3.288750633545794e-06
            ],
            [
                0.9971990732624402,
                0.9999852610162787,
                0.9999038975621809,
                0.9999646437408874,
                0.9953904279402757,
                0.9999885212277827,
                0.9933071478436095,
                0.9999339478395871,
                0.999993037742921,
                0.9999869928653425
            ],
            [
                7.8892625849535e-06,
                4.006370171458602e-05,
                8.481102105680693e-05,
                6.962257909121104e-06,
                1.473898899664279e-05,
                2.144495863614743e-05,
                1.6701417851043295e-05,
                8.939699500636112e-06,
                5.8291265491498626e-05,
                5.829127939986156e-05
            ],
            [
                2.2603251062270446e-06,
                5.422219615967477e-06,
                1.5534971989992774e-06,
                1.99472900813862e-06,
                7.338207180864763e-07,
                3.726639284050988e-06,
                4.222834451169694e-06,
                2.2603251062270446e-06,
                6.144172404028807e-06,
                2.5612816000145246e-06
            ],
            [
                0.9999810748472494,
                0.9999785550413659,
                0.99998329858413,
                0.9998911030388706,
                0.9997965729300476,
                0.9999038975507474,
                0.9999599362934916,
                0.9999687980923515,
                0.9999898700078131,
                0.9999869928746369
            ],
            [
                0.9992903295390635,
                0.9988304896330883,
                0.9992903297047985,
                0.9994472213216888,
                0.9996200154234739,
                0.999373665975387,
                0.9997040427958999,
                0.9993736657565971,
                0.9998204719486441,
                0.9324533097989076
            ],
            [
                0.9998415638398226,
                0.9986749775102299,
                0.9399133458285746,
                0.9989677687935037,
                0.9984988175965099,
                0.9997965730272278,
                0.9999910603026327,
                0.999841563839848,
                0.9996200155144881,
                0.9980732655699442
            ],
            [
                0.9997040429721055,
                0.9998601779593687,
                0.9994472213991579,
                0.9999687980886264,
                0.9706877660687704,
                0.8933094017937621,
                0.9999251537460085,
                0.9999546021097193,
                0.9796676447280406,
                0.9999417087344838
            ],
            [
                7.889262584350785e-06,
                1.553498310118888e-06,
                4.785095065045315e-06,
                9.422443692261927e-07,
                2.2603237589028734e-06,
                2.260324567268294e-06,
                2.5612828212909852e-06,
                2.9023123311055552e-06,
                6.962253759752719e-06,
                1.4738985484549675e-05
            ],
            [
                0.9999952149066466,
                0.9999990577549569,
                0.9999980052700408,
                0.9999921107392962,
                0.9999982396574163,
                0.9999967112513267,
                0.9999952149072169,
                0.9999984465022455,
                0.9999852610180298,
                0.999991060304762
            ],
            [
                1.6701427816728442e-05,
                2.9023119851266288e-06,
                7.889264466115267e-06,
                4.222831934248571e-06,
                7.889263525778283e-06,
                2.7535700939406174e-05,
                1.1478769493331685e-05,
                3.726640172290235e-06,
                5.422218969661113e-06,
                1.7603425837702984e-06
            ],
            [
                0.9999930377429207,
                0.9999921107402382,
                0.9999898700090211,
                0.9999984465016899,
                0.9999898700041914,
                0.9999921107345934,
                0.9999930377420911,
                0.9999910603015656,
                0.9999910603058283,
                0.999997438717484
            ],
            [
                1.3709573702778664e-06,
                6.1441746017453204e-06,
                6.475951069961737e-07,
                4.222832941072913e-06,
                1.3709568799760888e-06,
                6.962254589332388e-06,
                2.9023133690425823e-06,
                6.475948753991907e-07,
                3.288748673319648e-06,
                1.7603434231241496e-06
            ],
            [
                5.144221967142812e-05,
                3.120191879561992e-05,
                4.539788481998745e-05,
                6.605214426644143e-05,
                3.120190018853766e-05,
                1.670142379734641e-05,
                3.120191507776674e-05,
                1.8925157255280296e-05,
                5.8291244514241416e-05,
                0.0001584362908790921
            ],
            [
                0.9997694932024783,
                0.9998911030647897,
                0.9999756997477088,
                0.9964063965665445,
                0.9998415637265896,
                0.9999417087136322,
                0.998674977386683,
                0.9999038976079374,
                0.9991959141496725,
                0.9996646499298982
            ],
            [
                3.726641061109272e-06,
                2.260324836776948e-06,
                1.7603430034743913e-06,
                1.99472900813862e-06,
                2.2603234895289998e-06,
                3.2887482811908074e-06,
                2.9023112931873767e-06,
                6.144176799283803e-06,
                4.7850939242083995e-06,
                8.315278294097538e-07
            ],
            [
                3.288747889229516e-06,
                6.962257079275089e-06,
                3.7266388397721442e-06,
                7.889261645090304e-06,
                1.553497754577351e-06,
                8.315282259089153e-07,
                3.2887494573232236e-06,
                7.889261644875049e-06,
                1.99472924590571e-06,
                1.3709576971379186e-06
            ],
            [
                0.9796676453587736,
                0.9999756997621669,
                0.9999910603004992,
                0.9890130594035196,
                0.9999810748562856,
                0.9998911030907593,
                0.9999832985761674,
                0.9525741264858408,
                0.9999885212332431,
                0.7981867705385762
            ],
            [
                2.9023112931688987e-06,
                5.4222202624563834e-06,
                6.962259569484628e-06,
                5.422218969720291e-06,
                2.43002378338943e-05,
                5.422220262555012e-06,
                9.422443692555439e-07,
                6.962254589528684e-06,
                2.144494841326852e-05,
                1.0129992187253088e-05
            ],
            [
                6.1441746016670885e-06,
                2.2603248367512505e-06,
                4.785095635413826e-06,
                3.288747889178668e-06,
                3.535626335262457e-05,
                3.120190393260949e-05,
                6.962259569560613e-06,
                6.605215253545261e-05,
                1.4738985483879434e-05,
                1.473898197154587e-05
            ],
            [
                2.2603248367656408e-06,
                1.0129994601301684e-05,
                3.2887478891128633e-06,
                7.88926258532661e-06,
                6.962254589617333e-06,
                2.9023119851055122e-06,
                1.5534983101478522e-06,
                5.422218969661113e-06,
                5.422218323349895e-06,
                6.14417313680765e-06
            ],
            [
                0.9999970976887069,
                0.999992110733653,
                0.999996273358939,
                0.9999970976866309,
                0.9999974387171787,
                0.9999938558253986,
                0.9999952149032239,
                0.9999962733598275,
                0.9999974387187053,
                0.9999982396572065
            ],
            [
                0.9999977396748938,
                0.9999989322972572,
                0.999995777167059,
                0.9999984465020603,
                0.999997097688361,
                0.9999970976880149,
                0.999999266178757,
                0.9999984465020603,
                0.9999984465018751,
                0.9999970976873229
            ],
            [
                9.422448185388577e-07,
                1.3709576971242028e-06,
                6.962257079059797e-06,
                7.889261642794245e-06,
                8.939699500766203e-06,
                6.144177530794679e-06,
                2.561283431986506e-06,
                4.78509506499309e-06,
                3.726638395215427e-06,
                6.144177531459659e-06
            ],
            [
                1.473898021366358e-05,
                6.962257078819179e-06,
                1.473898196763166e-05,
                1.4738988998787566e-05,
                1.670142183983204e-05,
                2.7535684524701807e-05,
                3.7266383955611403e-06,
                1.473898899908247e-05,
                2.4300240723831244e-05,
                1.8925145970336176e-05
            ],
            [
                1.5534975693869924e-06,
                6.144173137014406e-06,
                1.2098652508347793e-06,
                9.422443692446175e-07,
                1.0129992187105678e-05,
                2.5612812947077304e-06,
                9.422447062150634e-07,
                2.2603248367656408e-06,
                4.785094494628999e-06,
                1.3709567165530083e-06
            ],
            [
                1.892514597632595e-05,
                2.144495096161541e-05,
                1.147876401423365e-05,
                6.144175333926503e-06,
                1.9947304344830644e-06,
                1.670141785420273e-05,
                3.288749065209246e-06,
                1.0129990978644356e-05,
                2.9023112927307205e-06,
                6.962258738283349e-06
            ],
            [
                6.1441753337365085e-06,
                4.78509563550957e-06,
                3.7266379512518984e-06,
                4.222832941072913e-06,
                4.785095635296322e-06,
                4.222832941111319e-06,
                4.785096776394765e-06,
                1.0129993394314164e-05,
                2.5612812947380135e-06,
                8.939693106329072e-06
            ],
            [
                1.2098655392921197e-06,
                4.222832437677995e-06,
                1.7603430034655858e-06,
                2.561283432005142e-06,
                8.315277302747361e-07,
                2.260324028404236e-06,
                1.5534977545384963e-06,
                9.422445938964242e-07,
                9.422444815765128e-07,
                1.0677028700320085e-06
            ],
            [
                4.7850950647493785e-06,
                3.726638395527247e-06,
                4.785096205882502e-06,
                1.2098653950606901e-06,
                1.7603436329394601e-06,
                4.7850944945245504e-06,
                4.785096205778054e-06,
                1.99472924590571e-06,
                3.7266388397382506e-06,
                2.5612834319655406e-06
            ],
            [
                5.422218969769604e-06,
                1.2098652508347793e-06,
                1.5534973841895917e-06,
                1.0677028700363782e-06,
                3.288749457432399e-06,
                7.889263525778283e-06,
                7.338211554758494e-07,
                1.3709575337016483e-06,
                7.889264466344872e-06,
                5.422217030663578e-06
            ],
            [
                0.9999485577802613,
                0.9999251537906257,
                0.999975699765066,
                0.9999151889485693,
                0.9999485577741026,
                0.9992903297263461,
                0.9999852610215436,
                0.9999885212318748,
                0.9996200155158589,
                0.9986749773252177
            ],
            [
                4.222831934156396e-06,
                1.994730196992497e-06,
                2.2603248366762157e-06,
                5.4222202624563834e-06,
                4.222833443968609e-06,
                1.147876675548402e-05,
                6.962257079173776e-06,
                6.144176066795103e-06,
                5.422218322940583e-06,
                3.288749849368453e-06
            ],
            [
                5.422217030614265e-06,
                2.902310947208574e-06,
                1.5534971989568904e-06,
                6.9622595694023114e-06,
                4.785093353787868e-06,
                4.222834954607099e-06,
                1.012999580884213e-05,
                6.962254589617333e-06,
                2.260325375634003e-06,
                4.222835457852533e-06
            ],
            [
                1.0129993394959082e-05,
                7.88925976397226e-06,
                9.610242635548565e-05,
                6.144172404520556e-06,
                3.5356242267696286e-05,
                3.120192624733229e-05,
                1.3007125363057018e-05,
                2.4300252313904224e-05,
                1.30071253611406e-05,
                2.7535700942411318e-05
            ],
            [
                0.9999994284993485,
                0.9999989322968754,
                0.9999952149066464,
                0.9999989322966208,
                0.9999977396754328,
                0.9999945777790918,
                0.999997097686977,
                0.9999930377420909,
                0.9999986290424664,
                0.999995777165549
            ],
            [
                6.14417313680765e-06,
                1.4738981971250963e-05,
                0.0003799844833451715,
                4.222833947820683e-06,
                6.962259569117366e-06,
                8.939693106329072e-06,
                1.0129993392342568e-05,
                2.9023116391477434e-06,
                7.889261644875049e-06,
                3.7266410609940346e-06
            ],
            [
                5.422218323349895e-06,
                2.56128282131428e-06,
                7.88926540679677e-06,
                1.3007133113017532e-05,
                1.3709572068422585e-06,
                4.785094494019719e-06,
                1.9947306725669014e-06,
                3.7266397282926013e-06,
                2.561283432035425e-06,
                1.994729483680993e-06
            ],
            [
                0.9999990577552937,
                0.9999990577550691,
                0.9999967112505427,
                0.999998446502801,
                0.999997097686977,
                0.9999952149066464,
                0.9999910603015654,
                0.999996273358939,
                0.9999980052705164,
                0.9999994956526519
            ],
            [
                4.222831934321543e-06,
                1.760343423160973e-06,
                1.370957860567974e-06,
                1.7603434231777837e-06,
                8.939693107093343e-06,
                8.315278294097538e-07,
                1.5534975693933505e-06,
                1.760343213322473e-06,
                4.222834954687752e-06,
                1.2098653950656417e-06
            ],
            [
                0.9999986290427932,
                0.9999970976873229,
                0.9999910603047624,
                0.99999893229713,
                0.9999938558261309,
                0.9999962733607161,
                0.999997097686631,
                0.9999970976880149,
                0.9999869928761935,
                0.9999869928699867
            ],
            [
                1.5534979397677313e-06,
                2.4300232031037035e-05,
                2.5612831266946347e-06,
                1.3007130014636887e-05,
                1.55349775456958e-06,
                1.7603427936079236e-06,
                8.939698435340743e-06,
                5.422218969720291e-06,
                2.260324297853209e-06,
                2.144495863614743e-05
            ],
            [
                0.9984988178992644,
                0.9978172830577026,
                0.9996200155163675,
                0.9996200154238939,
                0.9998766054545734,
                0.9997040428296547,
                0.9996200154705231,
                0.9994472212549605,
                0.9997388097839707,
                0.9997040429709516
            ],
            [
                4.2228324375973415e-06,
                4.785094494185095e-06,
                3.288748281295496e-06,
                2.9023119851266288e-06,
                5.82912653227068e-05,
                2.561282210618905e-06,
                3.726639284017094e-06,
                1.0129987355122296e-05,
                1.0129988563730593e-05,
                4.222833947774596e-06
            ],
            [
                8.315283250343497e-07,
                2.2603234895053587e-06,
                1.1478766757561534e-05,
                4.222834954687752e-06,
                1.994729245917502e-06,
                7.889266347356409e-06,
                2.260324028372372e-06,
                5.4222176771176554e-06,
                1.99472900813862e-06,
                9.422444815765128e-07
            ],
            [
                4.785093924103951e-06,
                6.1441746016670885e-06,
                2.260324297853209e-06,
                2.9023112931873767e-06,
                1.994729483705484e-06,
                4.222831934156396e-06,
                1.9947306726213275e-06,
                2.902311293147782e-06,
                1.1478773598329648e-05,
                7.889259763010786e-06
            ],
            [
                2.902311639073834e-06,
                5.422218323290717e-06,
                6.962257909121104e-06,
                1.9947297215043796e-06,
                2.260324028427877e-06,
                6.144175333926503e-06,
                8.93969417199781e-06,
                7.889266347133978e-06,
                2.260324836776948e-06,
                6.962258739068529e-06
            ],
            [
                6.962254589781966e-06,
                2.1444948410928083e-05,
                7.889262585541864e-06,
                1.3007133114886634e-05,
                8.939698434332555e-06,
                1.1478770861650256e-05,
                7.889262585642319e-06,
                1.4738976698757546e-05,
                3.726639728262097e-06,
                6.144177531381426e-06
            ],
            [
                1.553498495295912e-06,
                2.902312677060767e-06,
                6.144173869240119e-06,
                6.144176798870286e-06,
                2.5612812947077304e-06,
                6.144176799166453e-06,
                1.0677029973056687e-06,
                2.260324028404236e-06,
                1.994729483680993e-06,
                1.0129988564099116e-05
            ],
            [
                0.9999938558275954,
                0.9999930377429206,
                0.9999898700041906,
                0.9999938558232009,
                0.9999974387171787,
                0.9999938558239336,
                0.9999962733602717,
                0.9999974387184,
                0.9999869928699859,
                0.999983298578157
            ],
            [
                1.5534979397740895e-06,
                3.726640616670918e-06,
                6.1441731370702875e-06,
                1.553497754583709e-06,
                2.2603234895176927e-06,
                1.7603434231705793e-06,
                3.2887486733420804e-06,
                9.422443692555439e-07,
                1.4738985485461206e-05,
                6.962255419279419e-06
            ],
            [
                2.5612819054028872e-06,
                5.4222176771176554e-06,
                5.422217030495909e-06,
                2.5612825160271407e-06,
                6.14417753171671e-06,
                1.3709570434122812e-06,
                1.7603432133136672e-06,
                8.939694172770212e-06,
                6.962259569313662e-06,
                1.2098653950656417e-06
            ],
            [
                1.8925155007633607e-05,
                2.2603248367512505e-06,
                8.939700566801578e-06,
                5.422219615829396e-06,
                9.610239185355072e-05,
                2.753568453552033e-05,
                2.144495608046625e-05,
                1.7603427936263351e-06,
                6.962256249758443e-06,
                3.288749849477628e-06
            ],
            [
                4.5397879417962496e-05,
                3.12019076377484e-05,
                7.88926258381982e-06,
                1.8925143724239906e-05,
                2.1444956070012293e-05,
                4.0063706494441236e-05,
                2.4300237828059798e-05,
                8.939698434820389e-06,
                1.1478772229300848e-05,
                1.6701419845680582e-05
            ],
            [
                1.3007126912258525e-05,
                4.222831934286977e-06,
                6.962256249429175e-06,
                1.7603432132624344e-06,
                2.753570422573402e-05,
                6.962255419728997e-06,
                1.1478769493540482e-05,
                1.4738985484549675e-05,
                4.222831934286977e-06,
                1.4738988999672284e-05
            ],
            [
                1.4738978456719842e-05,
                2.1444950965282096e-05,
                5.422220908876325e-06,
                4.7850967763512445e-06,
                1.5534983101478522e-06,
                2.260325375677174e-06,
                4.222833444467892e-06,
                2.561283432005142e-06,
                4.7850944943330625e-06,
                3.2887490653872164e-06
            ],
            [
                2.902310947208574e-06,
                1.7603434231705793e-06,
                2.902310947190096e-06,
                4.785092783319532e-06,
                8.31528424162821e-07,
                1.7603434231705793e-06,
                6.144177531599359e-06,
                5.422221555340727e-06,
                2.561282516042282e-06,
                1.2098655392811161e-06
            ],
            [
                1.0129989772412744e-05,
                1.1478770861650256e-05,
                1.0129989772412744e-05,
                7.484624506431508e-05,
                4.222834954753043e-06,
                4.785096206013061e-06,
                7.889261645090304e-06,
                1.012998977213635e-05,
                1.8925157263094544e-05,
                6.962257079629686e-06
            ],
            [
                0.9999982396572065,
                0.999997438717484,
                0.9999967112497586,
                0.9999921107392964,
                0.9999885212264044,
                0.9999957771675625,
                0.9999945777810307,
                0.9999967112493665,
                0.9999967112501505,
                0.9999970976883609
            ],
            [
                3.2887502415243994e-06,
                3.2887498493983645e-06,
                1.3709576971379186e-06,
                1.1478765387667046e-05,
                7.889262585441413e-06,
                4.222834451254188e-06,
                7.88925976418034e-06,
                4.222832437639588e-06,
                8.939699500327152e-06,
                6.9622579092224155e-06
            ],
            [
                7.484623610449812e-05,
                2.7535687798506256e-05,
                7.889266347004826e-06,
                6.605214460571739e-05,
                8.481107163160885e-05,
                5.144222587049821e-05,
                8.939695237341456e-06,
                2.4300252313904224e-05,
                0.0011695103750711763,
                3.12019076377484e-05
            ],
            [
                2.43002523073625e-05,
                8.93969310662177e-06,
                2.430023783309869e-05,
                1.3007130012980722e-05,
                6.144174601935314e-06,
                2.4300252315495453e-05,
                8.939695237666677e-06,
                3.535623804983752e-05,
                4.006367784548767e-05,
                4.0063711272110856e-05
            ],
            [
                0.9971990727766549,
                0.9999910603047618,
                0.9820137879323497,
                0.9996200155156378,
                0.9991959142434857,
                0.9998911030387961,
                0.9999869928699883,
                0.9999724643121909,
                0.9999151889890939,
                0.999841563745628
            ],
            [
                0.9998766054545734,
                0.9997040428297409,
                0.9999852610145146,
                0.9999810748472484,
                0.9914225147367658,
                0.9997040427950044,
                0.9991959142482559,
                0.9998911030907467,
                0.9999599362982616,
                0.9996200155614821
            ],
            [
                3.535623804983752e-05,
                4.006370172507966e-05,
                1.4738988997768797e-05,
                5.144221363067589e-05,
                4.0063692174115624e-05,
                0.012431650567337199,
                4.006369694959736e-05,
                1.6701415868193372e-05,
                1.67014178590634e-05,
                5.1442195232584995e-05
            ],
            [
                1.1478770861650256e-05,
                1.7603430034655858e-06,
                3.726639284103523e-06,
                2.902311639183378e-06,
                3.288749065406658e-06,
                6.144173869446876e-06,
                3.1201903929204235e-05,
                3.726639728348526e-06,
                1.6701425823882575e-05,
                4.222834954753043e-06
            ],
            [
                3.72664061671159e-06,
                4.785096205830278e-06,
                1.76034363298589e-06,
                6.962255419380732e-06,
                6.9622537593854575e-06,
                4.785093353787868e-06,
                7.889262585441413e-06,
                1.4738976700929127e-05,
                4.222833444168322e-06,
                3.726637951126493e-06
            ],
            [
                0.9999962733620488,
                0.9999970976883609,
                0.9999938558268634,
                0.9999974387165681,
                0.9999962733607166,
                0.9999967112513267,
                0.999997097686631,
                0.9999977396748938,
                0.9999980052693274,
                0.9999986290429566
            ],
            [
                6.144173869446876e-06,
                3.2887490653872164e-06,
                3.2887482812745586e-06,
                6.144172404129392e-06,
                6.144174601410037e-06,
                2.260325375664839e-06,
                7.889264466230069e-06,
                6.962256249606473e-06,
                6.1441746016670885e-06,
                3.288749065406658e-06
            ],
            [
                4.2228334445370225e-06,
                3.288750241500471e-06,
                8.93969736955767e-06,
                5.422220262505697e-06,
                1.9947299592933255e-06,
                1.670141586949968e-05,
                6.962255419653012e-06,
                7.889264466545779e-06,
                3.288749849477628e-06,
                1.6701415868649062e-05
            ],
            [
                0.9999977396748939,
                0.9999970976890529,
                0.9999930377429213,
                0.9999974387180947,
                0.9999962733611605,
                0.9999974387184001,
                0.9999991684717742,
                0.9999974387184,
                0.9999974387184,
                0.9999974387168734
            ],
            [
                3.726641060956752e-06,
                1.0129993393742954e-05,
                1.5534979397592542e-06,
                6.144177531599359e-06,
                5.422220262333096e-06,
                6.144175334015912e-06,
                2.5612812946681295e-06,
                1.147876402018431e-05,
                2.902312331125353e-06,
                2.561283126639892e-06
            ],
            [
                1.9947290081177566e-06,
                2.7535687813231466e-05,
                3.2887490653872164e-06,
                5.42222090882208e-06,
                2.2603242978377903e-06,
                1.994729245917502e-06,
                5.422217677078203e-06,
                2.561281600049467e-06,
                2.5612834320214477e-06,
                3.726638839806038e-06
            ],
            [
                1.5534971989992774e-06,
                4.785094494463623e-06,
                4.785093353687772e-06,
                9.422449308566668e-07,
                4.222831934286977e-06,
                9.422449308716635e-07,
                1.0677033791437343e-06,
                2.902313368897403e-06,
                2.5612816000331606e-06,
                1.7603430034655858e-06
            ],
            [
                0.9999038975392132,
                0.9997040429355176,
                0.6513548646660542,
                0.957912268029248,
                0.6791787056691698,
                0.994779873856671,
                0.43782349911420193,
                0.9998415638208902,
                0.9975273772005666,
                0.9820137881297458
            ],
            [
                0.9999980052700407,
                0.9999957771680659,
                0.999997097686977,
                0.9999962733593833,
                0.9999938558268633,
                0.9999986290424663,
                0.999997097686631,
                0.999997438717484,
                0.999996711251719,
                0.9999987901337396
            ],
            [
                2.4300246523773334e-05,
                1.4738985485461206e-05,
                1.1478768124992398e-05,
                2.144495863614743e-05,
                2.144495096723246e-05,
                6.962253759752719e-06,
                5.422218323399208e-06,
                3.726639728348526e-06,
                1.0129994602656007e-05,
                1.8925157262061825e-05
            ],
            [
                6.144175334094145e-06,
                2.5612815999679353e-06,
                2.90231163910023e-06,
                2.753569765908901e-05,
                6.144176799099397e-06,
                5.422217676797111e-06,
                3.7266401725681614e-06,
                3.2887494572873306e-06,
                6.962255419570695e-06,
                3.120190392795564e-05
            ],
            [
                0.9999967112497589,
                0.9999967112501509,
                0.9999982396574163,
                0.9999938558224687,
                0.9999991684720715,
                0.9999982396572065,
                0.999997097686631,
                0.999997097687669,
                0.9999986290429567,
                0.9999945777803845
            ],
            [
                2.2603253755476615e-06,
                5.043474683050556e-07,
                6.144173869240119e-06,
                1.0129993394811673e-05,
                3.726640172503764e-06,
                1.2098656834834034e-06,
                4.222834451065997e-06,
                2.902311293147782e-06,
                5.42221767672807e-06,
                2.5612831266165976e-06
            ],
            [
                2.5612822107167428e-06,
                1.0677024881980089e-06,
                1.0677033791437343e-06,
                6.144173869312763e-06,
                8.939693106873817e-06,
                4.006369214729855e-05,
                2.1444943300075563e-05,
                4.222832941142044e-06,
                1.9947297214944016e-06,
                1.3709576971316842e-06
            ],
            [
                3.726638839833152e-06,
                6.962255419804982e-06,
                6.144177531599359e-06,
                1.3709576971379186e-06,
                1.670141587068447e-05,
                1.6701423833436905e-05,
                3.726639284050988e-06,
                2.260324028372372e-06,
                2.902311639126627e-06,
                7.338208930421943e-07
            ],
            [
                0.9933071477569287,
                0.9999910603036978,
                0.999512142827093,
                0.9902915242437952,
                0.9998766053957648,
                0.9999832985761785,
                0.9997965730992656,
                0.9982992779840693,
                0.9579122759893239,
                0.9999546021475917
            ],
            [
                0.9999485577926372,
                0.9525741281688025,
                0.9997040429715629,
                0.9996646500174255,
                0.9914225162890632,
                0.9998601778595592,
                0.999903897607966,
                0.9669140220880034,
                0.6224593382055109,
                0.7772998611746912
            ],
            [
                4.2228349546493465e-06,
                2.4300246523773334e-05,
                0.000261190276788453,
                6.605213674902834e-05,
                2.1444953523537147e-05,
                1.300712536258383e-05,
                1.473898899908247e-05,
                1.1478766756653273e-05,
                5.1442195248304415e-05,
                2.4300252317086683e-05
            ],
            [
                4.4508505193932864e-07,
                2.5612831267086116e-06,
                5.422220262195015e-06,
                1.2098659719716573e-06,
                1.5534983101549167e-06,
                3.7266388397721442e-06,
                2.2603237589676295e-06,
                1.7603427936183298e-06,
                2.2603234895289998e-06,
                1.3709573702722555e-06
            ],
            [
                7.889259763469998e-06,
                1.4738981970956057e-05,
                1.7603440527046419e-06,
                3.7266406168624155e-06,
                3.2887494573561262e-06,
                4.222833444429485e-06,
                1.8925148238291944e-05,
                1.760343423160973e-06,
                1.3709568799760888e-06,
                8.939695238211425e-06
            ],
            [
                9.422447062240614e-07,
                2.9023116391477434e-06,
                1.3709570434122812e-06,
                2.902312677084523e-06,
                8.939699500636112e-06,
                6.962258739530771e-06,
                2.144495608046625e-05,
                4.785093924251918e-06,
                2.2603251062147097e-06,
                1.3007123811229494e-05
            ],
            [
                1.3007131565140219e-05,
                1.6701415871049018e-05,
                2.1444943300075563e-05,
                6.144177531532303e-06,
                0.00048785723574728873,
                6.962257909722651e-06,
                7.88925976397226e-06,
                0.00043055703773599877,
                2.4300234937946394e-05,
                2.260325106237323e-06
            ],
            [
                8.93969950101825e-06,
                4.78509563535725e-06,
                1.1478770861859053e-05,
                1.9947292459265734e-06,
                3.7266388396975786e-06,
                3.7266383955611403e-06,
                2.902311639126627e-06,
                1.3709568799823232e-06,
                3.7266379512518984e-06,
                8.939699500896292e-06
            ],
            [
                0.9999921107392962,
                0.9999980052705164,
                0.9999967112505427,
                0.9999977396746245,
                0.9999962733611603,
                0.9999987901343165,
                0.9999945777810305,
                0.9999938558224694,
                0.9999962733607162,
                0.9999987901344607
            ],
            [
                4.785096776394765e-06,
                3.288749065406658e-06,
                6.962257079705671e-06,
                1.553497754583709e-06,
                4.222832941142044e-06,
                7.889266347133978e-06,
                1.3709573702778664e-06,
                7.88926164518358e-06,
                4.785096205973894e-06,
                2.561281905390075e-06
            ],
            [
                1.147876675686207e-05,
                1.3007126911974612e-05,
                8.93969417214416e-06,
                4.5397868635383903e-05,
                7.484621820719341e-05,
                6.144172404380855e-06,
                8.939695237341456e-06,
                2.4300252316291068e-05,
                6.962255419380732e-06,
                1.1478765388711023e-05
            ],
            [
                0.9999974387187054,
                0.99999893229713,
                0.9999980052695653,
                0.9999967112509348,
                0.9999987901337396,
                0.9999977396765106,
                0.9999945777829696,
                0.9999987901337396,
                0.9999987901343165,
                0.9999980052705164
            ],
            [
                0.9999869928668843,
                0.999989870006605,
                0.999991060302631,
                0.9999646437535097,
                0.9999980052702785,
                0.9999339478632457,
                0.999992110736474,
                0.9999832985781566,
                0.9999970976866309,
                0.9999910603058276
            ],
            [
                0.9999485577740872,
                0.9998204719482784,
                0.9999251537995159,
                0.9999898700078128,
                0.9046505325302033,
                0.9999546021367807,
                0.9999151889485612,
                0.9999485577618268,
                0.9996200154707332,
                0.9999687980923457
            ],
            [
                2.5612812946681295e-06,
                3.726641061027928e-06,
                4.222833444467892e-06,
                2.2603237589028734e-06,
                2.9023112932045342e-06,
                4.222834451355964e-06,
                4.222833444467892e-06,
                7.889261644982674e-06,
                4.7850933538313875e-06,
                7.338209805224048e-07
            ],
            [
                0.9999977396762411,
                0.9999980052693274,
                0.9999952149072169,
                0.9999945777823234,
                0.9999982396561572,
                0.9999970976873229,
                0.9999962733620488,
                0.999997438716568,
                0.9999921107392957,
                0.9999970976880149
            ],
            [
                1.2098653950480359e-06,
                2.9023126769762986e-06,
                2.260325375520937e-06,
                3.288748673319648e-06,
                1.3709567165386693e-06,
                1.3709573702566696e-06,
                2.561283431916622e-06,
                1.2098653950656417e-06,
                1.2098656835076114e-06,
                2.9023133690637e-06
            ],
            [
                3.288750633545794e-06,
                2.2603248367512505e-06,
                3.726638395415398e-06,
                6.475949526020042e-07,
                3.2887498494551953e-06,
                6.475947982002148e-07,
                1.7603430034743913e-06,
                6.962257079705671e-06,
                1.2098659719716573e-06,
                2.260324297853209e-06
            ],
            [
                8.939699501132077e-06,
                1.2098661161982042e-06,
                1.0129988564264954e-05,
                7.338207180884785e-07,
                1.370957860567974e-06,
                1.5534973842030142e-06,
                1.9947304348703948e-06,
                5.4222170304318e-06,
                9.422447062240614e-07,
                5.422219616184461e-06
            ],
            [
                1.0129990978441666e-05,
                3.726638839806038e-06,
                1.4738985482753428e-05,
                6.144172403715875e-06,
                6.962258738701267e-06,
                7.889264465986113e-06,
                6.144173869072478e-06,
                5.4222170304318e-06,
                9.610243785962923e-05,
                8.939698434657777e-06
            ],
            [
                1.473897670007122e-05,
                2.902311639126627e-06,
                2.7535704228438656e-05,
                6.962256249758443e-06,
                1.3007128463873485e-05,
                4.222831934248571e-06,
                1.8925150495232307e-05,
                1.99472900813862e-06,
                4.785095635592258e-06,
                9.422447062240614e-07
            ]
        ]
    },
    {
        "q_id": "8022_mmlu_math",
        "cot_ids": [
            1,
            2,
            3,
            4,
            6,
            7,
            8,
            9,
            10,
            12,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            54,
            55,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            66,
            67,
            68,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            104,
            105,
            106,
            109,
            110,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999938558232012,
                0.9999852610233015,
                0.9999938558232011,
                0.9999756997537192,
                0.9999869928668851,
                0.9999970976883609,
                0.9999993524053562,
                0.999994577781681,
                0.9999852610127591,
                0.9999921107355335
            ],
            [
                8.93969630317306e-06,
                1.6701419846288166e-05,
                1.4738980212644815e-05,
                1.9947299592824403e-06,
                6.1441767990323395e-06,
                6.144175334172377e-06,
                1.4738980211920955e-05,
                3.1201918802543923e-05,
                6.962256249112569e-06,
                4.222834954607099e-06
            ],
            [
                2.902313368963394e-06,
                1.8925148239772175e-05,
                NaN,
                1.2098653950480359e-06,
                3.5356238065786484e-05,
                3.120192623836512e-05,
                2.5612816000331606e-06,
                1.300712846411008e-05,
                6.144172404028807e-06,
                1.300712381094558e-05
            ],
            [
                0.9999599362887179,
                0.9999785550541436,
                1.9947299592570416e-06,
                0.9999952149060758,
                0.9999869928761884,
                0.9999921107336528,
                0.9999970976883609,
                0.9999724643056193,
                0.9999977396754327,
                0.999933947871098
            ],
            [
                0.9999930377429213,
                0.999972464312219,
                0.9998204721003049,
                0.9999885212318762,
                0.9999930377454118,
                0.9999977396757023,
                0.9999339478474997,
                0.9998601778930637,
                0.9998766054552628,
                0.9990889487257028
            ],
            [
                0.9999974387171954,
                0.9999921107392952,
                0.9999962733589397,
                0.9999810748473089,
                0.9999921107374152,
                5.422220908634683e-06,
                0.9999930377404307,
                0.9999546021422242,
                0.999988521236004,
                0.9999967112501512
            ],
            [
                0.9999984465015047,
                0.99999893229713,
                0.9999994956527722,
                0.9999994956524716,
                0.9999996940978825,
                0.9999938558275957,
                0.999989870005398,
                0.9999996940977002,
                0.9999970976869769,
                0.9999967112493665
            ],
            [
                2.7535687801010546e-05,
                1.99473067264854e-06,
                2.2603242978377903e-06,
                NaN,
                1.5534973841705173e-06,
                1.3709570434054234e-06,
                4.222833947820683e-06,
                8.939698434495167e-06,
                1.9947306726594253e-06,
                NaN
            ],
            [
                0.999998239656367,
                0.9999970976887068,
                0.9999984465018751,
                0.9999994956524716,
                0.999997097687669,
                0.9999992661792819,
                0.999999168471675,
                0.9999982396574163,
                0.9999952149037941,
                0.9999977396751633
            ],
            [
                3.7266410605974813e-06,
                7.889266347004826e-06,
                7.889261644501938e-06,
                2.9023130230846496e-06,
                1.1478770861441461e-05,
                9.422445938917108e-07,
                1.1478772229551402e-05,
                9.422448185388577e-07,
                3.2887498494282754e-06,
                2.9023109471452223e-06
            ],
            [
                7.88925976359915e-06,
                1.0129994599901296e-05,
                2.260324028372372e-06,
                4.539789028526512e-05,
                7.88926352599354e-06,
                3.726640172337686e-06,
                2.1444956077189637e-05,
                4.785093924047376e-06,
                4.22283344433731e-06,
                7.889264465986113e-06
            ],
            [
                0.9999938558268635,
                0.9999980052702836,
                0.9999962733598275,
                0.9999785550439195,
                0.9999970976876689,
                0.9999869928668843,
                0.9999962733611603,
                0.9999938558224687,
                0.9669140218496496,
                0.9999974387168733
            ],
            [
                0.00012339456008432324,
                5.422217030495909e-06,
                4.539786863059458e-05,
                3.535626756251187e-05,
                1.0129995809763438e-05,
                4.006371128012683e-05,
                3.120191880867338e-05,
                3.535623805498234e-05,
                5.1442207499350526e-05,
                0.00023050668654621317
            ],
            [
                0.9999957771670591,
                0.9999990577551814,
                0.9999994956523514,
                0.9999986290426297,
                0.9999994284993485,
                0.9999994284997573,
                0.9999938558253986,
                0.9999982396574163,
                0.9999977396762415,
                0.9999997617631183
            ],
            [
                9.422447062150634e-07,
                8.939698435096828e-06,
                1.3709572067955008e-06,
                9.422449308716635e-07,
                2.1444948409679848e-05,
                2.2603248365960415e-06,
                8.315283250305684e-07,
                1.670142980687079e-05,
                8.939693106182721e-06,
                1.760342583722268e-06
            ],
            [
                0.9999938558268632,
                0.9999910602994533,
                0.999985261016273,
                0.9999599363173769,
                0.9999756997534762,
                0.9999921107374143,
                0.9999921107393043,
                0.9999970976887081,
                0.9999485577679644,
                0.9999885212359914
            ],
            [
                1.1478773598329648e-05,
                1.3007126909916233e-05,
                1.0129989771288745e-05,
                2.5612812946681295e-06,
                1.0129995807165349e-05,
                4.222832941034507e-06,
                0.9998204719487146,
                7.889261644875049e-06,
                3.5356242224994204e-05,
                1.14787681240737e-05
            ],
            [
                0.9999989322967482,
                0.999998790134028,
                0.9999997897566338,
                0.9999967112517189,
                0.9999997300422868,
                0.999993855826131,
                0.9999952149072167,
                0.9999990577549568,
                0.9999930377445811,
                0.9999967112521108
            ],
            [
                0.9999974387171787,
                0.9999967112497585,
                0.9999756997534802,
                0.9999989322971299,
                0.9999989322973845,
                0.9999991684722698,
                0.9999977396757022,
                0.9999990577552937,
                0.9999996940977731,
                0.9999989322971299
            ],
            [
                0.9999898700114362,
                0.9999996940978825,
                0.9999724643056253,
                0.9999810748562741,
                0.9999687980997952,
                0.9999952149032236,
                0.9999930377412606,
                0.9999992661791944,
                0.9999151889890594,
                0.9999785550490348
            ],
            [
                0.9999957771670591,
                0.9999910602994342,
                0.9999869928653365,
                0.9999945777829694,
                0.9999962733611603,
                0.9999957771670591,
                0.9999852610180312,
                0.9999938558275957,
                0.9999251537462852,
                0.999964643736673
            ],
            [
                0.9999756997563729,
                0.9999852610233002,
                0.9999151889788636,
                0.9999910602994336,
                0.9997040428673362,
                0.9999910603068932,
                0.9999756997535008,
                0.9999974387180947,
                0.9999921107345932,
                0.9999952149049395
            ],
            [
                4.7850933538313875e-06,
                1.8925150493166868e-05,
                9.422447061953531e-07,
                4.539786322642463e-05,
                1.7603440526133836e-06,
                2.2603251061458426e-06,
                1.9947304348595095e-06,
                1.0677027427413698e-06,
                4.222832437677995e-06,
                1.1478772229050293e-05
            ],
            [
                0.9999967112497584,
                0.9999687980774769,
                0.9999885212264089,
                0.9999898700078147,
                0.9999921107364742,
                0.999999057755069,
                0.9999962733607161,
                0.9999930377412606,
                0.9999810748449961,
                0.9999977396757022
            ],
            [
                0.9999810748562732,
                0.999975699762171,
                0.9999810748517628,
                0.9999938558224684,
                0.9999921107336532,
                0.9999952149072165,
                0.9999977396765106,
                0.9999151889283443,
                0.999891103116832,
                0.9999756997650636
            ],
            [
                0.9999724642990546,
                0.9999957771680698,
                0.9999869928731266,
                0.9999980052698034,
                0.9999970976880161,
                0.9999921107336527,
                1.1478770859917257e-05,
                0.9999938558276299,
                0.9999991684715762,
                0.9999984465026158
            ],
            [
                0.9999810748517622,
                0.9999038975510327,
                0.9999967112513267,
                0.9999885212277709,
                0.9999974387187053,
                0.9999982396567868,
                0.9999970976883609,
                0.9999910602994387,
                0.9999996533674201,
                0.9999986290421394
            ],
            [
                0.9999993524050474,
                0.999998239656367,
                0.9999986290424663,
                0.9999997897566589,
                0.9999945777797377,
                0.9999986290421394,
                0.9999987901343165,
                0.9999974387171787,
                0.9999992661789321,
                0.9999910603068934
            ],
            [
                2.260323489490968e-06,
                1.3709575336860625e-06,
                1.4738978456398127e-05,
                1.553498495308628e-06,
                8.315281267649641e-07,
                1.3007130013572209e-05,
                1.1478764019328247e-05,
                2.9023109470871505e-06,
                1.3007133115430804e-05,
                1.0677027427471959e-06
            ],
            [
                0.9999957771670589,
                0.9999974387187053,
                0.9999989322966208,
                0.9999989322972572,
                0.9953904282799958,
                0.9999977396759716,
                0.9999977396748938,
                0.999998790134028,
                0.9999982396567867,
                0.999998790134028
            ],
            [
                0.9999994284996211,
                0.9999997300421581,
                0.9999910602994362,
                0.9999991684720715,
                0.9999852610215436,
                0.999996273358939,
                0.999999168471675,
                0.999989870006606,
                0.9999982396574163,
                0.9997694933408589
            ],
            [
                4.5397852394305204e-05,
                3.535626333989112e-05,
                7.889260704308795e-06,
                5.829128637164443e-05,
                0.00013982204065167932,
                0.00010889687024170175,
                7.484621833788234e-05,
                0.00015843616002064165,
                1.0129992186774007e-05,
                7.484623617964428e-05
            ],
            [
                0.9999987901347492,
                0.999989870009021,
                0.9999910603058279,
                0.9999977396754327,
                0.9999957771650454,
                0.9999869928668841,
                0.9999869928684351,
                0.999998629042303,
                0.9999885212305063,
                0.9999687980774769
            ],
            [
                0.9999980052700408,
                0.9999930377437505,
                0.9999998555019963,
                0.9999987901347492,
                0.9999993524052019,
                0.9999998724809571,
                0.9999989322975119,
                0.999999057755743,
                0.9999996072138465,
                0.9999962733598278
            ],
            [
                6.962255419051463e-06,
                1.3007130013288297e-05,
                7.889260703763482e-06,
                1.1478772230407462e-05,
                3.2887498494282754e-06,
                8.9396941718352e-06,
                2.2603251062013478e-06,
                5.422220261948442e-06,
                3.726637951170554e-06,
                2.9023123310290063e-06
            ],
            [
                0.9999994284997573,
                0.9999832985721857,
                0.9999984465015047,
                0.9999599363221565,
                0.9999910603004991,
                0.9999930377437507,
                0.9999869928699887,
                0.9999646437324408,
                0.9999996940978095,
                0.9999994284994167
            ],
            [
                0.9998911031187319,
                0.990291523957269,
                0.999972464312258,
                0.9999945777816767,
                0.9999724643023452,
                0.9997965730513342,
                0.9999852610162734,
                0.8670357666736772,
                0.9999921107345933,
                0.9999967112521109
            ],
            [
                0.9999992661786695,
                0.999996711249384,
                0.9998601779426642,
                0.9999945777784447,
                0.999972464312183,
                0.9999852610145165,
                0.999991060300499,
                0.9999885212264018,
                0.9149009625340366,
                0.3486451488696663
            ],
            [
                0.9999984465015046,
                0.9999910603036963,
                0.9999970976866309,
                0.9999980052705163,
                0.9999995549147358,
                0.9999785550413645,
                0.9999724643154654,
                0.9999991684718732,
                0.9999986290432834,
                0.9999921107336524
            ],
            [
                0.9999982396567867,
                0.9999974387187054,
                0.9999995549147358,
                0.9999852610110029,
                0.9999980052707541,
                0.999999057755743,
                0.9999952149072167,
                0.9999970976876689,
                0.999999057755743,
                0.9999885212264044
            ],
            [
                0.9999756997505795,
                0.9999993524054334,
                0.999986992876188,
                0.9999970976883609,
                0.9999898700114359,
                0.9999945777797374,
                0.9999989322971299,
                0.9999724642957725,
                0.9999982396565769,
                0.9999921107364742
            ],
            [
                1.0129988563730593e-05,
                2.5612825159677387e-06,
                6.962253759670401e-06,
                5.1442219756013625e-05,
                6.962254589528684e-06,
                3.5356242271040426e-05,
                7.889259763728304e-06,
                4.0063696957321844e-05,
                7.889266347004826e-06,
                2.4300252313904224e-05
            ],
            [
                0.999998239656367,
                0.9999852610110019,
                0.9999898700078157,
                0.9999885212291416,
                0.9999977396754328,
                0.9999991684718732,
                0.9999945777810304,
                0.9999991684717741,
                0.9999339478239369,
                0.9999990577549568
            ],
            [
                0.00010889690924064936,
                5.144219525429276e-05,
                2.4300249416363357e-05,
                0.00013982207363327857,
                1.4738985483504099e-05,
                5.422217030209884e-06,
                1.6701429805655623e-05,
                8.481102088527284e-05,
                2.4300240719941574e-05,
                7.889266347004826e-06
            ],
            [
                2.753568781022632e-05,
                5.1442207499350526e-05,
                1.892515049199645e-05,
                4.006367783922064e-05,
                6.605212884908979e-05,
                1.0129993392342568e-05,
                1.8925143722381014e-05,
                1.670141586907437e-05,
                8.939700566289352e-06,
                4.006367783499403e-05
            ],
            [
                0.9999785550490348,
                0.9999984465022455,
                6.1441775312976045e-06,
                0.999978555049031,
                0.9999785550464806,
                0.9999339478474597,
                0.9999810748427351,
                0.9999921107336528,
                0.999985261021543,
                0.9999898700090208
            ],
            [
                0.9999984465024306,
                0.9999957771655487,
                0.9999974387184,
                0.9999952149055052,
                0.9999930377437505,
                0.9999982396572064,
                0.9999930377462402,
                0.9999970976883608,
                0.9999687980849129,
                0.9999910603068932
            ],
            [
                0.9940889307770939,
                0.9999810748562726,
                0.999988521226415,
                0.9999832985841305,
                0.9999910603015647,
                0.9999687980997952,
                0.9999852610180304,
                0.999985261014516,
                0.9999885212291378,
                0.9999785550515884
            ],
            [
                1.1478770861441461e-05,
                1.3007126913820052e-05,
                1.300712536258383e-05,
                5.144220742524465e-05,
                3.726638395493353e-06,
                0.9999974387184051,
                3.1201903931474406e-05,
                2.1444948406091176e-05,
                8.481103117361599e-05,
                0.00013982202309079152
            ],
            [
                0.9999962733593832,
                0.9999724643187554,
                0.9999756997679619,
                0.9999957771650453,
                0.999996273360716,
                0.9999038975737626,
                0.999820471991165,
                0.9999339478711289,
                0.9999756997650652,
                0.9999974387168733
            ],
            [
                0.9999910603058282,
                0.9999970976869771,
                0.9999991684721706,
                0.9999930377404307,
                0.9999810748585323,
                0.9999967112517189,
                0.9999687980774756,
                0.9999986290427931,
                0.9999869928761891,
                0.9999756997534811
            ],
            [
                2.1444956074147067e-05,
                1.3007131564383116e-05,
                7.484623612410147e-05,
                2.4300246525276163e-05,
                4.539785237613882e-05,
                2.1444940738662144e-05,
                9.610240345767146e-05,
                3.7266397281434697e-06,
                4.539785780557527e-05,
                4.006367783922064e-05
            ],
            [
                6.144177531459659e-06,
                1.2098661161927025e-06,
                2.260323758923431e-06,
                3.7266406167827664e-06,
                4.0063696959216535e-05,
                4.222835458002318e-06,
                1.9947290081177566e-06,
                2.5612822106421996e-06,
                1.0129992187253088e-05,
                5.422221554926484e-06
            ],
            [
                0.9995694429107091,
                0.9999599363078219,
                0.9999967112505427,
                0.9999810748449914,
                0.9999852610145155,
                0.9999930377445808,
                0.9999910603068932,
                0.9999984465018751,
                0.9999952149060757,
                0.9999993524052789
            ],
            [
                1.8925143726890553e-05,
                1.1478768125201194e-05,
                1.147876675548402e-05,
                5.422217677028889e-06,
                2.5612831266608576e-06,
                1.4738985485461206e-05,
                1.1478773597390071e-05,
                4.006367785146321e-05,
                1.1478768125201194e-05,
                0.9998204719911309
            ],
            [
                1.5534979397500702e-06,
                1.0129988563343644e-05,
                4.22283294098842e-06,
                6.962253759157502e-06,
                2.9023133690188264e-06,
                3.5356242272712497e-05,
                5.422218969217281e-06,
                2.2603234893594005e-06,
                4.222832941034507e-06,
                1.670142979997471e-05
            ],
            [
                0.9999974387177895,
                0.9999938558253981,
                0.9999646437454558,
                0.9999339478317045,
                0.999933947831744,
                0.9999785550515884,
                0.9999852610127591,
                0.9999910602994353,
                0.999992110734593,
                6.1441767987808774e-06
            ],
            [
                0.9999885212264021,
                0.9579122747878032,
                0.9999251537370814,
                0.9999646437497449,
                0.999876605454541,
                0.9999724642957734,
                0.9999832985781607,
                0.9999980052695652,
                0.9999756997679652,
                0.9999687980849209
            ],
            [
                3.1201922531407855e-05,
                2.753568124348506e-05,
                4.5397890268254766e-05,
                1.3007128463069061e-05,
                1.994729959270648e-06,
                2.260324028306588e-06,
                3.726640616748873e-06,
                2.7535684534618784e-05,
                2.9023119851055122e-06,
                6.1441767990323395e-06
            ],
            [
                0.9999952149066462,
                0.9999938558268633,
                0.9999921107364782,
                0.9999945777790913,
                0.9999962733616046,
                0.9999987901343165,
                0.99998329858413,
                0.9999885212277707,
                0.9999990577549568,
                0.9999151889283604
            ],
            [
                0.9999546021205596,
                0.9999869928730862,
                0.9999832985701927,
                0.9999898700066056,
                0.9999993524051246,
                0.9999756997505767,
                0.9999852610197867,
                0.9999921107345932,
                0.9999898700078134,
                0.9924227601748362
            ],
            [
                0.9999869928684346,
                0.9999967112493664,
                0.9999885212277704,
                0.999996273362049,
                0.9999957771675623,
                0.9999967112501505,
                0.9999952149066462,
                0.9999898700053974,
                0.9999785550413632,
                0.9999251537370873
            ],
            [
                0.9999977396754327,
                0.9999945777784448,
                0.9999898700090202,
                0.9999952149049351,
                0.9999599362935055,
                0.9999921107364742,
                0.9999921107383551,
                0.999995777166052,
                0.9999869928761911,
                0.99999893229713
            ],
            [
                0.9999151889182516,
                0.9999945777816766,
                0.9995121429524331,
                0.9999038975850787,
                0.9999785550413666,
                0.999975699759271,
                0.9999930377420906,
                0.999995214904935,
                0.999954602136796,
                0.9999930377454105
            ],
            [
                0.9999910602995693,
                0.9999724643023645,
                0.9933071503449694,
                0.9999785550541431,
                0.9999945777797377,
                0.9999967112501515,
                0.9999646437324317,
                0.9875683515365085,
                0.9999724642990576,
                0.9999852610180312
            ],
            [
                0.9999974387174841,
                0.9999852610110004,
                0.9999898700078128,
                0.9999989322968753,
                0.9999986290432834,
                0.9999957771675623,
                0.9999991684717741,
                0.9999869928668841,
                0.9999974387184,
                0.9999646437366474
            ],
            [
                0.9999996533672136,
                0.9999885212332438,
                0.9999952149037941,
                0.9999980052700408,
                0.9999982396565769,
                0.9999921107364742,
                0.9999910603068933,
                0.999999554914895,
                0.9999994956526519,
                0.9999832985821414
            ],
            [
                0.9999945777797381,
                0.9999957771655487,
                0.9999921107336528,
                0.9999945777784447,
                0.9999869928668849,
                0.9999982396565767,
                0.9999339478632154,
                0.9999980052702785,
                0.9999974387177893,
                0.999989870007814
            ],
            [
                0.9999938558232009,
                0.999993855826131,
                0.9999984465018751,
                0.9999930377437511,
                0.9999921107345934,
                0.9999910603036964,
                0.9999930377454107,
                0.999975699747698,
                0.9999977396759716,
                0.9999921107346033
            ],
            [
                2.753568450937557e-05,
                7.889261644057078e-06,
                3.2887490653109436e-06,
                3.7266392838544054e-06,
                6.962256249112569e-06,
                1.147876538789672e-05,
                3.2887482811908074e-06,
                4.2228319341064674e-06,
                5.829127939137956e-05,
                1.14787735942999e-05
            ],
            [
                0.9999977396765105,
                0.9999952149049349,
                0.9999724643187504,
                0.9999996072138934,
                0.9998204719485762,
                0.9999898700102282,
                0.9998911030777563,
                0.9999982396569965,
                0.9999852610162749,
                0.999964643736649
            ],
            [
                0.9999962733602717,
                0.9999995549148419,
                0.9999938558239336,
                0.999998239656367,
                0.9999996940978095,
                0.9999990577555183,
                0.999999057755743,
                0.9999995549150542,
                0.9999996072136125,
                0.9999993524053562
            ],
            [
                0.9999996072138934,
                0.999978555043919,
                0.9999646437492984,
                0.9999993524051246,
                0.9999990577556307,
                0.9999885212346115,
                0.9999921107355342,
                0.9999990577552937,
                0.9999993524052019,
                0.9999852610215426
            ],
            [
                5.422217676654099e-06,
                4.222832941072913e-06,
                1.3007123810638006e-05,
                6.962256248871951e-06,
                4.222834451065997e-06,
                2.1444940739364273e-05,
                8.939696302051047e-06,
                2.902311984989368e-06,
                4.222834954607099e-06,
                4.785093353352668e-06
            ],
            [
                0.9978172837955245,
                0.9999980052707557,
                0.9999938558246674,
                0.9999898700078128,
                0.9999921107355536,
                0.9999869928730863,
                0.9999417087136139,
                0.9953904275941456,
                0.9999930377454121,
                0.9999967112517242
            ],
            [
                0.9999756997505811,
                1.0129988563546333e-05,
                0.9840936051101058,
                0.9999952149066461,
                0.9999962733616045,
                0.999964643732439,
                0.9999832985801468,
                0.999999168471675,
                0.9999810748540172,
                0.9999974387187053
            ],
            [
                0.9999962733620487,
                0.9998766054398833,
                0.9999785550541431,
                0.9999982396569965,
                0.9999980052700407,
                0.9999832985801483,
                0.9999962733611601,
                0.9999974387177893,
                0.9999756997534754,
                0.9999986290426297
            ],
            [
                1.0129990977004428e-05,
                2.56128159999123e-06,
                6.605214458937832e-05,
                6.962253759043525e-06,
                1.7603438428564603e-06,
                6.1441746017453204e-06,
                1.2098662603862553e-06,
                3.726640616748873e-06,
                1.0129987356541108e-05,
                1.994729721436347e-06
            ],
            [
                1.4738976700661033e-05,
                8.939700565834043e-06,
                4.7850967763512445e-06,
                3.288750241473551e-06,
                7.889264466230069e-06,
                3.535626333641835e-05,
                2.1444940736477737e-05,
                1.0129989771473008e-05,
                6.962259569117366e-06,
                4.785093353687772e-06
            ],
            [
                0.9999756997505828,
                0.999999855501979,
                0.9999952149072167,
                0.9999885212305066,
                0.9999997300422225,
                0.9999962733589393,
                0.9999980052707541,
                0.9999852610162737,
                0.9999996533672962,
                0.999997097686977
            ],
            [
                0.9999852610127608,
                0.985936375642777,
                0.9999962733589512,
                0.9999852610145143,
                0.9999957771645422,
                0.9999885212346123,
                0.9999832985721857,
                0.9999885212278579,
                0.9999945777784828,
                0.999997739675433
            ],
            [
                0.9999945777803838,
                0.9999957771665581,
                0.9999962733611651,
                1.8925145982350146e-05,
                0.9999970976890534,
                0.9999599362890221,
                0.9999982396561571,
                0.9999962733607158,
                0.9999756997621633,
                1.4738978456719842e-05
            ],
            [
                0.9999957771680659,
                0.999988521233244,
                0.9999952149060758,
                0.9999987901347491,
                0.9999996940977731,
                0.9999993524051246,
                0.9999995549150542,
                0.9999996072137529,
                0.9999993524052018,
                0.9999970976887069
            ],
            [
                0.9999967112497584,
                0.9999957771660521,
                0.999993037742921,
                0.9999974387180947,
                0.9999921107374152,
                0.9999986290424663,
                0.999997438716568,
                0.9999957771655489,
                0.9999982396572064,
                0.9999945777790913
            ],
            [
                0.9999980052707541,
                0.999925153790678,
                0.9999974387168733,
                0.9999898700053984,
                0.9999977396748945,
                0.9999546021259709,
                0.9997694933410937,
                0.999985261021544,
                0.9999810748472489,
                0.999994577780384
            ],
            [
                3.5356250704701545e-05,
                7.889260704179641e-06,
                2.4300249421225448e-05,
                0.00023050679617348047,
                1.012999580884213e-05,
                1.4738983727578497e-05,
                2.1444950968441685e-05,
                7.889265406567165e-06,
                5.144220135754627e-05,
                2.260324028281919e-06
            ],
            [
                0.999985261019786,
                0.989013057328927,
                0.9626731083722525,
                0.991422512851833,
                0.999989870006605,
                0.9924227581893769,
                0.962673109309294,
                0.9999910603004997,
                0.9770226317207704,
                0.9999038975453414
            ],
            [
                0.9999785550541559,
                7.484626290009348e-05,
                1.994729008105057e-06,
                3.535626333989112e-05,
                6.962257079173776e-06,
                4.2228324375973415e-06,
                6.144172404129392e-06,
                0.9999151889688097,
                2.7535704226635563e-05,
                6.605212098183028e-05
            ],
            [
                0.9999921107345932,
                0.9999970976873228,
                0.9999962733598274,
                0.9999417087136521,
                0.9999151889182516,
                0.9999945777829694,
                0.9998911030908497,
                0.9999810748585295,
                0.9999910603036961,
                0.999983298570192
            ],
            [
                0.9997040429715629,
                0.9999957771655488,
                0.9999930377420907,
                0.9999962733611603,
                0.9999957771650453,
                0.9999646437577242,
                0.9999724642990537,
                0.999996273360716,
                0.9999930377429208,
                0.9999957771675623
            ],
            [
                0.9999921107336526,
                0.9999930377454104,
                0.9999930377412606,
                0.9999984465022455,
                0.9999952149072165,
                0.9999987901343165,
                0.9999984465022455,
                0.9999986290426297,
                0.999995214903795,
                0.9999996940977002
            ],
            [
                0.999999789756684,
                0.9999945777790913,
                0.999993855822469,
                0.9999957771670589,
                0.9999921107336528,
                0.999996711250168,
                0.9999986290421395,
                0.9999986290427932,
                0.9999990577556307,
                0.9999885212264018
            ],
            [
                2.144494328864643e-05,
                6.1441746017453204e-06,
                1.1478768122987964e-05,
                1.300713001414004e-05,
                4.5397884864412536e-05,
                1.1478770859624945e-05,
                8.939698434657777e-06,
                1.670142383167491e-05,
                4.5397884871679096e-05,
                1.3007128463069061e-05
            ],
            [
                6.962259569313662e-06,
                5.422219616026655e-06,
                5.82912932832059e-05,
                1.994729245878497e-06,
                7.889260704179641e-06,
                6.605215245616007e-05,
                6.962257909323729e-06,
                8.939694172290508e-06,
                2.7535694373763664e-05,
                5.422219615898437e-06
            ],
            [
                0.9999974387187053,
                0.9999930377437506,
                0.9999885212332438,
                0.9999832985821387,
                0.9999785550515873,
                0.9999930377404306,
                0.999964643732433,
                0.9999977396762411,
                0.9999938558253986,
                0.999569443014658
            ],
            [
                0.999999554914895,
                3.2887478891487563e-06,
                0.9999957771680656,
                0.9999869928699853,
                0.9999970976866309,
                0.9999930377420982,
                0.999996711250544,
                0.9999945777790926,
                0.9999984465018751,
                0.9999980052695652
            ],
            [
                0.9999921107336536,
                0.9933071476423861,
                0.9999982396569966,
                0.9999930377437505,
                0.999995214903794,
                0.999959936298269,
                0.9999952149055472,
                0.9999910603058296,
                5.144222585927004e-05,
                0.9999962733620487
            ],
            [
                0.9999974387171787,
                0.9999970976866309,
                0.9999982396572065,
                0.9999967112501507,
                0.9999962733593835,
                0.9999930377445805,
                0.9999977396765105,
                0.999992110738355,
                0.9999785550567036,
                0.9999869928699856
            ],
            [
                0.9999724643121931,
                0.9999417087344762,
                0.9999852610215426,
                0.9999898700126464,
                0.9875683516051121,
                0.999983298570192,
                0.9999546021421896,
                0.9999832985741731,
                0.9999921107345933,
                0.9999724643056184
            ],
            [
                0.9999962733602716,
                0.9999977396757022,
                0.9999546021097508,
                0.9999986290424663,
                0.9999869928653338,
                0.9999810748427379,
                0.9999921107392957,
                0.9999251537995278,
                0.999995214905506,
                0.9999756997563777
            ],
            [
                0.9999417087483837,
                0.9999785550592668,
                0.9999687980923481,
                0.9669140242331868,
                0.9999646437545338,
                0.9997965729325515,
                0.9999687980737552,
                0.9820137881955445,
                0.9999832985741823,
                0.9994472213221391
            ],
            [
                2.5612828212676906e-06,
                1.7603425837494853e-06,
                4.785094494402695e-06,
                5.4222170304318e-06,
                1.0677033791495609e-06,
                4.2228349547223175e-06,
                4.7850944945245504e-06,
                1.994729721482609e-06,
                1.7603434231385591e-06,
                4.785096776303374e-06
            ],
            [
                0.9999885212359817,
                0.9999952149072178,
                0.9999984465026158,
                0.9999785550413645,
                0.9999994956527121,
                0.9999967112513267,
                0.9999938558239332,
                0.9999996940978461,
                0.9999996533675028,
                0.999995777168066
            ],
            [
                0.9999885212264009,
                0.9999945777790913,
                0.9999970976883616,
                0.999995777166053,
                0.9999832985801665,
                0.9999980052693274,
                0.9999898700126449,
                0.9999952149060757,
                0.9999952149066462,
                0.9999974387168734
            ],
            [
                0.9999417087484003,
                0.9992903297360879,
                0.9999921107402358,
                0.999978555049031,
                0.9999967112513267,
                0.999820471948213,
                0.9999962733593833,
                0.9998766054693945,
                0.9999930377420905,
                1.0129988562901417e-05
            ],
            [
                7.889259762666377e-06,
                1.2098661161861e-06,
                1.300713156215912e-05,
                3.726641060956752e-06,
                3.2887482811908074e-06,
                2.561283432005142e-06,
                2.2603237589542675e-06,
                6.96225541916544e-06,
                4.78509563535725e-06,
                1.1478764019328247e-05
            ],
            [
                2.561283431986506e-06,
                3.2887498494282754e-06,
                3.2887494572095624e-06,
                6.1441746017453204e-06,
                4.222832941111319e-06,
                1.1478772230762415e-05,
                0.9999646437619418,
                3.726639728262097e-06,
                2.561283126679493e-06,
                1.5534971989696065e-06
            ],
            [
                1.7603440527046419e-06,
                7.889261644358435e-06,
                6.962256249327861e-06,
                2.902312331081799e-06,
                2.9023112929973233e-06,
                1.0677031245851707e-06,
                1.5534983101301911e-06,
                4.785092783210732e-06,
                7.484621828233953e-05,
                6.962258738827909e-06
            ],
            [
                0.9991959142406799,
                0.99998987001146,
                0.9997965729297487,
                0.9999546021206986,
                0.9999339478397837,
                0.9999962733598282,
                0.9999898700102304,
                0.9998204720392728,
                0.9994472214192567,
                0.9992903294690132
            ],
            [
                0.9999991684718732,
                0.9999994284994167,
                0.9999987901341723,
                0.9999910603068933,
                0.999996711252139,
                0.9999970976890531,
                0.9999980052702785,
                0.9999984465016899,
                0.9999982396561571,
                0.9999930377462402
            ],
            [
                0.999986992876188,
                0.9999910603036979,
                0.9999832985701943,
                0.9999957771650456,
                0.9999952149072167,
                0.9999962733598274,
                0.9999832985761651,
                0.9999910603038678,
                0.9999957771655487,
                0.9999974387174841
            ]
        ]
    },
    {
        "q_id": "8731_mmlu_math",
        "cot_ids": [
            1,
            3,
            5,
            6,
            7,
            9,
            10,
            14,
            15,
            18,
            21,
            23,
            25,
            26,
            27,
            31,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            43,
            44,
            46,
            48,
            49,
            50,
            51,
            54,
            59,
            61,
            63,
            70,
            71,
            73,
            77,
            79,
            80,
            82,
            87,
            88,
            94,
            96,
            99,
            101,
            103,
            104,
            106,
            108,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            125,
            126
        ],
        "rewards": [
            [
                2.7535700943413033e-05,
                1.9947301959819916e-06,
                0.0035936023546553203,
                NaN,
                NaN,
                0.01590639497736425,
                7.484626277430532e-05,
                NaN,
                1.4738987237553233e-05,
                NaN
            ],
            [
                7.889263525261671e-06,
                6.962257908753841e-06,
                3.2887494567788457e-06,
                4.222834951876411e-06,
                3.7266383952696564e-06,
                2.7535697653779924e-05,
                1.473898722495269e-05,
                NaN,
                0.009708474762317364,
                6.962256249429175e-06
            ],
            [
                0.9999930377413476,
                0.9999974387171792,
                NaN,
                0.9999980052695652,
                0.9999974387165682,
                NaN,
                0.9999952149072746,
                0.9999952149055125,
                0.9999724643156389,
                0.7981867705385763
            ],
            [
                NaN,
                2.902313368897403e-06,
                0.0001233945451214138,
                NaN,
                2.7535691076718644e-05,
                0.00023050671311967017,
                NaN,
                NaN,
                3.120190761663585e-05,
                5.144223203551027e-05
            ],
            [
                1.8925152744771773e-05,
                3.120190756487605e-05,
                1.012998735462479e-05,
                NaN,
                7.889264465067689e-06,
                NaN,
                NaN,
                6.962254589781966e-06,
                1.4738988998117324e-05,
                NaN
            ],
            [
                6.60521367274031e-05,
                NaN,
                1.89251482355036e-05,
                4.006367779491416e-05,
                NaN,
                0.0001584361598339217,
                0.00037998457267903477,
                0.00020342694853270045,
                8.481107161556607e-05,
                0.0019267348652575646
            ],
            [
                NaN,
                5.422219615582823e-06,
                1.8925141467679015e-05,
                1.147876675124548e-05,
                1.1478768122987964e-05,
                NaN,
                0.9999998144608317,
                5.422219615898437e-06,
                4.785093921000978e-06,
                6.144173133963328e-06
            ],
            [
                2.1444940739364273e-05,
                2.1444953515423628e-05,
                NaN,
                NaN,
                5.829125836280125e-05,
                8.315278293899016e-07,
                NaN,
                NaN,
                4.539785776065476e-05,
                0.0002305067886883745
            ],
            [
                1.370957533676711e-06,
                1.0129988561648438e-05,
                5.829127823740304e-05,
                NaN,
                5.42222090821551e-06,
                NaN,
                NaN,
                3.120190762537599e-05,
                0.00013982212288394296,
                1.2098655391782321e-06
            ],
            [
                5.82912792416722e-05,
                0.13296424535145934,
                NaN,
                7.484626286742124e-05,
                NaN,
                0.0003353500197084342,
                0.0004305571190763682,
                7.484622713542509e-05,
                0.00013982208942628374,
                3.535623803067304e-05
            ],
            [
                2.2603242977308917e-06,
                4.222833444429485e-06,
                7.889261644057078e-06,
                1.6701425823457267e-05,
                3.1201907642061724e-05,
                8.939697367492512e-06,
                NaN,
                NaN,
                NaN,
                4.7850944945245504e-06
            ],
            [
                NaN,
                8.939696290652038e-06,
                NaN,
                1.8925155002022494e-05,
                1.4738988987366645e-05,
                NaN,
                1.1478766754064213e-05,
                1.1478769487464542e-05,
                6.605213637659373e-05,
                4.0063696955427154e-05
            ],
            [
                3.7266388397721442e-06,
                NaN,
                0.9995694429797997,
                4.006370172318498e-05,
                NaN,
                1.670141586907437e-05,
                0.00015843621636396602,
                3.5356246483883486e-05,
                4.0063711244273545e-05,
                1.6701425823457267e-05
            ],
            [
                NaN,
                NaN,
                5.422218968714274e-06,
                NaN,
                1.1478764008095073e-05,
                NaN,
                1.300712380455751e-05,
                1.3007133115667397e-05,
                2.7535691068003722e-05,
                NaN
            ],
            [
                2.4300234903469775e-05,
                5.829129323316207e-05,
                4.006371126117997e-05,
                2.4300246486733047e-05,
                NaN,
                0.0001584362539523188,
                0.9999938558253991,
                NaN,
                0.00010889693461778054,
                NaN
            ],
            [
                3.1201911328358685e-05,
                NaN,
                2.1444950951785568e-05,
                2.430023493564795e-05,
                3.120190016481442e-05,
                0.8354835350552604,
                3.120192250564146e-05,
                0.9999970976880159,
                8.93969310584124e-06,
                3.120191508446373e-05
            ],
            [
                5.42221767672807e-06,
                9.61024261212637e-05,
                1.1478772222347966e-05,
                NaN,
                6.9622537587775775e-06,
                7.48462539462643e-05,
                1.3007126904001353e-05,
                1.3709576970387918e-06,
                1.1478764012521528e-05,
                NaN
            ],
            [
                1.209865683184104e-06,
                NaN,
                5.1442201245264654e-05,
                6.144176798132662e-06,
                7.889260703462123e-06,
                1.6701421797058122e-05,
                0.00013982209020545688,
                NaN,
                NaN,
                NaN
            ],
            [
                6.144173135025058e-06,
                2.7535684522397864e-05,
                2.7535700908352998e-05,
                9.610243462596773e-05,
                1.994730672095211e-06,
                8.939693105467234e-06,
                1.370957041811292e-06,
                4.0063692134764465e-05,
                9.610240323743297e-05,
                2.561282515662579e-06
            ],
            [
                6.962259568889411e-06,
                6.96225707894582e-06,
                4.7850939242083995e-06,
                1.3007133114318805e-05,
                NaN,
                3.726637951126493e-06,
                NaN,
                NaN,
                NaN,
                1.4738985485166298e-05
            ],
            [
                NaN,
                8.481102095191198e-05,
                1.6701419848961534e-05,
                4.0063687388140825e-05,
                5.144220136765162e-05,
                NaN,
                2.430023783150746e-05,
                NaN,
                0.0001398221235756373,
                1.8925155007633607e-05
            ],
            [
                1.4738987238035806e-05,
                6.605212886590941e-05,
                8.481102096980583e-05,
                0.0007096702625911509,
                1.1478765385098868e-05,
                3.1201907645920996e-05,
                7.889259762666377e-06,
                4.5397890240179425e-05,
                NaN,
                1.6701421835335913e-05
            ],
            [
                1.1478770858706246e-05,
                7.8892625849535e-06,
                6.605216032342332e-05,
                3.12019187588432e-05,
                0.00013982210650502827,
                6.962259566204604e-06,
                NaN,
                4.785092780534255e-06,
                1.4738976694012237e-05,
                NaN
            ],
            [
                NaN,
                NaN,
                0.9706877682946817,
                0.9999785550567132,
                0.9999994284992805,
                NaN,
                NaN,
                NaN,
                0.999994577779743,
                NaN
            ],
            [
                NaN,
                1.8925152741191683e-05,
                NaN,
                NaN,
                8.939697367037201e-06,
                NaN,
                NaN,
                1.7603430033399058e-06,
                NaN,
                4.539786857361818e-05
            ],
            [
                0.9999982396559476,
                0.999997438718707,
                0.9999151889389745,
                NaN,
                3.5356242264223526e-05,
                0.9999885212292875,
                0.9999852610218514,
                NaN,
                0.9999756997506067,
                1.4738976697631541e-05
            ],
            [
                1.3007123808910861e-05,
                NaN,
                NaN,
                4.222832436049568e-06,
                1.8925157198067588e-05,
                1.1478764018576587e-05,
                4.785096204650886e-06,
                6.962254588281262e-06,
                1.892514372640862e-05,
                NaN
            ],
            [
                NaN,
                0.8519528038477824,
                0.9999810748450123,
                0.9706877687186648,
                NaN,
                0.9999970976866316,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                5.422220905887864e-06,
                2.4300237808257835e-05,
                1.4738985480608657e-05,
                7.889260703906985e-06,
                NaN,
                5.422217673931937e-06,
                NaN
            ],
            [
                NaN,
                NaN,
                1.8925157250667477e-05,
                NaN,
                8.939693102865466e-06,
                NaN,
                7.484624502565293e-05,
                NaN,
                5.422221554482653e-06,
                NaN
            ],
            [
                NaN,
                0.9999810748585384,
                1.6701421841259862e-05,
                0.0021827168540629917,
                4.785095634843714e-06,
                2.902311292920774e-06,
                3.120192622644674e-05,
                4.539786854620345e-05,
                0.0024726234506656118,
                NaN
            ],
            [
                3.2887490634145927e-06,
                1.9947294835630703e-06,
                NaN,
                NaN,
                NaN,
                6.605214451056634e-05,
                1.3007128453983806e-05,
                NaN,
                1.6701423828576233e-05,
                2.144495863045236e-05
            ],
            [
                NaN,
                0.8519527963298946,
                0.9999921107393018,
                NaN,
                0.9796676455071812,
                7.889262582800945e-06,
                0.9998911030944893,
                NaN,
                0.9997965730370153,
                0.9999962733616131
            ],
            [
                NaN,
                NaN,
                0.005220126747859396,
                NaN,
                2.144494073054863e-05,
                NaN,
                5.8291258543467846e-05,
                1.9947294835630703e-06,
                1.1478764013398468e-05,
                2.4300237821252875e-05
            ],
            [
                3.535623802655717e-05,
                1.3709568799243436e-06,
                1.5534977544932838e-06,
                NaN,
                4.5397852378781204e-05,
                2.4300252300909177e-05,
                3.7266397278180926e-06,
                1.0129989769464556e-05,
                1.1478773592378984e-05,
                0.9999910603026385
            ],
            [
                0.9999952149032304,
                0.9999785550490916,
                0.9999910603006067,
                0.9999952149049351,
                NaN,
                0.999996711249759,
                0.9998204720593906,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                4.785093351846877e-06,
                1.0129990978644356e-05,
                NaN,
                NaN,
                4.222831932666232e-06,
                NaN,
                5.42222155426567e-06,
                1.994729721323867e-06,
                1.6701415862785876e-05
            ],
            [
                NaN,
                1.473898196677375e-05,
                NaN,
                0.9999599362887367,
                0.9999974387180961,
                0.651354857898194,
                0.9999910603058294,
                0.9999930377462486,
                0.9525741227833249,
                4.222833947674739e-06
            ],
            [
                0.9999992661786697,
                0.9999724643024672,
                1.8925145981283003e-05,
                0.9999599362889023,
                NaN,
                7.889264465699106e-06,
                9.610238042212629e-05,
                0.9999957771650482,
                0.9999986290423043,
                0.9999885212291522
            ],
            [
                2.144495096457996e-05,
                0.00023050663048172873,
                4.539788485169606e-05,
                0.00029595723633088874,
                0.00043055703093467196,
                1.300712689874894e-05,
                0.00048785703661097463,
                NaN,
                0.06754668738548217,
                1.3007123807302014e-05
            ],
            [
                0.9999980052702818,
                0.9999921107364914,
                0.9999921107393461,
                0.9902915251123275,
                0.9999987901340285,
                0.9999994956525317,
                NaN,
                0.9999986290432838,
                NaN,
                0.9999982396567915
            ],
            [
                NaN,
                NaN,
                6.605213654959562e-05,
                7.484622706844701e-05,
                0.037326890958432175,
                NaN,
                0.9999832985761751,
                NaN,
                NaN,
                3.5356250689524286e-05
            ],
            [
                2.43002522163972e-05,
                1.8925143723620274e-05,
                1.8925145960215522e-05,
                NaN,
                NaN,
                3.288750240564259e-06,
                1.4738983721251418e-05,
                NaN,
                2.753568116454994e-05,
                4.0063706494441236e-05
            ],
            [
                0.9999977396748947,
                0.9999984465022457,
                0.9999982396574181,
                NaN,
                NaN,
                0.9999977396748958,
                NaN,
                0.9999984465026162,
                0.9999990577555186,
                0.9999970976883622
            ],
            [
                2.4300240732671408e-05,
                NaN,
                NaN,
                0.0007096703313205741,
                NaN,
                NaN,
                5.144220746454321e-05,
                NaN,
                NaN,
                4.539785776693042e-05
            ],
            [
                0.9999987901337397,
                NaN,
                0.9999986290424668,
                0.9999977396759717,
                NaN,
                3.120190391853445e-05,
                NaN,
                0.9999724643190556,
                0.9999756997478096,
                0.9999930377404375
            ],
            [
                NaN,
                1.4738976691331275e-05,
                0.1824255171389905,
                NaN,
                NaN,
                0.16451646699291617,
                0.029312230804354206,
                0.43782349911420193,
                3.288750633025344e-06,
                0.9975273767532035
            ],
            [
                4.5397852367551086e-05,
                1.0129987346351444e-05,
                NaN,
                0.00010889692145386834,
                8.481104091280437e-05,
                1.3007125360146898e-05,
                3.1201903931474406e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                8.939695237666677e-06,
                1.3709572067181944e-06,
                5.4222189561292065e-06,
                1.892514822937613e-05,
                0.7549149868676284,
                1.8925148230890784e-05,
                1.3007133112307748e-05,
                2.753569434872079e-05,
                1.0129994602222992e-05,
                4.539787942093518e-05
            ],
            [
                6.605217610793098e-05,
                5.144220750870732e-05,
                1.3007134665130082e-05,
                1.67014178554179e-05,
                NaN,
                NaN,
                NaN,
                1.8925145981833788e-05,
                3.120190018524592e-05,
                NaN
            ],
            [
                NaN,
                NaN,
                6.962259566204604e-06,
                NaN,
                0.00026119021483609673,
                5.1442213552827284e-05,
                2.7535691095550887e-05,
                NaN,
                8.939694171331106e-06,
                NaN
            ],
            [
                1.0129994600859455e-05,
                1.1478765388314311e-05,
                NaN,
                1.3007130010922344e-05,
                NaN,
                5.144223202577919e-05,
                0.007577241982206047,
                4.006369210678142e-05,
                1.300712846115264e-05,
                NaN
            ],
            [
                2.7535700933696396e-05,
                2.260323758557508e-06,
                5.1442195149496606e-05,
                4.006367781356952e-05,
                3.5356259096177054e-05,
                7.338208929731178e-07,
                1.0129990978847043e-05,
                4.006367782114826e-05,
                2.1444943290362748e-05,
                NaN
            ],
            [
                0.0001398221398060431,
                0.003593602683964457,
                0.0007096702723742576,
                0.010986940394081131,
                0.9046505344582186,
                NaN,
                0.0004305570827149416,
                0.05340332810495602,
                NaN,
                0.0008040860073220181
            ],
            [
                3.535625071344775e-05,
                3.7266388394569345e-06,
                3.726640172120768e-06,
                NaN,
                0.0001795278996950181,
                1.4738988988010078e-05,
                2.4300232040584407e-05,
                5.422219614705025e-06,
                0.0035936020812037056,
                6.605213677497863e-05
            ],
            [
                2.2603251060738913e-06,
                NaN,
                NaN,
                NaN,
                6.144176066051891e-06,
                1.994729958696456e-06,
                NaN,
                NaN,
                0.0,
                NaN
            ],
            [
                1.3007128464559612e-05,
                NaN,
                5.043472277769247e-07,
                NaN,
                2.753569108453202e-05,
                7.889264458825275e-06,
                NaN,
                7.889266344766165e-06,
                NaN,
                4.5397884871679096e-05
            ],
            [
                0.9978172835404562,
                0.999992110738382,
                0.00017952792261014615,
                3.120192624233791e-05,
                NaN,
                0.999998005269329,
                0.8354835391516133,
                NaN,
                0.9999898700056581,
                NaN
            ],
            [
                NaN,
                4.785096775920397e-06,
                5.422221554374162e-06,
                0.7772998611746911,
                NaN,
                8.939694169330997e-06,
                1.892515724357613e-05,
                3.7266388392671313e-06,
                NaN,
                1.3007125360146898e-05
            ],
            [
                NaN,
                0.00020342699545202963,
                5.1442201347440924e-05,
                NaN,
                0.0005527787334302619,
                NaN,
                1.8925141464512013e-05,
                5.144219518617526e-05,
                3.1201907631845964e-05,
                0.9953904270471748
            ],
            [
                1.892515272983176e-05,
                NaN,
                7.889263524443698e-06,
                3.120190763332158e-05,
                NaN,
                1.0129995807939249e-05,
                1.6701425802374098e-05,
                3.7266388395620047e-06,
                3.726639726997871e-06,
                0.00015843625380709215
            ],
            [
                NaN,
                5.422217030032353e-06,
                0.9999982396567897,
                0.9999898700054063,
                NaN,
                NaN,
                4.785096775580942e-06,
                2.144495608046625e-05,
                1.7603432126220266e-06,
                0.9999952149037971
            ]
        ]
    },
    {
        "q_id": "8533_mmlu_math",
        "cot_ids": [
            0,
            2,
            8,
            9,
            10,
            11,
            12,
            14,
            15,
            16,
            17,
            18,
            21,
            22,
            23,
            24,
            29,
            30,
            32,
            34,
            35,
            36,
            37,
            39,
            40,
            41,
            43,
            47,
            49,
            51,
            53,
            54,
            58,
            59,
            60,
            61,
            63,
            65,
            67,
            68,
            69,
            71,
            73,
            74,
            75,
            80,
            84,
            86,
            87,
            88,
            89,
            90,
            91,
            95,
            97,
            98,
            101,
            103,
            106,
            108,
            110,
            112,
            113,
            117,
            118,
            119,
            122,
            124,
            127
        ],
        "rewards": [
            [
                3.726640170066823e-06,
                2.2603253753174176e-06,
                4.785096775058701e-06,
                3.7266388390502134e-06,
                NaN,
                8.315282258956806e-07,
                2.260324296916815e-06,
                2.5612831263929686e-06,
                NaN,
                4.785096773996813e-06
            ],
            [
                7.3382106794623e-07,
                1.30071315602427e-05,
                1.4738988959055636e-05,
                1.5534979394696104e-06,
                6.1441760657054305e-06,
                1.4738988990369329e-05,
                9.422444815628016e-07,
                7.88926634383339e-06,
                2.9023119827720788e-06,
                5.422218321993744e-06
            ],
            [
                1.4738976694012237e-05,
                1.3709575336093795e-06,
                1.4738981966291175e-05,
                5.422220903126249e-06,
                2.2603240281606297e-06,
                5.422217676397663e-06,
                1.147876812069122e-05,
                2.2603242974060834e-06,
                7.889265401788488e-06,
                1.0129994600638342e-05
            ],
            [
                5.8291286290217195e-05,
                1.6701417860795016e-05,
                1.3007125350754073e-05,
                4.222833443154396e-06,
                2.561282210618905e-06,
                2.9023126768680736e-06,
                1.8925157257345735e-05,
                2.26032537546132e-06,
                2.1444953506061874e-05,
                4.0063682591672956e-05
            ],
            [
                3.2887478884069663e-06,
                1.6701423811563878e-05,
                3.2887490645272776e-06,
                NaN,
                2.260324566421325e-06,
                NaN,
                NaN,
                NaN,
                1.0129995804696242e-05,
                1.0129994599072117e-05
            ],
            [
                NaN,
                2.4300249362084747e-05,
                5.422219614576807e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.9947306723419413e-06,
                3.120192248396136e-05
            ],
            [
                NaN,
                1.3007123795188342e-05,
                8.93969523617066e-06,
                NaN,
                NaN,
                2.1444958561253383e-05,
                NaN,
                NaN,
                6.962255408451543e-06,
                NaN
            ],
            [
                5.422217676486429e-06,
                6.1441753313895225e-06,
                NaN,
                6.144173123748356e-06,
                0.00010889687839387975,
                1.3007129985417377e-05,
                6.9622587284686045e-06,
                NaN,
                3.535625910878189e-05,
                5.422220904073088e-06
            ],
            [
                1.9947292456281383e-06,
                9.422447061199401e-07,
                2.5612822082987563e-06,
                4.4508510491763256e-07,
                4.785094493305991e-06,
                3.0590229979550844e-07,
                3.927861065856269e-07,
                2.9023126765196424e-06,
                5.715007194755931e-07,
                8.939699497595294e-06
            ],
            [
                1.3007131538428617e-05,
                4.785095634460739e-06,
                3.288749849000549e-06,
                2.2603245671490605e-06,
                1.0129993388915298e-05,
                1.7603430032662588e-06,
                2.1444956069076118e-05,
                1.0129990958909939e-05,
                3.120191496834468e-05,
                1.5534971988904843e-06
            ],
            [
                4.785093915587094e-06,
                1.1478764016112805e-05,
                3.726640615752405e-06,
                6.144176797998549e-06,
                5.422220907160179e-06,
                5.8291279317586125e-05,
                NaN,
                3.120190761300358e-05,
                3.2887486731252264e-06,
                6.144173868983067e-06
            ],
            [
                1.370956716216975e-06,
                2.260324296916815e-06,
                NaN,
                5.422217024321732e-06,
                0.9990889488886748,
                1.1478766749575118e-05,
                1.4738978435781506e-05,
                5.144223802012381e-05,
                0.00017952790050735195,
                3.726637949408095e-06
            ],
            [
                1.6701427808495672e-05,
                1.0,
                1.3007131561804229e-05,
                NaN,
                1.0677033788475582e-06,
                8.93970054731268e-06,
                1.670142376283563e-05,
                NaN,
                NaN,
                3.726637950329997e-06
            ],
            [
                2.2603242977308917e-06,
                1.670141983085553e-05,
                5.422221546483834e-06,
                1.2098658270370427e-06,
                NaN,
                1.3709570429434557e-06,
                1.5534977543661227e-06,
                4.785093353187292e-06,
                2.260323487938879e-06,
                1.0129990974903845e-05
            ],
            [
                4.78509677368347e-06,
                2.2603240276549155e-06,
                4.006369649020899e-05,
                2.1444943278894603e-05,
                7.889266344981421e-06,
                8.939699492326704e-06,
                2.2603253753174176e-06,
                1.3007125355060104e-05,
                6.144173867753695e-06,
                1.3007133103127848e-05
            ],
            [
                7.88926258381982e-06,
                1.8925148237775583e-05,
                7.889264465067689e-06,
                4.006371125884805e-05,
                1.3007126906036072e-05,
                7.889266345770692e-06,
                1.0129990978847043e-05,
                8.939699494570733e-06,
                6.962255414631664e-06,
                8.481107119166687e-05
            ],
            [
                9.422449308241022e-07,
                1.1478768118310953e-05,
                NaN,
                1.1478769493540482e-05,
                4.785095635017795e-06,
                4.785095063069508e-06,
                2.1444953516281788e-05,
                1.5534978508075662e-06,
                4.222831930976356e-06,
                4.7850944942634305e-06
            ],
            [
                NaN,
                2.902311983500617e-06,
                1.3007123776402689e-05,
                1.0677028696634876e-06,
                NaN,
                NaN,
                NaN,
                1.6701417853595148e-05,
                1.994729483218373e-06,
                NaN
            ],
            [
                8.939693100361262e-06,
                5.422221554374162e-06,
                6.144174599867732e-06,
                4.539787929707341e-05,
                7.88926351873225e-06,
                5.4222196154940574e-06,
                4.2228349546493465e-06,
                6.962253758182361e-06,
                1.4738976681250846e-05,
                2.1444948364587412e-05
            ],
            [
                5.829129315979273e-05,
                0.00048785721006051625,
                5.1442225903808436e-05,
                7.889264462958184e-06,
                NaN,
                1.8925148165072113e-05,
                2.753570090334442e-05,
                2.9023130227599746e-06,
                4.222834448185525e-06,
                5.422218318886929e-06
            ],
            [
                7.889260699343567e-06,
                8.93969310418261e-06,
                6.962255418658875e-06,
                3.7266388388061806e-06,
                4.222832940339353e-06,
                6.962258737814774e-06,
                2.561281294123034e-06,
                4.222834945885029e-06,
                7.338212429006964e-07,
                3.726641056679395e-06
            ],
            [
                6.1441745847799705e-06,
                2.9023119829938083e-06,
                NaN,
                NaN,
                2.144495096083526e-05,
                NaN,
                NaN,
                NaN,
                4.222832938511214e-06,
                4.2228354563508465e-06
            ],
            [
                1.5534981248330927e-06,
                NaN,
                NaN,
                6.9622554171645e-06,
                1.1478773593172406e-05,
                2.260324835864195e-06,
                7.889261643554814e-06,
                2.902311984250272e-06,
                6.962257908753841e-06,
                0.00026119038710502556
            ],
            [
                1.3007130010922344e-05,
                3.7266410585367577e-06,
                4.539788480710582e-05,
                2.5612831263929686e-06,
                1.4738980192671623e-05,
                NaN,
                3.288749849000549e-06,
                8.939697367037201e-06,
                7.889261643181705e-06,
                NaN
            ],
            [
                4.785093919677971e-06,
                0.00023050674052480853,
                4.222832436272325e-06,
                6.475949524703663e-07,
                3.288749848444206e-06,
                4.222835455551995e-06,
                4.222832939064264e-06,
                6.144176062330242e-06,
                3.288749848276705e-06,
                2.260323757126707e-06
            ],
            [
                NaN,
                1.2098653949534047e-06,
                5.4222202621161125e-06,
                7.338213303682682e-07,
                NaN,
                2.1444945839255133e-05,
                7.889266347004826e-06,
                1.9947290076496946e-06,
                1.0129994597524319e-05,
                1.3007130007988564e-05
            ],
            [
                1.0129993391236997e-05,
                NaN,
                6.144177530671741e-06,
                4.785092781709294e-06,
                1.7603425828929402e-06,
                3.1201911286587615e-05,
                5.422218968714274e-06,
                4.785095062773571e-06,
                1.0129994599072117e-05,
                2.2603251059484907e-06
            ],
            [
                NaN,
                1.1478770859332632e-05,
                1.147876948232818e-05,
                NaN,
                NaN,
                3.726637951170554e-06,
                5.829125123919394e-05,
                3.726640172337686e-06,
                1.1478764005255457e-05,
                8.939700553621976e-06
            ],
            [
                1.6701423811563878e-05,
                NaN,
                2.144494324449018e-05,
                NaN,
                3.7266397241779347e-06,
                5.8291292846806735e-05,
                NaN,
                4.222833944970936e-06,
                2.4300246489738706e-05,
                6.144176062553765e-06
            ],
            [
                2.2603245671490605e-06,
                4.222834449337713e-06,
                2.2603240275973545e-06,
                6.962254588977791e-06,
                1.7603432131119386e-06,
                4.78509449293172e-06,
                NaN,
                8.93969416907082e-06,
                3.7266392839832006e-06,
                3.288747886205525e-06
            ],
            [
                4.222833946845163e-06,
                8.939693068977414e-06,
                3.1201900162771276e-05,
                5.4222183164803815e-06,
                0.00010889694732060871,
                4.539785231272163e-05,
                2.1444956064317223e-05,
                8.939700561817559e-06,
                5.422219614705025e-06,
                1.1478768116974664e-05
            ],
            [
                6.47595029750346e-07,
                6.475948753741589e-07,
                5.4222202617511845e-06,
                7.889259761030436e-06,
                1.7603434230729168e-06,
                2.2603248364233586e-06,
                1.553497754476329e-06,
                3.726639283752725e-06,
                2.902313022802209e-06,
                5.043474683009273e-07
            ],
            [
                1.0129990976728036e-05,
                2.9023126767836054e-06,
                3.726641060536473e-06,
                0.9890130585433227,
                4.785095633999427e-06,
                3.2887506327561457e-06,
                7.889266344766165e-06,
                NaN,
                1.0129993390942177e-05,
                1.6701423811563878e-05
            ],
            [
                2.5612828211442287e-06,
                1.2098659718187066e-06,
                4.7850933529174686e-06,
                9.422445936997504e-07,
                3.288750632678377e-06,
                6.9622554185195676e-06,
                8.939698429893283e-06,
                2.9023130228840374e-06,
                1.7603425837366772e-06,
                1.5534979392661533e-06
            ],
            [
                4.222833406499439e-06,
                2.9023126767836054e-06,
                3.7266392838544054e-06,
                6.962258723909496e-06,
                2.2603240050663556e-06,
                1.3709570432277435e-06,
                1.3007133108001712e-05,
                1.8925154987702108e-05,
                2.2603251029923236e-06,
                2.2603245668941476e-06
            ],
            [
                1.5534983100765009e-06,
                8.315281298876022e-07,
                NaN,
                1.6701417851711638e-05,
                2.2603234880211088e-06,
                1.1478769487046951e-05,
                3.7266383941918447e-06,
                1.553498309286692e-06,
                6.144177530146464e-06,
                1.9947299588742466e-06
            ],
            [
                NaN,
                1.9947301968963442e-06,
                5.422217676486429e-06,
                1.0677031244603883e-06,
                4.222834953896582e-06,
                6.962254588281262e-06,
                1.1478770850604989e-05,
                1.9947292458603553e-06,
                1.1478769491014062e-05,
                3.2887494572514376e-06
            ],
            [
                2.144494834196318e-05,
                7.889261631600955e-06,
                5.422217675756574e-06,
                NaN,
                0.00023050682381337665,
                0.34864514210180597,
                NaN,
                0.00015843617684157225,
                0.0010322309150307505,
                0.999512142869015
            ],
            [
                0.00247262293553739,
                1.9947304343125304e-06,
                2.14449558897205e-05,
                3.726639727994339e-06,
                1.3007134662054344e-05,
                1.760343632920248e-06,
                1.9947299591354906e-06,
                1.994729483535857e-06,
                2.4300240699432402e-05,
                3.28875063243909e-06
            ],
            [
                3.7266388382164344e-06,
                4.222834953420345e-06,
                2.406102985083497e-06,
                1.300712999772033e-05,
                6.144174599867732e-06,
                2.902311984102453e-06,
                6.475951069855719e-07,
                1.7603436308565326e-06,
                1.9947292451963607e-06,
                1.1478769488257963e-05
            ],
            [
                1.2098656832853378e-06,
                4.22283394762097e-06,
                3.466324971128275e-07,
                3.9278605978547293e-07,
                3.0590211750759763e-07,
                1.760342793266906e-06,
                2.902311638759718e-06,
                1.7603434229832599e-06,
                1.3709567163940317e-06,
                5.043472277356416e-07
            ],
            [
                1.7603425833476294e-06,
                5.715005832130605e-07,
                5.715007195057402e-07,
                3.4663266236317903e-07,
                4.222834954461155e-06,
                9.422449303450579e-07,
                3.927863407065117e-07,
                8.315282255693501e-07,
                2.9023112919177154e-06,
                3.059021174967472e-07
            ],
            [
                7.33821330394297e-07,
                1.1478769490053603e-05,
                1.994729958068745e-06,
                1.3007125347631017e-05,
                1.553497568892479e-06,
                1.67014297980912e-05,
                6.144176788308849e-06,
                1.1478765388105516e-05,
                1.14787653519422e-05,
                1.3007126908733257e-05
            ],
            [
                3.7266406165319545e-06,
                3.288750633139005e-06,
                4.785094494185095e-06,
                2.26032348933062e-06,
                4.222835457526079e-06,
                9.422450431474948e-07,
                3.7266383946527958e-06,
                1.2098658276290391e-06,
                2.2603253754921562e-06,
                2.9023130228444433e-06
            ],
            [
                6.96225790109201e-06,
                1.1478766754064213e-05,
                5.422217029391264e-06,
                1.3007125358230479e-05,
                2.26032348933062e-06,
                1.7603430033607189e-06,
                3.288749065029781e-06,
                7.889266342800164e-06,
                8.93969843377968e-06,
                1.3007130006048483e-05
            ],
            [
                4.450849458153541e-07,
                1.2098655391243142e-06,
                2.5612822103812995e-06,
                7.338210679622478e-07,
                4.785096205582214e-06,
                4.450851580273012e-07,
                1.0677032518209896e-06,
                4.450848927478102e-07,
                3.288750633192845e-06,
                8.315284239208146e-07
            ],
            [
                1.3007130006521673e-05,
                NaN,
                4.222833438207667e-06,
                1.6701419840455358e-05,
                7.889259761030436e-06,
                3.726638394564673e-06,
                2.4300231986394238e-05,
                4.785093920078354e-06,
                4.22283193320392e-06,
                NaN
            ],
            [
                1.4738976572886251e-05,
                8.93970055837021e-06,
                2.5612815994461346e-06,
                2.902311638205396e-06,
                1.0129994594944656e-05,
                1.3709578604495207e-06,
                2.9023116376246774e-06,
                1.3709576970213355e-06,
                7.889259753740449e-06,
                8.939697366029015e-06
            ],
            [
                1.4738987149939243e-05,
                1.3007131557498195e-05,
                NaN,
                2.753569106650115e-05,
                2.2603253752310765e-06,
                NaN,
                2.7535681218241846e-05,
                1.4738983697605298e-05,
                2.561281294369958e-06,
                NaN
            ],
            [
                4.4508526412562144e-07,
                1.0677029971978802e-06,
                1.5534981249291695e-06,
                1.7603425835173373e-06,
                6.962254588116627e-06,
                1.7603432130222817e-06,
                5.422217673557147e-06,
                3.466327037357575e-07,
                5.715007194755931e-07,
                1.7603425836246058e-06
            ],
            [
                6.475948753182055e-07,
                9.422444813961216e-07,
                6.47594566274984e-07,
                7.889265405677441e-06,
                8.315277301945715e-07,
                3.7266397276079535e-06,
                3.28874867308036e-06,
                1.3709576967482697e-06,
                2.5612825156159896e-06,
                1.9947297211642184e-06
            ],
            [
                8.939700562110258e-06,
                1.3007130005527972e-05,
                2.2603251057429158e-06,
                2.9023116388072315e-06,
                2.2603237580312362e-06,
                6.605213336732207e-05,
                3.2887498477024157e-06,
                8.315284240879503e-07,
                4.222831933649433e-06,
                1.5534983098744568e-06
            ],
            [
                4.4508521108475657e-07,
                NaN,
                1.3007131541646312e-05,
                NaN,
                6.144175327902573e-06,
                1.670142767555624e-05,
                7.889259762666377e-06,
                3.726639283752725e-06,
                NaN,
                6.144173868781898e-06
            ],
            [
                7.889260701926633e-06,
                1.9947292456607935e-06,
                9.422445937837332e-07,
                1.7603427930267533e-06,
                1.7603438428188364e-06,
                1.5534973840150989e-06,
                3.288750239044785e-06,
                1.994730433191359e-06,
                1.7603440524628877e-06,
                1.994729245555571e-06
            ],
            [
                2.144495863482118e-05,
                1.892515046211642e-05,
                2.7535694306248064e-05,
                1.3007133109421283e-05,
                1.4738983633154876e-05,
                NaN,
                NaN,
                NaN,
                9.422447062030659e-07,
                NaN
            ],
            [
                2.90231336827709e-06,
                4.22283193338827e-06,
                1.9947297210880223e-06,
                6.144174601499446e-06,
                2.902312330965655e-06,
                1.3007128457012223e-05,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.0677033791291683e-06,
                1.7603430033399058e-06,
                1.3709570433387154e-06,
                1.0677024881382882e-06,
                7.338208054248423e-07,
                2.561283126160022e-06,
                4.222832938050339e-06,
                8.315280275552294e-07,
                5.043475283710534e-07,
                8.315280274977528e-07
            ],
            [
                4.785094493636744e-06,
                2.9023109469023766e-06,
                NaN,
                1.370957533625589e-06,
                NaN,
                7.338207179493245e-07,
                6.1441753313895225e-06,
                1.0129989768322136e-05,
                1.89251482218717e-05,
                1.6701417847458553e-05
            ],
            [
                7.889263523238269e-06,
                NaN,
                8.93969630226244e-06,
                2.90231302150879e-06,
                NaN,
                1.3007126874284998e-05,
                8.939696604523167e-06,
                6.962255418924822e-06,
                1.0129995805359584e-05,
                NaN
            ],
            [
                1.8925145968614975e-05,
                1.7603427932989266e-06,
                1.3709573700091645e-06,
                8.939696301384342e-06,
                7.889262571550252e-06,
                1.5534981249291695e-06,
                NaN,
                8.939697360662863e-06,
                7.338208054635517e-07,
                5.422221554374162e-06
            ],
            [
                2.5612812944538183e-06,
                2.9023126768258393e-06,
                7.889259761905808e-06,
                1.760343422832764e-06,
                1.0129992186202796e-05,
                2.561283126304449e-06,
                1.0677027426418351e-06,
                4.785092781300206e-06,
                NaN,
                6.1441753308083655e-06
            ],
            [
                6.605215220434614e-05,
                NaN,
                5.422218321855664e-06,
                5.144220749598207e-05,
                NaN,
                1.0129992175920999e-05,
                NaN,
                7.338210677580215e-07,
                NaN,
                NaN
            ],
            [
                2.260324028331257e-06,
                1.9947301968673173e-06,
                4.222834953712232e-06,
                1.0677028699858827e-06,
                3.2887498489407274e-06,
                2.902311639073834e-06,
                1.0677028699625768e-06,
                2.9023126767360923e-06,
                6.9622562487453084e-06,
                5.422219615188307e-06
            ],
            [
                2.382369667488067e-07,
                4.45085211079899e-07,
                7.338208929998139e-07,
                1.5534979396645902e-06,
                2.1024331594580783e-07,
                8.315281267248819e-07,
                3.9278615336542386e-07,
                3.0590226336807627e-07,
                9.422447052406933e-07,
                3.059022269055932e-07
            ],
            [
                4.785095062634308e-06,
                7.889263523008662e-06,
                5.829125143894502e-05,
                0.9770226297972673,
                4.785096205582214e-06,
                1.0129990977262395e-05,
                4.222834450029027e-06,
                0.0005527786741949143,
                2.9023130227599746e-06,
                8.939697368110433e-06
            ],
            [
                3.72664061504742e-06,
                4.7850927830148924e-06,
                2.561281904923017e-06,
                5.422218968221128e-06,
                3.7266410605974813e-06,
                5.422217029736466e-06,
                8.93970056529743e-06,
                6.144172403928222e-06,
                3.7266406163624873e-06,
                3.927863875342063e-07
            ],
            [
                2.5612831264302397e-06,
                8.315283246921376e-07,
                2.2603245667543567e-06,
                4.785096205347206e-06,
                2.56128129449109e-06,
                3.927861533982897e-07,
                4.4508505187557226e-07,
                1.994730672496148e-06,
                6.96225624580722e-06,
                5.043475885498987e-07
            ],
            [
                NaN,
                1.9947301961053565e-06,
                1.3709575333525227e-06,
                5.043472878263805e-07,
                1.0677024880528344e-06,
                2.561281599138645e-06,
                7.338209800181798e-07,
                7.338209801623393e-07,
                1.0677027422087383e-06,
                9.42244930372481e-07
            ],
            [
                3.2887506328937356e-06,
                3.7266401705820042e-06,
                5.422220907909759e-06,
                1.76034279349265e-06,
                3.7266410604686857e-06,
                4.7850933535006355e-06,
                1.0129992185060374e-05,
                1.8925143721072897e-05,
                1.1478769488633793e-05,
                3.2887490642879904e-06
            ]
        ]
    },
    {
        "q_id": "7799_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            6,
            7,
            8,
            9,
            11,
            12,
            13,
            14,
            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,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            61,
            62,
            63,
            64,
            66,
            67,
            69,
            70,
            71,
            72,
            73,
            74,
            76,
            78,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            101,
            102,
            103,
            104,
            105,
            107,
            108,
            111,
            112,
            113,
            114,
            116,
            117,
            118,
            119,
            120,
            121,
            123,
            124,
            125
        ],
        "rewards": [
            [
                0.9996200154696498,
                0.9999869928669514,
                0.9998601779258601,
                0.9995694429087928,
                0.9971990735121612,
                0.9999785550413615,
                0.9999756997563714,
                0.9999339478238459,
                0.9999832985721857,
                0.9996200155603212
            ],
            [
                4.785094494576774e-06,
                2.753569109254574e-05,
                1.892514372737249e-05,
                5.422218969720291e-06,
                1.0129995809247506e-05,
                4.785096205973894e-06,
                5.422217029943586e-06,
                6.144177531660828e-06,
                1.3007130009739366e-05,
                1.3007134666431358e-05
            ],
            [
                6.605215255419451e-05,
                2.4300252313904224e-05,
                9.610240338425864e-05,
                8.481105142266346e-05,
                NaN,
                6.605212101883346e-05,
                1.1478773597640625e-05,
                1.6701417857058377e-05,
                7.484625400398525e-05,
                1.4738980214280206e-05
            ],
            [
                1.8925141470949294e-05,
                1.8925148238291944e-05,
                1.3007133114011233e-05,
                0.0001088969594958043,
                5.422221555133606e-06,
                4.5397884864412536e-05,
                5.71500378896509e-07,
                2.4300240725599276e-05,
                1.300713311614059e-05,
                1.8925155008528632e-05
            ],
            [
                0.9978172832498913,
                0.9998911031299785,
                0.9947798735664964,
                0.9997694931753952,
                0.9999646437324624,
                0.9997694932023174,
                0.9998766054406177,
                0.9997040429007811,
                0.9996646498111788,
                0.999933947839643
            ],
            [
                6.962256249758443e-06,
                1.5534973840984598e-06,
                1.473898899256772e-05,
                3.2887482812745586e-06,
                1.4738985484549675e-05,
                8.93969630362837e-06,
                2.2603253755476615e-06,
                0.0009110514113083478,
                1.012998977198894e-05,
                1.1478768124783601e-05
            ],
            [
                0.9998415637264859,
                0.9999599362887237,
                0.9990889489970757,
                0.9999898700126436,
                0.9998911030648404,
                0.9999151889283214,
                0.9998415637077331,
                0.999975699759271,
                0.999968798081203,
                0.9999599362934934
            ],
            [
                1.6701415862785876e-05,
                6.605215251046346e-05,
                1.670142382493073e-05,
                7.889261644760245e-06,
                5.829127934684904e-05,
                0.00015843623535638724,
                3.120190020204515e-05,
                0.00023050679557654998,
                9.61024378393533e-05,
                9.610238051931088e-05
            ],
            [
                3.535625489632318e-05,
                4.0063692174115624e-05,
                8.481103120631853e-05,
                5.829127942742807e-05,
                2.4300234936443568e-05,
                5.144221970062134e-05,
                1.6701419846834993e-05,
                0.00010889688301423978,
                0.00013982214054859745,
                0.00013982202386386111
            ],
            [
                0.9997388097840392,
                0.9968273172429318,
                0.9953904285406616,
                0.9999151889587016,
                0.9998204720980665,
                0.9998911031037886,
                0.9980732653355532,
                0.9982992778743716,
                0.9986749776601191,
                0.9978172839212838
            ],
            [
                0.999925153737218,
                0.9999756997650743,
                0.9998415637832303,
                0.9995694428203254,
                0.9997965730512482,
                0.9890130587558419,
                0.998299277700239,
                0.9998911031038012,
                0.9995121428362325,
                0.9999599363175071
            ],
            [
                0.9998601779095931,
                0.9999599363173941,
                0.9999852610233041,
                0.999981074844998,
                0.9999810748495068,
                0.9998911030649592,
                0.9999646437366636,
                0.9999756997563796,
                0.9999724643121898,
                0.9999599362935166
            ],
            [
                4.5397857817300854e-05,
                2.7535700942411318e-05,
                5.829124466818968e-05,
                2.144495096723246e-05,
                2.7535697661092444e-05,
                8.481106124762124e-05,
                1.0129992183991656e-05,
                9.610239198289712e-05,
                4.222833444168322e-06,
                0.00010889687031696483
            ],
            [
                0.9999646437619342,
                0.9999546021151381,
                0.9999756997621647,
                0.9992903297102886,
                0.9989677687893023,
                0.9997040430064716,
                0.9997694932299439,
                0.9991959141687532,
                0.999876605454541,
                0.9996646497302664
            ],
            [
                0.9996200155173954,
                0.9999038975508774,
                0.9999417087483575,
                0.9996200154695172,
                0.9971990728703003,
                0.9999724643154654,
                0.9999251537549172,
                0.9997388096281703,
                0.9999910603036964,
                0.9999038975736347
            ],
            [
                0.9999339478238508,
                0.9999832985702116,
                0.9999546021367987,
                0.9998911031297709,
                0.9999910603036964,
                0.999738809659496,
                0.9998766053959857,
                0.9998204720338842,
                0.9996200155632619,
                0.9999785550592636
            ],
            [
                0.9982992773503923,
                0.8354835371034368,
                0.9995694428296443,
                0.40733340004593027,
                0.9999485577802613,
                0.8670357701094303,
                0.9998601779765635,
                0.9999038975971876,
                0.9579122702820997,
                0.9999151889385346
            ],
            [
                0.9999251537727649,
                0.9998601778927362,
                0.999954602142276,
                0.9999251537549951,
                0.9998766053958816,
                0.9999832985781592,
                0.9997040429356898,
                0.9999151889587096,
                0.9999724642990765,
                0.9999417087483646
            ],
            [
                7.889261645269683e-06,
                1.2098653950315304e-06,
                1.6701425819994037e-05,
                1.3007134660776729e-05,
                4.539787943778038e-05,
                4.785094494628999e-06,
                7.889262585541864e-06,
                1.300713466685723e-05,
                1.3007130014873483e-05,
                3.1201918806289706e-05
            ],
            [
                8.939695238211425e-06,
                1.067703379154416e-06,
                3.288747889178668e-06,
                5.043474081957179e-07,
                1.5534979397500702e-06,
                6.962255419279419e-06,
                4.785094494672519e-06,
                5.422220262505697e-06,
                1.5534979397500702e-06,
                1.0129995809763438e-05
            ],
            [
                0.9998601778761356,
                0.9999251537995464,
                0.9996200154695835,
                0.9999339478553424,
                0.9997040427600956,
                0.9994472213193091,
                0.9971990728442877,
                0.999964643732436,
                0.9989677691655184,
                0.9996200154244688
            ],
            [
                8.939695238211425e-06,
                1.0129990979215566e-05,
                5.422220908703723e-06,
                1.7603430033607189e-06,
                2.5612831265909735e-06,
                2.144495863411905e-05,
                2.4300237830711845e-05,
                1.8925148239772175e-05,
                1.5534975692866768e-06,
                2.7535684533717236e-05
            ],
            [
                0.9998204719697047,
                0.9999251537819165,
                0.999903897562857,
                0.9986749773970043,
                0.999664650012557,
                0.9997694933120754,
                0.9999339478397837,
                0.9998204719504332,
                0.9990889487151063,
                0.9997694932854785
            ],
            [
                0.9991959140429518,
                0.9998204719918885,
                0.9999852610215443,
                0.9999869928730944,
                0.9996646498091688,
                0.9999810748472489,
                0.9995121427681696,
                0.9999962733616046,
                0.9999251537727964,
                0.9975273771592187
            ],
            [
                0.00015843619725398262,
                0.0001584362165022771,
                3.535625069312567e-05,
                5.8291293265817787e-05,
                0.0,
                4.5397890257685224e-05,
                3.535626334490732e-05,
                8.481103095395362e-05,
                2.7535694380675497e-05,
                5.14422075023447e-05
            ],
            [
                0.9840936082590286,
                0.9988304900013482,
                0.9980732652838393,
                0.9993736658216329,
                0.9933071481377052,
                0.995929862555917,
                0.9984988180690513,
                0.9997965730993071,
                0.9999810748585306,
                0.999738809753899
            ],
            [
                0.9998415638020614,
                0.9999038975621116,
                0.999948557786439,
                0.9998601779760731,
                0.9999151889689875,
                0.9999898700114368,
                0.9999756997621986,
                0.9999687980737564,
                0.9999832985701973,
                0.9990889489844661
            ],
            [
                4.539785235268768e-05,
                1.3007133113372426e-05,
                0.0003353500649014583,
                5.829125847900465e-05,
                8.481105132208768e-05,
                NaN,
                0.00017952792239334968,
                0.0001233945453943154,
                0.00017952805145784122,
                8.481105133072609e-05
            ],
            [
                0.9999151889485854,
                0.9999687980849105,
                0.9998601779425829,
                0.9999724642957716,
                0.9991959142447484,
                0.9999485577618328,
                0.9999810748427421,
                0.9997965729560688,
                0.999620015515273,
                0.9997388096597697
            ],
            [
                5.144223813015987e-05,
                3.12019262448351e-05,
                1.8925150493717652e-05,
                2.144494072376136e-05,
                1.4738988999940381e-05,
                1.4738983728784933e-05,
                3.535624225110421e-05,
                5.1442232044492805e-05,
                4.0063677828144015e-05,
                2.430023203298187e-05
            ],
            [
                3.2887506333812835e-06,
                1.5534984952492866e-06,
                2.4300246516082393e-05,
                9.422447062094932e-07,
                1.7603438428188364e-06,
                2.260323489410794e-06,
                9.422444815495185e-07,
                9.422443692390473e-07,
                1.2098662603862553e-06,
                1.7603434231385591e-06
            ],
            [
                1.7603436330091044e-06,
                4.78509563555309e-06,
                1.9947290080343035e-06,
                8.939700566565793e-06,
                1.1478766756214804e-05,
                2.9023119850527192e-06,
                1.7603432133136672e-06,
                6.144177531660828e-06,
                1.1478769493916314e-05,
                4.222832437747125e-06
            ],
            [
                0.9998766053662268,
                0.9999921107374148,
                0.9996646497697713,
                0.9998911031166918,
                0.9999599362982922,
                0.9994472212563114,
                0.998299277891172,
                0.999964643732433,
                0.9996200155591827,
                0.9998911031036649
            ],
            [
                0.9999756997534794,
                0.9995121429402,
                0.999195914240025,
                0.9820137901366065,
                0.990291524422874,
                0.9996200154233301,
                0.9859363760430977,
                0.9875683497413793,
                0.9999485577619428,
                0.9940889313407687
            ],
            [
                0.9997965730995557,
                0.9999546021259709,
                0.9994472214664327,
                0.9998601778593477,
                0.9999038975850683,
                0.9999756997621677,
                0.9999339478395968,
                0.9993736659752047,
                0.9998415637076825,
                0.9999546021368187
            ],
            [
                0.9999038975851193,
                0.9999038976193724,
                0.9997040427956243,
                0.9999339478474694,
                0.9998911030777682,
                0.9998601779426642,
                0.9999339478317593,
                0.9999417087553126,
                0.9994472213334908,
                0.9999724643154692
            ],
            [
                0.9992903296385045,
                0.9999038975860122,
                0.9998204720558904,
                0.9984988179589429,
                0.9997388095977412,
                0.9940889304651574,
                0.9998204719708303,
                0.9999339478317756,
                0.9999832985801649,
                0.9999151889485854
            ],
            [
                0.9999910603036978,
                0.9999938558239365,
                0.9999785550593676,
                0.9999785550593832,
                0.9999885212277747,
                0.9999251537371668,
                0.9999898700066728,
                0.9999546021260055,
                0.9999952149055101,
                0.9999852610182727
            ],
            [
                0.9999417087415112,
                0.9990889489044634,
                0.999860177909463,
                0.9999687980886287,
                0.9997388096594276,
                0.9994472213977107,
                0.9995121427683967,
                0.9999251537727715,
                0.9996646500120887,
                0.9999724643187513
            ],
            [
                0.9998204720135393,
                0.9046505440982948,
                0.9999832985702019,
                0.9999832985702152,
                0.5,
                0.9999599362980677,
                0.9999546021479644,
                0.9997965730899339,
                0.9999417087205882,
                0.9999339478398923
            ],
            [
                0.9997965729299204,
                0.9770226278737641,
                0.9914225142061335,
                0.9999646437324287,
                0.9990889489784262,
                0.9999646437619537,
                0.9968273171177516,
                0.996406397938805,
                0.9980732653158526,
                0.9997388097213952
            ],
            [
                0.9999251537370873,
                0.9999646437366505,
                0.9999810748472499,
                0.9999417087205692,
                0.9998911030519014,
                0.9999945777823233,
                0.9995694428219036,
                0.9999756997621633,
                0.9999038976078997,
                0.9998415637644547
            ],
            [
                0.00013982204050520296,
                1.670142382493073e-05,
                0.0001584361599676224,
                0.00010889690924064936,
                7.48462272100267e-05,
                8.48110413379375e-05,
                1.0129990973503458e-05,
                1.8925152744083297e-05,
                0.00029595720242961995,
                2.4300246523066122e-05
            ],
            [
                1.892515500663531e-05,
                0.9995121427682832,
                0.9999687980849168,
                0.9999038976195017,
                0.9999339478319819,
                0.9999417087205882,
                0.9999546021422301,
                0.9998911031167924,
                0.9999546021313743,
                0.9999546021259533
            ],
            [
                0.9992903296247999,
                0.9989677690808878,
                0.9997388097239563,
                0.9998766054584712,
                0.9991959140632952,
                0.9998415637283715,
                0.9989677687626525,
                0.9149009544128984,
                0.7549149813536518,
                0.7310585727705127
            ],
            [
                1.2098658277264215e-06,
                1.147876949187012e-05,
                5.043474683126242e-07,
                5.715002426343175e-07,
                1.2098658277181688e-06,
                1.7603427934462202e-06,
                3.7266379512518984e-06,
                9.42244481511812e-07,
                1.473898197063434e-05,
                3.288750633139005e-06
            ],
            [
                0.9994472214714816,
                0.9988304897371204,
                0.9999546021153141,
                0.9988304898922845,
                0.9995121428835189,
                0.9964063982614445,
                0.9997388097550692,
                0.999512142821757,
                0.9997040429723724,
                0.9996646497333982
            ],
            [
                0.9999546021421849,
                0.9999417087066693,
                0.999876605454541,
                0.9999251537549172,
                0.9999785550515878,
                0.9999724643121888,
                0.9998911030778981,
                0.9998911031298249,
                0.9999151889893673,
                0.9999151889687554
            ],
            [
                7.889259762106714e-06,
                6.605214457784486e-05,
                3.120190392670705e-05,
                8.481102100559352e-05,
                2.144495352474637e-05,
                1.670142980222277e-05,
                1.6701425823882575e-05,
                4.5397890231261374e-05,
                4.006368738143655e-05,
                4.539786862564012e-05
            ],
            [
                4.006370649866785e-05,
                7.484621828233953e-05,
                1.1478764017428212e-05,
                5.829128636782753e-05,
                6.605213678458984e-05,
                2.43002465110435e-05,
                8.481106149073081e-05,
                1.892515500388139e-05,
                3.120192252437034e-05,
                1.4738983725809062e-05
            ],
            [
                0.9998204719706789,
                0.9999417087416744,
                0.9149009636941993,
                0.9999251537370873,
                0.9999151889485385,
                0.9998911031300673,
                0.9999485577679555,
                0.9999546021422125,
                0.9999339478396218,
                0.9997965730025531
            ],
            [
                2.144495863958007e-05,
                1.0677029973114952e-06,
                1.7603434230729168e-06,
                5.1442207514695673e-05,
                1.0129992187658463e-05,
                5.422220908116881e-06,
                3.535624227734284e-05,
                9.422447062030659e-07,
                1.8925148239772175e-05,
                2.561281905293402e-06
            ],
            [
                0.9999417087275134,
                0.9997965729539054,
                0.9998601778592275,
                0.9998415637642217,
                0.9999038976079185,
                0.999088948882158,
                0.9999485577863694,
                0.9995694429097949,
                0.999738809659496,
                0.9999417087205654
            ],
            [
                0.9998415637455221,
                0.9999852610180288,
                0.9999687980849237,
                0.999738809722216,
                0.9995694429107969,
                0.9999885212291382,
                0.9999417087558263,
                0.9999869928730887,
                0.999876605381109,
                0.9998601778928846
            ],
            [
                0.9968273167039207,
                0.9997965730509908,
                0.9999785550541431,
                0.9953904276496974,
                0.9999038975392132,
                0.9997388096289302,
                0.9990889488776546,
                0.9998415637269378,
                0.9999339478474694,
                0.9997388096931397
            ],
            [
                6.475948753965404e-07,
                1.994729008056074e-06,
                4.222832941142044e-06,
                4.222835458044565e-06,
                1.994730434847717e-06,
                5.715006514105942e-07,
                4.22283294098842e-06,
                3.288748280891699e-06,
                1.5534973841309562e-06,
                6.1441767990323395e-06
            ],
            [
                0.999948557780254,
                0.9999417087344724,
                0.9986749776992475,
                2.4300252313020203e-05,
                0.9998204720785809,
                0.9996646497309396,
                0.999978555056703,
                0.8354835371034368,
                0.9999832985761689,
                0.9998766054398187
            ],
            [
                0.0002305066580679484,
                0.0001795279013588658,
                3.120190388402792e-05,
                7.484625383844588e-05,
                0.0002034269725502577,
                0.00048785717446801817,
                1.6701429805655623e-05,
                0.00043055708261473784,
                NaN,
                0.0002959572387247301
            ],
            [
                1.1478773595009805e-05,
                9.42244256915735e-07,
                1.0129988564578197e-05,
                6.475948753794598e-07,
                4.785093353787868e-06,
                8.939694172656384e-06,
                2.902311293147782e-06,
                1.3007126913346863e-05,
                2.5612819053586272e-06,
                9.422449308420983e-07
            ],
            [
                0.996406397421081,
                0.9999898700053977,
                0.9986749775177783,
                0.9999756997650643,
                0.9964063967249464,
                0.9953904283675966,
                0.9989677689127069,
                0.9999485577618208,
                0.9999485577986026,
                0.9999417087136563
            ],
            [
                0.9996646499700762,
                0.9999910603005002,
                0.9998911030519679,
                0.9997388097531315,
                0.9997040429717438,
                0.9998766054251287,
                0.9999251537460085,
                0.9999785550439222,
                0.9999151889890027,
                0.9997965730750231
            ],
            [
                0.99908894868141,
                0.9986749776915451,
                0.9999151889891291,
                0.99908894902256,
                0.999290329713302,
                0.9999646437619502,
                0.9999485578048636,
                0.9999852610110029,
                0.9995121429422151,
                0.9997694933127764
            ],
            [
                0.9996646498998475,
                0.9999485578047951,
                0.9999921107392983,
                0.9997965729541156,
                0.9996646499741839,
                0.999933947871151,
                0.9999546021151355,
                0.9999599363031632,
                0.9996646500184793,
                0.99997855505926
            ],
            [
                0.0001398220239696496,
                0.0002611904330981433,
                0.00013982202338781298,
                0.00017952794472077916,
                4.5397874048967995e-05,
                0.0001795280512854487,
                5.8291286355952725e-05,
                7.484621831392271e-05,
                4.222833444283541e-06,
                0.0001795280507865552
            ],
            [
                0.9995121428792897,
                0.9998911031037379,
                0.999796573002346,
                0.9999599363173673,
                0.9999930377445803,
                0.9999832985761651,
                0.9990889487676644,
                0.9975273767669861,
                0.9997040429357845,
                0.9999687980812015
            ],
            [
                0.00010889689585966568,
                8.481105143870621e-05,
                0.00012339458962413525,
                2.7535704220525098e-05,
                5.829129329974581e-05,
                6.605216829064421e-05,
                0.00013982205731540148,
                7.484623611103256e-05,
                5.144220137401424e-05,
                1.8925145982866508e-05
            ],
            [
                0.9999599363173673,
                0.9995121427657854,
                0.9999599362982728,
                0.9998204721003886,
                0.9998766054544944,
                0.999820472055611,
                0.9995694430112636,
                0.9984988179378286,
                0.9999810748585273,
                0.999860177975949
            ],
            [
                0.9995694429272177,
                0.9997965730032102,
                0.9996646498931935,
                0.9999810748540177,
                0.9998911030909859,
                0.999373665972873,
                0.9991959139643376,
                0.9992903295413339,
                0.9999687980997966,
                0.9988304895880756
            ],
            [
                0.999948557798614,
                0.9999785550490321,
                0.999964643749356,
                0.9999038975622977,
                0.9999038975735655,
                0.9999910603068946,
                0.9999151889384605,
                0.9995694429612494,
                0.9982992775010042,
                0.9999151889485854
            ],
            [
                0.999876605455182,
                0.9993736657718997,
                0.9999810748472552,
                0.999948557774238,
                0.9998415638038225,
                0.9999599363221586,
                0.9990889486980462,
                0.9999785550516384,
                0.9999646437324866,
                0.9999251537371668
            ],
            [
                0.9999546021314105,
                0.9999756997651623,
                0.9999832985822538,
                0.9999869928670174,
                0.867035758084294,
                0.9998766054549899,
                0.9999910603005029,
                0.962673109309294,
                0.9999485577865359,
                0.9999885212332462
            ],
            [
                1.0129990979694647e-05,
                NaN,
                4.2228319341064674e-06,
                1.670142980687079e-05,
                1.6701421842961097e-05,
                3.120190765307203e-05,
                6.14417753110761e-06,
                2.90231094702116e-06,
                8.939695238439078e-06,
                2.1444940742640888e-05
            ],
            [
                9.610239189829757e-05,
                0.0007096704521440263,
                0.00037998457282274723,
                0.00033535026707982396,
                0.00020342692463945134,
                0.00012339458948050277,
                0.0005527786105217464,
                0.0003799845727453636,
                5.8291251564902706e-05,
                0.00013982212373432013
            ],
            [
                5.422218969769604e-06,
                1.0129994602222992e-05,
                3.5356242266024216e-05,
                1.670141785809127e-05,
                6.144173868983067e-06,
                1.6701419848475466e-05,
                6.144175333289463e-06,
                1.4738985483128763e-05,
                NaN,
                1.0129992186202796e-05
            ],
            [
                2.9023123308072772e-06,
                3.726640171686931e-06,
                2.753570092478113e-05,
                2.4300234934056724e-05,
                6.14417753110761e-06,
                2.1444940741392653e-05,
                6.96225375863827e-06,
                7.889262585082652e-06,
                1.4738987239295859e-05,
                1.6701419848475466e-05
            ],
            [
                0.998299277470368,
                0.991422514380371,
                0.9999417087275205,
                0.9999038975506201,
                0.9991959139598948,
                0.9993736657476342,
                0.9999810748585282,
                0.999796573002346,
                0.9989677689235107,
                0.9999417087066587
            ],
            [
                0.00020342699731660927,
                3.535625491265802e-05,
                0.00026119030924656896,
                1.3007133113703658e-05,
                3.535625490931388e-05,
                2.7535684518791692e-05,
                0.0003353500266649593,
                0.0001584361978348892,
                0.00010889687026705351,
                4.5397874023865346e-05
            ],
            [
                6.144176066521288e-06,
                6.962258739169842e-06,
                1.670142781520948e-05,
                1.3709575336947905e-06,
                2.9023123310290063e-06,
                6.475949525834513e-07,
                6.962253759670401e-06,
                2.1444958637941764e-05,
                1.1478772228528306e-05,
                6.962255419475714e-06
            ],
            [
                0.9999910603004989,
                0.9998911031168733,
                0.998967768816432,
                0.999373665976553,
                0.999512142940427,
                0.2450850131323717,
                0.99989110303972,
                0.9999038975508111,
                0.9997040427950044,
                0.9982992779473056
            ],
            [
                0.9999756997476907,
                0.9999546021476033,
                0.9999756997621694,
                0.9998415638400323,
                0.9999756997592687,
                0.9998911031037506,
                0.9999962733620488,
                0.9999724643056193,
                0.9999852610180298,
                0.9999546021367857
            ],
            [
                0.9999885212264212,
                0.9999756997596227,
                0.9999485577986672,
                0.9999957771650467,
                0.9999970976880167,
                0.9999898700114764,
                0.9999417087137993,
                0.999959936303353,
                0.9999921107374234,
                0.9999810748563294
            ],
            [
                2.2603234894745224e-06,
                2.56128159999123e-06,
                3.2887498494282754e-06,
                4.785095634843714e-06,
                1.3709576970949014e-06,
                1.6701421842140854e-05,
                2.2603234893861252e-06,
                3.288750241374845e-06,
                1.760342583722268e-06,
                3.120190393260949e-05
            ],
            [
                0.999704042794393,
                0.9998601779759103,
                0.9993736658950487,
                0.9989677691633576,
                0.9999832985741741,
                0.9988304895754285,
                0.9999646437535213,
                0.9999921107374146,
                0.9986749776668974,
                0.9995694430120777
            ],
            [
                0.9989677688290366,
                0.9998911030911016,
                0.999891103039086,
                0.9999546021313769,
                0.9998415638412818,
                0.9982992777213878,
                0.9999852610233023,
                0.9989677691058568,
                0.999620015522746,
                0.9992903296621161
            ],
            [
                0.999569442869325,
                0.9999546021421803,
                0.9999417087205692,
                0.9998601778592663,
                0.999447221324744,
                0.9998204720337877,
                0.9996646497705518,
                0.9971990724820622,
                0.999569442910158,
                0.9999546021097171
            ],
            [
                0.999933947863225,
                0.9999756997621677,
                0.9999546021097268,
                0.9999646437619555,
                0.9999785550490444,
                0.9999251537549356,
                0.9998766054398349,
                0.9998204720555091,
                0.9999910603015649,
                0.9999724643121858
            ],
            [
                0.9999546021313577,
                0.9999339478317647,
                0.9999910603015656,
                0.9992903296303314,
                0.9998415638209155,
                0.9999485577679585,
                0.9998911030910144,
                0.9996646498905104,
                0.9999599362935166,
                0.9997388096291354
            ],
            [
                0.999959936303039,
                0.9999687980812332,
                0.9999417087206302,
                0.9999910603004993,
                0.999983298574177,
                0.9999038975966373,
                0.9995694429626398,
                0.9999724643056231,
                0.9999687980774912,
                0.9999417087553203
            ],
            [
                0.00015843627322597727,
                0.0017007221894705111,
                0.00029595723945666,
                6.605216817242619e-05,
                4.5397890257685224e-05,
                5.8291293278964903e-05,
                9.610246058755327e-05,
                0.0001398220569919328,
                0.0003353499895309714,
                0.00033535022406251745
            ],
            [
                0.999860177942768,
                0.9999417087414281,
                0.9997694933727981,
                0.9999151889385346,
                0.9999546021367883,
                0.9998766054692957,
                0.9999687980775083,
                0.9995694429669987,
                0.9999339478790523,
                0.9999852610215523
            ],
            [
                0.999860177942941,
                0.9999546021390794,
                0.9997965730039087,
                0.9999646437329291,
                0.999088948602149,
                0.9997388095975969,
                NaN,
                0.9982992774968535,
                0.9986749773917666,
                0.9998766054547386
            ],
            [
                0.9999339478553472,
                0.9626731097108832,
                0.999664649732325,
                0.9999646437493069,
                0.9997694932297292,
                0.9999417087414095,
                0.9999339478553996,
                0.9953904280428327,
                0.9996200155163675,
                0.9998911030907103
            ],
            [
                4.785095635413826e-06,
                4.006371127619171e-05,
                0.00013982205721164737,
                3.120191508060445e-05,
                8.939695238089467e-06,
                5.144219521911119e-05,
                0.0009110511869831869,
                3.120190392534495e-05,
                1.1478770860481005e-05,
                3.535626756251187e-05
            ],
            [
                2.4300252317086683e-05,
                1.3007125363057018e-05,
                6.144177531532303e-06,
                9.422444815220956e-07,
                1.1478772230762415e-05,
                2.1444940743225995e-05,
                2.4300246519706854e-05,
                3.120192624846737e-05,
                4.539788484641129e-05,
                2.7535700945316292e-05
            ],
            [
                0.9999151889182762,
                0.9953904276240582,
                0.998073265103177,
                0.9997040429006089,
                0.9999687980737786,
                0.9999852610127595,
                0.9997388097850195,
                0.9998415637268547,
                0.9998601779593259,
                0.9996646497704347
            ],
            [
                0.9995121428796303,
                0.9997040428660531,
                0.9998911030778711,
                0.9999546021259581,
                0.9999646437366431,
                0.9993736657457032,
                0.999933947831719,
                0.999972464315468,
                0.9980732654038333,
                0.9999038975621404
            ],
            [
                0.9999930377445815,
                0.9996200155632619,
                0.9999756997621719,
                0.9999599363173711,
                0.9999687980960651,
                0.9999852610145155,
                0.9999339478396766,
                0.9999852610127589,
                0.99994170874838,
                0.999903897608017
            ],
            [
                8.939695237813028e-06,
                2.561282515988704e-06,
                3.726637951079042e-06,
                3.120191136899467e-05,
                3.1201922530272776e-05,
                7.889266347133978e-06,
                3.2887502415243994e-06,
                1.3007128463873485e-05,
                1.3007128463352975e-05,
                3.288750241473551e-06
            ],
            [
                0.9999251537638318,
                0.9998204719922593,
                0.9989677689266319,
                0.9998601779266475,
                0.9994472213930157,
                0.9999785550566989,
                0.9997694932359132,
                0.999447221334938,
                0.9997694932585831,
                0.9924227576045942
            ],
            [
                2.260324028281919e-06,
                1.012999460251781e-05,
                3.120192624960245e-05,
                4.006370650070828e-05,
                4.222833443968609e-06,
                3.5356242272712497e-05,
                4.539789028757721e-05,
                0.00012339457479049144,
                3.7266388396128453e-06,
                1.8925152750176348e-05
            ],
            [
                0.9991959141433592,
                0.9947798739219603,
                0.9990889488716148,
                0.9933071476919181,
                0.9924227599402229,
                0.9999724642990628,
                0.9990889488792971,
                0.9999339478792396,
                0.9975273772384691,
                0.991422514998122
            ],
            [
                0.9991959140442145,
                0.9998766053958636,
                0.9999038976080374,
                0.9999832985821396,
                0.9998911030777563,
                0.9986749775119246,
                0.999373665746104,
                0.9999038975395677,
                0.9998766053809492,
                0.9984988178797207
            ],
            [
                3.2887482811908074e-06,
                1.4738981968060613e-05,
                1.670142184171555e-05,
                6.962258738574625e-06,
                3.726639728184142e-06,
                1.0129993394811673e-05,
                2.260324028281919e-06,
                3.726637951079042e-06,
                1.300712691403299e-05,
                1.8925143726890553e-05
            ],
            [
                0.996406396663253,
                0.99781728396033,
                0.9995121428229208,
                0.9933071492862257,
                0.9997694933394337,
                0.999978555054148,
                0.996827317151624,
                0.9999038975621404,
                0.9982992776668355,
                0.9997388096004772
            ],
            [
                0.999664649890969,
                NaN,
                0.9992903295373299,
                0.9997965729546424,
                0.9997965730512927,
                0.9975273763236427,
                0.9999756997650677,
                0.9998766054696027,
                0.9999485577618628,
                0.9998911030521819
            ],
            [
                0.9999810748562757,
                0.99992515377279,
                0.9997388095976653,
                0.9999546021097218,
                0.9998415637266149,
                0.9999151889485933,
                0.9999930377454105,
                0.9999930377404305,
                0.9999687980812043,
                0.9999898700078147
            ]
        ]
    },
    {
        "q_id": "8841_mmlu_math",
        "cot_ids": [
            0,
            3,
            5,
            7,
            10,
            12,
            13,
            15,
            16,
            18,
            19,
            21,
            22,
            23,
            24,
            27,
            28,
            29,
            30,
            31,
            34,
            37,
            39,
            40,
            42,
            44,
            45,
            48,
            52,
            55,
            56,
            57,
            63,
            64,
            66,
            67,
            68,
            69,
            71,
            73,
            74,
            76,
            77,
            78,
            80,
            82,
            85,
            86,
            87,
            89,
            90,
            91,
            93,
            94,
            95,
            96,
            98,
            99,
            100,
            101,
            104,
            106,
            109,
            110,
            116,
            117,
            122,
            126
        ],
        "rewards": [
            [
                1.670141586907437e-05,
                NaN,
                NaN,
                NaN,
                1.4738978456398127e-05,
                NaN,
                NaN,
                NaN,
                2.5612822106654943e-06,
                NaN
            ],
            [
                0.5312093733737562,
                0.9997694932303799,
                0.999512142950645,
                0.22270014914315836,
                NaN,
                0.9994472214802286,
                0.2018132246607271,
                0.16451646289656316,
                0.4378234991142019,
                NaN
            ],
            [
                0.6224593312018546,
                0.06754669020109236,
                NaN,
                0.9996200154832473,
                0.025957355832061484,
                0.6224593312018546,
                0.2942149597859341,
                0.998073265034449,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                2.2603251057429158e-06,
                4.222833947674739e-06,
                NaN,
                NaN
            ],
            [
                2.1444945840269323e-05,
                0.999981074851779,
                NaN,
                3.535626333281696e-05,
                2.753570420569971e-05,
                NaN,
                NaN,
                3.535624227425594e-05,
                0.00026119027393098386,
                NaN
            ],
            [
                NaN,
                0.00012339453034163755,
                0.00013982205705906782,
                5.144221362768171e-05,
                7.889264462958184e-06,
                NaN,
                1.1478766746777263e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                6.1441746018123775e-06,
                NaN,
                NaN,
                NaN,
                2.7535704224732304e-05,
                1.8925148237775583e-05,
                NaN
            ],
            [
                0.9998415637473915,
                0.5621765008857981,
                0.9999687980849155,
                0.999954602120557,
                0.9991959141641701,
                0.11920292671569667,
                0.9999852610197881,
                0.8807970670261976,
                NaN,
                0.5
            ],
            [
                NaN,
                NaN,
                NaN,
                0.8670357563664174,
                NaN,
                NaN,
                0.9971990733794969,
                NaN,
                NaN,
                5.8291251531398806e-05
            ],
            [
                3.120190391705884e-05,
                NaN,
                NaN,
                NaN,
                3.535626332111248e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                0.00010889693483960863,
                NaN,
                NaN,
                NaN,
                4.539786322642463e-05,
                8.939694170729447e-06,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                0.651354857898194,
                0.40733340004593027,
                0.9997694933139836,
                NaN,
                NaN,
                0.9999599362986582,
                0.99979657307687,
                NaN
            ],
            [
                3.2887506330851655e-06,
                2.1444950968441685e-05,
                7.484625398547097e-05,
                1.4738981972082061e-05,
                9.610240349752414e-05,
                2.5612812944118885e-06,
                NaN,
                5.144221973879711e-05,
                9.610246013728763e-05,
                2.56128159959988e-06
            ],
            [
                1.4738978443234588e-05,
                NaN,
                NaN,
                1.0129987355343409e-05,
                NaN,
                NaN,
                3.2887506315477448e-06,
                4.222833443891798e-06,
                NaN,
                2.4300234925658572e-05
            ],
            [
                1.0,
                NaN,
                0.7057850154599563,
                NaN,
                0.02033235208119306,
                0.06008664554541884,
                NaN,
                0.9996646500134058,
                1.1478764012062179e-05,
                0.13296423504419935
            ],
            [
                1.1478769486170011e-05,
                5.422217029391264e-06,
                9.610239198289712e-05,
                5.422218968083048e-06,
                3.5356254892335935e-05,
                NaN,
                1.1478764018012839e-05,
                0.004609573106660815,
                6.605212085976786e-05,
                NaN
            ],
            [
                0.9999885212265511,
                0.9997040428363282,
                0.9997694931804791,
                0.9988304899098273,
                0.9947798751213484,
                0.9996200154315881,
                0.9998911031167798,
                0.24508501864634827,
                NaN,
                0.9999417087206002
            ],
            [
                NaN,
                4.785095063939907e-06,
                NaN,
                NaN,
                NaN,
                3.7266401663249848e-06,
                NaN,
                NaN,
                4.006368735141308e-05,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                8.481101083448713e-05,
                NaN,
                0.00037998448407478843,
                4.539787942093518e-05,
                NaN
            ],
            [
                3.120191881094355e-05,
                5.144222588771473e-05,
                2.753570420970657e-05,
                2.7535697664698622e-05,
                NaN,
                NaN,
                0.00037998446787950417,
                NaN,
                NaN,
                NaN
            ],
            [
                1.8925152747388e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                8.481103090212316e-05,
                0.00010889693419472267,
                0.00010889693373522161,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                0.9999832985722032,
                0.9999984465018752,
                0.9999151889690362,
                NaN,
                0.00010889689617180939,
                NaN,
                2.7535681233968765e-05,
                NaN
            ],
            [
                4.5397874029150114e-05,
                2.14449535222109e-05,
                6.605213675431452e-05,
                2.1444945840269323e-05,
                1.892515049199645e-05,
                0.00012339461875639704,
                3.53562380286151e-05,
                8.93969629861996e-06,
                NaN,
                NaN
            ],
            [
                NaN,
                8.939700564890901e-06,
                NaN,
                0.00023050668648584945,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                4.539787404186659e-05,
                2.1444953514565465e-05,
                NaN,
                0.00013982202373365993,
                0.37754066879814546,
                NaN,
                9.610240336258435e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                3.1201907643310305e-05,
                NaN,
                5.8291286355952725e-05,
                NaN,
                3.5356238062828204e-05,
                NaN,
                3.535625070315809e-05,
                5.144223199845732e-05,
                NaN,
                4.7850933538313875e-06
            ],
            [
                0.04742587502882471,
                0.9999485577869495,
                NaN,
                0.9999687980775028,
                NaN,
                0.999447221471964,
                0.0009110510879601233,
                0.9999251537853884,
                0.004609571987079774,
                0.9999646437366874
            ],
            [
                0.9999992661791944,
                0.9999967112493667,
                0.9999832985701977,
                0.9999962733593833,
                NaN,
                0.9999921107392986,
                0.9999646437577925,
                0.9953904287308194,
                0.9984988175368316,
                0.9999546021205649
            ],
            [
                7.484624485357914e-05,
                0.00033535006885292113,
                1.4738987240824012e-05,
                1.47389819699641e-05,
                5.829129331543752e-05,
                NaN,
                0.000108896934912495,
                5.8291265441454815e-05,
                NaN,
                NaN
            ],
            [
                0.9998415637655357,
                0.996827317010244,
                0.9999646437371489,
                NaN,
                0.9971990730322287,
                0.40733340004593027,
                0.9998766054698486,
                0.08509904674726423,
                0.9999938558254693,
                0.9997040428710733
            ],
            [
                0.0015011823384021832,
                0.000804086098609902,
                0.0001584362919971074,
                0.0003353500675747937,
                0.0010322312428694739,
                NaN,
                0.00015843621558481343,
                NaN,
                NaN,
                3.535624226936835e-05
            ],
            [
                NaN,
                NaN,
                4.006367772116721e-05,
                NaN,
                9.610243759883879e-05,
                3.5356242264223526e-05,
                NaN,
                3.1201900203407254e-05,
                1.3007128461838766e-05,
                NaN
            ],
            [
                4.222832940834793e-06,
                5.422218966465532e-06,
                0.0031726821731393514,
                1.0129988561648438e-05,
                2.4300252313020203e-05,
                5.829127942361117e-05,
                NaN,
                1.8925150491445666e-05,
                1.4738983725406915e-05,
                5.1442232053101066e-05
            ],
            [
                NaN,
                NaN,
                5.82912515784739e-05,
                NaN,
                1.473898021366358e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                4.78509449293172e-06,
                NaN,
                2.7535697646567574e-05
            ],
            [
                0.9997694932152689,
                0.7981867753392728,
                0.37754066879814546,
                0.32082129433083023,
                0.9999038976102244,
                0.9996646499354791,
                NaN,
                0.012431653665936593,
                0.10669058613457583,
                0.02595735545530691
            ],
            [
                0.9999339478240247,
                0.9999945777792504,
                0.999860177864509,
                0.999959936317381,
                0.9999646437619537,
                0.9999756997593257,
                0.9959298624615375,
                0.9995694428720807,
                0.9999151889591206,
                0.99997569975639
            ],
            [
                NaN,
                0.4073334000459302,
                NaN,
                0.9998911030652539,
                0.9993736658142003,
                0.00037998443118862055,
                0.00037998443575425303,
                0.008577486593774985,
                NaN,
                0.22270013366638425
            ],
            [
                2.430023783309869e-05,
                1.0129994598777299e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                2.4300246523066122e-05,
                NaN
            ],
            [
                0.9989677690134233,
                0.9999852610180298,
                0.999997739676246,
                0.9999785550477314,
                0.9999687980923697,
                0.9999910603026313,
                0.9999756997593156,
                0.9995121427686521,
                0.9999151889689127,
                0.9993736658404696
            ],
            [
                0.00033535018231358767,
                0.00012339461873844297,
                1.8925154994724604e-05,
                4.539785779797843e-05,
                7.484624508282935e-05,
                8.481104135336322e-05,
                NaN,
                NaN,
                NaN,
                0.0002305067133611251
            ],
            [
                5.1442195232584995e-05,
                0.0001398221236224284,
                2.561282821352716e-06,
                NaN,
                NaN,
                1.300712536258383e-05,
                4.0063687367153544e-05,
                1.3007130013572209e-05,
                NaN,
                2.561281905100056e-06
            ],
            [
                0.9999852610198042,
                0.999994577779739,
                0.9999898700066053,
                NaN,
                0.999860177859901,
                0.9999869928761891,
                0.9997965730757956,
                0.9999898700054003,
                0.9999910603005024,
                0.9999687980886642
            ],
            [
                2.7535704221626983e-05,
                1.473898021366358e-05,
                6.605215248979934e-05,
                NaN,
                6.96225458885115e-06,
                0.00037998453531379794,
                2.1444953520182517e-05,
                NaN,
                1.0129990979381404e-05,
                NaN
            ],
            [
                0.9999869928761931,
                0.9999832985721872,
                0.9999785550465105,
                0.99997246431547,
                0.9999977396765115,
                0.9999987901341723,
                0.9999930377412626,
                0.9999938558253997,
                0.9999980052709919,
                0.9999832985721853
            ],
            [
                NaN,
                4.0063692185483734e-05,
                NaN,
                1.0129990979694647e-05,
                2.2603237587774727e-06,
                6.1441746017453204e-06,
                4.785096205077381e-06,
                NaN,
                NaN,
                1.473898197063434e-05
            ],
            [
                NaN,
                NaN,
                4.785095623102023e-06,
                NaN,
                NaN,
                0.00010889696109138246,
                NaN,
                9.610240318988942e-05,
                NaN,
                0.0001233945894966614
            ],
            [
                0.9999251537821451,
                0.9999852610233009,
                0.9999810748585579,
                0.9999967112505485,
                0.999959936303095,
                0.9998415638023795,
                NaN,
                0.9999945777784459,
                0.9465966703884945,
                0.9999987901341723
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                0.2942149721629888,
                0.9991959139721476,
                NaN,
                NaN,
                NaN,
                0.00017952798487777037
            ],
            [
                NaN,
                NaN,
                NaN,
                2.7535681236473055e-05,
                1.1478770859917257e-05,
                5.422220260794484e-06,
                4.222833945815874e-06,
                1.0129994600638342e-05,
                NaN,
                NaN
            ],
            [
                0.9999957771660528,
                0.999988521234621,
                NaN,
                0.9999952149072197,
                0.9998766054264179,
                NaN,
                0.9997040429486148,
                0.9999980052709921,
                0.9999991684719725,
                0.9997388097222843
            ],
            [
                0.00043055708667298853,
                0.9998204720048466,
                NaN,
                NaN,
                NaN,
                0.22270013882530887,
                0.9999151889192678,
                0.7057850340255385,
                NaN,
                0.06754668785475053
            ],
            [
                0.02033235382498389,
                4.222832940500659e-06,
                0.00970847752013139,
                0.22270013366638425,
                0.053403331494692494,
                0.6224593312018545,
                6.144172403470001e-06,
                0.4378234991142019,
                2.26032537546132e-06,
                0.0019267346772073699
            ],
            [
                0.037326885336183654,
                NaN,
                0.7057850340255386,
                NaN,
                0.04742587805815601,
                0.22270014914315833,
                0.9998601779599017,
                NaN,
                NaN,
                NaN
            ],
            [
                8.481106145679419e-05,
                9.610241484924595e-05,
                9.610244882331567e-05,
                NaN,
                1.6701417817990734e-05,
                NaN,
                5.144219523595344e-05,
                NaN,
                NaN,
                6.605217604545803e-05
            ],
            [
                0.9999724642990628,
                0.9999852610180324,
                0.9998204719489235,
                0.9999977396746248,
                0.9999994284993488,
                0.9999910603058321,
                0.9999977396762411,
                0.9997694931767165,
                0.9999151889488507,
                0.9999546021422456
            ],
            [
                0.9999151889286763,
                0.9999646437408835,
                0.9999485577864229,
                0.5621765008857981,
                0.9995121429192249,
                0.9997040429407014,
                0.9999898700078186,
                0.9999546021110093,
                0.06008665332986379,
                0.999704042866966
            ],
            [
                0.9998601779095931,
                0.9997694932613397,
                0.9999852610110255,
                0.5,
                0.9999417087067576,
                0.999964643757835,
                0.9999251537883267,
                0.9999785550465029,
                0.999978555046495,
                0.9999724643023933
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                3.5356259112640515e-05,
                1.0129988563730593e-05,
                3.1201918788014855e-05,
                6.605216030564256e-05,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                0.9999852610163052,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                0.9986749773356929,
                NaN,
                NaN,
                0.9999251537372034,
                0.9999038975738788,
                NaN,
                NaN,
                NaN,
                0.7549149868676283,
                0.9953904281667557
            ],
            [
                0.9995121429268031,
                NaN,
                0.4687906266262437,
                NaN,
                0.5621765008857982,
                0.999088948876807,
                0.9999687980978501,
                0.003172682815240087,
                0.06008664491424768,
                0.02931223075135632
            ],
            [
                0.9999852610197869,
                0.999983298578174,
                0.9999339478397973,
                0.9999485577986821,
                4.785092780203504e-06,
                NaN,
                0.9999724643089193,
                0.999995214904366,
                0.999876605439948,
                0.9999251537728863
            ],
            [
                0.07585818211049715,
                0.012431653128541071,
                NaN,
                NaN,
                0.9971990724235338,
                0.18242551936144574,
                0.9999151889704949,
                NaN,
                0.0,
                4.222835457526079e-06
            ],
            [
                1.6701415862785876e-05,
                1.994730434735237e-06,
                NaN,
                2.43002465110435e-05,
                NaN,
                5.422221550626256e-06,
                3.5356250689524286e-05,
                NaN,
                6.96225873895455e-06,
                NaN
            ],
            [
                NaN,
                2.144495096457996e-05,
                4.222833947498071e-06,
                4.785096775058701e-06,
                1.6701427812931038e-05,
                NaN,
                NaN,
                2.430024649530801e-05,
                NaN,
                1.892514596944115e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.0129987355988324e-05,
                NaN,
                1.0129992186202796e-05
            ],
            [
                5.422218292789686e-06,
                5.422217676797111e-06,
                NaN,
                1.4738987242137685e-05,
                2.4300243614475748e-05,
                8.93969309375927e-06,
                6.605216033495677e-05,
                0.00037998442786112564,
                4.7850967745625735e-06,
                1.2098656831554947e-06
            ]
        ]
    },
    {
        "q_id": "7725_mmlu_math",
        "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,
            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,
            69,
            70,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            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,
            32,
            37,
            66,
            68,
            71,
            82,
            93
        ],
        "rewards": [
            [
                0.9999996072137061,
                0.9999996072137061,
                0.9999994284995529,
                0.9999984465024306,
                0.9999991684719723,
                0.9999994284997574,
                0.9999990577556308,
                0.999998790134028,
                0.9999984465018752,
                0.9999994284994167
            ],
            [
                0.9999996533673375,
                0.9999992661792819,
                0.9999993524053563,
                0.9999991684716749,
                0.9999989322967482,
                0.9999996072138465,
                0.9999989322970028,
                0.999998446502801,
                0.9999996533672549,
                0.9999991684722697
            ],
            [
                0.9999994284995529,
                0.9999996533673788,
                0.9999991684719723,
                0.9999993524053563,
                0.9999986290421395,
                0.9999991684721706,
                0.9999994284996891,
                0.9999992661790196,
                0.9999994284994848,
                0.9999997897567091
            ],
            [
                0.9999995549147359,
                0.999999266178757,
                0.9999994284997573,
                0.9999967112497588,
                0.9999995549151073,
                0.9999997617630332,
                0.9999993524053562,
                0.9999996072137061,
                0.9999990577549568,
                0.9999991684720715
            ],
            [
                0.9999991684720715,
                0.99999893229713,
                0.9999991684718732,
                0.9999996940976636,
                0.9999996072137998,
                0.9999993524054335,
                0.9999994956525317,
                0.9999997897567091,
                0.9999992661792819,
                0.9999995549147359
            ],
            [
                0.9999993524052019,
                0.9999995549150011,
                0.9999994956523514,
                0.9999996072136592,
                0.9999996533673788,
                0.9999982396561572,
                0.9999995549149481,
                0.9999991684717741,
                0.9999996533674202,
                0.9999987901340281
            ],
            [
                7.889265406681968e-06,
                2.2603237589028734e-06,
                1.0129988563343644e-05,
                1.1478768124553928e-05,
                3.2887498494282754e-06,
                6.962258739271155e-06,
                2.2603234895053587e-06,
                2.5612812946681295e-06,
                3.726638839656906e-06,
                4.785094494576774e-06
            ],
            [
                0.9999990577555185,
                0.9999992661786696,
                0.999999554914842,
                0.9999995549150542,
                0.9999997300422547,
                0.9999995549151073,
                0.9999994284994167,
                0.9999994956527721,
                0.9999993524053563,
                0.9999995549147358
            ],
            [
                0.9999996072136592,
                0.9999997617630332,
                0.9999994284994849,
                0.9999967112497586,
                0.999999554914895,
                0.9999991684718733,
                0.9999994956526519,
                0.9999995549148419,
                0.9999994956527721,
                0.9999997617629764
            ],
            [
                0.9999987901337396,
                0.9999987901347491,
                0.9999994956526519,
                0.9999996072136125,
                0.9999995549149481,
                0.9999994284993485,
                0.9999995549150542,
                0.9999991684720715,
                0.9999994956524114,
                0.9999996072139402
            ],
            [
                0.9999992661789321,
                0.9999994956525918,
                0.9999996533674201,
                0.9999996072136592,
                0.999999694097846,
                0.9999996072138465,
                0.9999994956527721,
                0.9999991684717741,
                0.9999990577549568,
                0.9999993524049703
            ],
            [
                0.9999995549151073,
                0.9999989322967482,
                0.9999996072139402,
                0.9999994284992805,
                0.9999993524049703,
                0.9999996533672136,
                0.9999996072138465,
                0.9999996940976272,
                0.9999991684716749,
                0.9999994284994167
            ],
            [
                0.9999997300421903,
                0.9999994284992805,
                0.9999986290432835,
                0.999999352404893,
                0.9999994284996891,
                0.9999991684719725,
                0.999999653367379,
                0.9999996072139402,
                0.999999495652712,
                0.9999996533672135
            ],
            [
                0.9999989322966208,
                0.9999994956525317,
                0.9999996533672136,
                0.9999986290421394,
                0.999999730042126,
                0.9999997300422869,
                0.9999996072137529,
                0.9999994956527721,
                0.9999992661791071,
                0.9999994284994848
            ],
            [
                0.9999993524054335,
                0.9999991684718733,
                0.9999996072138934,
                0.9999993524053563,
                0.9999982396561572,
                0.9999993524049702,
                0.9999986290429566,
                0.9999991684720715,
                0.9999997300421581,
                0.9999993524054335
            ],
            [
                0.9999990577549569,
                0.9999990577549568,
                0.9999994284992805,
                0.99999893229713,
                0.9999987901338839,
                0.9999996940977366,
                0.9999994956524115,
                0.9999994284992804,
                0.999999168471675,
                0.999999352405279
            ],
            [
                0.9999996533675028,
                0.9999998874647976,
                0.999999266179107,
                0.9999993524050474,
                0.9999996072137529,
                0.9999989322967482,
                0.9999991684717742,
                0.9999996533675028,
                0.9999986290421395,
                0.9999992661791944
            ],
            [
                0.9999990577552939,
                0.999999057755743,
                0.999999266178757,
                0.9999991684719723,
                0.9999997300421581,
                0.999999694097773,
                0.9999992661792819,
                0.9999989322968754,
                0.999998932296621,
                0.9999994956527722
            ],
            [
                0.999999168471675,
                0.9999989322972573,
                0.9999994956527721,
                0.9999996072137529,
                0.999999653367379,
                0.9999995549147358,
                0.9999996533673375,
                0.9999992661792819,
                0.9999993524053563,
                0.999998790134028
            ],
            [
                0.9999993524049703,
                0.9999986290429566,
                0.9999992661787571,
                0.9999996940976636,
                0.9999994956524716,
                0.9999994956525918,
                0.9999989322968754,
                0.9999992661788445,
                0.9999996072137061,
                0.9999994956527721
            ],
            [
                0.9999995549151073,
                0.9999996940977731,
                0.9999995549149481,
                0.9999995549151073,
                0.9999996072136125,
                0.9999994284994848,
                0.9999995549147359,
                0.9999992661791944,
                0.9999992661789321,
                0.9999996940977001
            ],
            [
                0.9999996940976636,
                0.9999994284994167,
                0.9999990577550691,
                0.9999994956527121,
                0.9999996940978461,
                0.9999995549147889,
                0.9999993524049703,
                0.9999996072136592,
                0.9999991684722697,
                0.9999998362623528
            ],
            [
                0.9999996072137998,
                0.9999992661789321,
                0.999999554914842,
                0.9999993524051246,
                0.9999994956523512,
                0.9999998874647842,
                0.999998629042303,
                0.9999993524052018,
                0.9999994284994167,
                0.9999989322975119
            ],
            [
                0.9999987901343166,
                0.9999991684720715,
                0.9999996533672962,
                0.9999996072136592,
                0.9999957771675624,
                0.9999996533672549,
                0.9999992661786695,
                0.9999984465016899,
                0.999999855502048,
                0.9999996533675028
            ],
            [
                0.9999994956527721,
                0.9999982396567868,
                0.9999997617630049,
                0.9999990577555185,
                0.9999997617631469,
                0.9999994284993485,
                0.9999991684720715,
                0.999999352404893,
                0.9999990577549568,
                0.9999994284994167
            ],
            [
                0.9999991684721706,
                0.9999991684718732,
                0.999999495652652,
                0.9999994284995529,
                0.9999996072137061,
                0.999999266179107,
                0.9999984465018751,
                0.9999996072139402,
                0.9999991684718732,
                0.999998005269803
            ],
            [
                0.9999996072136592,
                0.9999996940977001,
                0.9999994956526519,
                0.9999992661791944,
                0.9999994284997573,
                0.9999997300422869,
                0.9999994284996891,
                0.999999266178932,
                0.9999991684722697,
                0.9999986290432835
            ],
            [
                0.9999997617629764,
                0.9999997300422225,
                0.9999995549148419,
                0.9999996533675028,
                0.9999998144608319,
                0.9999996072139402,
                0.9999996940977002,
                0.9999994284997573,
                0.9999996533674614,
                0.999999789756684
            ],
            [
                0.9999994284997573,
                0.9999994956525317,
                0.9999997300420937,
                0.9999986290424664,
                0.9999987901344608,
                0.999998790134605,
                0.999999266178932,
                0.9999994284994849,
                0.9999989322975119,
                0.9999996072136125
            ],
            [
                0.9999994284996211,
                0.9999994956527722,
                0.9999996940976271,
                0.9999992661787571,
                0.9999994956524716,
                0.999999266179107,
                0.9999996533672135,
                0.9999994956524114,
                0.9999995549151073,
                0.9999995549147359
            ],
            [
                0.9999987901344607,
                0.9999991684721706,
                0.9999984465024306,
                0.9999993524054335,
                0.9999990577557432,
                0.9999990577555185,
                0.9999995549148419,
                0.9999994956525918,
                0.999995214904365,
                0.999998790134028
            ],
            [
                0.9999993524054334,
                0.9999992661790196,
                0.9999995549150011,
                0.9999992661790195,
                0.9999994956527121,
                0.9999993524052789,
                0.9999992661792819,
                0.9999991684718732,
                0.9999986290424663,
                0.9999994956524716
            ],
            [
                0.9999996940978825,
                0.9999997300420937,
                0.9999993524049703,
                0.9999994284993485,
                0.9999993524052019,
                0.9999996940978095,
                0.9999994284993485,
                0.9999995549151073,
                0.9999994284996891,
                0.9999996533673788
            ],
            [
                0.9999987901337396,
                0.9999984465018751,
                0.9999993524050474,
                0.9999986290424664,
                0.999999352404893,
                0.999998790134605,
                0.9999994956524716,
                0.9999993524052019,
                0.9999993524054334,
                0.9999996072139402
            ],
            [
                0.9999996533672962,
                0.9999994956525317,
                0.9999998362623332,
                0.9999991684722697,
                0.9999989322970027,
                0.9999990577556308,
                0.9999996940976636,
                0.9999995549151073,
                0.999999814460876,
                0.9999991684717741
            ],
            [
                0.9999995549147889,
                0.9999994284997573,
                0.9999987901338838,
                0.9999992661790196,
                0.9999995549147359,
                0.9999995549151073,
                0.9999994956526519,
                0.9999992661788445,
                0.9999995549151073,
                0.9999986290423029
            ],
            [
                0.999999352405279,
                0.9999994284992805,
                0.9999987901340281,
                0.9999993524051246,
                0.9999995549150542,
                0.9999989322972572,
                0.9999993524051246,
                0.9999995549150542,
                0.9999994284993485,
                0.9999995549147359
            ],
            [
                0.9999994284994167,
                0.9999993524050474,
                0.9999995549147889,
                0.9999999123575568,
                0.9999992661790196,
                0.9999996533674614,
                0.9999994956525317,
                0.9999992661789321,
                0.9999993524052018,
                0.9999996533674615
            ],
            [
                0.9999994284994167,
                0.9999992661787571,
                0.9999990577552939,
                0.9999995549150011,
                0.9999980052695652,
                0.9999994956524716,
                0.999999266179107,
                0.9999992661788445,
                0.9999993524049702,
                0.9999994284996893
            ],
            [
                0.9999995549151073,
                0.9999995549148419,
                0.9999991684720715,
                0.9999987901347492,
                0.9999996072137061,
                0.9999994956523514,
                0.9999996072136592,
                0.999999057755743,
                0.9999990577552937,
                0.9999989322972573
            ],
            [
                0.9999998555020135,
                0.9999995549147359,
                0.9999998724808963,
                0.9999993524052018,
                0.9999995549147359,
                0.9999991684715758,
                0.9999994284993485,
                0.999999694097773,
                0.9999994956524114,
                0.9999994284994848
            ],
            [
                0.9999989322968754,
                0.9999998362623332,
                0.9999996533672135,
                0.9999986290427931,
                0.9999994956527121,
                0.9999996072137061,
                0.9999998362622943,
                0.9999992661790195,
                0.9999991684718732,
                0.999999266178932
            ],
            [
                0.9999998724809267,
                0.9999992661791944,
                0.9999997300421903,
                0.999999887464905,
                0.9999994284996891,
                0.9999994284992805,
                0.9999989322975118,
                0.9999989322973846,
                0.9999996072138934,
                0.9999996533672549
            ],
            [
                0.9999995549150011,
                0.9999994284993485,
                0.999999554914895,
                0.9999995549151072,
                0.9999993524049702,
                0.9999996072138934,
                0.9999994284997573,
                0.9999993524051246,
                0.9999993524053562,
                0.9999998144609423
            ],
            [
                0.9999994284996211,
                0.9999991684720715,
                0.9999996533673375,
                0.9999994956525918,
                0.999999730042126,
                0.999999653367379,
                0.9999996072136125,
                0.9999992661791071,
                0.9999993524051246,
                0.9999995549150011
            ],
            [
                0.9999987901346051,
                0.9999991684716749,
                0.9999994284994167,
                0.9999994956527721,
                0.9999994956525917,
                0.9999987901341723,
                0.9999996533672962,
                0.9999986290424664,
                0.9999994956523512,
                0.9999989322966208
            ],
            [
                0.9999991684718732,
                0.9999991684720715,
                0.9999992661790196,
                0.9999997617631752,
                0.9999991684720715,
                0.999999694097846,
                0.9999997300421581,
                0.9999995549150011,
                0.999999495652712,
                0.9999996533672135
            ],
            [
                0.9999997897565838,
                0.9999993524052019,
                0.9999996072138465,
                0.9999996072139402,
                0.9999998362623332,
                0.9999998362622943,
                0.9999993524053563,
                0.9999992661790195,
                0.9999994956525918,
                0.9999994284993485
            ],
            [
                0.9999992661786695,
                0.999999352404893,
                0.9999989322970027,
                0.9999997897567341,
                0.9999991684717741,
                0.9999996072138465,
                0.9999990577550693,
                0.999999352405279,
                0.9999994284992805,
                0.9999995549147359
            ],
            [
                0.9999993524051246,
                0.9999996072136592,
                0.9999990577557432,
                0.9999994284994168,
                0.9999996072136592,
                0.9999993524054335,
                0.9999994956525918,
                0.9999996072136125,
                0.9999986290426297,
                0.9999993524052019
            ],
            [
                0.9999991684718732,
                0.9999995549148419,
                0.999999266178757,
                0.9999986290426298,
                0.9999994284995529,
                0.9999998144608319,
                0.9999992661791944,
                0.999999266179107,
                0.999999266179107,
                0.9999990577556308
            ],
            [
                0.999999495652652,
                0.9999997300421903,
                0.9999987901337396,
                0.9999994956527722,
                0.9999996072137061,
                0.999999554914789,
                0.9999996533674201,
                0.9999992661789321,
                0.9999996940977001,
                0.9999997300420937
            ],
            [
                0.9999990577550691,
                0.9999995549150542,
                0.9999996533672549,
                0.9999994956525918,
                0.9999995549149481,
                0.9999996533673375,
                0.9999996940977731,
                0.9999996072137529,
                0.9999991684719723,
                0.9999992661788446
            ],
            [
                0.9999995549151073,
                0.9999992661789321,
                0.9999987901337396,
                0.999999168471675,
                0.9999996940976272,
                0.9999989322967482,
                0.9999992661788446,
                0.9999989322975119,
                0.9999996940976272,
                0.9999994956526519
            ],
            [
                0.9999990577555185,
                0.9999992661791945,
                0.9999995549151073,
                0.9999994956527121,
                0.9999996533674202,
                0.9999987901338838,
                0.9999993524052019,
                0.9999996072137998,
                0.9999993524052019,
                0.9999996533673788
            ],
            [
                0.999998005270992,
                0.9999993524051246,
                0.9999993524053562,
                0.9999992661786696,
                0.9999997617631752,
                0.9999994956526519,
                0.9999996072139402,
                0.9999995549150011,
                0.9999993524049703,
                0.9999996533674202
            ],
            [
                0.9999994284996211,
                0.9999996072137529,
                0.9999997617631469,
                0.999999554914789,
                0.9999996533673375,
                0.999999554914895,
                0.9999995549150542,
                0.9999994284992805,
                0.9999990577551815,
                0.999999554914842
            ],
            [
                0.9999995549148419,
                0.9999993524051246,
                0.9999994956526519,
                0.9999996072136125,
                0.9999994956527121,
                0.9999994284994849,
                0.9999994956525317,
                0.9999996072137998,
                0.9999994284994167,
                0.999999554914895
            ],
            [
                0.9999957771650457,
                0.9999997617630332,
                0.9999996072138465,
                0.9999994956527121,
                0.9999996533673375,
                0.999999057755743,
                0.999999352405279,
                0.9999994956526519,
                0.999998790134028,
                0.999999266178932
            ],
            [
                0.9999995549150541,
                0.9999995549149481,
                0.9999986290424664,
                0.9999987901341725,
                0.9999993524054334,
                0.9999992661790195,
                0.9999997617630899,
                0.9999996533674614,
                0.9999996533672549,
                0.9999992661787571
            ],
            [
                0.9999989322967481,
                0.9999974387177895,
                0.9999997897565587,
                0.999999352405279,
                0.9999996072137998,
                0.9999993524053562,
                0.9999991684722697,
                0.9999994956523514,
                0.9999992661786696,
                0.9999992661789321
            ],
            [
                0.9999996533672136,
                0.9999996072139402,
                0.9999994284992805,
                0.9999996533674614,
                0.9999998724809875,
                0.9999996940976271,
                0.9999994956525918,
                0.999999554914789,
                0.9999991684718733,
                0.9999996533672549
            ],
            [
                0.999999730042126,
                0.9999993524051246,
                0.9999996533672962,
                0.999998932296621,
                0.9999994956524716,
                0.9999991684719723,
                0.9999994956527721,
                0.999999266178932,
                0.9999995549150542,
                0.9999989322966208
            ],
            [
                0.9999998144608981,
                0.999998629042303,
                0.9999990577551815,
                0.9999998362622357,
                0.9999992661791945,
                0.9999992661787571,
                0.9999992661792819,
                0.9999998144608538,
                0.9999996072137998,
                0.9999994284992805
            ],
            [
                0.9999994284993485,
                0.9999996072138934,
                0.9999994284996211,
                0.9999994284994849,
                0.9999992661792819,
                0.9999994284994848,
                0.9999996533674614,
                0.9999995549147359,
                0.9999995549147889,
                0.9999982396561572
            ],
            [
                0.999999694097846,
                0.9999997617631183,
                0.9999992661790195,
                0.9999987901343165,
                0.999999730042319,
                0.9999995549147359,
                0.9999992661792819,
                0.9999986290427932,
                0.99999893229713,
                0.99999862904312
            ],
            [
                0.9999993524050474,
                0.9999991684720715,
                0.9999994956524715,
                0.9999994956524114,
                0.9999995549147359,
                0.9999994284994848,
                0.9999994956524114,
                0.9999993524051246,
                0.999999814460854,
                0.9999982396569966
            ],
            [
                0.9999994284994167,
                0.99999893229713,
                0.9999993524054335,
                0.9999993524051246,
                0.9999994284996893,
                0.9999996533674201,
                0.9999996533673375,
                0.9999995549151072,
                0.9999991684721706,
                0.9999994284996211
            ],
            [
                0.9999982396559474,
                0.999999266178932,
                0.9999982396574163,
                0.9999996940978095,
                0.9999996072137998,
                0.999999352404893,
                0.9999992661790195,
                0.9999996072138934,
                0.9999996533675028,
                0.9999996072137529
            ],
            [
                0.999999352404893,
                0.9999977396757022,
                0.9999993524054335,
                0.9999994284996211,
                0.9999991684718732,
                0.999998790134028,
                0.999999428499553,
                0.9999993524052018,
                0.999999057755743,
                0.9999987901343166
            ],
            [
                0.9999997300422225,
                0.9999992661787571,
                0.9999993524049702,
                0.9999998144609424,
                0.9999993524051246,
                0.9999996072136592,
                0.9999994284994167,
                0.9999995549150011,
                0.9999996533673375,
                0.9999993524052018
            ],
            [
                0.9999995549150011,
                0.9999993524049703,
                0.9999993524054335,
                0.99999893229713,
                0.999999554914895,
                0.9999991684717741,
                0.9999987901347491,
                0.9999994284995529,
                0.999999554914895,
                0.9999994284995529
            ],
            [
                0.9999989322966208,
                0.9999990577555185,
                0.9999994284993485,
                0.9999994284995529,
                0.9999997617630332,
                0.9999990577550693,
                0.9999995549151072,
                0.9999994956525918,
                0.9999994284996893,
                0.999999266178757
            ],
            [
                0.9999996533675028,
                0.9999996072136125,
                0.9999994956524114,
                0.999999554914895,
                0.9999989322966208,
                0.9999994284996891,
                0.9999992661792819,
                0.9999996533675028,
                0.9999989322967481,
                0.999999352405279
            ],
            [
                0.9999993524053562,
                0.9999991684721706,
                0.9999992661791944,
                0.9999997300421903,
                0.999999554914895,
                0.9999994284992805,
                0.9999991684722697,
                0.9999991684721706,
                0.9999994956525317,
                0.9999996940978095
            ],
            [
                0.9999994956524716,
                0.9999997617630332,
                0.9999991684717742,
                0.9999991684719723,
                0.9999996533674202,
                0.9999994284997574,
                0.9999977396746245,
                0.9999994956524716,
                0.9999995549150011,
                0.9999992661788445
            ],
            [
                0.9999994956525318,
                0.9999994956524716,
                0.999999554914842,
                0.999999554914895,
                0.9999987901343165,
                0.9999996072139402,
                0.999999168471675,
                0.9999996072137529,
                0.9999994956524716,
                0.9999995549147358
            ],
            [
                0.9999996940976272,
                0.9999997617630332,
                0.9999997617630332,
                0.9999991684718733,
                0.999999730042319,
                0.9999991684719723,
                0.9999989322968754,
                0.9999994284995529,
                0.9999993524049703,
                0.9999991684720715
            ],
            [
                0.9999991684719723,
                0.9999991684720715,
                0.9999993524049702,
                0.999999352404893,
                0.9999996533672549,
                0.9999996072137529,
                0.9999997300422225,
                0.9999990577550691,
                0.9999991684717741,
                0.9999996533672549
            ],
            [
                0.9999991684718732,
                0.9999995549147889,
                0.9999992661790195,
                0.9999992661790196,
                0.9999957771645426,
                0.999999554914895,
                0.9999993524053562,
                0.9999980052707541,
                0.9999990577552939,
                0.999999554914789
            ],
            [
                0.9999998874647976,
                0.9999996533674201,
                0.999998790134028,
                0.9999987901346049,
                0.9999994284995529,
                0.9999995549147358,
                0.9999986290431201,
                0.9999994284994167,
                0.9999990577550693,
                0.9999957771650453
            ],
            [
                0.9999992661792819,
                0.9999994956527721,
                0.9999992661792819,
                0.9999996533672135,
                0.9999990577556307,
                0.9999994284993485,
                0.9999994284993485,
                0.9999996940978095,
                0.9999996940977002,
                0.9999997897565838
            ],
            [
                0.9999993524053562,
                0.9999996533673375,
                0.9999982396559474,
                0.9999996533673375,
                0.999998005269803,
                0.9999994284995529,
                0.9999989322975119,
                0.9999994284996893,
                0.9999991684722697,
                0.999999495652712
            ],
            [
                0.9999996940978825,
                0.999999266179107,
                0.9999993524051246,
                0.9999982396574163,
                0.9999996072136125,
                0.9999996533674202,
                0.9999991684717742,
                0.9999997300422547,
                0.9999995549151073,
                0.9999995549150011
            ],
            [
                0.9999994956527721,
                0.9999995549150542,
                0.999999730042126,
                0.9999990577552939,
                0.9999994284996891,
                0.9999996072136592,
                0.9999996072136125,
                0.9999993524053562,
                0.9999990577549569,
                0.9999993524053562
            ],
            [
                0.9999989322970028,
                0.9999991684721706,
                0.9999995549148419,
                0.999999352405279,
                0.9999994956524114,
                0.9999993524050474,
                0.9999996072137529,
                0.9999994284996891,
                0.9999995549150542,
                0.9999994284993485
            ],
            [
                0.9999991684720715,
                0.9999996940976636,
                0.9999997300422225,
                0.9999991684719723,
                0.9999993524049702,
                0.9999989322975119,
                0.9999996072138465,
                0.9999996940977002,
                0.9999997300420937,
                0.9999995549147359
            ],
            [
                0.9999996940978461,
                0.9999992661787571,
                0.9999993524054335,
                0.9999990577549569,
                0.999999554914895,
                0.9999996072139402,
                0.9999994956526519,
                0.9999995549147359,
                0.9999994284996211,
                0.9999989322973846
            ],
            [
                0.999999495652712,
                0.9999997617631468,
                0.9999991684715759,
                0.9999996940977366,
                0.9999996533672135,
                0.9999994956527721,
                0.9999993524051246,
                0.9999997897567341,
                0.9999994284996891,
                0.9999992661791944
            ],
            [
                0.9999993524054334,
                0.999999428499553,
                0.9999996533672135,
                0.9999993524054335,
                0.9999994284993485,
                0.999999352404893,
                0.9999994284994167,
                0.9999996533675028,
                0.9999994956526519,
                0.9999996533672135
            ],
            [
                0.9999990577557432,
                0.9999997300422225,
                0.9999996533675028,
                0.9999995549147359,
                0.9999995549150011,
                0.9999994956523514,
                0.9999994284992805,
                0.9999995549150542,
                0.9999994284994167,
                0.9999996072136125
            ],
            [
                0.9999995549149481,
                0.9999987901338839,
                0.999999554914895,
                0.9999996940978095,
                0.999999694097846,
                0.9999996072137998,
                0.9999994284993485,
                0.9999996533672549,
                0.9999996533673375,
                0.9999996533672549
            ],
            [
                0.9999996072137998,
                0.9999992661791071,
                0.9999999123575359,
                0.9999995549147889,
                0.999999653367379,
                0.9999993524054334,
                0.9999986290423029,
                0.9999996533674614,
                0.9999995549149481,
                0.9999989322975118
            ],
            [
                0.999999694097846,
                0.9999994284996211,
                0.999999352405279,
                0.9999994956527721,
                0.9999996940978095,
                0.9999991684718732,
                0.9999997617631468,
                0.999999554914895,
                0.9999994956527722,
                0.9999993524051246
            ],
            [
                0.9999993524053563,
                0.9999992661787571,
                0.9999996533673375,
                0.9999986290431201,
                0.9999996072137529,
                0.9999990577549569,
                0.9999994284996211,
                0.9999990577552939,
                0.9999993524054335,
                0.9999997300422225
            ],
            [
                0.9999990577551815,
                0.9999994956527721,
                0.9999992661791945,
                0.999999554914895,
                0.9999992661791071,
                0.999999495652652,
                0.9999994284993485,
                0.9999987901341723,
                0.9999996533675028,
                0.9999993524050474
            ],
            [
                0.9999992661786696,
                0.9999989322972572,
                0.9999992661790195,
                0.999998629042303,
                0.9999996533673375,
                0.9999996072137998,
                0.9999993524049703,
                0.9999993524054335,
                0.9999991684717741,
                0.9999993524049702
            ],
            [
                0.9999995549151073,
                0.9999995549147359,
                0.9999992661788445,
                0.999999168471675,
                0.9999994284996891,
                0.999999168471675,
                0.9999998874648781,
                0.9999993524050474,
                0.9999987901337396,
                0.9999996940977366
            ],
            [
                0.9999994956523514,
                0.9999990577554062,
                0.9999990577552937,
                0.9999996072137998,
                0.9999990577551815,
                0.9999986290426297,
                0.9999994956525917,
                0.9999990577551814,
                0.9999980052702786,
                0.9999993524051246
            ],
            [
                0.9999991684717742,
                0.9999992661790195,
                0.9999995549151072,
                0.9999992661788446,
                0.9999996533672962,
                0.9999997617630332,
                0.9999996072139402,
                0.9999991684717742,
                0.9999993524053563,
                0.999999352405279
            ],
            [
                0.9999989322975118,
                0.9999994956524716,
                0.9999996533675028,
                0.9999994284997574,
                0.9999998144608098,
                0.9999996533673375,
                0.9999986290431201,
                0.9999996072136125,
                0.9999991684721706,
                0.9999996533672962
            ],
            [
                0.9999994956524716,
                0.999999352404893,
                0.9999989322966208,
                0.9999991684722697,
                0.9999996072139402,
                0.9999994284993485,
                0.9999996072136592,
                0.9999994284994167,
                0.999999266179107,
                0.9999994956525918
            ],
            [
                0.9999990577555185,
                0.999998629042303,
                0.9999995549147359,
                0.9999994956524715,
                0.9999993524053563,
                0.999999730042319,
                0.9999994956524716,
                0.9999996072136592,
                0.9999994956527121,
                0.9999989322968754
            ],
            [
                0.999999266179107,
                0.9999974387168735,
                0.9999997300421581,
                0.9999993524049703,
                0.9999992661790196,
                0.9999993524049702,
                0.9999995549149481,
                0.9999993524051246,
                0.9999996940978825,
                0.9999993524054335
            ],
            [
                0.9999991684722698,
                0.9999997300421903,
                0.999998629042303,
                0.9999989322968754,
                0.9999986290432835,
                0.999999266179107,
                0.9999993524051246,
                0.9999993524053562,
                0.9999991684722698,
                0.9999980052695655
            ],
            [
                0.9999996072136592,
                0.9999995549150542,
                0.9999994956523514,
                0.9999984465024306,
                0.9999989322975119,
                0.9999993524049703,
                0.999999495652652,
                0.9999989322967482,
                0.9999991684715759,
                0.9999995549147889
            ],
            [
                0.9999993524050474,
                0.9999994284992805,
                0.999999352405279,
                0.9999994956523514,
                0.9999990577557432,
                0.9999996940978095,
                0.9999977396762411,
                0.999999352405279,
                0.9999994284996211,
                0.9999996533674614
            ],
            [
                0.9999995549150542,
                0.999999554914842,
                0.9999991684717742,
                0.9999996533672962,
                0.9999986290432835,
                0.999999266179282,
                0.999999495652712,
                0.9999996072136592,
                0.9999994956525917,
                0.9999993524053562
            ],
            [
                0.9999994956525918,
                0.9999992661788446,
                0.9999994956524114,
                0.9999994956523514,
                0.9999993524052019,
                0.9999994956527721,
                0.9999996072139402,
                0.9999994284996891,
                0.9999991684720715,
                0.9999991684720715
            ],
            [
                0.9999995549147359,
                0.9999999006880668,
                0.9999996072137061,
                0.9999995549148419,
                0.9999995549147889,
                0.9999993524053563,
                0.9999996072138934,
                0.9999986290429567,
                0.999999694097846,
                0.9999994284994167
            ],
            [
                0.999999266178932,
                0.9999990577550691,
                0.9999986290429567,
                0.9999987901341724,
                0.9999992661786695,
                0.9999989322970027,
                0.9999989322966208,
                0.9999991684719723,
                0.9999995549151073,
                0.9999996533673375
            ],
            [
                0.9999990577554061,
                0.9999986290431201,
                0.9999982396569966,
                0.9999984465016899,
                0.9999998362623332,
                0.999998629042303,
                0.999998932296621,
                0.9999986290432834,
                0.9999994956524716,
                0.9999994956524716
            ],
            [
                0.9999996072136592,
                0.9999994956523514,
                0.9999994956525317,
                0.9999991684715759,
                0.999999653367379,
                0.999999266178757,
                0.9999996533672136,
                0.9999996533672136,
                0.9999996940977002,
                0.9999994284992805
            ],
            [
                0.9999997300421903,
                0.9999996533675028,
                0.9999996533675028,
                0.9999996072136125,
                0.9999994956527721,
                0.9999996940978095,
                0.9999998724808963,
                0.9999994284996891,
                0.9999995549147889,
                0.9999994284994849
            ],
            [
                0.9999993524049702,
                0.999999694097846,
                0.9999996072136125,
                0.9999994956525317,
                0.9999996940976636,
                0.9999996533673375,
                0.999999266178932,
                0.999999168471675,
                0.9999996533672135,
                0.9999992661788446
            ],
            [
                0.9999996533672135,
                0.9999994956525317,
                0.999999266178932,
                0.9999993524054334,
                0.9999996072137998,
                0.9999994956524716,
                0.9999997300420937,
                0.999999352405279,
                0.9999991684715759,
                0.9999999006880668
            ],
            [
                0.9999982396561572,
                0.9999987901341723,
                0.9999996533672136,
                0.999975699759271,
                0.9999991684716749,
                0.9999987901343166,
                0.999999554914789,
                0.9999992661788445,
                0.9999994284995529,
                0.9999980052693275
            ],
            [
                0.9999984465024306,
                0.9999991684718732,
                0.999999495652712,
                0.9999995549150542,
                0.9999991684715758,
                0.999999266178757,
                0.9999997617631752,
                0.9999996533672962,
                0.9999996072136125,
                0.9999984465024307
            ],
            [
                0.9999994284996891,
                0.999999887464811,
                0.9999996940977366,
                0.9999989322966208,
                0.9999977396762412,
                0.9999994284997573,
                0.9999999317439872,
                0.9999990577555185,
                0.9999996533673788,
                0.9999990577549568
            ],
            [
                0.9999994956527721,
                0.9999996533674201,
                0.9999987901337396,
                0.9999996940977731,
                0.9999995549147359,
                0.9999998362623528,
                0.9999995549149481,
                0.9999995549150011,
                0.9999986290432835,
                0.9999992661789321
            ],
            [
                0.9999996533672136,
                0.999999730042126,
                0.9999996072139402,
                0.999999352404893,
                0.9999995549148419,
                0.9999998144608538,
                0.9999997897566089,
                0.9999984465022455,
                0.999999730042126,
                0.9999994284996211
            ],
            [
                0.9999996072136592,
                0.9999996072137998,
                0.9999992661791944,
                0.9999996533674615,
                0.9999994284993485,
                0.9999991684722697,
                0.9999997617630332,
                0.9999994284997573,
                0.9999986290432834,
                0.9999994956526519
            ],
            [
                0.9999993524054334,
                0.9999998555019962,
                0.9999990577552939,
                0.9999997617631752,
                0.9999990577556308,
                0.9999993524051246,
                0.9999997300422225,
                0.9999990577550691,
                0.9999990577556308,
                0.9999986290426297
            ],
            [
                0.999999057755743,
                0.9999994956523512,
                0.9999995549150542,
                0.9999992661788446,
                0.9999996940978461,
                0.9999992661791945,
                0.9999992661786695,
                0.9999990577552939,
                0.9999996940978825,
                0.9999992661790196
            ],
            [
                0.9999996940977002,
                0.999999730042319,
                0.9999989322967482,
                0.9999996072139402,
                0.9999992661789321,
                0.999999653367379,
                0.9999996533672549,
                0.999999554914789,
                0.9999994956527121,
                0.999998790134028
            ],
            [
                0.9999994956525317,
                0.9999995549151073,
                0.9999994284994849,
                0.9999997300420937,
                0.9999997300422225,
                0.999999789756684,
                0.9999991684719725,
                0.9999994956527121,
                0.9999996940976636,
                0.9999994284997573
            ],
            [
                0.9999996533674615,
                0.9999993524054335,
                0.9999989322973846,
                0.999999694097846,
                0.9999995549150011,
                0.9999994284996891,
                0.9999990577552939,
                0.999999554914895,
                0.9999987901346049,
                0.9999993524052019
            ],
            [
                0.9999996072138465,
                0.999999789756634,
                0.999999730042126,
                0.999999694097846,
                0.9999996533672549,
                0.9999998144609203,
                0.9999990577552937,
                0.9999996072137061,
                0.9999992661787571,
                0.9999997300420937
            ]
        ]
    },
    {
        "q_id": "7922_mmlu_math",
        "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": [
            [
                0.9999756997650695,
                0.9999938558275964,
                0.9999885212346117,
                0.9993736658386114,
                0.999992110740236,
                0.999985261016272,
                0.9999756997476845,
                0.9999485577679679,
                0.9999885212305079,
                0.9999910603058283
            ],
            [
                0.9999852610233037,
                0.9999785550464846,
                0.9999945777797379,
                0.9999832985721857,
                0.999993037740431,
                0.9999151889284265,
                0.9999930377429206,
                0.9999687980998082,
                0.9999938558275956,
                0.9999898700102279
            ],
            [
                0.9999810748495092,
                0.9999852610197877,
                0.9999785550516034,
                0.9998911030520788,
                0.9999687980886571,
                0.9999151889891112,
                0.9993736659701768,
                0.9999852610110026,
                0.9999785550413764,
                0.9994472213206277
            ],
            [
                0.9994472213899285,
                0.9999930377412605,
                0.9998601779097498,
                0.9999485577679873,
                0.9999546021476569,
                0.9999546021313743,
                0.9999756997476862,
                0.9999852610215458,
                0.999978555059262,
                0.9998766054105033
            ],
            [
                0.9990889488858139,
                0.9997965729301778,
                0.9902915244497359,
                0.9997694933135142,
                0.999738809723432,
                0.9998415638213696,
                0.9999038975735949,
                0.999959936312614,
                0.9996646499729741,
                0.9999417087067435
            ],
            [
                0.9999810748540298,
                0.9999921107402385,
                0.9999785550567211,
                0.9999832985821435,
                0.999992110735535,
                0.99998699287309,
                0.9999724643089193,
                0.9999952149072169,
                0.9999967112497586,
                0.9999832985821441
            ],
            [
                0.9999417087414438,
                0.9997388097853083,
                0.9999756997679602,
                0.9999485577925504,
                0.9999546021205942,
                0.9999646437408712,
                0.9999251537639369,
                0.999876605469714,
                0.9999724643023561,
                0.999620015472734
            ],
            [
                0.9999945777810308,
                0.9999945777784451,
                0.9999962733611605,
                0.999995777168066,
                0.9999852610127649,
                0.9999546021259734,
                0.999994577779092,
                0.9999938558261313,
                0.9999910603005011,
                0.9999974387171787
            ],
            [
                0.0009110510041428568,
                9.610240339544534e-05,
                0.00029595709778089656,
                0.9964063974702689,
                3.535625492063251e-05,
                0.00023050666014043624,
                3.120191509059319e-05,
                6.605215252536083e-05,
                0.0007096702907433823,
                0.0003799845752437494
            ],
            [
                4.7850950648799385e-06,
                6.96225375863827e-06,
                1.3709572068354007e-06,
                1.5534971989696065e-06,
                4.785095635296322e-06,
                6.144174601499446e-06,
                2.902313022952668e-06,
                1.7603430034439723e-06,
                6.962258739068529e-06,
                1.4738978447095178e-05
            ],
            [
                0.9999930377454104,
                0.9999952149072165,
                0.9999687980997979,
                0.9999810748562741,
                0.9999810748585336,
                0.9999832985781578,
                0.9999930377420913,
                0.9999952149032237,
                0.9999921107383557,
                0.9999957771670591
            ],
            [
                0.999972464315473,
                0.9999546021367783,
                0.9998204720563266,
                0.9999339478238761,
                0.9999485577618736,
                0.9998601778764243,
                0.9999599362887799,
                0.9999485577925354,
                0.9999417087205958,
                0.9999756997563805
            ],
            [
                0.9999984465026158,
                0.9999938558261314,
                0.9999869928653388,
                0.9999852610180312,
                0.9999832985761679,
                0.9999930377445809,
                0.9999485578048176,
                0.9999952149037941,
                0.999993855826131,
                0.9999756997621767
            ],
            [
                0.999997097686977,
                0.9999832985781592,
                0.9999885212277715,
                0.9999977396765105,
                0.999986992873088,
                0.9999810748562789,
                0.9999974387180947,
                0.9999898700053989,
                0.9999945777784447,
                0.9999962733598275
            ],
            [
                0.9999785550464778,
                0.9998415637269378,
                0.9999921107364751,
                0.9999921107355341,
                0.9999852610145172,
                0.9999921107345942,
                0.9999810748495098,
                0.9999832985781617,
                0.9995694428592421,
                0.999986992866886
            ],
            [
                0.999995777168066,
                0.9999921107355337,
                0.9999898700126449,
                0.9999869928715386,
                0.9999930377404312,
                0.9999756997476879,
                0.9999930377437507,
                0.999981074842744,
                0.9999938558232012,
                0.9999724643154754
            ],
            [
                0.9997694932859883,
                0.9999251537995921,
                0.9999546021205351,
                0.999954602136841,
                0.9999785550413652,
                0.999978555056703,
                0.9996200155204467,
                0.9998415637834425,
                0.9998911031040214,
                0.9999724642957742
            ],
            [
                5.4222202621161125e-06,
                5.422217030288788e-06,
                6.144177530291754e-06,
                4.222834954403545e-06,
                4.785093353013212e-06,
                7.889259761704902e-06,
                3.2887498494282754e-06,
                4.2228349543420954e-06,
                6.9622562487453084e-06,
                2.5612815999679353e-06
            ],
            [
                0.9999546021368017,
                0.9999646437535097,
                0.9999485577618493,
                0.9998911030781548,
                0.9998766053959319,
                0.9999151889283604,
                0.9999599363126097,
                0.9999785550567036,
                0.9999038975737402,
                0.9999832985721847
            ],
            [
                0.9999898700102287,
                0.9999885212318762,
                0.999997438717484,
                0.9999810748495133,
                0.9999898700053994,
                0.9999756997505892,
                0.9999852610180324,
                0.999948557774106,
                0.9999724643056286,
                0.9999910603036972
            ],
            [
                0.9998415637269676,
                0.999915188989147,
                0.9999910602994336,
                0.9999485577863967,
                0.9999599363078845,
                0.9999967112501507,
                0.9997965730762958,
                0.9999546021422212,
                0.9998204719924134,
                0.9998415637458471
            ],
            [
                0.999988521234614,
                0.9999921107364749,
                0.9999810748427408,
                0.9999832985801549,
                0.999933947847567,
                0.9997965731012575,
                0.9998601779260209,
                0.999992110739296,
                0.9999724643023589,
                0.9999885212332466
            ],
            [
                0.999968798081195,
                0.9999945777784449,
                0.9999945777784451,
                0.9999852610127603,
                0.9999930377445811,
                0.9999869928699903,
                0.9999938558246666,
                0.9999970976880149,
                0.9999962733620488,
                0.9999898700102293
            ],
            [
                0.9999646437535248,
                0.9999756997621777,
                0.9998204719486101,
                0.9999810748449967,
                0.999972464305641,
                0.9999724642990556,
                0.9999810748495105,
                0.99997855505926,
                0.9999724643154672,
                0.9999898700114366
            ],
            [
                0.9999724643023546,
                0.9999785550464741,
                0.9999151889284529,
                0.9999339478553626,
                0.9999832985781578,
                0.9999869928668849,
                0.9999921107355341,
                0.999948557774137,
                0.9999910603015654,
                0.9999785550464785
            ],
            [
                0.9999938558224686,
                0.9999810748517721,
                0.9999852610197907,
                0.9999810748495079,
                0.9999945777823234,
                0.9999945777810304,
                0.9999810748472489,
                0.9999869928746402,
                0.9999417087414523,
                0.9999852610110065
            ],
            [
                0.999620015428537,
                0.9998415637081411,
                0.9999417087275694,
                0.9999945777784449,
                0.9770226297554521,
                0.9998766054695668,
                0.9999810748449961,
                0.9998766054547386,
                0.999954602142202,
                0.9999151889690262
            ],
            [
                0.9999687980737819,
                0.9999852610162754,
                0.9999962733602717,
                0.9999869928684351,
                0.9999962733598275,
                0.9999938558224688,
                0.9999852610127599,
                0.9999930377429209,
                0.9999251537728232,
                0.9999957771660521
            ],
            [
                0.9999921107374146,
                0.999959936307828,
                0.9998415637083441,
                0.999981074849511,
                0.9999898700102291,
                0.9999785550567057,
                0.999989870007814,
                0.9999930377412611,
                0.9999921107392967,
                0.9999852610110037
            ],
            [
                0.999988521229139,
                0.9999785550413672,
                0.9999938558275957,
                0.9999785550567065,
                0.9999898700114362,
                0.9999945777823233,
                0.999981074847252,
                0.9999885212264018,
                0.9999957771660526,
                0.9999952149066462
            ],
            [
                0.999948557774109,
                0.9999869928699877,
                0.9998911030390022,
                0.9999810748427408,
                0.9999251537817438,
                0.9999251537372883,
                0.9999869928746405,
                0.9999546021313623,
                0.9997694933132257,
                0.9999832985801492
            ],
            [
                0.9999756997505854,
                0.9999945777823235,
                0.999986992866886,
                0.999986992869988,
                0.9999974387171787,
                0.9999977396765105,
                0.9999938558253986,
                0.9998911031296458,
                0.9999977396754327,
                0.9999945777784448
            ],
            [
                0.9999832985841355,
                0.9999910603047645,
                0.99997855504393,
                0.9999832985761737,
                0.9999952149066462,
                0.9999930377429205,
                0.9999921107345934,
                0.9999957771650454,
                0.9999938558239337,
                0.9999962733593833
            ],
            [
                0.9999151889485612,
                0.999088948654813,
                0.9998601779093775,
                0.9994472212561827,
                0.9982992774814365,
                0.9988304899193465,
                0.999664649974057,
                0.9999417087275647,
                0.9995694429709817,
                0.9998601779262772
            ],
            [
                0.9999885212305081,
                0.9999938558268636,
                0.9999945777829695,
                0.9999852610110069,
                0.9999930377445817,
                0.9999832985761693,
                0.9999938558261308,
                0.9999970976869769,
                0.9999910603005008,
                0.9999910603015668
            ],
            [
                0.9999546021422212,
                0.9999251537460603,
                0.9998601779262996,
                0.9997388097852323,
                0.999948557780254,
                0.99995993630786,
                0.9999724642957762,
                0.9999898700041914,
                0.9998204719697047,
                0.999985261014518
            ],
            [
                0.9999930377412611,
                0.9999938558268632,
                0.9999945777816768,
                0.9999962733593833,
                0.9999885212291387,
                0.9999339478554053,
                0.99999457778297,
                0.9999417087067299,
                0.9999921107402365,
                0.9999898700053991
            ],
            [
                0.9998911031167418,
                0.9999724643023409,
                0.9999756997621702,
                0.9999785550567023,
                0.9998601779762012,
                0.9998601779760528,
                0.9998204720773193,
                0.9998766053958636,
                0.9996200155630407,
                0.9999485577680165
            ],
            [
                0.9999869928730871,
                0.9999810748495068,
                0.999985261014516,
                0.9999687980998393,
                0.9999852610233023,
                0.9999984465018751,
                0.9999957771655487,
                0.9999785550439309,
                0.9999546021097396,
                0.9999930377437507
            ],
            [
                0.9999417087137148,
                0.9999885212305069,
                0.9999785550567089,
                0.9999852610233009,
                0.9999339478711452,
                0.9999339478396482,
                0.9999339478475212,
                0.9999785550464814,
                0.9999852610197931,
                0.9999810748540237
            ],
            [
                0.9999885212318762,
                0.9999756997650845,
                0.9999852610145172,
                0.9999869928668866,
                0.9999945777797377,
                0.999992110737415,
                0.9999756997563999,
                0.9999852610145165,
                0.9999810748427408,
                0.9999724643187728
            ],
            [
                0.9999646437324344,
                0.999876605395702,
                0.9999885212332428,
                0.9999898700066056,
                0.9999785550515903,
                0.9999417087483723,
                0.9989677689172686,
                0.999738809753063,
                0.9998601778594738,
                0.9999251537638628
            ],
            [
                2.43002436174814e-05,
                1.0129990977520359e-05,
                0.004070137932969145,
                0.998073265303316,
                6.144176798691468e-06,
                5.144223815074485e-05,
                2.4300237804191365e-05,
                4.539785237613882e-05,
                0.00015843615934522262,
                2.4300237834601515e-05
            ],
            [
                2.1444943291142893e-05,
                8.481106149073081e-05,
                0.00017952802996101694,
                4.785096205830278e-06,
                0.9940889304460034,
                0.001700722355697024,
                0.990291525765965,
                0.0009110512984569965,
                0.9626731145299533,
                2.753569434230981e-05
            ],
            [
                0.9999938558239341,
                0.9999910603068946,
                0.9999785550516085,
                0.9999898700102291,
                0.9999980052707541,
                0.9999921107402366,
                0.9999921107345932,
                0.9999869928684372,
                0.9999957771680659,
                0.9999810748562817
            ],
            [
                0.9999251537638443,
                0.999964643732436,
                0.999948557780265,
                0.9998601779598549,
                0.999876605425486,
                0.9999546021422125,
                0.9999038976194913,
                0.9999898700078128,
                0.9996646497719275,
                0.9999885212277693
            ],
            [
                0.9999945777829696,
                0.9999938558232014,
                0.9999945777810306,
                0.999985261023302,
                0.9999930377454109,
                0.9999910603015654,
                0.9999417087553695,
                0.9999921107336528,
                0.9999921107383553,
                0.9999910603026323
            ],
            [
                0.9999921107392965,
                0.9999417087205692,
                0.9999724643089007,
                0.9999930377420909,
                0.9999810748449992,
                0.9999930377404309,
                0.9999957771670591,
                0.9999852610162749,
                0.9999832985701967,
                0.9999885212359824
            ],
            [
                0.9999980052700407,
                0.9999952149072169,
                0.9999945777790913,
                0.9999869928746383,
                0.9999967112513268,
                0.9999785550490391,
                0.9999970976880149,
                0.9999151889385346,
                0.9999485578048097,
                0.9999952149060758
            ],
            [
                0.9999930377420908,
                0.9999967112521109,
                0.9999810748562783,
                0.9999852610162754,
                0.9999962733620488,
                0.9999869928699899,
                0.999994577779738,
                0.9999810748495079,
                0.999994577780384,
                0.9999832985801511
            ],
            [
                0.9999546021151833,
                0.9999485577619046,
                0.9998601778596243,
                0.9999599363078551,
                0.999978555054148,
                0.9999785550439215,
                0.9998766053814806,
                0.9999646437450908,
                0.9999038976081925,
                0.9999485577864431
            ],
            [
                0.999903897562355,
                0.9998601779092757,
                0.9998601778929295,
                0.9993736659057605,
                0.9999599363126119,
                0.9999417087275401,
                0.9997694931756702,
                0.9999038975509013,
                0.9993736659039753,
                0.9999251537907063
            ],
            [
                1.3709576971061233e-06,
                2.561282515886208e-06,
                3.28874945711983e-06,
                4.222833946845163e-06,
                4.7850944945245504e-06,
                4.2228324375973415e-06,
                3.2887486731641103e-06,
                2.5612828212676906e-06,
                1.7603440526806268e-06,
                2.9023112930659533e-06
            ],
            [
                0.9999938558232012,
                0.9999921107392962,
                0.9999885212291395,
                0.999985261023302,
                0.9999038975507579,
                0.999989870012645,
                0.9999687980774852,
                0.9999756997592832,
                0.9999967112517189,
                0.9999957771645419
            ],
            [
                3.7266410608720178e-06,
                3.7266406165827946e-06,
                8.939698434153684e-06,
                1.0129988562661878e-05,
                3.2887482811908074e-06,
                1.0129995808639442e-05,
                1.3007131561047124e-05,
                1.3709578605542582e-06,
                6.144173868983067e-06,
                8.939693106182721e-06
            ],
            [
                0.9999810748427401,
                0.9998911031043163,
                0.9999151889486873,
                0.9999756997592744,
                0.9994472214585218,
                0.9999599362982811,
                0.9998911030649734,
                0.9998415638212037,
                0.9998415637082289,
                0.9999785550490391
            ],
            [
                0.999993037742921,
                0.9999869928715373,
                0.999993855827596,
                0.9999930377445805,
                0.9999938558224687,
                0.9999687980960721,
                0.9999977396754327,
                0.9999810748427401,
                0.9999967112513267,
                0.9999962733611603
            ],
            [
                0.999993037745411,
                0.9999832985781602,
                0.9999832985701956,
                0.99998329857418,
                0.9999832985761737,
                0.9999921107402371,
                0.9999885212318762,
                0.999992110738356,
                0.9999898700041926,
                0.999992110739296
            ],
            [
                0.9999952149043646,
                0.9999938558246663,
                0.9999869928699867,
                0.9999957771675625,
                0.9999930377404307,
                0.9999970976890528,
                0.999988521231877,
                0.9999898700078147,
                0.9999885212291404,
                0.999991060301566
            ],
            [
                0.9999646437535324,
                0.9999885212318752,
                0.9999151889891026,
                0.9999852610197867,
                0.999959936312614,
                0.9999756997534912,
                0.9999910603068946,
                0.9999485577679806,
                0.9999921107364748,
                0.9998766054253622
            ],
            [
                0.9999910603036967,
                0.9999687980960955,
                0.999989870006606,
                0.9999832985781592,
                0.9999785550592636,
                0.9999756997621809,
                0.9999852610162737,
                0.9999930377445811,
                0.999993037742921,
                0.9999885212318752
            ],
            [
                0.9999687980774866,
                0.9999810748562789,
                0.9999785550515979,
                0.9999646437409038,
                0.9999485577802578,
                0.9999724642990687,
                0.9999945777784451,
                0.9999952149072169,
                0.9999756997476926,
                0.9999910603068956
            ],
            [
                0.9999885212359817,
                0.9999930377412608,
                0.9999599363173963,
                0.9999921107392967,
                0.9999898700066064,
                0.9999832985781602,
                0.9999852610197885,
                0.999993037743751,
                0.9999832985801526,
                0.9999898700053984
            ],
            [
                0.9999417087275961,
                0.9999898700126437,
                0.9998766053960935,
                0.9999810748540182,
                0.9999910603004991,
                0.9999832985741761,
                0.9999646437535161,
                0.999985261021543,
                0.9998204720560314,
                0.9999599362935286
            ],
            [
                0.9999251537996269,
                0.9999646437408835,
                0.9999810748517628,
                0.999995777164542,
                0.999948557792504,
                0.9999869928730887,
                0.9996200155157815,
                0.9999756997505781,
                0.9999910603068937,
                0.9999756997650734
            ],
            [
                0.9999646437451019,
                0.9999417087415112,
                0.9999599363126306,
                0.9999151889184656,
                0.9997965729547312,
                0.9995694428616595,
                0.9999251537995921,
                0.9999756997534923,
                0.9999724642957917,
                0.9999599363030588
            ],
            [
                0.9999810748585329,
                0.9999938558224694,
                0.9999898700114365,
                0.9999967112497585,
                0.999993855826131,
                0.9999974387171787,
                0.9999810748450029,
                0.9999810748495086,
                0.9999952149072168,
                0.9999810748585329
            ],
            [
                0.9984988179434126,
                0.9953904275791895,
                0.9996646497723958,
                0.9997965730995557,
                0.9993736659067443,
                0.9992903297018677,
                0.9999151889587016,
                0.9993736658297944,
                0.9993736659123551,
                0.999796572930092
            ],
            [
                0.9999417087553695,
                0.9999957771650453,
                0.9999646437366568,
                0.9999967112493665,
                0.9999038975852501,
                0.9999756997650858,
                0.9999885212359804,
                0.999989870009021,
                0.9999756997621767,
                0.999933947823881
            ],
            [
                0.9999038975393356,
                0.999841563840392,
                0.9999151889385877,
                0.999968798081195,
                0.999933947855428,
                0.9997388096915893,
                0.999954602120542,
                0.9999756997679626,
                0.999948557780254,
                0.9999785550541453
            ],
            [
                0.9999962733620488,
                0.9999910603015651,
                0.9999898700126436,
                0.9999869928730878,
                0.9999910603036964,
                0.9999852610145189,
                0.9999898700053991,
                0.9999910603047626,
                0.9999832985721941,
                0.9999599363030796
            ],
            [
                0.999978555054146,
                0.9999898700126437,
                0.9999952149060758,
                0.9999756997534802,
                0.9999910603058291,
                0.9999852610233023,
                0.9999930377420903,
                0.9999832985761699,
                0.9999898700102291,
                0.9999885212277709
            ],
            [
                0.999933947871162,
                0.9998601778925937,
                0.99996879809608,
                0.9995121428851934,
                0.9999910603015656,
                0.9999930377445811,
                0.9999417087345535,
                0.9999724643187576,
                0.999954602136796,
                0.999959936298279
            ],
            [
                0.9999785550567057,
                0.9999952149055058,
                0.9999852610233015,
                0.9999945777810313,
                0.9999898700090213,
                0.9999987901341723,
                0.9998911030389356,
                0.9999599362887198,
                0.9999885212318762,
                0.9999967112521108
            ],
            [
                0.9998601779595803,
                0.9999724643056483,
                0.9999251537639728,
                0.9999945777810305,
                0.9999724643089131,
                0.9999810748562856,
                0.9998204720987116,
                0.9999885212318759,
                0.9999724643089107,
                0.9999785550592636
            ],
            [
                0.999993855827596,
                0.9999930377420909,
                0.999983298578164,
                0.999996273360272,
                0.9999962733616047,
                0.9999898700102293,
                0.9999724643056253,
                0.9999930377454107,
                0.9999810748449955,
                0.9999977396754327
            ],
            [
                0.9999898700041909,
                0.9999938558239339,
                0.9999945777797378,
                0.9999952149066462,
                0.9999967112521109,
                0.9999910603068939,
                0.9999962733620489,
                0.9999945777803841,
                0.9999921107345945,
                0.9999756997563796
            ],
            [
                0.9999945777829701,
                0.9999832985801492,
                0.9999852610110069,
                0.9999898700102291,
                0.9999687980737704,
                0.9999957771670589,
                0.9999938558261314,
                0.9999852610180346,
                0.9999930377420907,
                0.9999945777810307
            ],
            [
                0.9999687980811988,
                0.9999599363126013,
                0.9998601779593483,
                0.9999687980737588,
                0.999876605454525,
                0.9997388096292115,
                0.999959936298279,
                0.9998911030779931,
                0.9999251537816986,
                0.999978555054146
            ],
            [
                0.9999898700041923,
                0.9999910603058285,
                0.9999945777784448,
                0.9999910603036976,
                0.9999810748495098,
                0.9999921107355347,
                0.9999921107336532,
                0.9999930377437508,
                0.9999952149043647,
                0.9999952149060757
            ],
            [
                0.999992110738355,
                0.999954602120542,
                0.9999885212264026,
                0.9999930377437506,
                0.9999938558239341,
                0.9999724643023409,
                0.9999687980812294,
                0.9999967112517189,
                0.9999546021313848,
                0.9999646437408798
            ],
            [
                0.9998204720776067,
                0.9998204720767708,
                0.9999687980997993,
                0.9999546021205397,
                0.9998601779597837,
                0.9999599363221608,
                0.9998601779430304,
                0.9999546021313769,
                0.9992903296208372,
                0.9999599362934934
            ],
            [
                0.9999810748472581,
                0.9999756997679742,
                0.999975699750598,
                0.9999832985761757,
                0.9999687980849485,
                0.9999832985721882,
                0.9999832985701943,
                0.9999785550515963,
                0.9999756997679742,
                0.9999417087345585
            ],
            [
                0.9999251537460739,
                0.9999038975507579,
                0.9999417087484687,
                0.9998601779260209,
                0.9999832985821396,
                0.9995121428832917,
                0.9999599362935143,
                0.999704042794746,
                0.9999785550490401,
                0.999820472098197
            ],
            [
                0.9999785550464871,
                0.9999898700126435,
                0.9999646437450999,
                0.9999852610162783,
                0.9999810748517651,
                0.9999930377420907,
                0.9999910603058285,
                0.9999957771660521,
                0.9999938558253983,
                0.9999967112517187
            ],
            [
                0.9999599362935339,
                0.9999251537728434,
                0.9999756997592744,
                0.9999898700114358,
                0.9997965731006301,
                0.9999832985761674,
                0.9998766053665034,
                0.9999546021476413,
                0.9999038975396697,
                0.9999945777803845
            ],
            [
                0.9999957771670591,
                0.9999724642990652,
                0.9999810748472509,
                0.9998911031298106,
                0.9999687980812015,
                0.9999785550567057,
                0.9999785550464791,
                0.999972464315471,
                0.9999938558224687,
                0.9999869928684348
            ],
            [
                0.9999646437451162,
                0.9999869928668873,
                0.999954602120585,
                0.9999885212305066,
                0.9999646437577323,
                0.9999785550567043,
                0.946596676038055,
                0.9999869928730875,
                0.9996646498921203,
                0.9998911031300816
            ],
            [
                0.9999810748517612,
                0.9999852610162737,
                0.9999921107364745,
                0.9999810748585306,
                0.9999885212318754,
                0.9999599363078162,
                0.9999546021368043,
                0.9999251537639957,
                0.9999852610127611,
                0.9999687980737564
            ],
            [
                0.9999339478238508,
                0.9999724642957707,
                0.9999546021422393,
                0.9998911030521089,
                0.9999599362887435,
                0.999738809601845,
                0.9999038975965528,
                0.9997694933401279,
                0.9999687980886298,
                0.999903897573855
            ],
            [
                0.9999151889588594,
                0.999820471948819,
                0.9999852610233009,
                0.999915188928401,
                0.999972464315472,
                0.9999546021097396,
                0.9999151889386154,
                0.9999599363030525,
                0.9998204719702113,
                0.9999339478790071
            ],
            [
                0.9999852610197881,
                0.9999957771650453,
                0.9999938558253986,
                0.9999038975851088,
                0.9999599362887301,
                0.9999251537549879,
                0.9999938558268633,
                0.9999952149055055,
                0.9999852610215424,
                0.9999810748449967
            ],
            [
                0.9999485578047775,
                0.9997040429371107,
                0.9999485578047914,
                0.9999339478474645,
                0.9997694932584691,
                0.9998601779261898,
                0.9999832985701962,
                0.9999417087414608,
                0.9999885212332436,
                0.9998415638021374
            ],
            [
                0.9999852610162749,
                0.9999970976876689,
                0.9999869928653384,
                0.9999967112493666,
                0.9999852610233002,
                0.9997694931752275,
                0.9999852610233055,
                0.9999756997505882,
                0.9999339478791008,
                0.9999832985841333
            ],
            [
                0.9999869928715373,
                0.9999785550464846,
                0.9999785550515891,
                0.9999687980997938,
                0.9999785550592636,
                0.9999646437324888,
                0.9999910603047626,
                0.9999417087275961,
                0.9997694933149025,
                0.999985261014516
            ],
            [
                0.9999898700066067,
                0.9999852610145168,
                0.9999970976866309,
                0.9999930377454103,
                0.9999756997534849,
                0.9999952149055056,
                0.9999898700041902,
                0.9999646437535161,
                0.9999646437408679,
                0.9999646437577411
            ],
            [
                0.9999967112521109,
                0.9999869928761882,
                0.9999957771680659,
                0.9999785550439266,
                0.9999898700090227,
                0.999954602115177,
                0.9999962733620489,
                0.9999952149032239,
                0.9999930377454103,
                0.9999832985821483
            ],
            [
                0.9999898700126444,
                0.9999952149037943,
                0.999997438716568,
                0.999991060305828,
                0.9999921107383551,
                0.9999898700126437,
                0.9998204719917109,
                0.9999952149055058,
                0.9999646437493017,
                0.999995214904935
            ],
            [
                0.9999151889485459,
                0.9996200154247563,
                0.9959298620859067,
                0.9992903295341513,
                0.9995121429405406,
                0.9947798742145529,
                0.9996200155168097,
                0.9997040427964424,
                0.9997040427954434,
                0.9940889317813107
            ],
            [
                0.999986992874641,
                0.9999869928668857,
                0.9999945777784449,
                0.9999756997621788,
                0.9998911030650004,
                0.9999869928699899,
                0.9999952149072169,
                0.9999724643154878,
                0.9999898700066073,
                0.9999810748585355
            ],
            [
                0.9999417087484261,
                0.9998766053669702,
                0.9989677687408046,
                0.9999885212346113,
                0.999948557780265,
                0.9999687980774731,
                0.9999724642990565,
                0.9999417087067083,
                0.007577239517014925,
                0.9999546021205622
            ],
            [
                0.9999810748495156,
                0.9999485577802507,
                0.9999646437535306,
                0.9999885212291387,
                0.9999485577680091,
                0.9999151889183183,
                0.9999251537551465,
                0.9999687980774912,
                0.9999832985741829,
                0.9999485577986978
            ],
            [
                0.9999756997621702,
                0.9999869928746392,
                0.9999852610162746,
                0.9999785550567233,
                0.9999910603036969,
                0.999986992868439,
                0.9999687980737645,
                0.9999898700078143,
                0.9999910603015663,
                0.999983298574178
            ],
            [
                0.9999869928653358,
                0.9999852610110056,
                0.9999785550515924,
                0.9999869928715376,
                0.9999921107345942,
                0.9999832985841349,
                0.9999898700053996,
                0.9999967112493665,
                0.9999974387184,
                0.9999785550413729
            ],
            [
                0.9999921107392964,
                0.9999869928730897,
                0.9999970976883609,
                0.9999417087067125,
                0.9999938558239336,
                0.9999869928699874,
                0.9999832985801532,
                0.999993037743751,
                0.9999982396565769,
                0.9999885212305096
            ],
            [
                0.9999898700066073,
                0.9999687980774823,
                0.999985261014516,
                0.9999952149037942,
                0.9999756997621694,
                0.9999339478475102,
                0.9999910603068946,
                0.9999785550490375,
                0.9999724642990713,
                0.9999485578047951
            ],
            [
                0.9999687980997889,
                0.9999417087344838,
                0.9999785550464837,
                0.9999599362982728,
                0.9999785550464765,
                0.9999038975850683,
                0.999569442910158,
                0.9999599363030525,
                0.9999910603015654,
                0.9999038976081353
            ],
            [
                0.9999810748495133,
                0.9999921107336532,
                0.9999898700126442,
                0.999985261011005,
                0.9999945777784449,
                0.9999885212359824,
                0.9999921107392958,
                0.9999785550413688,
                0.9999945777829699,
                0.9999785550541569
            ],
            [
                0.9999885212264026,
                0.9999785550490361,
                0.9999910603026312,
                0.999991060301566,
                0.9999967112493665,
                0.9999687980886429,
                0.9999832985721853,
                0.999989870011438,
                0.9999921107345949,
                0.9999921107336545
            ],
            [
                0.9999921107355337,
                0.999988521233244,
                0.9998204720553105,
                0.9999938558275957,
                0.9999921107345933,
                0.9999810748540223,
                0.9999869928761882,
                0.9999785550567081,
                0.9999921107345938,
                0.9999485577741191
            ],
            [
                0.9999485577679945,
                0.9999546021368187,
                0.9999832985841344,
                0.9998911030520932,
                0.9999785550515988,
                0.9998911031170142,
                0.999992110737415,
                0.9999885212332442,
                0.9999970976866309,
                0.9999546021313719
            ],
            [
                0.9991959139624201,
                0.9978172832356927,
                0.9968273172768042,
                0.9971990732474829,
                0.9996646497705518,
                0.9940889308564462,
                0.9992903294672382,
                0.9993736658973441,
                0.9994472213225892,
                0.9989677689598839
            ],
            [
                0.997199073410712,
                0.9998204720767708,
                0.9999339478395824,
                0.9149009578933864,
                0.9993736658254949,
                0.9999599362982748,
                0.9993736657464684,
                0.999841563821342,
                0.9820137924395611,
                0.9984988177198802
            ],
            [
                0.9999832985721882,
                0.9999945777803843,
                0.9999962733620488,
                0.9999921107355347,
                0.9999957771645421,
                0.9999885212332457,
                0.9999852610197926,
                0.9999832985701943,
                0.9999938558239335,
                0.9999785550567036
            ],
            [
                0.9996646498128179,
                0.999891103039086,
                0.9997965729787901,
                0.9999038975851299,
                0.9984988179913995,
                0.9998415638218053,
                0.9998766054104387,
                0.9997388095994055,
                0.9989677688074288,
                0.9999339478238364
            ],
            [
                0.9999930377404328,
                0.9999952149072171,
                0.9999974387168734,
                0.9999967112505427,
                0.9999952149055054,
                0.9999952149072169,
                0.9999921107364758,
                0.9999952149049351,
                0.9999974387168734,
                0.9999957771660526
            ],
            [
                0.999948557761917,
                0.9999546021151928,
                0.9999339478239608,
                0.9995121428297894,
                0.9999485577864075,
                0.9999832985701973,
                0.9999785550413645,
                0.9999417087345258,
                0.999903897585194,
                0.9999485577987233
            ],
            [
                0.9997965730264612,
                0.9999756997563835,
                0.9999599362935078,
                0.8354835452961425,
                0.9984988179357346,
                0.9999546021367857,
                0.9999646437324751,
                0.9999038976197178,
                0.9999910603015654,
                0.9999485577924947
            ],
            [
                0.9999852610110026,
                0.9999869928668881,
                0.9999852610110056,
                0.9999869928699887,
                0.9999810748495147,
                0.9999921107374156,
                0.9999930377412608,
                0.9999852610162767,
                0.9999898700126444,
                0.999968798088688
            ],
            [
                0.9999921107392964,
                0.9999810748472515,
                0.9999945777790915,
                0.9999938558261312,
                0.9999970976890529,
                0.9999982396567867,
                0.9999921107392962,
                0.9999785550413696,
                0.9999810748472566,
                0.9999952149032237
            ],
            [
                0.9999885212318768,
                0.9999885212359809,
                0.999993855826131,
                0.9999921107402369,
                0.9999898700066069,
                0.9999930377462408,
                0.9999938558232019,
                0.9999885212318768,
                0.9999921107374147,
                0.9999852610110065
            ],
            [
                0.9998911030522595,
                0.9999785550515924,
                0.9998911030521089,
                0.9999921107345932,
                0.9997694932025857,
                0.9999687980849168,
                0.9999599363126355,
                0.9998911030388207,
                0.9997965730274053,
                0.9999724643187554
            ],
            [
                0.9999930377412609,
                0.9999898700053982,
                0.9999852610233032,
                0.9999962733611601,
                0.9999898700053984,
                0.9999945777829695,
                0.9999646437408912,
                0.9999687980923714,
                0.9999785550439274,
                0.9999756997505854
            ],
            [
                0.9999546021097627,
                0.9999945777810312,
                0.9999646437493162,
                0.9999810748517628,
                0.999989870007814,
                0.9999687980774927,
                0.9999885212318793,
                0.9999921107345933,
                0.9999756997534821,
                0.9999869928761923
            ],
            [
                4.222834954280646e-06,
                5.422217029391264e-06,
                1.3709572068272963e-06,
                6.962255416759247e-06,
                1.473897669245728e-05,
                6.144176065314267e-06,
                1.3709578605455302e-06,
                1.0129988561077228e-05,
                1.5534973841705173e-06,
                2.5612831264302397e-06
            ],
            [
                0.9999832985821483,
                0.9999898700114365,
                0.9999852610110037,
                0.9999417087275778,
                0.9999852610127591,
                0.9999869928668906,
                0.9999599362982748,
                0.9999756997534811,
                0.9999898700114368,
                0.9999724643122028
            ],
            [
                0.9999756997534839,
                0.999985261023306,
                0.9999898700053997,
                0.9999921107402375,
                0.9999785550515988,
                0.9999546021422125,
                0.9999852610162787,
                0.9999869928730869,
                0.9999938558224687,
                0.9999984465018751
            ],
            [
                0.9999756997621831,
                0.9999938558232017,
                0.9999967112505427,
                0.9999852610180315,
                0.9999810748472509,
                0.9999417087553479,
                0.9999921107336528,
                0.9999930377412606,
                0.9999898700066079,
                0.9999938558275958
            ]
        ]
    },
    {
        "q_id": "8982_mmlu_math",
        "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": [
            [
                0.00015843629097590995,
                3.120191878131786e-05,
                9.610237888954644e-05,
                4.006369198814498e-05,
                0.0003353500850392844,
                4.006368252433876e-05,
                0.00015843628653381618,
                2.753570407437481e-05,
                4.0063701563302636e-05,
                1.4738981951170529e-05
            ],
            [
                0.9999724643187611,
                0.9999810748427421,
                0.9989677689194293,
                0.9997694932050405,
                0.9997694932630903,
                0.9984988175129252,
                0.999664649938855,
                0.9992903296285564,
                0.9998204721027707,
                0.9997965730051637
            ],
            [
                3.12019075573845e-05,
                1.6701421818931145e-05,
                0.9978172832950227,
                4.539787401825028e-05,
                0.0004305570135869053,
                0.9997694933468886,
                0.9997965729328179,
                0.00029595713364544704,
                2.753569434711804e-05,
                3.120192616798991e-05
            ],
            [
                2.7535700923478902e-05,
                0.9465966677520327,
                1.8925157250667477e-05,
                2.1444950932047874e-05,
                1.1478766751997141e-05,
                0.9902915213606257,
                0.9940889323778208,
                7.88925976316864e-06,
                1.1478768123280277e-05,
                0.9324533135530545
            ],
            [
                1.3007134661628471e-05,
                4.5397863104874985e-05,
                5.144223188355573e-05,
                0.00020342695949820218,
                1.1478770853569882e-05,
                1.4738976682752188e-05,
                9.610244855203764e-05,
                0.00012339460277907598,
                0.0001088968956013945,
                5.82912445630129e-05
            ],
            [
                3.2887490648622804e-06,
                3.2887494567788457e-06,
                1.1478764016780948e-05,
                7.889259760542522e-06,
                5.422217675362059e-06,
                5.4222183212934785e-06,
                2.90231336806592e-06,
                7.889263522779056e-06,
                5.422220904290072e-06,
                7.88926070097951e-06
            ],
            [
                1.4738976686988113e-05,
                2.430025225511712e-05,
                1.0129988542651073e-05,
                1.6701427807280505e-05,
                1.8925145966893773e-05,
                2.4300243618542217e-05,
                3.120192251631124e-05,
                0.00015843626533532598,
                2.1444948371764756e-05,
                1.8925155003330605e-05
            ],
            [
                4.539786315574087e-05,
                5.1442219421414326e-05,
                3.5356254855807646e-05,
                3.120191493815145e-05,
                0.00023050671023562498,
                0.0006263340851673317,
                0.00013982210578281806,
                0.00010889689526073005,
                3.72663854015739e-06,
                5.829125135158043e-05
            ],
            [
                0.9975273770317288,
                3.7266401719851935e-06,
                1.300713000155317e-05,
                2.7535704207102113e-05,
                1.8925145960215522e-05,
                4.785096205347206e-06,
                2.1444945844872185e-05,
                2.5612831262112703e-06,
                6.144173867753695e-06,
                7.88925976126004e-06
            ],
            [
                0.9998204720597353,
                0.9996200155672857,
                0.9996200155202145,
                0.9999810748473483,
                0.9988304898161303,
                0.9997040428014883,
                0.9991959142384818,
                0.9997965730301549,
                0.99408893212061,
                0.053403333942835626
            ],
            [
                0.9989677688591675,
                0.9959298613874978,
                0.9993736658549341,
                0.9859363743126794,
                0.9997694933709939,
                0.9997040430174765,
                0.9993736659131931,
                0.9978172839060709,
                0.9984988176345506,
                0.9995121427865051
            ],
            [
                2.1444953509026425e-05,
                1.8925141463066202e-05,
                1.0129992185981682e-05,
                1.3007126853369984e-05,
                1.7603425826047563e-06,
                6.9622570786798724e-06,
                1.4738985418463857e-05,
                2.90231163910023e-06,
                3.1201900186835035e-05,
                8.939694169835089e-06
            ],
            [
                6.605213629778175e-05,
                4.785095064148803e-06,
                0.0001795280276624502,
                0.00012339463247150773,
                4.5397890237206746e-05,
                5.1442219658328595e-05,
                8.48110206742489e-05,
                8.481103042084043e-05,
                2.4300249362084747e-05,
                1.670142581075876e-05
            ],
            [
                0.9947798748021565,
                0.9982992773640305,
                0.9995694429170972,
                0.9984988175057709,
                0.9997388096933677,
                6.144174600862407e-06,
                0.13296422989056964,
                0.9953904275257742,
                0.9947798755300109,
                0.9999151889892037
            ],
            [
                0.9984988177839211,
                0.9990889486830523,
                0.9995694429965587,
                0.9997040430180619,
                0.9997388096329657,
                0.9997694933719462,
                0.9991959142511087,
                0.9999038976085115,
                0.999620015567529,
                0.9986749778938108
            ],
            [
                3.1201918620817016e-05,
                2.144495092658685e-05,
                7.484623580173539e-05,
                2.7535697596682154e-05,
                7.484622694429252e-05,
                1.4738988974605243e-05,
                3.1201900131669995e-05,
                1.0129993388915298e-05,
                1.892515724357613e-05,
                8.481104989551601e-05
            ],
            [
                5.829125146227052e-05,
                7.484626197546885e-05,
                0.0002959570567325676,
                0.9999910603037038,
                3.535625478866761e-05,
                1.892515498164348e-05,
                0.00017952800631190112,
                0.9999957771655491,
                0.0001233946318377292,
                4.539786316564981e-05
            ],
            [
                4.539785225029534e-05,
                5.4222209064007344e-06,
                2.1444953470955293e-05,
                1.0129988561372045e-05,
                1.8925150469896243e-05,
                8.939698432202356e-06,
                6.9622545872301346e-06,
                6.962257891669855e-06,
                2.753569759467872e-05,
                7.889262578983744e-06
            ],
            [
                2.4300249391876106e-05,
                9.610240289903478e-05,
                8.481103997368594e-05,
                7.484623582024966e-05,
                4.222835457906302e-06,
                6.605212085304002e-05,
                2.7535697639856078e-05,
                1.0129987351621326e-05,
                6.605212068147983e-05,
                5.1442207290506706e-05
            ],
            [
                5.829125150595281e-05,
                6.962254585203866e-06,
                4.006371122853307e-05,
                2.1444953513707305e-05,
                1.3007125359034903e-05,
                7.889263523238269e-06,
                3.120190013643735e-05,
                2.1444948353665366e-05,
                4.785096775389454e-06,
                1.0129994590964606e-05
            ],
            [
                4.222833946937338e-06,
                2.144495604044475e-05,
                4.785093353013212e-06,
                2.430023491169112e-05,
                1.1478770845468629e-05,
                4.222832940162684e-06,
                1.1478765373531616e-05,
                7.889259759509296e-06,
                1.0129989762278356e-05,
                3.535625905424669e-05
            ],
            [
                0.9997965729801604,
                0.9997694932602867,
                0.9998911030915595,
                0.9997388096386275,
                0.9999810748585432,
                0.9998204721013184,
                0.99984156370999,
                0.9995121429516668,
                0.9982992775859952,
                0.9996200154758736
            ],
            [
                7.484619428949192e-05,
                1.3007129992704509e-05,
                9.610238947917035e-05,
                0.0001088969602246682,
                4.539786853530362e-05,
                5.14422256216072e-05,
                8.481106119455672e-05,
                0.00017952802552582796,
                4.0063711199092564e-05,
                5.144219477934163e-05
            ],
            [
                2.9023126768258393e-06,
                2.4300234904884198e-05,
                2.1444940721576954e-05,
                1.9947297212331575e-06,
                1.012999458141985e-05,
                6.962254587597396e-06,
                1.670142382493073e-05,
                2.5612812938854287e-06,
                2.753570421601738e-05,
                6.962256246896338e-06
            ],
            [
                1.6701419825205004e-05,
                1.670142380779686e-05,
                2.1444956020629035e-05,
                0.22270013882530884,
                1.0129988558055338e-05,
                3.5356263257316566e-05,
                1.1478770845468629e-05,
                1.3007134663521234e-05,
                2.7535697592675292e-05,
                2.7535691051475422e-05
            ],
            [
                0.00010889688174031335,
                3.5356242165056954e-05,
                3.120192614778541e-05,
                0.9999938558254066,
                5.829126520650338e-05,
                2.4300243529168176e-05,
                5.14422073226941e-05,
                2.144494072961245e-05,
                6.60521519775214e-05,
                2.430024938029549e-05
            ],
            [
                2.4300246475771248e-05,
                3.5356242202356964e-05,
                1.1478773593172406e-05,
                3.120191495949103e-05,
                3.5356259116499136e-05,
                1.6701417841747264e-05,
                2.1444956006898462e-05,
                3.120191349341703e-05,
                1.6701415862117537e-05,
                1.3007126910294786e-05
            ],
            [
                0.0002959570372718557,
                0.00013982212200304984,
                0.000335350191699535,
                NaN,
                3.1201914702962125e-05,
                1.4738980175781542e-05,
                0.0002959571551900122,
                0.00012339455873597364,
                3.1201907583945445e-05,
                0.9999339478574002
            ],
            [
                0.9992903296312807,
                0.26894142722948733,
                2.1444958619530313e-05,
                6.962258737092915e-06,
                0.993307149233598,
                0.18242552158390102,
                0.999195913955452,
                0.02931222810146209,
                0.9989677689291528,
                1.3007134658505415e-05
            ],
            [
                2.7535687797204028e-05,
                5.829125152122041e-05,
                7.484626275905827e-05,
                0.007577241828131578,
                0.0003799845848835389,
                6.605213641888309e-05,
                8.481106104893778e-05,
                0.0008040858095004613,
                0.001926734938686693,
                0.004609572429356985
            ],
            [
                0.0021827164098486007,
                0.03308597624352061,
                0.06754668410060376,
                0.022977372084420553,
                0.0010322312774420001,
                0.008577485025637611,
                0.008577486205700558,
                0.00017952805017795734,
                0.0001398220398053714,
                0.22270013366638425
            ],
            [
                0.9992903296881218,
                0.9998911030912886,
                0.9995694428831783,
                0.9997694932395954,
                0.9994472213016543,
                0.9995121428096941,
                0.9997965729604315,
                0.9996200154884098,
                0.9997694932425465,
                0.9995121427881514
            ],
            [
                0.9971990736207638,
                0.9859363747775679,
                0.9971990734282705,
                0.9796676474735837,
                0.9991959138936269,
                0.9980732650908641,
                0.9968273178511603,
                0.9984988176244297,
                0.9959298623765959,
                0.9998204720791687
            ],
            [
                1.8925150393819213e-05,
                1.3007134654767206e-05,
                4.0063687306232136e-05,
                1.3007128450482197e-05,
                1.8925150472994405e-05,
                3.1201918599477444e-05,
                1.670141784666869e-05,
                1.892515496381185e-05,
                8.939693102280066e-06,
                1.1478766751997141e-05
            ],
            [
                7.48462181396708e-05,
                1.3007125347631017e-05,
                2.4300232013798725e-05,
                1.67014178590634e-05,
                0.00010889693408063965,
                3.5356267474535235e-05,
                4.006368255581968e-05,
                1.1478764012939119e-05,
                0.0009110510150041331,
                3.5356242202356964e-05
            ],
            [
                0.9997694932057515,
                0.4687906266262438,
                0.37754067580180184,
                0.9996200155335797,
                0.025957360070550783,
                0.1645164628965632,
                0.9971990736155613,
                0.07585817532042317,
                0.9992903296140261,
                0.9989677687343222
            ],
            [
                0.00013982202226889645,
                3.1201926179794786e-05,
                0.9995121428636506,
                0.994088930864655,
                7.889260703462123e-06,
                7.484623562421623e-05,
                0.00013982212247299513,
                5.8291251536063904e-05,
                5.1442238010018466e-05,
                7.484622700419163e-05
            ],
            [
                0.9997388096631059,
                0.9997965730281955,
                0.9988304895661813,
                0.9998204720385467,
                0.9997388097581016,
                0.9998415637846757,
                0.9997965729312374,
                0.9996646498952815,
                0.9998601778601187,
                0.9996200154328705
            ],
            [
                0.00017952798539494773,
                3.535625907251083e-05,
                1.8925154990456026e-05,
                3.120190758167528e-05,
                1.6701421824277888e-05,
                4.53978847760578e-05,
                3.5356259091803945e-05,
                2.753568121974442e-05,
                1.3007125360809367e-05,
                0.00023050663957652873
            ],
            [
                6.60521362420367e-05,
                4.539787933439709e-05,
                4.006368703310598e-05,
                4.0063677536362585e-05,
                7.484622621679082e-05,
                9.610241411511755e-05,
                4.0063687453434584e-05,
                1.3007126904001353e-05,
                7.48462179975466e-05,
                1.892515272680245e-05
            ],
            [
                1.3007125358230479e-05,
                7.889265403166124e-06,
                6.962253756232077e-06,
                5.4222170229803784e-06,
                4.7850927830845245e-06,
                6.144174598593655e-06,
                8.939696297286554e-06,
                7.889266346129453e-06,
                6.962254588977791e-06,
                8.939699500489763e-06
            ],
            [
                1.892515725225098e-05,
                2.4300243585745217e-05,
                1.4738976543288403e-05,
                4.2228334438149845e-06,
                1.670141586150995e-05,
                1.8925157155244123e-05,
                4.222835456581284e-06,
                1.3007131562514014e-05,
                8.939700564890901e-06,
                1.0129989768027317e-05
            ],
            [
                4.5397873849798294e-05,
                5.829129317633263e-05,
                1.8925141455079837e-05,
                2.4300234870407578e-05,
                5.8291286299547405e-05,
                2.4300234830803665e-05,
                5.8291265411767815e-05,
                1.4738988961200408e-05,
                2.430024939965545e-05,
                9.610244819685922e-05
            ],
            [
                7.889262582341733e-06,
                1.3007133059736272e-05,
                3.7266379506485954e-06,
                0.9669140251866016,
                4.7850933534310035e-06,
                7.889263518043432e-06,
                1.3007131551441357e-05,
                2.260324027708365e-06,
                2.7535700830619886e-05,
                1.012998856048759e-05
            ],
            [
                1.0129992180269573e-05,
                1.012998856015592e-05,
                1.8925157219685868e-05,
                5.422219614833243e-06,
                6.144175332887123e-06,
                1.892515272363544e-05,
                4.222835455828521e-06,
                6.1441738684354385e-06,
                7.889263524257144e-06,
                8.9396994898225e-06
            ],
            [
                0.9975273764316072,
                0.997817283518144,
                0.9988304895131452,
                0.9996646499790622,
                0.9988304896556626,
                0.9986749776461008,
                0.9997388095692805,
                0.9996646497410281,
                0.9902915242527491,
                0.9796676443941232
            ],
            [
                0.00020342696962020437,
                3.120192233276818e-05,
                2.4300249383301144e-05,
                1.3007128441491578e-05,
                8.481108076179376e-05,
                3.120192621804711e-05,
                7.484619865885675e-05,
                0.0001584362523594355,
                6.605217554615506e-05,
                1.8925157249015125e-05
            ],
            [
                0.0004305571110851209,
                0.017986213679718945,
                0.008577487227365923,
                0.0005527787592854319,
                0.0002959571616309937,
                0.010986942215674622,
                3.5356246473207964e-05,
                0.005911069567678038,
                0.00013982202296262467,
                0.0013250226016092554
            ],
            [
                6.962255416961874e-06,
                8.939699497855469e-06,
                1.1478772218923723e-05,
                7.889264464106214e-06,
                1.3007125356479674e-05,
                3.7266410608245674e-06,
                1.147877085766227e-05,
                1.4738981930527094e-05,
                7.889264462211963e-06,
                2.1444945759368197e-05
            ],
            [
                0.9996200153987111,
                0.9997040430212136,
                0.9996646498693872,
                0.9953904283312743,
                0.9989677691937285,
                0.9975273772884313,
                0.9989677688912191,
                0.9999151889690671,
                0.9993736659193505,
                0.9968273176169997
            ],
            [
                0.00010889686990262187,
                3.5356267424887605e-05,
                3.5356250648880135e-05,
                3.535626751337872e-05,
                8.48110507556548e-05,
                4.0063682546783496e-05,
                0.000335350132651979,
                4.006368251413662e-05,
                2.753570418897106e-05,
                0.00015843623386723748
            ],
            [
                4.539787931391861e-05,
                4.7850963011434045e-06,
                2.7535691063295662e-05,
                0.00026119041865119646,
                8.939695232316787e-06,
                0.0003799845607951203,
                4.539785773786421e-05,
                0.9998415637091878,
                1.6701425808449937e-05,
                5.8291272311027895e-05
            ],
            [
                2.1444943257908684e-05,
                3.535625904858737e-05,
                2.753569106169292e-05,
                1.012998856048759e-05,
                1.3007133101897553e-05,
                3.120190364951972e-05,
                2.1444955985834514e-05,
                2.753569747988215e-05,
                2.4300237786245837e-05,
                5.8291250888887385e-05
            ],
            [
                0.9999417087276407,
                1.0129992152704034e-05,
                0.9999930377420919,
                0.9999485578049886,
                0.9999251537733607,
                0.9999724642991056,
                0.9999724643155748,
                0.9999546021211376,
                0.999964643745324,
                0.9998415637519628
            ],
            [
                0.9947798732569769,
                0.9998204719964934,
                0.9996646499372646,
                0.9924227588336882,
                0.9859363722335945,
                0.9980732653559253,
                0.9990889486476076,
                0.9971990727753542,
                0.9996646500109276,
                0.9998911030393285
            ],
            [
                0.9993736657744137,
                0.9989677688649296,
                0.9986749773004159,
                0.9998766054694967,
                0.9991959140941141,
                0.9996646498966767,
                0.9986749774048608,
                0.9997388095712261,
                0.9996200155361665,
                0.9982992778291089
            ],
            [
                0.8354835391516132,
                7.484622685281027e-05,
                0.00010889689426884192,
                NaN,
                5.144223192135723e-05,
                0.0003353501805866515,
                2.144495092518259e-05,
                0.9996646497392523,
                0.9996646498607524,
                0.00012339458777486703
            ],
            [
                2.4300234919028452e-05,
                1.1478765366390824e-05,
                7.889262582571338e-06,
                1.0129987350147233e-05,
                7.889266345397582e-06,
                6.962253757295868e-06,
                6.144173133136295e-06,
                7.889266343316778e-06,
                1.3007130004439633e-05,
                4.785092780377583e-06
            ],
            [
                0.9992903297390188,
                0.9999687980998413,
                0.14804719051380197,
                0.9999485577680282,
                0.9997694933740522,
                0.22270013366638422,
                0.9999251538000473,
                0.9998415638026008,
                0.9982992777257361,
                0.9998415638028936
            ],
            [
                4.539786305070613e-05,
                5.829128617783064e-05,
                7.484622672429949e-05,
                2.144494073054863e-05,
                4.006367783499403e-05,
                9.610244834787996e-05,
                6.605215976164754e-05,
                3.5356242142676954e-05,
                8.481104089059131e-05,
                8.48110610008095e-05
            ],
            [
                0.9989677689636053,
                0.9997388097547729,
                0.9996646497787961,
                0.9993736657483994,
                0.9995121429057144,
                0.999925153765113,
                0.9992903297376565,
                0.9997040427664419,
                0.9890130587760818,
                0.9997388096088975
            ],
            [
                0.00020342701837748134,
                5.1442237675419046e-05,
                4.006368729282359e-05,
                4.5397863124032274e-05,
                0.00037998460356615933,
                0.0002959572301310121,
                2.753568448703733e-05,
                5.829129316573014e-05,
                6.605213588738283e-05,
                7.48462624470383e-05
            ],
            [
                2.1444956065331412e-05,
                1.670141585731762e-05,
                1.300713311155064e-05,
                5.422218968595919e-06,
                1.3007131552624333e-05,
                1.67014178576052e-05,
                5.144223747406056e-05,
                3.5356246446326235e-05,
                1.3007129991190302e-05,
                5.42222155426567e-06
            ],
            [
                0.9999984465024307,
                1.8925144456644613e-05,
                0.00023050673352261426,
                0.00010889693411866731,
                0.00010889692138256647,
                0.0008040860747123043,
                0.00010889693281146606,
                0.00020342699430368535,
                4.5397879217141284e-05,
                0.9999990577550693
            ],
            [
                4.539789015265042e-05,
                0.9999546021476767,
                3.535624635371931e-05,
                0.00020342694281169803,
                0.9980732654168176,
                0.00012339455975396863,
                0.999876605382689,
                3.535625489632318e-05,
                0.9997388096641623,
                0.9998601779606158
            ],
            [
                4.5397873821062376e-05,
                0.00020342705733832468,
                2.4300231964293844e-05,
                0.0002959570760210621,
                8.48110810406911e-05,
                3.535626318991927e-05,
                0.00012339461794666872,
                5.829126520650338e-05,
                9.610240273822571e-05,
                0.00029595700761579966
            ],
            [
                6.9622562478334885e-06,
                1.1478770856576534e-05,
                6.962257905169877e-06,
                1.1478773595343877e-05,
                1.0129995798468197e-05,
                3.7266397280960194e-06,
                1.892514145845339e-05,
                1.892515272363544e-05,
                1.1478766744689312e-05,
                1.892515046555882e-05
            ],
            [
                1.4738980192671623e-05,
                4.006369681113957e-05,
                2.144494838221871e-05,
                1.0129987354366822e-05,
                5.422217030121119e-06,
                2.2603251058292572e-06,
                1.3007123797175743e-05,
                4.006369680356083e-05,
                7.889266343316778e-06,
                8.93969736518344e-06
            ],
            [
                0.00012339460268032863,
                0.9999962733589395,
                5.1442237979702405e-05,
                0.00012339460310763532,
                0.9999970976876711,
                0.9999989322966208,
                0.00029595702556098536,
                4.5397857563136625e-05,
                8.93969416907082e-06,
                0.00017952800526709818
            ],
            [
                9.61024138214662e-05,
                1.3007131553807308e-05,
                1.6701417848187652e-05,
                4.539785232659414e-05,
                1.0129994600398803e-05,
                1.8925154971385126e-05,
                2.7535681187990065e-05,
                1.3007123798453357e-05,
                2.1444948398445745e-05,
                2.1444956018912713e-05
            ],
            [
                2.4300246497960055e-05,
                1.1478772223642496e-05,
                1.0129994594944656e-05,
                1.1478770854029233e-05,
                8.939700553621976e-06,
                4.222834954280646e-06,
                3.7266401706904634e-06,
                6.144173862534448e-06,
                1.3007131561804229e-05,
                2.753568778107642e-05
            ],
            [
                0.022977369868210328,
                1.8925155003330605e-05,
                0.05340332810495602,
                1.1478772227651366e-05,
                0.9990889488446999,
                0.07585817532042317,
                0.005220124796435466,
                0.00013982202119880533,
                1.3007128460797749e-05,
                0.03732688868276006
            ],
            [
                2.4300240706150922e-05,
                0.9914225154099561,
                0.9579122752383734,
                7.88926258343236e-06,
                5.144223804819424e-05,
                1.0129990964843162e-05,
                2.4300232017599995e-05,
                1.0129994587353076e-05,
                1.8925148223661747e-05,
                4.006370634257487e-05
            ],
            [
                9.610243728840728e-05,
                0.06754668456987209,
                0.060086648070103596,
                0.002472623569541371,
                0.0001088969089855471,
                4.006369210357503e-05,
                0.0003353501746545768,
                2.1444943287710254e-05,
                0.002472623483973795,
                0.0052201248568884894
            ],
            [
                2.1444956061196638e-05,
                1.4738978441840487e-05,
                5.8291264965614555e-05,
                5.144223794190091e-05,
                2.1444953481409255e-05,
                2.1444956044501514e-05,
                7.484621779388972e-05,
                9.61023909488251e-05,
                2.4300246493981982e-05,
                2.4300237794201987e-05
            ],
            [
                0.0001088969080459469,
                8.481106116247119e-05,
                2.7535704096813236e-05,
                6.605216018165782e-05,
                0.00010889690777975326,
                3.120192618660529e-05,
                0.9999977396746254,
                4.539785215715135e-05,
                8.48110609020848e-05,
                3.535625484268833e-05
            ],
            [
                0.00017952789665986747,
                0.9947798751672927,
                0.9999485577681783,
                0.9978172835100306,
                NaN,
                0.9994472213531074,
                0.9998601778628,
                3.120192245603829e-05,
                0.9986749775361102,
                0.9999417087349428
            ],
            [
                0.999195914043092,
                0.9997965730524824,
                0.9984988176132619,
                0.9998601779108809,
                0.9980732649305737,
                0.9996200155713761,
                0.999195913997074,
                0.9998204719949262,
                0.9997388095775794,
                0.9997965730528732
            ],
            [
                4.222831933726245e-06,
                0.9997388097284476,
                0.9997965729334808,
                0.9997694932238538,
                0.01798620769203627,
                0.9998415637668497,
                0.999620015474337,
                0.042087728366189174,
                0.998830489661918,
                0.9988304897489515
            ],
            [
                8.939700562402957e-06,
                4.539787938592359e-05,
                1.8925148205003943e-05,
                4.222834450328596e-06,
                1.1478770845468629e-05,
                2.753569106169292e-05,
                1.012999218369684e-05,
                7.484625377419046e-05,
                2.1444958614225316e-05,
                2.7535687774465103e-05
            ],
            [
                5.144221339413591e-05,
                6.605215213033978e-05,
                4.539787924191364e-05,
                1.6701429786729373e-05,
                4.006368724152135e-05,
                9.610239133057177e-05,
                6.605212041044362e-05,
                4.539787935388468e-05,
                3.5356237914914405e-05,
                2.7535694337100886e-05
            ],
            [
                0.9975273773826131,
                0.9940889314912644,
                3.535626326580554e-05,
                0.9997965729640304,
                0.9998415638421463,
                0.9998766054112287,
                1.147877084843352e-05,
                5.8291265170878976e-05,
                0.9982992778810917,
                2.1444950898033508e-05
            ],
            [
                0.9978172835582045,
                0.22270013882530884,
                0.9964063981605675,
                0.9995121427792958,
                0.9991959139341264,
                0.9994472212836457,
                0.9997388097887205,
                0.060086644703857287,
                0.4687906266262437,
                0.08509905196799639
            ],
            [
                6.60521207602918e-05,
                2.7535694345515298e-05,
                2.7535681236473055e-05,
                0.0001795280245802812,
                1.6701417848916754e-05,
                2.753569104967234e-05,
                0.0001233946174601136,
                1.3007133110320344e-05,
                5.829127939562056e-05,
                6.605214309579518e-05
            ],
            [
                3.120191868460872e-05,
                0.00012339454323803358,
                0.9997040428372841,
                7.484623586490171e-05,
                5.8291251275666535e-05,
                4.5397863004134124e-05,
                0.9968273175021285,
                0.0007096703863041173,
                3.535625061440978e-05,
                3.5356267474535235e-05
            ],
            [
                2.4300246493981982e-05,
                1.4738985469509454e-05,
                1.147877222485351e-05,
                7.484622686261196e-05,
                4.0063711217164954e-05,
                3.120190013870751e-05,
                8.481108109252156e-05,
                2.7535700892525892e-05,
                9.610240231592715e-05,
                5.8291279135647154e-05
            ],
            [
                2.7535703949360714e-05,
                7.4846253614641e-05,
                2.4300240711101413e-05,
                8.93969522730838e-06,
                4.539785767808029e-05,
                5.144222492246673e-05,
                8.481106110570448e-05,
                2.1444940712293222e-05,
                1.8925152736303473e-05,
                3.535625478866761e-05
            ],
            [
                1.4738983724146862e-05,
                1.3007126909537681e-05,
                4.785092782858221e-06,
                4.006368258380272e-05,
                2.1444948406091176e-05,
                1.3007126908307386e-05,
                3.5356246441695886e-05,
                1.300713310000479e-05,
                1.6701425816409292e-05,
                1.1478766753082876e-05
            ],
            [
                3.535625475059587e-05,
                3.120190385315366e-05,
                4.006369207151113e-05,
                4.00637063801771e-05,
                3.120191880379252e-05,
                9.610243761002552e-05,
                0.000108896933980817,
                1.0129988558055338e-05,
                6.605216026239207e-05,
                3.120191504553037e-05
            ],
            [
                8.481105066433447e-05,
                3.120191500580244e-05,
                8.481101055497299e-05,
                2.1444950916288928e-05,
                0.00013982202252726443,
                6.605217596856826e-05,
                9.610245932904685e-05,
                1.892514143752361e-05,
                0.0001233945439831268,
                4.0063711105815703e-05
            ],
            [
                0.04742587587030561,
                0.9999687980998114,
                0.32082128783705344,
                0.985936371252163,
                0.03308597529010575,
                0.46879062662624377,
                1.0129992184802409e-05,
                0.4073334000459302,
                0.9993736657944162,
                0.9995694428266383
            ],
            [
                5.422219615395428e-06,
                3.1201907503354536e-05,
                5.422218321589366e-06,
                2.1444953502863275e-05,
                1.3007125342804474e-05,
                5.422220907298259e-06,
                1.1478765372946989e-05,
                3.535623793497923e-05,
                7.88926351873225e-06,
                1.300713309797007e-05
            ],
            [
                1.6701427800050252e-05,
                1.4738987220234187e-05,
                9.610239160884131e-05,
                2.7535684498857565e-05,
                4.0063706237055435e-05,
                8.939700557589678e-06,
                2.7535700874895704e-05,
                1.892514367067619e-05,
                1.4738978451920916e-05,
                1.4738983710366698e-05
            ],
            [
                0.9984988178141093,
                0.993307149750587,
                0.9986749774969819,
                0.9964063971342902,
                0.9994472214836695,
                0.9993736658632049,
                0.9994472212844818,
                0.9995121428844838,
                0.9997040428719,
                0.9995121429483459
            ],
            [
                0.0001233945942814186,
                4.539787391916088e-05,
                0.00017952792029852078,
                0.00020342706288471092,
                2.7535684494049335e-05,
                1.3007129998382795e-05,
                2.75357041631268e-05,
                3.120192247805892e-05,
                1.012998976043574e-05,
                0.00029595712692030533
            ],
            [
                2.144494839938192e-05,
                1.147877359392407e-05,
                1.4738983712565087e-05,
                5.1442194842967864e-05,
                1.1478763997446522e-05,
                3.535626747993731e-05,
                4.53978683430702e-05,
                5.829128619521875e-05,
                1.1478770850604989e-05,
                1.670142579143758e-05
            ],
            [
                2.4300232013798725e-05,
                3.5356237959931644e-05,
                0.0001795279197917916,
                5.144222554600421e-05,
                7.88926283605631e-06,
                1.89251482218717e-05,
                3.1201911030739795e-05,
                0.0001584361577062366,
                2.144494327788042e-05,
                1.8925154984741643e-05
            ],
            [
                2.4300246390021658e-05,
                4.539787393897876e-05,
                3.1201914995586685e-05,
                0.0001584362670135013,
                8.481106115136466e-05,
                3.535625062547117e-05,
                2.1444945825992654e-05,
                1.7603427759438738e-06,
                0.00013982207076885118,
                0.9999898700114376
            ],
            [
                9.610244849051068e-05,
                0.9999687980924049,
                5.829125131129093e-05,
                5.8291251268880934e-05,
                5.1442237637243264e-05,
                7.484626239585179e-05,
                2.430024937870426e-05,
                0.9999599363224334,
                0.00023050677921797194,
                5.144223551287382e-05
            ],
            [
                0.00015843620976652636,
                5.8291244363685945e-05,
                0.00023050667452712408,
                4.539785770549502e-05,
                9.610243642283476e-05,
                0.00017952802511313074,
                0.9999987901344609,
                0.0001795280244131127,
                0.0001233945870423414,
                4.539786307646937e-05
            ],
            [
                0.9998204721004774,
                0.9998415637087382,
                0.9995121428865275,
                0.9997388096986874,
                0.9997388096940668,
                0.9993736657406024,
                0.9971990729086689,
                0.9999251537732343,
                0.9991959140118523,
                0.9999339478241241
            ],
            [
                1.8925145971919677e-05,
                1.670142780381727e-05,
                6.144174597967793e-06,
                1.6701417845878833e-05,
                7.889265404959923e-06,
                1.3007130007515371e-05,
                1.0129994599624903e-05,
                1.1478769489343698e-05,
                6.962256248314727e-06,
                1.670141785809127e-05
            ],
            [
                0.999860177893019,
                0.9995121428983915,
                0.9986749774999087,
                0.9992903295996611,
                0.9940889304405308,
                0.9990889490200168,
                0.9947798740041763,
                0.9997694933127764,
                0.9980732653330906,
                0.9998204719516244
            ],
            [
                8.93969736456552e-06,
                4.785093924047376e-06,
                3.120191867870629e-05,
                3.535623797433717e-05,
                1.6701415858046724e-05,
                2.1444943276710197e-05,
                7.484621784507621e-05,
                2.144494327218535e-05,
                3.535625905424669e-05,
                3.12019150514328e-05
            ],
            [
                2.7535704219423216e-05,
                7.484621830139833e-05,
                4.00636825989602e-05,
                1.147877359392407e-05,
                6.60521285376864e-05,
                0.037326888950486185,
                2.753570091316123e-05,
                2.7535700919171523e-05,
                3.120191503327146e-05,
                2.144495351004062e-05
            ],
            [
                1.3007134654767206e-05,
                1.14787735942999e-05,
                1.147876810152382e-05,
                1.892514139084469e-05,
                1.8925157242612258e-05,
                1.8925157218446604e-05,
                2.4300240703498875e-05,
                3.535624642703312e-05,
                0.0001088969083866114,
                1.8925143716804326e-05
            ],
            [
                0.22270014398423355,
                0.012431652545409786,
                0.007577242556483639,
                0.02033235104233902,
                0.9995121428522405,
                0.9996200154366954,
                1.0129995805359584e-05,
                0.9964063974577636,
                0.08509904558710156,
                0.022977372502573448
            ],
            [
                0.9999993524053563,
                0.9999996940978461,
                0.9999974387184001,
                0.9999982396567869,
                7.484622697043032e-05,
                0.00017952802707736046,
                0.000709670308864834,
                0.9999982396574167,
                0.9999989322975119,
                0.0010322311289482067
            ],
            [
                2.430024649115313e-05,
                2.753570091616638e-05,
                4.0063687306232136e-05,
                9.610245899903851e-05,
                1.6701415855859424e-05,
                1.1478773591961393e-05,
                9.610243644101317e-05,
                4.0063711217164954e-05,
                3.535625483162694e-05,
                1.0129989767363975e-05
            ],
            [
                6.60521679244567e-05,
                5.1442231804958556e-05,
                4.539786282114907e-05,
                0.00020342694223160674,
                1.4738980203985296e-05,
                2.7535694353228506e-05,
                0.00010889693463520988,
                3.7266383485644795e-06,
                8.481107137554162e-05,
                5.1442225836439433e-05
            ],
            [
                2.7535681222849733e-05,
                8.939697367264857e-06,
                1.3007130006048483e-05,
                2.7535687767453096e-05,
                8.939695234170549e-06,
                3.1201900143474856e-05,
                1.0129994591443684e-05,
                2.1444943168347954e-05,
                1.4738978446451746e-05,
                1.6701423815087867e-05
            ],
            [
                3.535625482005107e-05,
                0.0001584362698488799,
                4.006368731264491e-05,
                6.605216000288915e-05,
                0.000626334234585675,
                0.0002959571085187339,
                1.1478765374158004e-05,
                0.00015843621195645214,
                5.144222558492851e-05,
                5.1442195075016483e-05
            ],
            [
                0.9999724643057633,
                0.0001088969212732369,
                5.829125142113282e-05,
                0.00012339458873002304,
                5.82912856820575e-05,
                8.481108067294151e-05,
                3.12019150080726e-05,
                4.0063706444596424e-05,
                5.8291265316769404e-05,
                6.605214443655996e-05
            ],
            [
                0.9999251537639957,
                0.9964063980621917,
                0.9997965729829367,
                0.9998415637659944,
                0.9997694933188261,
                0.9989677689445184,
                0.9999646437537651,
                0.9997965729617574,
                0.9990889487974401,
                0.9796676488463553
            ],
            [
                0.00010889686966178009,
                9.610240273822571e-05,
                8.939699185480258e-06,
                9.610239160884131e-05,
                0.002472622593841471,
                8.481102023122205e-05,
                2.7535684500460307e-05,
                0.999994577781032,
                0.9999885212291393,
                3.1201914891386007e-05
            ],
            [
                0.7310585669110202,
                0.9997040429400642,
                0.9999546021478132,
                0.9999339478482571,
                0.9984988180252522,
                0.9997388097323692,
                0.9997694932038869,
                0.9994472212745128,
                0.9989677689429578,
                0.9984988175610868
            ],
            [
                0.00013982202031994728,
                2.753569427399284e-05,
                7.484620895387416e-05,
                1.473898899256772e-05,
                5.829124379115109e-05,
                0.0002034269393903433,
                0.000487857197713836,
                0.00017952789990397858,
                4.5397879217141284e-05,
                4.5397873964411704e-05
            ],
            [
                2.4300243574253006e-05,
                5.82912792302215e-05,
                5.8291265213288994e-05,
                1.8925157249015125e-05,
                4.539789020153454e-05,
                1.0129988561077228e-05,
                0.06754669724011829,
                0.00010889686966178009,
                5.144223805268551e-05,
                5.8291251358366035e-05
            ],
            [
                7.484621787448121e-05,
                2.753568120842504e-05,
                7.484625363315528e-05,
                1.670142581373592e-05,
                9.610244892958953e-05,
                0.9997040428233688,
                6.605212860208155e-05,
                2.1444940694505896e-05,
                9.610240183489833e-05,
                7.48462179975466e-05
            ],
            [
                0.00010889693453538725,
                2.430024935112295e-05,
                6.605216004421738e-05,
                3.1201922481918207e-05,
                7.484624430849726e-05,
                0.000123394543372689,
                1.892515046555882e-05,
                9.610238012987338e-05,
                4.006367760515421e-05,
                5.144221945959009e-05
            ],
            [
                4.539785227077382e-05,
                7.484621805799024e-05,
                3.535625486558282e-05,
                5.82912723593753e-05,
                1.892515266277381e-05,
                5.1442219688644636e-05,
                0.00015843621488403716,
                0.00013982203949207473,
                3.535625062830082e-05,
                2.430023199947767e-05
            ],
            [
                3.1201922481918207e-05,
                4.0063701635592195e-05,
                1.1478769489009626e-05,
                1.0129988561077228e-05,
                1.300712845966209e-05,
                3.535625478866761e-05,
                9.61024031647193e-05,
                3.5356254902111115e-05,
                6.60521365779487e-05,
                1.0129992178648069e-05
            ],
            [
                7.889260135890724e-06,
                4.006369200475991e-05,
                0.00012339452728765338,
                0.00017952789777780592,
                0.00010889688082131166,
                4.539787942093518e-05,
                0.00010889689424507463,
                7.484620895387416e-05,
                0.00012339454342655116,
                7.484622586393069e-05
            ],
            [
                6.605212042966605e-05,
                0.9990889487017549,
                0.97068776908965,
                0.999569442871279,
                3.5356237793239226e-05,
                4.006368260129212e-05,
                0.9998911030915959,
                0.9796676483640301,
                0.00010889693288593691,
                4.0063711137296645e-05
            ],
            [
                6.605217598875182e-05,
                3.120191134459038e-05,
                6.144175330383673e-06,
                4.0063682527545155e-05,
                8.939699483383115e-06,
                1.892514821808506e-05,
                9.610244824859781e-05,
                0.0004878571609008625,
                0.00012339457426802834,
                0.00037998443551104735
            ],
            [
                0.9991959141714657,
                0.9964063982647793,
                0.9999599363078653,
                0.9999485577682411,
                0.9999339478398543,
                0.9996200154827276,
                0.9997388096338852,
                0.9999646437325821,
                0.9940889321561818,
                0.9993736657594027
            ],
            [
                0.9999251537821059,
                0.9999724643056662,
                0.9996646497749326,
                0.9998766053684531,
                0.9959298623860338,
                0.998299277809146,
                0.9999038975743094,
                0.999796573027361,
                0.9989677688532854,
                0.999769493232573
            ],
            [
                4.222834450820197e-06,
                1.4738980177926314e-05,
                1.4738980205164923e-05,
                1.6701417842658638e-05,
                8.9397005654763e-06,
                8.939698429568063e-06,
                7.889260702744606e-06,
                1.1478764002833434e-05,
                6.144177531208195e-06,
                1.8925154997134284e-05
            ]
        ]
    },
    {
        "q_id": "8925_mmlu_math",
        "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,
            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": [
            [
                2.90231163910023e-06,
                5.422220262195015e-06,
                2.9023112929973233e-06,
                4.7850939242083995e-06,
                1.0129989769464556e-05,
                6.475950297821511e-07,
                6.1441767987808774e-06,
                1.6701429801675944e-05,
                8.315284241560147e-07,
                6.47594798194325e-07
            ],
            [
                0.9999996533674202,
                0.9999980052702785,
                0.9999994956524715,
                0.9999995549149481,
                0.9999974387187053,
                0.9999994956523514,
                0.9999997300422225,
                0.9999995549151072,
                0.9999994956525918,
                0.999999730042126
            ],
            [
                7.88926164421493e-06,
                1.0677029973114952e-06,
                1.067703379154416e-06,
                3.288748281220719e-06,
                6.1441746017453204e-06,
                3.726637950973972e-06,
                1.0677026154473471e-06,
                1.0677033791495609e-06,
                5.422218322348809e-06,
                8.315279285205827e-07
            ],
            [
                0.9999996072136592,
                0.9999998362623137,
                0.9999995549150542,
                0.9999996072136125,
                0.9999997897567342,
                0.999999266179107,
                0.9999997617631183,
                0.9999997897566089,
                0.999997097688707,
                0.9999997617631752
            ],
            [
                0.9999992661788445,
                0.9999991684716749,
                0.9999998144608981,
                0.9999994284993485,
                0.9999998362623332,
                0.9999994284993485,
                0.9999990577556307,
                0.9999998144608317,
                0.9999996072139402,
                0.9999994956525317
            ],
            [
                0.999999057755069,
                0.9999996072138466,
                0.9999995549147889,
                0.9999989322975118,
                0.9999984465016899,
                0.9999991684715759,
                0.9999980052693275,
                0.9999952149055065,
                0.9999990577555185,
                0.9999987901347492
            ],
            [
                0.9999994284995529,
                0.9999995549148419,
                0.9999998144608981,
                0.9999986290431201,
                0.9999997300421581,
                0.9999991684718732,
                0.9999996072137529,
                0.9999996072139402,
                0.9999994284994167,
                0.9999991684720715
            ],
            [
                0.999999057755743,
                0.999998932296621,
                0.999999653367379,
                0.9999995549151073,
                0.9999989322975118,
                0.9999995549150542,
                0.9999832985821404,
                0.9999994284995529,
                0.9999994956527721,
                0.999999352404893
            ],
            [
                0.9999993524050473,
                0.9999994284992805,
                0.9999994956525917,
                0.9999987901340281,
                0.9999992661792819,
                0.9999987901337396,
                0.9999996072138466,
                0.9999990577551814,
                0.999999653367379,
                0.9999990577549569
            ],
            [
                0.9999994284996891,
                0.999999730042126,
                0.9999991684717741,
                0.9999987901341724,
                0.9999910603058291,
                0.9999970976883609,
                0.9999957771675626,
                0.9999982396569966,
                0.9999987901337396,
                0.9999984465022455
            ],
            [
                2.2603248367358324e-06,
                1.0677033791437343e-06,
                1.2098652508287273e-06,
                2.2603237588597026e-06,
                5.043475885606781e-07,
                1.994729008074216e-06,
                1.994729721436347e-06,
                1.3709575336530204e-06,
                2.2603251061664e-06,
                5.422220262505697e-06
            ],
            [
                0.999999057755069,
                0.9999986290424663,
                0.9999994284995529,
                0.9999987901346049,
                0.9999996940976636,
                0.9999987901341723,
                0.9999994284997573,
                0.9999996533673375,
                0.9999982396572064,
                0.999999168471675
            ],
            [
                0.9999994284994167,
                0.9999993524052018,
                0.9999991684721705,
                0.9999997897567341,
                0.9999995549148419,
                0.9999991684719723,
                0.9999994284992805,
                0.999999554914895,
                0.9999984465020603,
                0.9999987901341723
            ],
            [
                0.9999970976880149,
                0.9999987901338837,
                0.9999982396567867,
                0.9999996533672549,
                0.9999990577551815,
                0.9999989322970028,
                0.999999266178932,
                0.9999987901346049,
                0.9999991684719723,
                0.9999994956527121
            ],
            [
                1.5534977545603963e-06,
                3.288748673319648e-06,
                3.4663257978465195e-07,
                2.260324567302214e-06,
                2.902311639073834e-06,
                9.422443692446175e-07,
                1.9947292458930106e-06,
                5.71500515159253e-07,
                6.9622554187981796e-06,
                1.760342583722268e-06
            ],
            [
                0.999997438717484,
                0.9999996533674615,
                0.9999987901344607,
                0.9999996940976636,
                0.999999730042126,
                0.9999989322972573,
                0.9999990577555185,
                0.9999997300422225,
                0.9999994284997573,
                0.9999995549149481
            ],
            [
                0.999999168471675,
                0.9999832985702019,
                0.9999994284992805,
                0.9999996072136125,
                0.9999995549150011,
                0.999997438716568,
                0.9999982396572065,
                0.999998446502801,
                0.9999986290423029,
                0.9999993524052018
            ],
            [
                0.9999992661787571,
                0.9999986290423029,
                0.9999980052705164,
                0.9999989322975118,
                0.9999987901337396,
                0.9999977396751634,
                0.9999991684717741,
                0.9999984465022456,
                0.9999974387177893,
                0.9999962733620489
            ],
            [
                0.9999996072137061,
                0.9999995549150011,
                0.9999987901346049,
                0.99999893229713,
                0.9999991684721706,
                0.9999974387171787,
                0.9999982396563669,
                0.9999982396561572,
                0.9999995549147359,
                0.9999977396762411
            ],
            [
                0.999999653367379,
                0.9999991684722697,
                0.9999984465015047,
                0.9999987901340281,
                0.9999998144608319,
                0.9999982396559474,
                0.9999994284995529,
                0.9999994956524114,
                0.9999996533673788,
                0.9999997617629764
            ],
            [
                0.9999984465020603,
                0.9999996072136592,
                0.9999990577556308,
                0.9999991684721706,
                0.9999980052693275,
                0.9999995549147358,
                0.999997438716568,
                0.9999992661790195,
                0.9999957771665557,
                0.9999994284995529
            ],
            [
                4.450848927478102e-07,
                3.0590237278838124e-07,
                6.144172404380855e-06,
                9.422443692446175e-07,
                6.475946437966953e-07,
                1.2098662603862553e-06,
                9.422448185435711e-07,
                1.9947304347570075e-06,
                3.288748673265808e-06,
                4.222834451169694e-06
            ],
            [
                3.2887502413389517e-06,
                1.0677032518501217e-06,
                2.260324028372372e-06,
                2.260323489490968e-06,
                2.5612816000331606e-06,
                3.4663253846473677e-07,
                1.2098662604049616e-06,
                1.209865827740176e-06,
                3.726639728224814e-06,
                1.2098659719232413e-06
            ],
            [
                0.999999694097846,
                0.9999996533674615,
                0.9999980052700407,
                0.9999996533674615,
                0.9999987901343165,
                0.9999997617629764,
                0.9999993524052019,
                0.9999995549150011,
                0.9999996072136125,
                0.9999994284996893
            ],
            [
                0.999998629042303,
                0.9999993524052789,
                0.9999977396746245,
                0.9999999006880312,
                0.9999996940977002,
                0.9999996940976636,
                0.999999352404893,
                0.9999994284994849,
                0.9999996940978825,
                0.9999994956525317
            ],
            [
                0.9999989322972572,
                0.9999996072138465,
                0.9999997617631468,
                0.999999168471675,
                0.9999996940977366,
                0.9999996072139402,
                0.9999962733616046,
                0.9999991684717741,
                0.9999992661788446,
                0.9999995549147359
            ],
            [
                0.9999991684718732,
                0.9999980052700408,
                0.9999990577549569,
                0.9999993524054334,
                0.9999996072139402,
                0.9999991684720715,
                0.9999989322971299,
                0.9999992661786696,
                0.9999991684720715,
                0.9999992661787571
            ],
            [
                0.9999987901343166,
                0.9999984465028011,
                0.9999984465026158,
                0.999999428499553,
                0.9999991684720715,
                0.9999992661788445,
                0.9999987901341723,
                0.9999990577552937,
                0.9999993524053563,
                0.9999994284997573
            ],
            [
                0.9999996072137529,
                0.9999998362623528,
                0.9999997897567091,
                0.9999993524050473,
                0.9999998874647574,
                0.9999984465016899,
                0.9999993524053563,
                0.9999998362622357,
                0.9999984465022455,
                0.999999789756634
            ],
            [
                1.9947292458930106e-06,
                1.5534973841705173e-06,
                1.994729245842213e-06,
                2.561281294616881e-06,
                1.7603434231241496e-06,
                1.5534983100920427e-06,
                1.2098652508056196e-06,
                1.3709578605355551e-06,
                4.785096205830278e-06,
                5.043472278280699e-07
            ],
            [
                0.99999976176309,
                0.9999994284993485,
                0.999999694097846,
                0.9999984465020603,
                0.9999996940976636,
                0.9999994284993485,
                0.9999994284994848,
                0.9999990577552939,
                0.99999976176309,
                0.9999999226557592
            ],
            [
                0.9999997300422869,
                0.9999996072136592,
                0.9999997300421903,
                0.9999990577550691,
                0.9999989322972572,
                0.9999970976876689,
                0.9999995549147889,
                0.9999994956524114,
                0.9999992661788446,
                0.9999986290423029
            ],
            [
                0.9999994284994167,
                0.9999996072136125,
                0.9999990577557432,
                0.9999993524052018,
                0.9999991684717742,
                0.9999994956526519,
                0.9999989322968754,
                0.9999991684721706,
                0.9999995549150541,
                0.9999977396748938
            ],
            [
                0.9999989322970027,
                0.9999989322973846,
                0.9999980052705164,
                0.9999984465020603,
                0.9999986290421395,
                0.9999970976869771,
                0.9999991684719725,
                0.9999980052695652,
                0.9999977396748939,
                0.9999984465018751
            ],
            [
                0.9999994284996891,
                0.999997438717484,
                0.9999967112505427,
                0.9999977396759717,
                0.99999862904312,
                0.9999989322966208,
                0.9999994956527121,
                0.999994577780384,
                0.9999993524051246,
                0.9999967112509347
            ],
            [
                0.9999982396569966,
                0.9999994284994167,
                0.999999352404893,
                0.9999991684716749,
                0.9999994956525317,
                0.9999998144609645,
                0.9999987901343165,
                0.9999993524052018,
                0.9999994284994849,
                0.999999554914895
            ],
            [
                2.9023123310290063e-06,
                1.5534971989696065e-06,
                4.222831934156396e-06,
                2.561283126639892e-06,
                8.315284241257637e-07,
                3.288748673265808e-06,
                2.561282210562998e-06,
                3.9278610661545617e-07,
                1.5534981249164537e-06,
                3.7266406165827946e-06
            ],
            [
                0.9999989322973845,
                0.9999989322973845,
                0.9999994284996893,
                0.9999990577556308,
                0.9999993524051246,
                0.999997438717484,
                0.9999987901346049,
                0.999998239656367,
                0.999999554914789,
                0.9999990577552939
            ],
            [
                0.9999987901347492,
                0.999998629042303,
                0.9999986290426298,
                0.9999980052709919,
                0.9999991684719725,
                0.9999982396567867,
                0.999999266178932,
                0.9999984465015047,
                0.9999938558268635,
                0.9999993524051246
            ],
            [
                0.9999996940978095,
                0.9999993524049703,
                0.9999989322971301,
                0.9999994284996891,
                0.9999992661791945,
                0.999998239656367,
                0.999999694097773,
                0.9999980052702785,
                0.9999962733593832,
                0.9999997300422547
            ],
            [
                0.9999998362623528,
                0.999999554914895,
                0.9999997617631184,
                0.9999996072137998,
                0.9999995549149481,
                0.9999997897567091,
                0.9999996940977001,
                0.9999996533674615,
                0.9999997617631184,
                0.999999554914842
            ],
            [
                0.9999990577556308,
                0.9999995549148419,
                0.9999989322966208,
                0.9999994284994168,
                0.9999997617630048,
                0.9999982396565769,
                0.9999992661790196,
                0.999999495652652,
                0.9999987901337396,
                0.9999987901344608
            ],
            [
                0.9999991684716749,
                0.9999996072139402,
                0.9999967112497585,
                0.9999989322970027,
                0.9999992661786695,
                0.9999990577550691,
                0.9999997617631469,
                0.9999996940978095,
                0.999999554914842,
                0.9999995549150542
            ],
            [
                0.999997097689053,
                0.9999987901340281,
                0.9999996072137061,
                0.9999987901344607,
                0.9999997300421581,
                0.9999986290424664,
                0.9999997617631468,
                0.9999996533673788,
                0.9999994284997573,
                0.9999998144608317
            ],
            [
                2.902313023063532e-06,
                6.962258737650141e-06,
                4.785093353739995e-06,
                2.9023126769050284e-06,
                1.994729483608425e-06,
                8.9396941718352e-06,
                9.422448185435711e-07,
                1.3007128461838766e-05,
                2.2603253755949437e-06,
                7.338212429537553e-07
            ],
            [
                0.9999994284994167,
                0.999999057755743,
                0.9999994284992805,
                0.999999694097846,
                0.9999994284995529,
                0.9999980052695652,
                0.9999991684721706,
                0.9999991684715759,
                0.9999990577552937,
                0.9999982396567867
            ],
            [
                0.9999980052700408,
                0.999999352404893,
                0.9999997300421903,
                0.9999994956525918,
                0.9999989322973845,
                0.9999994284994167,
                0.9999986290432834,
                0.9999989322973846,
                0.999998005269803,
                0.9999994284996211
            ],
            [
                0.999999057755743,
                0.9999982396559473,
                0.9999997897566089,
                0.9999989322970028,
                0.9999952149055055,
                0.9999989322967481,
                0.999997097688361,
                0.9999994956524114,
                0.999994577782323,
                0.9999986290421395
            ],
            [
                0.9999989322973845,
                0.9999991684716749,
                0.9999996940978095,
                0.9999987901341723,
                0.9999990577549568,
                0.999998239656367,
                0.9999994284993486,
                0.999997097686977,
                0.9999977396762411,
                0.9999974387171787
            ],
            [
                0.9999987901347491,
                0.9999995549150541,
                0.9999994284994167,
                0.9999996533674614,
                0.9999996533672135,
                0.9999996072137998,
                0.9999977396757022,
                0.9999996533673375,
                0.9999997617631469,
                0.999999168471675
            ],
            [
                1.7603436329714805e-06,
                1.994730197071414e-06,
                8.93969950000193e-06,
                3.2887490653109436e-06,
                1.9947290080343035e-06,
                4.785096205717126e-06,
                1.3709570433885908e-06,
                6.475947209953583e-07,
                1.7603432133136672e-06,
                2.260324567302214e-06
            ],
            [
                0.9999993524052018,
                0.9999998362623137,
                0.9999987901341723,
                0.9999967112501507,
                0.999999730042126,
                0.9999980052698029,
                0.9999993524052018,
                0.9999990577556308,
                0.9999995549147889,
                0.999999554914895
            ],
            [
                0.9999989322972572,
                0.999998790134028,
                0.9999990577552937,
                0.9999986290421394,
                0.9999992661791944,
                0.999997097686977,
                0.999998446502801,
                0.9999992661792819,
                0.99999893229713,
                0.9999990577557432
            ],
            [
                0.9999986290423029,
                0.9999994956526519,
                0.999999730042126,
                0.9999996533675028,
                0.9999997300422547,
                0.9999998144608098,
                0.9999724642990652,
                0.9999992661791944,
                0.9999990577549569,
                0.9999996533672136
            ],
            [
                4.222834450820197e-06,
                1.0677032518209896e-06,
                2.9023119850210436e-06,
                1.7603432132624344e-06,
                1.99472995920443e-06,
                1.0129992186202796e-05,
                1.7603440527046419e-06,
                2.2603248367173307e-06,
                2.9023109471452223e-06,
                1.2098652508144226e-06
            ],
            [
                0.9999991684720715,
                0.9999938558239335,
                0.999999266178932,
                0.9999984465022455,
                0.9999990577552937,
                0.9999994284993485,
                0.9999987901337396,
                0.9999930377454107,
                0.9999982396572065,
                0.9999991684715758
            ],
            [
                0.9999992661787571,
                0.999999352404893,
                0.9999990577552937,
                0.999999352405279,
                0.9999994284994849,
                0.9999995549151073,
                0.9999994284994167,
                0.999999855502048,
                0.9999996533674614,
                0.9999996072137061
            ],
            [
                0.999999554914789,
                0.999999352405279,
                0.9999992661790196,
                0.9999998724810027,
                0.9999994956524114,
                0.9999994284994849,
                0.9999990577551815,
                0.9999992661791944,
                0.9999997617631468,
                0.9999993524049702
            ],
            [
                0.9999982396572065,
                0.9999970976880149,
                0.9999987901346049,
                0.9999987901341723,
                0.9999986290429566,
                0.9999994284996211,
                0.9999989322972572,
                0.9999987901337396,
                0.9999987901337396,
                0.999998446502801
            ],
            [
                4.785096776133645e-06,
                7.889265406681968e-06,
                1.9947292458930106e-06,
                2.902311984989368e-06,
                1.0677026154551157e-06,
                1.9947301970451086e-06,
                3.288749457409966e-06,
                1.0677027427471959e-06,
                1.209865683500459e-06,
                1.55349775456958e-06
            ],
            [
                3.7266397280960194e-06,
                1.5534984953199313e-06,
                7.338209804920378e-07,
                1.9947292458930106e-06,
                9.422442569208767e-07,
                2.430023203572232e-05,
                6.144175334015912e-06,
                2.260324567268294e-06,
                1.0677029972920738e-06,
                2.561281905376098e-06
            ],
            [
                0.9999977396759716,
                0.9999984465024306,
                0.9999987901344608,
                0.9999991684721706,
                0.9999982396559474,
                0.99999893229713,
                0.999989870009022,
                0.9999986290431201,
                0.9999986290427931,
                0.9999989322970028
            ],
            [
                0.9999997617629764,
                0.9999998874648245,
                0.9999994956526519,
                0.9999980052700408,
                0.9999996940978825,
                0.9999996072138465,
                0.9999984465020603,
                0.9999994956524716,
                0.9999996072138465,
                0.9999995549147358
            ],
            [
                0.9999930377404309,
                0.9999967112521106,
                0.9999990577550691,
                0.9999987901344607,
                0.9999967112497586,
                0.9999992661790196,
                0.9999996940976636,
                0.9999962733620488,
                0.9999967112521109,
                0.999999057755743
            ],
            [
                7.88925976397226e-06,
                1.5534973841705173e-06,
                2.56128159999123e-06,
                2.561282210701601e-06,
                1.7603432132912532e-06,
                5.422219615829396e-06,
                1.99472924590571e-06,
                1.5534979397500702e-06,
                1.5534973841450852e-06,
                4.785092783267308e-06
            ],
            [
                0.9999977396762411,
                0.999998629042303,
                0.9999996072139402,
                0.9999987901343165,
                0.9999987901344607,
                0.999999352404893,
                0.9999984465022455,
                0.9999967112517189,
                0.9999994284996893,
                0.9999986290429566
            ],
            [
                0.9999991684722698,
                0.999999352405279,
                0.9999989322970027,
                0.9999993524049703,
                0.9999989322973846,
                0.9999996533674614,
                0.9999994284996211,
                0.9999984465026159,
                0.9999991684715759,
                0.9999993524050473
            ],
            [
                5.422220908703723e-06,
                1.2098655392662613e-06,
                6.144172404380855e-06,
                4.2228349546493465e-06,
                1.0129989768911772e-05,
                1.3709575336860625e-06,
                4.222835457852533e-06,
                2.902312330965655e-06,
                2.260323489490968e-06,
                2.9023109471452223e-06
            ],
            [
                0.9999921107383553,
                0.9999992661786695,
                0.9999785550439274,
                0.9999980052702792,
                0.9999885212359813,
                0.9999957771645421,
                0.9999930377445811,
                0.9999910603047624,
                0.9999930377420908,
                0.9999898700041909
            ],
            [
                1.5534971989427613e-06,
                1.9947301970287804e-06,
                8.315284241401329e-07,
                9.422448185388577e-07,
                8.315282259009745e-07,
                1.3709575336405514e-06,
                1.7603425837702984e-06,
                6.47594566597747e-07,
                8.315282259051341e-07,
                1.7603440527046419e-06
            ],
            [
                0.9999986290427932,
                0.9999990577556307,
                0.9999995549149481,
                0.9999993524049703,
                0.9999994284993485,
                0.9999996533672136,
                0.9999996072137998,
                0.99999862904312,
                0.9999989322968754,
                0.9999980052709919
            ],
            [
                4.785093923916815e-06,
                1.1478764017428212e-05,
                1.994729245842213e-06,
                1.994730672468935e-06,
                2.5612812945889277e-06,
                1.0129990976728036e-05,
                1.7603432132464244e-06,
                2.2603251061664e-06,
                9.422449308566668e-07,
                1.2098652507957165e-06
            ],
            [
                0.9999984465016899,
                0.9999992661790196,
                0.9999962733607162,
                0.9999996940976636,
                0.9999997617630616,
                0.999999352405279,
                0.9999993524054334,
                0.9999998555020306,
                0.9999994956524716,
                0.999997097686977
            ],
            [
                0.9999339478711677,
                0.9999151889789185,
                0.9999832985821387,
                0.999964643732436,
                0.9999756997505811,
                0.9999756997505828,
                0.999991060303783,
                0.9999852610127603,
                0.9998766054252257,
                0.9997965729544204
            ],
            [
                3.726640172503764e-06,
                1.3709573702647743e-06,
                2.90231163910023e-06,
                1.5534977545603963e-06,
                1.2098656835076114e-06,
                1.3709572068272963e-06,
                3.7266379512112265e-06,
                3.726640172503764e-06,
                8.315280276580819e-07,
                1.9947306726358406e-06
            ],
            [
                0.9999974387168733,
                0.9999898700066059,
                0.9999810748585282,
                0.9999977396762411,
                0.9999785550515903,
                0.999997097688707,
                0.999995214905506,
                0.9999974387184,
                0.9999898700102279,
                0.9999980052700407
            ],
            [
                0.9999994284997573,
                0.9999994284994849,
                0.9999986290421394,
                0.99999893229713,
                0.9999989322966208,
                0.9999987901341723,
                0.9999982396565767,
                0.9999991684717742,
                0.9999994284997573,
                0.999999554914895
            ],
            [
                0.999954602120557,
                0.9999546021260118,
                0.9998204719698691,
                0.9999977396751634,
                0.9999852610215454,
                0.9999869928684358,
                0.9998601779426847,
                0.9999898700102287,
                0.9999910603058273,
                0.9999885212346119
            ],
            [
                0.999999352404893,
                0.9999996533675028,
                0.9999986290429566,
                0.9999996072139402,
                0.9999994284994849,
                0.9999989322970027,
                0.9999995549147358,
                0.9999994284994849,
                0.9999996072138465,
                0.9999993524051246
            ],
            [
                0.9999996533675028,
                0.9999997300420937,
                0.9999994284994167,
                0.9999986290424664,
                0.999999653367379,
                0.9999996072137061,
                0.9999996940978095,
                0.9999997617630899,
                0.9999982396565769,
                0.9999995549149481
            ],
            [
                0.9999989322973846,
                0.999999554914895,
                0.9999977396759716,
                0.9999980052693275,
                0.9999952149060758,
                0.9999977396762411,
                0.9999984465015047,
                0.9999990577554061,
                0.9999992661791944,
                0.9999974387168733
            ],
            [
                0.999999168471675,
                0.9999993524049703,
                0.9999992661792819,
                0.9999992661789321,
                0.9999995549148419,
                0.9999990577556308,
                0.9999986290429566,
                0.9999990577550691,
                0.9999994956524114,
                0.9999993524049702
            ],
            [
                0.9999987901347492,
                0.9999982396569966,
                0.9999994284996211,
                0.9999995549149481,
                0.9999994284992805,
                0.9999984465020603,
                0.9999994284997573,
                0.9999998362623332,
                0.9999989322972572,
                0.9999996940978095
            ],
            [
                0.9999952149055056,
                0.9999832985821396,
                0.9999832985801516,
                0.9999724643187544,
                0.9999980052709919,
                0.9999038975736549,
                0.9999898700053983,
                0.9999945777784447,
                0.9999785550515884,
                0.9998204720768021
            ],
            [
                0.9999994284996211,
                0.9999996940977366,
                0.9999995549148419,
                0.9999991684715759,
                0.9999996940977731,
                0.9999996940976272,
                0.9999993524051246,
                0.9999994284992805,
                0.9999997617631752,
                0.999996273358939
            ],
            [
                0.999998005269803,
                0.9999982396574163,
                0.9999986290423029,
                0.9999962733607166,
                0.9999952149032239,
                0.9999938558275955,
                0.9999970976866311,
                0.9999993524053562,
                0.9999945777810302,
                0.9999980052695652
            ],
            [
                0.9999852610232999,
                0.9999898700114359,
                0.9998911031167924,
                0.9999885212277715,
                0.9999869928762549,
                0.9999724643121848,
                0.999704042795719,
                0.9999756997679594,
                0.9999785550439183,
                0.9999687980849155
            ],
            [
                0.999999352405279,
                0.9999832985801492,
                0.9999982396574163,
                0.9999970976866309,
                0.9999986290421394,
                0.9999982396561572,
                0.9999977396748938,
                0.9999967112505427,
                0.9999938558246657,
                0.999997097686977
            ],
            [
                0.9999987901347491,
                0.9999995549147359,
                0.999999352404893,
                0.9999998144608981,
                0.9999987901338838,
                0.999999352405279,
                0.9999980052709919,
                0.999999057755743,
                0.9999994284996891,
                0.999997438717484
            ],
            [
                6.475948753930064e-07,
                1.7603425837494853e-06,
                9.422443692176231e-07,
                9.422448185264317e-07,
                9.422444815726566e-07,
                1.5534975693488444e-06,
                5.422218969769604e-06,
                2.260324028372372e-06,
                4.785093924156175e-06,
                5.715006513999389e-07
            ],
            [
                1.7603440525925705e-06,
                6.962255419051463e-06,
                4.785094494576774e-06,
                3.7266388395620047e-06,
                2.2603245671490605e-06,
                2.561283431916622e-06,
                1.2098653950315304e-06,
                1.0677033791204289e-06,
                1.7603427935342762e-06,
                6.144177531381426e-06
            ],
            [
                0.9999869928653384,
                0.9999930377412607,
                0.9999485577925429,
                0.999996273360716,
                0.9999485577618699,
                0.9999980052695652,
                0.9999852610127582,
                0.9999756997563777,
                0.9999885212332457,
                0.9999687980998067
            ],
            [
                0.9399133565584851,
                0.999738809722634,
                0.9999251538003163,
                0.9999546021368911,
                0.8933094138654242,
                0.9525741216052517,
                0.9999485577802474,
                0.9991959141915752,
                0.6513548714339145,
                0.9149009613738742
            ],
            [
                0.999999168471675,
                0.9999992661786696,
                0.9999993524051246,
                0.9999987901341724,
                0.9999991684720715,
                0.9999989322973845,
                0.9999992661786695,
                0.9999997617630048,
                0.9999994284996891,
                0.9999984465016899
            ],
            [
                0.9999977396759716,
                0.9999996940977366,
                0.9999984465020603,
                0.9999994956523514,
                0.9999990577554061,
                0.9999974387177893,
                0.9999974387177893,
                0.9999986290432834,
                0.9999998144609423,
                0.999999266178932
            ],
            [
                0.8175744761936437,
                0.9999546021151456,
                NaN,
                0.9999251537829096,
                0.5926665999540698,
                0.5,
                0.9399133515091156,
                0.4378234991142019,
                0.679178699175393,
                0.999915188928401
            ],
            [
                0.9999994284993486,
                0.9999977396765105,
                0.9999993524050474,
                0.9999994956527722,
                0.9999982396561571,
                0.9999994284997573,
                0.9999990577555185,
                0.9999996533672962,
                0.9999957771680658,
                0.9999980052693274
            ],
            [
                1.7603438428028262e-06,
                5.422217029736466e-06,
                1.9947292458603553e-06,
                5.422220908762902e-06,
                7.338209805040511e-07,
                1.3709576971316842e-06,
                2.9023112930949896e-06,
                9.422450431912e-07,
                1.7603434230921292e-06,
                4.222831934156396e-06
            ],
            [
                0.9999991684719723,
                0.9999997300422225,
                0.9999989322972572,
                0.9999996940978095,
                0.9999982396574163,
                0.9999984465018751,
                0.9999980052702787,
                0.999997097688015,
                0.9999992661792819,
                0.9999993524052019
            ],
            [
                0.9999938558261318,
                0.9999989322968754,
                0.9999986290427932,
                0.9999990577555186,
                0.9999994956525918,
                0.9999957771665557,
                0.9999957771660524,
                0.9999967112509347,
                0.9999993524052019,
                0.9999977396746245
            ],
            [
                0.9999967112505428,
                0.9999885212264024,
                0.999975699759271,
                0.9999724643023452,
                0.9999921107392958,
                0.9999546021313694,
                0.9999785550592593,
                0.9999810748472499,
                0.9999869928668873,
                0.9998911030390718
            ],
            [
                0.9999993524053562,
                0.9999938558253983,
                0.9999980052702786,
                0.9999982396565769,
                0.9999991684720715,
                0.9999984465026158,
                0.9999992661788446,
                0.9999996940976272,
                0.9999993524050474,
                0.99999893229713
            ],
            [
                0.999999554914895,
                0.999999730042126,
                0.9999996072137998,
                0.9999994284994167,
                0.9999982396565769,
                0.9999987901343166,
                0.9999987901341723,
                0.9999986290426297,
                0.9999997617630049,
                0.9999993524052018
            ],
            [
                0.9999986290421394,
                0.9999992661790195,
                0.999999266178757,
                0.9999974387180948,
                0.9999994284992804,
                0.9999974387187054,
                0.9999996072138934,
                0.9999974387184,
                0.9999986290426298,
                0.9999982396561572
            ],
            [
                2.260324567268294e-06,
                1.76034300345598e-06,
                8.939695236593446e-06,
                3.726637951028202e-06,
                3.288750633488963e-06,
                5.715005832853093e-07,
                3.288748673319648e-06,
                2.9023112931688987e-06,
                1.4738988998117324e-05,
                1.76034300345598e-06
            ],
            [
                0.9999991684721706,
                0.9999989322971299,
                0.9999990577551814,
                0.9999982396569966,
                0.9999967112493666,
                0.9999986290424664,
                0.9999989322968754,
                0.99999893229713,
                0.9999986290421395,
                0.9999996940978461
            ],
            [
                0.9999967112517191,
                0.9999967112509347,
                0.999876605426671,
                0.9999910603015801,
                0.9999852610187955,
                0.9999945777810307,
                0.9999852610162758,
                0.9999910603038269,
                0.8807970670261976,
                0.9999785550592668
            ],
            [
                0.9999982396574163,
                0.9999997300423191,
                0.9999994284996893,
                0.9999962733589393,
                0.9999977396748939,
                0.9999984465018751,
                0.9999974387177895,
                0.999999352405279,
                0.9999994284993485,
                0.9999994284995529
            ],
            [
                0.999999266178757,
                0.9999982396567867,
                0.9999957771675627,
                0.9999997897565587,
                0.999999352404893,
                0.9999982396572065,
                0.9999991684721706,
                0.9999994956524114,
                0.9999982396572064,
                0.9999994956524716
            ],
            [
                0.9999993524052018,
                0.9999987901346049,
                0.9999994956526519,
                0.9999996533673375,
                0.9999987901346049,
                0.9999977396748938,
                0.9999974387187053,
                0.999998790134028,
                0.9999993524051246,
                0.9999991684715759
            ],
            [
                0.999999266179107,
                0.9999995549149481,
                0.9999993524054335,
                0.9999996072136592,
                0.9999986290431201,
                0.9999991684722698,
                0.9999998362623528,
                0.9999990577556307,
                0.9999994284996211,
                0.9999994284993485
            ],
            [
                0.9999990577555185,
                0.9999982396559474,
                0.9999991684718733,
                0.9999996072136592,
                0.9999997300422869,
                0.9999987901340281,
                0.9999994284993485,
                0.9999992661786696,
                0.9999996072137998,
                0.999999730042319
            ],
            [
                0.9999993524051246,
                0.9999994956527121,
                0.9999993524051246,
                0.9999993524054335,
                0.9999984465022455,
                0.9999996072136592,
                0.9999991684715759,
                0.9999992661787571,
                0.9999994284993485,
                0.9999994956526519
            ],
            [
                0.9999996940976272,
                0.999998005269803,
                0.9999991684722698,
                0.9999992661790196,
                0.9999994956524716,
                0.9999980052700408,
                0.9999980052707541,
                0.999999730042126,
                0.9999991684717742,
                0.9999989322966208
            ],
            [
                0.999997097688361,
                0.9999990577551814,
                0.9999974387168734,
                0.9999994956527121,
                0.9999991684718732,
                0.9999756997476887,
                0.9999980052705163,
                0.9999970976873229,
                0.9999984465020603,
                0.9999962733620488
            ],
            [
                1.7603425836870455e-06,
                1.7603438428028262e-06,
                3.7266388396128453e-06,
                6.475949525878687e-07,
                2.561283432005142e-06,
                3.2887498494282754e-06,
                6.962257909323729e-06,
                1.3709578604831862e-06,
                1.370957370236096e-06,
                1.994730434798734e-06
            ],
            [
                0.999999554914895,
                0.9999996533672549,
                0.9999989322967482,
                0.9999994284997573,
                0.999999694097846,
                0.9999992661792819,
                0.9999984465022455,
                0.9999990577549569,
                0.9999986290423029,
                0.999997097687669
            ],
            [
                0.9999991684716749,
                0.9999989322975118,
                0.9999997617630616,
                0.9999998144608981,
                0.9999995549147889,
                0.999999730042126,
                0.9999996940977731,
                0.9999997300422225,
                0.9999997617631468,
                0.999998790134028
            ],
            [
                5.422218969769604e-06,
                1.7603436329714805e-06,
                1.5534975693347152e-06,
                6.144173136885882e-06,
                9.422447062202052e-07,
                8.939695236398313e-06,
                1.2098653950205268e-06,
                3.7266392839832006e-06,
                2.260323758923431e-06,
                1.7603438428028262e-06
            ],
            [
                1.7603440526806268e-06,
                2.561282515886208e-06,
                1.5534984953199313e-06,
                1.7603436329394601e-06,
                2.5612815999679353e-06,
                2.5612819052374947e-06,
                1.2098661161789477e-06,
                3.288748673265808e-06,
                1.553498495308628e-06,
                6.475948753847607e-07
            ],
            [
                1.0129992186774007e-05,
                1.5534977545497995e-06,
                8.315281267800897e-07,
                4.785096776251149e-06,
                6.962253759043525e-06,
                4.222831934202483e-06,
                1.994730196992497e-06,
                9.422450431860582e-07,
                2.260323489490968e-06,
                2.902312331081799e-06
            ],
            [
                0.9999986290426297,
                0.9999986290429567,
                0.9999967112497584,
                0.9999994284994849,
                0.9999977396751634,
                0.9999996072137061,
                0.9999995549148419,
                0.9999982396567867,
                0.999998005269803,
                0.9999989322973845
            ],
            [
                0.9999991684719723,
                0.9999991684721706,
                0.999999730042126,
                0.9999977396765105,
                0.999999694097773,
                0.9999970976866309,
                0.9999970976873229,
                0.9999982396567867,
                0.9999987901338838,
                0.9999991684715759
            ],
            [
                0.999975699767969,
                0.9999957771665667,
                0.9999785550413773,
                0.9999417087136605,
                0.9999945777811098,
                0.9999646437535286,
                0.9999756997592866,
                0.9999599363173919,
                0.999985261014518,
                0.9999967112501509
            ],
            [
                3.9278605979011705e-07,
                7.88925976359915e-06,
                8.31527829351332e-07,
                2.2603234893861252e-06,
                3.7266388397382506e-06,
                8.315282258832022e-07,
                5.715003788933905e-07,
                3.2887482811220126e-06,
                6.962258738283349e-06,
                2.5612822106841303e-06
            ],
            [
                2.902311985079115e-06,
                2.902313368897403e-06,
                1.0677033791495609e-06,
                4.450851580497677e-07,
                5.422218969463855e-06,
                2.9023116391477434e-06,
                2.9023116391477434e-06,
                1.3709575336654889e-06,
                1.0677029972920738e-06,
                1.7603434231705793e-06
            ]
        ]
    },
    {
        "q_id": "8225_mmlu_math",
        "cot_ids": [
            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,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999974387180948,
                0.9999993524050474,
                0.9999970976883611,
                0.9999991684721707,
                0.99999893229713,
                0.9999994284995529,
                0.9999930377420914,
                0.9999977396765105,
                0.9999982396569966,
                0.9999990577554061
            ],
            [
                0.9999998555019619,
                0.999999653367379,
                0.9999998362622747,
                0.9999997300422548,
                0.9999997897565838,
                0.9999998555019791,
                0.999999814460854,
                0.9999996940978825,
                0.9999998362623528,
                0.999999887464744
            ],
            [
                0.9999998144609645,
                0.9999994956524716,
                0.9999993524050476,
                0.9999994956524716,
                0.9999997300422225,
                0.9999997617630048,
                0.999999653367379,
                0.9999991684721706,
                0.9999999006880785,
                0.999999653367503
            ],
            [
                0.9999996940977366,
                0.9999997617631183,
                0.9999998144609424,
                0.9999997617630899,
                0.9999999006880786,
                0.9999994956526519,
                0.9999998724810027,
                0.9999999226557961,
                0.9999998144609645,
                0.9999997897567342
            ],
            [
                0.9999998874648648,
                0.9999998362623528,
                0.9999999123574942,
                0.9999998144609645,
                0.9999998724809419,
                0.9999996940977002,
                0.999999789756634,
                0.9999997617631184,
                0.9999998144608097,
                0.9999998362623723
            ],
            [
                0.9999994284993488,
                0.9999996940977366,
                0.9999997300422547,
                0.9999998555020135,
                0.9999998555019618,
                0.999999814460854,
                0.9999997300421581,
                0.9999996072138934,
                0.99999976176309,
                0.9999998362622943
            ],
            [
                0.9999997300422547,
                0.9999852610113883,
                0.9999982396567868,
                0.9999993524054335,
                0.9999997617629764,
                0.9999998724809723,
                0.9999997897567091,
                0.9999992661790195,
                0.9999997897565838,
                0.9999967112509347
            ],
            [
                5.4222202623972055e-06,
                4.222834954607099e-06,
                1.0129988563730593e-05,
                2.902312331125353e-06,
                1.3709576971160984e-06,
                2.561283432005142e-06,
                3.288747889229516e-06,
                1.300713311614059e-05,
                2.2603234894560207e-06,
                1.670142781520948e-05
            ],
            [
                0.9999989322970028,
                0.9999987901347492,
                0.9999970976877339,
                0.9999974387184004,
                0.9999996533672136,
                0.9999991684720715,
                0.9999994284997574,
                0.9999990577556308,
                0.9999997897567091,
                0.999999653367379
            ],
            [
                0.9999997617631184,
                0.9999997617631752,
                0.9999996533673375,
                0.9999996533675028,
                0.9999994284997575,
                0.9999998724809571,
                0.9999998555020307,
                0.9999998874649051,
                0.9999994956524716,
                0.9999994284996893
            ],
            [
                0.9999994284996214,
                0.9999997617631184,
                0.9999998874648379,
                0.9999998874647441,
                0.9999999226557869,
                0.9999998874648246,
                0.9999999006881141,
                0.9999999006880075,
                0.9999996940977731,
                0.9999999226557408
            ],
            [
                0.9999990577557432,
                0.9999996533674202,
                0.9999996940978826,
                0.9999996072136125,
                0.9999994956527722,
                0.99999976176309,
                0.9999997617629764,
                0.9999996940976272,
                0.9999995549151073,
                0.9999996533674202
            ],
            [
                0.9999996533672136,
                0.9999998362622747,
                0.9999998362623528,
                0.9999996940977366,
                0.9999998144608317,
                0.9999998362623332,
                0.9999997617630616,
                0.9999996940976638,
                0.9999999123575987,
                0.9999998362623332
            ],
            [
                0.9999999123574836,
                0.9999997897567341,
                0.9999998362623528,
                0.9999999006881377,
                0.9999998724810026,
                0.9999998362622552,
                0.9999997617630332,
                0.9999996940978095,
                0.9999994956524115,
                0.9999994956527121
            ],
            [
                0.9999994284994848,
                0.9999986290429567,
                0.9999996072137998,
                0.9999994956525317,
                0.9999994956525918,
                0.999999352404893,
                0.9999994284996891,
                0.9999998555019618,
                0.999999789756634,
                0.9999990577551815
            ],
            [
                0.9999996533674615,
                0.9999996533672549,
                0.9999998362623332,
                0.9999996072136593,
                0.9999996940977002,
                0.9999997300421583,
                0.9999997300420939,
                0.9999990577554062,
                0.9999996940978825,
                0.9999997300421903
            ],
            [
                0.9999998555020307,
                0.9999998144609424,
                0.9999996533674201,
                0.999999814460854,
                0.9999996533674615,
                0.9999998362623138,
                0.9999997897566089,
                0.9999998362622746,
                0.9999995549147889,
                0.9999997897565587
            ],
            [
                0.9999995549149481,
                0.999999887464905,
                0.9999998874648648,
                0.9999998144608098,
                0.9999997897565588,
                0.9999998144609202,
                0.9999997617631752,
                0.9999994284996893,
                0.9999996940976636,
                0.9999997617631469
            ],
            [
                0.9999998874649318,
                0.9999998874649184,
                0.9999999226558423,
                0.9999999123575987,
                0.9999994284997574,
                0.9999997897566089,
                0.9999998362623137,
                0.9999996533672962,
                0.9999998724809419,
                0.9999998144608317
            ],
            [
                0.9999998144609423,
                0.9999997617631184,
                0.9999996072136125,
                0.9999996940976636,
                0.9999998362623722,
                0.9999998555020134,
                0.9999996533673375,
                0.9999997300423191,
                0.999999653367379,
                0.9999997897566089
            ],
            [
                0.9999997897565838,
                0.9999998555020134,
                0.9999995549149481,
                0.9999997617631184,
                0.9999996533672963,
                0.9999996072136592,
                0.9999997300422869,
                0.9999996533673375,
                0.9999996940977002,
                0.9999998144608981
            ],
            [
                0.9999997897567342,
                0.9999998724809571,
                0.9999998555020134,
                0.9999996940978461,
                0.9999998555019618,
                0.9999996940977366,
                0.9999998362623138,
                0.9999998555020135,
                0.9999996940977001,
                0.9999997300421261
            ],
            [
                1.4738987242432592e-05,
                7.88926540679677e-06,
                2.430024651882284e-05,
                2.9023133690637e-06,
                1.1478765386330758e-05,
                1.0129990978441666e-05,
                1.3007133113703658e-05,
                8.939695237959376e-06,
                8.939695238089467e-06,
                2.7535691091443854e-05
            ],
            [
                0.9999999123574628,
                0.9999998362623137,
                0.9999999006880667,
                0.9999996072138934,
                0.9999999006880312,
                0.9999999317439384,
                0.9999999468421249,
                0.9999998874649051,
                0.9999998555019273,
                0.9999999468421122
            ],
            [
                0.9999997300421583,
                0.9999998362623332,
                0.9999998874648514,
                0.9999998874649318,
                0.999999789756659,
                0.9999999123574419,
                0.9999998362623528,
                0.9999997300422225,
                0.9999999006880667,
                0.9999996940977002
            ],
            [
                0.9998766054260174,
                0.999796572955921,
                0.9999151889388376,
                0.9998204719710603,
                0.9997694932610044,
                0.9999810748517772,
                0.999991060301585,
                0.9993736656931645,
                0.999964643762085,
                0.9997388096020123
            ],
            [
                0.9999998555020134,
                0.9999996940978095,
                0.9999997617629763,
                0.9999999123575987,
                0.9999994956527722,
                0.9999998362623138,
                0.9999996533672136,
                0.9999993524050474,
                0.9999998362623528,
                0.9999997617630616
            ],
            [
                0.9999998144609202,
                0.9999998874648915,
                0.999999789756634,
                0.9999997897565838,
                0.9999998874647976,
                0.9999997897567342,
                0.9999997300421904,
                0.9999998362623332,
                0.9999998724809267,
                0.9999997617631753
            ],
            [
                5.422217676925328e-06,
                6.475947209985977e-07,
                8.939695237813028e-06,
                1.6701417861189946e-05,
                2.902311293147782e-06,
                7.484625356672172e-05,
                6.144172404028807e-06,
                2.902312677084523e-06,
                8.939700565996655e-06,
                7.484620041444411e-05
            ],
            [
                0.9999996940977366,
                0.9999998362622552,
                0.99999976176309,
                0.9999997617631468,
                0.9999998362623722,
                0.9999998555019274,
                0.9999997300422547,
                0.9999998555019962,
                0.9999999123575255,
                0.9999997897566589
            ],
            [
                2.5612825159421147e-06,
                4.222833444429485e-06,
                1.1478773597118638e-05,
                8.93969417199781e-06,
                1.1478768124553928e-05,
                3.7266410609940346e-06,
                3.726640172503764e-06,
                1.9947299590520376e-06,
                1.994729721396435e-06,
                2.430023492769181e-05
            ],
            [
                0.9999999226557408,
                0.9999996072137062,
                0.999999789756684,
                0.9999994284996893,
                0.99999992265575,
                0.9999992661792819,
                0.999999789756659,
                0.999999694097773,
                0.9999999226558146,
                0.9999998555020307
            ],
            [
                0.9999993524054334,
                0.9999994956523514,
                0.9999996940977001,
                0.9999995549147358,
                0.9999993524049703,
                0.9999996533672549,
                0.9999998724809571,
                0.9999989322968755,
                0.999999352405279,
                0.9999997617629764
            ],
            [
                6.962257908348587e-06,
                1.994729483694599e-06,
                3.288748673295719e-06,
                1.012998735687278e-05,
                6.144177531208195e-06,
                3.7266410609940346e-06,
                1.7603425837606927e-06,
                2.260324028372372e-06,
                7.889266347248781e-06,
                1.1478766756214804e-05
            ],
            [
                0.999999789756634,
                0.9999998555020135,
                0.9999998144608981,
                0.9999998144608097,
                0.9999999006879838,
                0.999999814460876,
                0.9999996940977367,
                0.999999814460854,
                0.9999996533673375,
                0.9999998144608981
            ],
            [
                0.999999814460876,
                0.9999998144609645,
                0.9999996533672136,
                0.9999998724809419,
                0.9999998555020306,
                0.9999999226558054,
                0.9999998724810027,
                0.9999998144608098,
                0.9999997897566589,
                0.9999998724809419
            ],
            [
                0.9999810748427433,
                0.9999938558253998,
                0.999999352405279,
                0.9999987901346049,
                0.9999952149066467,
                0.9999991684716749,
                0.9999990577551815,
                0.9999987901338839,
                0.9999930377429207,
                0.999996273361163
            ],
            [
                0.9999999397642868,
                0.9999996940978461,
                0.9999998362622552,
                0.9999998362622552,
                0.9999997897566089,
                0.9999997300422548,
                0.999999855501979,
                0.9999997897567091,
                0.999999789756634,
                0.9999998555020135
            ],
            [
                0.9999998724809875,
                0.999999789756684,
                0.9999998362623528,
                0.9999998362623723,
                0.999999730042126,
                0.9999998555019963,
                0.9999995549147889,
                0.9999998144609424,
                0.9999996072137529,
                0.9999997300423191
            ],
            [
                0.9999938558262289,
                0.999995777165046,
                0.9999938558224687,
                0.9999785550541692,
                0.9999987901337396,
                0.999985261023302,
                0.9999982396574163,
                0.9999987901347492,
                0.999996273358939,
                0.999993855826188
            ],
            [
                0.999999814460876,
                0.9999996072139402,
                0.9999996072138466,
                0.9999994956524114,
                0.9999996940978095,
                0.9999994956525918,
                0.9999997617630048,
                0.99999976176309,
                0.9999998874648514,
                0.999999554914895
            ],
            [
                0.9999998874647977,
                0.9999997300422226,
                0.9999994956527721,
                0.99999976176309,
                0.9999997617631752,
                0.9999996072138934,
                0.9999996072138935,
                0.9999997300421583,
                0.9999997300423191,
                0.9999996940978825
            ],
            [
                0.9999998362622747,
                0.999999653367503,
                0.9999998144609645,
                0.9999997300420939,
                0.9999997617630049,
                0.9999998144608097,
                0.9999998144609645,
                0.9999998874647843,
                0.9999994956527122,
                0.9999998555019274
            ],
            [
                0.999998629042303,
                0.9999990577555186,
                0.9999977396765106,
                0.999999266179107,
                0.9999987901341724,
                0.9999986290432835,
                0.9999992661788445,
                0.999999352404893,
                0.9999987901338839,
                0.9999967112521116
            ],
            [
                0.9999997617630616,
                0.9999996940978095,
                0.9999998362622746,
                0.999999694097846,
                0.9999996940977366,
                0.999999352405279,
                0.9999998362623137,
                0.9999998144608097,
                0.9999998555019791,
                0.9999998362622357
            ],
            [
                6.144172404520556e-06,
                2.4300246520590875e-05,
                1.0129990979381404e-05,
                1.300712536203966e-05,
                6.9622587393661365e-06,
                3.120192252800261e-05,
                1.4738983727578497e-05,
                2.144495352474637e-05,
                1.6701419847381817e-05,
                1.6701425824307884e-05
            ],
            [
                0.9999998362623138,
                0.9999997617631184,
                0.9999994284993486,
                0.9999998555020307,
                0.9999998362622357,
                0.9999998555019446,
                0.9999998555019274,
                0.9999998362623138,
                0.9999996072139402,
                0.9999995549147358
            ],
            [
                0.9999991684715759,
                0.999998629042957,
                0.9999989322970027,
                0.9999990577551815,
                0.9999982396561572,
                0.9999980052705164,
                0.9999967112497585,
                0.9999989322966208,
                0.9999986290424664,
                0.9999982396572065
            ],
            [
                0.00010889692176918111,
                1.3007134657984903e-05,
                0.00010889689604980399,
                6.9622554173544636e-06,
                8.939695236983711e-06,
                1.0129994596455602e-05,
                5.829125856000775e-05,
                7.484622705265544e-05,
                2.4300252308334918e-05,
                6.144172404218801e-06
            ],
            [
                0.9999996940978095,
                0.99999976176309,
                0.9999995549151073,
                0.9999998555019962,
                0.9999997617630616,
                0.9999996533674614,
                0.9999997300423191,
                0.9999999468421502,
                0.9999998362623722,
                0.9999997617631752
            ],
            [
                0.9999998144609423,
                0.999999653367503,
                0.9999997617630048,
                0.9999991684720716,
                0.9999997897566089,
                0.9999996072138467,
                0.9999996940976636,
                0.9999998144608983,
                0.9999995549150011,
                0.9999997617629764
            ],
            [
                0.9999990577549569,
                0.9999997617629763,
                0.9999998555019446,
                0.9999996940978095,
                0.9999994284993486,
                0.9999996072136125,
                0.9999996940977731,
                0.999999428499553,
                0.9999997897565587,
                0.9999986290429567
            ],
            [
                0.9999987901343166,
                0.9999991684720715,
                0.9999852610110019,
                0.9999995549149481,
                0.999999266178757,
                0.9999984465022455,
                0.999999057755743,
                0.9999999006880549,
                0.9999996072136125,
                0.9999993524049702
            ],
            [
                0.9999995549150542,
                0.9999998555020135,
                0.9999995549150543,
                0.9999997897565587,
                0.999999814460854,
                0.9999998555019446,
                0.9999998362623723,
                0.9999997300423191,
                0.9999997897567091,
                0.9999999468421122
            ],
            [
                0.9999994956527722,
                0.999999495652652,
                0.9999997617630617,
                0.9999995549147358,
                0.999999855502048,
                0.9999997617629764,
                0.9999997300422547,
                0.9999998144609645,
                0.9999997617631753,
                0.9999996533672962
            ],
            [
                0.9999997300420939,
                0.9999997300421583,
                0.9999999123575987,
                0.999999814460854,
                0.9999997617630333,
                0.9999996940978825,
                0.9999996072136593,
                0.9999998362623528,
                0.999999789756634,
                0.999999352404893
            ],
            [
                0.9999991684719723,
                0.9999980052693276,
                0.9999993524049703,
                0.9999987901338839,
                0.9999982396565769,
                0.9999974387180949,
                0.9999970976873247,
                0.9999990577554065,
                0.9999980052709921,
                0.9999945777790923
            ],
            [
                0.9999998555019446,
                0.9999998144608097,
                0.9999998362622552,
                0.9999997300422547,
                0.9999997897567342,
                0.9999996533672962,
                0.9999997897565838,
                0.999999789756684,
                0.9999997897565587,
                0.9999996940976638
            ],
            [
                0.999999814460854,
                0.9999998362622357,
                0.999999814460876,
                0.9999996072136125,
                0.9999998144609202,
                0.9999999123575151,
                0.9999997300422225,
                0.9999996533675028,
                0.9999998724810027,
                0.9999997617631469
            ],
            [
                0.9999998144608319,
                0.9999998874648379,
                0.9999998144609645,
                0.9999998724810026,
                0.9999993524051247,
                0.9999997300420939,
                0.9999989322966208,
                0.9999996072138934,
                0.9999997300422547,
                0.9999994956527121
            ],
            [
                0.999999814460876,
                0.9999996533672962,
                0.999999653367379,
                0.9999997897565587,
                0.9999999123575046,
                0.9999995549150541,
                0.9999997300422547,
                0.9999991684717741,
                0.9999996072137061,
                0.9999996072136125
            ],
            [
                0.9999998724809115,
                0.999999900687972,
                0.9999998362623137,
                0.9999998144608983,
                0.9999996533674202,
                0.9999997300422547,
                0.999999789756684,
                0.9999999006881022,
                0.9999999317439465,
                0.9999997300422869
            ],
            [
                6.9622537593854575e-06,
                4.0063696922780274e-05,
                1.1478768123280277e-05,
                4.222835457664342e-06,
                4.785094494402695e-06,
                7.889266346129453e-06,
                2.260323758835034e-06,
                1.012999097799944e-05,
                5.144221973879711e-05,
                3.5356250689524286e-05
            ],
            [
                0.9999999006881141,
                0.9999997617631184,
                0.9999998555019963,
                0.9999997897567091,
                0.9999998144608981,
                0.999999814460854,
                0.9999998555020135,
                0.9999996533672549,
                0.9999996940978825,
                0.9999998555019446
            ],
            [
                0.9999993524053562,
                0.9999992661788446,
                0.9999989322972573,
                0.9999996940976636,
                0.99999862904214,
                0.9999986290427934,
                0.999999730042126,
                0.9999982396572065,
                0.9999957771670593,
                0.9999996072137998
            ],
            [
                0.999999814460854,
                0.9999998724809419,
                0.9999997617631752,
                0.9999998724809723,
                0.9999998874648917,
                0.9999998362622357,
                0.9999996940977002,
                0.9999996072138934,
                0.9999997617631469,
                0.999999653367503
            ],
            [
                0.9999998724809115,
                0.999999887464744,
                0.999999789756684,
                0.9999999123575987,
                0.9999996533674615,
                0.9999995549151073,
                0.9999998724809874,
                0.9999996533674202,
                0.9999998144609203,
                0.9999997300422225
            ],
            [
                4.785094494463623e-06,
                7.889265406438011e-06,
                9.610240337377108e-05,
                2.5612831264302397e-06,
                1.8925141467679015e-05,
                1.0129993393319151e-05,
                1.1478764017428212e-05,
                5.144221974927673e-05,
                4.222833444168322e-06,
                5.422217676575195e-06
            ],
            [
                0.9999998874648781,
                0.9999998874648782,
                0.999999855502048,
                0.9999998724808964,
                0.9999997300421581,
                0.9999999006880312,
                0.9999998724809419,
                0.9999997300422547,
                0.9999996072137529,
                0.9999999226558146
            ],
            [
                0.9999998144609202,
                0.9999998144609424,
                0.9999998362622943,
                0.9999999006880904,
                0.9999995549150542,
                0.9999996940978461,
                0.9999996940977002,
                0.9999996940978825,
                0.9999996940977366,
                0.9999997617630617
            ],
            [
                0.9995694429695663,
                0.9996646498531228,
                0.9984988176684032,
                0.999959936298309,
                0.9997040427615593,
                0.9999599362887458,
                0.9998415637649571,
                0.9999687980849485,
                0.9990889486935427,
                0.9998766053962423
            ],
            [
                1.0129993393540266e-05,
                1.3709568799679844e-06,
                5.422218969384951e-06,
                1.3709568799679844e-06,
                4.222833947728508e-06,
                6.962253759581752e-06,
                3.2887494573561262e-06,
                4.7850967763512445e-06,
                1.0129994601688632e-05,
                4.2228329408924035e-06
            ],
            [
                0.999999855502048,
                0.9999996533674202,
                0.999999814460854,
                0.9999997617630616,
                0.9999998555019619,
                0.9999999123574836,
                0.9999997300420939,
                0.9999997617630332,
                0.9999998144608319,
                0.9999997300421903
            ],
            [
                0.9999997617630333,
                0.9999994284993486,
                0.9999989322970029,
                0.9999993524054335,
                0.9999984465026158,
                0.9999977396746245,
                0.9999997897565838,
                0.9999996533673788,
                0.9999995549151073,
                0.9999996533674202
            ],
            [
                0.9999997897565587,
                0.999999855501979,
                0.9999996072138466,
                0.9999996072139402,
                0.9999998724809115,
                0.9999997300422225,
                0.999999730042126,
                0.9999998724809419,
                0.9999998555019619,
                0.9999997897567342
            ],
            [
                0.999999653367379,
                0.9999996072139402,
                0.9999998144609202,
                0.9999996940976636,
                0.9999998555019274,
                0.9999998874648915,
                0.9999998362622943,
                0.9999998555020307,
                0.9999999006881141,
                0.9999998362622943
            ],
            [
                0.9999987901343167,
                0.9999998555019963,
                0.9999997617630616,
                0.9999998362622747,
                0.9999996940976272,
                0.9999996940977001,
                0.9999997617630049,
                0.9999997300421261,
                0.9999997897565588,
                0.9999996940976272
            ],
            [
                0.9999996533672549,
                0.9999996533674202,
                0.9999997897567091,
                0.999999694097773,
                0.9999998144608317,
                0.9999997617630333,
                0.9999999123575777,
                0.9999998144608981,
                0.9999996533674615,
                0.9999998144608317
            ],
            [
                0.9999997300420939,
                0.9999998144608317,
                0.9999995549149481,
                0.9999998362623137,
                0.999999653367379,
                0.999999855502048,
                0.9999994956524114,
                0.9999999006881496,
                0.9999998874647574,
                0.9999997617631753
            ],
            [
                0.9999998362622747,
                0.9999998362622942,
                0.9999998144609423,
                0.9999998144608981,
                0.9999999123574419,
                0.9999996940978461,
                0.9999997617630616,
                0.9999998874648648,
                0.99999976176309,
                0.9999999123574523
            ],
            [
                0.9999998362623137,
                0.9999998724809571,
                0.9999996533672549,
                0.9999999123574836,
                0.9999999226558514,
                0.9999998555019446,
                0.9999999226558515,
                0.999999653367255,
                0.9999997897565838,
                0.999999912357515
            ],
            [
                1.0129988563546333e-05,
                3.120191136649749e-05,
                7.88925976359915e-06,
                5.422220908762902e-06,
                6.605216038349344e-05,
                3.2887482811908074e-06,
                8.93969417214416e-06,
                4.785093924251918e-06,
                2.7535684522397864e-05,
                0.00043055703172377625
            ],
            [
                6.144176799099397e-06,
                2.902313022984344e-06,
                6.1441738691562974e-06,
                3.2887490652451393e-06,
                1.3709568799243436e-06,
                1.7603436330091044e-06,
                1.0129988564264954e-05,
                2.2603253755949437e-06,
                2.430023203572232e-05,
                7.889260704050487e-06
            ],
            [
                0.9999996940976638,
                0.99999976176309,
                0.9999997897565838,
                0.9999997300422547,
                0.999999730042126,
                0.9999996533674202,
                0.9999998555020135,
                0.9999998874648648,
                0.9999997617630332,
                0.999999653367255
            ],
            [
                0.9999997617629764,
                0.9999998144608317,
                0.9999999006879838,
                0.9999998555020307,
                0.9999998362622552,
                0.9999998874648379,
                0.9999998874648112,
                0.9999997300422547,
                0.9999997300420939,
                0.9999997617631468
            ],
            [
                0.9999998362622747,
                0.9999994956527122,
                0.9999998362623332,
                0.9999997300423191,
                0.9999996940976272,
                0.999999694097773,
                0.9999994956526519,
                0.9999994956523512,
                0.9999998555020134,
                0.9999998874649051
            ],
            [
                0.999999554914895,
                0.9999998144609645,
                0.999999900688055,
                0.9999999123574419,
                0.9999999317440116,
                0.9999997617630332,
                0.9999999530883843,
                0.9999998555020135,
                0.999999922655787,
                0.9999997300421904
            ],
            [
                6.962257079376403e-06,
                1.7603427936183298e-06,
                8.939697369785323e-06,
                7.889264465397747e-06,
                5.422221554581283e-06,
                3.7266383953679482e-06,
                4.2228344511197656e-06,
                6.1441767987808774e-06,
                3.2887486729876365e-06,
                3.7266392839425286e-06
            ],
            [
                0.9999996940976271,
                0.9999998144608538,
                0.9999994284996211,
                0.9999999006881259,
                0.9999998144608538,
                0.9999998874648648,
                0.9999999317439465,
                0.9999999006880311,
                0.9999998555020134,
                0.9999996533673375
            ],
            [
                0.9999998362623332,
                0.9999996533674202,
                0.9999998362623528,
                0.9999998362623528,
                0.9999997897567091,
                0.9999996940978825,
                0.9999997617629764,
                0.9999996533674615,
                0.9999996533673376,
                0.9999995549150542
            ],
            [
                0.9999998144609203,
                0.9999998144609202,
                0.999999694097846,
                0.9999997617630616,
                0.99999976176309,
                0.999999814460876,
                0.9999999123575359,
                0.9999997897567342,
                0.9999998874648917,
                0.9999996533672136
            ],
            [
                0.999999855502048,
                0.9999997300421904,
                0.9999997897565838,
                0.999999855502048,
                0.9999998555020134,
                0.9999997617631184,
                0.9999999006880075,
                0.9999998362622942,
                0.9999998724810026,
                0.9999996533672963
            ],
            [
                2.7535704221626983e-05,
                1.473898020838208e-05,
                6.962254588724508e-06,
                4.222832437443716e-06,
                3.288747889038086e-06,
                1.3007130013288297e-05,
                2.5612834318257725e-06,
                2.902311984873224e-06,
                3.2887498492518007e-06,
                6.962254588585202e-06
            ],
            [
                0.9999996940978095,
                0.9999999006881259,
                0.9999998362623723,
                0.9999998724809115,
                0.9999996072139402,
                0.999999872480957,
                0.9999995549147359,
                0.9999999123574942,
                0.9999996940976272,
                0.9999998724810026
            ],
            [
                3.288748673295719e-06,
                3.7266379512857925e-06,
                6.1441767990323395e-06,
                1.4738987239295859e-05,
                1.3007134664822509e-05,
                7.889263525405172e-06,
                4.785093924251918e-06,
                1.0129987355122296e-05,
                7.889259763857458e-06,
                4.222832437443716e-06
            ],
            [
                0.9999997897567342,
                0.9999998724809267,
                0.9999997300422869,
                0.9999999468420996,
                0.9999998144609424,
                0.9999998362622357,
                0.9999998555019791,
                0.9999996940978095,
                0.9999996072139402,
                0.99999976176309
            ],
            [
                0.9999997300423191,
                0.999999789756684,
                0.999999789756634,
                0.9999999226558054,
                0.9999999006879838,
                0.9999997897565838,
                0.9999999006880194,
                0.9999998362623332,
                0.9999998362623332,
                0.9999998144609202
            ],
            [
                0.9999997617630049,
                0.9999996533672963,
                0.9999996533672549,
                0.9999998144609644,
                0.9999997617630616,
                0.99999976176309,
                0.9999996072136125,
                0.9999996940978095,
                0.9999998362623528,
                0.9999997617631468
            ],
            [
                0.9999999006881496,
                0.9999996940978825,
                0.9999994956525319,
                0.9999993524050474,
                0.9999997300423191,
                0.9999997300420939,
                0.9999994284994168,
                0.9999994956523514,
                0.9999997617630048,
                0.9999997300421903
            ],
            [
                3.288747889178668e-06,
                3.726640616670918e-06,
                4.539785780045566e-05,
                6.962256249327861e-06,
                1.3007134665934505e-05,
                1.6701419850389357e-05,
                6.96225956921868e-06,
                7.889261645090304e-06,
                5.422218969769604e-06,
                3.2887482812506295e-06
            ],
            [
                0.9999999317439139,
                0.9999997300422225,
                0.9999999123574942,
                0.9999991684717742,
                0.999999855501979,
                0.9999999226557408,
                0.99999976176309,
                0.9999999226558238,
                0.9999996072136593,
                0.9999996072138935
            ],
            [
                0.9999997897566089,
                0.9999997300422869,
                0.999999653367379,
                0.9999997897565587,
                0.9999998362623528,
                0.9999996072136593,
                0.9999996533672963,
                0.9999997617629764,
                0.999999887464744,
                0.9999996072137529
            ],
            [
                1.3007125359792008e-05,
                0.00023050663126645703,
                7.889264465397747e-06,
                2.1444945846588504e-05,
                6.144176797439742e-06,
                2.430024072091399e-05,
                6.144173869072478e-06,
                1.0129995808418327e-05,
                1.012999338780973e-05,
                1.1478769491306371e-05
            ],
            [
                0.9999995549149481,
                0.9999998874648514,
                0.9999997617630333,
                0.9999996072136592,
                0.9999996072139402,
                0.9999997617631752,
                0.9999998144609202,
                0.999999814460854,
                0.9999996940978461,
                0.9999995549147889
            ],
            [
                3.7266379512518984e-06,
                2.7535684513582775e-05,
                1.0129989770662257e-05,
                7.889259763857458e-06,
                3.288747889178668e-06,
                1.4738983719589221e-05,
                3.726641061027928e-06,
                4.785096205778054e-06,
                2.5612828213352452e-06,
                6.1441724044534996e-06
            ],
            [
                0.9999970976866311,
                0.9999984465016899,
                0.9999986290426297,
                0.9999980052709919,
                0.9999980052700408,
                0.9999994956527722,
                0.9999952149072172,
                0.9959298626502966,
                0.9999994956527721,
                0.9999970976883609
            ],
            [
                7.889264465699106e-06,
                1.553498495338299e-06,
                6.962256249606473e-06,
                4.2228334445370225e-06,
                2.9023116391477434e-06,
                1.1478765387416494e-05,
                1.553497384196656e-06,
                1.300712691308661e-05,
                1.2098656835136636e-06,
                5.422217677028889e-06
            ],
            [
                0.9999997897567342,
                0.999999789756684,
                0.9999999226557592,
                0.999999887464744,
                0.9999997300422225,
                0.9999998724810027,
                0.9999998144608097,
                0.9999997300422225,
                0.9999997617629764,
                0.9999998362623528
            ],
            [
                0.9999994284993486,
                0.9999997300422225,
                0.999999730042319,
                0.9999994956527122,
                0.9999997617631468,
                0.9999998362623723,
                0.9999996940978825,
                0.999999266178932,
                0.9999998874649318,
                0.9999997617631469
            ],
            [
                0.9999998362623138,
                0.9999998724808964,
                0.9999997300421903,
                0.9999998555020306,
                0.9999995549149482,
                0.9999998874648246,
                0.999999887464811,
                0.9999996072139402,
                0.9999996533672136,
                0.9999997897567342
            ],
            [
                0.9999994284993485,
                0.9999995549151073,
                0.9999997897565587,
                0.99999976176309,
                0.9999991684721706,
                0.9999998555019791,
                0.9999997897566589,
                0.9999994956524114,
                0.9999997617630048,
                0.9999998724809723
            ],
            [
                0.9999997897567342,
                0.9999998724809267,
                0.9999996940976636,
                0.9999997300422225,
                0.9999998724809419,
                0.9999974387165682,
                0.999999814460876,
                0.9999996533672549,
                0.9999994284994849,
                0.9999990577555185
            ],
            [
                0.9999998724808963,
                0.9999997617630616,
                0.9999998555019791,
                0.9999999317439546,
                0.9999999006881023,
                0.9999994284997574,
                0.9999998874647574,
                0.9999998362622746,
                0.9999997300422225,
                0.9999997617631468
            ],
            [
                0.999999814460876,
                0.9999996533673375,
                0.9999997617630048,
                0.9999998362622942,
                0.9999997617631184,
                0.9999998724809723,
                0.9999998555019274,
                0.9999992661790195,
                0.9999998362622942,
                0.9999997897566589
            ],
            [
                1.6701425824307884e-05,
                1.6701429805199933e-05,
                1.4738985482753428e-05,
                3.120190392534495e-05,
                2.7535681231364308e-05,
                1.6701421842140854e-05,
                1.8925157259824262e-05,
                1.0129990979031306e-05,
                6.962257909323729e-06,
                2.7535697660090726e-05
            ],
            [
                0.9999996940978095,
                0.9999994956527721,
                0.9999994956524114,
                0.9999993524049703,
                0.9999998144609202,
                0.9999987901347491,
                0.9999987901340281,
                0.9999993524049702,
                0.9999992661786696,
                0.9999986290424664
            ],
            [
                0.9999991684722697,
                0.9999938558246662,
                0.9999967112513272,
                0.999999730042319,
                0.9999980052695653,
                0.999999266179282,
                0.9999991684722698,
                0.9999997897567341,
                0.9999990577550693,
                0.9999996533673375
            ],
            [
                0.9999997897565587,
                0.9999998555020306,
                0.9999997300421903,
                0.999999900687972,
                0.9999997617631752,
                0.999999900687972,
                0.999999814460876,
                0.999999653367503,
                0.9999997897565838,
                0.9999997300421903
            ],
            [
                0.9999996940978825,
                0.999999554914789,
                0.9999995549150542,
                0.9999996072136125,
                0.9999997617629764,
                0.9999997617630332,
                0.9999996072136125,
                0.9999994956525318,
                0.9999999006880075,
                0.9999996940978461
            ],
            [
                0.999999900688043,
                0.9999997617630332,
                0.9999999006881497,
                0.9999997617630333,
                0.9999998874647306,
                0.9999996940976272,
                0.9999998362623723,
                0.9999998144609423,
                0.999999789756684,
                0.9999998362622552
            ],
            [
                0.9999998362622943,
                0.9999996533672136,
                0.9999998555020135,
                0.9999998144609202,
                0.9999997617630616,
                0.9999997300421261,
                0.9999997617631469,
                0.999999352404893,
                0.9999998144608981,
                0.99999976176309
            ],
            [
                0.9999151889183805,
                0.9998911030520234,
                0.9999952149032243,
                0.9999852610215463,
                0.9999646437366961,
                0.9996200154760506,
                0.9999810748472673,
                0.9999852610127665,
                0.9999898700054081,
                0.99999457778039
            ],
            [
                0.999999855501979,
                0.9999996072138466,
                0.9999998144608097,
                0.9999998874648379,
                0.9999998724809723,
                0.9999999123574628,
                0.999999789756634,
                0.9999997617630616,
                0.9999998555019962,
                0.999999266179282
            ],
            [
                0.9999996072137529,
                0.9999998362623137,
                0.9999996533672136,
                0.9999996072137529,
                0.9999995549150011,
                0.9999996072138935,
                0.9999996072136125,
                0.9999996940976636,
                0.9999996940978461,
                0.9999997300421581
            ],
            [
                0.9999993524051247,
                0.9999997897566589,
                0.9999999397642796,
                0.999999554914789,
                0.9999996533672136,
                0.9999996533674615,
                0.9999994956525318,
                0.9999998144609423,
                0.9999998724809571,
                0.9999994956527722
            ],
            [
                0.9999999586005999,
                0.9999997300421261,
                0.9999998362623332,
                0.9999998144609645,
                0.999999789756634,
                0.9999996940978825,
                0.9999998362622552,
                0.9999994284994849,
                0.99999976176309,
                0.9999996533672549
            ]
        ]
    },
    {
        "q_id": "7951_mmlu_math",
        "cot_ids": [
            0,
            2,
            3,
            4,
            7,
            11,
            12,
            18,
            19,
            20,
            21,
            22,
            27,
            28,
            31,
            32,
            35,
            36,
            37,
            39,
            41,
            43,
            44,
            47,
            48,
            50,
            52,
            53,
            54,
            55,
            57,
            59,
            62,
            65,
            66,
            67,
            69,
            70,
            72,
            74,
            78,
            80,
            81,
            82,
            86,
            87,
            88,
            89,
            91,
            93,
            94,
            96,
            99,
            101,
            102,
            104,
            105,
            106,
            108,
            109,
            113,
            115,
            116,
            118,
            121,
            122,
            125,
            126
        ],
        "rewards": [
            [
                0.999998790134028,
                0.9999977396751634,
                0.9999967112493665,
                0.9999982396563669,
                0.9999986290421394,
                0.9999852610180373,
                0.9999938558239336,
                0.9999952149043646,
                0.9999945777803841,
                0.9999987901340281
            ],
            [
                0.9999785550439201,
                0.9999869928684351,
                0.9999945777803839,
                0.9999810748472484,
                0.9999417087414243,
                0.9999957771645418,
                0.9999930377445803,
                0.9999952149055052,
                0.9999938558275955,
                0.9999756997621677
            ],
            [
                0.9999930377404307,
                0.9996646498900617,
                0.9999546021097193,
                0.999964643732439,
                0.9999869928715357,
                0.9999251537995278,
                0.999996273358939,
                0.9999852610197855,
                0.9999910603047618,
                0.9999898700102277
            ],
            [
                5.8291251620035695e-05,
                0.000626334020277299,
                1.8925143723000643e-05,
                3.7266388395620047e-06,
                6.9622537593854575e-06,
                6.962257908348587e-06,
                0.00010889696099789775,
                1.6701419849447602e-05,
                5.8291258493848154e-05,
                6.605217615406483e-05
            ],
            [
                0.9796676451361619,
                0.5621765008857981,
                0.3486451217982255,
                0.9902915257122414,
                0.9999869928670265,
                0.9046505325302034,
                0.9999251537550445,
                0.6791786926816161,
                0.8519528000888387,
                0.8670357529306639
            ],
            [
                8.93969630333567e-06,
                0.9999756997477102,
                6.962254589332388e-06,
                2.5612819051722694e-06,
                1.4738978455325741e-05,
                4.222831934202483e-06,
                3.2887482810801374e-06,
                2.1444943296369872e-05,
                1.8925152747388e-05,
                2.5612819053166966e-06
            ],
            [
                0.9998204719977576,
                0.053403329799824234,
                0.817574478416099,
                0.867035771827307,
                0.4073334000459302,
                0.9999151889438107,
                0.9999339478492114,
                0.8933094010836642,
                0.40733340004593027,
                0.9999810748473089
            ],
            [
                0.9997040427678541,
                0.9241418210233833,
                0.9995694429132268,
                0.8933094053442511,
                0.9999930377437514,
                0.9999785550416176,
                0.999991060305828,
                0.9998204720554777,
                0.9840936090462592,
                0.9999151889689399
            ],
            [
                0.9626731107817876,
                0.9999724642959656,
                0.9999687980946047,
                0.7772998508568416,
                0.9999417087137297,
                0.2018132174596823,
                0.9999546021312777,
                0.9995121427745558,
                0.9999832985722603,
                0.8354835391516133
            ],
            [
                1.3007125361448172e-05,
                9.422450431860582e-07,
                1.3709576971242028e-06,
                1.5534981249023245e-06,
                4.222834954461155e-06,
                8.939695236593446e-06,
                7.338213304243302e-07,
                2.260323758882316e-06,
                1.370956879949281e-06,
                7.889259763010786e-06
            ],
            [
                0.9999989322970027,
                0.9999977396762411,
                0.9999982396569965,
                0.999996273360716,
                0.9999994284992805,
                0.999999266178932,
                0.9999945777784447,
                0.999995777166052,
                0.9999994956527121,
                0.9999980052705163
            ],
            [
                0.7981867825403177,
                0.999978555041368,
                0.7981867705385762,
                0.8670357615200474,
                0.9997040429725532,
                0.999796573003438,
                0.5,
                0.0028009271017361875,
                0.7057850216484838,
                0.02297737057907019
            ],
            [
                0.999948557767984,
                0.9999785550413702,
                0.9999885212332477,
                0.9999417087276058,
                0.9999832985742014,
                0.9947798742097167,
                0.9525741311981335,
                0.9999832985703117,
                0.9999646437375821,
                0.9999974387177907
            ],
            [
                0.9999921107374145,
                0.9999810748517607,
                0.9999930377404306,
                0.9999930377412606,
                0.9999986290427931,
                0.9999970976890529,
                0.9999687980849095,
                0.9999945777797375,
                0.9999984465026158,
                0.9999938558268632
            ],
            [
                0.9999885212277768,
                0.8354835391516132,
                0.9149009625340366,
                0.9978172833807216,
                0.999954602142276,
                0.9999599363221765,
                0.9999151889793146,
                0.99997855505672,
                0.9999930377454106,
                0.9999599362935236
            ],
            [
                0.9324533158993962,
                0.999986992869989,
                0.9998766054109683,
                0.9999910603048118,
                0.999981074856302,
                0.8670357477770337,
                0.9999756997597394,
                0.999992110739334,
                0.999959936322189,
                0.9998766054259134
            ],
            [
                2.144494329192304e-05,
                2.7535681245588654e-05,
                2.1444958628814052e-05,
                4.006370171458602e-05,
                8.93969630011598e-06,
                1.147877222879974e-05,
                1.3007130011300897e-05,
                2.1444943296369872e-05,
                5.8291286364010624e-05,
                4.5397879450662006e-05
            ],
            [
                0.9999251537727775,
                0.9999810748585277,
                0.999954602125951,
                0.9999339478238608,
                0.9999151889890187,
                0.9999810748472526,
                0.9997965730024289,
                0.9999832985801483,
                0.999983298570192,
                0.9999687980849129
            ],
            [
                0.9999485578051502,
                0.7310585903489891,
                0.8354835350552603,
                0.7981867705385762,
                0.9999945777791551,
                0.6513548714339145,
                0.8670357598021707,
                0.8354835411997898,
                0.7549149868676283,
                0.9999945777804476
            ],
            [
                0.9999921107383551,
                0.9999910603026798,
                0.9999869928670265,
                0.9998601778760318,
                0.9964063969292014,
                0.8519528038477824,
                0.9999151889792813,
                0.9999646437582664,
                0.9971990736701877,
                0.9999546021370312
            ],
            [
                0.9999339478789471,
                0.9999417087344762,
                0.9999785550592574,
                0.9999810748427356,
                0.9999646437450749,
                0.9999945777823229,
                0.9996200154241041,
                0.9999485578047399,
                0.9999945777816769,
                0.999993855823201
            ],
            [
                0.43782349911420193,
                0.9999930377429848,
                0.9999417087205619,
                0.003593603246707989,
                NaN,
                0.4687906266262437,
                0.9399133544545811,
                0.09534947004048375,
                0.7549149868676283,
                0.9999417087484788
            ],
            [
                0.9999921107402361,
                0.9999980052700408,
                0.9999970976869769,
                0.9999984465024306,
                0.9999957771680658,
                0.9999967112505427,
                0.9999898700066057,
                0.999995214903224,
                0.9999785550490328,
                0.9999885212346117
            ],
            [
                0.9999785550567016,
                0.9999417087066731,
                0.9998766054251933,
                0.9999599362982768,
                0.9999810748472494,
                0.9999251537995338,
                0.9999885212277702,
                0.9998204720770398,
                0.999981074858529,
                0.9999687980923566
            ],
            [
                1.4738988998117324e-05,
                1.670141586084161e-05,
                1.3007131563176482e-05,
                5.422220908314139e-06,
                1.9947301970106386e-06,
                1.0677024881887838e-06,
                1.1478764020372226e-05,
                1.1478772228528306e-05,
                1.5534979397592542e-06,
                3.2887498494282754e-06
            ],
            [
                1.0677026154619133e-06,
                2.9023133690637e-06,
                4.4508505193791187e-07,
                1.5534973841705173e-06,
                5.715007195431641e-07,
                4.222832941034507e-06,
                2.902312331081799e-06,
                7.3382080556433e-07,
                2.260325375677174e-06,
                1.3709573702647743e-06
            ],
            [
                0.9999485577618361,
                0.9999957771665555,
                0.9999251537906066,
                0.9999970976890528,
                0.9999885212305063,
                0.9999687980811913,
                0.9999898700090202,
                0.9999952149055052,
                0.9999957771655487,
                0.9999687980737552
            ],
            [
                0.00010889689623677332,
                1.300712846217e-05,
                0.00013982207385299317,
                1.8925148237775583e-05,
                3.120191507481552e-05,
                0.00023050682375301286,
                8.939698435096828e-06,
                5.1442195242316055e-05,
                1.1478768124553928e-05,
                4.785094494672519e-06
            ],
            [
                0.7549149923816048,
                0.999569442835857,
                0.9984988179634798,
                0.9980732657127729,
                0.9989677689365954,
                0.00043055702851725754,
                0.9968273175234827,
                0.003172682597279272,
                0.999664649972496,
                0.9997965730041041
            ],
            [
                0.9999151889688855,
                0.999860177859307,
                0.9997694931752811,
                0.9998766054398672,
                0.9996200154247563,
                0.9998601778759504,
                0.9995694429621763,
                0.9998204720987456,
                0.9914225165108199,
                0.9999687980737564
            ],
            [
                0.9999724643155011,
                0.9997040429738621,
                0.9999339478396165,
                0.9999885212264018,
                0.9999599363090393,
                0.9241418257242036,
                0.9999038975966703,
                0.9999646437450943,
                0.9999938558224836,
                0.9999724642957742
            ],
            [
                1.553498495295912e-06,
                7.338210679949506e-07,
                1.2098656835076114e-06,
                3.288749849114211e-06,
                1.2098655391947376e-06,
                1.0677028700320085e-06,
                7.338210679909462e-07,
                1.3709578605118645e-06,
                8.315282258956806e-07,
                2.260323758746637e-06
            ],
            [
                0.9999852610127591,
                0.9999952149037941,
                0.9999930377454104,
                0.9999938558232008,
                0.9999967112509347,
                0.9999687980737504,
                0.9999832985781563,
                0.9999980052695652,
                0.999997438717484,
                0.9999974387168733
            ],
            [
                0.9999910602994334,
                0.9999990577555183,
                0.9999945777803839,
                0.9999986290429567,
                0.9999921107336525,
                0.9999910603047616,
                0.9999885212305062,
                0.9999921107345929,
                0.9999982396572064,
                0.9999957771670589
            ],
            [
                6.962257078249291e-06,
                1.1478770859917257e-05,
                3.1201907645920996e-05,
                6.9622570786798724e-06,
                3.120191878472311e-05,
                3.120191135991401e-05,
                6.144177530425867e-06,
                0.000203426900527191,
                3.5356246490314526e-05,
                0.00013982210689156329
            ],
            [
                1.4738978456398127e-05,
                2.1444943297072005e-05,
                2.144494329769612e-05,
                5.422219615967477e-06,
                3.2887498494282754e-06,
                1.147877222879974e-05,
                2.753568780802255e-05,
                7.889262585211807e-06,
                5.422217030614265e-06,
                2.9023119851266288e-06
            ],
            [
                0.9999952149037942,
                0.9999945777797377,
                0.9999910603068939,
                0.9999869928685471,
                0.9998766054546704,
                0.9999970976876689,
                0.9999810748517645,
                0.9999785550592579,
                0.9999251537816741,
                0.9999910603026309
            ],
            [
                1.2098656834834034e-06,
                5.422221554926484e-06,
                2.2603234894745224e-06,
                1.067702615468225e-06,
                2.9023112930659533e-06,
                6.962254588977791e-06,
                1.9947306726213275e-06,
                4.785092782692845e-06,
                1.2098659719122375e-06,
                2.9023116390104826e-06
            ],
            [
                0.999991060300499,
                0.9999852610232997,
                0.9999930377454102,
                0.9999957771650454,
                0.9999756997621669,
                0.9998204720131397,
                0.9999885212359796,
                0.9999339478553375,
                0.9999810748472499,
                0.9999930377420904
            ],
            [
                0.9999785550567669,
                0.999985261018032,
                0.9999885212332854,
                0.904650530602188,
                0.9995694430102364,
                0.8519528038477824,
                0.9999251537562523,
                0.999933947850605,
                0.9997965730026834,
                0.9999485577679776
            ],
            [
                0.9997694933714633,
                0.0028009271108405983,
                0.0003799844368928975,
                0.017986212462442638,
                0.0002034269727278367,
                0.3775406687981454,
                0.053403334131154334,
                0.9999646437325821,
                0.4378234991142019,
                0.0004305570320243873
            ],
            [
                3.1201922514835635e-05,
                2.1444956065331412e-05,
                3.120190765193695e-05,
                3.535625069312567e-05,
                6.605216039839083e-05,
                2.7535687809124434e-05,
                1.670141587031992e-05,
                1.6701429803316423e-05,
                0.00017952805162239774,
                2.1444956067203762e-05
            ],
            [
                0.0001795279008129566,
                9.610242610867865e-05,
                4.539785778179383e-05,
                7.484625391903742e-05,
                0.00010889693446566985,
                3.1201922520397544e-05,
                4.006369693473136e-05,
                0.00013982210655588814,
                2.4300249415479343e-05,
                0.0010322308984647539
            ],
            [
                1.6701415868193372e-05,
                6.96225375833433e-06,
                4.7850956351657615e-06,
                5.422220908634683e-06,
                4.539785781036459e-05,
                2.4300243627117176e-05,
                8.939698433145498e-06,
                7.484620044058188e-05,
                4.0063706494441236e-05,
                8.939695237666677e-06
            ],
            [
                0.9399133519298964,
                0.2689414272294874,
                0.9999546021477249,
                0.974042641624845,
                0.9999756997691139,
                0.999860177959924,
                0.9999945777830086,
                0.5,
                0.9999646437619757,
                0.43782349911420193
            ],
            [
                1.670141985166528e-05,
                1.3709567165087443e-06,
                4.222832437443716e-06,
                1.3709575336093795e-06,
                2.2603253754921562e-06,
                1.9947306725669014e-06,
                3.288750633488963e-06,
                7.889264465555602e-06,
                6.144177531381426e-06,
                6.1441775312976045e-06
            ],
            [
                0.9999852610110012,
                0.9999251537995719,
                0.9998766054251933,
                0.99979657309939,
                0.9999885212277696,
                0.9995694429631032,
                0.9999485577679585,
                0.9999810748562717,
                0.9998601778759911,
                0.9997040427950044
            ],
            [
                0.9525741301883566,
                0.9999151889297647,
                0.9998911030685765,
                0.9902915237781903,
                0.9796676469541566,
                0.3775406758018019,
                0.9998415638024603,
                0.9740426442621272,
                0.9999970976880249,
                0.9999785550593877
            ],
            [
                0.5621765008857981,
                0.9999785550465339,
                0.9669140182743434,
                0.46879062662624377,
                0.8807970779778824,
                0.22270013882530887,
                0.9999810748583716,
                0.5312093733737563,
                0.6224593312018546,
                0.43782349911420193
            ],
            [
                1.473898372822193e-05,
                2.7535691100960147e-05,
                5.4222183221120994e-06,
                8.93969630333567e-06,
                1.3007123812767362e-05,
                7.889263526093993e-06,
                5.42221767672807e-06,
                4.222835458002318e-06,
                1.012999339309804e-05,
                2.561283126502453e-06
            ],
            [
                0.999988521231875,
                0.9999785550592557,
                0.9999785550515878,
                0.9999832985741741,
                0.9999869928730863,
                0.9999852610145151,
                0.9999945777816767,
                0.9999785550592579,
                0.9999869928699856,
                0.9999785550541431
            ],
            [
                0.9999810748585295,
                0.9999957771675626,
                0.9999885212291383,
                0.9999885212359796,
                0.9999251537549232,
                0.9999852610110012,
                0.999998790134028,
                0.9999724643056221,
                0.9999930377420906,
                0.9999687980811913
            ],
            [
                0.999995777167072,
                0.9998601778763552,
                0.9999417087557008,
                0.9999339478396017,
                0.7981867825403177,
                0.9999724643122361,
                0.9999869928731032,
                0.999981074842744,
                0.9999852610145252,
                0.5621765008857981
            ],
            [
                0.9993736659750226,
                0.9998911030831316,
                0.020332353416862622,
                0.9991959139567147,
                0.46879062662624377,
                0.9999546021107009,
                0.5621765008857981,
                0.5312093733737562,
                0.9999151889589281,
                0.9998911031298644
            ],
            [
                0.9999832985781935,
                0.99998107485853,
                0.9999687980812059,
                0.999981074845007,
                0.9999832985721941,
                0.9998766053811916,
                0.9999869928716947,
                0.9953904284637438,
                0.9999646437408763,
                0.9999938558275958
            ],
            [
                0.9999957771650453,
                0.9999785550490304,
                0.999891103103726,
                0.9999885212277698,
                0.9999756997476814,
                0.9999852610215433,
                0.9999810748495044,
                0.9999832985841293,
                0.9999599363078145,
                0.9999832985721836
            ],
            [
                0.9999967112509346,
                0.9999957771675622,
                0.9999967112493664,
                0.999997438717484,
                0.9999952149060758,
                0.999998239656367,
                0.9999995549150011,
                0.9999938558224684,
                0.9999980052693274,
                0.9999982396559473
            ],
            [
                0.9999599363043639,
                0.20181322226037884,
                NaN,
                0.9999910603027689,
                0.9999599362998399,
                0.2689414272294874,
                0.5926665999540698,
                NaN,
                0.9971990731518867,
                0.22270013882530884
            ],
            [
                0.9999898700090201,
                0.9999832985741752,
                0.9999930377429204,
                0.9999957771665554,
                0.9999756997534777,
                0.9999986290432835,
                0.9999898700041899,
                0.9999986290423029,
                0.9999980052702785,
                0.9999977396746244
            ],
            [
                1.8925157264919016e-05,
                2.14449509695729e-05,
                5.422219615829396e-06,
                6.962256248606003e-06,
                3.726638395493353e-06,
                6.144177531208195e-06,
                3.2887502413389517e-06,
                5.422217675756574e-06,
                7.889259763326495e-06,
                7.889260703619978e-06
            ],
            [
                0.9999810748472515,
                0.9999852610197889,
                0.9997694931864687,
                0.9859363714975209,
                0.9770226293372992,
                0.9984988180423531,
                0.9940889314173847,
                0.9971990736955499,
                0.9999852610128234,
                0.977022627413796
            ],
            [
                1.0129988563546333e-05,
                1.3007125361448172e-05,
                1.8925145977014425e-05,
                3.2887482810382622e-06,
                8.93969950000193e-06,
                3.726637951126493e-06,
                1.300713466619476e-05,
                1.3007134662432895e-05,
                8.939698434153684e-06,
                4.785096205778054e-06
            ],
            [
                1.3007123809289414e-05,
                8.481108176384966e-05,
                6.144172403335888e-06,
                7.484624503218738e-05,
                0.00012339457420877998,
                2.7535687811228037e-05,
                6.605216825123819e-05,
                0.00013982205735608936,
                6.962254589332388e-06,
                1.6701421842140854e-05
            ],
            [
                0.9999687980775199,
                0.679178699175393,
                0.9999485578049299,
                0.9999885212292556,
                0.05340332829327471,
                0.9579122737364724,
                0.06008664575580924,
                0.9999921107345979,
                0.9999977396754519,
                0.9669140206578809
            ],
            [
                7.889262582571338e-06,
                8.31528424151477e-07,
                2.9023119850210436e-06,
                1.7603432132464244e-06,
                1.994729483694599e-06,
                2.2603234893594005e-06,
                1.7603438427852151e-06,
                2.2603248365014775e-06,
                5.043474081957179e-07,
                1.067702742726318e-06
            ],
            [
                3.726638394957837e-06,
                7.889266346129453e-06,
                4.7850939242083995e-06,
                4.222834954211514e-06,
                4.00636826148464e-05,
                4.2228319339950885e-06,
                4.222832437324657e-06,
                2.4300237828943813e-05,
                3.5356246490314526e-05,
                5.4222176759932836e-06
            ],
            [
                0.9999885212318825,
                0.9995121427704686,
                0.9999546021205734,
                0.9999921107355365,
                0.9999339478284685,
                0.9998911030651161,
                0.9999810748562746,
                0.999841563821455,
                0.9999980052700455,
                0.9999151889793146
            ],
            [
                0.26894141551050293,
                0.9465966685053075,
                0.5926665999540698,
                0.9046505376715775,
                0.9999756997593172,
                0.999954602115151,
                0.4687906266262437,
                0.8519528000888386,
                0.9626731129235967,
                0.9914225145625284
            ]
        ]
    },
    {
        "q_id": "7852_mmlu_math",
        "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,
            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": [
            [
                0.9993736659567689,
                0.9997040428771526,
                0.32082129433083023,
                0.9993736659404097,
                0.10669059749614015,
                0.9986749777528564,
                0.9995694429865384,
                0.9975273773406907,
                0.9980732648893816,
                0.9964063979363039
            ],
            [
                1.3007134649798706e-05,
                2.1444953506061874e-05,
                1.300713311112477e-05,
                1.892515724543503e-05,
                1.300712534701587e-05,
                3.7266379489200294e-06,
                6.144174600024198e-06,
                1.8925143715220825e-05,
                1.0129988557686814e-05,
                1.0129987352284668e-05
            ],
            [
                0.9975273765435916,
                0.9999724643155534,
                0.9984988180762057,
                0.999796573101506,
                0.9997388097060211,
                0.9988304899708866,
                0.999569442842245,
                0.9984988176069798,
                0.9990889488119571,
                0.9998204720795186
            ],
            [
                0.2450850131323717,
                0.9840936107081903,
                0.11920292515117027,
                0.22270014398423357,
                0.32082128783705344,
                0.04742586829697803,
                0.40733340004593027,
                0.9990889490146657,
                0.9971990731109168,
                0.13296422989056964
            ],
            [
                0.9999417087554116,
                0.9998766054703514,
                0.9990889486857544,
                0.9996646497398866,
                0.9990889488836946,
                0.9999038975990908,
                0.9999646437535679,
                0.9986749775501285,
                0.9995694428868106,
                0.9991959141759552
            ],
            [
                0.9994472212759599,
                0.9982992776462796,
                0.20181321745968234,
                0.6513548782017745,
                0.1329642333263228,
                0.9996646499347278,
                0.10669059465574897,
                0.9996200153959033,
                0.9940889302161554,
                0.07585818837825822
            ],
            [
                1.3007123792349202e-05,
                4.785095063469892e-06,
                3.535625479509864e-05,
                1.4738987232888351e-05,
                1.6701429791650804e-05,
                1.1478773588745944e-05,
                1.1478772227651366e-05,
                1.147877220986201e-05,
                1.0129995807165349e-05,
                2.4300240681044865e-05
            ],
            [
                2.430025227686393e-05,
                1.147876948232818e-05,
                1.300712839492964e-05,
                8.939698433373153e-06,
                2.430024066159651e-05,
                1.300712995891871e-05,
                8.939700560549195e-06,
                1.4738985468758785e-05,
                4.785093923603471e-06,
                5.42221767462234e-06
            ],
            [
                4.539787396804498e-05,
                4.006370166357524e-05,
                9.610240229914708e-05,
                0.00033534998283787785,
                5.8291286335171815e-05,
                8.481107113243204e-05,
                0.995929861802768,
                0.00033535023462902703,
                2.144495601391978e-05,
                3.1201900183543295e-05
            ],
            [
                0.9988304899103712,
                0.9992903294906433,
                0.9992903295305189,
                0.20181322466072713,
                0.9998415637270507,
                0.5926665999540698,
                0.9995694429019915,
                0.9968273176685445,
                0.13296424019782926,
                0.9994472214759837
            ],
            [
                0.07585818785594477,
                0.37754066879814546,
                0.9992903297427752,
                0.9996200154774876,
                0.9998601778777976,
                0.02595735733907982,
                0.9997388095869649,
                0.9999038975513445,
                0.07585818211049714,
                0.9991959141208645
            ],
            [
                0.9984988178151563,
                0.9988304899581035,
                0.9998601778931329,
                0.9994472214304799,
                0.6513548782017745,
                0.9999038975603596,
                0.9964063980038331,
                0.9947798752470907,
                0.9990889489746114,
                0.033085978865411605
            ],
            [
                0.9986749778465179,
                0.9626731085061155,
                0.9995121428304139,
                0.0007096702726219312,
                0.98756835000436,
                0.9997040427646766,
                0.9924227579407567,
                0.9992903297598233,
                0.9953904279018168,
                0.9993736659370942
            ],
            [
                0.9980732654620393,
                0.22270013366638422,
                0.20181321745968234,
                0.22270013366638422,
                0.9995694429816785,
                0.998498817630537,
                NaN,
                0.9980732653886103,
                0.7310585727705127,
                0.1645164608483867
            ],
            [
                0.9996200154324725,
                0.9994472213541364,
                0.9989677688950606,
                0.9993736657000506,
                0.9999038975509599,
                0.9992903296615382,
                0.9997694931790841,
                0.9999038975966262,
                0.9996200155332924,
                0.9997694933256607
            ],
            [
                0.998299277737793,
                0.05340333431947304,
                0.06754668691621382,
                0.9984988180435745,
                0.9993736659265646,
                0.4073334000459302,
                0.9971990731284753,
                0.9988304894722123,
                0.9995694428270891,
                0.9971990733749447
            ],
            [
                0.3208213073183839,
                0.9998415638014321,
                0.9995694428726317,
                0.9924227592643964,
                0.7549149923816048,
                0.9997965729819007,
                0.22270013366638422,
                0.11920292202211756,
                0.9998766054255417,
                0.18242552602881168
            ],
            [
                0.18242552158390105,
                0.9980732654262202,
                0.9999417087485101,
                0.22270013366638422,
                0.0004878572076763297,
                0.999373665900441,
                0.11920292828022305,
                0.00015843629077766394,
                0.18242551491653522,
                0.43782349911420193
            ],
            [
                0.999841563748007,
                0.9996646500207819,
                NaN,
                0.9996200154560634,
                0.9995694430179772,
                0.20181321265898594,
                0.9996200154825508,
                0.9990889490162022,
                0.9993736657379062,
                0.9978172835617541
            ],
            [
                0.9986749773748214,
                0.9999339478711793,
                0.9993736658318346,
                0.9998601779767322,
                0.9996646499513142,
                0.999948557774454,
                0.9996200155741951,
                0.9995121429838248,
                0.9999038975627256,
                0.9995694428190729
            ],
            [
                0.9998601779768583,
                0.9740426438382782,
                0.9988304897620065,
                0.0010322308367624216,
                0.999512142765899,
                0.9997388096047862,
                0.9997388095840238,
                0.9998601778771425,
                0.999820472036734,
                0.9986749776896966
            ],
            [
                0.9914225155129145,
                0.8670357632379241,
                0.9999485577942477,
                0.8519528019683106,
                0.9964063978104161,
                0.9995694429899453,
                0.9993736658030149,
                0.9995694428183464,
                0.11920291732853862,
                0.9980732650492243
            ],
            [
                0.999620015456992,
                0.9999417087345933,
                0.9995121429379009,
                0.9999646437451655,
                0.9999599362983915,
                0.9998415637683711,
                0.9999251537820678,
                0.9998601778793152,
                0.9995121429214671,
                0.9996200154503371
            ],
            [
                0.5312093733737562,
                0.1329642264548166,
                0.9975273765768998,
                0.6224593312018546,
                0.04208772641371775,
                0.9998911031182169,
                0.9947798737091655,
                0.025957358893192575,
                0.9999151889394977,
                0.14804719803168945
            ],
            [
                0.9740426444975988,
                0.8354835411997897,
                0.9997388096000895,
                0.9998911030651161,
                0.22270012850745968,
                0.18242552158390105,
                0.2942149659744614,
                0.9995121428994417,
                0.9820137884587393,
                0.3208212943308302
            ],
            [
                4.539789019426799e-05,
                0.00020342691456480582,
                0.9994472212329323,
                2.753568440169123e-05,
                1.892515047774492e-05,
                7.48462265620274e-05,
                0.9989677690133033,
                5.144219495300383e-05,
                8.939693101369448e-06,
                5.422220257026851e-06
            ],
            [
                1.4738985476533587e-05,
                0.00015843621022756336,
                1.4738980192671623e-05,
                9.61024488107306e-05,
                NaN,
                4.7850967745625735e-06,
                1.0129990976451642e-05,
                3.120190015232851e-05,
                4.006370626562147e-05,
                5.144221343830002e-05
            ],
            [
                0.999964643745163,
                NaN,
                0.999512142899016,
                0.05340332377362639,
                0.9999251537553844,
                0.9992903294573312,
                0.9995121429858117,
                0.9990889489034038,
                0.9993736658320532,
                0.9840936056349263
            ],
            [
                2.4300234868462743e-05,
                8.939699496164318e-06,
                5.144222575222819e-05,
                2.430023782222529e-05,
                0.00029595703830516775,
                4.006371116615417e-05,
                1.3007134641707146e-05,
                2.7535681179776003e-05,
                2.4300246483727398e-05,
                4.006370425608843e-05
            ],
            [
                0.09534947325384278,
                0.9902915257480572,
                0.0019267350645012426,
                0.9997040430075739,
                0.9992903294481673,
                0.9997040430179415,
                0.9990889487784727,
                0.08509903804604459,
                0.9997694933450441,
                0.9990889489141062
            ],
            [
                0.9975273769547753,
                0.9993736658273167,
                0.9997694932343505,
                0.2450850131323717,
                NaN,
                0.998967769053878,
                0.0008040858472408821,
                0.999972464312336,
                0.9991959138949832,
                0.679178686187839
            ],
            [
                3.5356250638847714e-05,
                7.484624455462813e-05,
                5.1442237953129084e-05,
                3.12019038250036e-05,
                4.006369207151113e-05,
                3.5356263260146225e-05,
                1.300712380455751e-05,
                9.6102390775431e-05,
                1.4738980205164923e-05,
                1.147876537896029e-05
            ],
            [
                0.9998601779267451,
                0.9998601778779969,
                0.00033535014104274144,
                0.9998911030802923,
                0.9933071490447577,
                0.5312093733737563,
                NaN,
                0.07585817584273655,
                0.5312093733737563,
                0.9994472212876333
            ],
            [
                0.9998415638410881,
                0.9999339478636935,
                0.9998204720573531,
                0.9998415637459024,
                0.9999038975974813,
                0.9964063977337163,
                0.9999417087349275,
                0.9996646498987743,
                0.9991959141870856,
                0.9999485578049051
            ],
            [
                0.9992903294705818,
                0.9989677690079014,
                0.9997040429153249,
                0.9999885212332528,
                0.9999810748517903,
                0.9999151889489568,
                0.9995121428581727,
                0.9992903297427751,
                0.9984988177095848,
                0.9999417087136605
            ],
            [
                1.6701425736025902e-05,
                2.7535684457586915e-05,
                7.484625349593185e-05,
                8.481104094612394e-05,
                1.6701423806824726e-05,
                4.006370157496225e-05,
                1.147876675162131e-05,
                2.753568769172345e-05,
                4.5397873957475446e-05,
                7.889260692082281e-06
            ],
            [
                0.9995694428857334,
                0.9997040428469713,
                0.679178699175393,
                0.9997388097718417,
                0.9998204719732935,
                0.0019267348406319426,
                0.9991959142406798,
                0.999841563803456,
                0.9999251537823586,
                0.9998911030789566
            ],
            [
                0.9999038975861967,
                0.24508501864634824,
                0.5312093733737563,
                0.9988304896401596,
                0.999664649779606,
                0.7549149813536516,
                0.014957072542317871,
                0.3208213138121609,
                0.00029595712893526455,
                0.999738809725803
            ],
            [
                3.5356246402852425e-05,
                0.9996646497956363,
                0.9990889489190864,
                0.9820137867808721,
                0.06754669395523943,
                0.00015843615937519005,
                0.5,
                0.11920292515117027,
                0.9997694932076495,
                0.08509904326677628
            ],
            [
                0.042087723860486016,
                0.0001795280284225444,
                0.00043055701100665986,
                0.2942149783515162,
                0.9997388098009179,
                NaN,
                0.11920291419948607,
                0.10669058613457583,
                0.9988304895206248,
                0.10669059678604235
            ],
            [
                0.9990889488950327,
                0.00033535010611375493,
                0.7772998714925403,
                0.9995121429104827,
                0.9940889316280787,
                0.999841563730875,
                0.5312093733737562,
                0.22270012850745968,
                0.9997040428440694,
                0.9975273764362014
            ],
            [
                0.9999756997650822,
                0.13296423332632276,
                0.9984988178486599,
                0.8519528057272544,
                0.0011695103000048648,
                0.3208213138121609,
                0.2942149659744614,
                0.18242552380635635,
                0.5,
                0.679178699175393
            ],
            [
                0.9996200154293108,
                0.9997388097246402,
                0.9984988180514269,
                0.9991959142268837,
                0.9953904274039878,
                0.999195914204623,
                0.7057850402140659,
                0.9998601779439805,
                0.9989677687601316,
                0.9992903294373109
            ],
            [
                0.9995121428532624,
                0.9988304895093376,
                0.999841563766739,
                0.9990889489048874,
                0.9995121427767981,
                0.9989677690879704,
                0.9997040427624033,
                0.999820472030298,
                0.999664649833102,
                0.9982992773422885
            ],
            [
                0.9999151889909493,
                0.9999417087276407,
                0.9999151889489568,
                0.9999339478477125,
                0.11920293453832885,
                0.9995694429767936,
                0.9998911030526619,
                0.9999910603005027,
                0.999933947871197,
                0.37754066879814546
            ],
            [
                0.9997965729338775,
                0.0007096704163551847,
                0.0011695102868138647,
                0.9992903294890335,
                0.24508500761839525,
                0.9997040429024086,
                0.99990389757428,
                0.9959298618216439,
                0.9996646499509825,
                0.9998911031045729
            ],
            [
                0.9999546021314331,
                0.9994472214805824,
                0.9964063967916419,
                0.00015843615845081115,
                0.999903897540025,
                7.484621806670283e-05,
                0.0600866476493228,
                0.999986992874653,
                0.6513548646660543,
                0.9999038975743696
            ],
            [
                0.9947798751697109,
                0.20181322226037884,
                0.0011695100826933594,
                0.9993736657291619,
                0.14804719239327382,
                0.9998601779771961,
                0.9997965729273425,
                0.9999339478319313,
                0.9998204720566296,
                0.9999417087485267
            ],
            [
                0.4378234991142018,
                0.06008665438181588,
                0.9999038975510453,
                0.999876605396781,
                0.1192029235866439,
                0.9999038975858388,
                0.9992903295255654,
                0.9998911030787078,
                0.9997965729551929,
                0.46879062662624377
            ],
            [
                0.9924227584169869,
                0.9998204719937298,
                0.24508500210441886,
                0.9998911030523387,
                0.999769493260099,
                0.9994472214120211,
                0.9998204720816867,
                0.9997040429067398,
                0.9997965730258871,
                0.9964063977754009
            ],
            [
                0.9995121427927494,
                0.9995694428244839,
                0.2689414330889797,
                0.9968273179012325,
                0.9998415637654712,
                0.9997965729811904,
                0.9998204719926486,
                0.9997694932612057,
                0.999769493179017,
                0.9998204719530348
            ],
            [
                0.001325022141774431,
                0.3208213073183839,
                0.9997040430250713,
                0.9992903296703306,
                0.7772998560157665,
                0.2018132150593341,
                0.9968273174837197,
                0.9990889490066125,
                0.9992903296133656,
                0.13296425222296634
            ],
            [
                0.0002959571925270402,
                0.1824255149165352,
                0.9991959141312466,
                0.9971990730393823,
                0.9998601778600943,
                0.9986749777312895,
                0.9933071494719702,
                0.0009110513587503459,
                0.9991959139672839,
                0.9984988179835471
            ],
            [
                0.5621765008857982,
                NaN,
                0.00037998448341150027,
                0.9995694429241365,
                0.9995121428484373,
                0.04742587570200943,
                0.001032231271559869,
                0.9995694428916454,
                0.9990889486430511,
                0.9998601779101078
            ],
            [
                0.999738809732468,
                0.9996200155077557,
                0.9993736657902262,
                NaN,
                0.9999251537823357,
                0.34864514210180597,
                0.9999251537742744,
                0.9978172835739244,
                0.9999417087276304,
                0.9995694429988133
            ],
            [
                5.422221554038823e-06,
                3.7266410605974813e-06,
                4.785096204650886e-06,
                2.4300242772980712e-05,
                8.939693100361262e-06,
                2.14449483174666e-05,
                1.4738983721733992e-05,
                2.4300249339277128e-05,
                4.7850967718904455e-06,
                1.1478773593172406e-05
            ],
            [
                0.9998601778816344,
                0.9999251537731004,
                0.9998601779465845,
                0.9998204720373296,
                0.9998415637112301,
                0.9996200154827276,
                0.9996646497635172,
                0.9995694428331766,
                NaN,
                0.9996646497934898
            ],
            [
                0.6224593312018546,
                0.9959298624011346,
                0.9980732651763821,
                0.5312093733737563,
                0.9914225153307572,
                0.9959298617971052,
                0.9997694932594148,
                0.4378234991142019,
                0.7310585786300049,
                0.022977372335312288
            ],
            [
                0.999959936303167,
                0.9999756997698522,
                0.9998415637278713,
                0.9998415638043159,
                0.9997965731024886,
                0.9998766053664871,
                0.9999038975395551,
                0.9997965730554776,
                0.9997388096030231,
                0.9998766053815955
            ],
            [
                0.9997040429067398,
                0.007577239629069049,
                0.9998911030918749,
                0.994088932514635,
                0.999569442997686,
                0.9998911031182597,
                0.34864513533394575,
                0.9997388096937553,
                0.9964063973468822,
                0.9997040428025648
            ],
            [
                0.9964063968766788,
                0.9953904277501178,
                0.9982992774162108,
                0.05340332452690108,
                0.9971990724144293,
                0.06754669301670264,
                0.0330859754092826,
                0.7310585786300048,
                0.9924227605180019,
                0.9875683497642471
            ],
            [
                0.9975273768858619,
                0.9964063975969905,
                0.0005527786945510347,
                0.029312229479407058,
                0.037326883462100995,
                0.9933071498837039,
                0.9989677690497966,
                0.99330715007564,
                0.9968273177311345,
                0.9986749778964296
            ],
            [
                0.9997694933252917,
                0.9998911030785287,
                0.9999756997679945,
                NaN,
                0.9998911030781089,
                0.9999417087140456,
                0.9999151889488815,
                0.34864512179822543,
                0.999664649778406,
                0.7981867849406659
            ],
            [
                3.53562674909987e-05,
                4.006370622248093e-05,
                0.9997694932623726,
                4.006370132428075e-05,
                4.539787379595972e-05,
                3.120191502237466e-05,
                3.120190376166595e-05,
                6.14417606112322e-06,
                2.7535697565829318e-05,
                0.9995694428323749
            ],
            [
                0.0031726832806159297,
                0.9959298614063739,
                0.9997040428435786,
                0.0008040860633948512,
                0.0005527787132349309,
                0.9994472214038529,
                0.6791786861878392,
                0.0011695103639200208,
                0.9997040428665009,
                0.8807970748488297
            ],
            [
                0.9996200155283287,
                0.9975273773717018,
                0.9995694428401658,
                0.9993736658142003,
                0.999373665864808,
                0.9975273770828395,
                0.9959298624936266,
                0.9990889485974866,
                0.9996200155711218,
                0.9995121427750667
            ],
            [
                0.998498817892808,
                0.998830489754527,
                0.9999038975514787,
                0.9998766054550653,
                0.9998766054569003,
                NaN,
                0.9997965730303205,
                0.9998415637877762,
                0.9996646497457502,
                0.9997965730799481
            ],
            [
                0.9982992776413382,
                0.4073334000459302,
                0.9914225139843766,
                0.5312093733737563,
                0.1824255304737224,
                0.6791787056691697,
                0.9989677687644533,
                0.9999151889598189,
                0.9999038975741514,
                0.9997388096023466
            ],
            [
                2.753568759415642e-05,
                1.892515272680245e-05,
                1.1478765371735978e-05,
                4.7850939176760526e-06,
                3.120190759915557e-05,
                5.829124424578618e-05,
                0.9890130560538113,
                3.120191118965148e-05,
                2.4300243556219075e-05,
                0.9997965730335999
            ],
            [
                0.9995121429197641,
                0.999769493369706,
                0.6513548578981939,
                0.3208212943308302,
                0.1329642419157059,
                0.2942149783515162,
                0.18242551936144574,
                0.991422514237813,
                0.9990889486923241,
                0.3486451217982255
            ],
            [
                0.9997040429778834,
                0.20181322226037884,
                0.998674977872244,
                0.9988304895682211,
                0.9999038975852277,
                0.9924227584099834,
                0.9996200154912841,
                0.999664649804027,
                0.2942149659744614,
                0.9997388096957008
            ],
            [
                0.9995694428216781,
                0.9992903297296897,
                0.9996646497410281,
                0.9999599362982922,
                0.9995694429306247,
                0.9997965730060869,
                0.9996646500200989,
                0.9997965730763906,
                0.999915188948705,
                0.9994472212547033
            ],
            [
                0.9999485577877788,
                0.9995121428916364,
                0.9991959139445086,
                0.26894141551050293,
                0.9997388095800569,
                0.0010322309720513926,
                0.09534946297109421,
                0.9980732650169872,
                0.9996200154092795,
                0.999704042873295
            ],
            [
                2.1444940656902878e-05,
                0.9975273768766734,
                1.892515272363544e-05,
                1.4738980201465192e-05,
                8.939697328921256e-06,
                1.1478772216167625e-05,
                2.7535687744012967e-05,
                3.535625482005107e-05,
                2.753569424233864e-05,
                6.605215178625816e-05
            ],
            [
                2.4300246477539277e-05,
                3.120192243379064e-05,
                3.535626323004896e-05,
                3.535624217997696e-05,
                5.422219612012453e-06,
                0.00017952797901642673,
                2.4300249384892373e-05,
                1.1478772182635109e-05,
                2.753570420970657e-05,
                1.4738983718463215e-05
            ],
            [
                0.9998415638417889,
                0.9982992779704312,
                0.99979657303257,
                0.9998766054403214,
                0.9999339478250594,
                0.999860177920109,
                0.9999251537378274,
                0.9999417087076858,
                0.9999485577743548,
                0.9998911031306567
            ],
            [
                2.7535681224252135e-05,
                1.4738978450955768e-05,
                7.889263524443698e-06,
                2.1444953481409255e-05,
                6.60521758296861e-05,
                4.0063682591672956e-05,
                1.0129988551901002e-05,
                6.144177525664837e-06,
                3.1201922400646195e-05,
                0.00037998459969697745
            ],
            [
                0.00012339455813092196,
                8.93969842332381e-06,
                0.0003353501790841194,
                1.1478769479572082e-05,
                1.8925152739677025e-05,
                3.120191132245625e-05,
                0.014063624395963635,
                5.8291286159594326e-05,
                2.1444943259312946e-05,
                0.00015843621200255584
            ],
            [
                2.753569433890398e-05,
                1.6701417844299117e-05,
                0.00013982201951839615,
                1.6701423792728773e-05,
                1.4738988982594524e-05,
                4.006370159769848e-05,
                3.5356245947277814e-05,
                2.753569418824602e-05,
                3.5356237890219234e-05,
                2.75356943166659e-05
            ],
            [
                0.9995121429538523,
                0.9992903295613129,
                0.9999251537728716,
                0.9890130579361248,
                0.9997388097392544,
                0.9996646499686226,
                0.9994472214754692,
                0.9980732650899686,
                0.9997694933176525,
                0.999738809603631
            ],
            [
                0.999704042980837,
                NaN,
                0.9968273175934365,
                0.9940889302298368,
                0.9997694933709267,
                0.9993736657587833,
                0.9996646498190134,
                0.9999832985702045,
                0.999664649889125,
                0.9996200155104973
            ],
            [
                0.0953494674697966,
                0.999876605440896,
                0.9996646497913824,
                0.9998766054261683,
                0.9998911031039929,
                0.9999251537378383,
                0.9998204719928888,
                NaN,
                0.9986749775533635,
                0.9968273175868092
            ],
            [
                0.0953494616857507,
                0.7981867705385762,
                0.11920292828022307,
                0.24508502416032488,
                0.999512142941165,
                0.9998415637836084,
                0.34864514210180597,
                0.11920291107043361,
                0.999948557786653,
                0.999620015478781
            ],
            [
                3.1201922480102066e-05,
                7.88926163292119e-06,
                3.288748669069309e-06,
                6.9622595564025216e-06,
                3.535625897218662e-05,
                8.939697361443396e-06,
                4.222835455413733e-06,
                4.222832937389751e-06,
                1.5534971985217185e-06,
                8.939700547898078e-06
            ],
            [
                0.9982992777660575,
                0.9996646497816646,
                0.9994472212526131,
                0.999704042758649,
                0.9999599362887481,
                0.9997694933443466,
                0.007577241015738978,
                0.9980732656460598,
                0.9997965730089697,
                0.9998601779281366
            ],
            [
                0.02931223096334787,
                0.9996200155463811,
                0.5,
                0.999933947871222,
                0.9999485577926047,
                0.9999251537464943,
                0.24508501864634824,
                0.9997965730295629,
                0.4073334000459302,
                0.9820137936239377
            ],
            [
                NaN,
                0.5312093733737563,
                0.08509905254807777,
                0.04742587788985983,
                0.033085982083187186,
                0.08509903920620716,
                0.16451646904109266,
                0.5926665999540698,
                0.09534947261117097,
                0.06754668597767712
            ],
            [
                0.047425877048378896,
                0.04742587637519416,
                0.999664649786143,
                0.9988304895631895,
                0.3208213073183839,
                0.9997965729795272,
                0.13296424019782924,
                0.4687906266262437,
                0.9982992772628319,
                0.04208772686428808
            ],
            [
                0.0006263340687717587,
                0.9947798746183792,
                0.9997694931847583,
                0.9998601778789001,
                0.993307150038491,
                0.9995121429070201,
                0.9998601779776721,
                0.9999339478403315,
                0.9999832985841466,
                0.9999251537996634
            ],
            [
                0.9998766053677386,
                0.9998601779268692,
                0.999876605399722,
                0.999933947856118,
                0.9999251537731374,
                0.9996646499498506,
                0.9998766053825399,
                0.9982992775802633,
                0.9999417087418284,
                0.9995694428746609
            ],
            [
                0.9890130550316946,
                0.9993736657019816,
                0.5,
                0.9982992776059583,
                0.9998204720785392,
                0.9996200155308602,
                0.999769493372228,
                0.999195913987487,
                0.867035763237924,
                0.999512142916273
            ],
            [
                0.999796572931782,
                0.9999339478791605,
                0.9998415637536502,
                0.999891103041336,
                0.9996200154801076,
                0.9998204719511699,
                0.9998601779770373,
                0.9986749772997997,
                0.9999485577926469,
                0.9999339478476101
            ],
            [
                0.9996646500247723,
                0.10669059110526011,
                0.9953904284017824,
                0.22270014398423355,
                0.9984988176684032,
                0.9991959140216263,
                0.8519527982093666,
                0.8670357649558006,
                0.9999038976110298,
                0.9989677691994907
            ],
            [
                0.9998766053984867,
                0.9998911030786539,
                0.9953904277244785,
                0.9997388096405198,
                0.9999546021261274,
                0.9999485577744218,
                0.0008040859334779844,
                0.2689414213699951,
                0.9998415638060009,
                0.9999724643023877
            ],
            [
                4.006369189224475e-05,
                5.144223744786149e-05,
                2.7535700886916288e-05,
                7.889264454577566e-06,
                3.120190733445412e-05,
                7.484623569609516e-05,
                0.00015843616247335774,
                7.484620009207818e-05,
                0.00033535013617414785,
                0.00012339454407828327
            ],
            [
                8.939695232316787e-06,
                2.4300249383301144e-05,
                2.4300246355014616e-05,
                1.8925145961179394e-05,
                5.829127204384482e-05,
                1.0129995777499219e-05,
                2.4300249313110237e-05,
                4.006368706575287e-05,
                5.829127215411085e-05,
                2.144494581132591e-05
            ],
            [
                0.9998766053974184,
                0.025957357715834423,
                0.999373665698411,
                0.9999038975531666,
                0.9992903296747887,
                0.9999251537922889,
                0.9998601779276566,
                0.999088948899854,
                0.9998911031169002,
                0.9992903297632082
            ],
            [
                1.1478772206270732e-05,
                2.753568223778705e-05,
                1.4738981962698681e-05,
                4.785093351098334e-06,
                1.4738978391116629e-05,
                5.8291271797018575e-05,
                1.1478766743561818e-05,
                6.144174600180663e-06,
                5.422217673754406e-06,
                1.1478764004044448e-05
            ],
            [
                2.4300243539953176e-05,
                1.3007126874284998e-05,
                9.610242555213935e-05,
                3.535625895752386e-05,
                1.1478772165096307e-05,
                6.144172403201774e-06,
                1.0129987339496916e-05,
                1.4738988943934983e-05,
                4.5397884676638064e-05,
                2.7535684361021608e-05
            ],
            [
                0.9994472213967782,
                0.9968273165220412,
                0.9995694428708782,
                0.998967768998418,
                0.9982992777014249,
                0.9924227572334148,
                0.9975273767669861,
                0.9989677688787345,
                0.9996200155729901,
                0.9968273168865365
            ],
            [
                0.0758581784543034,
                0.9982992779158787,
                0.4073334000459302,
                0.9914225158534696,
                0.9947798736946568,
                0.9964063979279669,
                0.9978172832473559,
                0.9890130552239741,
                0.08509904094645106,
                0.22270012850745968
            ],
            [
                0.06008664428307652,
                0.8807970764133561,
                0.9964063969967307,
                0.9986749774496889,
                0.9994472212362124,
                0.9996200155256203,
                0.9997694932645793,
                0.9999339478426892,
                0.9998601778670356,
                0.06754669817865513
            ],
            [
                0.9997965730839791,
                0.9998766053837213,
                0.9999339478716978,
                0.9999546021152097,
                0.999876605455735,
                0.9875683499128884,
                0.9997388096978667,
                0.9999038975752016,
                0.9975273763270884,
                0.9997965729575488
            ],
            [
                0.9971990730972603,
                0.9982992777709988,
                0.9998911030788012,
                0.0,
                0.5312093733737562,
                0.9995121429925101,
                0.02033235196988727,
                0.9978172838208791,
                0.9924227601398192,
                0.9995694429377141
            ],
            [
                0.09534947261117098,
                0.9998415637757754,
                0.9998601779294062,
                0.9994472213106907,
                0.9998204719735808,
                0.001325022216950097,
                0.0009110512692110148,
                0.9984988176650877,
                0.9959298624256733,
                0.9993736659076186
            ],
            [
                0.9984988176273961,
                0.05340332528017579,
                0.9996200155154278,
                0.9998601779139203,
                0.9999485577986323,
                0.5621765008857982,
                0.9999485577803285,
                0.6224593241981982,
                0.9971990729886576,
                0.3775406687981454
            ],
            [
                0.00013982213863423135,
                0.000261190196786928,
                3.5356259025178387e-05,
                6.605212033932063e-05,
                0.00012339459968559107,
                0.998967768794344,
                0.0002959569726295795,
                5.1442199608198866e-05,
                0.00010889694532257115,
                5.829127905167534e-05
            ],
            [
                0.9996646499785353,
                0.9980732650868344,
                0.9933071476454819,
                0.9968273173578032,
                0.9994472212945473,
                0.999447221351017,
                0.914900957313305,
                0.00043055700526999785,
                0.9998204720796544,
                0.9993736658566466
            ],
            [
                0.6513548782017745,
                0.9998415638419296,
                0.9995121429707119,
                0.9990889489369943,
                0.9999251538075793,
                0.9997388096660393,
                0.9525741222784364,
                0.9999038975746743,
                0.9995121428964616,
                0.9914225137863796
            ],
            [
                0.9971990729353317,
                0.9997040430136359,
                0.9999921107392981,
                0.999948557768173,
                0.9999251537732343,
                0.9999898700102298,
                0.9999417087069895,
                0.9999724643187554,
                0.9999251538006376,
                0.9953904285043392
            ],
            [
                0.9998601778603485,
                0.9999339478794387,
                0.9997694932508701,
                0.9997388097943063,
                0.9997694932323853,
                0.999447221237338,
                0.9997965730834937,
                0.9998766054403591,
                0.817574471748733,
                0.9999339478397309
            ],
            [
                0.9997694932321975,
                0.2689414096510109,
                0.9579122701319097,
                0.9995694429716832,
                0.9999251537376466,
                0.9924227570443234,
                0.5312093733737563,
                0.11920292828022307,
                0.9995121429527454,
                0.40733340004593027
            ],
            [
                2.7535684351805832e-05,
                1.012999216832942e-05,
                1.6701425805958843e-05,
                3.7266401714225625e-06,
                1.1478764002165291e-05,
                7.88926256603971e-06,
                1.1478764000202618e-05,
                1.1478768081897073e-05,
                1.0129988517075569e-05,
                6.1441775143098946e-06
            ],
            [
                0.07585817166422973,
                0.999373665876212,
                0.2689414272294874,
                0.1645164710892692,
                0.05340333450779176,
                0.00017952796539742315,
                0.999290329686677,
                0.4687906266262437,
                0.6791786926816161,
                0.9994472213981932
            ],
            [
                0.40733340004593027,
                0.9997694932928965,
                0.9997694932171267,
                0.9975273766308821,
                0.0024726233025016307,
                0.9992903295669269,
                0.40733340004593027,
                0.9992903297697303,
                0.26894141551050293,
                0.9993736659273662
            ],
            [
                0.9975273771408417,
                0.9999910603036988,
                0.9999646437408746,
                0.14804720179063335,
                0.9994472214199642,
                0.9999646437451684,
                0.9982992775873788,
                0.9998204720163655,
                0.999820471974375,
                NaN
            ],
            [
                0.9964063972610118,
                0.8933093996634686,
                0.9982992778156685,
                0.9982992772351604,
                0.9998601778680365,
                0.9968273178482149,
                0.6513548646660542,
                0.11920292671569666,
                0.8354835432479661,
                0.22270014398423357
            ],
            [
                0.07585818263281054,
                0.9994472214265244,
                0.998073265241752,
                0.9989677689136672,
                0.9999339478320515,
                0.033085976958581766,
                0.9989677687926635,
                0.43782349911420193,
                0.02931222757148327,
                0.9992903294837084
            ],
            [
                0.9890130585635627,
                0.9995121427904788,
                0.9997694933682104,
                0.9995121427727108,
                0.9990889489057351,
                0.9998204720861636,
                0.9996200155499186,
                0.9992903296911352,
                NaN,
                0.9978172840734119
            ],
            [
                4.22283394432571e-06,
                6.605215954827846e-05,
                5.829124444893003e-05,
                0.00013982201963639096,
                2.9023123305485934e-06,
                1.6701419836749094e-05,
                7.889262584006375e-06,
                2.7535700880905993e-05,
                1.012999459934851e-05,
                7.889261641674914e-06
            ],
            [
                0.9989677687266394,
                0.9964063969583807,
                0.9997388096685929,
                0.9996646497798694,
                0.9991959141877871,
                0.9998766054734808,
                0.9998204720804903,
                0.9999599363079118,
                0.9959298616102337,
                0.9997040429490971
            ],
            [
                0.9988304895512224,
                0.9980732656147181,
                0.9980732657884407,
                0.9995694429714828,
                0.7310585844894971,
                0.9980732653348816,
                0.9999339478570071,
                0.9980732656241206,
                0.9998601779109664,
                0.9924227577796789
            ],
            [
                0.9924227601328159,
                0.9997388096652566,
                0.9997965729633023,
                0.9998911030934244,
                0.9997388096185643,
                0.9997965729686356,
                0.9997040428151626,
                0.9997694933148354,
                0.9989677691080177,
                0.9999151889296709
            ],
            [
                0.9996200155666557,
                0.00037998452038981385,
                0.99987660539665,
                0.9989677689864136,
                0.0005527786321641911,
                0.999512142971166,
                0.998299277603191,
                0.9988304899469524,
                0.9975273763018202,
                0.2018132246607271
            ],
            [
                1.1478772222807315e-05,
                5.8291250907547785e-05,
                8.939700564468113e-06,
                1.8925152735477297e-05,
                1.0129993388915298e-05,
                1.8925143661588257e-05,
                7.484620892446916e-05,
                8.939699497595294e-06,
                1.147876812106705e-05,
                7.484626251565003e-05
            ],
            [
                0.00010889694042650782,
                1.892514367783638e-05,
                7.48461983256001e-05,
                3.120191500580244e-05,
                1.3007131554942966e-05,
                2.4300240674326342e-05,
                1.3007123802522791e-05,
                0.0001795279850083707,
                0.9986749773105831,
                3.120192549170684e-05
            ],
            [
                0.999978555046504,
                0.9999724643187865,
                0.9999832985841466,
                0.999972464295789,
                0.9998204721023214,
                0.9999251537381574,
                0.9999038975531666,
                0.9999646437579378,
                0.9999251537554039,
                0.9999151889590872
            ]
        ]
    },
    {
        "q_id": "8265_mmlu_math",
        "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": [
            [
                0.9999646437366672,
                0.9999687980923667,
                0.999959936298299,
                0.9999785550464814,
                0.9999599362935143,
                0.9999417087067253,
                0.9999599362935121,
                0.9999832985801511,
                0.999959936312614,
                0.9999599362887508
            ],
            [
                0.9999921107392965,
                0.9999885212359829,
                0.9999724643023561,
                0.9999910603026316,
                0.9999930377412617,
                0.9999921107336545,
                0.999992110736476,
                0.9999898700102337,
                0.9999810748427463,
                0.9996646499366206
            ],
            [
                0.99998699287154,
                0.9999930377437518,
                0.9999910603015668,
                0.9999910603026337,
                0.9999885212291416,
                0.9999756997563815,
                0.9999724642957929,
                0.9999930377462417,
                0.9999756997650704,
                0.9999921107364758
            ],
            [
                0.9999869928761923,
                0.9999921107374159,
                0.9999785550592731,
                0.9999852610180356,
                0.9999756997505924,
                0.9999921107392965,
                0.9999898700102303,
                0.9999921107345945,
                0.9999910603058293,
                0.9999885212346142
            ],
            [
                0.9999852610233023,
                0.999954602115151,
                0.9999785550439222,
                0.9999885212277713,
                0.9999885212264031,
                0.9999930377445809,
                0.9999938558224687,
                0.9999417087067125,
                0.9999756997563752,
                0.9999930377462408
            ],
            [
                0.9999869928668881,
                0.9999339478556071,
                0.9997040429053018,
                0.9999869928653397,
                0.9999038975967863,
                0.9999869928746422,
                0.9999756997563835,
                0.9999646437577489,
                0.9999910603047638,
                0.9999785550490408
            ],
            [
                0.9999646437493181,
                0.9999885212332457,
                0.9999810748472558,
                0.9999852610110059,
                0.9999599363221695,
                0.9999921107383563,
                0.9999599363126306,
                0.9999785550515954,
                0.9999724643023546,
                0.9999599363078551
            ],
            [
                0.9999898700041944,
                0.9999852610215467,
                0.9999832985801549,
                0.9999599363031463,
                0.9999921107402371,
                0.9999599362935732,
                0.9999852610162804,
                0.9999810748427427,
                0.9999810748472637,
                0.9999756997650724
            ],
            [
                0.9999852610180329,
                0.9999852610145189,
                0.999972464295789,
                0.999975699767969,
                0.9999869928684382,
                0.9999785550464846,
                0.9999885212346156,
                0.9999910603068948,
                0.9999785550464864,
                0.999975699759281
            ],
            [
                0.999841563784074,
                0.9999251537996939,
                0.9999724643154906,
                0.9999785550490434,
                0.9999339478632615,
                0.999664649813657,
                0.999948557774137,
                0.9999599362887388,
                0.9999599363222194,
                0.9997694932036522
            ],
            [
                0.9999546021097627,
                0.999954602115177,
                0.9999687980849346,
                0.9999852610110059,
                0.9999646437619613,
                0.9999687980812203,
                0.9999869928746405,
                0.9999485578048254,
                0.9999885212291404,
                0.999876605396282
            ],
            [
                0.999989870012645,
                0.999972464295789,
                0.9999852610180336,
                0.999991060301567,
                0.9999921107364751,
                0.9999724642990652,
                0.9999885212359829,
                0.9999910603036981,
                0.999992110733655,
                0.9999869928746405
            ],
            [
                0.9999151889689214,
                0.9997694932587575,
                0.9999869928715408,
                0.999925153772901,
                0.9999852610180351,
                0.9999339478711562,
                0.9999599363030746,
                0.9999687980737803,
                0.9999546021259874,
                0.9999646437577411
            ],
            [
                0.9999810748472546,
                0.9999417087415464,
                0.9999687980923714,
                0.9999599362982898,
                0.9986749774624749,
                0.9999485577987365,
                0.9997965731005827,
                0.9999687980812186,
                0.9999546021314138,
                0.9999599363173987
            ],
            [
                0.9999938558232018,
                0.9999910603026327,
                0.9999938558246669,
                0.9999957771660526,
                0.999992110738357,
                0.9999910603058293,
                0.9999885212318764,
                0.9999810748472552,
                0.9999921107345953,
                0.9999756997534923
            ],
            [
                0.9999724643154776,
                0.9998601779764942,
                0.9999852610197921,
                0.9999869928684411,
                0.9999646437493142,
                0.9999687980923636,
                0.9999687980886414,
                0.9999832985841378,
                0.999986992873089,
                0.9999832985761744
            ],
            [
                0.9999785550592659,
                0.9999852610145223,
                0.9999724642957902,
                0.9999910603005011,
                0.999959936317406,
                0.9999546021259874,
                0.9999756997679721,
                0.9999724643089218,
                0.9999869928684406,
                0.9999810748472573
            ],
            [
                0.99998699287309,
                0.9999724643056438,
                0.9999785550439292,
                0.9999785550490408,
                0.9999785550515988,
                0.99998987001023,
                0.9999832985801554,
                0.9999898700078153,
                0.9999832985761709,
                0.999954602126061
            ],
            [
                0.9999599363030746,
                0.9999869928715396,
                0.9999852610127654,
                0.9999910603068951,
                0.9999852610180336,
                0.9999885212318776,
                0.9999852610215476,
                0.9999885212305086,
                0.9999724643089181,
                0.9999852610197902
            ],
            [
                0.9999898700066079,
                0.9999756997505913,
                0.9999687980998164,
                0.9999832985741856,
                0.9999687980812089,
                0.999981074845,
                0.9999810748562796,
                0.999959936317406,
                0.9999810748450022,
                0.9999785550592685
            ],
            [
                0.9999869928746399,
                0.999993855826864,
                0.9999930377437515,
                0.999983298580152,
                0.9999952149037947,
                0.9999898700102295,
                0.9999724643023534,
                0.9999810748517658,
                0.99999457778297,
                0.9999962733607163
            ],
            [
                0.9999885212318793,
                0.9999930377404321,
                0.9999921107392977,
                0.99999457778297,
                0.999996273361605,
                0.9999898700078147,
                0.999985261023306,
                0.9999952149066472,
                0.9999852610110079,
                0.9999962733607167
            ],
            [
                0.9999910603058294,
                0.9986749773048833,
                0.9999885212332453,
                0.9999339478711913,
                0.99997569975349,
                0.9999756997592781,
                0.9999832985781597,
                0.9999546021205913,
                0.9999724643023691,
                0.9999756997621719
            ],
            [
                0.999989870011438,
                0.9999810748585369,
                0.9999810748495147,
                0.9999724643056425,
                0.9999785550413773,
                0.999991060301566,
                0.9999910603047645,
                0.9999852610215495,
                0.9999756997679812,
                0.9999724642990713
            ],
            [
                0.9999646437324774,
                0.9999910602994351,
                0.9999756997621891,
                0.99990389756239,
                0.9999885212332457,
                0.9999724643187834,
                0.9999485577925075,
                0.9999756997650734,
                0.9999251537731189,
                0.9999756997476946
            ],
            [
                0.9999898700078153,
                0.9999785550567114,
                0.9998911030912093,
                0.9999724643187624,
                0.9999785550515972,
                0.9999921107392965,
                0.99998987001023,
                0.9999910603015664,
                0.9999485578047914,
                0.9999852610127625
            ],
            [
                0.9999546021206174,
                0.9999832985721891,
                0.9999724643154838,
                0.9999885212291401,
                0.9999885212291427,
                0.9999646437493306,
                0.9999832985841449,
                0.999983298578164,
                0.9999832985841355,
                0.9999885212291404
            ],
            [
                0.9999599362983018,
                0.9999810748427427,
                0.9999810748472581,
                0.9999339478318156,
                0.9999251537817575,
                0.9999546021368187,
                0.9999646437535449,
                0.9999756997650775,
                0.9999546021368343,
                0.9999417087554116
            ],
            [
                0.9999832985841349,
                0.9999910603036976,
                0.9999869928761915,
                0.9999810748427433,
                0.9999938558224694,
                0.9999724643187624,
                0.999992110736476,
                0.9999898700066077,
                0.9999417087554913,
                0.9999952149037944
            ],
            [
                0.9999810748517691,
                0.9999910603026323,
                0.9999952149066467,
                0.9999646437451162,
                0.9999724643089206,
                0.9999151889387327,
                0.999993037742922,
                0.9999938558239343,
                0.9999962733598279,
                0.9999930377437517
            ],
            [
                0.9999852610110074,
                0.9999930377445817,
                0.999988521227774,
                0.9999898700066077,
                0.9999938558224707,
                0.9999938558224697,
                0.9999898700066077,
                0.9999930377404317,
                0.9999898700066073,
                0.9999756997563877
            ],
            [
                0.9999151889895265,
                0.9999930377462416,
                0.9999852610127625,
                0.9999810748427493,
                0.9999898700066073,
                0.9999810748517747,
                0.9999599363221718,
                0.9999938558224694,
                0.9999646437493181,
                0.9999945777810306
            ],
            [
                0.9999599363126283,
                0.9999687980886459,
                0.9999485578047951,
                0.9999852610197898,
                0.9998601779767831,
                0.9999898700090254,
                0.999964643757743,
                0.9999485577925429,
                0.9999485578048022,
                0.9999756997621767
            ],
            [
                0.999959936293519,
                0.9999869928668902,
                0.9999646437408817,
                0.9999646437493369,
                0.9999339478318334,
                0.9999810748495092,
                0.9999485577802507,
                0.999915188938682,
                0.9999599362935313,
                0.9999785550515979
            ],
            [
                0.999959936317424,
                0.9999546021314138,
                0.9999756997506004,
                0.9999599363221838,
                0.999903897539506,
                0.9996200155680928,
                0.9999339478318583,
                0.9999756997621798,
                0.9999251537639369,
                0.999981074851767
            ],
            [
                0.9999599363030772,
                0.9999898700066069,
                0.9999810748562803,
                0.9999724643056345,
                0.9999687980886474,
                0.9999852610180329,
                0.999985261023302,
                0.9999599362935263,
                0.9999151889184082,
                0.9999546021367987
            ],
            [
                0.9999785550464871,
                0.9999810748427478,
                0.9999687980998132,
                0.9999646437409201,
                0.9999921107374166,
                0.9999885212264044,
                0.9999945777784455,
                0.999978555056717,
                0.9999885212346149,
                0.9999910603036991
            ],
            [
                0.9999869928699883,
                0.9999938558232019,
                0.9999832985741806,
                0.9999485577987409,
                0.9999852610197898,
                0.9999921107364752,
                0.9999869928746481,
                0.9999945777816771,
                0.9999921107402375,
                0.9999869928669027
            ],
            [
                0.9999724643023631,
                0.9999724643023462,
                0.9999251537995921,
                0.9999945777784457,
                0.9999810748449987,
                0.9999756997679633,
                0.9999921107392967,
                0.9999885212346137,
                0.9999687980774897,
                0.999981074851767
            ],
            [
                0.999972464318766,
                0.9999417087136733,
                0.9999756997679862,
                0.9999251537372807,
                0.9998601779598772,
                0.9999852610145172,
                0.9999852610162783,
                0.9999852610162783,
                0.9999898700126468,
                0.9971990728813556
            ],
            [
                0.9999151889386432,
                0.9999417087207032,
                0.9999852610197937,
                0.9999885212291447,
                0.9999885212291397,
                0.9999756997650809,
                0.9999646437451182,
                0.999959936312657,
                0.9999756997592781,
                0.9999810748495118
            ],
            [
                0.9998204719914993,
                0.9996646498527618,
                0.9999038975395299,
                0.999915188928435,
                0.9995121428888832,
                0.9993736658427286,
                0.9995694429662221,
                0.9995694429647941,
                0.9993736659910175,
                0.9997965730761124
            ],
            [
                0.9999898700090224,
                0.9995121428885143,
                0.9999898700054001,
                0.9999785550439274,
                0.9999898700126449,
                0.999986992869989,
                0.9999852610162764,
                0.9999852610127608,
                0.9999898700090223,
                0.9999885212264044
            ],
            [
                0.9999910603005008,
                0.9999485577925354,
                0.9999339478239425,
                0.9999810748517691,
                0.9999810748585343,
                0.9998415638411849,
                0.9997040427992236,
                0.9999952149055061,
                0.9996200155189874,
                0.9999832985781628
            ],
            [
                0.9999785550464864,
                0.9999339478556071,
                0.999975699767971,
                0.9999785550541535,
                0.9999852610197916,
                0.9999785550439318,
                0.9999756997621809,
                0.9999785550413746,
                0.999373665844186,
                0.9999546021259992
            ],
            [
                0.9999724643089143,
                0.9999756997650755,
                0.9999687980812059,
                0.9999785550515924,
                0.9999869928699883,
                0.9999910603036981,
                0.9999810748427433,
                0.9999898700078153,
                0.9999832985741784,
                0.9999930377429215
            ],
            [
                0.9999869928730909,
                0.9999852610145213,
                0.999995777165549,
                0.9999869928684394,
                0.999988521229141,
                0.9999724643056358,
                0.9999785550592668,
                0.9999898700078147,
                0.9999910603068949,
                0.9999810748427413
            ],
            [
                0.9999339478554222,
                0.9999485577618964,
                0.9999339478790124,
                0.9999417087345535,
                0.9999785550592636,
                0.9999485577618847,
                0.9998766053959677,
                0.999975699767971,
                0.9998766054696027,
                0.9999687980774836
            ],
            [
                0.9999869928715408,
                0.999992110738356,
                0.9999869928746405,
                0.9999038976197933,
                0.9999832985781592,
                0.9999417087484173,
                0.999988521231877,
                0.9999687980737786,
                0.9999646437619502,
                0.9999852610197894
            ],
            [
                0.9999485577741718,
                0.9999869928699895,
                0.9999852610162777,
                0.9999921107336547,
                0.9999852610145198,
                0.9999852610233045,
                0.9999898700102311,
                0.9999885212305096,
                0.9999151889386061,
                0.9999785550465105
            ],
            [
                0.9999599362888102,
                0.9999832985821441,
                0.9999885212277727,
                0.9999832985721898,
                0.9999910603036979,
                0.9999785550490444,
                0.9999599363126256,
                0.9999687980737689,
                0.9999756997505903,
                0.9999151889690066
            ],
            [
                0.9999970976869772,
                0.9999930377404317,
                0.9999885212332469,
                0.9999910603036983,
                0.9999810748495147,
                0.999981074845,
                0.9999756997593094,
                0.9997388095988128,
                0.9999869928699883,
                0.9999930377420918
            ],
            [
                0.9999756997592771,
                0.9999885212264054,
                0.9999930377420918,
                0.9999898700078143,
                0.9999869928761923,
                0.9999930377404325,
                0.999972464302351,
                0.9999852610197916,
                0.9999869928684385,
                0.9999869928730912
            ],
            [
                0.9998204720990381,
                0.9999646437493283,
                0.9996646498538448,
                0.999948557780265,
                0.9999646437535324,
                0.9999546021314201,
                0.9999251537461021,
                0.9999852610110059,
                0.9992903296434167,
                0.9999485577619212
            ],
            [
                0.9999339478632947,
                0.9999485578048022,
                0.9999885212359829,
                0.9999810748540218,
                0.9999785550567105,
                0.9999251537550597,
                0.9999687980998051,
                0.9999885212305096,
                0.9994472213477369,
                0.9999546021097687
            ],
            [
                0.9999832985801543,
                0.9999485577680091,
                0.9999869928653375,
                0.999986992865338,
                0.999986992865338,
                0.9999910603026313,
                0.9999921107383563,
                0.9999898700066079,
                0.9999885212264037,
                0.9999885212359862
            ],
            [
                0.999925153755067,
                0.9999646437619673,
                0.9999339478633308,
                0.9999485577864191,
                0.9998204720777947,
                0.9997388095986608,
                0.9999038975853941,
                0.998967768719677,
                0.9999485577986746,
                0.9999687980923682
            ],
            [
                0.9999646437535538,
                0.999991060299435,
                0.9999485577864038,
                0.9997694932882687,
                0.9999724643056345,
                0.9999869928668889,
                0.9999885212359819,
                0.9999687980737645,
                0.9999724643089167,
                0.9999921107336541
            ],
            [
                0.9999910602994357,
                0.9999945777823238,
                0.9999852610215472,
                0.9999930377462416,
                0.9999910603005019,
                0.9999898700090238,
                0.9999930377462416,
                0.9999938558239345,
                0.999994577778446,
                0.9999921107402371
            ],
            [
                7.889264465067689e-06,
                4.222833947121688e-06,
                6.9622554185195676e-06,
                4.222834954514924e-06,
                1.473898196677375e-05,
                7.889264465986113e-06,
                1.0129988561372045e-05,
                7.889263525103816e-06,
                6.9622545892184106e-06,
                6.144176066353646e-06
            ],
            [
                0.9999785550439292,
                0.9999898700053996,
                0.9999910603047626,
                0.9999785550592712,
                0.9999898700090227,
                0.9999810748495092,
                0.9999724642990675,
                0.9999810748449967,
                0.9999898700114443,
                0.9999810748427421
            ],
            [
                0.9999832985701962,
                0.9999832985701994,
                0.9999938558224692,
                0.9999810748517685,
                0.9999938558268638,
                0.9999832985741806,
                0.9999930377437511,
                0.9999898700041936,
                0.9999852610127611,
                0.9999832985741818
            ],
            [
                0.999978555056717,
                0.9999869928715408,
                0.9999810748495147,
                0.9999810748495163,
                0.9999910603036991,
                0.9999885212318768,
                0.9999885212264044,
                0.9999869928684378,
                0.999975699759281,
                0.9999832985741823
            ],
            [
                0.9999756997621777,
                0.9999810748472581,
                0.9999945777784457,
                0.9999810748495187,
                0.99998987001023,
                0.9999546021476268,
                0.999981074851773,
                0.9999785550592677,
                0.9999898700041918,
                0.9999852610127625
            ],
            [
                0.9999910603026337,
                0.999954602120585,
                0.9999832985721927,
                0.9999810748585392,
                0.9999910603015658,
                0.9999724642990765,
                0.9999852610162767,
                0.9999599362982833,
                0.9999785550592685,
                0.9999599363030898
            ],
            [
                0.9999885212346167,
                0.999978555056715,
                0.9999898700114396,
                0.999876605470091,
                0.9999785550490427,
                0.9999930377437524,
                0.9999756997563889,
                0.9999832985721934,
                0.9998204720559976,
                0.9999962733616047
            ],
            [
                0.9999898700078149,
                0.9999957771670602,
                0.9999724643122014,
                0.9999938558268636,
                0.9999921107383573,
                0.999996711250935,
                0.9999885212346142,
                0.9999910603036983,
                0.9999852610197902,
                0.9999852610197911
            ],
            [
                0.9999967112497589,
                0.9999921107336541,
                0.9999810748517691,
                0.999986992868439,
                0.9999938558275966,
                0.9999885212277733,
                0.9999938558232019,
                0.9999785550541559,
                0.9999921107374165,
                0.9999921107336545
            ],
            [
                0.9999724643023497,
                0.9999810748427448,
                0.9999724643122014,
                0.9999885212291413,
                0.9999546021368614,
                0.9999898700090233,
                0.9999910603036979,
                0.9999785550413702,
                0.9999852610233051,
                0.9999251537996486
            ],
            [
                0.9999756997534868,
                0.9999485577804095,
                0.9999910603026321,
                0.9999930377437515,
                0.999992110738357,
                0.9999785550541578,
                0.9999898700041916,
                0.9999646437535704,
                0.9999339478554895,
                0.9999339478318522
            ],
            [
                0.9999785550413702,
                0.9999898700078154,
                0.9999930377437513,
                0.9999945777797382,
                0.9999945777790918,
                0.9999921107355346,
                0.9999952149043655,
                0.9999646437324546,
                0.9999599363174188,
                0.9999898700041931
            ],
            [
                0.9999898700126444,
                0.9999852610233028,
                0.9999724643056319,
                0.9999957771645426,
                0.9999832985801543,
                0.9999938558261321,
                0.9999957771650457,
                0.9999952149060765,
                0.9999869928653392,
                0.9999910603058296
            ],
            [
                0.9999898700054028,
                0.9999930377404325,
                0.9999546021477209,
                0.9999869928761903,
                0.9999910603036986,
                0.9999852610145189,
                0.9999945777810312,
                0.9999885212318783,
                0.9999756997476992,
                0.999981074856284
            ],
            [
                0.9999885212332453,
                0.9999687980960859,
                0.9999810748449961,
                0.9999038975625634,
                0.9999785550592643,
                0.9999756997592791,
                0.9999785550439259,
                0.9999885212277717,
                0.9999724643023462,
                0.9999885212318764
            ],
            [
                0.9999852610215458,
                0.9999885212346156,
                0.9999852610197911,
                0.9999785550490401,
                0.9999832985701973,
                0.9999832985801554,
                0.9999756997505924,
                0.999981074851773,
                0.9999885212305106,
                0.999992110734595
            ],
            [
                0.9999724643122173,
                0.9999785550567141,
                0.9999869928699895,
                0.999985261021549,
                0.9999724643187587,
                0.9999546021422271,
                0.9999930377412624,
                0.9999687980998132,
                0.9999898700102304,
                0.9999724643187611
            ],
            [
                0.9999646437324844,
                0.999981074851767,
                0.9999810748562803,
                0.9999756997534934,
                0.9999756997476992,
                0.9999785550541578,
                0.99998699287154,
                0.999933947863388,
                0.9999485577925706,
                0.9999687980737874
            ],
            [
                0.9999417087484839,
                0.9997388097236524,
                0.9999546021314363,
                0.9999038975738676,
                0.9999485578048138,
                0.999925153781868,
                0.9999646437577469,
                0.9998415637837214,
                0.9998911030520503,
                0.9999687980886588
            ],
            [
                0.9999852610180329,
                0.9999687980737819,
                0.9999832985821525,
                0.9999485577802684,
                0.9999885212318783,
                0.9999756997592754,
                0.9999339478711793,
                0.9999151889689306,
                0.9999756997505863,
                0.9999810748562856
            ],
            [
                0.9999646437577359,
                0.9999756997505873,
                0.9999832985721865,
                0.9999832985741806,
                0.9999869928684372,
                0.9999832985761689,
                0.9999417087206043,
                0.9999485577925354,
                0.999989870009023,
                0.999993037745411
            ],
            [
                0.999993037742921,
                0.9999785550567105,
                0.9999810748427433,
                0.9999785550439356,
                0.9999957771670596,
                0.9999852610215463,
                0.9999898700126487,
                0.9999921107345944,
                0.9999546021259847,
                0.9998911030910287
            ],
            [
                0.9999921107392991,
                0.9999930377404326,
                0.9999724643154851,
                0.9999785550490482,
                0.9999810748562847,
                0.9999785550490482,
                0.9999910603015675,
                0.9999885212305103,
                0.9999417087554314,
                0.9999869928684406
            ],
            [
                0.9999724643056309,
                0.9998766054255596,
                0.999978555046489,
                0.999820472013615,
                0.9999910602994371,
                0.9999724642990738,
                0.9999869928684394,
                0.9999687980737704,
                0.9999724643187728,
                0.9999485577864349
            ],
            [
                0.9999869928746405,
                0.9999921107402375,
                0.9999756997506042,
                0.9999910603005006,
                0.999968798096083,
                0.9999885212318773,
                0.9999898700066079,
                0.9999898700054001,
                0.9999869928761911,
                0.9999724642990664
            ],
            [
                0.999989870004192,
                0.9999756997650734,
                0.9999885212332446,
                0.999992110733654,
                0.9999810748562817,
                0.9999869928715386,
                0.999975699747705,
                0.9999869928761911,
                0.9999921107336538,
                0.999988521227772
            ],
            [
                0.9999910603036978,
                0.99998699287154,
                0.9999930377437517,
                0.9999910603047654,
                0.9999910603036979,
                0.9999852610110069,
                0.999994577779092,
                0.9999546021314201,
                0.9999930377420916,
                0.9999898700066079
            ],
            [
                0.9999599363221742,
                0.9999885212318776,
                0.999993037746241,
                0.999988521226404,
                0.9999785550490417,
                0.9999339478318396,
                0.9999756997505913,
                0.9999687980923834,
                0.9999687980960859,
                0.9999930377454116
            ],
            [
                0.999954602142233,
                0.999964643753523,
                0.9999646437577469,
                0.9999646437577359,
                0.9999785550439251,
                0.9999756997505903,
                0.9999687980923607,
                0.999985261014518,
                0.9999852610233041,
                0.9999724643056319
            ],
            [
                0.9999869928746431,
                0.999983298582147,
                0.9999885212264057,
                0.9999832985761725,
                0.9999785550413696,
                0.9999921107355355,
                0.9999921107364749,
                0.9999869928668906,
                0.9999898700078147,
                0.9999910603047633
            ],
            [
                0.9999687980774978,
                0.9999687980737751,
                0.9999967112513296,
                0.999991060304763,
                0.9999599362982922,
                0.9999724643023616,
                0.9999646437577571,
                0.9999546021314502,
                0.9999785550592614,
                0.9999832985701962
            ],
            [
                0.9999885212277733,
                0.9999869928653397,
                0.9999810748540244,
                0.9999921107383586,
                0.9999930377454114,
                0.9999852610197907,
                0.9999938558239342,
                0.9999938558246667,
                0.999995214905506,
                0.9999921107374168
            ],
            [
                0.999986992869988,
                0.9999885212277724,
                0.9999898700066077,
                0.999954602120621,
                0.9999938558239347,
                0.9999921107383567,
                0.9999339478791403,
                0.9999599363126687,
                0.9999938558224694,
                0.9999251537461021
            ],
            [
                0.99999385582247,
                0.9999869928684402,
                0.9999785550567105,
                0.9999921107402373,
                0.9999832985702006,
                0.9998204720133199,
                0.9999852610180346,
                0.9999852610197949,
                0.9999945777803851,
                0.9999930377412621
            ],
            [
                0.9999724643089539,
                0.9999921107402371,
                0.9999921107374157,
                0.9999852610110074,
                0.9999869928746405,
                0.9999898700126454,
                0.9999898700078157,
                0.999981074854034,
                0.9999810748472588,
                0.9999910603005008
            ],
            [
                0.999876605381425,
                0.9992903294705818,
                0.9999852610127625,
                0.9999852610180346,
                0.9999885212359819,
                0.9999832985781612,
                0.9999869928715396,
                0.9999810748517658,
                0.9999962733611609,
                0.999991060305829
            ],
            [
                0.9999885212346133,
                0.9999832985841328,
                0.9999852610233041,
                0.9999417087345216,
                0.9999687980960814,
                0.9999945777816772,
                0.9999724642957877,
                0.9999546021151996,
                0.9999869928668873,
                0.9999852610110046
            ],
            [
                0.9999810748585377,
                0.9995121429057144,
                0.9999151889490482,
                0.9999599362887689,
                0.9999687980737836,
                0.99998329857418,
                0.9999785550413696,
                0.9999546021313904,
                0.9998601778762881,
                0.9999832985721885
            ],
            [
                0.9999724643122055,
                0.9998204720146938,
                0.9999810748427448,
                0.9998766054403214,
                0.999975699756396,
                0.9999546021369192,
                0.9999687980774944,
                0.9999810748450044,
                0.9999687980886588,
                0.9999687980849346
            ],
            [
                0.999985261014518,
                0.9999832985841333,
                0.9999339478318973,
                0.9999898700041918,
                0.999994577779738,
                0.9999952149055062,
                0.9999546021205704,
                0.9999898700053996,
                0.9999869928668877,
                0.9999921107402366
            ],
            [
                0.9999546021151535,
                0.9999646437577469,
                0.9999898700066073,
                0.999985261012762,
                0.9999921107392968,
                0.9999810748449987,
                0.9999852610215463,
                0.9999785550464837,
                0.9999852610145195,
                0.999989870004192
            ],
            [
                0.9999910603068956,
                0.9999724643187587,
                0.9999832985761703,
                0.9999898700114389,
                0.9999756997592832,
                0.9999810748585329,
                0.9999869928699883,
                0.9999756997476916,
                0.9999885212264035,
                0.9999756997534849
            ],
            [
                0.9998415637839242,
                0.999841563802746,
                0.9999546021206008,
                0.9995694430211463,
                0.9997694933412681,
                0.9999151889285349,
                0.9999756997505854,
                0.9990889489360406,
                0.999290329642137,
                0.9998766054550653
            ],
            [
                0.9999687980923798,
                0.999988521229141,
                0.999995777166556,
                0.9999724643023485,
                0.9999785550567132,
                0.9999810748585355,
                0.9999921107364755,
                0.9999785550464846,
                0.999988521226404,
                0.9999885212264044
            ],
            [
                0.999994577781677,
                0.9999724642957877,
                0.9999910603015666,
                0.9999945777797383,
                0.9999938558261313,
                0.9999832985721908,
                0.9999910603015675,
                0.9999869928746422,
                0.9999869928761919,
                0.9999898700041926
            ],
            [
                0.9999724642957851,
                0.9999546021206279,
                0.9999646437366768,
                0.999985261016281,
                0.9999852610233055,
                0.9999885212277724,
                0.9999756997505957,
                0.9999869928746418,
                0.9999417087414969,
                0.9999930377404328
            ],
            [
                0.9999646437366768,
                0.9999599363222226,
                0.9997388096327985,
                0.9999756997505957,
                0.9999885212318773,
                0.9999724642957917,
                0.9996646499348546,
                0.999972464302351,
                0.9999599363030631,
                0.9999687980775102
            ],
            [
                0.9999724643023497,
                0.9999485577803603,
                0.999447221336578,
                0.9999885212359844,
                0.9999832985801561,
                0.9999832985781624,
                0.9996200154738727,
                0.9999785550515979,
                0.9999724642957877,
                0.9999832985701989
            ],
            [
                0.9999546021205622,
                0.999964643736683,
                0.9998766054253442,
                0.9999646437619519,
                0.9999485578047775,
                0.9991959140681588,
                0.9999599362982898,
                0.9999687980998067,
                0.9999546021422125,
                0.9999485578048176
            ],
            [
                0.999972464315495,
                0.9999910602994365,
                0.9999724643187757,
                0.9999785550515996,
                0.999981074842744,
                0.9999852610197926,
                0.999993037742093,
                0.9999957771655493,
                0.9999832985781673,
                0.9999852610180373
            ],
            [
                0.9999910603026321,
                0.9999810748540204,
                0.9999646437619653,
                0.9999885212264031,
                0.999988521234613,
                0.9999898700054003,
                0.9999910603036979,
                0.9999852610127665,
                0.9999785550592636,
                0.9999756997564309
            ],
            [
                0.9999910603047633,
                0.9999724643023485,
                0.9999599363174135,
                0.9999910603036976,
                0.9999339478398923,
                0.999981074842744,
                0.9999921107345944,
                0.9999785550516178,
                0.9999852610197907,
                0.9999832985702026
            ],
            [
                0.9999785550413729,
                0.9999646437451019,
                0.9999251537817928,
                0.9998766053962423,
                0.9999339478397001,
                0.9999646437535324,
                0.9997040429754207,
                0.9999898700090235,
                0.9999485577618493,
                0.9999832985761709
            ],
            [
                0.9999910603058298,
                0.9999938558232019,
                0.9999898700054003,
                0.9999910603015668,
                0.9999930377412614,
                0.999993855823202,
                0.9999885212332469,
                0.9999930377437519,
                0.9999910603068951,
                0.9999910603036983
            ],
            [
                0.9999869928746395,
                0.9999832985841344,
                0.9999646437451117,
                0.9999852610162758,
                0.9999832985741811,
                0.99998987001023,
                0.9997388095693566,
                0.9999785550464837,
                0.9999810748540223,
                0.9999646437619757
            ],
            [
                0.9999151889689492,
                0.9999646437324605,
                0.9999251537461169,
                0.9999687980886489,
                0.9999810748427421,
                0.9999724642990675,
                0.9999869928715388,
                0.999925153773004,
                0.9999599363221718,
                0.9999756997621788
            ],
            [
                0.999972464302351,
                0.9999151889486779,
                0.999988521231879,
                0.9999546021368159,
                0.9999724643154935,
                0.9999646437408855,
                0.9999898700041923,
                0.9999885212277724,
                0.99997569976797,
                0.9999546021476413
            ],
            [
                0.9999852610197949,
                0.999983298578164,
                0.9999852610180362,
                0.9999810748540244,
                0.9999910603015668,
                0.9999810748450007,
                0.9999869928730909,
                0.9999852610197916,
                0.9999785550516025,
                0.9999869928761923
            ],
            [
                0.9999687980886555,
                0.9999599363078527,
                0.9999869928668885,
                0.9999832985702019,
                0.9999930377420928,
                0.9999599363221864,
                0.9999832985821441,
                0.999975699767971,
                0.9999785550464929,
                0.9999810748427433
            ],
            [
                0.9999910603068967,
                0.9999910603068951,
                0.9999546021476632,
                0.9999785550413824,
                0.9999756997650845,
                0.999991060301568,
                0.9999952149072174,
                0.9999756997506027,
                0.9999785550516044,
                0.9999599363126486
            ],
            [
                0.9999945777797382,
                0.9999938558239344,
                0.999995214906647,
                0.999996711251327,
                0.9999930377454121,
                0.9999938558275966,
                0.9999952149060768,
                0.9999921107392967,
                0.999986992868439,
                0.999991060304764
            ],
            [
                0.9999898700126456,
                0.9999251537996787,
                0.9999930377437515,
                0.9999785550567233,
                0.9999832985741818,
                0.9999885212359819,
                0.9999938558246666,
                0.9999810748585347,
                0.9999756997650704,
                0.99997855504393
            ],
            [
                0.9997040427645733,
                0.9999546021314231,
                0.9999852610145203,
                0.9999921107383567,
                0.9999724643089305,
                0.9999724643122003,
                0.9999898700078149,
                0.9999921107336545,
                0.9999910603005011,
                0.9999898700090224
            ],
            [
                0.9999832985801618,
                0.9999546021259903,
                0.9999885212346142,
                0.9999852610127639,
                0.9999810748585377,
                0.9999898700114384,
                0.9999938558246667,
                0.9999921107374166,
                0.999991060301566,
                0.9999832985841378
            ],
            [
                0.9999852610197931,
                0.9999921107345953,
                0.9999756997563877,
                0.9999852610162773,
                0.9999756997650755,
                0.9999869928668889,
                0.9999832985721947,
                0.999989870007816,
                0.9999898700126474,
                0.999985261021549
            ],
            [
                0.9999832985741842,
                0.9999930377445821,
                0.9999945777790926,
                0.9999832985841398,
                0.9999785550516034,
                0.9999810748517677,
                0.999981074842751,
                0.9999938558239345,
                0.9999785550464919,
                0.9999885212291427
            ],
            [
                0.9999485577986458,
                0.9999869928699887,
                0.9998911030521977,
                0.9999646437577411,
                0.9999339478239136,
                0.9999417087137148,
                0.9999485577618493,
                0.9999785550439337,
                0.9991959140930853,
                0.9999724643056453
            ],
            [
                0.9999546021097568,
                0.9999599362887661,
                0.9999832985701994,
                0.9999832985761725,
                0.9999546021368043,
                0.9999485577618628,
                0.9999810748517715,
                0.9998601778768312,
                0.9999832985841349,
                0.9999885212318776
            ],
            [
                0.9999952149037947,
                0.9999945777823238,
                0.9999945777790924,
                0.9999921107345953,
                0.9999921107402377,
                0.9999945777823238,
                0.9996646497352325,
                0.9999869928730897,
                0.9999921107364755,
                0.9999910603015666
            ]
        ]
    },
    {
        "q_id": "7727_mmlu_math",
        "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,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9993736658710018,
                0.9964063970050677,
                0.9980732655305432,
                0.0015011824846317468,
                0.01098694011072217,
                0.025957355408212594,
                0.000626334114533626,
                0.004070137932969145,
                0.008577485619629007,
                0.06008664680776122
            ],
            [
                0.0003799845017293072,
                0.0010322312152594715,
                0.0015011820658358986,
                0.9947798743668946,
                0.9995694428276404,
                0.9999945777797379,
                0.008577485160275657,
                0.0007096702937567444,
                0.017986213877115107,
                0.9669140206578809
            ],
            [
                0.00015843619516548517,
                0.0011695103582084537,
                0.0007096703368106724,
                0.0052201262980887606,
                0.0031726833984326093,
                0.0035936022937956605,
                0.00013982203493503233,
                0.0008040859403526346,
                0.008577483758456102,
                0.0002959570181297495
            ],
            [
                0.9997388096740418,
                0.0005527785098667031,
                0.010986943349110722,
                0.0011695100420324506,
                0.998967768885337,
                0.16451646699291614,
                0.999373665785344,
                0.007577243032713869,
                0.06008665648572012,
                0.9996646500279237
            ],
            [
                0.04742587334586296,
                0.0004305571828560466,
                0.015906393227962633,
                0.0008040858926042158,
                0.022977367275662786,
                0.000911051091403943,
                0.0031726824404358575,
                0.9959298630013886,
                0.0010322312802030008,
                0.01098694284311245
            ],
            [
                0.006692849373317978,
                0.002472623541401698,
                0.0013250227222292709,
                0.9902915246646304,
                0.0010322312409487783,
                0.9924227591243288,
                0.9999724643123725,
                0.9996200155342209,
                0.06754668785475053,
                0.007577242773588594
            ],
            [
                0.005911067581134942,
                0.0028009266335093834,
                0.0040701374308698334,
                0.003172683413896049,
                0.9968273172937403,
                0.003172683041300812,
                0.0005527786870260234,
                0.0004305571805263095,
                0.9994472213359349,
                0.002182716460050907
            ],
            [
                0.0008040859007415563,
                0.00522012626665318,
                0.002472622999282348,
                0.0028009274399000378,
                0.005911067701531476,
                0.0019267342303643624,
                0.02297737062088548,
                0.9947798733416111,
                0.047425870316531935,
                0.007577241407928499
            ],
            [
                0.9989677690257879,
                0.9997965731059869,
                0.0010322308709748039,
                0.05340332433858241,
                0.015906389670846583,
                0.9988304896742931,
                0.02033235107944095,
                0.999841563843262,
                0.999195914149766,
                0.0017007221333369478
            ],
            [
                0.9998415637489476,
                0.0013250222474517,
                0.00591106975374547,
                0.9998415637694869,
                0.9998415637659276,
                0.9999785550592828,
                0.001501182341892149,
                0.00020342697116514156,
                0.003172683462495431,
                0.014063629574305644
            ],
            [
                0.9993736657114547,
                0.0015011824437991465,
                0.002800926455323093,
                0.0035936030574594134,
                0.999512142876423,
                0.004070137508261077,
                0.014063626772060482,
                0.9999724642957902,
                0.029312229108421867,
                0.004070138121728302
            ],
            [
                0.0015011824516515697,
                0.0003353502752169155,
                0.00048785721485727256,
                0.00026119033422662957,
                0.042087731970752044,
                0.000552778694229453,
                0.0004305571227338044,
                0.0008040858900320679,
                0.001501182004063521,
                0.00013982208658830315
            ],
            [
                6.144175334015912e-06,
                1.1478772227651366e-05,
                1.3007128457485415e-05,
                4.222834954561012e-06,
                1.473897844934719e-05,
                2.561282210618905e-06,
                1.4738983720715225e-05,
                2.902310947190096e-06,
                7.8892654060075e-06,
                1.8925157254522964e-05
            ],
            [
                0.9998204719950202,
                0.0013250227074406093,
                0.06008664680776121,
                0.007577241800118039,
                0.001926734588555142,
                0.01798620588257211,
                0.0003799845287472449,
                0.0002959572380702987,
                0.9998204720571469,
                0.00029595698424572745
            ],
            [
                0.004609571322595734,
                0.001700722321700637,
                0.004609571510616932,
                0.9999810748562847,
                0.002182716740981009,
                0.0003353500950594145,
                0.0031726827533863403,
                0.9992903294673208,
                0.9998766053815183,
                0.9989677687966247
            ],
            [
                0.0002611904280063734,
                0.0002305067945771944,
                0.9997388097933412,
                0.020332352823231696,
                0.989013057602166,
                0.005911068872661508,
                0.001169510055495427,
                0.0013250225758831486,
                0.002800926684884265,
                0.0008040860979551732
            ],
            [
                0.0008040859521377491,
                0.0015011821120779342,
                0.99998107484732,
                0.9964063973035301,
                0.999796573027139,
                0.002800926383788454,
                0.0006263342999493798,
                0.04208773257151254,
                0.005911067999786532,
                0.029312233242257107
            ],
            [
                0.9859363718461873,
                0.0001584362535028076,
                0.0004878570265349518,
                0.0006263340112415175,
                0.001169510157895647,
                0.025957357009419556,
                0.0028009276076813483,
                0.0008040857748933853,
                0.0031726824080362797,
                0.0011695103224431639
            ],
            [
                0.04208773091942118,
                0.00591106781098287,
                0.0011695104907984157,
                0.0013250221970778405,
                0.9991959142215057,
                0.004070137966945793,
                0.0019267343973708051,
                0.0004305571095069122,
                0.005220126157837709,
                0.00023050662734952265
            ],
            [
                1.0129989768322136e-05,
                6.144177529531776e-06,
                7.8892625810789e-06,
                3.726640172337686e-06,
                9.422447062240614e-07,
                1.6701423825538316e-05,
                1.760343632774555e-06,
                2.5612831265630198e-06,
                2.561282821209454e-06,
                8.939695235959266e-06
            ],
            [
                0.0007096705247536888,
                0.99896776886625,
                0.0003799844739706997,
                0.0008040859902523073,
                0.9982992773644257,
                0.00026119033342866593,
                0.0013250223103034907,
                0.015906391128680936,
                0.00029595701110322767,
                0.0031726832894521805
            ],
            [
                0.00757723977614009,
                0.9997040429110108,
                0.0013250222774911584,
                0.014063630039194296,
                0.2689414096510108,
                0.9984988175588183,
                0.9997694932912131,
                0.025957359693796152,
                9.610243662279739e-05,
                0.0005527785928669148
            ],
            [
                0.025957358799003925,
                0.00026119032917285993,
                0.006692850311327844,
                0.9997388096444563,
                0.000552778575244242,
                0.01798620841582198,
                0.007577242661534422,
                0.001032230909148621,
                0.0600866484908844,
                0.9999485577742193
            ],
            [
                0.006692851704412043,
                0.0009110510718006624,
                0.00043055707438550733,
                0.010986941740036293,
                0.001501181985915704,
                0.00037998446487259825,
                0.0011695103141477928,
                0.004609572275521429,
                0.0019267346422837646,
                0.0024726235798783933
            ],
            [
                0.01798621351522214,
                0.9999251537550597,
                0.9999980052709929,
                0.6224593312018545,
                0.24508501864634824,
                0.03732688747799252,
                0.2018132246607271,
                0.5312093733737563,
                0.9997040429344154,
                0.2018132270610754
            ],
            [
                0.014063626655838345,
                0.00013982212247299513,
                0.0031726831974079025,
                0.03732689082456911,
                0.0011695105175883896,
                0.0028009271758721046,
                0.9978172836667226,
                0.0003799845193064432,
                0.9953904274766324,
                0.029312229691398597
            ],
            [
                0.00757724047647842,
                0.0008040860100344653,
                0.9999546021208411,
                NaN,
                0.9997040430175884,
                0.9999485577748491,
                0.9999921107364751,
                0.9999339478242443,
                0.012431649423942781,
                0.009708474511607036
            ],
            [
                0.008577486791772148,
                0.04742587418734383,
                0.0085774839564532,
                0.9996200154756637,
                0.022977367317478067,
                0.009708476302395231,
                0.0013250222118664963,
                0.5,
                0.00103223083844303,
                0.9579122735862823
            ],
            [
                5.14422135311195e-05,
                0.003172683340260624,
                0.002800927036054367,
                0.00023050682057385456,
                0.001169510082149401,
                0.004609572867361028,
                0.00043055702448405826,
                0.0006263342905128133,
                0.9999646437409352,
                8.481103079352604e-05
            ],
            [
                0.0035936020011690904,
                0.012431648566397037,
                0.9998415638060425,
                0.002472623096335486,
                0.0059110687851003756,
                0.9999339478559729,
                0.000487857038938394,
                0.999290329743064,
                0.010986941446557333,
                0.03732688948593844
            ],
            [
                0.0011695104897104982,
                0.003593602220430592,
                0.012431651733599612,
                0.05340332622176919,
                0.0006263340519389706,
                0.00017952800674027032,
                0.002472623207171322,
                0.0009110511565716082,
                0.003172683323324476,
                0.0011695100938445121
            ],
            [
                0.00013982210653147538,
                0.00015843627152244483,
                6.605213649769506e-05,
                0.0003353501700981972,
                0.0040701377177837185,
                0.0001584362528158623,
                0.00017952790062228017,
                4.0063701672028456e-05,
                0.0001233946033069254,
                0.00013982212264184994
            ],
            [
                0.9992903294729347,
                0.999569442818146,
                0.9988304894613331,
                0.9971990727220285,
                0.9993736658471007,
                0.9989677691873663,
                0.9998601779265763,
                0.9986749776439441,
                0.9992903296473795,
                0.9980732649055003
            ],
            [
                0.0019267348213791841,
                0.0003353502648845655,
                0.0003353502226477955,
                0.9525741288419872,
                0.9999756997593366,
                0.0008040860996387612,
                0.0013250221599521532,
                0.00013982207186335536,
                0.0015011819463046049,
                0.002472622679983295
            ],
            [
                0.9993736657746323,
                0.987568347488892,
                0.26894142136999516,
                0.20181322226037882,
                0.004070137629066923,
                0.9989677690461952,
                0.9990889486876617,
                0.9982992774529744,
                0.999891103104416,
                0.0035936021312253405
            ],
            [
                0.9999921107355381,
                0.0015011819164654073,
                0.9994472214850845,
                0.00026119021127946046,
                0.9999987901338842,
                0.07585818054355695,
                0.01798620765913692,
                0.0003799845114133141,
                0.009708474735455542,
                0.0004878570859125317
            ],
            [
                0.00015843627123890696,
                0.0013250224504876421,
                0.0006263342954679216,
                0.004609572666520145,
                0.0003799844659780784,
                0.0010322311110617286,
                0.0002611903960194213,
                0.0001584361954651592,
                0.0003353501442917228,
                0.0007096705432466567
            ],
            [
                0.012431653220012646,
                0.9998601779266962,
                0.020332352229600788,
                0.22270014914315836,
                0.9994472213526572,
                0.014063626281344797,
                0.0021827164331749242,
                0.01098694493794545,
                0.9999952149072209,
                0.9999989322967482
            ],
            [
                0.6791786861878392,
                0.9999852610216089,
                8.481108163797566e-05,
                0.9978172830536458,
                0.042087731670371796,
                0.0005527786047975934,
                0.9997694932588178,
                0.00017952798491956246,
                0.006692850202976862,
                0.9998601779892783
            ],
            [
                0.9990889489273516,
                0.9999869928653365,
                0.014063626475048356,
                0.014063625054555655,
                0.999996273359828,
                0.0007096703502676052,
                0.9978172839689506,
                0.0017007223386988305,
                0.00460957113243794,
                0.9999599363128127
            ],
            [
                0.0124316494811125,
                0.9993736658766128,
                0.002182716381451336,
                0.9989677691096982,
                0.99994170872073,
                0.999996273360272,
                0.9975273764419442,
                0.9840936060722767,
                0.0007096702615178987,
                0.00669284989340264
            ],
            [
                0.9991959141879274,
                0.042087727615238615,
                0.1824255149165352,
                0.9999251537830566,
                0.9999546021098393,
                0.03308597672022804,
                0.9999724643059528,
                0.02931223122833731,
                0.0015011823411941556,
                0.05340333356619821
            ],
            [
                0.0031726833314243722,
                0.005911069923395192,
                0.0003799844737164393,
                0.9968273167252749,
                0.022977367693815594,
                0.009708474198219135,
                0.9999599362982967,
                0.9993736658323082,
                0.9875683490096068,
                0.0004878570281244089
            ],
            [
                0.9999151889689967,
                0.999959936298358,
                0.999841563718095,
                0.9997965730287874,
                0.99994170872537,
                0.9998415638057935,
                0.5,
                0.1645164608483867,
                0.0005527786558326011,
                0.8807970748488297
            ],
            [
                0.0017007223060860176,
                0.00522012586040877,
                0.9994472214648249,
                0.9998766053845543,
                0.0007096704919782062,
                0.004609571989216378,
                0.0031726831870989435,
                0.9980732653501047,
                0.007577239797150239,
                0.0013250223409591443
            ],
            [
                0.002472623675208717,
                0.9953904276347412,
                0.02297737016091733,
                0.0005527787294104906,
                0.03732688814730781,
                0.5621765008857982,
                0.005911068347294736,
                0.0011695100584871994,
                0.002800926661472927,
                0.0010322308390432473
            ],
            [
                0.015906392586515418,
                0.0017007228023937985,
                0.025957356067533095,
                0.02033235204409113,
                0.0011695101149229107,
                0.9986749777556292,
                0.003593603357589317,
                0.9992903294896939,
                0.005911068057248517,
                0.007577242591500567
            ],
            [
                0.007577240679576548,
                0.0017007220548685544,
                0.0028009275660611775,
                0.0028009267388604078,
                9.610244785706252e-05,
                5.829129319244845e-05,
                0.001032231119464772,
                0.00015843623344538856,
                0.0007096704449614905,
                0.001325022271637315
            ],
            [
                0.0002959570604352696,
                0.0002034269000980419,
                0.00020342689927525958,
                0.00857748552459038,
                0.0006263341150072759,
                0.008577484138610534,
                0.00023050668169699354,
                0.9859363732795938,
                0.00017952796550451544,
                0.005220125688722155
            ],
            [
                0.9999687980923594,
                0.0017007221742511994,
                0.06754669020109236,
                0.005220125350185182,
                0.0021827163358128774,
                0.9964063976770251,
                0.017986208679016794,
                0.02931223276527609,
                0.017986210159487682,
                0.01406362657835692
            ],
            [
                0.9999151889594982,
                0.9996200154692628,
                0.10669060317692272,
                0.003172683122299773,
                0.008577484003972504,
                0.047425872167789755,
                0.009708474816041004,
                0.002800927475017056,
                0.46879062662624377,
                0.042087731520181665
            ],
            [
                0.0011695102877657927,
                0.004609572019128846,
                0.003172683230543842,
                0.03732688734412946,
                0.0031726824639991867,
                0.0013250226385809064,
                0.0003353501799036824,
                0.010986942853232413,
                0.00043055718010044354,
                0.9996646499777353
            ],
            [
                0.017986209633098018,
                0.9997694932886041,
                0.9988304894738442,
                0.5926665999540698,
                0.9982992772181621,
                0.00103223119593247,
                0.0002611904208854954,
                0.00020342689593085643,
                0.9998204720142002,
                0.0003799844597210609
            ],
            [
                0.0019267343700587584,
                0.9924227591523422,
                0.0006263340606468414,
                0.9706877664927535,
                0.022977370746331337,
                0.01590639541471469,
                0.02595735418376027,
                0.00043055707754192446,
                0.0001584361566135793,
                0.0011695103505930306
            ],
            [
                0.008577487354084116,
                0.993307148391556,
                0.9999599363031332,
                0.037326886273225016,
                0.9999687980890305,
                0.9975273772631631,
                0.7772998508568416,
                0.0017007225620472007,
                0.0008040860226146086,
                0.8519527982093666
            ],
            [
                0.009708474789179185,
                0.005220126182018925,
                0.001169510355896629,
                0.002182716127904353,
                0.0019267344206532059,
                0.004070138372777992,
                0.0013250226481319163,
                0.0002034269455523334,
                0.009708478478203327,
                0.0002959570154000835
            ],
            [
                0.9978172837919749,
                0.004070138455832028,
                0.0015011825415181918,
                0.002472622946448689,
                0.9988304899047956,
                0.9999852610162996,
                0.9991959141417223,
                0.005911068267942467,
                0.01590639159518795,
                0.9991959139514301
            ],
            [
                0.07585818002124356,
                0.9986749774016258,
                0.9998415637306582,
                0.0021827164052847545,
                0.05340332753999997,
                0.00020342701545926595,
                0.9984988175036769,
                0.1645164608483867,
                0.0124316494811125,
                0.9999810748540204
            ],
            [
                0.000335350143013595,
                0.0005527787173833349,
                0.002800927090030516,
                0.00033534998138413013,
                0.0008040858152527186,
                0.00017952802829978003,
                0.0007096704062831235,
                0.000911051395625718,
                0.0003799844445759838,
                0.003593602651450389
            ],
            [
                0.008577484859320028,
                0.0011695103734393,
                0.002472623560352906,
                0.0008040860768635557,
                0.001926734983460553,
                0.00150118227505931,
                0.0005527787263233062,
                0.000911051269846797,
                0.0017007222181302532,
                0.006692849416658365
            ],
            [
                0.00017952800665668606,
                0.0002034270197448399,
                0.0019267345697501243,
                0.00012339458821653693,
                0.001169510448641606,
                0.0035936025414027768,
                0.000179528027260201,
                0.0002034269468723371,
                0.0024726229005063776,
                0.9989677688148715
            ],
            [
                0.0011695102953812153,
                0.0066928506085191155,
                0.005220126288416274,
                0.005911069876878333,
                0.9998415637101006,
                0.0006263341086312195,
                0.004070137119417284,
                0.0006263342053651134,
                0.006692850555891493,
                0.0007096702390621608
            ],
            [
                0.0013250222343575773,
                3.288747888089911e-06,
                3.5356250660713247e-05,
                0.0004305570647408995,
                0.0003799845977071126,
                0.00020342697080406427,
                5.14422319797437e-05,
                0.00020342694839951624,
                0.0003353499768179965,
                0.00033534997493495414
            ],
            [
                2.260323758746637e-06,
                1.5534981249291695e-06,
                3.288749065167371e-06,
                1.760342793266906e-06,
                3.7266383950256237e-06,
                3.2887490648622804e-06,
                1.5534971989258068e-06,
                1.3709567165461505e-06,
                7.338207180801359e-07,
                3.726638839395927e-06
            ],
            [
                0.0002959569892228466,
                0.029312227783474795,
                0.0008040858239512541,
                0.0010322311878895563,
                0.9995694428763895,
                0.002182716047276418,
                0.00023050665303093117,
                0.004070138180243641,
                0.0015011825087125118,
                0.0001584362144921557
            ],
            [
                0.001169510383774517,
                0.005220126281161909,
                0.003172683380760108,
                0.00015843615925532046,
                0.0015011820129629309,
                0.003172683106836335,
                0.0028009274359981472,
                0.005911067627651785,
                0.006692849484764688,
                0.001032230951523961
            ],
            [
                1.3007128458384476e-05,
                3.120190763491069e-05,
                3.120190017071685e-05,
                6.605216000288915e-05,
                2.1444940739364273e-05,
                1.67014198374782e-05,
                0.9997694931753952,
                2.1444940739364273e-05,
                5.144219505443152e-05,
                0.9984988180456685
            ],
            [
                0.9999991684715759,
                0.9465966737782308,
                0.029312228631440916,
                0.0008040859988573121,
                0.9924227588511967,
                0.9999885212264031,
                0.015906393752783098,
                0.9964063966315726,
                0.9999990577557432,
                0.00857748476428141
            ],
            [
                0.20181322226037884,
                0.1192029110704336,
                0.0011695102770226072,
                0.20181322946142377,
                0.0009110512489719482,
                0.22270013366638425,
                0.0005527786321641911,
                0.0019267345831822799,
                0.0003799845415265975,
                0.0019267345102009033
            ],
            [
                0.0259573576687401,
                0.04742587654349034,
                0.0028009276037794574,
                0.020332352266702717,
                0.08509904442693891,
                0.9995121427994479,
                0.0028009267876340314,
                0.9980732650093757,
                0.999989870007817,
                0.9995121428580591
            ],
            [
                0.9999485577825226,
                0.999796572955625,
                0.010986940707799988,
                0.0009110512543760968,
                0.0008040859770642024,
                0.004070138006585215,
                0.0005527785473952747,
                0.9980732654257725,
                0.0009110512746151635,
                0.014063624111865125
            ],
            [
                0.0330859768394049,
                0.015906391857598158,
                0.9902915232499077,
                0.18242551713899047,
                0.9978172836981624,
                0.00026119042301339917,
                0.5,
                0.6791786926816161,
                0.9984988176237317,
                0.9964063982047533
            ],
            [
                6.962257073360915e-06,
                7.33820718009391e-07,
                6.144176794276899e-06,
                1.0677033791437343e-06,
                1.994730672468935e-06,
                2.902311292960369e-06,
                8.939693104865575e-06,
                2.5612819050161955e-06,
                2.561283431888668e-06,
                1.5534973841592143e-06
            ],
            [
                0.004070137404443556,
                0.08509905370824052,
                0.2689414272294874,
                0.817574478416099,
                0.9999038975406905,
                0.999948557762252,
                0.0002611903661147786,
                0.00010889690780193605,
                0.004070137270424578,
                0.005220126501210978
            ],
            [
                0.9993736659704683,
                0.9988304896745651,
                0.00029595701916306156,
                0.9399133552961427,
                0.9999938558246689,
                0.9999885212318768,
                0.005911069159971482,
                0.010986942134714905,
                0.987568348769494,
                0.9996200155405663
            ],
            [
                2.9023119851055122e-06,
                2.9023133686360798e-06,
                4.785095634756674e-06,
                3.28875024125221e-06,
                2.902313022952668e-06,
                7.88926352407059e-06,
                4.785095635296322e-06,
                5.422217029943586e-06,
                1.0677028698693545e-06,
                3.288749849368453e-06
            ],
            [
                0.0002305066545936808,
                0.01590639249904534,
                0.0002959571618548781,
                0.0028009275530548744,
                0.0004878572184619357,
                0.00015843619497184967,
                0.9706877704675951,
                8.481106025420401e-05,
                0.0003799844589472249,
                0.9968273172760678
            ],
            [
                7.484620876546434e-05,
                0.0009110513202855197,
                7.484625253210063e-05,
                0.0008040857654933555,
                0.0004878572232870752,
                0.0002959572375019766,
                0.03732688319437491,
                0.0013250222774911584,
                0.0001795279219780407,
                0.0001088968823392489
            ],
            [
                0.04208773061904093,
                0.9999417087426156,
                0.022977371958974688,
                0.9999987901347492,
                0.029312229850392255,
                0.01590639480242408,
                0.9999417087346039,
                0.0004878570210570014,
                0.000709670463867246,
                0.002472623640177694
            ],
            [
                0.16451646494473965,
                0.9998911030651462,
                0.9999646437452678,
                0.9947798754743941,
                0.002800927610282609,
                0.005220124963285811,
                0.01243165346012554,
                0.0008040857932725484,
                0.07585817949893017,
                0.20181322226037884
            ],
            [
                7.338207180801359e-07,
                2.9023133690188264e-06,
                1.0129992185981682e-05,
                1.7603425837494853e-06,
                8.939695234983602e-06,
                2.902310946944611e-06,
                2.9023112927307205e-06,
                8.939698431129126e-06,
                6.9622554148849475e-06,
                2.902313023039776e-06
            ],
            [
                0.0015011820250033095,
                0.0007096702487627092,
                0.0015011822942541195,
                0.06754668973182398,
                0.00020342692351478465,
                0.0008040859630343036,
                0.0006263342230359017,
                0.9999485577987454,
                0.001926734513782811,
                0.0024726229975595114
            ],
            [
                0.017986208876412908,
                0.004070137225122389,
                0.006692852385475534,
                0.9997694933432667,
                0.002472622712717189,
                0.014063624486358617,
                0.00037998452425899487,
                0.0015011821914746408,
                0.9999151889703529,
                0.000626334130783462
            ],
            [
                0.005911067876653709,
                0.0019267350600238567,
                0.0006263342940105368,
                0.0010322312158596888,
                0.005220126317433734,
                0.7981867705385762,
                0.0009110513825921811,
                0.0003353501367497932,
                0.012431652865560291,
                0.0017007220807611471
            ],
            [
                0.9992903296053988,
                0.008577483940613431,
                0.006692850828316835,
                0.037326890021390696,
                0.9998601778962292,
                0.0003799845607951203,
                0.9999339478791676,
                0.9940889297728771,
                0.0010322312524729536,
                0.04208773212094217
            ],
            [
                0.0028009275556561348,
                4.53978631524379e-05,
                0.0005527785255277262,
                1.0129993392342568e-05,
                0.00012339460392454514,
                0.00015843627274649856,
                0.0009110510600386944,
                0.0002959570974106263,
                0.00012339455948286233,
                7.48462538460694e-05
            ],
            [
                0.005220125942624898,
                0.005911069376138042,
                0.9947798747828115,
                0.00407013677210053,
                0.012431649332471234,
                0.9999038975649014,
                0.008577487219446038,
                0.999995214904963,
                0.9999485577803114,
                0.07585817897661679
            ],
            [
                0.01243165305993739,
                0.9995121428971995,
                0.0010322310290720375,
                0.020332351821479543,
                0.0006263342758660963,
                0.04208773076923105,
                0.9998415638239077,
                0.014063629793836395,
                0.010986942772272693,
                0.9997965729588214
            ],
            [
                0.0011695101856375406,
                0.9997965729911289,
                0.0008040858316209308,
                0.00023050662926774734,
                0.02297737179171353,
                6.605212857805352e-05,
                0.0021827161659363986,
                0.0021827165969662953,
                0.004070137296850855,
                0.9992903295636658
            ],
            [
                0.025957358045494698,
                0.0001233945441483041,
                0.012431649561150107,
                0.00970847778874968,
                0.0019267344676657464,
                0.0013250222248065704,
                0.0024726234403285897,
                0.9995121427924656,
                0.00043055706529202,
                0.006692849664317724
            ],
            [
                0.09534946232842245,
                0.000430557126942361,
                0.06754669067036073,
                0.00023050676811104136,
                0.9999417087419828,
                0.0031726831267178983,
                0.00017952802761543406,
                0.0028009270971839817,
                0.0002305068231627894,
                0.029312233401250783
            ],
            [
                0.9971990726960158,
                0.6513548714339145,
                0.001169510109891293,
                0.0019267342514080689,
                0.0002034270196442118,
                0.0015011824872492212,
                0.0007096704350132658,
                0.0015011824366447167,
                0.0035936030166084008,
                0.029312231493326745
            ],
            [
                0.004070138323700608,
                0.02931222783647268,
                0.9999038976201079,
                0.9997965730802499,
                0.003593603331744797,
                0.047425868970162655,
                0.0015011823165898986,
                0.02297736857193652,
                0.0066928509242848554,
                0.029312230486366886
            ],
            [
                0.0259573574803628,
                0.996827317756907,
                0.0024726227397082945,
                0.5312093733737563,
                0.0017007222469876497,
                0.9992903296027982,
                0.9998415638229095,
                0.0006263341208003789,
                0.9996200155171081,
                0.0011695104196757984
            ],
            [
                0.020332355309061308,
                0.9971990731726967,
                0.0031726828262853986,
                0.9975273770460857,
                0.003172682587706669,
                0.0010322309797341739,
                0.006692850565178721,
                0.0028009264058991607,
                0.005911068002522817,
                0.0007096703271514017
            ],
            [
                0.00017952792034553686,
                0.0024726235873440213,
                0.07585818419975078,
                0.9993736657255913,
                0.007577239926712827,
                0.015906388008915584,
                0.0007096703198450304,
                0.0017007225316085718,
                0.0005527786403645232,
                0.9626731162701729
            ],
            [
                0.9999417087345632,
                0.995929862957974,
                0.9999646437493,
                0.9997040430124046,
                0.9940889316718592,
                0.03308597910376533,
                0.9989677687302407,
                0.00757724100173221,
                0.22270014914315836,
                0.9989677689400769
            ],
            [
                0.017986211475461908,
                0.999820472082162,
                0.022977369951840902,
                0.9997388097882266,
                0.005911068454009857,
                0.029312230062383794,
                0.020332352415110444,
                0.9999957771660523,
                0.007577241604023266,
                0.005911067652278348
            ],
            [
                6.60521676034419e-05,
                0.007577242080253438,
                0.00020342701558949056,
                8.48110410719979e-05,
                0.00043055713954298034,
                0.00029595707088894474,
                9.610246012330421e-05,
                0.00017952794305431906,
                7.484620004306986e-05,
                6.605215228027477e-05
            ],
            [
                0.000430557134081877,
                0.001169510024353795,
                0.017986214008712555,
                0.0001398221059231913,
                3.5356246473207964e-05,
                0.0008040861227880982,
                5.8291286313118594e-05,
                0.0001233945287221821,
                0.0003799845190521828,
                0.00026119043040786485
            ],
            [
                0.00017952802909383038,
                0.998498817636819,
                0.006692852128528846,
                0.007577241484965728,
                0.002182716022428816,
                0.9996646499852675,
                0.017986209665997375,
                0.008577485809706261,
                0.0021827166507182648,
                0.025957355078552343
            ],
            [
                0.0013250224749813582,
                0.0013250225443031981,
                0.0028009266139999356,
                0.9999982396572065,
                0.0259573580454947,
                0.0015011821291787627,
                0.001501181935136718,
                0.9953904271860541,
                0.0035936031466646872,
                0.007577240588532559
            ],
            [
                0.0028009267804805665,
                0.0009110510349253035,
                0.9990889487470014,
                0.007577242332375305,
                0.00023050670234809687,
                0.0013250224560333891,
                0.003593602341316217,
                0.010986944168827973,
                0.014063627275689756,
                0.007577240448464886
            ],
            [
                0.0010322311710834686,
                0.0011695103879901978,
                0.0011695104324588308,
                0.9986749775422721,
                0.014063625390308462,
                0.00015843627109368027,
                0.0010322308195962091,
                0.0010322308253582944,
                0.9999151889892328,
                0.0017007224361419654
            ],
            [
                0.0021827162470714314,
                0.006692849382605204,
                0.017986206376062318,
                0.002800926503446397,
                0.002182716303865956,
                0.00037998444837883524,
                0.005911067772674882,
                0.00026119030168491437,
                0.0035936029148977183,
                0.004070138008472807
            ],
            [
                0.07585817897661679,
                0.037326889218212304,
                0.0017007224885201234,
                0.9999599363031495,
                0.9998766054754341,
                0.005220126353705557,
                0.7057850340255386,
                0.9998911031382653,
                0.04208772325972563,
                0.4687906266262437
            ],
            [
                0.000626334135920742,
                0.0006263340666221168,
                0.0005527786606563261,
                0.9997965730653213,
                0.9999756997621856,
                0.00033535014565766084,
                0.002472623450091333,
                0.0010322312692790426,
                0.9995694429826805,
                0.001169510024353795
            ],
            [
                0.000487857040840066,
                0.0011695100180982704,
                0.010986940788759695,
                0.0003353499783790678,
                0.001032230883579366,
                0.001325022136382734,
                0.0003353502222575274,
                0.00013982213887429003,
                0.00012339457422852945,
                0.00091105112700774
            ],
            [
                0.0024726234219516617,
                0.0008040861121253733,
                0.9998601779296991,
                0.0024726233099672573,
                3.535625897553077e-05,
                0.020332353416862622,
                0.007577241456952191,
                0.999948557805288,
                0.0004878571942510889,
                0.9992903297179665
            ],
            [
                0.0005527786507194526,
                0.000911051385241274,
                0.0007096705495210567,
                0.004070138404867051,
                0.00591106754556324,
                0.00247262307795856,
                0.0009110513991225205,
                0.9997040429752225,
                0.0001088969475123316,
                0.0024726230762357236
            ],
            [
                0.998674977824643,
                NaN,
                0.005220125023738836,
                0.0002034269685843269,
                0.000552778764141316,
                0.00591107020796893,
                0.008577486894730675,
                0.9324533149608596,
                0.0010322311332697722,
                0.0019267343033457284
            ],
            [
                0.9999485578059086,
                0.010986943652709694,
                0.0017007221453938044,
                0.0004878570291462027,
                0.004609571264907414,
                0.012431650315790417,
                0.005220124716637477,
                0.0008040859755209134,
                0.99752737691515,
                0.0003353501851137611
            ],
            [
                0.00015843623483772053,
                0.0003353501702543044,
                0.00043055708446850666,
                0.1329642436335826,
                8.4811030771313e-05,
                0.00037998443303477214,
                9.610242567519328e-05,
                5.829125848409385e-05,
                0.0010322310141866477,
                0.0024726228011561326
            ],
            [
                0.001169510062702879,
                0.0006263342779064352,
                0.00020342706914141357,
                0.0008040860140096035,
                0.0003799844789232508,
                0.00015843615799899502,
                5.144223811144626e-05,
                0.9975273768123541,
                0.003593602032015765,
                0.0003353500554081909
            ],
            [
                0.07585818211049714,
                0.0015011820380906775,
                0.5312093733737563,
                0.00317268325631624,
                0.9995121428711153,
                0.9999546021314201,
                0.010986940242281685,
                0.010986941618596723,
                0.00407013784991512,
                0.5
            ],
            [
                0.0001233945451214138,
                0.00012339453028597998,
                0.9465966700118571,
                0.000430556982198096,
                0.9984988177495449,
                0.0003799845740166661,
                0.0004305570310348757,
                0.0004878571157716235,
                0.0004305570316235725,
                0.00015843615952272183
            ],
            [
                0.0028009275784171652,
                0.0015011823644024268,
                0.9990889487231597,
                0.9996200154405204,
                0.007577242290354993,
                0.004070136832503441,
                0.9998415637373387,
                0.0021827168657261565,
                0.13296423847995262,
                0.02595735536111827
            ],
            [
                0.00218271593064482,
                0.06754669113962909,
                0.004070138019798356,
                0.025957358563532287,
                0.0035936031950189497,
                0.008577486490816463,
                0.9626731168056252,
                0.0008040858769842634,
                0.001169510331282494,
                0.0013250224777542317
            ],
            [
                0.0011695099952520082,
                0.0019267348957037883,
                0.9933071502737674,
                0.00048785704470017625,
                4.53978848619353e-05,
                0.020332351302052524,
                0.001032231015267039,
                0.0031726834308321975,
                0.9998601779445542,
                0.001032231251872736
            ],
            [
                0.00043055701997489146,
                0.9999910603037067,
                0.002800926733007573,
                0.9999957771670591,
                0.9996200155240504,
                0.003593603173342901,
                0.9989677690790871,
                0.9999785550541559,
                0.0009110512687871599,
                0.006692851190518726
            ],
            [
                0.009708474198219135,
                0.9986749775313346,
                0.012431652796956613,
                0.9999898700090235,
                0.9971990732910541,
                0.022977369491872766,
                0.004070138567199943,
                0.0046095711388477525,
                0.012431649778395039,
                0.9999967112517194
            ],
            [
                0.9999687980739241,
                0.9971990724788106,
                0.0005527785967902106,
                0.0010322312152594715,
                0.00037998456192271033,
                0.004070136941983721,
                0.0028009271114909132,
                0.9997388097644776,
                0.022977367317478067,
                0.9993736658988743
            ],
            [
                0.0002611902391777777,
                0.9770226320552927,
                0.00026119024155646847,
                0.003172683069282271,
                0.0015011826046865781,
                0.0021827164666431294,
                0.0006263340387860781,
                0.0017007225215282466,
                0.0004878571017503387,
                0.0005527786047975934
            ],
            [
                0.004070136840053806,
                0.9996646500293287,
                0.003593602771502334,
                0.012431647994699905,
                0.16451645470385742,
                0.00170072203589383,
                0.03308597612434375,
                0.9998911030837369,
                0.020332352266702717,
                0.008577486863051128
            ],
            [
                0.0013250223435779694,
                0.00033535005854984763,
                0.03732688787958169,
                0.0002611902941916568,
                0.00029595720252434025,
                0.0006263341124204187,
                0.0009110513024836172,
                0.001169510192301035,
                0.0007096703773053089,
                0.0007096704034761556
            ],
            [
                0.9999038975742227,
                0.998299277335173,
                0.0028009263337142078,
                0.9994472213539756,
                0.00033534998500386437,
                0.003593602030348377,
                0.9998766054255219,
                0.9999869928653345,
                0.0031726821746120596,
                0.00026119020245626677
            ],
            [
                0.9999339478242443,
                0.003593601852771579,
                0.0017007223464073136,
                0.008577486807611922,
                0.0031726822460383963,
                0.9999151889300659,
                0.006692851370071809,
                0.005911070145034352,
                0.008577486633374418,
                0.9940889309959968
            ]
        ]
    },
    {
        "q_id": "8160_mmlu_math",
        "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,
            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,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            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,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                8.315283250082584e-07,
                1.9947290080343035e-06,
                1.5534979396024226e-06,
                4.450849988780466e-07,
                2.561281599776919e-06,
                4.785096204285318e-06,
                6.475950297906914e-07,
                1.067702742726318e-06,
                2.5612816000145246e-06,
                6.475948753930064e-07
            ],
            [
                0.999995214903795,
                0.9999980052700408,
                0.9999993524050473,
                0.9999993524051246,
                0.9999974387168736,
                0.9999957771655493,
                0.9999869928668889,
                0.9999994956524114,
                0.9999982396563671,
                0.9999994284997573
            ],
            [
                0.9999977396762412,
                0.9999984465018752,
                0.9999989322972572,
                0.9968273177996155,
                0.9999982396572065,
                0.9999986290427932,
                0.9999984465024306,
                0.9999982396561572,
                0.9999945777790926,
                0.9999977396746245
            ],
            [
                0.9999991684719723,
                0.9999990577556308,
                0.999999266179107,
                0.999999266178932,
                0.9999992661791944,
                0.9999996533672962,
                0.9999990577555186,
                0.9999989322971301,
                0.9999991684719723,
                0.9999997617630332
            ],
            [
                0.9999998555020135,
                0.9999992661786695,
                0.999999352405279,
                0.9999980052693274,
                0.9999989322968754,
                0.99999893229713,
                0.9999990577550691,
                0.9999994284994167,
                0.99999862904312,
                0.9999993524049702
            ],
            [
                1.5534981249023245e-06,
                2.9023130217727535e-06,
                1.3709573702111586e-06,
                3.7266383942867467e-06,
                2.753569437266178e-05,
                1.994729245479375e-06,
                1.7603430033399058e-06,
                3.120191130088966e-05,
                5.422217674937953e-06,
                5.422220261849814e-06
            ],
            [
                0.9999957771660719,
                0.9999921107392983,
                0.9914225135963023,
                0.9914225149902022,
                0.999999266178757,
                0.9999970976873269,
                0.9999945777816774,
                0.9933071479612477,
                0.9999485577986746,
                0.9997388095703218
            ],
            [
                0.9999997300420937,
                0.999999855502048,
                0.9999997617629763,
                0.9999994956523514,
                0.9999997617630049,
                0.9999994284994849,
                0.9999996533674202,
                0.9999996940977731,
                0.9999991684715759,
                0.9999992661790195
            ],
            [
                0.9999984465020603,
                0.9999987901343165,
                0.9999984465024306,
                0.9999995549150542,
                0.999998239656367,
                0.9999984465020604,
                0.9999997897565587,
                0.9999982396567868,
                0.9999974387177893,
                0.9999982396561572
            ],
            [
                0.9999952149060856,
                0.9999810748472546,
                0.9999869928653355,
                0.9999962733598278,
                0.9999417087553565,
                0.9959298613950482,
                0.9959298619858644,
                0.999986992866886,
                0.9999967112493665,
                0.9999869928731082
            ],
            [
                0.9999885212346179,
                0.9999938558254082,
                0.9999938558239345,
                0.999996273359386,
                0.9626731118526922,
                0.9999991684720716,
                0.9999921107364778,
                0.999999266178757,
                0.9999967112505443,
                0.9999977396762421
            ],
            [
                1.2098655392354511e-06,
                1.7603425837366772e-06,
                3.2887486728201357e-06,
                2.144495351940237e-05,
                6.962256249429175e-06,
                1.370957370247318e-06,
                1.9947299591100915e-06,
                1.5534979397267575e-06,
                7.338210679168642e-07,
                3.288749849209925e-06
            ],
            [
                0.9999980052709921,
                0.9999996072136592,
                0.9999994956524715,
                0.9999998724808963,
                0.9999996940976636,
                0.9999989322970027,
                0.999999730042126,
                0.9999994956525917,
                0.9999997617629764,
                0.9999977396748938
            ],
            [
                4.4508521110175827e-07,
                5.715007194256945e-07,
                1.6373772528581146e-07,
                5.715002426202836e-07,
                9.422442568763144e-07,
                1.994729245693449e-06,
                9.42244593835151e-07,
                2.6995790618252024e-07,
                1.6373770576683237e-07,
                5.043473480643696e-07
            ],
            [
                7.338212429420757e-07,
                2.9023133687786197e-06,
                9.42244593835151e-07,
                7.338209805133949e-07,
                2.5612825159421147e-06,
                1.3709567164663505e-06,
                6.475945665900901e-07,
                1.5534981248881956e-06,
                2.5612822106841303e-06,
                3.2887486732358968e-06
            ],
            [
                1.5534973839359769e-06,
                2.5612828211442287e-06,
                2.260324028372372e-06,
                1.147877222485351e-05,
                6.962257907880012e-06,
                2.2603251060142746e-06,
                0.9953904287714149,
                2.2603248365960415e-06,
                2.561282210530385e-06,
                6.962258736497698e-06
            ],
            [
                0.9968273175168556,
                0.9999852610197877,
                0.9999810748497618,
                0.9971990728852574,
                0.9986749777148064,
                0.9998601779302646,
                0.9999785550439207,
                0.9964063966140652,
                0.9999546021262408,
                0.9999810748428811
            ],
            [
                0.9999967112501575,
                0.9999992661792824,
                0.987568348346438,
                0.9999945777784492,
                0.9999832985721969,
                0.9999898700054032,
                0.9999962733620525,
                0.9999945777787829,
                0.9999962733607166,
                0.9999921107402375
            ],
            [
                0.9999995549147358,
                0.999999495652652,
                0.9999980052693274,
                0.9999980052705164,
                0.9999869928699877,
                0.9999990577551815,
                0.9999977396765106,
                0.9999810748450036,
                0.9999986290426298,
                0.9999987901337397
            ],
            [
                1.5534981249397663e-06,
                2.902311984873224e-06,
                2.561281599914358e-06,
                8.939700564468113e-06,
                2.26032537546132e-06,
                6.96225956837018e-06,
                4.222834954211514e-06,
                1.3709573702248741e-06,
                6.144174601097106e-06,
                1.1478773592796574e-05
            ],
            [
                8.939696298945184e-06,
                8.315280276456036e-07,
                1.9947301969217434e-06,
                5.715004469827863e-07,
                8.939699497042417e-06,
                3.2887494570719725e-06,
                1.4738988989779516e-05,
                2.9023126764615702e-06,
                5.04347528431602e-07,
                2.561283431916622e-06
            ],
            [
                0.9999980052698031,
                0.9999852610110236,
                0.9998415637272535,
                0.9999921107383588,
                0.9999970976883609,
                0.9999910603005008,
                0.9999967112517412,
                0.9999962733593838,
                0.9999962733616047,
                0.9999938558268642
            ],
            [
                0.9669140198236428,
                0.999983298582142,
                0.9999938558232014,
                0.9953904272010103,
                0.9999930377429238,
                0.9999930377429209,
                0.9999992661791944,
                0.9964063967399529,
                0.9999339478241169,
                0.9933071498403635
            ],
            [
                0.9999995549147358,
                0.9999994956525917,
                0.9999989322970027,
                0.9999991684721707,
                0.999999352404893,
                0.9999994284996893,
                0.9999993524049702,
                0.999999057755743,
                0.9999996072139402,
                0.9999987901337396
            ],
            [
                0.9999974387177895,
                0.9999986290432835,
                0.9999987901346049,
                0.9999982396572065,
                0.9999998724809874,
                0.9999993524049703,
                0.9999970976887071,
                0.999999352405279,
                0.9999993524049703,
                0.9999991684718733
            ],
            [
                0.9999996072136592,
                0.9999994956527722,
                0.999998932296621,
                0.9999991684722697,
                0.999998790134028,
                0.9999997617631752,
                0.9999994956527121,
                0.9999993524050474,
                0.9999998724809723,
                0.9999995549149481
            ],
            [
                0.9999991684720715,
                0.9999952149037944,
                0.9999991684720715,
                0.9999989322973846,
                0.9999989322975118,
                0.9999994956524716,
                0.9999852610197881,
                0.9999996072136592,
                0.9999984465022455,
                0.9999989322966208
            ],
            [
                0.9999991684717741,
                0.9999991684720715,
                0.999999428499553,
                0.999999814460876,
                0.9999993524054335,
                0.9999967112513267,
                0.9999995549150542,
                0.9999994956524716,
                0.9999996940977366,
                0.9999984465018751
            ],
            [
                0.9999989322967487,
                0.9999987901337399,
                0.9999984465024307,
                0.9999992661790195,
                0.9999987901344609,
                0.9999987901347499,
                0.9999990577554064,
                0.9999991684717742,
                0.9999984465022457,
                0.9999992661791947
            ],
            [
                0.9999996072137061,
                0.9999994956526519,
                0.999997097686631,
                0.9999996940978095,
                0.999999789756684,
                0.999999554914895,
                0.9999997617631183,
                0.9999994284994167,
                0.9999997897567091,
                0.9999996940978095
            ],
            [
                1.2098656834723998e-06,
                1.9947301968963442e-06,
                3.9278638753849313e-07,
                1.3709573701637772e-06,
                3.9278615341365085e-07,
                5.043472278159142e-07,
                4.450848927478102e-07,
                9.422447062150634e-07,
                3.059021539864825e-07,
                1.3709567164962755e-06
            ],
            [
                0.9999987901343165,
                0.9999910603068942,
                0.9999987901344607,
                0.9999957771650456,
                0.9999990577552939,
                0.9999991684722698,
                0.9999952149072165,
                0.9999986290423029,
                0.9999994284997573,
                0.9999987901341723
            ],
            [
                0.9999994284996212,
                0.9999994284996891,
                0.9999986290423029,
                0.9999982396569966,
                0.9999996072137998,
                0.9999952149037948,
                0.999998932296621,
                0.999995777168066,
                0.9999962733607163,
                0.9999938558246667
            ],
            [
                0.9999995549148419,
                0.9999996072137061,
                0.9999996533672135,
                0.9999996940976636,
                0.9999993524054334,
                0.9999996072137529,
                0.9999996072137998,
                0.9999995549150542,
                0.9999994284996211,
                0.9999996072137998
            ],
            [
                1.2098659718847284e-06,
                5.043472879481655e-07,
                5.043476486833397e-07,
                8.315277302588544e-07,
                3.927861534179377e-07,
                5.043475885576967e-07,
                3.927862470757885e-07,
                1.7603434229576435e-06,
                1.7603434226854702e-06,
                1.209866260303728e-06
            ],
            [
                0.9999996940976636,
                0.999999789756634,
                0.9999994956525918,
                0.9999997617629763,
                0.999999352405279,
                0.999999814460876,
                0.999999653367379,
                0.9999998362622552,
                0.9999998555019619,
                0.9999996072137998
            ],
            [
                0.9999997897565588,
                0.9999996072137061,
                0.9999994956527121,
                0.9999998555020307,
                0.9999995549149481,
                0.9999993524051246,
                0.9999997617631469,
                0.9999997300422225,
                0.9999994284996893,
                0.9999997300423191
            ],
            [
                0.9999977396757026,
                0.9999970976866317,
                0.9999993524052019,
                0.9999984465026164,
                0.9999990577557432,
                0.999999266179282,
                0.9999974387165689,
                0.9999993524054335,
                0.9999989322970028,
                0.9999984465028029
            ],
            [
                0.9999984465024309,
                0.999986992869987,
                0.9999957771680664,
                0.9999339478713017,
                0.999959936317406,
                0.9999898700114396,
                0.9999151889488606,
                0.9999885212264018,
                0.9999952149072313,
                0.999959936317406
            ],
            [
                0.9999994956527722,
                0.9999990577555185,
                0.999998790133884,
                0.9999997300422547,
                0.999999554914842,
                0.9999990577554063,
                0.9999996533672135,
                0.9999998362623137,
                0.999999814460876,
                0.9999994956527121
            ],
            [
                0.9999990577549568,
                0.999997097686977,
                0.9999970976883609,
                0.9999990577554061,
                0.9999990577552939,
                0.9999970976880149,
                0.9999885212264026,
                0.9999962733593833,
                0.999998446502801,
                0.9999970976873229
            ],
            [
                0.9999996533672962,
                0.9999990577555185,
                0.99999844650169,
                0.9999987901341724,
                0.9999984465015048,
                0.9999984465018752,
                0.9999996533674615,
                0.9999982396569967,
                0.9999987901337397,
                0.9999990577549569
            ],
            [
                7.338208055369664e-07,
                2.2603251053070966e-06,
                1.0677033791204289e-06,
                1.5534975693601474e-06,
                1.3709572067955008e-06,
                1.3709576970213355e-06,
                8.31528424151477e-07,
                7.338208930144969e-07,
                3.927861533861436e-07,
                2.5612828213352452e-06
            ],
            [
                0.9999970976880151,
                0.9999974387168736,
                0.9999977396765106,
                0.9999996072137529,
                0.999999168471675,
                0.9999977396762413,
                0.999999554914895,
                0.999998629042303,
                0.9999984465028011,
                0.999998629042303
            ],
            [
                0.9999986290421394,
                0.9999990577549569,
                0.9999852610197942,
                0.9999945777816768,
                0.9999986290431201,
                0.9999990577555185,
                0.9999970976869769,
                0.9999992661791944,
                0.9999967112493666,
                0.9999930377429209
            ],
            [
                0.9999993524051247,
                0.999999428499553,
                0.9999987901340281,
                0.999999694097846,
                0.9999980052707542,
                0.9999996533673375,
                0.9999994956526519,
                0.999997739675988,
                0.9999962733607164,
                0.9999991684717741
            ],
            [
                0.999998932297512,
                0.9999974387187055,
                0.9999984465026159,
                0.9999980052698032,
                0.9999987901344607,
                0.999998005270992,
                0.9999993524049703,
                0.9999990577549569,
                0.9999984465018751,
                0.999999168471675
            ],
            [
                0.9999994956527722,
                0.9999970976876691,
                0.9984988173946154,
                0.9999957771680663,
                0.9999898700078143,
                0.9999977396762412,
                0.9999945777829702,
                0.9999984465015048,
                0.9999986290426297,
                0.9953904273762119
            ],
            [
                2.9023112930659533e-06,
                1.1478764020560142e-05,
                2.9023109469842055e-06,
                1.1478768124992398e-05,
                2.2603251060985603e-06,
                2.5612812945889277e-06,
                1.553497384196656e-06,
                1.2098653950315304e-06,
                1.9947294834796172e-06,
                2.9023126768680736e-06
            ],
            [
                0.9999998555019618,
                0.9999984465015047,
                0.9999970976883618,
                0.9999997300422225,
                0.9999996072136125,
                0.9999996072138466,
                0.9999994956524716,
                0.9999994284992805,
                0.9999957771665564,
                0.9999986290429567
            ],
            [
                0.9999994956524114,
                0.9999996533673375,
                0.9999989322968755,
                0.9999980052702792,
                0.9999994284994849,
                0.9999996940977366,
                0.999999352405279,
                0.9999990577556308,
                0.999999653367379,
                0.9999987901338838
            ],
            [
                4.450849458125204e-07,
                3.466325797827604e-07,
                1.5534979397394734e-06,
                3.059022633803178e-07,
                2.3823685319076597e-07,
                1.0677026154473471e-06,
                5.043476486833397e-07,
                5.71500515151976e-07,
                8.315279285251204e-07,
                3.927862470816829e-07
            ],
            [
                0.9999962733611605,
                0.9999992661790196,
                0.9999970976866311,
                0.9999945777797385,
                0.9999984465018752,
                0.9999974387184001,
                0.9999869928699907,
                0.9999970976873231,
                0.9999982396565771,
                0.9999986290429567
            ],
            [
                0.9999996533673376,
                0.9999997897565838,
                0.9999970976869775,
                0.9999996533673788,
                0.999999554914895,
                0.9999996940976638,
                0.9999970976866314,
                0.9999996940977001,
                0.9999996940978825,
                0.9999991684719725
            ],
            [
                0.9999995549148419,
                0.9999994284994167,
                0.9999991684717742,
                0.9999997617629763,
                0.9999996940978825,
                0.999999694097846,
                0.9999995549147359,
                0.9999996940977366,
                0.9999962733620488,
                0.9999945777829696
            ],
            [
                0.9999977396754328,
                0.9999992661788445,
                0.9999995549150542,
                0.9999991684718732,
                0.9999997617631469,
                0.9999990577554061,
                0.9999989322968754,
                0.9999991684718733,
                0.9999982396567868,
                0.9999984465028012
            ],
            [
                0.9999992661791944,
                0.9999986290421395,
                0.9999997300421903,
                0.9999990577549569,
                0.9999995549150542,
                0.9999991684720715,
                0.9999996533672135,
                0.9999996940977001,
                0.9999997300420937,
                0.9999995549147358
            ],
            [
                0.9999977396754328,
                0.9999910602994342,
                0.9999952149037944,
                0.9999898700102291,
                0.9999977396759717,
                0.9999977396754327,
                0.9999986290426297,
                0.9999977396765105,
                0.9999417087415015,
                0.9999945777784455
            ],
            [
                0.9999977396754329,
                0.9999970976869773,
                0.9999982396569966,
                0.9999990577556308,
                0.9999974387187058,
                0.9999952149032248,
                0.9999977396746247,
                0.9999921107364785,
                0.9999945777816786,
                0.999986992874646
            ],
            [
                0.9999994284996211,
                0.9999996940977731,
                0.9999995549148419,
                0.9999996940977731,
                0.9999994956525317,
                0.9999996072137529,
                0.9999995549150542,
                0.9999994956524716,
                0.9999998144608097,
                0.9999993524053562
            ],
            [
                0.9999945777829695,
                0.9999984465018751,
                0.9999990577555185,
                0.9999974387184,
                0.9999945777790914,
                0.9999974387180947,
                0.9999980052702786,
                0.9999970976890528,
                0.9999982396559473,
                0.9999982396567867
            ],
            [
                0.9999938558268648,
                0.9999987901337396,
                0.9999967112493665,
                0.9999957771670593,
                0.9999974387171787,
                0.9999957771660526,
                0.999997438717484,
                0.9999993524051246,
                0.9999991684722697,
                0.999995777168066
            ],
            [
                0.9999980052709919,
                0.999994577781032,
                0.9875683467685534,
                0.999993855827596,
                0.9999785550541535,
                0.9999852610198073,
                0.9999967112509349,
                0.9999930377429215,
                0.9999810748449972,
                0.9999945777810306
            ],
            [
                0.9999993524052019,
                0.9999996533674614,
                0.9999996072137998,
                0.9999993524052789,
                0.9999998144609645,
                0.999999694097773,
                0.999999352405279,
                0.9999989322968754,
                0.9999991684719723,
                0.9999995549147359
            ],
            [
                0.9999974387177893,
                0.9999977396757025,
                0.9999687980774944,
                0.999978555046489,
                0.9999990577556307,
                0.9999921107355342,
                0.9999977396765106,
                0.9999898700066073,
                0.999933947823931,
                0.9999967112521112
            ],
            [
                0.9999994284992804,
                0.9999987901347492,
                0.9999996072138934,
                0.9999989322972572,
                0.9999982396561572,
                0.9999986290421394,
                0.9999970976876693,
                0.9999952149037943,
                0.9999980052705163,
                0.9999987901338839
            ],
            [
                0.9999994284994849,
                0.9999832985701949,
                0.999983298580152,
                0.9999945777829696,
                0.9999910603036973,
                0.9999989322966208,
                0.9999724643089064,
                0.9999962733589389,
                0.9999869928761944,
                0.9999962733589393
            ],
            [
                0.9999986290429568,
                0.999999352405279,
                0.9999996072137998,
                0.9999993524052019,
                0.9999991684716751,
                0.9999987901338839,
                0.9999994284997574,
                0.9999989322968755,
                0.9999991684720716,
                0.9999991684715759
            ],
            [
                0.99999457777974,
                0.9999962733593843,
                0.9999992661786696,
                0.9999921107383591,
                0.9999982396565771,
                0.9999977396757023,
                0.999999168471576,
                0.9999984465022456,
                0.9999991684720716,
                0.9999991684717742
            ],
            [
                0.9999994284992805,
                0.9999980052705165,
                0.999999352404893,
                0.9999980052707541,
                0.9999993524049703,
                0.9999980052705164,
                0.9999982396567867,
                0.9999995549150541,
                0.99999893229713,
                0.999999694097846
            ],
            [
                1.9947301970287804e-06,
                3.288747889178668e-06,
                3.927862470861484e-07,
                1.3007123812317831e-05,
                4.4508499887035535e-07,
                4.4508505192819656e-07,
                6.475947209953583e-07,
                4.450848927621807e-07,
                8.315279285012978e-07,
                2.260324028372372e-06
            ],
            [
                0.9999990577557433,
                0.9999994284994167,
                0.9999997300421581,
                0.9999989322975119,
                0.9999996072138934,
                0.9999974387168734,
                0.9999990577550693,
                0.9999977396754329,
                0.9999986290421397,
                0.9999994284993486
            ],
            [
                1.0129995807939249e-05,
                5.422217027754022e-06,
                6.144173135628569e-06,
                8.315281267037064e-07,
                1.3007126902392506e-05,
                6.144173135025058e-06,
                3.288750241374845e-06,
                2.561282515783711e-06,
                6.9622537576631295e-06,
                5.422221554670048e-06
            ],
            [
                9.422444813961216e-07,
                2.6995777745466066e-07,
                8.31528027618756e-07,
                1.3709568798956654e-06,
                1.3709575336654889e-06,
                2.5612825157464395e-06,
                3.4663253845007707e-07,
                7.338209804506587e-07,
                1.3709578602637359e-06,
                3.92786293909545e-07
            ],
            [
                0.9999962733593842,
                0.9999952149032242,
                0.9999980052707544,
                0.99984156372768,
                0.999998239657212,
                0.9999957771675632,
                0.999996273359838,
                0.999998239656367,
                0.999993037743751,
                0.9999952149060762
            ],
            [
                0.9999996072137061,
                0.9999998362623332,
                0.9999995549148419,
                0.9999990577557432,
                0.9999990577550691,
                0.9999967112517189,
                0.9999997617631184,
                0.9999995549148419,
                0.9999989322973846,
                0.9999996533675028
            ],
            [
                0.9999967112501507,
                0.9999996072136592,
                0.9999994284996893,
                0.9999980052693275,
                0.9999984465024306,
                0.9999962733611607,
                0.999999789756684,
                0.9999994956524115,
                0.9999989322975118,
                0.9999995549149481
            ],
            [
                0.9999992661791944,
                0.9999982396569966,
                0.9999989322967483,
                0.9999989322968754,
                0.9999974387165681,
                0.9999986290429566,
                0.9999957771675633,
                0.9999995549147358,
                0.999997739675972,
                0.9999997300421903
            ],
            [
                0.9999991684721706,
                0.9999938558239345,
                0.9999990577551815,
                0.9999974387177893,
                0.9999982396561572,
                0.9999990577555185,
                0.9999952149037946,
                0.999992110733655,
                0.9999921107392964,
                0.9999995549151081
            ],
            [
                0.9999982396574163,
                0.999998629042303,
                0.9999982396561572,
                0.9999945777790915,
                0.9999995549147359,
                0.999998790134028,
                0.9999992661790195,
                0.9999930377404312,
                0.9999994284994848,
                0.9999898700041923
            ],
            [
                0.9999945777823233,
                0.9999987901341726,
                0.9999869928655155,
                0.9992903296569562,
                0.999891103104096,
                0.9999970976873236,
                0.999983298574177,
                0.999998790134605,
                0.9996200155247027,
                0.9999898700078136
            ],
            [
                0.999993855822498,
                0.9999962733620504,
                0.9947798740839745,
                0.9999980052702803,
                0.9999962733611604,
                0.9999984465020603,
                0.9999952149037947,
                0.999999168471675,
                0.9999994956524114,
                0.9999980052693274
            ],
            [
                0.9999984465020618,
                0.9999990577556308,
                0.9999982396559484,
                0.9999989322970033,
                0.9999982396559474,
                0.9999982396565782,
                0.999993855827596,
                0.9999977396757023,
                0.9999980052693275,
                0.9999984465020603
            ],
            [
                0.9999984465026167,
                0.9999989322970028,
                0.9999982396563672,
                0.9999993524053562,
                0.99999844650169,
                0.9999962733611614,
                0.9999989322975118,
                0.9999997300423191,
                0.9999990577551815,
                0.9999987901347493
            ],
            [
                1.2098658277264215e-06,
                2.56128282131428e-06,
                1.3709576970213355e-06,
                4.22283193393364e-06,
                1.370956716450141e-06,
                3.2887486729876365e-06,
                6.962253759043525e-06,
                1.3007133114886634e-05,
                1.3709567164962755e-06,
                4.785092783267308e-06
            ],
            [
                3.2887490649759413e-06,
                1.2098659718539182e-06,
                8.315277302588544e-07,
                5.043475284182996e-07,
                1.7603440526806268e-06,
                2.260325106045111e-06,
                5.715004470129334e-07,
                2.9023116390104826e-06,
                2.260324028372372e-06,
                3.288749065029781e-06
            ],
            [
                0.9999991684717742,
                0.999998932297512,
                0.9999987901344609,
                0.9999994956526519,
                0.9999994284997574,
                0.9999982396569966,
                0.9999992661790195,
                0.9999974387165691,
                0.9999984465024314,
                0.9999977396759717
            ],
            [
                0.9999994956527121,
                0.9999989322966208,
                0.9999996533675028,
                0.9978172836793999,
                0.9999989322968754,
                0.999999266179107,
                0.9999992661792819,
                0.9999982396569966,
                0.9999994956524715,
                0.999999495652652
            ],
            [
                0.9999921107392972,
                0.9999151889789105,
                0.9999910603026321,
                0.9999785550592742,
                0.999989870006606,
                0.9999921107374148,
                0.9999957771645422,
                0.9999989322970031,
                0.9999945777803844,
                0.999995777165549
            ],
            [
                1.0677027426262978e-06,
                1.8553910183379568e-07,
                5.043473480678099e-07,
                3.7266392836984955e-06,
                8.315281267581578e-07,
                7.338212429006964e-07,
                5.043475284004103e-07,
                5.04347528438253e-07,
                9.422445937528824e-07,
                1.3709572066334069e-06
            ],
            [
                1.209865395009523e-06,
                1.994729483630195e-06,
                1.2098655392354511e-06,
                1.06770312455264e-06,
                2.699577452746696e-07,
                1.0677033791291683e-06,
                2.9023130228840374e-06,
                1.3709576970387918e-06,
                7.338207180714596e-07,
                9.42244930849811e-07
            ],
            [
                0.9999977396748939,
                0.9999485577987365,
                0.9999970976869775,
                0.9998601779769601,
                0.9999885212264054,
                0.9999974387168736,
                0.9999957771670605,
                0.9999885212277717,
                0.9999967112509351,
                0.9999957771665557
            ],
            [
                2.2603242978007868e-06,
                1.067702997240607e-06,
                6.144174601410037e-06,
                7.338212429367364e-07,
                6.96225375863827e-06,
                1.209865683500459e-06,
                2.9023123307122503e-06,
                1.7603436328994344e-06,
                0.9999724642990765,
                9.422448185015797e-07
            ],
            [
                0.9999987901340285,
                0.9999970976883863,
                0.9999930377454507,
                0.9999970976883609,
                0.9999938558254334,
                0.9933071505833416,
                0.9999991684722698,
                0.9999962733620489,
                0.9999991684718735,
                0.9964063978771116
            ],
            [
                0.9796676485866417,
                0.9999980052693275,
                0.9999930377462408,
                0.9999910603068953,
                0.9999930377404336,
                0.9999921107345946,
                0.9999910603015684,
                0.9999898700042035,
                0.9999980052702786,
                0.9999980052695654
            ],
            [
                0.9999869928731052,
                0.9999974387174844,
                0.9999984465022455,
                0.9999987901341724,
                0.9999991684715759,
                0.9999982396559475,
                0.999998239656577,
                0.999999057755743,
                0.9999980052695653,
                0.9999987901344608
            ],
            [
                0.9999646437451117,
                0.9999957771675627,
                0.9999930377404321,
                0.9999967112501507,
                0.999997739675972,
                0.9999852610215486,
                0.9999952149055061,
                0.9999885212264035,
                0.9999930377404321,
                0.9999938558275966
            ],
            [
                0.9999989322972578,
                0.9999996533672963,
                0.9999987901340281,
                0.9999987901338839,
                0.9999997300422547,
                0.9999994956525318,
                0.9999997617630332,
                0.9999986290424667,
                0.9999987901341725,
                0.9999989322967487
            ],
            [
                0.9999993524049703,
                0.9999994284996211,
                0.9999998144608097,
                0.999999554914842,
                0.9999994284993486,
                0.9999987901347497,
                0.9999998362623723,
                0.999999814460854,
                0.9999994956524115,
                0.9999991684717743
            ],
            [
                0.9999996940978825,
                0.9999997300421581,
                0.9999996072137998,
                0.9999997897567342,
                0.9999993524052789,
                0.9999996940977366,
                0.9999997300422547,
                0.9999994284994168,
                0.9999997897566338,
                0.9999996940977001
            ],
            [
                3.2887502412970765e-06,
                1.067703379136937e-06,
                1.0677029972993568e-06,
                2.2603253754921562e-06,
                7.338212429367364e-07,
                9.422449308035348e-07,
                1.5534979396815448e-06,
                2.5612819052374947e-06,
                1.3709570433536782e-06,
                3.288749065209246e-06
            ],
            [
                1.2098653950403334e-06,
                1.0677031245783732e-06,
                4.222835458002318e-06,
                1.5534981248528732e-06,
                1.2098656834834034e-06,
                2.260323489435463e-06,
                1.5534973841592143e-06,
                7.338208929998139e-07,
                4.785093353787868e-06,
                1.3709570433387154e-06
            ],
            [
                8.31528424146183e-07,
                1.5534983100016177e-06,
                1.760344052650207e-06,
                8.315284241257637e-07,
                5.715006514074756e-07,
                3.288749065077638e-06,
                2.260324836567261e-06,
                1.0677029972993568e-06,
                1.0677027427068966e-06,
                2.9023116387069255e-06
            ],
            [
                0.9999987901344608,
                0.9999997300422868,
                0.9999930377462414,
                0.9999990577554061,
                0.9999977396765105,
                0.9999995549151072,
                0.999997097687669,
                0.999998239656577,
                0.9999974387165682,
                0.9999984465015048
            ],
            [
                0.9999986290431202,
                0.9999987901341724,
                0.9999987901340283,
                0.9999990577556309,
                0.9999986290424666,
                0.9999992661787571,
                0.999999168471675,
                0.999999428499553,
                0.9999980052702789,
                0.9999980052705167
            ],
            [
                0.9999990577550691,
                0.9999987901338839,
                0.9999996533673788,
                0.9999992661789321,
                0.9999952149066469,
                0.9999991684719725,
                0.9999990577550691,
                0.9999994956523514,
                0.9999995549150011,
                0.9999993524054335
            ],
            [
                0.999999495652652,
                0.9999989322966208,
                0.9998601778600943,
                0.9999962733602725,
                0.9999977396748941,
                0.9999974387168741,
                0.9999977396762411,
                0.9999898700078145,
                0.9999994284992805,
                0.9999930377404326
            ],
            [
                0.9999970976883615,
                0.9999967112509347,
                0.9999995549151073,
                0.9999967112493665,
                0.9626731099786093,
                0.9999987901338838,
                0.9999974387165681,
                0.9999991684717741,
                0.999995777167563,
                0.9999987901337396
            ],
            [
                0.999999266179107,
                0.9999989322975119,
                0.999999168471675,
                0.999997097686631,
                0.9999987901347491,
                0.9999992661789321,
                0.9999980052709919,
                0.9999921107364748,
                0.9999724643056297,
                0.9999982396572065
            ],
            [
                0.9999996940977366,
                0.9999993524052019,
                0.9999995549147359,
                0.9999992661786696,
                0.9999993524049703,
                0.999999428499553,
                0.9999994284992805,
                0.9999995549149481,
                0.9999996533672549,
                0.9999995549148419
            ],
            [
                0.9999996533674614,
                0.9999996072139402,
                0.9999997300420939,
                0.9999996533674202,
                0.9999995549149481,
                0.9999997897567342,
                0.9999999226557869,
                0.99999844650169,
                0.999999554914789,
                0.9999996940977002
            ],
            [
                0.9999898700126459,
                0.9999756997650787,
                0.9999546021313986,
                0.9999646437493771,
                0.9999251537638889,
                0.9999646437577657,
                0.9999339478791676,
                0.9999546021422212,
                0.9999756997592781,
                0.9999852610110069
            ],
            [
                0.9999996072138934,
                0.9999996533672136,
                0.9999996940978095,
                0.9999992661786696,
                0.9999990577551816,
                0.999998005270041,
                0.9999997300421903,
                0.9999994284993486,
                0.999999653367379,
                0.9999992661789321
            ],
            [
                0.9999810748540369,
                0.9999987901343166,
                0.9999952149032243,
                0.9999957771655488,
                0.9999982396569966,
                0.9999687980886387,
                0.9706877713155612,
                0.9770226276646877,
                0.9999980052709919,
                0.9999980052709919
            ],
            [
                1.0677028700053041e-06,
                1.3709578605118645e-06,
                4.22283193338827e-06,
                3.72664106039412e-06,
                3.7266397278791014e-06,
                3.726637951079042e-06,
                2.902313022984344e-06,
                1.2098662604049616e-06,
                2.5612831265909735e-06,
                8.315279285251204e-07
            ],
            [
                0.9999962733598278,
                0.9999970976876689,
                0.9999938558275967,
                0.9999952149043648,
                0.9999930377462413,
                0.9999546021368187,
                0.9999957771660523,
                0.9999869928668877,
                0.9999885212291404,
                0.999995777165549
            ],
            [
                0.9999957771645427,
                0.9999987901343167,
                0.9999921107383563,
                0.9999995549147359,
                0.9999984465024307,
                0.9999990577551815,
                0.999999789756684,
                0.9999986290432835,
                0.9999997617630048,
                0.9999980052695653
            ],
            [
                0.9999996940976636,
                0.9999991684715759,
                0.9999996072138466,
                0.9999996072139402,
                0.9999998724809723,
                0.9999980052698038,
                0.999999730042126,
                0.9999998724808964,
                0.9999996072137061,
                0.9999997300423191
            ],
            [
                0.9999984465024306,
                0.9999952149066464,
                0.9999974387187054,
                0.9999980052702787,
                0.999999352404893,
                0.9999994284995529,
                0.999999266178932,
                0.9999994284992805,
                0.9999980052702786,
                0.9999994956523512
            ],
            [
                0.9999910603005008,
                0.9999984465015109,
                0.9999952149032239,
                0.9999898700102313,
                0.9999991684715779,
                0.9999984465016899,
                0.999988521233248,
                0.999997097686985,
                0.9999962733611608,
                0.9999898700126487
            ],
            [
                0.9999952149032237,
                0.9999832985763484,
                0.998498817847962,
                0.9999898700102291,
                0.9997040429017627,
                0.9999986290427932,
                0.9999974387168911,
                0.9999992661792826,
                0.9999977396746244,
                0.9914225153386771
            ],
            [
                0.9999945777790976,
                0.9999910603068974,
                0.9399133473013075,
                0.9999930377446089,
                0.9953904279936908,
                0.9999945777810307,
                0.999983298580152,
                0.9998766053963412,
                0.9978172836373111,
                0.9999938558224694
            ],
            [
                0.999999266178757,
                0.9999994956524716,
                0.999999352404893,
                0.9999992661791071,
                0.9999992661787571,
                0.9999997300420937,
                0.9999989322967482,
                0.9999989322966208,
                0.9999984465018754,
                0.9999994956527722
            ],
            [
                0.9999930377437514,
                0.9999991684716749,
                0.9999986290424664,
                0.9933071479395775,
                0.9999938558224694,
                0.999986992873089,
                0.977022632682522,
                0.9999982396565772,
                0.9999938558232012,
                0.9999992661792819
            ]
        ]
    },
    {
        "q_id": "7946_mmlu_math",
        "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,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            48,
            49,
            50,
            51,
            52,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            74,
            75,
            76,
            77,
            78,
            79,
            82,
            83,
            84,
            86,
            87,
            88,
            89,
            90,
            92,
            93,
            94,
            95,
            96,
            97,
            99,
            100,
            101,
            102,
            104,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            119,
            121,
            122,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                6.9622570786798724e-06,
                1.012999580884213e-05,
                1.4738983725406915e-05,
                0.00010889696086955431,
                1.300713311517055e-05,
                1.0129992185981682e-05,
                7.484621822189592e-05,
                1.3007128461838766e-05,
                1.8925148232956223e-05,
                1.4738987231708724e-05
            ],
            [
                6.144172404520556e-06,
                1.2098659719232413e-06,
                2.4300246523066122e-05,
                6.962259567217739e-06,
                1.3007134657984903e-05,
                2.5612828208367393e-06,
                6.1441775296994185e-06,
                4.222833444383398e-06,
                1.2098653950480359e-06,
                2.1444945856418342e-05
            ],
            [
                1.9947304347570075e-06,
                1.9947299589504427e-06,
                2.260324836250676e-06,
                2.5612825160096693e-06,
                5.715005151485975e-07,
                1.3709576970824327e-06,
                2.2603240281606297e-06,
                2.2603242972087315e-06,
                1.5534977545243671e-06,
                4.2228339464303755e-06
            ],
            [
                0.9999987901341723,
                0.999999168471675,
                0.999999266178757,
                0.9999994284993485,
                0.9999996072136125,
                0.9999995549149481,
                0.999999266178932,
                0.9999992661791944,
                0.9999980052702786,
                0.9999980052693274
            ],
            [
                0.9999998724809267,
                0.9999997617630617,
                0.9999996940978825,
                0.9999998724809419,
                0.9999999226557684,
                0.9999994284993485,
                0.9999998362622552,
                0.9999998144609423,
                0.9999998362622746,
                0.9999999397642508
            ],
            [
                0.9999832985821387,
                0.9999984465022455,
                0.9999974387180947,
                0.9999987901347491,
                0.9999982396574162,
                0.9999977396759716,
                0.9999980052695652,
                0.9999984465020603,
                0.9999982396565769,
                0.9999995549147889
            ],
            [
                0.9999996072138465,
                0.9999994956524715,
                0.9999994956523514,
                0.9999998555019446,
                0.9999993524054334,
                0.9999997617631184,
                0.9999998874647842,
                0.9999994956527721,
                0.9999997897567341,
                0.9999991684715759
            ],
            [
                0.9999885212318762,
                0.9999898700090213,
                0.9999974387184,
                0.9999952149037942,
                0.9999977396765105,
                0.9999974387168734,
                0.9999930377412609,
                0.9999980052705163,
                0.9999962733598275,
                0.9999974387168733
            ],
            [
                1.670142781432848e-05,
                1.1478772229300848e-05,
                1.3007133114011233e-05,
                2.7535697662094155e-05,
                0.00017952805093282765,
                2.1444958635523312e-05,
                4.0063692167994334e-05,
                5.829127245988703e-05,
                4.0063682625048554e-05,
                3.7266383954560706e-06
            ],
            [
                1.1478773596847203e-05,
                2.7535704224732304e-05,
                1.4738976694494812e-05,
                2.1444958614225316e-05,
                4.0063711254184204e-05,
                5.422220260202708e-06,
                2.4300240731964193e-05,
                2.430025228428967e-05,
                7.889266346129453e-06,
                6.962254588116627e-06
            ],
            [
                0.9999990577557432,
                0.9999998362623528,
                0.9999996533674615,
                0.9999977396765106,
                0.9999994284997573,
                0.999998790134605,
                0.9999995549151073,
                0.9999989322968754,
                0.9999987901346049,
                0.9999986290426297
            ],
            [
                1.8925152749659986e-05,
                0.0002611902106942874,
                0.00010889689588977092,
                0.9999599363030484,
                3.5356242257020764e-05,
                2.430023782717578e-05,
                7.48462539462643e-05,
                0.999891103090875,
                0.9999038975507369,
                2.753569764256071e-05
            ],
            [
                0.9999998144609644,
                0.9999992661792819,
                0.9999996072138465,
                0.999999730042126,
                0.9999997897567341,
                0.9999998555020307,
                0.9999994956527721,
                0.9999997617630332,
                0.9999998362622357,
                0.9999997300420937
            ],
            [
                1.0129995806317745e-05,
                9.422448185101494e-07,
                1.5534981249164537e-06,
                3.7266401722360055e-06,
                4.785096775058701e-06,
                5.422219613353806e-06,
                3.726640616748873e-06,
                1.0129988561906404e-05,
                1.994729483608425e-06,
                4.785095063069508e-06
            ],
            [
                6.9622570786798724e-06,
                1.5534977545243671e-06,
                1.012998855982425e-05,
                4.2228354571957855e-06,
                6.144173868044274e-06,
                5.422217675628357e-06,
                4.222832436955956e-06,
                6.144176065314267e-06,
                1.9947301970106386e-06,
                2.2603245672025095e-06
            ],
            [
                4.7850927830148924e-06,
                5.8291279365509446e-05,
                6.144175333837093e-06,
                5.8291244647832884e-05,
                9.610240323743297e-05,
                5.4222170304318e-06,
                1.670141586907437e-05,
                6.962254587597396e-06,
                2.4300249411766472e-05,
                5.829127939986156e-05
            ],
            [
                2.5612819051722694e-06,
                1.0129993394129904e-05,
                4.222834954514924e-06,
                2.9023123306594577e-06,
                8.315281267142941e-07,
                8.315277302444853e-07,
                3.5356254903911806e-05,
                5.422218320464995e-06,
                1.760343213227212e-06,
                1.0129992183991656e-05
            ],
            [
                1.0677027427413698e-06,
                2.561281294369958e-06,
                3.2887478883351803e-06,
                6.144177527833006e-06,
                2.9023123294716244e-06,
                3.2887498488151014e-06,
                2.561282821106957e-06,
                1.3709572067680694e-06,
                5.42221767672807e-06,
                7.338211554591642e-07
            ],
            [
                0.9999996940977003,
                0.9859363706839659,
                0.9999994284994167,
                0.9999997617630049,
                0.9999996940976271,
                0.9999997300422547,
                0.9999994956525918,
                0.9999994956527126,
                0.999999168471676,
                0.9999997897565838
            ],
            [
                6.605216804699975e-05,
                0.00017952800860263153,
                7.484625393972985e-05,
                0.002800927435347832,
                0.9997965729548229,
                0.0002959569920041779,
                0.999986992876188,
                0.0008040859687865621,
                5.829129320305095e-05,
                0.0002305066861370812
            ],
            [
                8.315282258756395e-07,
                6.9622579086271995e-06,
                2.1444945840269323e-05,
                2.260323489410794e-06,
                2.5612834317535587e-06,
                3.288748672879957e-06,
                5.715003107655392e-07,
                2.2603251060142746e-06,
                1.7603430033399058e-06,
                2.561282210590951e-06
            ],
            [
                1.892514147143123e-05,
                1.0129988564430787e-05,
                3.535625911829982e-05,
                1.4738983724146862e-05,
                2.1444940743772097e-05,
                1.8925150493166868e-05,
                2.260323758835034e-06,
                1.1478770859917257e-05,
                7.889263525534328e-06,
                3.1201900203407254e-05
            ],
            [
                3.2887482807182155e-06,
                6.475951069932288e-07,
                3.7266406162269133e-06,
                1.7603438427852151e-06,
                5.422218967944967e-06,
                1.1478773597640625e-05,
                3.2887506334201674e-06,
                1.3709567164962755e-06,
                2.902311292920774e-06,
                4.785096205260165e-06
            ],
            [
                5.82912516391202e-05,
                5.8291272448012225e-05,
                7.889265406567165e-06,
                2.144495608105136e-05,
                2.7535700932494338e-05,
                2.144494327788042e-05,
                1.3007131564643372e-05,
                0.000108896896105261,
                4.0063687394553603e-05,
                3.5356238042506135e-05
            ],
            [
                0.9999546021205518,
                0.00010889694799084654,
                0.9999038976195668,
                0.9999724643187544,
                3.535624648542694e-05,
                0.0002034269963280861,
                0.00026119021144665273,
                0.0002611903693294325,
                0.0002034270684192587,
                0.00013982208984333465
            ],
            [
                0.9999994956526519,
                0.9999957771645422,
                0.999999266178932,
                0.9999977396751633,
                0.9999957771665555,
                0.9999991684717741,
                0.999998239656367,
                0.9999987901344607,
                0.9999982396572064,
                0.9999987901337396
            ],
            [
                4.7850950643402904e-06,
                1.5534971988904843e-06,
                1.4738980213985297e-05,
                6.144172403715875e-06,
                4.785095633616451e-06,
                9.422445938797133e-07,
                3.2887498493325602e-06,
                2.2603248365960415e-06,
                9.422447061876404e-07,
                3.1201926243586504e-05
            ],
            [
                1.8925152750692706e-05,
                6.144172403715875e-06,
                1.6701421840804172e-05,
                1.5534979396984994e-06,
                2.2603248365960415e-06,
                1.2098652508056196e-06,
                5.422218969217281e-06,
                4.222832437324657e-06,
                7.88926634455091e-06,
                2.561283126679493e-06
            ],
            [
                1.7603434230729168e-06,
                1.209866116137134e-06,
                3.726638838711279e-06,
                5.715003788853339e-07,
                2.2603234893594005e-06,
                4.222832436379863e-06,
                1.0677026154376365e-06,
                9.422445938861406e-07,
                2.561281904923017e-06,
                2.9023112928785396e-06
            ],
            [
                2.9023123309287002e-06,
                2.9023109465275493e-06,
                1.3007123808153756e-05,
                1.99472900796355e-06,
                1.9947301969217434e-06,
                1.370957533574467e-06,
                3.288748280658394e-06,
                1.994729721436347e-06,
                2.9023130229209922e-06,
                4.7850927830845245e-06
            ],
            [
                0.9999977396759716,
                0.9999992661786695,
                0.9999970976866309,
                0.9999991684715758,
                0.9999984465018751,
                0.9999962733607161,
                0.9999989322970027,
                0.9999967112509347,
                0.9999977396759716,
                0.9999995549149481
            ],
            [
                9.422447061953531e-07,
                1.5534971989258068e-06,
                1.209866116137134e-06,
                1.0677031245050577e-06,
                2.5612831266165976e-06,
                7.33821067986608e-07,
                9.422448185388577e-07,
                1.9947301969707264e-06,
                1.5534971988495103e-06,
                7.338213304243302e-07
            ],
            [
                0.9999995549148419,
                0.9999997617631184,
                0.9999995549149481,
                0.9999996072139402,
                0.9999997617631183,
                0.9999996533672962,
                0.9999995549147359,
                0.9999998362623137,
                0.9999996940977366,
                0.9999996072138934
            ],
            [
                0.00026119030746825014,
                8.481101078697588e-05,
                7.484623607019228e-05,
                5.829125856424875e-05,
                7.48462449695656e-05,
                0.0001398220224418199,
                0.00015843625415286997,
                0.0001088969089855471,
                0.00013982205705906782,
                0.0002034269725502577
            ],
            [
                1.3709575336093795e-06,
                5.422221554847581e-06,
                2.561282515662579e-06,
                1.2098656833491588e-06,
                1.5534975693488444e-06,
                3.288750241410738e-06,
                3.927861066113479e-07,
                3.2887486724851334e-06,
                1.994729721323867e-06,
                5.422218322457301e-06
            ],
            [
                2.2603240282243575e-06,
                2.9023133687311063e-06,
                1.994730434778778e-06,
                1.3709578605355551e-06,
                1.5534977545384963e-06,
                9.42244818532859e-07,
                2.90231094702116e-06,
                4.222835457906302e-06,
                7.889266346129453e-06,
                8.939693106020111e-06
            ],
            [
                0.99999862904312,
                0.9999984465026158,
                0.9999989322973845,
                0.999998239656367,
                0.9999990577554061,
                0.999999887464811,
                0.9999938558275955,
                0.9999977396759716,
                0.9999970976890529,
                0.9999970976883608
            ],
            [
                0.9999998724808963,
                0.9999998362622942,
                0.9999998144608983,
                0.99999976176309,
                0.9999998144608319,
                0.9999998362623137,
                0.9999993524054335,
                0.9999995549150542,
                0.9999999226558237,
                0.9999998362622357
            ],
            [
                0.9999997300421581,
                0.9999998874648112,
                0.9999999006880312,
                0.9999997897566089,
                0.9999994284995529,
                0.9999998362622747,
                0.9999993524050474,
                0.9999992661786695,
                0.9999998724808963,
                0.9999997300421903
            ],
            [
                1.8925143725341476e-05,
                2.7535700945316292e-05,
                4.006368738143655e-05,
                8.93970056424046e-06,
                2.7535691096552598e-05,
                3.5356259128846735e-05,
                3.535625487510076e-05,
                3.120190765193695e-05,
                2.1444956070870452e-05,
                1.892514147143123e-05
            ],
            [
                1.892514147143123e-05,
                2.7535700939406174e-05,
                4.0063682616886836e-05,
                3.726640172385136e-06,
                2.4300237825230942e-05,
                4.785093923847183e-06,
                6.605212891684883e-05,
                8.939696303010449e-06,
                7.484625392611642e-05,
                2.561282210530385e-06
            ],
            [
                0.9999996940978461,
                0.9999989322972572,
                0.9999994956527722,
                0.9999996533675028,
                0.9999989322975118,
                0.9999991684717741,
                0.9999995549149481,
                0.9999997617630049,
                0.9999997897566089,
                0.9999996072137998
            ],
            [
                1.370957370247318e-06,
                4.785095064044355e-06,
                4.785096205077381e-06,
                6.47594875389178e-07,
                9.422444815323792e-07,
                2.260323758713745e-06,
                2.2603253754284284e-06,
                1.5534979396645902e-06,
                9.422448185264317e-07,
                9.422444815409489e-07
            ],
            [
                0.9999999317440116,
                0.9999997897566089,
                0.9999997617631469,
                0.9999999226557869,
                0.9999999226557961,
                0.9999999006881377,
                0.9999994284992804,
                0.9999998724808963,
                0.999999814460876,
                0.9999999123575359
            ],
            [
                7.889266347133978e-06,
                7.889266344766165e-06,
                5.144223816721283e-05,
                2.1444940731484803e-05,
                1.1478764015361142e-05,
                6.144176797283277e-06,
                5.144220135754627e-05,
                1.1478768121401121e-05,
                4.222833444037741e-06,
                5.4222202617511845e-06
            ],
            [
                1.3709573702111586e-06,
                2.561282821209454e-06,
                8.939693104410264e-06,
                1.3709576970537545e-06,
                1.7603434230537046e-06,
                1.7603430034151537e-06,
                3.288749848605725e-06,
                7.338208930315157e-07,
                9.422450431800595e-07,
                2.56128129423019e-06
            ],
            [
                5.422221553654169e-06,
                1.0129989768616954e-05,
                1.7603440522963817e-06,
                2.26032348933062e-06,
                2.260325105981383e-06,
                4.539787938262061e-05,
                8.93969736518344e-06,
                2.260324567054496e-06,
                2.5612822103393692e-06,
                0.00010889692164083773
            ],
            [
                6.475950297768503e-07,
                8.315282258956806e-07,
                1.9947290080343035e-06,
                2.9023112926251358e-06,
                1.1478769480699576e-05,
                4.78509563509613e-06,
                1.2098659719122375e-06,
                1.5534975693488444e-06,
                1.3709567165087443e-06,
                5.715003788933905e-07
            ],
            [
                0.9999994956525317,
                0.9999993524049702,
                0.9999995549148419,
                0.9999998555019618,
                0.9999994284997573,
                0.9999992661788446,
                0.9999994956525317,
                0.9999991684722698,
                0.9999993524054334,
                0.9999997617630049
            ],
            [
                4.785093353187292e-06,
                2.7535687791694597e-05,
                2.1444958632714784e-05,
                5.422220261652556e-06,
                1.8925145983348442e-05,
                1.892515049571424e-05,
                8.939699498587217e-06,
                5.422217027576489e-06,
                1.6701415858046724e-05,
                7.889262585082652e-06
            ],
            [
                0.9999990577550691,
                0.9999986290432834,
                0.0,
                0.9999970976876691,
                0.9999990577550691,
                0.9999992661788446,
                0.9999994956524114,
                0.9999991684719723,
                0.9999993524053562,
                0.9999993524049703
            ],
            [
                6.962258738827909e-06,
                5.422219616026655e-06,
                1.9947299590520376e-06,
                3.7266383944765502e-06,
                1.670141586949968e-05,
                3.2887486731641103e-06,
                1.7603430034151537e-06,
                9.422450431654909e-07,
                1.994729245722476e-06,
                1.7603438428188364e-06
            ],
            [
                4.7850956342431385e-06,
                5.422219615582823e-06,
                2.260324028331257e-06,
                1.9947299591354906e-06,
                6.962257908880483e-06,
                2.2603242972087315e-06,
                4.222833945815874e-06,
                1.5534977544367678e-06,
                2.9023133686835932e-06,
                1.0129992179053445e-05
            ],
            [
                0.9998204719698691,
                0.9999938558239332,
                0.9999980052700407,
                0.9999977396759716,
                0.9999952149055052,
                0.9999962733616045,
                0.9999952149043644,
                0.9999990577551814,
                0.9999974387171787,
                0.9999962733620487
            ],
            [
                2.9023123310290063e-06,
                4.222834954607099e-06,
                1.370957206783032e-06,
                3.288749065167371e-06,
                1.5534973841450852e-06,
                1.553498495308628e-06,
                6.47594720987407e-07,
                1.7603430033399058e-06,
                1.7603432133032607e-06,
                1.553498310118888e-06
            ],
            [
                0.999999789756684,
                0.9999999006880549,
                0.9999996533674201,
                0.9999999006880194,
                0.9999995549151073,
                0.9999998555020135,
                0.9999997617630049,
                0.9999998362622357,
                0.9999996072137061,
                0.9999998724809419
            ],
            [
                0.00043055718205441666,
                0.00048785723134789675,
                0.00010889689602128323,
                0.00037998452243495244,
                7.48462539462643e-05,
                2.144494585197151e-05,
                0.9999546021421873,
                5.144221359250013e-05,
                0.001032231157518555,
                7.484620042097855e-05
            ],
            [
                1.1478772226356834e-05,
                6.9622537593854575e-06,
                2.5612822106841303e-06,
                1.6701425820540864e-05,
                1.892514146884943e-05,
                8.315278294038928e-07,
                1.0129993394811673e-05,
                8.315282258956806e-07,
                3.2887494573561262e-06,
                1.300712691308661e-05
            ],
            [
                7.338213304083124e-07,
                6.475947209985977e-07,
                2.260324028255194e-06,
                1.994729008105057e-06,
                3.7266406162269133e-06,
                1.2098662603961589e-06,
                6.475947209953583e-07,
                1.5534971989568904e-06,
                2.561282821209454e-06,
                1.9947294835630703e-06
            ],
            [
                5.422221554670048e-06,
                3.2887490652810324e-06,
                1.2098658277181688e-06,
                1.3709575336530204e-06,
                1.5534979396984994e-06,
                9.422445938917108e-07,
                1.7603438426203097e-06,
                7.889264466230069e-06,
                1.5534971989696065e-06,
                1.5534971988707037e-06
            ],
            [
                9.422443691996268e-07,
                2.2603242977802297e-06,
                8.315281267430323e-07,
                1.5534975691524517e-06,
                1.9947297213746646e-06,
                9.422443691996268e-07,
                1.2098661161927025e-06,
                3.726637951170554e-06,
                2.260323489435463e-06,
                1.370957533676711e-06
            ],
            [
                9.610237997885274e-05,
                2.7535687794499397e-05,
                4.0063692172075196e-05,
                7.484620928658632e-05,
                6.962257079275089e-06,
                4.0063687390327e-05,
                5.829127941597736e-05,
                1.9947292456281383e-06,
                6.962258736269744e-06,
                2.9023109467598367e-06
            ],
            [
                2.4300240719941574e-05,
                3.12019002122609e-05,
                5.829126553136402e-05,
                2.1444948412137308e-05,
                6.144173868781898e-06,
                1.300713001414004e-05,
                4.006371123640331e-05,
                3.535625911829982e-05,
                5.8291272467944936e-05,
                7.484624511822428e-05
            ],
            [
                4.222831933726245e-06,
                2.902313368820854e-06,
                2.2603237589028734e-06,
                1.0677033791437343e-06,
                7.889259762494174e-06,
                1.3709572068272963e-06,
                4.222832437324657e-06,
                8.315283250150648e-07,
                7.338211554725124e-07,
                3.7266410608720178e-06
            ],
            [
                8.939699499026267e-06,
                2.9023126767836054e-06,
                4.78509449410676e-06,
                1.5534977545384963e-06,
                6.144174601499446e-06,
                2.5612831265630198e-06,
                2.902311292920774e-06,
                3.726638395415398e-06,
                1.4738988992031526e-05,
                4.785093923768848e-06
            ],
            [
                1.5534983101061718e-06,
                2.260324028331257e-06,
                9.422445938454347e-07,
                1.7603438427243761e-06,
                1.0677027427068966e-06,
                2.902311638654133e-06,
                1.2098662603862553e-06,
                2.260323758882316e-06,
                4.785093923116048e-06,
                9.422450431732037e-07
            ],
            [
                0.9999999123575881,
                0.9999996533674202,
                0.9999990577555185,
                0.9999997300421581,
                0.99999976176309,
                0.9999997617630617,
                0.9999998362623137,
                0.9999994284993485,
                0.9999993524052789,
                0.9999997617630049
            ],
            [
                0.9999998144608098,
                0.9999998724809267,
                0.9999984465018751,
                0.9999992661791944,
                0.999999352404893,
                0.9999986290426299,
                0.9999993524051246,
                0.9999998362623528,
                0.9999994956523514,
                0.9999999123574941
            ],
            [
                0.9999996940977366,
                0.9999998362623137,
                0.9999994284996211,
                0.9999998144609202,
                0.9999977396757023,
                0.9999990577555185,
                0.9999996072136125,
                0.9999996533672549,
                0.9999982396559474,
                0.9999994956523514
            ],
            [
                9.422444815323792e-07,
                6.144177530794679e-06,
                8.315280276456036e-07,
                1.9947299592407137e-06,
                1.0677032518209896e-06,
                2.5612819052072116e-06,
                1.067703251864202e-06,
                2.260324567177841e-06,
                2.9023130228840374e-06,
                1.9947290080343035e-06
            ],
            [
                0.999999814460876,
                0.9999998362623137,
                0.9999997617630616,
                0.9999997897565838,
                0.9999998362622942,
                0.9999996072136592,
                0.9999999123574628,
                0.999999887464811,
                0.9999996940978461,
                0.9999998362622357
            ],
            [
                0.9999997300420937,
                0.9999994956525317,
                0.9999997300420937,
                0.99999976176309,
                0.99999992265575,
                0.999999554914895,
                0.9999997300422225,
                0.9999997300421581,
                0.9999996940976636,
                0.9999997300421903
            ],
            [
                6.144174601208867e-06,
                1.892514146382353e-05,
                4.785096775842062e-06,
                6.9622554187981796e-06,
                1.8925141467059383e-05,
                8.93969949923766e-06,
                6.144173868312501e-06,
                3.7266383948154845e-06,
                1.300712380997554e-05,
                4.785093353687772e-06
            ],
            [
                1.9947297214182054e-06,
                1.7603432132464244e-06,
                2.902311984683171e-06,
                7.338210678941723e-07,
                2.5612831262578596e-06,
                4.222833947674739e-06,
                6.144176066051891e-06,
                9.422447061876404e-07,
                1.3709575336654889e-06,
                1.7603434229832599e-06
            ],
            [
                1.9947297211642184e-06,
                6.144173868882483e-06,
                3.726637950973972e-06,
                3.72663839473414e-06,
                1.994729245722476e-06,
                3.2887482810382622e-06,
                6.96225458885115e-06,
                4.785093923324944e-06,
                1.994729245749689e-06,
                2.5612812945889277e-06
            ],
            [
                0.9999970976869769,
                0.9999962733598274,
                0.9999980052702786,
                0.9999910603047615,
                0.9999974387177893,
                0.9999986290427931,
                0.9999987901338838,
                0.9999957771660521,
                0.9999952149066462,
                0.9999962733616045
            ],
            [
                0.9999996533672136,
                0.9999995549149481,
                0.9999986290432834,
                0.9999995549149481,
                0.9999997300422868,
                0.9999997617629764,
                0.9999997300422225,
                0.9999994284996211,
                0.9999996533672962,
                0.9999996533674614
            ],
            [
                1.2098661161789477e-06,
                2.9023126764615702e-06,
                7.889264465986113e-06,
                2.5612825157464395e-06,
                7.338211554464836e-07,
                6.144174599353632e-06,
                1.0677028700203557e-06,
                6.475948753930064e-07,
                1.5534973841154145e-06,
                2.2603253755476615e-06
            ],
            [
                7.338211554725124e-07,
                1.5534984952662413e-06,
                2.9023133689317184e-06,
                2.561282210590951e-06,
                1.7603436329714805e-06,
                9.422445938728576e-07,
                4.222833443891798e-06,
                6.475947981904966e-07,
                1.9947304346826253e-06,
                1.7603425837494853e-06
            ],
            [
                0.9999998874649051,
                0.9999994284996891,
                0.9999998555020135,
                0.9999997617630332,
                0.9999997617631752,
                0.9999994956527722,
                0.999999789756634,
                0.9999986290427932,
                0.9999992661789321,
                0.9999996940976636
            ],
            [
                0.9999986290431201,
                0.9999977396746244,
                0.999998446502801,
                0.9999994284994167,
                0.9999977396759716,
                0.9999986290424664,
                0.9999930377445804,
                0.9999993524054334,
                0.9999982396569965,
                0.9999982396567867
            ],
            [
                0.999999887464905,
                0.99999976176309,
                0.9999998724809267,
                0.9999996940977002,
                0.9999999006881377,
                0.9999999468421883,
                0.9999999317439872,
                0.9999999226557408,
                0.9999998724809571,
                0.9999999006880075
            ],
            [
                1.9947290080125335e-06,
                1.9947290080125335e-06,
                6.475950297906914e-07,
                9.422450431860582e-07,
                5.422218968931258e-06,
                1.2098656834349874e-06,
                2.2603240281606297e-06,
                2.9023119844508833e-06,
                7.338213304243302e-07,
                6.47594875389178e-07
            ],
            [
                0.9999997897565838,
                0.9999999006880785,
                0.9999997617631469,
                0.999999789756684,
                0.9999990577551815,
                0.9999994284997573,
                0.9999997897567341,
                0.9999998362622943,
                0.9999996533672136,
                0.9999996072136592
            ],
            [
                1.209865971934245e-06,
                7.338208055436404e-07,
                1.7603434231241496e-06,
                4.222834953520201e-06,
                1.2098655392574583e-06,
                2.5612828212676906e-06,
                6.144176798132662e-06,
                5.422218968822766e-06,
                5.422217027754022e-06,
                2.2603253755476615e-06
            ],
            [
                2.5612819052072116e-06,
                1.012999339309804e-05,
                1.9947301969707264e-06,
                2.26032537546132e-06,
                6.144175333289463e-06,
                1.2098653950403334e-06,
                2.2603251057881422e-06,
                1.7603434231097403e-06,
                5.422218967649081e-06,
                1.0677029972993568e-06
            ],
            [
                2.144494837847401e-05,
                1.892515724357613e-05,
                1.4738983708865354e-05,
                1.8925143724239906e-05,
                3.1201907642061724e-05,
                6.9622587329010695e-06,
                7.88926164299515e-06,
                3.1201900154598675e-05,
                1.8925148216088467e-05,
                3.535626756251187e-05
            ],
            [
                1.7603438427660027e-06,
                2.2603245671202796e-06,
                1.553497754476329e-06,
                4.222835457664342e-06,
                1.7603432132079998e-06,
                5.043473480643696e-07,
                1.3709572067955008e-06,
                1.7603432131631714e-06,
                1.209865394936899e-06,
                1.5534973841592143e-06
            ],
            [
                0.9999998144609645,
                0.999999855502048,
                0.9999999006880668,
                0.9999999123574419,
                0.999999789756634,
                0.999999814460876,
                0.9999998555019446,
                0.9999998724809571,
                0.999999730042126,
                0.9999998362622746
            ],
            [
                3.2887486731252264e-06,
                3.7266379512112265e-06,
                1.0129989771823107e-05,
                2.2603245672867952e-06,
                1.9947304348332037e-06,
                2.2603251062013478e-06,
                4.785096205651846e-06,
                4.785093353739995e-06,
                3.2887482811220126e-06,
                1.7603440527046419e-06
            ],
            [
                0.9999998144608317,
                0.9999997897565587,
                0.9999998144609423,
                0.9999998144609423,
                0.9999996940978095,
                0.9999996072138934,
                0.9999996940976272,
                0.9999998144609423,
                0.9999994956525318,
                0.9999998555019963
            ],
            [
                2.5612831266608576e-06,
                3.7266379512518984e-06,
                2.9023116390104826e-06,
                4.785094494672519e-06,
                7.889265406567165e-06,
                3.2887486731252264e-06,
                8.9396941702904e-06,
                4.785093924156175e-06,
                1.3709567165087443e-06,
                1.76034300345598e-06
            ],
            [
                6.605213667550255e-05,
                6.60521760632388e-05,
                0.00012339457460376925,
                0.0011695105046693665,
                0.00012339455989760105,
                9.610243774636368e-05,
                5.1442238118931704e-05,
                0.0002611903393867945,
                9.61024148058974e-05,
                0.9995694429636544
            ],
            [
                0.99999862904312,
                0.9999987901346049,
                0.9999921107345937,
                0.9999930377462406,
                0.9999957771680659,
                0.9999938558239336,
                0.9999994284992805,
                0.9999982396561571,
                0.9999980052695652,
                0.9999986290432834
            ],
            [
                6.96225458885115e-06,
                3.288750241204353e-06,
                4.222833444168322e-06,
                1.0677026153638352e-06,
                2.902311639126627e-06,
                5.422218965873757e-06,
                1.3007128451097345e-05,
                1.8925148236674017e-05,
                4.785095633041987e-06,
                3.7266383950256237e-06
            ],
            [
                2.4300232031037035e-05,
                0.0001233946042513091,
                8.481105119991589e-05,
                7.484625393972985e-05,
                0.00015843629188645847,
                6.605213677497863e-05,
                5.144221363404434e-05,
                0.00012339458912680775,
                9.610240343739553e-05,
                6.605216035177641e-05
            ],
            [
                0.9999980052705164,
                0.999991060299435,
                0.9999994284993486,
                0.9999997300420937,
                0.9999986290432835,
                0.9999991684718732,
                0.9999989322975118,
                0.9999974387165681,
                0.9999994284995529,
                0.9999992661790195
            ],
            [
                1.3709575336093795e-06,
                5.4222176755001384e-06,
                2.9023112928785396e-06,
                9.422448184801556e-07,
                6.962255419279419e-06,
                4.2228339475595195e-06,
                6.144172403470001e-06,
                6.144173136019732e-06,
                4.22283344433731e-06,
                8.31528424151477e-07
            ],
            [
                7.889264465986113e-06,
                5.8291286270284484e-05,
                1.0129992186774007e-05,
                1.4738985478142165e-05,
                4.006368256456438e-05,
                6.962259568230874e-06,
                8.93969736942758e-06,
                1.8925157260443894e-05,
                2.1444956072586775e-05,
                1.892515725300831e-05
            ],
            [
                5.829129327005879e-05,
                1.6701425823457267e-05,
                1.1478770859332632e-05,
                7.889266344981421e-06,
                5.422220908481809e-06,
                6.144172403067661e-06,
                1.0129993384861544e-05,
                2.4300246517938825e-05,
                2.144495096161541e-05,
                2.1444958633416914e-05
            ],
            [
                6.605212874576922e-05,
                7.484626291860775e-05,
                1.4738987237553233e-05,
                7.484624503872184e-05,
                0.00010889693522226211,
                0.0002034269975297041,
                3.535626334645077e-05,
                2.7535700934898458e-05,
                7.484620040790966e-05,
                7.889266345770692e-06
            ],
            [
                4.7850933529174686e-06,
                1.760344052693435e-06,
                6.9622554173544636e-06,
                4.785096205173126e-06,
                2.260323758806253e-06,
                5.422218322763051e-06,
                1.9947290080343035e-06,
                8.939699497335115e-06,
                6.144175334094145e-06,
                6.144176064856046e-06
            ],
            [
                0.9999998144609202,
                0.9999998362623137,
                0.999999814460854,
                0.9999993524054335,
                0.9999986290427931,
                0.9999996533674615,
                0.9999997617629764,
                0.9999994284994849,
                0.999998932296621,
                0.9999993524051246
            ],
            [
                2.90231094702116e-06,
                1.2098655392222467e-06,
                1.2098658276862581e-06,
                1.994729007841999e-06,
                1.5534975693792215e-06,
                4.785094493932679e-06,
                2.9023126765196424e-06,
                5.04347528438253e-07,
                4.450850519360903e-07,
                2.561282515886208e-06
            ],
            [
                3.120191134947124e-05,
                1.012999218369684e-05,
                1.9947299591826594e-06,
                2.1444955991763626e-05,
                4.785096205260165e-06,
                5.829128633093081e-05,
                2.2603240281935217e-06,
                2.26032537546132e-06,
                2.144494329496561e-05,
                7.889259762307618e-06
            ],
            [
                0.9999998144609202,
                0.9999997897567091,
                0.9999995549147889,
                0.9999998362622943,
                0.999999887464811,
                0.9999998555020135,
                0.9999994284992805,
                0.9999997300421581,
                0.9999998362622746,
                0.9999996533672136
            ],
            [
                0.9999994956525918,
                0.999999814460876,
                0.9999987901347492,
                0.9999996533675028,
                0.9999997617630616,
                0.9999997300421581,
                0.9999998555020307,
                0.9999994284993485,
                0.9999997897567341,
                0.9999998555020135
            ],
            [
                0.999999887464811,
                0.9999995549151073,
                0.9999998874648782,
                0.9999998144608317,
                0.9999996072137529,
                0.9999997300421581,
                0.9999997897567341,
                0.9999998874649184,
                0.9999998555020307,
                0.999999814460854
            ],
            [
                5.043475885576967e-07,
                1.9947299590810645e-06,
                1.209865250822125e-06,
                7.338211554591642e-07,
                2.2603248365960415e-06,
                1.0677032518413822e-06,
                1.5534971989696065e-06,
                9.422450431800595e-07,
                2.902313368963394e-06,
                1.7603438427852151e-06
            ],
            [
                7.338209805133949e-07,
                4.785093353100252e-06,
                1.2098662604049616e-06,
                2.902311292960369e-06,
                1.3709575336530204e-06,
                2.5612812946890944e-06,
                4.222834954461155e-06,
                2.260323489192885e-06,
                2.260324028351814e-06,
                2.9023123308072772e-06
            ],
            [
                2.902311639073834e-06,
                2.5612831264675113e-06,
                6.962254588433232e-06,
                4.785095064523075e-06,
                3.726641060956752e-06,
                3.288747889038086e-06,
                1.0129993391531815e-05,
                2.9023123310290063e-06,
                2.90231198483099e-06,
                6.144172403715875e-06
            ],
            [
                9.610241477233725e-05,
                0.00015843625426351888,
                0.0001795280507865552,
                0.000295957236726992,
                7.484620044058188e-05,
                0.0002959570630702156,
                0.0001795279441800938,
                7.484623602717382e-05,
                0.0001795280507499871,
                0.9999546021367908
            ],
            [
                0.9999997897567341,
                0.9999996940976272,
                0.9999996533672136,
                0.9999996533673788,
                0.999999352404893,
                0.9999991684719723,
                0.9999998362623528,
                0.9999991684722698,
                0.9999998362622943,
                0.9999994284993485
            ]
        ]
    },
    {
        "q_id": "7840_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            12,
            13,
            14,
            17,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            35,
            37,
            39,
            40,
            42,
            43,
            44,
            45,
            46,
            47,
            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,
            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,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127,
            15,
            16,
            18
        ],
        "rewards": [
            [
                0.9999994956524114,
                0.9999992661788445,
                0.999999554914842,
                0.999999730042126,
                0.9999991684720715,
                0.9999994956527722,
                0.9999996533673375,
                0.999999730042126,
                0.9999994284994167,
                0.9999998362623332
            ],
            [
                1.994730196992497e-06,
                5.422218323231539e-06,
                1.012998856312253e-05,
                2.430024651882284e-05,
                1.147876812538911e-05,
                1.3007126913583456e-05,
                1.0129993395088066e-05,
                4.785093923603471e-06,
                1.1478765387416494e-05,
                6.962253759271479e-06
            ],
            [
                0.9999991684715759,
                0.9999996533673375,
                0.9999898700102293,
                0.9999962733589393,
                0.9999996940976272,
                0.9999997300420937,
                0.9999997300422869,
                0.9999984465028013,
                0.9999998362623528,
                0.9999996072138465
            ],
            [
                0.9999998555020135,
                0.9999997617630049,
                0.9999996533672962,
                0.9999994956524716,
                0.9999992661789321,
                0.9525741311981335,
                0.9999996940977001,
                0.9999993524054335,
                0.9999974387174841,
                0.9999998555019446
            ],
            [
                0.9999998362622942,
                0.9999997617631469,
                0.9999997617631468,
                0.999999887464744,
                0.9999998144608097,
                0.9999999226557316,
                0.9999999006879838,
                0.9999998724809723,
                0.9999998724810026,
                0.9999999006880904
            ],
            [
                8.939695235959266e-06,
                6.144173868882483e-06,
                1.4738987241494252e-05,
                0.9241418246795768,
                5.422221555192784e-06,
                5.422220262037209e-06,
                5.422217676654099e-06,
                7.484624503218738e-05,
                8.939698434820389e-06,
                6.9622537593854575e-06
            ],
            [
                0.9999997300422226,
                0.9999999317439058,
                0.999999653367379,
                0.9999996533672549,
                0.9999999226557131,
                0.9999998362622357,
                0.9999998555019618,
                0.9999991684721707,
                0.999999653367255,
                0.9999998144609202
            ],
            [
                1.1478766754941153e-05,
                4.006369216362198e-05,
                0.9875683507590003,
                2.7535684526905577e-05,
                4.006370649866785e-05,
                4.539789024909747e-05,
                0.9525741246345829,
                0.97068776908965,
                0.0004305571369126324,
                0.00010889692225641063
            ],
            [
                0.9999999123575464,
                0.9999987901338839,
                0.9999996533674201,
                0.999999855501979,
                0.9999997897565587,
                0.9999996072137998,
                0.9999998144609202,
                0.9999998724809419,
                0.9999999317439058,
                0.9999993524052018
            ],
            [
                6.962259569560613e-06,
                1.9947306726358406e-06,
                1.370956879949281e-06,
                6.1441731363550164e-06,
                7.889264466230069e-06,
                1.5534977545102382e-06,
                1.4738988993050295e-05,
                1.994729959270648e-06,
                6.1441767987808774e-06,
                9.610243775685123e-05
            ],
            [
                0.9999997897567342,
                0.999999352405279,
                0.9999998874647977,
                0.9999997617629764,
                0.9999999123575987,
                0.9999998362622552,
                0.9999998874647709,
                0.9999998874647977,
                0.9999999317439546,
                0.9999999123574732
            ],
            [
                0.9999996940978095,
                0.9999993524050474,
                0.9999999317439708,
                0.9999994284997573,
                0.8807970889295664,
                0.999999266179107,
                0.9999994284994167,
                0.9999967112505427,
                0.9999997300422225,
                0.9999980052705164
            ],
            [
                0.9149009474519223,
                0.9999998362622746,
                0.999999814460854,
                0.9999997617629764,
                0.9999998724808963,
                0.9999996533674202,
                0.9999999226558423,
                0.9999997300420943,
                0.9999997300421903,
                0.9999997300421903
            ],
            [
                0.9999996072136125,
                0.9999996533674202,
                0.9999997300422869,
                0.9999999006881022,
                0.999999931743979,
                0.9999952149066546,
                0.9999998144608097,
                0.9999997617630048,
                0.999999789756684,
                0.9999998362622942
            ],
            [
                0.9999982396561572,
                0.9997694932588178,
                0.9999885212264044,
                0.9999885212318764,
                0.9999885212305183,
                0.999997097686631,
                0.9999910603068939,
                0.9999952149072167,
                0.9999980052695652,
                0.9999991684715759
            ],
            [
                0.9999996072137061,
                0.9999996533674202,
                0.9999995549149481,
                0.9999999006881022,
                0.9999997617631468,
                0.99999992265575,
                0.9999996940978825,
                0.9999998724809115,
                0.999999814460876,
                0.999999789756634
            ],
            [
                0.9999995549147889,
                0.9999980052693275,
                0.9999998144608981,
                0.9999989322968754,
                0.9999990577555185,
                0.9999921107364749,
                0.9999991684719725,
                0.9999995549148419,
                0.9999998555019962,
                0.9999991684721706
            ],
            [
                0.9999997617629763,
                0.9999998144609203,
                0.9999994956525318,
                0.999999266179107,
                0.9999996072137061,
                0.99999976176309,
                0.9999999123574732,
                0.9999996533672136,
                0.9999984465020607,
                0.999999554914842
            ],
            [
                0.9999996533674615,
                0.9999994956524716,
                0.9999998874647976,
                0.9999999226557408,
                0.9999996533672548,
                0.999999352405279,
                0.9999998144608981,
                0.999999789756634,
                0.999999900688043,
                0.9999998555019618
            ],
            [
                0.9999996533672549,
                0.9999997300421581,
                0.9999998144608319,
                0.9999996940978095,
                0.9999998362622552,
                0.9999990577552939,
                0.9999997897566089,
                0.9999997300422869,
                0.9999998144609424,
                0.9999992661788446
            ],
            [
                0.999999694097846,
                0.9999990577549569,
                0.9999990577555185,
                0.9999980052693275,
                0.999999168471675,
                0.9999984465015047,
                0.9999986290424666,
                0.9999982396574163,
                0.9999998144609424,
                0.9999997300422869
            ],
            [
                1.3007126913346863e-05,
                3.120192251903545e-05,
                1.0129993393540266e-05,
                1.0129995809929273e-05,
                7.88926164421493e-06,
                8.93970056668775e-06,
                2.144495608105136e-05,
                4.22283394786293e-06,
                5.4222215552470286e-06,
                1.0129988563914856e-05
            ],
            [
                0.9999999226557408,
                0.9999996533672962,
                0.999999730042126,
                0.9999998362622746,
                0.999999352404893,
                0.9999998362623332,
                0.9999997897565838,
                0.999999814460854,
                0.9999997617630332,
                0.9999999397642653
            ],
            [
                0.9999999317439872,
                0.9999999006880904,
                0.9999977396751635,
                0.9999997617629764,
                0.9999998555020307,
                0.9999998362622552,
                0.9999999123574836,
                0.999999855502048,
                0.9999997300422869,
                0.9999998874648112
            ],
            [
                1.892514824021969e-05,
                8.939699500636112e-06,
                8.939698434657777e-06,
                2.1444948412137308e-05,
                7.889266347004826e-06,
                1.892514598469098e-05,
                6.605212892597951e-05,
                2.4300243626409964e-05,
                1.6701415867221242e-05,
                1.892515500715167e-05
            ],
            [
                0.9999998362622943,
                0.9999996072139402,
                0.9999994956527121,
                0.9999997300422869,
                0.9999984465028013,
                0.9999999634651487,
                0.9999998724809267,
                0.999999352405279,
                0.9999999006881377,
                0.9999999468421693
            ],
            [
                0.9999997897565587,
                0.9999998555019963,
                0.9999994284992805,
                0.999999730042319,
                0.9999986290423029,
                0.9999993524049703,
                0.9999996940978095,
                0.9999991684721706,
                0.9999998144608097,
                0.9999991684717742
            ],
            [
                7.88926258532661e-06,
                2.144495096457996e-05,
                1.1478766755233466e-05,
                1.6701417858577338e-05,
                1.0129987355785634e-05,
                1.0129987356541108e-05,
                1.8925157255968775e-05,
                1.1478764019787597e-05,
                2.7535684519993744e-05,
                0.00013982212402930744
            ],
            [
                0.999993037742092,
                NaN,
                0.9999990577554061,
                0.9999962733589389,
                0.999993037741261,
                0.9999898700041944,
                0.9999885212332564,
                0.9999952149066472,
                0.9999151889596388,
                NaN
            ],
            [
                5.8291251611977796e-05,
                2.7535691100960147e-05,
                0.9999997617630048,
                2.4300252316291068e-05,
                0.9999994956527721,
                6.962255419653012e-06,
                5.144220752910515e-05,
                8.481103122174425e-05,
                0.9999998362622552,
                2.1444950965282096e-05
            ],
            [
                5.8291244672006574e-05,
                1.300713311517055e-05,
                3.7266383954560706e-06,
                8.939700566289352e-06,
                4.0063692179945426e-05,
                2.1444948408275583e-05,
                1.1478769492893215e-05,
                1.8925155008528632e-05,
                2.144495608046625e-05,
                3.120191879561992e-05
            ],
            [
                1.8925150493166868e-05,
                2.4300237830711845e-05,
                7.889265406904397e-06,
                7.484620047815493e-05,
                2.4300249421932663e-05,
                9.610244927358124e-05,
                7.484624502565293e-05,
                8.939695237959376e-06,
                NaN,
                2.753570094621784e-05
            ],
            [
                2.4300243620398656e-05,
                8.939695237959376e-06,
                5.4222170304318e-06,
                6.9622537593854575e-06,
                4.5397863219323224e-05,
                2.4300252315495453e-05,
                2.7535684530912436e-05,
                4.22283294098842e-06,
                1.0129995807441742e-05,
                2.5612812947077304e-06
            ],
            [
                0.9999998362622746,
                0.9999995549150542,
                0.9999997897565838,
                0.9999977396746442,
                0.9999997617630049,
                0.999999814460876,
                0.9999997617630048,
                0.9669140222071801,
                0.9999997897567342,
                0.9999998724809875
            ],
            [
                0.8519527963298946,
                0.8354835391516133,
                0.5926665999540698,
                0.9999724643168117,
                0.9890130586850022,
                0.9399133479324787,
                0.9999910603049756,
                0.9999546021260254,
                0.9999952149043648,
                0.7981867801399695
            ],
            [
                0.9999998362623528,
                0.9999995549151073,
                0.9999994956526519,
                0.9999997897565587,
                0.9999997300422547,
                0.9999991684721706,
                0.9999997897567342,
                0.9999996072139402,
                0.9999992661792819,
                0.9999996533674202
            ],
            [
                0.9999990577551814,
                0.9999990577554061,
                0.9999977396754327,
                0.9999994956524715,
                0.999997097686977,
                0.9999974387184012,
                0.9999962733607161,
                0.9999974387187053,
                0.9999987901341725,
                0.9999957771655508
            ],
            [
                0.9999982396574163,
                0.9999994956525918,
                0.9999992661791944,
                0.9999998362622552,
                0.9999967112493665,
                0.9999997300420937,
                0.9999994284995529,
                0.9999995549150011,
                0.9999996072137061,
                0.999998239656367
            ],
            [
                1.473898724181597e-05,
                6.962258739454786e-06,
                1.7603427936079236e-06,
                8.939695237666677e-06,
                1.0129988564430787e-05,
                0.9999910602994334,
                0.9999485577679497,
                2.4300232034838305e-05,
                3.120190020204515e-05,
                0.9999646437535068
            ],
            [
                0.999999554914895,
                0.9999990577556308,
                0.9999962733593835,
                0.9999997300422869,
                0.999999057755743,
                0.9999996940977001,
                0.9999869928668941,
                0.9999997897566589,
                0.9999997897565838,
                0.9999997617629764
            ],
            [
                0.9999987901344607,
                0.9999993524051246,
                0.9999977396759716,
                0.9999990577554061,
                0.9999998724809419,
                0.9875683508733398,
                0.9999987901347495,
                0.9999997300420937,
                0.9999984465020606,
                0.9999996072139402
            ],
            [
                0.9999999006879838,
                0.999999352405279,
                0.9999998724809875,
                0.9999998874648112,
                0.999999653367503,
                0.9999998144609644,
                0.9999997897566589,
                0.9999996533675028,
                0.9999999226558053,
                0.999999789756634
            ],
            [
                0.9999998362622357,
                0.9999996940977731,
                0.9999999006880194,
                0.9999994284994849,
                0.999999814460876,
                0.9999996533672962,
                0.9999998724809419,
                0.9999998874648245,
                0.99999976176309,
                0.9999997897565587
            ],
            [
                0.9999984465016899,
                0.999997438717484,
                0.9999994956524114,
                0.9999980052693274,
                0.9999974387168736,
                0.9999992661788445,
                0.999999789756684,
                0.9999994284995529,
                0.9999869928669578,
                0.9999599363042869
            ],
            [
                2.260324028351814e-06,
                8.939699500636112e-06,
                6.96225873895455e-06,
                9.422444815006715e-07,
                2.5612819051722694e-06,
                7.889262584350785e-06,
                6.962259569003389e-06,
                4.785096776251149e-06,
                1.5534984952492866e-06,
                1.670141785651155e-05
            ],
            [
                2.4300234924597754e-05,
                8.939693104637921e-06,
                6.962254589433702e-06,
                8.939699499823059e-06,
                6.962255419051463e-06,
                1.6701429805655623e-05,
                4.785096205512581e-06,
                1.670141985245514e-05,
                4.222832437386106e-06,
                3.120191508060445e-05
            ],
            [
                5.144223201941656e-05,
                5.1442207520496894e-05,
                1.3007123811229494e-05,
                0.0001584361602027512,
                3.120191134288775e-05,
                3.535625070624499e-05,
                6.605217604545803e-05,
                4.539785780045566e-05,
                5.8291279438030564e-05,
                0.9999984465020603
            ],
            [
                0.9999997897565838,
                0.9999994956527121,
                0.999999789756684,
                0.9999995549150542,
                0.9999999397642508,
                0.9999996940976636,
                0.9999997300421581,
                0.9999998362623332,
                0.9999984465015048,
                0.999999900688043
            ],
            [
                2.90231163910023e-06,
                2.9023116390421582e-06,
                4.785093924103951e-06,
                1.7603434231241496e-06,
                1.9947299591354906e-06,
                3.726640171768275e-06,
                1.3709568798420497e-06,
                3.28874945711983e-06,
                3.2887498492936755e-06,
                6.14417606659952e-06
            ],
            [
                0.9999994284996211,
                0.9999996072137998,
                0.9999996940977731,
                0.9999962733593835,
                0.9999994284993486,
                0.9999996533675028,
                0.9999996940978095,
                0.9999992661787571,
                0.9999996072136125,
                0.9999996533674615
            ],
            [
                0.9999997300422225,
                0.999999730042126,
                0.9999996533672135,
                0.9999999397642868,
                0.9999998144608981,
                0.9999997617630048,
                0.9999999006881497,
                0.9999997617629764,
                0.9999999123574836,
                0.9999994956525317
            ],
            [
                2.7535694377870696e-05,
                0.9999910602994336,
                0.9999938558232011,
                2.753568780802255e-05,
                0.999975699759268,
                4.539786320924914e-05,
                0.999991060302631,
                4.785095065045315e-06,
                1.012999460150437e-05,
                3.120190392534495e-05
            ],
            [
                0.9999996072136125,
                0.9999995549150011,
                0.9999995549150011,
                0.999996711250543,
                0.999999814460876,
                NaN,
                0.9999970976869775,
                0.999999694097846,
                0.9999997617631184,
                0.9999996533672549
            ],
            [
                8.939694172290508e-06,
                1.0129990978847043e-05,
                1.670141586949968e-05,
                5.422218969720291e-06,
                1.8925148231579266e-05,
                8.939698435340743e-06,
                1.4738976700929127e-05,
                6.962253759486771e-06,
                6.962253759752719e-06,
                4.006370650653807e-05
            ],
            [
                0.9999996072138934,
                0.9999999123575672,
                0.9999997897567091,
                0.999999789756684,
                0.9999992661790196,
                0.9999997617631752,
                0.9999998874649051,
                0.9999996940978825,
                0.9999998144608981,
                0.9999998362622552
            ],
            [
                0.9999996940978825,
                0.9999999317439627,
                0.9999998874647574,
                0.9999998724809875,
                0.9999997300421903,
                0.9999998874648781,
                0.9999998362622357,
                0.9999998555019446,
                0.9999993524053563,
                0.999999789756634
            ],
            [
                0.9999970976869847,
                0.9999921107374627,
                0.9999995549149482,
                0.9820137907616943,
                NaN,
                NaN,
                0.9999997617631183,
                0.999989870009533,
                0.9999957771670637,
                0.9999987901344607
            ],
            [
                0.9999987901340284,
                0.9999996533674614,
                0.999996711252111,
                0.9999997617631469,
                0.9999990577555185,
                0.9999991684720716,
                0.9999998144609202,
                0.9999986290429567,
                0.9999996533672136,
                0.9999997300422869
            ],
            [
                8.939693106873817e-06,
                3.2887494564857185e-06,
                2.1444940742640888e-05,
                5.422218322763051e-06,
                4.222831933864508e-06,
                6.962255419570695e-06,
                1.1478765388314311e-05,
                2.902313022952668e-06,
                4.222831934052698e-06,
                1.5534973841592143e-06
            ],
            [
                0.9999992661792819,
                0.9999996072138466,
                0.9999994956525918,
                0.9999996072136592,
                0.9999982396572069,
                0.9999996072137998,
                0.9999996072136593,
                0.9999996072137998,
                0.9999992661792819,
                0.9999990577554062
            ],
            [
                4.00636778604994e-05,
                2.9023112930949896e-06,
                6.1441746017453204e-06,
                5.829127242638312e-05,
                1.147876402018431e-05,
                5.422220908634683e-06,
                6.962255419653012e-06,
                8.939694171135975e-06,
                7.889261644057078e-06,
                3.7266410609940346e-06
            ],
            [
                0.9999999468421124,
                0.99999976176309,
                0.999999887464744,
                0.9999999397642222,
                0.9999998362623332,
                0.999999931743971,
                0.9999999226558238,
                0.9999998555020135,
                0.9999999317439872,
                0.9999999226557316
            ],
            [
                0.9999998362622942,
                0.9999994956524114,
                0.9999999226557131,
                0.9999997897567342,
                0.999999946842144,
                0.9999998724809723,
                0.9999999586006443,
                0.9999999317439058,
                0.9999999123575151,
                0.9999999006881377
            ],
            [
                0.9999996533674202,
                0.9999992661790195,
                0.9999997617630333,
                0.9999989322966208,
                0.9999974387165681,
                0.9999994956524114,
                0.9999957771655502,
                0.999999730042126,
                0.9999992661790195,
                0.9999992661786696
            ],
            [
                0.9999996072137061,
                0.9999995549147358,
                0.9999986290429567,
                0.9999992661788447,
                0.9999998555019274,
                0.9999992661792819,
                0.9999986290429566,
                0.9999970976883638,
                0.9999996533672549,
                0.9999996533672136
            ],
            [
                NaN,
                0.9999910603058293,
                0.9999339478475789,
                0.9999038975623424,
                0.9999832985821392,
                0.9999957771680656,
                0.9999687980997979,
                0.9999930377404314,
                0.999995777166556,
                0.9999785550413881
            ],
            [
                2.430023493228869e-05,
                1.4738981970956057e-05,
                3.1201903920010065e-05,
                1.670142781520948e-05,
                0.00010889694804630358,
                2.1444948407573453e-05,
                5.8291272486605336e-05,
                1.4738983727578497e-05,
                6.144175334094145e-06,
                0.00013982209018104417
            ],
            [
                0.9999986290429567,
                0.9999996533674614,
                0.999999653367379,
                0.999997438716568,
                0.9999974387165682,
                0.999999730042126,
                0.9999996072137998,
                0.9999996940977366,
                0.9999980052700408,
                0.999998446502801
            ],
            [
                1.6701429807630274e-05,
                8.939698434332555e-06,
                1.4738983724575818e-05,
                7.889265406681968e-06,
                2.144495096161541e-05,
                3.288748673265808e-06,
                5.4222202614355715e-06,
                5.8291265478351516e-05,
                7.889259764079887e-06,
                2.1444943294263477e-05
            ],
            [
                0.9999996533674202,
                0.9999994956524716,
                0.9999994956527721,
                0.9999999123574732,
                0.9999980052693275,
                0.9999987901337396,
                0.999999168471675,
                0.9999952149043646,
                0.999999694097846,
                0.9999997300421581
            ],
            [
                0.9999998724809723,
                0.999999554914895,
                0.9999997617631184,
                0.9999996940978095,
                0.999999946842144,
                0.9999998724810027,
                0.9999999123574941,
                0.9999998362622357,
                0.9999998144608097,
                0.9999998362623528
            ],
            [
                0.9999977396751634,
                0.9999986290421395,
                0.9999990577551814,
                0.9999984465020603,
                0.9999945777790913,
                0.9999991684718732,
                0.999997097686977,
                0.9999885212277811,
                0.9999996072138934,
                0.9999962733620492
            ],
            [
                2.260323758882316e-06,
                1.209866116149238e-06,
                2.2603251062013478e-06,
                8.315277302649045e-07,
                5.043475885576967e-07,
                2.7535681242383173e-05,
                4.450850519360903e-07,
                1.5534984953298217e-06,
                9.422445938642879e-07,
                9.422444815726566e-07
            ],
            [
                0.999999266179107,
                0.9999967112509349,
                0.9999980052700408,
                0.9999987901346049,
                0.9999997617631468,
                0.9999993524052018,
                0.9999986290423029,
                0.9999991684718732,
                0.999999814460876,
                0.9999998874649184
            ],
            [
                0.999999855501979,
                0.9999999123575359,
                0.999999855502048,
                0.999999931743979,
                0.9999998874649318,
                0.9999997897565587,
                0.9999999317439546,
                0.999999814460854,
                0.9999997897565587,
                NaN
            ],
            [
                0.9999998362623332,
                0.9999999397642365,
                0.9999998874647842,
                0.9999998724810027,
                0.9999997617630616,
                0.9999998724809875,
                0.9999999586006245,
                0.9999996940977002,
                0.9999999006879957,
                0.99999976176309
            ],
            [
                0.9999996940976272,
                0.9999996940978461,
                0.9999994284994168,
                0.9999994284997574,
                0.9999994284997574,
                0.9999998874647574,
                0.9999994956525317,
                0.9999992661788445,
                0.9999986290432835,
                0.9999995549150011
            ],
            [
                0.999998005269803,
                0.9999987901346049,
                0.9999339478711082,
                0.9999994956524114,
                0.9999930377412606,
                0.9999987901338838,
                0.9999987901347491,
                0.9999994284994167,
                0.9999995549150011,
                0.9999998555020135
            ],
            [
                9.610246078681677e-05,
                1.670141786036971e-05,
                2.7535697666401535e-05,
                5.829125856000775e-05,
                0.9999930377404305,
                9.610241481708411e-05,
                0.9999832985781584,
                2.753568124769226e-05,
                0.9998415637834701,
                3.5356246483883486e-05
            ],
            [
                3.1201926224857616e-05,
                4.539785238918559e-05,
                4.0063682630732606e-05,
                7.484623612410147e-05,
                5.144220750533887e-05,
                4.0063696957321844e-05,
                5.1442195242316055e-05,
                3.535625913952226e-05,
                5.144221358089769e-05,
                7.484622725903504e-05
            ],
            [
                0.00010889692218114752,
                0.00010889687027972941,
                2.4300249406550775e-05,
                7.484624498426811e-05,
                5.144219523595344e-05,
                7.484626267846674e-05,
                0.00010889688324557471,
                2.1444950953735936e-05,
                5.829126551991333e-05,
                5.8291286322448804e-05
            ],
            [
                0.9999998144608317,
                0.9999998555020135,
                0.999999931743979,
                0.9999999530883843,
                0.999999653367379,
                0.9999994284994168,
                0.9999999468421122,
                0.9999997897566089,
                0.9999999397642293,
                0.9999990577557432
            ],
            [
                0.9999997617630333,
                0.9999999468421756,
                0.9999995549147889,
                0.9999999006880668,
                0.9999996940976271,
                0.9999998144608981,
                0.9999995549149481,
                0.9999998144609203,
                0.9999997617630049,
                0.9999997300422869
            ],
            [
                0.999999694097846,
                0.9999996940978825,
                0.9999998555019274,
                0.999999789756634,
                0.9999998144608317,
                0.9999998362623723,
                0.9999998144608097,
                0.9999996533675028,
                0.9999998555019274,
                0.9999997897565587
            ],
            [
                0.9999987901343169,
                0.9999991684720716,
                0.999999912357515,
                0.9999993524054334,
                0.9999996940976636,
                0.9999997617631753,
                0.9999997617629764,
                0.9999998144609423,
                0.9999980052698033,
                0.9999999123574419
            ],
            [
                4.5397857795336036e-05,
                1.6701425824307884e-05,
                1.4738983726908257e-05,
                3.12019076363863e-05,
                8.939698433974813e-06,
                6.144172404587612e-06,
                3.1201911373535005e-05,
                4.22283394786293e-06,
                1.1478765385746131e-05,
                0.00015843617898078353
            ],
            [
                8.939693106329072e-06,
                2.1444940740066406e-05,
                1.8925157264919016e-05,
                1.7603438428564603e-06,
                6.962259568509485e-06,
                1.147876812538911e-05,
                1.3007125360809367e-05,
                3.2887486733420804e-06,
                1.3007126911335805e-05,
                2.753569108693614e-05
            ],
            [
                0.9999998555019963,
                0.9999995549149481,
                0.999999912357515,
                0.9999998874648112,
                0.9999999123575882,
                0.9999998724809419,
                0.9999980052702894,
                0.9999997300420939,
                0.999999887464744,
                0.9999998724809419
            ],
            [
                6.605212889714584e-05,
                4.539786864000808e-05,
                1.147876675466972e-05,
                1.8925141468298646e-05,
                2.1444956079218013e-05,
                6.1441738691562974e-06,
                5.144220137401424e-05,
                1.670142781520948e-05,
                1.670141785596473e-05,
                1.0129994601301684e-05
            ],
            [
                0.9999921107374147,
                3.120191137012976e-05,
                1.8925152752999112e-05,
                6.605215254938888e-05,
                0.00010889690922797348,
                2.4300232042706045e-05,
                7.889261644982674e-06,
                6.1441738691562974e-06,
                6.605212106256447e-05,
                1.8925148239772175e-05
            ],
            [
                6.60521210438226e-05,
                1.4738980213985297e-05,
                4.0063711285810896e-05,
                3.120191135991401e-05,
                4.0063696959216535e-05,
                4.0063711278232147e-05,
                6.962258739454786e-06,
                9.610244921065592e-05,
                1.8925155006118952e-05,
                2.7535681238877168e-05
            ],
            [
                1.0129995809929273e-05,
                1.3007131562514014e-05,
                0.0001398221240089635,
                6.60521683089055e-05,
                8.939696304116203e-06,
                1.473898372275276e-05,
                1.4738980213020151e-05,
                8.481102115861673e-05,
                3.120190393487965e-05,
                5.829129330780371e-05
            ],
            [
                0.9999998874648648,
                0.9999996533675028,
                0.9999998555019446,
                0.999999855502048,
                0.999999931743979,
                0.9999998362623723,
                0.9999997300422868,
                0.9999998144608981,
                0.9999996072136125,
                0.9999996940978095
            ],
            [
                1.0677031245312763e-06,
                1.7603434230088762e-06,
                2.561283126502453e-06,
                1.3709576970949014e-06,
                1.0677024881499412e-06,
                1.209865827507999e-06,
                7.88926070328992e-06,
                1.8925152747388e-05,
                1.7603425835749741e-06,
                1.2098652508056196e-06
            ],
            [
                0.9999999123575777,
                0.9999999468421312,
                0.9999998874647306,
                0.9999999123575672,
                0.9999995549150011,
                0.9999998874649318,
                0.9999998724809723,
                0.9999999123574732,
                0.9999999226557316,
                0.9999998874649318
            ],
            [
                0.9999982396563699,
                0.9999999317439058,
                0.9999997897566089,
                0.9999997617631752,
                0.9999999123575359,
                0.9999997617630333,
                0.999999554914842,
                0.9999998144609645,
                0.9999994284992805,
                0.9999984465018755
            ],
            [
                1.6701421837705495e-05,
                1.6701415871049018e-05,
                5.8291251573808804e-05,
                4.006367784140681e-05,
                3.120192625073753e-05,
                1.8925145960215522e-05,
                4.0063682616886836e-05,
                1.6701419849933667e-05,
                3.535625066302841e-05,
                1.4738985482753428e-05
            ],
            [
                0.9999998724809115,
                0.999999939764258,
                0.9999998724809115,
                0.9999999123574419,
                0.9999998144609645,
                0.999999900688043,
                0.9999998555020135,
                0.9999997897566089,
                0.9999998144608097,
                0.9999997897567091
            ],
            [
                0.9999999586005999,
                0.9999997300422547,
                0.9999997897566089,
                0.9999998362622747,
                0.9999999123574941,
                0.999999855501979,
                0.9999998724809874,
                0.9999997617630333,
                0.9999997617631752,
                0.999999855501979
            ],
            [
                0.9999999397642437,
                0.9999996940977731,
                0.9999999123575672,
                0.9999997897565838,
                0.999999266179107,
                0.9999997897567091,
                0.9999997617629764,
                0.9999998874647306,
                0.9999998362623137,
                0.999999855502048
            ],
            [
                0.9999982396574197,
                0.9999977396754341,
                0.9999986290429573,
                0.9999977396762607,
                0.9999970976883669,
                0.9999992661790202,
                0.9999987901338853,
                0.9999957771665564,
                0.9953904288547425,
                0.9999974387180978
            ],
            [
                0.999999554914895,
                0.9999930377420914,
                0.9999997617631183,
                0.9999996072139402,
                0.9999984465018751,
                0.99999457778297,
                0.9999996072137998,
                0.9999930377437514,
                0.9999994956525318,
                0.9999930377462418
            ],
            [
                0.9999756997477279,
                0.9999832985761689,
                0.9999930377420913,
                0.9999599363078431,
                0.9999938558232012,
                0.999995214907219,
                0.9999921107383554,
                0.9999485577618773,
                0.9999852610215486,
                0.9999898700042353
            ],
            [
                0.9999994956524115,
                0.9999982396572065,
                0.999999554914895,
                0.9999986290423029,
                0.9999995549151072,
                0.9999996533674202,
                0.9999996940976272,
                0.9999997300421903,
                0.9999993524053562,
                0.9999993524052019
            ],
            [
                5.829127248999813e-05,
                2.7535700945316292e-05,
                0.0001398220887081424,
                3.120190392795564e-05,
                6.605214466722918e-05,
                2.1444953516281788e-05,
                0.9999980052705163,
                4.006370172507966e-05,
                5.1442213657997754e-05,
                6.1441775312976045e-06
            ],
            [
                1.7603430034439723e-06,
                6.144177531381426e-06,
                2.2603237589542675e-06,
                6.96225458885115e-06,
                5.043475280930805e-07,
                6.144176797730321e-06,
                1.0129990970702682e-05,
                3.726638839395927e-06,
                4.222834954134701e-06,
                3.1201922523121745e-05
            ],
            [
                5.144223816384438e-05,
                3.535625070778844e-05,
                0.00012339457488744337,
                6.60521682560438e-05,
                3.535624649610246e-05,
                4.539789028295303e-05,
                5.829125859393574e-05,
                7.484623606311329e-05,
                8.481102105680693e-05,
                1.8925152752138513e-05
            ],
            [
                0.9999998144608319,
                0.9999998144609423,
                0.9999952149032241,
                0.9999993524052018,
                0.9999996072137061,
                0.9999993524050474,
                0.9999987901337397,
                0.9999986290421394,
                0.9999974387177895,
                0.9999990577550693
            ],
            [
                0.0002305067961131167,
                8.481103126000007e-05,
                0.0001398221402617477,
                0.0006263341022915974,
                8.481103120631853e-05,
                0.00020342702164493557,
                6.605214466722918e-05,
                9.610240331853667e-05,
                2.7535704218321328e-05,
                0.0003799845701474846
            ],
            [
                2.430024072648329e-05,
                2.4300249405489955e-05,
                3.535624227734284e-05,
                4.222833947674739e-06,
                5.4222202621161125e-06,
                7.889263525405172e-06,
                5.829128628512799e-05,
                1.4738987241494252e-05,
                2.4300249420429837e-05,
                1.0129993393945642e-05
            ],
            [
                0.9999998724808963,
                0.999999789756684,
                0.9999999226557776,
                0.9999998874649184,
                0.9999997897565838,
                0.999999912357515,
                0.9999999530883452,
                0.999999931743979,
                0.9999998555020135,
                0.999999352405279
            ],
            [
                5.829129325648758e-05,
                7.889265406567165e-06,
                1.89251482218717e-05,
                1.0129990979215566e-05,
                1.1478766755985128e-05,
                1.3007123812317831e-05,
                1.0129993394129904e-05,
                1.4738985483879434e-05,
                4.006371126992468e-05,
                3.120191508060445e-05
            ],
            [
                0.9999993524054335,
                0.9999999317440197,
                0.9999999123574732,
                0.9999997897566089,
                0.9999967112509358,
                0.9999998724809875,
                0.9999999123575778,
                0.9999999530883675,
                0.9999998362623332,
                0.9999999006879721
            ],
            [
                0.9999998555019962,
                0.9999998362622942,
                0.9999996533672549,
                0.9999998144609424,
                0.9999993524053562,
                0.9999987901347492,
                0.9999984465016899,
                0.9999996940976272,
                0.9999982396569966,
                0.999999694097846
            ],
            [
                0.9997040429016766,
                0.999933947840396,
                0.9999546021205443,
                0.9999599363078454,
                0.996406397521958,
                0.9999038975965423,
                0.9999251537460537,
                0.9796676463976277,
                0.9999930377437544,
                0.9999151889688683
            ],
            [
                0.9999998874647842,
                0.9999998724809267,
                0.9999996072138934,
                0.9999997897566089,
                0.9999994284996893,
                0.9999994284996893,
                0.99999893229713,
                0.9999982396567868,
                0.9999994956526519,
                0.9999997617631184
            ],
            [
                0.9999994284992806,
                0.9999997300422869,
                0.9999994956525317,
                0.9999997300422869,
                0.9999993524050474,
                0.9999997897567341,
                0.9999997617629764,
                0.9999992661786696,
                0.9999997617631752,
                0.9999992661788446
            ]
        ]
    },
    {
        "q_id": "8264_mmlu_math",
        "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,
            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": [
            [
                0.9999994284996211,
                0.9999990577550691,
                0.9999991684721706,
                0.9999994956527721,
                0.9999990577549568,
                0.999998239656367,
                0.9999990577554061,
                0.9999986290426297,
                0.9999987901341723,
                0.999999352404893
            ],
            [
                0.9999984465018752,
                0.9999987901337396,
                0.9999977396759717,
                0.9999994284996211,
                0.9999991684722698,
                0.9999990577554061,
                0.9999990577550691,
                0.9999992661788445,
                0.9999994956525917,
                0.9999987901337396
            ],
            [
                0.9999993524051246,
                0.9999990577551815,
                0.9999986290427931,
                0.9999990577551816,
                0.9999993524053562,
                0.9999998144609645,
                0.9999994956527121,
                0.9999998362623528,
                0.9999992661788445,
                0.9999996072136125
            ],
            [
                0.9999995549151073,
                0.9999995549150011,
                0.9999990577554061,
                0.9999996940977731,
                0.9999990577556308,
                0.9999989322968754,
                0.9999996072136592,
                0.999999694097846,
                0.9999996940978095,
                0.999999428499553
            ],
            [
                0.9999980052695652,
                0.9999982396574163,
                0.9999984465016899,
                0.9999987901346049,
                0.9999974387187054,
                0.9999984465024307,
                0.9999984465018752,
                0.9999990577550693,
                0.9999991684721706,
                0.9999982396559474
            ],
            [
                0.9999994284996893,
                0.9999989322968754,
                0.9999990577556308,
                0.9999987901344607,
                0.9999992661791071,
                0.9999986290431201,
                0.9999989322966208,
                0.9999991684716749,
                0.9999990577550691,
                0.9999992661791944
            ],
            [
                0.9999982396565772,
                0.999999266179282,
                0.9999990577556308,
                0.9999987901347492,
                0.9999989322972572,
                0.9999987901347492,
                0.9999989322972573,
                0.9999993524052789,
                0.9999992661788445,
                0.999999428499553
            ],
            [
                0.9999992661791944,
                0.9999990577551815,
                0.9999994284997573,
                0.9999994284994168,
                0.9999982396559474,
                0.9999991684722697,
                0.9999987901341724,
                0.9999982396561572,
                0.999999730042126,
                0.9999992661788445
            ],
            [
                0.9999995549150011,
                0.9999997300422225,
                0.9999991684722698,
                0.9999996533674201,
                0.999999694097846,
                0.9999994284993485,
                0.9999996940978095,
                0.999998790134028,
                0.9999997617631468,
                0.9999990577557432
            ],
            [
                0.999999653367379,
                0.9999997617629764,
                0.9999992661792819,
                0.9999996533672549,
                0.999999694097846,
                0.9999997617630048,
                0.9999994284992805,
                0.9999996533672136,
                0.9999996940976636,
                0.9999993524052019
            ],
            [
                0.9999945777829696,
                0.9999980052709919,
                0.9999974387180947,
                0.9999724642957752,
                0.9999945777784462,
                0.9999832985721836,
                0.9999977396746365,
                0.9999885212332431,
                0.9999832985781563,
                0.9999785550413609
            ],
            [
                0.9999910603068934,
                0.9999910603058275,
                0.9999982396561575,
                0.9999952149055054,
                0.9999970976873248,
                0.9999910603068932,
                0.9999977396746244,
                0.999995777168066,
                0.999989870010228,
                0.9999756997505795
            ],
            [
                0.999988521234612,
                0.9999930377412607,
                0.9999910603015651,
                0.9999930377404308,
                0.9999957771670589,
                0.9999977396759716,
                0.9999980052705163,
                0.9999970976866309,
                0.9999967112517187,
                0.9999938558239337
            ],
            [
                0.9999994956525317,
                0.9999992661788446,
                0.999999694097846,
                0.9999994284996211,
                0.9999990577551815,
                0.999999266178932,
                0.9999997300421903,
                0.9999995549147359,
                0.9999995549149481,
                0.9999998144608538
            ],
            [
                0.9999994284992805,
                0.9999997897566089,
                0.9999994956525918,
                0.999998790134605,
                0.9999993524053562,
                0.9999998144609423,
                0.9999992661790195,
                0.9999995549150011,
                0.999998790134028,
                0.9999998362622357
            ],
            [
                0.9999994284992805,
                0.9999982396565769,
                0.9999989322970027,
                0.999999266179107,
                0.999999057755743,
                0.9999994956525917,
                0.9999986290421394,
                0.9999992661786695,
                0.9999991684717741,
                0.9999992661786695
            ],
            [
                0.9999998144608098,
                0.9999990577550691,
                0.9999994284993485,
                0.9999990577556307,
                0.9999984465028011,
                0.9999982396565769,
                0.9999995549150542,
                0.999999057755743,
                0.9999993524053562,
                0.9999991684721706
            ],
            [
                0.43782349911420193,
                0.5621765008857981,
                0.9988304898788215,
                0.2018132150593341,
                0.679178699175393,
                0.40733340004593027,
                0.679178692681616,
                0.5621765008857981,
                0.9998766054288291,
                0.017986209600198668
            ],
            [
                0.9999990577552937,
                0.9999994956527721,
                0.9999990577551815,
                0.9999984465022455,
                0.9999992661789321,
                0.9999995549147889,
                0.999998790134605,
                0.9999996072136125,
                0.9999996533672136,
                0.9999993524049702
            ],
            [
                0.9999994956526519,
                0.9999994284995529,
                0.999999554914842,
                0.9999996072138934,
                0.999999554914895,
                0.9999986290431201,
                0.9999986290421395,
                0.999998629042303,
                0.9999994284993485,
                0.9999995549147359
            ],
            [
                0.9999992661788445,
                0.9999996940977366,
                0.9999991684715759,
                0.9999984465020603,
                0.9999994956527121,
                0.9999993524051246,
                0.9999993524049703,
                0.9999990577555185,
                0.9999980052702786,
                0.9999987901337396
            ],
            [
                0.9999990577552937,
                0.9999989322970028,
                0.9999991684715759,
                0.99999893229713,
                0.9999986290432834,
                0.9999994284995529,
                0.9999990577554061,
                0.999999168471675,
                0.999998239656577,
                0.999998629042303
            ],
            [
                0.9999993524054335,
                0.9999996072137998,
                0.9999996940978825,
                0.999999554914789,
                0.9999996940976272,
                0.9999996533674202,
                0.9999992661791944,
                0.9999992661791071,
                0.9999996940976636,
                0.9999990577556308
            ],
            [
                0.9999995549149481,
                0.9999997300421581,
                0.9999997617630049,
                0.9999998144609424,
                0.9999998144608983,
                0.9999993524054335,
                0.9999997617630616,
                0.9999995549149481,
                0.9999994956525317,
                0.9999990577554062
            ],
            [
                0.9999970976866309,
                0.9999990577551814,
                0.9999832985761661,
                0.9999970976880149,
                0.9999989322973845,
                0.999997438717484,
                0.9999986290432834,
                0.9999970976876689,
                0.9999980052695652,
                0.9999982396561571
            ],
            [
                0.9999996072137998,
                0.9999997617631752,
                0.999999266179107,
                0.9999992661791944,
                0.9999987901337396,
                0.9999996940976272,
                0.9999992661788446,
                0.9999995549147889,
                0.9999994956525918,
                0.9999992661790196
            ],
            [
                0.999999266179107,
                0.9999996533674615,
                0.9999994956525917,
                0.999999266178932,
                0.9999986290424663,
                0.9999986290426298,
                0.9999994284996211,
                0.9999992661791944,
                0.9999980052702787,
                0.9999986290421395
            ],
            [
                0.9999994956524114,
                0.9999996940977001,
                0.9999992661792819,
                0.99999844650169,
                0.9999991684717741,
                0.9999990577554061,
                0.9999990577551815,
                0.9999994956524716,
                0.9999990577554061,
                0.9999989322975119
            ],
            [
                0.9999989322970028,
                0.9999982396561572,
                0.9999992661790195,
                0.999999352404893,
                0.9999994284996211,
                0.9999993524053562,
                0.9999990577549569,
                0.9999989322975119,
                0.9999977396748938,
                0.9999986290429567
            ],
            [
                0.999999057755743,
                0.999999266179107,
                0.9999993524051246,
                0.9999994284994167,
                0.9999990577554061,
                0.999999730042126,
                0.9999996940976636,
                0.999999694097773,
                0.9999996072137061,
                0.999999694097773
            ],
            [
                0.9999984465020604,
                0.9999994956525317,
                0.9999995549150542,
                0.99999862904312,
                0.9999996533673375,
                0.9999993524054335,
                0.9999990577550693,
                0.9999996072137061,
                0.9999994284996211,
                0.9999992661789321
            ],
            [
                0.9999987901341723,
                0.9999994284995529,
                0.9999995549150542,
                0.9999996533672962,
                0.999999554914842,
                0.9999996940977002,
                0.9999995549147359,
                0.999999789756684,
                0.9999991684720715,
                0.999999266179107
            ],
            [
                0.9999984465018751,
                0.9999938558253983,
                0.9999984465020603,
                0.9999977396748938,
                0.9999982396569966,
                0.9999945777823229,
                0.9999987901346049,
                0.9999967112505427,
                0.9999952149043648,
                0.9999910603047618
            ],
            [
                0.9999990577557432,
                0.999999554914842,
                0.9999980052695653,
                0.9999984465020603,
                0.9999992661787571,
                0.9999980052695655,
                0.9999991684719723,
                0.9999991684721706,
                0.9999996072137529,
                0.9999992661791945
            ],
            [
                0.9999984465020603,
                0.9999982396567867,
                0.9999986290426298,
                0.9999974387184,
                0.9999990577552939,
                0.9999982396574163,
                0.9999987901347491,
                0.9999970976876691,
                0.9999982396567868,
                0.9999984465018751
            ],
            [
                0.9999996072137061,
                0.9999994284996891,
                0.9999993524051246,
                0.9999982396559474,
                0.9999996072137061,
                0.9999994284997573,
                0.9999994284992805,
                0.999999352404893,
                0.9999997897565838,
                0.9999996072137061
            ],
            [
                0.9999993524052019,
                0.9999996533674615,
                0.9999996533674615,
                0.9999992661790195,
                0.9999996072136125,
                0.9999990577554061,
                0.999999266178757,
                0.9999993524049703,
                0.9999998362623138,
                0.9999996940976272
            ],
            [
                0.9999986290424664,
                0.9999989322968754,
                0.9999982396574163,
                0.9999990577554061,
                0.9999992661788445,
                0.9999974387168734,
                0.999996273362049,
                0.9999991684720715,
                0.99999844650169,
                0.9999987901337396
            ],
            [
                0.9999990577557432,
                0.9999995549147359,
                0.9999996940977366,
                0.9999982396572065,
                0.9999990577549569,
                0.9999996072138465,
                0.9999994284993485,
                0.9999993524052019,
                0.9999996940978095,
                0.9999994956524114
            ],
            [
                0.999999168471675,
                0.9999994284996211,
                0.999999495652712,
                0.9999994284994848,
                0.9999996072137529,
                0.9999993524053562,
                0.9999993524049703,
                0.999999730042126,
                0.9999992661791945,
                0.9999991684719723
            ],
            [
                0.9999996940977001,
                0.9999993524049703,
                0.9999994956527722,
                0.9999997300420937,
                0.9999995549150542,
                0.9999996533673788,
                0.9999993524052019,
                0.9999996533672549,
                0.9999994284992805,
                0.9999993524053562
            ],
            [
                0.9999994956524114,
                0.9999997617631752,
                0.9999986290426297,
                0.9999997897566089,
                0.9999996533674202,
                0.9999997617630332,
                0.9999992661792819,
                0.999999694097846,
                0.9999994956523514,
                0.9999996533672135
            ],
            [
                0.999999554914789,
                0.9999989322970028,
                0.9999986290424663,
                0.9999993524051246,
                0.9999982396561572,
                0.9999980052695652,
                0.9999991684720715,
                0.9999992661788445,
                0.9999984465024306,
                0.9999994284994849
            ],
            [
                0.9999991684720715,
                0.9999994284993485,
                0.9999997617630616,
                0.9999991684717742,
                0.9999994956524115,
                0.9999991684718733,
                0.9999993524050474,
                0.999999352405279,
                0.999999266179107,
                0.999999266179107
            ],
            [
                0.999999694097846,
                0.9999997300420937,
                0.9999996072138465,
                0.9999997617631183,
                0.9999994956524716,
                0.9999994956526519,
                0.99999893229713,
                0.9999996533672962,
                0.9999990577551815,
                0.9999996940976272
            ],
            [
                0.9999994284994167,
                0.9999991684715759,
                0.999998932296621,
                0.9999989322975118,
                0.999999057755743,
                0.9999986290431201,
                0.9999993524053563,
                0.9999989322968754,
                0.9999991684722698,
                0.9999993524054335
            ],
            [
                0.9999982396561572,
                0.9999990577551815,
                0.9999994956526519,
                0.9999991684717742,
                0.9999993524053562,
                0.9999989322967482,
                0.9999996072136592,
                0.9999986290427931,
                0.99999844650169,
                0.9999990577549568
            ],
            [
                0.9999994284996211,
                0.999999730042126,
                0.9999990577549568,
                0.9999996072136592,
                0.9999997617630048,
                0.9999991684718732,
                0.9999996533672136,
                0.9999996940977001,
                0.999999266178757,
                0.9999996940977731
            ],
            [
                0.9999995549150011,
                0.999999554914789,
                0.9999987901340281,
                0.9999994284994167,
                0.9999984465016899,
                0.9999987901343166,
                0.9999990577556308,
                0.999999730042319,
                0.9999989322970027,
                0.9999980052693275
            ],
            [
                0.9999991684722698,
                0.9999991684722698,
                0.9999980052705164,
                0.9999982396574163,
                0.9999991684722698,
                0.9999974387174841,
                0.9999987901347491,
                0.9999989322968754,
                0.9999991684721706,
                0.9999990577555185
            ],
            [
                0.9999992661792819,
                0.9999980052695652,
                0.9999984465016899,
                0.9999989322975119,
                0.9999993524050474,
                0.9999986290426298,
                0.9999987901338839,
                0.9999994284993485,
                0.9999984465022456,
                0.999999168471675
            ],
            [
                0.999997097686977,
                0.9999995549150011,
                0.9999994284996893,
                0.9999993524050474,
                0.9999996940978095,
                0.9999991684715759,
                0.999998239656367,
                0.9999989322973845,
                0.999998790134028,
                0.9999992661791944
            ],
            [
                0.9999989322975119,
                0.9999996072136592,
                0.9999995549147359,
                0.9999994956523514,
                0.9999996940978095,
                0.9999993524053562,
                0.999998932296621,
                0.999999266178932,
                0.9999994956525918,
                0.9999977396757023
            ],
            [
                0.9999986290432835,
                0.9999995549149481,
                0.9999993524050474,
                0.9999991684718732,
                0.9999991684716749,
                0.9999996072136125,
                0.9999996072136592,
                0.9999993524051246,
                0.9999994956525918,
                0.9999987901341724
            ],
            [
                0.999999352405279,
                0.9999994284997574,
                0.9999989322973846,
                0.9999994956524716,
                0.9999996072136125,
                0.9999993524052019,
                0.9999994956525317,
                0.9999982396565769,
                0.9999987901344607,
                0.9999991684721706
            ],
            [
                1.553498124964492e-06,
                3.726639728262097e-06,
                5.422221555069497e-06,
                4.222834954561012e-06,
                4.222834954461155e-06,
                4.785094494402695e-06,
                2.5612819053586272e-06,
                1.553497754577351e-06,
                5.422217676797111e-06,
                1.7603436329978976e-06
            ],
            [
                0.9999994284997574,
                0.9999996072137529,
                0.9999991684719725,
                0.9999993524051246,
                0.9999991684715758,
                0.9999987901341723,
                0.9999990577554061,
                0.9999991684715759,
                0.9999992661790196,
                0.9999993524053562
            ],
            [
                0.9999982396574163,
                0.9999992661791945,
                0.9999992661789321,
                0.9999994956525317,
                0.9999993524050474,
                0.9999990577551814,
                0.999999554914895,
                0.9999995549151073,
                0.9999993524052019,
                0.9999990577549569
            ],
            [
                0.9999994956525918,
                0.9999996533672136,
                0.9999992661788445,
                0.9999991684719723,
                0.999999266178932,
                0.9999994956526519,
                0.99999862904312,
                0.999999730042319,
                0.9999992661792819,
                0.9999995549150011
            ],
            [
                0.9999986290429566,
                0.9999984465015047,
                0.9999986290429567,
                0.999999266178757,
                0.9999994284996211,
                0.9999990577552939,
                0.999999266178757,
                0.9999989322966208,
                0.9999992661786695,
                0.9999992661790195
            ],
            [
                0.999999352404893,
                0.9999996072137529,
                0.9999982396572065,
                0.9999992661791944,
                0.9999994284997573,
                0.9999992661791944,
                0.9999994284992804,
                0.9999996072136125,
                0.9999996072138934,
                0.9999994956525918
            ],
            [
                0.9999984465015047,
                0.9999996072137061,
                0.9999991684719723,
                0.999999352404893,
                0.9999989322967482,
                0.9999982396559475,
                0.9999989322972572,
                0.9999989322970027,
                0.9999993524051246,
                0.999998239656577
            ],
            [
                0.9999994284992805,
                0.999998932296621,
                0.9999987901347492,
                0.9999990577552937,
                0.9999992661787571,
                0.9999992661792819,
                0.9999980052705164,
                0.999999352404893,
                0.9999995549147358,
                0.999999266179107
            ],
            [
                0.9999994284993485,
                0.999999554914842,
                0.9999996072137998,
                0.9999996940976636,
                0.9999992661787571,
                0.9999994956524114,
                0.999999352404893,
                0.9999993524050473,
                0.9999996533672549,
                0.9999993524052019
            ],
            [
                0.9999984465020604,
                0.9999984465028011,
                0.9999991684717742,
                0.9999996940976636,
                0.9999997897566589,
                0.9999997617631468,
                0.9999996072138465,
                0.9999996940978825,
                0.9999998362623137,
                0.9999994956525917
            ],
            [
                0.9999987901343165,
                0.9999989322973846,
                0.9999986290426298,
                0.9999991684715759,
                0.9999986290421395,
                0.9999982396567868,
                0.9999984465022456,
                0.9999984465022456,
                0.9999984465015047,
                0.9999986290432835
            ],
            [
                0.9999989322968754,
                0.9999990577551815,
                0.999999266178757,
                0.99999893229713,
                0.9999982396563671,
                0.9999991684715759,
                0.9999982396574163,
                0.9999989322968754,
                0.9999987901338838,
                0.9999990577549568
            ],
            [
                0.999999168471675,
                0.9999991684720715,
                0.9999990577554061,
                0.9999989322973846,
                0.9999989322972573,
                0.9999982396574163,
                0.999999266179282,
                0.9999989322970028,
                0.9999993524051246,
                0.9999986290432835
            ],
            [
                0.9999952149037947,
                0.9999986290431201,
                0.9999991684715759,
                0.9999995549150542,
                0.9999986290424664,
                0.99999893229713,
                0.9999990577550693,
                0.9999994284995529,
                0.9999990577557432,
                0.9999991684720715
            ],
            [
                0.9999996072137529,
                0.9999996072136125,
                0.9999990577551815,
                0.9999990577552939,
                0.9999994956524114,
                0.9999992661789321,
                0.9999996072136592,
                0.9999991684722698,
                0.9999996072138465,
                0.9999993524052789
            ],
            [
                0.999999266179107,
                0.9999980052700408,
                0.9999994284992805,
                0.9999990577554061,
                0.9999987901338838,
                0.9999986290429566,
                0.9999984465015047,
                0.9999989322975118,
                0.9999990577552937,
                0.9999982396559474
            ],
            [
                0.9999994956523514,
                0.9999993524052789,
                0.9999994956526519,
                0.9999990577557432,
                0.9999986290432835,
                0.9999987901337396,
                0.9999987901343166,
                0.9999989322966208,
                0.9999987901340281,
                0.9999995549151073
            ],
            [
                0.9999990577549569,
                0.999997438716568,
                0.9999987901344608,
                0.9999987901340281,
                0.99999893229713,
                0.9999990577550691,
                0.9999987901344608,
                0.9999984465022455,
                0.9999977396748939,
                0.9999987901344607
            ],
            [
                0.9999993524052018,
                0.9999986290426298,
                0.9999994956524716,
                0.9999996072136592,
                0.999999554914789,
                0.999998005270992,
                0.9999986290432835,
                0.9999984465016899,
                0.9999986290421395,
                0.9999992661790195
            ],
            [
                0.9999989322973846,
                0.9999989322973846,
                0.9999994284996211,
                0.9999987901341724,
                0.9999986290426298,
                0.9999994284995529,
                0.9999991684722698,
                0.9999995549151073,
                0.9999996072138465,
                0.9999991684718732
            ],
            [
                0.9999987901338838,
                0.9999996072138934,
                0.9999990577555185,
                0.999998790134028,
                0.9999989322975118,
                0.9999989322968754,
                0.9999982396574163,
                0.9999986290423029,
                0.9999991684719725,
                0.9999994956524715
            ],
            [
                0.9999984465018751,
                0.999998932296621,
                0.9999995549147359,
                0.9999990577552937,
                0.9999990577554061,
                0.999999653367379,
                0.9999997300422225,
                0.9999994284994849,
                0.9999989322972573,
                0.99999862904312
            ],
            [
                0.9999990577551815,
                0.9999986290424664,
                0.9999994284992805,
                0.9999994284994167,
                0.9999984465020604,
                0.9999992661791945,
                0.9999992661786696,
                0.9999991684717742,
                0.9999980052709921,
                0.999998790134028
            ],
            [
                0.9999996940977366,
                0.9999998362623332,
                0.9999992661787571,
                0.9999991684719723,
                0.9999996940977002,
                0.9999997617631468,
                0.9999996072136125,
                0.9999996940977001,
                0.9999996072137061,
                0.9999987901341724
            ],
            [
                0.9999996072137998,
                0.9999990577555185,
                0.9999996533672136,
                0.999998790134028,
                0.9999994284995529,
                0.9999994284995529,
                0.9999990577552939,
                0.9999994284992805,
                0.9999990577554061,
                0.9999990577555185
            ],
            [
                0.999999266178932,
                0.9999996940976636,
                0.9999998874647842,
                0.9999994284993485,
                0.9999989322968755,
                0.9999991684716749,
                0.9999989322972573,
                0.9999987901347491,
                0.999999266178757,
                0.9999995549149481
            ],
            [
                0.9999984465022455,
                0.9999990577555185,
                0.9999989322973846,
                0.9999986290429567,
                0.9999989322967481,
                0.9999989322971301,
                0.9999996940978095,
                0.9999990577552939,
                0.9999980052705164,
                0.9999982396561572
            ],
            [
                0.9999982396567868,
                0.9999977396762412,
                0.9999984465018752,
                0.999999352404893,
                0.9999987901341724,
                0.9999982396565769,
                0.9999984465016899,
                0.9999984465028011,
                0.9999982396572065,
                0.9999990577550691
            ],
            [
                0.9999996072136592,
                0.999999554914895,
                0.999998790134605,
                0.9999994956525317,
                0.9999992661791944,
                0.9999995549151073,
                0.999998629042303,
                0.9999989322966208,
                0.999999352405279,
                0.9999994956524114
            ],
            [
                0.9999994956524716,
                0.9999992661790195,
                0.9999984465018751,
                0.9999990577552939,
                0.9999987901347492,
                0.9999996533672135,
                0.9999986290426298,
                0.9999977396759718,
                0.9999993524053562,
                0.9999989322970027
            ],
            [
                0.9999996533672549,
                0.9999993524051246,
                0.9999997300420937,
                0.9999994284992805,
                0.999999653367379,
                0.9999997300421581,
                0.9999993524051246,
                0.9999993524049703,
                0.9999992661787571,
                0.9999995549150011
            ],
            [
                0.9999996072137061,
                0.9999996072139402,
                0.9999990577551815,
                0.9999995549150011,
                0.9999995549149481,
                0.9999997300421903,
                0.999999554914895,
                0.9999996940977002,
                0.9999989322967481,
                0.9999995549149481
            ],
            [
                0.9999991684719723,
                0.999999266179107,
                0.9999990577557432,
                0.9999986290432835,
                0.9999989322973846,
                0.9999994956524114,
                0.9999991684716749,
                0.9999991684717742,
                0.9999987901344608,
                0.9999987901344607
            ],
            [
                0.9999994956527722,
                0.999999428499553,
                0.9999991684719723,
                0.9999997300421581,
                0.9999996072136592,
                0.9999987901338838,
                0.9999986290432835,
                0.999999694097773,
                0.9999990577554061,
                0.9999984465020603
            ],
            [
                0.9999992661790195,
                0.9999996533672549,
                0.999998790134605,
                0.9999987901340281,
                0.9999987901337397,
                0.9999995549151072,
                0.9999994956526519,
                0.9999987901344608,
                0.9999991684716749,
                0.9999997617631469
            ],
            [
                0.999999352404893,
                0.9999990577557432,
                0.9999992661791071,
                0.9999992661786696,
                0.9999974387165681,
                0.9999991684721706,
                0.9999994284997573,
                0.999998005269803,
                0.9999992661787571,
                0.9999990577551815
            ],
            [
                0.9999994956526519,
                0.9999996072137998,
                0.999999352405279,
                0.9999996072139402,
                0.9999997617631752,
                0.9999996940978095,
                0.9999997617631469,
                0.999999266178757,
                0.9999996533675028,
                0.9999990577557432
            ],
            [
                0.999999266179107,
                0.999999814460876,
                0.9999984465018751,
                0.9999996940977366,
                0.9999977396754328,
                0.9999977396746245,
                0.9999997617631184,
                0.9999974387171787,
                0.9999994284994849,
                0.9999994956525918
            ],
            [
                0.9999990577556308,
                0.9999995549147359,
                0.9999996940976271,
                0.9999995549150011,
                0.9999997617631183,
                0.9999997300421903,
                0.9999986290424663,
                0.9999996072137061,
                0.999999789756684,
                0.9999997617630616
            ],
            [
                0.9999996940976271,
                0.9999994284996893,
                0.9999989322973846,
                0.9999994284996891,
                0.999999266178932,
                0.9999991684719723,
                0.9999989322968755,
                0.9999993524053563,
                0.9999997617630332,
                0.9999991684717741
            ],
            [
                0.9999990577556307,
                0.999999352405279,
                0.9999994284996891,
                0.999999352404893,
                0.9999997300422547,
                0.9999994284997573,
                0.9999994956525317,
                0.9999997300420937,
                0.999999057755743,
                0.9999994956525917
            ],
            [
                0.9999991684717742,
                0.9999989322967481,
                0.9999987901347491,
                0.999998629042303,
                0.9999994956525317,
                0.999999694097846,
                0.9999993524050474,
                0.9999994956523514,
                0.9999980052700408,
                0.9999991684717742
            ],
            [
                0.9999994284996891,
                0.9999991684717741,
                0.9999997617630049,
                0.9999994284994167,
                0.999999653367379,
                0.9999994956526519,
                0.999999814460876,
                0.999999266178757,
                0.9999990577549568,
                0.9999996072136592
            ],
            [
                0.9999994284996891,
                0.9999995549150011,
                0.9999987901344608,
                0.9999992661790196,
                0.9999996072136125,
                0.9999994956527722,
                0.9999994284994167,
                0.9999994284996891,
                0.9999986290421394,
                0.99999893229713
            ],
            [
                0.9999997617630616,
                0.9999995549151073,
                0.9999997300422547,
                0.9999987901346049,
                0.9999996072139402,
                0.999999554914895,
                0.9999989322973845,
                0.9999993524050474,
                0.9999991684717741,
                0.999999694097846
            ],
            [
                0.9999994284994849,
                0.9999996533674615,
                0.9999984465015047,
                0.9999982396567868,
                0.9999992661792819,
                0.999999057755743,
                0.9999992661787571,
                0.9999992661786696,
                0.999999554914789,
                0.9999993524051246
            ],
            [
                0.9999982396574163,
                0.9999984465020603,
                0.9999974387174841,
                0.9999967112493667,
                0.9999970976883611,
                0.9999987901347492,
                0.9999986290432834,
                0.9999987901347492,
                0.9999982396561572,
                0.9999986290424663
            ],
            [
                0.9999986290431201,
                0.9999993524054335,
                0.9999990577550691,
                0.9999991684720715,
                0.9999980052700409,
                0.9999982396569966,
                0.9999970976883609,
                0.9999991684715759,
                0.9999986290429567,
                0.9999980052695654
            ],
            [
                0.9999997617631752,
                0.9999989322966208,
                0.9999994956527121,
                0.9999991684718732,
                0.9999990577552939,
                0.9999992661788446,
                0.9999994284996211,
                0.9999987901341724,
                0.9999996940977731,
                0.999999352405279
            ],
            [
                0.9999991684718733,
                0.9999994956523514,
                0.9999994284992805,
                0.9999991684720715,
                0.999998446502616,
                0.9999994284995529,
                0.9999994284996211,
                0.9999994284996212,
                0.9999991684719723,
                0.9999984465028011
            ],
            [
                0.9999994956523514,
                0.9999993524052019,
                0.9999996072139402,
                0.9999992661791944,
                0.9999994284995529,
                0.9999994956525317,
                0.9999996533675028,
                0.9999989322970028,
                0.9999987901337396,
                0.9999993524049703
            ],
            [
                0.9999980052709919,
                0.9999984465026158,
                0.9999987901344608,
                0.9999987901341724,
                0.999998239656367,
                0.9999990577556308,
                0.9999984465028011,
                0.999996273358939,
                0.9999962733589393,
                0.9999989322968754
            ],
            [
                0.9999997617630899,
                0.9999992661791944,
                0.9999996533673375,
                0.9999992661790195,
                0.9999997897567091,
                0.9999996072138934,
                0.9999996072136592,
                0.9999991684717741,
                0.9999996940976271,
                0.9999997617630616
            ],
            [
                0.999997438717484,
                0.9999984465020603,
                0.9999991684715759,
                0.9999990577550693,
                0.999998790134605,
                0.9999994956525917,
                0.999997097687323,
                0.9999989322970028,
                0.9999987901338838,
                0.9999989322967482
            ],
            [
                0.999998239656577,
                0.9999989322971301,
                0.9999986290426298,
                0.99999893229713,
                0.9999986290432835,
                0.9999990577549569,
                0.9999982396567867,
                0.9999987901338838,
                0.9999987901343165,
                0.9999980052707542
            ],
            [
                0.9999989322968754,
                0.9999990577550693,
                0.999997438717484,
                0.9999993524052789,
                0.9999992661791071,
                0.9999987901340281,
                0.9999986290421395,
                0.9999977396746245,
                0.9999991684719725,
                0.9999992661788445
            ],
            [
                0.9999991684720715,
                0.9999995549150011,
                0.9999993524054335,
                0.9999996072136592,
                0.9999997617631752,
                0.9999997300422225,
                0.9999998362623528,
                0.9999996533673788,
                0.9999997617631468,
                0.9999994956525918
            ],
            [
                0.9999990577549568,
                0.9999994284996211,
                0.9999994956524114,
                0.9999991684715759,
                0.9999994284994167,
                0.9999992661790195,
                0.9999984465024306,
                0.9999992661792819,
                0.9999991684722697,
                0.9999974387177896
            ],
            [
                0.9999996072137061,
                0.9999982396559474,
                0.9999987901341723,
                0.9999987901346049,
                0.9999984465018752,
                0.9999982396569966,
                0.9999984465015048,
                0.999999266178757,
                0.9999992661791945,
                0.9999989322966208
            ],
            [
                0.9999995549150011,
                0.999998629042303,
                0.9999990577551815,
                0.999999352404893,
                0.9999984465016899,
                0.9999994284995529,
                0.9999993524054334,
                0.9999990577554061,
                0.9999995549148419,
                0.9999986290431201
            ],
            [
                0.9999994284996211,
                0.9999986290421394,
                0.9999991684722697,
                0.999995214905506,
                0.9999992661792819,
                0.9999984465024306,
                0.9999996072136592,
                0.9999987901341723,
                0.9999994956525917,
                0.9999977396759716
            ],
            [
                0.9999986290427931,
                0.9999991684720715,
                0.9999996533674201,
                0.9999994956527121,
                0.9999996072138934,
                0.9999995549147359,
                0.9999995549147359,
                0.9999997897567091,
                0.9999996533672962,
                0.9999997897565838
            ],
            [
                0.9999992661788446,
                0.9999989322973846,
                0.9999994956524114,
                0.999999266178932,
                0.9999992661791944,
                0.9999997300421903,
                0.9999990577551815,
                0.9999993524049703,
                0.9999995549147359,
                0.9999995549151073
            ],
            [
                0.9999991684722698,
                0.9999989322967481,
                0.999999168471675,
                0.9999984465016899,
                0.9999982396574163,
                0.9999984465026159,
                0.999998446502801,
                0.9999987901347492,
                0.9999980052693275,
                0.9999977396759717
            ],
            [
                0.999999352404893,
                0.999999653367379,
                0.999999168471675,
                0.9999986290427931,
                0.9999990577554062,
                0.9999991684721706,
                0.9999990577554062,
                0.9999990577551815,
                0.9999994956525918,
                0.9999994284994167
            ],
            [
                0.9999997300420937,
                0.9999991684717741,
                0.9999994956527121,
                0.999999554914895,
                0.9999994956525317,
                0.99999976176309,
                0.9999995549150542,
                0.9999994956524716,
                0.9999996533673788,
                0.9999993524050474
            ],
            [
                0.9999991684721706,
                0.9999990577551815,
                0.9999994956524716,
                0.9999990577557432,
                0.999999057755743,
                0.9999993524050474,
                0.9999986290429567,
                0.9999994284992805,
                0.9999991684718732,
                0.9999992661786696
            ],
            [
                0.9999982396569966,
                0.9999989322966208,
                0.9999989322968754,
                0.9999995549148419,
                0.9999974387171787,
                0.9999987901338838,
                0.9999994956525317,
                0.9999991684722698,
                0.9999991684716749,
                0.9999977396759717
            ],
            [
                0.9999989322975119,
                0.9999994284995529,
                0.9999989322967482,
                0.9999987901337396,
                0.9999995549147359,
                0.9999982396559474,
                0.9999990577552939,
                0.9999980052700407,
                0.9999994284994849,
                0.9999986290429567
            ],
            [
                0.9999994956526519,
                0.999999057755743,
                0.9999993524052789,
                0.9999987901347492,
                0.9999989322972573,
                0.9999994956523514,
                0.9999996072138465,
                0.9999986290424664,
                0.9999974387168735,
                0.9999989322968754
            ],
            [
                0.9999990577552939,
                0.9999995549151073,
                0.9999989322973846,
                0.9999991684717742,
                0.999999266178757,
                0.9999991684717741,
                0.9999994284994848,
                0.9999994284994167,
                0.9999992661786696,
                0.999999057755743
            ],
            [
                0.9999991684717741,
                0.9999994284995529,
                0.9999992661789321,
                0.9999990577555185,
                0.9999982396567868,
                0.9999987901343165,
                0.999999266179107,
                0.9999991684719723,
                0.9999982396574163,
                0.9999989322966208
            ]
        ]
    },
    {
        "q_id": "8169_mmlu_math",
        "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,
            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,
            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,
            108,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999997617629763,
                0.9999995549147889,
                0.9999997617631469,
                0.999999554914895,
                0.9999982396572065,
                0.9999990577556308,
                0.9999984465024306,
                0.9999996533675028,
                0.9999970976890532,
                0.9999994284993486
            ],
            [
                4.7850967754851966e-06,
                1.2098652508287273e-06,
                2.561281294644835e-06,
                1.2098656835136636e-06,
                3.72664017246987e-06,
                5.4222170304318e-06,
                4.785096205077381e-06,
                3.726641060658489e-06,
                1.2098653950551882e-06,
                5.715003107689177e-07
            ],
            [
                1.3007134661628471e-05,
                1.4738983721733992e-05,
                1.5534979397677313e-06,
                1.3709568799760888e-06,
                7.889260704308795e-06,
                1.994729483680993e-06,
                4.785093924251918e-06,
                1.994730434847717e-06,
                4.2228324375973415e-06,
                2.5612822106654943e-06
            ],
            [
                0.9999990577554062,
                0.9999974387165687,
                0.9999991684721706,
                0.9999986290432835,
                0.9999986290427935,
                0.9999986290426297,
                0.9999996533674202,
                0.9999974387165684,
                0.9999982396572065,
                0.999999554914842
            ],
            [
                0.999999789756684,
                0.9999998555019962,
                0.9999998555019962,
                0.9999998555020307,
                0.999999352404893,
                0.9999997617629764,
                0.9999997897567341,
                0.9999998144609644,
                0.9999999006880668,
                0.9999998144609424
            ],
            [
                0.9999974387168734,
                0.9999995549151073,
                0.9999980052702788,
                0.9999982396567868,
                0.9999996072137998,
                0.9999977396759719,
                0.9999991684718733,
                0.9999980052700409,
                0.99999893229713,
                0.9999994284996893
            ],
            [
                8.939698434966738e-06,
                4.785096776433933e-06,
                2.561283431916622e-06,
                3.726640616477725e-06,
                2.2603245672497918e-06,
                1.370956716519966e-06,
                3.288750633488963e-06,
                2.2603248367173307e-06,
                1.760342793583908e-06,
                8.315282259009745e-07
            ],
            [
                3.2887506334560605e-06,
                1.5534981249164537e-06,
                3.7266388395620047e-06,
                2.1444950965906214e-05,
                1.2098658276862581e-06,
                2.2603245672867952e-06,
                6.9622562489985925e-06,
                5.422218323019487e-06,
                2.9023133689317184e-06,
                1.473898021366358e-05
            ],
            [
                0.9999994956525918,
                0.9999986290429566,
                0.9999996940976272,
                0.9999995549148419,
                0.9999996533674202,
                0.9999996072137529,
                0.9999990577556309,
                0.999999554914895,
                0.9999998362623723,
                0.9999998362622943
            ],
            [
                0.9999986290423029,
                0.9999982396559474,
                0.9999996072137529,
                0.9999993524054335,
                0.9999990577550693,
                0.9999967112509356,
                0.9999977396765108,
                0.9999982396569967,
                0.99998852123325,
                0.9999980052698033
            ],
            [
                0.9999994956524715,
                0.9999998724809116,
                0.999999789756684,
                0.999999855502048,
                0.9999989322970027,
                0.9999994956527121,
                0.9999989322975118,
                0.9999998555019446,
                0.999999352405279,
                0.9999994284996211
            ],
            [
                0.9999991684719723,
                0.9999980052707541,
                0.9999996940977001,
                0.9999997300421903,
                0.9999989322973846,
                0.9999997617630332,
                0.9999997897567341,
                0.999999352404893,
                0.9999994956523514,
                0.9999997617630048
            ],
            [
                1.9947306726049992e-06,
                5.715005832827105e-07,
                3.2887498491620677e-06,
                8.939700566435704e-06,
                2.902312677060767e-06,
                5.422220262333096e-06,
                1.9947290080125335e-06,
                2.9023123310290063e-06,
                4.4508521110762794e-07,
                5.422221555069497e-06
            ],
            [
                5.422221554847581e-06,
                3.726639283752725e-06,
                3.288749849060371e-06,
                2.5612828212909852e-06,
                8.315283250305684e-07,
                5.422219615967477e-06,
                1.5534983101393749e-06,
                2.561283432005142e-06,
                4.22283545795623e-06,
                8.315283250305684e-07
            ],
            [
                0.9999992661789321,
                0.9999996072137529,
                0.9999998724809267,
                0.9999997617630616,
                0.9999984465016899,
                0.9999997300421903,
                0.9999995549151073,
                0.9999989322970027,
                0.9999996533672549,
                0.9999996072138465
            ],
            [
                1.0677029972745947e-06,
                2.902311293147782e-06,
                2.902312677007974e-06,
                7.889262585082652e-06,
                1.7603434231505666e-06,
                9.422445938964242e-07,
                3.4663257978465195e-07,
                1.994729483680993e-06,
                1.0677031245429291e-06,
                1.994730672439908e-06
            ],
            [
                0.9999998362622943,
                0.9999990577554061,
                0.9999993524053562,
                0.9999997300422869,
                0.9999991684719723,
                0.99999976176309,
                0.9999994284996211,
                0.9999994284994168,
                0.9999996940976636,
                0.9999997617631468
            ],
            [
                0.9999997897567091,
                0.9999993524050474,
                0.9999995549150011,
                0.999999730042126,
                0.9999994284993485,
                0.9999997617631184,
                0.9999996072138934,
                0.999999352404893,
                0.9999993524048931,
                0.9999995549147358
            ],
            [
                0.9999998144609202,
                0.999999554914895,
                0.9999997897567091,
                0.9999962733589393,
                0.9999998144608317,
                0.9999997300422547,
                0.9999997897565838,
                0.9999994956526519,
                0.9999974387165684,
                0.9999986290427931
            ],
            [
                3.2887498493983645e-06,
                4.222832941111319e-06,
                1.5534981249496567e-06,
                1.7603430034151537e-06,
                4.222834954514924e-06,
                6.962258738701267e-06,
                1.994729245842213e-06,
                2.561281905100056e-06,
                1.9947297214182054e-06,
                3.9278605979011705e-07
            ],
            [
                6.144176065828368e-06,
                4.0063696941289896e-05,
                0.00012339458912680775,
                0.999996273361161,
                0.9999921107336531,
                3.5356254926549066e-05,
                0.00012339457475817416,
                0.00010889686980913723,
                7.484621823550934e-05,
                1.0129993394314164e-05
            ],
            [
                1.2098661161789477e-06,
                1.2098662603862553e-06,
                8.315277302701984e-07,
                2.9023112929973233e-06,
                1.994729483630195e-06,
                1.3709573702722555e-06,
                8.315279285205827e-07,
                4.785092783319532e-06,
                3.4663253846316044e-07,
                1.0677029973056687e-06
            ],
            [
                0.9999994956527721,
                0.999998790134028,
                0.9999982396559475,
                0.9999992661787571,
                0.9999982396563671,
                0.999999266178757,
                0.9999994956525317,
                0.9999996072136125,
                0.9999991684722698,
                0.9999980052702785
            ],
            [
                3.2887478891487563e-06,
                5.4222209070122355e-06,
                8.31528126775552e-07,
                7.8892625849535e-06,
                6.962256249112569e-06,
                2.5612825159421147e-06,
                1.76034363298589e-06,
                1.2098653950551882e-06,
                6.144176798255599e-06,
                1.7603432132624344e-06
            ],
            [
                0.9999997617630616,
                0.9999984465024307,
                0.9999994956525317,
                0.9999990577556308,
                0.9999998555019274,
                0.9999998362622552,
                0.999999694097846,
                0.9999993524052018,
                0.9999998724809571,
                0.999999057755743
            ],
            [
                6.144176799099397e-06,
                2.2603242977802297e-06,
                0.9999852610233005,
                1.2098656835076114e-06,
                6.1441746016670885e-06,
                1.7603432132784448e-06,
                4.78509506499309e-06,
                7.889261643554814e-06,
                1.9947301969471416e-06,
                1.994729721482609e-06
            ],
            [
                0.999998239656367,
                0.999999789756684,
                0.9999996072137529,
                0.9999997617631468,
                0.9999995549149481,
                0.9999999123575464,
                0.999999855502048,
                0.9999998724808963,
                0.9999998144609423,
                0.999999554914842
            ],
            [
                0.9999993524054334,
                0.9999974387177896,
                0.9999921107383557,
                0.9999967112493667,
                0.9999982396569966,
                0.9999991684720715,
                0.9999938558268652,
                0.9999994956525317,
                0.9999987901337397,
                0.9999994284996893
            ],
            [
                1.7603438428028262e-06,
                5.422217676200406e-06,
                4.450851049941403e-07,
                2.902312677104321e-06,
                1.7603434231505666e-06,
                4.7850933534310035e-06,
                2.5612819053399912e-06,
                2.2603242978007868e-06,
                4.785096776133645e-06,
                2.2603245672497918e-06
            ],
            [
                7.889265406904397e-06,
                2.902312677060767e-06,
                4.7850950648799385e-06,
                2.9023123311055552e-06,
                1.553498495281783e-06,
                1.7603432132784448e-06,
                1.9947292458930106e-06,
                4.7850967763512445e-06,
                5.422219615967477e-06,
                6.144174601410037e-06
            ],
            [
                4.785095065093186e-06,
                4.785096205830278e-06,
                2.561282210562998e-06,
                1.5534981249397663e-06,
                1.9947299591826594e-06,
                2.2603253755476615e-06,
                1.0677026154619133e-06,
                2.561282210618905e-06,
                1.0129992183070348e-05,
                5.422218969128516e-06
            ],
            [
                6.144174601499446e-06,
                2.5612819050161955e-06,
                2.902312677084523e-06,
                7.889265406904397e-06,
                2.561281294616881e-06,
                1.5534975693601474e-06,
                2.1444945853375776e-05,
                2.902312330965655e-06,
                6.475947981860793e-07,
                4.78509563550957e-06
            ],
            [
                1.5534977545497995e-06,
                2.9023123308072772e-06,
                3.2887490653647836e-06,
                2.56128159999123e-06,
                1.994729008074216e-06,
                5.715002426439334e-07,
                1.7603440527046419e-06,
                2.902313022984344e-06,
                3.2887482811908074e-06,
                9.422450431912e-07
            ],
            [
                3.535625910878189e-05,
                4.006369217615605e-05,
                2.561282210618905e-06,
                1.8925157262578186e-05,
                8.939699500766203e-06,
                1.3007130010922344e-05,
                8.93969949923766e-06,
                3.726640616630245e-06,
                3.535624648542694e-05,
                1.4738976697229395e-05
            ],
            [
                0.9999998555019618,
                0.9999885212291443,
                0.9999999006879957,
                0.9999986290424664,
                0.9999996072137061,
                0.9999996072138466,
                0.9999999006881496,
                0.9999995549151072,
                0.9999996072139402,
                0.9999945777829701
            ],
            [
                0.9999952149049353,
                0.9999977396754328,
                0.9999990577549569,
                0.9999997617630616,
                0.9999957771645427,
                0.9999992661786696,
                0.999999266178932,
                0.9999984465020604,
                0.9999990577555185,
                0.9999994284994167
            ],
            [
                0.9999980052707549,
                0.9999998362623723,
                0.9999996940977002,
                0.9999986290427934,
                0.9999996533673788,
                0.9999984465022456,
                0.9999996072136592,
                0.9999995549147359,
                0.999999694097846,
                0.9999997617630616
            ],
            [
                1.8925141469950998e-05,
                2.5612816000331606e-06,
                3.726638839833152e-06,
                1.47389854857293e-05,
                7.889262585541864e-06,
                0.9999967112517189,
                1.6701427816728442e-05,
                5.829125857569945e-05,
                4.5397884843438604e-05,
                0.9999982396565767
            ],
            [
                2.9023126768680736e-06,
                9.422445938917108e-07,
                3.726640616630245e-06,
                9.422443692330485e-07,
                1.1478770858706246e-05,
                1.2098655392662613e-06,
                1.5534979397267575e-06,
                4.785095634460739e-06,
                2.1444945822247952e-05,
                3.2887482812506295e-06
            ],
            [
                0.9999952149066468,
                0.9999997300422869,
                0.9999938558224692,
                0.999997438717484,
                0.9999930377445859,
                0.9999993524053563,
                0.9999869928684368,
                0.9999994956525317,
                0.9999998362622747,
                0.9999990577557432
            ],
            [
                0.9999962733616052,
                0.9999957771675626,
                0.999997438717179,
                0.9999993524050474,
                0.9999996072139402,
                0.9999982396567868,
                0.9999984465015047,
                0.9999987901344608,
                0.9999990577557432,
                0.9999994956525317
            ],
            [
                0.9999997617630049,
                0.9999996072139402,
                0.9999994956527722,
                0.9999997300420939,
                0.9999996940976272,
                0.9999996533672548,
                0.9999996072139402,
                0.999999789756684,
                0.9999995549151072,
                0.9999998144608097
            ],
            [
                1.5534983101061718e-06,
                2.9023119850210436e-06,
                1.994729008056074e-06,
                1.5534979396815448e-06,
                6.962259568230874e-06,
                2.5612831265630198e-06,
                1.7603440526662173e-06,
                3.2887478889034873e-06,
                2.5612819051722694e-06,
                2.260324836696773e-06
            ],
            [
                1.994729008105057e-06,
                4.7850927830148924e-06,
                2.561281294616881e-06,
                1.553498495338299e-06,
                2.561283431888668e-06,
                1.3709578605355551e-06,
                1.9947297214182054e-06,
                2.902312677007974e-06,
                1.0677033791495609e-06,
                5.422220262264056e-06
            ],
            [
                0.9999996533674201,
                0.9999993524050474,
                0.9999994284994167,
                0.9999998144608098,
                0.9999980052695653,
                0.9999996533674202,
                0.9999994284995529,
                0.9999996072137998,
                0.9999992661791945,
                0.9999996940977001
            ],
            [
                2.5612819053586272e-06,
                1.5534973841450852e-06,
                4.785096776194573e-06,
                7.338210679949506e-07,
                1.9947304347570075e-06,
                2.902311985079115e-06,
                6.1441767987808774e-06,
                3.2887490652810324e-06,
                4.222833444429485e-06,
                6.144176797998549e-06
            ],
            [
                1.3709573702647743e-06,
                4.222835458002318e-06,
                1.760344052693435e-06,
                7.484620042097855e-05,
                2.1444940738662144e-05,
                1.892514147046736e-05,
                3.120192623972722e-05,
                3.120191136263821e-05,
                5.82912932832059e-05,
                2.1444956079218013e-05
            ],
            [
                1.7603432131375548e-06,
                1.3709570433786157e-06,
                1.012999460150437e-05,
                1.994729721482609e-06,
                1.670141985245514e-05,
                1.553498495281783e-06,
                5.043475284430694e-07,
                1.3709567165087443e-06,
                2.902313368897403e-06,
                7.889264465397747e-06
            ],
            [
                0.9999997617631752,
                0.9999996533673375,
                0.9999996072139402,
                0.9999998362622552,
                0.999999428499553,
                0.9999974387184002,
                0.9999994284996893,
                0.999999789756684,
                0.9999996533672963,
                0.999998932296621
            ],
            [
                6.962254589332388e-06,
                1.3709570433661467e-06,
                9.422447062150634e-07,
                1.99472900796355e-06,
                6.144173869379821e-06,
                4.222832941034507e-06,
                5.42221767672807e-06,
                1.370957370247318e-06,
                6.1441760654483806e-06,
                8.31528424151477e-07
            ],
            [
                2.144495095279976e-05,
                6.144177531208195e-06,
                4.785093923603471e-06,
                0.9999869928668881,
                4.22283344433731e-06,
                4.785093923690512e-06,
                0.9999852610145213,
                4.22283394762097e-06,
                2.9023109469842055e-06,
                3.288750633545794e-06
            ],
            [
                0.9999997300420937,
                0.9999994956523514,
                0.9999987901347493,
                0.9999996940977366,
                0.9999997617630333,
                0.9999998362622357,
                0.9999996940978461,
                0.9999991684722698,
                0.9999986290429569,
                0.9999989322967482
            ],
            [
                0.9999998362622746,
                0.9999991684718732,
                0.999999789756684,
                0.9999994956526519,
                0.9999989322975118,
                0.9999996072137529,
                0.9999994284994167,
                0.9999990577551815,
                0.9999997617631469,
                0.9999994956527721
            ],
            [
                2.2603242978665707e-06,
                6.962258739169842e-06,
                5.422219616026655e-06,
                1.5534973841895917e-06,
                1.1478768123551712e-05,
                3.726637951126493e-06,
                3.2887494572514376e-06,
                2.2603251061232293e-06,
                6.1441767990323395e-06,
                1.3709576970949014e-06
            ],
            [
                0.9999995549147358,
                0.9999996533674202,
                0.999999694097846,
                0.9999997300422869,
                0.9999996940976636,
                0.9999997300423191,
                0.9999967112521115,
                0.9999996940977366,
                0.9999970976890542,
                0.9999991684720715
            ],
            [
                5.715007195384861e-07,
                2.561282821239737e-06,
                2.260324028281919e-06,
                6.9622562492265485e-06,
                3.288749849000549e-06,
                2.902311984873224e-06,
                4.7850950647493785e-06,
                2.902313022952668e-06,
                2.260323758835034e-06,
                3.726637951170554e-06
            ],
            [
                0.9999986290423029,
                0.9999996533673788,
                0.9999994284995529,
                0.9999989322967482,
                0.9999996072136592,
                0.9999992661790195,
                0.9999930377462418,
                0.9999994956526519,
                0.999996711249759,
                0.9999991684722698
            ],
            [
                1.0129992185539456e-05,
                1.7603432132912532e-06,
                1.9947290081177566e-06,
                1.7603425836870455e-06,
                4.785095634356291e-06,
                6.144176798870286e-06,
                1.5534983100765009e-06,
                7.889265405849647e-06,
                3.726641061027928e-06,
                7.338207180761315e-07
            ],
            [
                5.043474081931949e-07,
                6.144175334094145e-06,
                2.9023123310290063e-06,
                2.260324028281919e-06,
                4.785095635017795e-06,
                1.0677032518578904e-06,
                1.7603438428028262e-06,
                4.785093353013212e-06,
                2.260325375572331e-06,
                1.2098658277181688e-06
            ],
            [
                0.9999992661786696,
                0.9999996940976636,
                0.9999991684720715,
                0.9999996940977731,
                0.999999352405279,
                0.9999987901343166,
                0.9999952149037954,
                0.9999989322975119,
                0.9999997897567342,
                0.9999994956525918
            ],
            [
                0.9999994956523514,
                0.9999998724809419,
                0.999999352404893,
                0.9999998362622943,
                0.9999997300421903,
                0.9999997300421903,
                0.9999998144608097,
                0.9999990577550691,
                0.9999989322970027,
                0.9999996533672135
            ],
            [
                3.726639728224814e-06,
                1.067703379154416e-06,
                3.288750633545794e-06,
                1.55349775456958e-06,
                5.422221554926484e-06,
                3.726640172503764e-06,
                6.962258739169842e-06,
                3.726639728224814e-06,
                3.2887494572514376e-06,
                3.288750633569722e-06
            ],
            [
                0.9999986290429567,
                0.9999996072136592,
                0.9999997300423191,
                0.9999993524049702,
                0.9999997897565587,
                0.999999789756684,
                0.9999996940978825,
                0.9999996533675028,
                0.9999994956525318,
                0.9999996072139402
            ],
            [
                7.889264466230069e-06,
                7.889261643382609e-06,
                1.2098655392574583e-06,
                1.1478768124324254e-05,
                1.8925152752586028e-05,
                2.4300232038197563e-05,
                6.962255419051463e-06,
                6.962254589528684e-06,
                1.3709567165461505e-06,
                3.535626334156318e-05
            ],
            [
                4.222833444506298e-06,
                2.5612834317908303e-06,
                2.902311984989368e-06,
                6.144175333635923e-06,
                3.288749065167371e-06,
                4.7850944943330625e-06,
                6.144177531599359e-06,
                1.6701419848475466e-05,
                1.670142383495587e-05,
                8.939700566801578e-06
            ],
            [
                1.7603436329978976e-06,
                3.726639728184142e-06,
                1.8925155003330605e-05,
                9.422448185187191e-07,
                3.2887498493325602e-06,
                1.5534981248712412e-06,
                6.47594875389178e-07,
                8.939695237813028e-06,
                1.3709578605455302e-06,
                2.5612834317908303e-06
            ],
            [
                0.9999991684722697,
                0.9999991684715759,
                0.9999996072139402,
                0.9999987901344608,
                0.999996273359828,
                0.9999997300420937,
                0.999999653367379,
                0.9999898700126498,
                0.9999995549151073,
                0.9999992661786696
            ],
            [
                4.785093923982095e-06,
                2.2603251062013478e-06,
                3.726637951170554e-06,
                6.962257908880483e-06,
                1.5534971989568904e-06,
                1.7603432133136672e-06,
                5.422220908314139e-06,
                3.288748673265808e-06,
                6.962257079553702e-06,
                4.222832940423847e-06
            ],
            [
                0.9999997897565838,
                0.9999993524052019,
                0.9999994284996211,
                0.9999996940977002,
                0.9999996940976636,
                0.999999694097846,
                0.9999996533673375,
                0.999999789756684,
                0.9999997617631752,
                0.999999057755743
            ],
            [
                6.475950297868629e-07,
                1.7603436329978976e-06,
                3.2887506334560605e-06,
                3.2887506333394084e-06,
                3.7266379512112265e-06,
                2.9023109471452223e-06,
                1.3709572068272963e-06,
                3.7266397280960194e-06,
                9.422450431860582e-07,
                1.994730434847717e-06
            ],
            [
                1.9947306726049992e-06,
                4.222832437386106e-06,
                6.962259569313662e-06,
                6.144176797864436e-06,
                2.561282515988704e-06,
                2.90231163910023e-06,
                6.1441767987808774e-06,
                4.222833947282995e-06,
                6.144174600024198e-06,
                3.7266410609160796e-06
            ],
            [
                3.2887478889513447e-06,
                8.315282258590015e-07,
                1.760343423160973e-06,
                1.3709567164663505e-06,
                9.422443692330485e-07,
                1.5534971989568904e-06,
                4.222833443968609e-06,
                9.422443692261927e-07,
                1.7603432132784448e-06,
                1.3709567165386693e-06
            ],
            [
                4.785096774693134e-06,
                1.370957697068717e-06,
                1.2098655392662613e-06,
                3.2887478888496478e-06,
                1.7603432132784448e-06,
                1.9947304347098384e-06,
                3.726639283901856e-06,
                3.288747889038086e-06,
                1.7603425837062577e-06,
                3.2887502414436403e-06
            ],
            [
                5.144221364340114e-05,
                3.535624649172935e-05,
                4.5397890289724144e-05,
                5.829127937441555e-05,
                3.2887482812745586e-06,
                1.670142183934597e-05,
                2.1444950968441685e-05,
                2.561283431916622e-06,
                2.430023781904283e-05,
                1.473898899664279e-05
            ],
            [
                2.5612822106841303e-06,
                1.2098662603862553e-06,
                6.962257079275089e-06,
                3.72664061671159e-06,
                6.144176066353646e-06,
                1.760343842833246e-06,
                2.430024941459533e-05,
                1.0677031245905116e-06,
                2.2603248367173307e-06,
                1.5534973841705173e-06
            ],
            [
                0.9999898700053994,
                0.9999993524054335,
                0.9999980052695652,
                0.9999898700066067,
                0.9999996940976636,
                0.9999982396567867,
                0.9999997617631468,
                0.9999967112505427,
                0.9999967112497589,
                0.9999984465026158
            ],
            [
                0.9999996533675028,
                0.9999996533672962,
                0.9999997617630616,
                0.9999996533673375,
                0.9999991684716749,
                0.9999998724809419,
                0.999999730042126,
                0.999999730042319,
                0.9999996940977731,
                0.9999996072138465
            ],
            [
                0.9999991684718732,
                0.9999957771660524,
                0.9999987901346049,
                0.9999998874648379,
                0.999999900688043,
                0.999999554915001,
                0.9999997300421581,
                0.9999991684715759,
                0.9999997300420939,
                0.9999986290432835
            ],
            [
                1.9947304348332037e-06,
                1.067702615417244e-06,
                2.5612834320214477e-06,
                2.5612819053586272e-06,
                3.7266388392671313e-06,
                7.889260703906985e-06,
                1.7603432132464244e-06,
                1.3709568799243436e-06,
                8.315280276399315e-07,
                3.2887502414436403e-06
            ],
            [
                0.9999991684715759,
                0.9999997617630048,
                0.9999996072139402,
                0.9999990577551815,
                0.9999986290431202,
                0.9999987901344608,
                0.9999989322967481,
                0.99999976176309,
                0.9999982396569966,
                0.9999970976883611
            ],
            [
                7.889263525405172e-06,
                1.76034363298589e-06,
                3.2887494573561262e-06,
                2.9023123311055552e-06,
                4.78509563546605e-06,
                2.561282515914161e-06,
                2.260324028404236e-06,
                2.2603237589676295e-06,
                9.422448185478557e-07,
                4.785096205830278e-06
            ],
            [
                0.999998629042303,
                0.9999980052702786,
                0.9999992661790195,
                0.9999952149066491,
                0.9999998555020307,
                0.999999352404893,
                0.9999989322973846,
                0.9999999226557869,
                0.999999352404893,
                0.9999982396561573
            ],
            [
                1.2098652508391807e-06,
                3.726639728224814e-06,
                5.043476486902204e-07,
                2.561281294644835e-06,
                1.7603438428188364e-06,
                1.012998977108606e-05,
                8.3152792852928e-07,
                2.902313023063532e-06,
                1.3709570433536782e-06,
                8.939699498587217e-06
            ],
            [
                0.9999967112509354,
                0.999999266178757,
                0.9999994956524716,
                0.9999994284997574,
                0.9999980052707544,
                0.9999994956525317,
                0.999999730042126,
                0.9999992661787571,
                0.9999970976880159,
                0.9999984465015048
            ],
            [
                6.144173136885882e-06,
                8.939700565996655e-06,
                6.144175332887123e-06,
                3.288750241410738e-06,
                6.962259568775433e-06,
                3.288749849000549e-06,
                4.22283294098842e-06,
                5.422217676397663e-06,
                2.260325105981383e-06,
                2.2603248365014775e-06
            ],
            [
                2.260324297853209e-06,
                1.7603438427852151e-06,
                1.2098658277082653e-06,
                4.7850944945245504e-06,
                6.962257078553231e-06,
                5.715004470129334e-07,
                1.2098662603862553e-06,
                7.338208930355202e-07,
                8.315283250150648e-07,
                1.2098653949842147e-06
            ],
            [
                0.9999987901341723,
                0.9999997617629764,
                0.9999996533673788,
                0.9999994956524716,
                0.9999996533674615,
                0.9999994284993486,
                0.9999991684722698,
                0.9999995549150011,
                0.9999996940978825,
                0.9999993524054335
            ],
            [
                0.9999945777810317,
                0.999903897596873,
                0.9999980052707541,
                0.9947798731892694,
                0.9924227579127431,
                0.9999930377429219,
                0.9999898700041931,
                0.999994577780386,
                0.9953904288867915,
                0.9999984465020603
            ],
            [
                2.561283431942246e-06,
                1.994729008074216e-06,
                3.726638395527247e-06,
                1.7603425837606927e-06,
                8.315282259051341e-07,
                2.902311985079115e-06,
                1.994729959270648e-06,
                3.2887486732358968e-06,
                5.422218969217281e-06,
                1.0677033791495609e-06
            ],
            [
                1.9947292458930106e-06,
                6.144173868781898e-06,
                3.2887478891487563e-06,
                6.144173868983067e-06,
                3.7266388397721442e-06,
                4.5397863224112544e-05,
                1.3709576971316842e-06,
                1.7603438427467903e-06,
                3.535626334156318e-05,
                2.1444953513707305e-05
            ],
            [
                0.999998932297512,
                0.9999994956524114,
                0.9999984465015048,
                0.9999986290429568,
                0.9999994956527722,
                0.9999977396765108,
                0.9999998362622357,
                0.9999995549149481,
                0.9999997300421581,
                0.9999980052700412
            ],
            [
                0.9999995549150011,
                0.9999984465020607,
                0.9999996072136125,
                0.9999997617630616,
                0.9999986290429568,
                0.9999997897567091,
                0.9999987901343165,
                0.9999998362623723,
                0.9999996940976636,
                0.9999996072136593
            ],
            [
                0.9999993524048931,
                0.9999987901341723,
                0.9999984465020605,
                0.9999993524054334,
                0.999997097688361,
                0.9999997617631752,
                0.9999994284995529,
                0.9999990577557432,
                0.9999993524049703,
                0.9999980052709921
            ],
            [
                1.9947304348703948e-06,
                1.3709575336947905e-06,
                4.78509563555309e-06,
                1.7603432133032607e-06,
                6.475946437996402e-07,
                1.5534979396815448e-06,
                1.2098658277335738e-06,
                5.422217030288788e-06,
                1.0677024881887838e-06,
                8.939695237666677e-06
            ],
            [
                1.5534984953199313e-06,
                3.726640616748873e-06,
                3.726640172503764e-06,
                1.7603430034439723e-06,
                6.962259568775433e-06,
                3.726640172503764e-06,
                8.93969949923766e-06,
                1.9947299592824403e-06,
                1.7603425837606927e-06,
                1.5534975693792215e-06
            ],
            [
                1.2098661161927025e-06,
                2.5612819053399912e-06,
                4.785092782936557e-06,
                2.2603237589028734e-06,
                2.260325375572331e-06,
                2.5612819053399912e-06,
                3.2887506334560605e-06,
                6.9622570786798724e-06,
                1.2098656835076114e-06,
                2.5612812945260317e-06
            ],
            [
                0.999999730042319,
                0.9999994956525318,
                0.9999998144608981,
                0.9999995549150011,
                0.999999730042126,
                0.9999994284994167,
                0.999999352405279,
                0.9999997300422547,
                0.9999993524054335,
                0.9999989322970028
            ],
            [
                1.7603430034151537e-06,
                3.2887498494551953e-06,
                4.22283394786293e-06,
                1.7603440527046419e-06,
                3.288748280891699e-06,
                6.144176797864436e-06,
                4.7850927830845245e-06,
                5.422220908762902e-06,
                6.144176066521288e-06,
                8.315284241560147e-07
            ],
            [
                1.3709576971061233e-06,
                9.422450431732037e-07,
                1.0677032518700286e-06,
                1.0677024881761599e-06,
                1.76034300345598e-06,
                1.5534973841705173e-06,
                6.47594566597747e-07,
                3.288749456838667e-06,
                1.760343213227212e-06,
                1.209866116170145e-06
            ],
            [
                0.9999989322967482,
                0.9999991684721706,
                0.9999996533672962,
                0.9999977396762414,
                0.9999982396565772,
                0.999999554914895,
                0.9999986290424664,
                0.9999970976869773,
                0.9999989322970027,
                0.999996711249368
            ],
            [
                0.9999996940976636,
                0.9999994956527121,
                0.9999996533674201,
                0.9999991684722697,
                0.9999997617631752,
                0.9999996940976271,
                0.9999977396751634,
                0.9999989322968754,
                0.999999900688043,
                0.9999998724809115
            ],
            [
                0.9999994956525918,
                0.9999996072137529,
                0.9999977396751634,
                0.999999694097846,
                0.9999996940977731,
                0.9999977396751635,
                0.9999995549147359,
                0.999999653367503,
                0.9999998555020307,
                0.999999495652652
            ],
            [
                1.2098662604247682e-06,
                7.338212429537553e-07,
                8.93969736942758e-06,
                3.2887478891128633e-06,
                6.9622537593854575e-06,
                2.9023130228444433e-06,
                3.2887490653109436e-06,
                1.760344052714248e-06,
                2.5612819053586272e-06,
                5.422220908703723e-06
            ],
            [
                1.5534971989809095e-06,
                4.785094494185095e-06,
                2.2603245673279107e-06,
                2.5612819053586272e-06,
                2.5612819053166966e-06,
                3.288750241500471e-06,
                1.7603434231385591e-06,
                2.260323758939877e-06,
                2.9023116390104826e-06,
                5.422221555192784e-06
            ],
            [
                3.2887502414436403e-06,
                1.0677032518501217e-06,
                1.0677028700203557e-06,
                6.962257909007124e-06,
                5.71500242637956e-07,
                3.7266406167827664e-06,
                3.2887498489407274e-06,
                1.3709576970824327e-06,
                1.0129989771823107e-05,
                4.222835457664342e-06
            ],
            [
                4.222832437639588e-06,
                1.7603427936079236e-06,
                3.2887494573232236e-06,
                3.7266410608720178e-06,
                3.2887490653647836e-06,
                1.5534975693792215e-06,
                4.222835458002318e-06,
                5.422217676866151e-06,
                6.144176066264237e-06,
                1.3709578605455302e-06
            ],
            [
                1.0677024881761599e-06,
                4.222832941072913e-06,
                6.14417753110761e-06,
                2.5612831266946347e-06,
                1.01299946023704e-05,
                6.475947981904966e-07,
                7.889262585642319e-06,
                2.9023109465275493e-06,
                2.2603251060738913e-06,
                1.370957697068717e-06
            ],
            [
                0.999999266178757,
                0.9999996940977366,
                0.999999352404893,
                0.9999993524049702,
                0.9999994956524114,
                0.9999996072136592,
                0.9999997300423191,
                0.999999814460854,
                0.9999990577554062,
                0.9999995549147358
            ],
            [
                0.9999984465016899,
                0.9999994284994849,
                0.9999977396759717,
                0.9999989322972572,
                0.9999982396559475,
                0.9999984465015047,
                0.9999993524052019,
                0.9999996072137061,
                0.9999992661788445,
                0.999998790134028
            ],
            [
                5.422220908481809e-06,
                5.422220908481809e-06,
                2.260324028404236e-06,
                5.422220262333096e-06,
                2.260324836651547e-06,
                2.9023109470554753e-06,
                2.561282210701601e-06,
                2.9023112931688987e-06,
                2.2603242977802297e-06,
                2.9023123306594577e-06
            ],
            [
                0.9999994956527721,
                0.9999987901344608,
                0.9999996533673375,
                0.9999994284995529,
                0.9999998144608098,
                0.999999789756634,
                0.9999994284995529,
                0.9999996940976636,
                0.9999996533673375,
                0.9999997617630332
            ],
            [
                1.3709578605455302e-06,
                2.5612828213352452e-06,
                1.5534984953298217e-06,
                1.9947299592824403e-06,
                7.338213304283347e-07,
                1.2098662604126641e-06,
                3.726638839806038e-06,
                2.2603248366762157e-06,
                5.4222170304318e-06,
                1.3709576971242028e-06
            ],
            [
                0.9999995549147889,
                0.9999977396751637,
                0.9999994284994167,
                0.9999998144609423,
                0.999999789756684,
                0.9999980052705167,
                0.9999994956523514,
                0.9999991684717742,
                0.9999984465024309,
                0.9999996533672135
            ],
            [
                1.0677029972833341e-06,
                3.7266406168403854e-06,
                1.7603432132912532e-06,
                2.561282210460501e-06,
                1.994729721436347e-06,
                6.1441738691562974e-06,
                3.726640616748873e-06,
                2.9023112930659533e-06,
                2.260325375650449e-06,
                5.422218969661113e-06
            ],
            [
                1.300713311517055e-05,
                1.4738978456398127e-05,
                6.144172404587612e-06,
                1.4738976699106073e-05,
                1.3007134664822509e-05,
                6.6052121039017e-05,
                7.889259761905808e-06,
                1.473898899664279e-05,
                6.60521210438226e-05,
                9.61024148597335e-05
            ],
            [
                1.1478766757237902e-05,
                3.7266383952696564e-06,
                2.902312677084523e-06,
                3.927860597935108e-07,
                4.222834451012227e-06,
                3.2887502413389517e-06,
                1.7603430034311638e-06,
                1.7603436330091044e-06,
                1.3709572068079696e-06,
                4.785093353787868e-06
            ],
            [
                1.8925143715978147e-05,
                6.475951069896949e-07,
                7.338213304016384e-07,
                1.2098656834723998e-06,
                5.715006513952608e-07,
                6.475947981695877e-07,
                5.043474683156057e-07,
                5.715003107353922e-07,
                5.04347227807199e-07,
                1.2098659719601033e-06
            ],
            [
                2.1444943298944354e-05,
                1.4738985472887472e-05,
                1.9947290080343035e-06,
                1.5534979397394734e-06,
                4.222832437324657e-06,
                1.1478768123823146e-05,
                3.2887478886821466e-06,
                1.892514372479069e-05,
                3.726640616630245e-06,
                1.1478770859624945e-05
            ],
            [
                0.9999546021422047,
                0.999998629042303,
                0.9999990577551815,
                0.9999977396765105,
                0.9999417087554167,
                0.9999974387187053,
                0.9999930377420908,
                0.99999862904312,
                0.9999952149066461,
                0.9999957771665555
            ],
            [
                0.9999485577925504,
                0.9999994284994167,
                0.9999989322968754,
                0.9999921107345942,
                0.9999993524053562,
                0.9999980052702786,
                0.9999990577552939,
                0.9999977396762411,
                0.9999986290424664,
                0.999999266178932
            ],
            [
                3.7266397281434697e-06,
                2.5612825159677387e-06,
                2.260323489435463e-06,
                3.726638395527247e-06,
                1.067703379136937e-06,
                2.902311639073834e-06,
                1.2098659719524008e-06,
                1.300713001414004e-05,
                1.76034300345598e-06,
                6.144172403470001e-06
            ],
            [
                0.9999987901341724,
                0.9999997617630049,
                0.9999998144608317,
                0.9999996533675028,
                0.9999987901341724,
                0.9999984465020604,
                0.999999789756634,
                0.9999990577555186,
                0.9999998144609645,
                0.9999996533672136
            ],
            [
                4.222831934248571e-06,
                1.3709568799760888e-06,
                6.962257908196617e-06,
                2.260324028306588e-06,
                1.99473067264854e-06,
                6.475950297942253e-07,
                2.5612819053399912e-06,
                1.3709573702566696e-06,
                2.2603251061849014e-06,
                3.2887482811220126e-06
            ]
        ]
    },
    {
        "q_id": "8240_mmlu_math",
        "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": [
            [
                0.9999151889287085,
                0.9999339478555221,
                0.9999687980886474,
                0.9999339478239984,
                0.9999785550567073,
                0.9999038975854193,
                0.9999485577802684,
                0.9999646437577614,
                0.9999339478792325,
                0.9999599363031091
            ],
            [
                0.9999832985821441,
                0.9999810748585432,
                0.9999724643089352,
                0.9999485577618665,
                0.9998204720350075,
                0.9999546021259874,
                0.9999546021260088,
                0.9999599363221628,
                0.9999756997563912,
                0.9999921107383558
            ],
            [
                0.9999646437619848,
                0.9993736658293936,
                0.9999885212277715,
                0.9999646437409018,
                0.999959936317424,
                0.9999546021422393,
                0.999903897551009,
                0.9999339478318973,
                0.9997694932314665,
                0.999925153790837
            ],
            [
                0.9999485577986563,
                0.9999251537907063,
                0.9999599363078501,
                0.999876605381635,
                0.9994472214528941,
                0.9999251537639581,
                0.9999646437493162,
                0.9999724643121954,
                0.9999251537371462,
                0.9999646437366672
            ],
            [
                0.9995121427693617,
                0.9997388095678367,
                0.9999038975623312,
                0.9997694932861627,
                0.9998911030910874,
                0.999876605396282,
                0.9993736657614065,
                0.9998911030388326,
                0.999876605425872,
                0.9998601779596027
            ],
            [
                0.9997965729553349,
                0.9984988177683908,
                0.9998601779099126,
                0.9978172833614519,
                0.9999485577741295,
                0.9999599362982967,
                0.9997040427619297,
                0.9995694429663222,
                0.999903897596799,
                0.9998911030650431
            ],
            [
                4.222833444506298e-06,
                1.3007123810638006e-05,
                2.2603234894560207e-06,
                1.14787708624228e-05,
                7.889263525534328e-06,
                1.3007133115667397e-05,
                5.4222215552470286e-06,
                2.561282821352716e-06,
                7.889259763857458e-06,
                7.889263525778283e-06
            ],
            [
                0.9999962733611603,
                0.9993736658427286,
                0.9999869928730917,
                0.999903897551097,
                0.9999785550490391,
                0.9999599362983455,
                0.9997694933426162,
                0.9999546021422423,
                0.9999417087206486,
                0.9999251537550228
            ],
            [
                0.9998204719922227,
                0.9999485577987188,
                0.9999852610145213,
                0.9999724642958271,
                0.9999687980961307,
                0.999925153790837,
                0.9994472213330085,
                0.9999485577742627,
                0.9999785550413764,
                0.9997040428325394
            ],
            [
                0.9999546021314762,
                0.9999339478555087,
                0.9995121428856759,
                0.9999485577986821,
                0.9997040429727341,
                0.9999546021476443,
                0.9999687980998099,
                0.999959936317406,
                0.9995694429674871,
                0.9999599362935236
            ],
            [
                0.999820472077907,
                0.9998766054695308,
                0.9999599363126515,
                0.9994472213275094,
                0.9997040429746284,
                0.9997040427978546,
                0.9999724643056483,
                0.9999151889487421,
                0.9997040427972863,
                0.9999251537462013
            ],
            [
                1.9947306726358406e-06,
                1.0129995809597604e-05,
                1.8925145980181433e-05,
                5.422221555133606e-06,
                6.1441775309064404e-06,
                1.670142781520948e-05,
                2.1444945854624007e-05,
                0.9998415637086137,
                1.0129994601872894e-05,
                1.1478772229989872e-05
            ],
            [
                0.9997388096924633,
                0.9999599363221815,
                0.9998601779430528,
                0.999891103077925,
                0.9997694933160696,
                0.9997040427626014,
                0.9998415638412173,
                0.9997388097864939,
                0.9997965730766273,
                0.999959936317406
            ],
            [
                0.9999832985841359,
                0.9999251537910264,
                0.9999251537373134,
                0.9999724643089206,
                0.9999646437493241,
                0.9999339478791008,
                0.9999339478397765,
                0.9999546021314331,
                0.9999151889790573,
                0.9993736659089303
            ],
            [
                0.9999485577619656,
                0.9999417087207083,
                0.9999687980737751,
                0.9999869928684394,
                0.999925153790854,
                0.9999646437619778,
                0.9999339478790884,
                0.9999646437535384,
                0.9999485577618773,
                0.9999646437577681
            ],
            [
                0.9999151889488396,
                0.999820472055611,
                0.999948557768061,
                0.9999599362887661,
                0.9999485577679982,
                0.9999756997621758,
                0.9999417087346201,
                0.999891103065238,
                0.9999724642958047,
                0.9999724643154906
            ],
            [
                0.999891103078139,
                0.9998911030395091,
                0.9999038975624739,
                0.9994472213978716,
                0.9997694933141648,
                0.9999038975395299,
                0.9998415638215978,
                0.9999038975394349,
                0.9999038975738438,
                0.9996646497384523
            ],
            [
                0.9999151889487421,
                0.9998911031040357,
                0.999569442968176,
                0.9999339478553996,
                0.9999417087206302,
                0.9999038976196352,
                0.9998766054698289,
                0.999903897585285,
                0.9998766053814806,
                0.9999599362887558
            ],
            [
                0.9999646437535344,
                0.999959936317424,
                0.9999646437367007,
                0.9999832985761689,
                0.9999785550541535,
                0.9999724643089335,
                0.9999251537373303,
                0.9993736658289927,
                0.999968798088666,
                0.9999151889792061
            ],
            [
                0.9999339478554956,
                0.9999756997651024,
                0.9999546021314264,
                0.9999756997592939,
                0.9999599363078678,
                0.999948557804886,
                0.9998911030912252,
                0.9999646437409081,
                0.999941708748489,
                0.9999646437535449
            ],
            [
                0.9999646437451076,
                0.9998601779098658,
                0.999948557780272,
                0.9999724642957943,
                0.9999785550490348,
                0.9999852610145168,
                0.9999038975853451,
                0.9999485577680239,
                0.9999869928668871,
                0.9999756997505913
            ],
            [
                0.9999417087553785,
                0.9999417087414969,
                0.9999546021368159,
                0.9999485577803241,
                0.9997388095989572,
                0.9999810748427413,
                0.9999151889184954,
                0.9999756997476907,
                0.9999724643154788,
                0.9999599363174355
            ],
            [
                0.9999785550592607,
                0.9999898700041909,
                0.9999756997621856,
                0.999972464312192,
                0.9999785550567065,
                0.999860177976541,
                0.9999417087136692,
                0.9999910603036963,
                0.9999756997679753,
                0.9999485577802911
            ],
            [
                1.4738985482351282e-05,
                2.9023123311055552e-06,
                1.1478770861211786e-05,
                6.962254589433702e-06,
                1.4738988998117324e-05,
                5.144221359998557e-05,
                2.4300243627117176e-05,
                4.222834954687752e-06,
                1.3007128463069061e-05,
                0.9995694428677969
            ],
            [
                2.4300243626409964e-05,
                6.962258739454786e-06,
                0.9997694933697665,
                1.8925148236674017e-05,
                6.144176798870286e-06,
                2.144495351940237e-05,
                4.785092783415276e-06,
                7.889263525778283e-06,
                1.0129988564264954e-05,
                2.5612828212909852e-06
            ],
            [
                0.9998415638023241,
                0.9997388097853083,
                0.9999945777784451,
                0.9999724643187611,
                0.9953904276347412,
                0.9996646498128179,
                0.9999952149055052,
                0.9999869928653368,
                0.9998204720149917,
                0.9999785550464939
            ],
            [
                0.9999251537552504,
                0.999954602136907,
                0.9999546021422833,
                0.9999417087345085,
                0.999948557786439,
                0.9999417087276253,
                0.9997965729557197,
                0.9999417087137051,
                0.9998204720135786,
                0.9999038975968102
            ],
            [
                1.1478765388711023e-05,
                1.994729959270648e-06,
                5.144223812641715e-05,
                1.3007130013856124e-05,
                3.120191135560069e-05,
                2.4300234929636645e-05,
                2.9023116391477434e-06,
                1.1478765388523107e-05,
                5.422217676797111e-06,
                3.120192252437034e-05
            ],
            [
                0.9998766054106738,
                0.9999151889183534,
                0.9999038975623424,
                0.9998204720991113,
                0.9998204719490306,
                0.9999251537907135,
                0.9999038975853451,
                0.999925153799634,
                0.9992903297180903,
                0.9998601779265763
            ],
            [
                8.9396941718352e-06,
                1.3007123812057577e-05,
                2.4300234929636645e-05,
                8.939700566143004e-06,
                2.430024362393472e-05,
                1.1478768123280277e-05,
                2.1444956079218013e-05,
                2.7535694373763664e-05,
                1.4738978456049602e-05,
                1.1478768124992398e-05
            ],
            [
                1.012999580884213e-05,
                1.0129990978847043e-05,
                2.7535697652678035e-05,
                1.1478772229989872e-05,
                7.88926258532661e-06,
                1.670142582300158e-05,
                6.144173136952939e-06,
                6.962253759670401e-06,
                1.4738987240824012e-05,
                4.7850967763512445e-06
            ],
            [
                0.9999756997650809,
                0.99998699287154,
                0.99997569975639,
                0.999941708734578,
                0.9999546021477134,
                0.9999339478713157,
                0.9999599363221651,
                0.9999687980960907,
                0.9999646437367081,
                0.9999251537908627
            ],
            [
                0.9997694933132257,
                0.9993736659787389,
                0.9999339478554577,
                0.9999251537818761,
                0.9997694933138026,
                0.9999785550413746,
                0.999860177859604,
                0.9999974387184,
                0.9999756997505892,
                0.9984988176390875
            ],
            [
                0.9989677688403207,
                0.9994472213350988,
                0.9999038975509362,
                0.9989677689577232,
                0.9994472213981932,
                0.9999251537641264,
                0.9999151889386154,
                0.9997694933410333,
                0.9998766054696763,
                0.9999339478319247
            ],
            [
                0.9999151889790302,
                0.9999038975394474,
                0.9998415638025732,
                0.9994472213344556,
                0.9998911031299929,
                0.9995694429163081,
                0.999903897539506,
                0.999891103117,
                0.9998415638216555,
                0.9999485577987188
            ],
            [
                0.9999546021260055,
                0.9997388096932918,
                0.9998601779596922,
                0.9999417087276202,
                0.999903897596799,
                0.9998911031302559,
                0.9999251537372883,
                0.9999599363078431,
                0.9999251537731091,
                0.9999038975852388
            ],
            [
                0.9995694429143667,
                0.9998766054108534,
                0.9999546021422182,
                0.9999646437493123,
                0.9992903294708295,
                0.9998601778765159,
                0.9998601779599973,
                0.9999151889284437,
                0.9999339478317756,
                0.9999151889387017
            ],
            [
                0.9999599363078577,
                0.9999724643089131,
                0.999959936322208,
                0.9999832985741794,
                0.9999417087206302,
                0.9999832985761693,
                0.9999251537552057,
                0.9999251537729632,
                0.9998601778928216,
                0.9999038976197051
            ],
            [
                1.1478773598538445e-05,
                2.561281905293402e-06,
                3.535624226936835e-05,
                1.4738985484871391e-05,
                6.605216029362855e-05,
                1.0129992186589747e-05,
                1.892515049199645e-05,
                1.47389819699641e-05,
                1.4738981970312625e-05,
                1.8925141465820123e-05
            ],
            [
                0.9999485577742014,
                0.9999251537728793,
                0.9984988174026423,
                0.9998601779433823,
                0.9999810748517738,
                0.9999038975623312,
                0.999925153746234,
                0.9999151889891112,
                0.999915188948705,
                0.9997388097245643
            ],
            [
                1.8925155006118952e-05,
                1.4738980213341866e-05,
                2.7535687801010546e-05,
                4.785093924156175e-06,
                7.88926164518358e-06,
                1.3007126911974612e-05,
                2.144495607789177e-05,
                1.4738976699427788e-05,
                5.422217030614265e-06,
                3.7266388395620047e-06
            ],
            [
                0.9993736659097318,
                0.9999687980923834,
                0.9999339478554895,
                0.9999546021206174,
                0.9995121427699861,
                0.9999646437451076,
                0.9997388095695922,
                0.999860177959625,
                0.9999251537996939,
                0.9995694428602566
            ],
            [
                0.9999599363126231,
                0.9999417087276151,
                0.9999724643122083,
                0.9999546021098057,
                0.9999485577619656,
                0.9999869928699877,
                0.9996646498543424,
                0.9999646437408912,
                0.9996646498530056,
                0.9999546021368217
            ],
            [
                0.9998911030910731,
                0.9999599362935213,
                0.9999417087276351,
                0.9999687980849468,
                0.999769493369458,
                0.9999599363222107,
                0.9999646437409061,
                0.9999646437324796,
                0.999964643753547,
                0.9999832985781628
            ],
            [
                0.9998204720135028,
                0.9993736659085295,
                0.9999485577741333,
                0.9999810748562833,
                0.9998911030652063,
                0.9999546021260118,
                0.9999724643023631,
                0.9999546021476734,
                0.9995121427744423,
                0.999941708727689
            ],
            [
                0.9999724643089233,
                0.9998911030649876,
                0.9998601779263667,
                0.9998601778610382,
                0.9999038975968478,
                0.9999339478240112,
                0.9999038975510327,
                0.99929032954637,
                0.9993736657557956,
                0.9999599362935121
            ],
            [
                0.9999485578048176,
                0.9999485577925429,
                0.9998766054695848,
                0.9997694933406309,
                0.9999151889284529,
                0.9999599363078626,
                0.9991959138767442,
                0.9997694933688542,
                0.9999485577802795,
                0.9999646437577273
            ],
            [
                2.90231094702116e-06,
                4.22283193393364e-06,
                1.3007130013856124e-05,
                5.422218969306048e-06,
                3.2887482811908074e-06,
                6.144172404129392e-06,
                3.726639284017094e-06,
                1.0129988563343644e-05,
                4.222834450743383e-06,
                1.6701417858577338e-05
            ],
            [
                0.9999251537372034,
                0.9999785550413712,
                0.9999869928699883,
                0.999948557761856,
                0.9999810748585312,
                0.9999646437535178,
                0.9999852610180298,
                0.9999724643154692,
                0.9999756997534777,
                0.9999599363221943
            ],
            [
                0.9999646437451273,
                0.9999724643023497,
                0.9999646437619555,
                0.9999417087067868,
                0.9999485577619084,
                0.9995694429149428,
                0.9999251537461851,
                0.9999832985701973,
                0.99995993630786,
                0.9999038975739151
            ],
            [
                6.962254589332388e-06,
                8.939697368842181e-06,
                1.473898372500477e-05,
                0.9998601779265763,
                1.0129995807699706e-05,
                0.9998415637461053,
                3.1201926243586504e-05,
                6.962258739454786e-06,
                2.1444953523537147e-05,
                3.120191508446373e-05
            ],
            [
                0.9999546021422556,
                0.9999339478555707,
                0.9999417087207643,
                0.9999417087276458,
                0.9999646437366672,
                0.9998204720346757,
                0.9999785550541526,
                0.9999546021151928,
                0.999948557774238,
                0.9999485577619253
            ],
            [
                1.3007123812317831e-05,
                0.9991959139075164,
                1.4738976699749503e-05,
                1.1478769492392108e-05,
                5.144220135417782e-05,
                7.889262585082652e-06,
                1.4738976699427788e-05,
                3.726640172385136e-06,
                2.1444945853999886e-05,
                6.605212884908979e-05
            ],
            [
                0.9999599363221995,
                0.999959936317411,
                0.9999546021314075,
                0.9999339478397121,
                0.9999832985841328,
                0.999972464295784,
                0.9998601779095931,
                0.999948557780254,
                0.9999151889386061,
                0.9998415638218352
            ],
            [
                0.9997694933428107,
                0.9999910603068956,
                0.9999485577619125,
                0.9999151889691188,
                0.9999724643089275,
                0.9999339478633125,
                0.9999646437408953,
                0.9999756997506082,
                0.999941708755437,
                0.9999646437451117
            ],
            [
                6.962257079629686e-06,
                2.4300243620398656e-05,
                7.88925976359915e-06,
                1.0129990979031306e-05,
                1.3007134665934505e-05,
                5.422219616085833e-06,
                3.535625912190121e-05,
                1.3007123807727885e-05,
                7.889266347356409e-06,
                1.3007126911974612e-05
            ],
            [
                0.9999485577864229,
                0.9999546021260118,
                0.9999485577680239,
                0.9997694933133399,
                0.9999151889690262,
                0.9999485577680322,
                0.999373665834968,
                0.9999339478791605,
                0.9999151889488002,
                0.9998415637458196
            ],
            [
                7.889266347248781e-06,
                3.535625486815523e-05,
                6.962259569313662e-06,
                4.785092783267308e-06,
                2.1444948397509574e-05,
                2.1444943300075563e-05,
                6.962256249517824e-06,
                4.785092783319532e-06,
                6.96225541916544e-06,
                2.9023133690637e-06
            ],
            [
                0.9999038975625507,
                0.9999339478318156,
                0.999925153763988,
                0.9998766053812096,
                0.9999724642957817,
                0.9999546021368443,
                0.9999785550515979,
                0.9999151889489247,
                0.9999599363030979,
                0.9995694429655582
            ],
            [
                0.9998911030523878,
                0.9999832985741842,
                0.9998911031040516,
                0.9999646437451295,
                0.999959936317427,
                0.9996200155643231,
                0.999948557780265,
                0.9988304896673577,
                0.9998601778933952,
                0.9999038975622536
            ],
            [
                1.4738978456398127e-05,
                6.144176799099397e-06,
                1.1478766756214804e-05,
                7.484622716319649e-05,
                1.8925145971093502e-05,
                6.962255419051463e-06,
                2.430023203740195e-05,
                1.4738988997768797e-05,
                4.785092783210732e-06,
                1.1478766755734576e-05
            ],
            [
                0.9999038975622977,
                0.9999546021097719,
                0.9999038975509124,
                0.9999785550567141,
                0.9999646437535306,
                0.9999910603047634,
                0.9999832985721876,
                0.9999852610162783,
                0.9999756997534839,
                0.9999921107383561
            ],
            [
                0.9999646437577614,
                0.9998766054253622,
                0.9999885212305111,
                0.9999957771650456,
                0.9999417087068402,
                0.9999251537373732,
                0.9999724643023616,
                0.99997569975639,
                0.9999251537997412,
                0.9999687980812371
            ],
            [
                0.999769493176361,
                0.9999898700102298,
                0.9999687980924138,
                0.9995121428343023,
                0.9999339478712672,
                0.9999921107364755,
                0.999704043008745,
                0.9997040429024946,
                0.9999687980961118,
                0.9998204719921104
            ],
            [
                0.9999251537730209,
                0.9998601778602713,
                0.9999151889287404,
                0.9999339478398543,
                0.999968798088666,
                0.9999485577741841,
                0.9999485577925747,
                0.9999151889286245,
                0.9999687980849468,
                0.9999546021098057
            ],
            [
                0.9999546021097687,
                0.9993736659146141,
                0.9999832985721882,
                0.9999599363221651,
                0.9999038975852388,
                0.9998766053666093,
                0.9999687980960923,
                0.9999646437493283,
                0.9999485577925318,
                0.9999785550413702
            ],
            [
                0.9999485577680016,
                0.9999038975625116,
                0.9999038975738312,
                0.9999038975623424,
                0.9999251537908206,
                0.9999151889185262,
                0.9998415637652545,
                0.9999756997592761,
                0.9997040428364316,
                0.999933947863375
            ],
            [
                0.9999810748427427,
                0.9999151889487513,
                0.9999785550541526,
                0.9999546021097568,
                0.9999546021476502,
                0.9999810748517747,
                0.9999485577925429,
                0.9999898700066064,
                0.9999785550567105,
                0.9999852610110046
            ],
            [
                0.9997040430079097,
                0.9998415637085216,
                0.9999869928730897,
                0.9999646437493142,
                0.9984988174214883,
                0.9999339478712476,
                0.99992515377279,
                0.999903897562685,
                0.9999599362935143,
                0.9999038975624137
            ],
            [
                6.962257909412379e-06,
                3.120191879981973e-05,
                1.3007131563176482e-05,
                5.422220908703723e-06,
                1.67014178590634e-05,
                7.889262585441413e-06,
                2.4300246520590875e-05,
                1.1478769492392108e-05,
                1.4738983726184394e-05,
                1.4738985484227961e-05
            ],
            [
                0.9999546021368129,
                0.9999599363078789,
                0.9998766053666811,
                0.9995694428663064,
                0.9999687980774961,
                0.9998911030910002,
                0.9999756997563846,
                0.9999646437324665,
                0.9999785550592685,
                0.9999417087414969
            ],
            [
                1.0129995807699706e-05,
                4.222833947820683e-06,
                6.962259564254318e-06,
                6.962257908880483e-06,
                6.144176797730321e-06,
                1.0129993393540266e-05,
                7.889263524443698e-06,
                8.939695234170549e-06,
                1.6701421843356024e-05,
                5.422217030288788e-06
            ],
            [
                0.9999646437408855,
                0.9999724643187701,
                0.9996646499759303,
                0.9999724642990853,
                0.9999756997621917,
                0.9999485577865107,
                0.9999756997650714,
                0.9999724642990713,
                0.9984988175677177,
                0.999925153763944
            ],
            [
                0.9999546021260088,
                0.9998766054696584,
                0.9999339478239545,
                0.9999485577680016,
                0.999959936317406,
                0.9999646437366672,
                0.9999646437535384,
                0.9999339478318036,
                0.9999646437408953,
                0.9997040429363098
            ],
            [
                4.785096205717126e-06,
                6.962253759486771e-06,
                1.4738981970312625e-05,
                1.300712846361323e-05,
                1.3007128463873485e-05,
                2.753568780802255e-05,
                1.473898548194914e-05,
                4.222834954687752e-06,
                1.3709572068354007e-06,
                1.3007126909537681e-05
            ],
            [
                0.9999485578048591,
                0.9999339478633246,
                0.9999546021476473,
                0.9999251537371604,
                0.9998911030909717,
                0.9999151889689035,
                0.9999852610180368,
                0.9999251537461387,
                0.9999151889487804,
                0.999915188989147
            ],
            [
                0.9999417087484737,
                0.9998766054254681,
                0.9999339478317925,
                0.9998766054107978,
                0.9999546021422271,
                0.9999546021314231,
                0.9999417087136868,
                0.9999339478475732,
                0.9999756997563877,
                0.999964643736683
            ],
            [
                0.9998415637843829,
                0.999447221269464,
                0.9999724643154813,
                0.9998911031039929,
                0.9999417087207083,
                0.9998911031040659,
                0.9999599363221695,
                0.9999485577926571,
                0.9999885212359817,
                0.9999339478711793
            ],
            [
                0.999876605425872,
                0.999941708755437,
                0.9997694932590526,
                0.9999038975738199,
                0.999841563840929,
                0.999704042762498,
                0.9995121427708377,
                0.9999339478790946,
                0.9999038975741793,
                0.9998415637274932
            ],
            [
                1.6701429799367125e-05,
                5.422221555069497e-06,
                2.1444945853375776e-05,
                2.430023492769181e-05,
                1.8925141468298646e-05,
                2.7535687797204028e-05,
                1.892514147046736e-05,
                3.2887494572095624e-06,
                1.8925150487521332e-05,
                0.9996200155235531
            ],
            [
                0.9999646437619594,
                0.9999417087415261,
                0.9999038975737515,
                0.9999646437577571,
                0.9999339478476231,
                0.9997040427649866,
                0.9999038975853564,
                0.9999038975738312,
                0.9999599362935143,
                0.9999485577741883
            ],
            [
                1.473898724181597e-05,
                1.0129990979031306e-05,
                6.962259569313662e-06,
                1.147876675548402e-05,
                1.0129992185981682e-05,
                1.6701427816728442e-05,
                2.5612825160096693e-06,
                1.6701421840804172e-05,
                1.7603425837606927e-06,
                4.0063706481032684e-05
            ],
            [
                0.9999687980775083,
                0.9997694932047924,
                0.999994577780384,
                0.9999546021314201,
                0.9999038975509711,
                0.9999599362887558,
                0.9998766053963412,
                0.99995993630786,
                0.9998911030779377,
                0.9999546021097687
            ],
            [
                0.9999724643023534,
                0.9999898700078143,
                0.9999869928761882,
                0.9999756997592744,
                0.9999646437535286,
                0.9999724643056345,
                0.9999546021260254,
                0.9999832985761709,
                0.9999485577741333,
                0.9999885212305076
            ],
            [
                0.9999546021097478,
                0.9999546021476324,
                0.9999785550439243,
                0.9999038976083017,
                0.9999756997476907,
                0.999997438716568,
                0.9999898700053991,
                0.9999930377420914,
                0.9999724643023546,
                0.9999832985781634
            ],
            [
                0.9999546021205913,
                0.9999785550439346,
                0.9999417087414739,
                0.9999485577925545,
                0.9999546021368343,
                0.9988304896749731,
                0.9997965731008195,
                0.9999417087206773,
                0.9998415637274333,
                0.9999485577680239
            ],
            [
                4.785096205717126e-06,
                3.726639728224814e-06,
                7.8892625849535e-06,
                8.939693103418341e-06,
                7.889264465699106e-06,
                1.1478773596847203e-05,
                6.96225707894582e-06,
                6.962258739068529e-06,
                1.1478766752748805e-05,
                7.889259762307618e-06
            ],
            [
                0.9998415638404773,
                0.999964643749356,
                0.9997388096949561,
                0.9999251537819502,
                0.9998911031041562,
                0.9999251537551219,
                0.9998766053665553,
                0.9999339478791537,
                0.9999646437577896,
                0.9999785550439584
            ],
            [
                0.9999038975737963,
                0.99995460213681,
                0.9999038975852738,
                0.9999251537728716,
                0.9999038975739403,
                0.9999151889690066,
                0.9992903297247775,
                0.9999599363221995,
                0.9999417087484839,
                0.9999485577864472
            ],
            [
                1.1478768122069266e-05,
                2.1444958631232504e-05,
                2.561281905293402e-06,
                1.0129990976451642e-05,
                2.1444950958338794e-05,
                2.90231163910023e-06,
                1.473898899256772e-05,
                2.144494329192304e-05,
                6.9622570784012604e-06,
                8.939697367492512e-06
            ],
            [
                0.9999339478240521,
                0.9999251537732148,
                0.9999546021422182,
                0.9999724643023661,
                0.9998601779262325,
                0.9998911031168194,
                0.9999756997621958,
                0.9998415638215978,
                0.9999646437535861,
                0.9999810748450153
            ],
            [
                6.605214458361157e-05,
                2.7535704221626983e-05,
                6.144173137014406e-06,
                1.892515049199645e-05,
                2.1444940742640888e-05,
                1.1478768125201194e-05,
                6.144176798691468e-06,
                4.222834451169694e-06,
                1.4738987240824012e-05,
                2.430023783309869e-05
            ],
            [
                0.9999599363174162,
                0.9999151889386432,
                0.9999646437324686,
                0.9999038976194401,
                0.9999898700066079,
                0.9998911030650146,
                0.9999646437535286,
                0.9999599363173874,
                0.999954602136831,
                0.9999546021476133
            ],
            [
                0.9999687980812137,
                0.9999832985781624,
                0.9999038975397089,
                0.9998911031303382,
                0.9999417087554264,
                0.9999687980998132,
                0.9999599363221765,
                0.9999910603058285,
                0.999959936312681,
                0.9997388095980908
            ],
            [
                0.9998415637845443,
                0.9997388097877401,
                0.99997569975639,
                0.9999417087207138,
                0.9999251537461931,
                0.9999885212277727,
                0.9999724643154878,
                0.9999646437451205,
                0.9999724643187715,
                0.9999251537818918
            ],
            [
                0.9999599363030722,
                0.9999832985801516,
                0.9999810748517658,
                0.9998204719492501,
                0.9999810748585407,
                0.9999599363126283,
                0.999903897597031,
                0.9999852610127677,
                0.9999599363221838,
                0.9999646437577614
            ],
            [
                0.9999251537461239,
                0.9999599363127036,
                0.9998204720780219,
                0.9999687980812332,
                0.9999546021259874,
                0.9999898700102318,
                0.9999646437577657,
                0.9997694933406912,
                0.9999485577986978,
                0.9999339478791883
            ],
            [
                0.9999785550413824,
                0.9998601778595592,
                0.9999646437619537,
                0.9999646437619848,
                0.9999785550592762,
                0.9999546021422797,
                0.9999339478318973,
                0.9999646437451055,
                0.9999756997650845,
                0.999964643761994
            ],
            [
                2.7535704226635563e-05,
                1.0129995809247506e-05,
                1.6701419852090592e-05,
                3.288750241500471e-06,
                1.4738985481520185e-05,
                0.9986749774342841,
                5.422218323231539e-06,
                1.670142383167491e-05,
                2.430023492769181e-05,
                2.4300246519706854e-05
            ],
            [
                0.9999869928715426,
                0.9999417087414969,
                0.999664650012918,
                0.9999485577802758,
                0.9999151889489136,
                0.9998415637084915,
                0.9999339478554956,
                0.9999417087068236,
                0.9999546021476665,
                0.9996200154271773
            ],
            [
                4.785092783267308e-06,
                2.4300240731964193e-05,
                1.4738978457041559e-05,
                8.93969630388855e-06,
                2.1444945853375776e-05,
                1.3007130012673148e-05,
                1.1478768123823146e-05,
                1.892515049199645e-05,
                0.9995121427709511,
                1.4738983726184394e-05
            ],
            [
                0.9999417087414781,
                0.9999251537549744,
                0.9978172836084068,
                0.9990889486681644,
                0.9982992779799185,
                0.999664650011269,
                0.9997694933406309,
                0.999664650012918,
                0.9994472213264161,
                0.9997040427960807
            ],
            [
                0.9999687980923851,
                0.9986749774204197,
                0.9999251537371397,
                0.9999038976196576,
                0.9999646437367007,
                0.9997965729550065,
                0.9999417087485726,
                0.9998766054701557,
                0.9997965730527784,
                0.9996646498110714
            ],
            [
                8.939693106182721e-06,
                1.3007126911974612e-05,
                3.535625913039018e-05,
                1.892514146884943e-05,
                8.939700566435704e-06,
                6.9622579096593295e-06,
                0.9997040428704534,
                4.222832940777184e-06,
                6.144176066353646e-06,
                2.7535681245588654e-05
            ],
            [
                0.9999646437324605,
                0.9999546021151737,
                0.9999151889284529,
                0.9999910603058285,
                0.9999251537461931,
                0.9998415637273135,
                0.9999151889385877,
                0.9999852610110042,
                0.9999646437493069,
                0.9999646437450873
            ],
            [
                0.9999898700114365,
                0.9999687980886489,
                0.9999724642990652,
                0.9999724643056345,
                0.9999852610127589,
                0.9999756997592719,
                0.9999546021476294,
                0.9999599362934992,
                0.9999599363030746,
                0.9999687980886555
            ],
            [
                1.147876949310201e-05,
                7.889263525261671e-06,
                2.1444953524161264e-05,
                1.3007123811513407e-05,
                0.999796572958117,
                3.535626333461766e-05,
                7.889266347133978e-06,
                7.889264466344872e-06,
                2.902311639126627e-06,
                5.829129324249228e-05
            ],
            [
                6.962254588977791e-06,
                7.889266344981421e-06,
                1.8925145979561802e-05,
                6.9622562487453084e-06,
                7.889266346603015e-06,
                2.7535697655983693e-05,
                5.422218322851817e-06,
                1.67014178590634e-05,
                1.4738976698006875e-05,
                1.012999097799944e-05
            ],
            [
                0.9997388095994816,
                0.9999599363126355,
                0.999954602131393,
                0.9999832985741774,
                0.9997965729322911,
                0.9999785550490434,
                0.999975699767968,
                0.9999151889690164,
                0.9999339478396766,
                0.9999599363030846
            ],
            [
                4.006370173294989e-05,
                2.1444945849006956e-05,
                4.785095065045315e-06,
                5.1442225836439433e-05,
                1.6701421842961097e-05,
                1.4738987242700688e-05,
                1.147876538789672e-05,
                8.939699500896292e-06,
                1.6701417861949427e-05,
                2.2603251062147097e-06
            ],
            [
                3.1201907650801864e-05,
                3.5356246490314526e-05,
                1.6701425824307884e-05,
                1.0129988563914856e-05,
                1.0129995809247506e-05,
                8.939699500766203e-06,
                1.4738980213020151e-05,
                1.3007128462477575e-05,
                1.670142980687079e-05,
                5.422218969601935e-06
            ],
            [
                0.9999251537728793,
                0.9999599362935444,
                0.9999687980886521,
                0.9990889489086491,
                0.999964643736669,
                0.9995694428601689,
                0.999925153790781,
                0.9999756997592878,
                0.9999417087345882,
                0.9999339478397375
            ],
            [
                6.605217600797426e-05,
                4.2228349547223175e-06,
                2.144494073796001e-05,
                1.3007134665413997e-05,
                5.144221362094481e-05,
                1.8925148232267744e-05,
                1.1478769493331685e-05,
                1.6701423831188846e-05,
                1.8925148238291944e-05,
                1.8925148237775583e-05
            ],
            [
                0.9994472213890281,
                0.9999485577741557,
                0.9999038975509013,
                0.9997965729795745,
                0.9999251537372105,
                0.9999339478554827,
                0.9999038976196002,
                0.9997694932586367,
                0.9999646437535427,
                0.9997388096924633
            ],
            [
                0.999964643736669,
                0.9998415637081411,
                0.9999785550567089,
                0.9999687980960814,
                0.9999724642990753,
                0.9997965729304916,
                0.9999945777816769,
                0.9999546021205942,
                0.9998766054402282,
                0.9999810748427408
            ],
            [
                0.9999038975511235,
                0.9998766054554065,
                0.9999485578048636,
                0.9999485577925467,
                0.9999546021422456,
                0.9999417087137297,
                0.9998601778599723,
                0.9999038975853941,
                0.9997965730518255,
                0.9999810748427485
            ],
            [
                1.1478768124783601e-05,
                5.422218969217281e-06,
                4.222835458002318e-06,
                2.144495351004062e-05,
                4.785095064601411e-06,
                6.962259568775433e-06,
                1.1478769488633793e-05,
                8.939697367492512e-06,
                1.0129988563730593e-05,
                1.8925157257345735e-05
            ],
            [
                2.4300243622255085e-05,
                1.6701423833011596e-05,
                3.726640172385136e-06,
                1.1478768124553928e-05,
                2.7535697660090726e-05,
                3.1201911358551906e-05,
                2.753569436424737e-05,
                1.8925152750692706e-05,
                0.9997388097235079,
                8.939700565996655e-06
            ],
            [
                0.999986992873093,
                0.9998601779428534,
                0.9999724642990675,
                0.9999724643187611,
                0.9999151889891291,
                0.9999599362935362,
                0.9999038975852388,
                0.9999151889689682,
                0.9999724642990628,
                0.9996646500123227
            ],
            [
                0.999964643753563,
                0.9999417087206925,
                0.99937366583883,
                0.9998601778599723,
                0.9999151889286245,
                0.9999898700102289,
                0.9999785550465006,
                0.9999485577926522,
                0.9999251537640426,
                0.9999251537461615
            ],
            [
                0.9999546021260151,
                0.999915188979248,
                0.9998601778769839,
                0.9999151889389054,
                0.9999151889487328,
                0.9999546021368376,
                0.9999687980737689,
                0.9999724642958062,
                0.9999646437408634,
                0.9998766053817967
            ],
            [
                1.1478764019557924e-05,
                4.539786863769599e-05,
                1.670142781432848e-05,
                4.006369217615605e-05,
                4.006370169826257e-05,
                1.6701429806475863e-05,
                2.4300243626409964e-05,
                0.999876605425486,
                4.78509563535725e-06,
                1.8925148236674017e-05
            ],
            [
                0.9999756997563846,
                0.9999646437493104,
                0.9998415637649571,
                0.9999417087276304,
                0.9998415638028936,
                0.9996200155631845,
                0.9999417087137196,
                0.999954602131461,
                0.9999646437451367,
                0.9999339478633364
            ],
            [
                0.9994472213307897,
                0.9999546021368281,
                0.9999251537551465,
                0.9998911030522277,
                0.9999417087137297,
                0.9999756997534994,
                0.999915188989213,
                0.999903897539506,
                0.999915188989213,
                0.9982992775031784
            ],
            [
                0.9996646497702103,
                0.9999885212264054,
                0.9999687980849431,
                0.9999599363031239,
                0.9999599363031149,
                0.9995694429678753,
                0.9997694932858139,
                0.9998766054258109,
                0.9998766053667367,
                0.9998766054109486
            ],
            [
                0.9999687980774897,
                0.9999599362887508,
                0.9998204720777556,
                0.9999038975969499,
                0.9997388096932157,
                0.9999546021422155,
                0.9999724643154826,
                0.9999687980960938,
                0.9998766054404185,
                0.9996646500116203
            ],
            [
                0.99990389758532,
                0.9997694933139836,
                0.9999546021422301,
                0.999373665832782,
                0.9993736658276082,
                0.9998911031173106,
                0.9999038975395677,
                0.9978172833097284,
                0.9997694933421132,
                0.9997965730039087
            ],
            [
                2.7535687811228037e-05,
                4.222832941034507e-06,
                1.892515500560259e-05,
                1.3007134665934505e-05,
                1.473898197063434e-05,
                3.120190392795564e-05,
                1.7603440527222532e-06,
                4.222835458117536e-06,
                4.006369216362198e-05,
                2.4300234936443568e-05
            ]
        ]
    },
    {
        "q_id": "8116_mmlu_math",
        "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": [
            [
                0.9999962733589389,
                0.9999980052693274,
                0.9999986290426297,
                0.9999970976873229,
                0.999995777168066,
                0.9999967112513268,
                0.9999980052707541,
                0.9999982396572064,
                0.9999993524049702,
                0.9999980052709919
            ],
            [
                8.764253719973308e-08,
                1.0677029972920738e-06,
                6.475949525981759e-07,
                4.4508489275469177e-07,
                1.2098662604247682e-06,
                1.6373770576683237e-07,
                2.382369667914917e-07,
                3.927861534370498e-07,
                3.9278610661822475e-07,
                8.315279285351409e-07
            ],
            [
                2.1024331597066579e-07,
                5.715002426460124e-07,
                1.6373762769138607e-07,
                1.3709578605243332e-06,
                4.006371115566053e-05,
                1.637377643237766e-07,
                2.6995787399686675e-07,
                8.315279285251204e-07,
                3.059021539909339e-07,
                1.6373772528636992e-07
            ],
            [
                1.5534977545243671e-06,
                6.475951069932288e-07,
                8.315278294038928e-07,
                1.2098655392574583e-06,
                5.04347528440776e-07,
                5.715003789033962e-07,
                9.422442569097361e-07,
                1.7603436328994344e-06,
                7.338212429420757e-07,
                9.422449308716635e-07
            ],
            [
                0.999995214903224,
                0.9999962733607162,
                0.9999967112509347,
                0.9999938558224687,
                0.9999957771665555,
                0.9999930377454114,
                0.9999984465016899,
                0.9999962733598275,
                0.9999986290429567,
                0.9999898700114368
            ],
            [
                8.315278294001114e-07,
                5.715005832853093e-07,
                7.338211554758494e-07,
                6.475949525981759e-07,
                2.1024336609724313e-07,
                3.927860597945825e-07,
                3.4663249714325014e-07,
                3.927860597935108e-07,
                2.382368247924618e-07,
                4.4508505193386385e-07
            ],
            [
                4.450849988758202e-07,
                3.4663253846473677e-07,
                3.059023363231725e-07,
                5.04347348070562e-07,
                2.1024339116082313e-07,
                6.475950297868629e-07,
                3.466327450744504e-07,
                6.47594566594213e-07,
                3.059023363207381e-07,
                4.450852111100568e-07
            ],
            [
                0.9999970976876692,
                0.999994577778445,
                0.9999982396569966,
                0.9999945777797377,
                0.9999982396574163,
                0.9999945777816768,
                0.9999957771675626,
                0.999998629042303,
                0.9999967112493665,
                0.9999982396567868
            ],
            [
                2.1024329090867228e-07,
                1.6373764720923895e-07,
                5.715002425937749e-07,
                6.962258738701267e-06,
                1.2098656834922064e-06,
                2.1024334103505245e-07,
                6.475947982002148e-07,
                8.315278294072958e-07,
                2.1024336609724313e-07,
                3.927862002654366e-07
            ],
            [
                3.059021904484005e-07,
                6.47594720987407e-07,
                3.0590211752206485e-07,
                1.2751907328949007e-07,
                2.102433660952354e-07,
                6.47594566594213e-07,
                7.338211554641698e-07,
                1.1253513522391131e-07,
                3.4663274506893337e-07,
                2.5612825153504304e-06
            ],
            [
                0.9999957771675627,
                0.9999994284994848,
                0.9999986290421395,
                0.9999974387171787,
                0.9999962733620493,
                0.9999986290426297,
                0.9999982396561571,
                0.9999991684722698,
                0.9999993524053562,
                0.9999991684715758
            ],
            [
                1.7603434231385591e-06,
                2.6995771309523475e-07,
                1.3709573702647743e-06,
                8.315281267834927e-07,
                3.9278605979208185e-07,
                3.4663278639265633e-07,
                9.422443691233569e-07,
                1.209866116137134e-06,
                1.2098658277335738e-06,
                6.144173136556186e-06
            ],
            [
                2.699578096373564e-07,
                5.715005832624392e-07,
                5.043475885576967e-07,
                3.0590229985449037e-07,
                1.8553907971590097e-07,
                1.275190884913241e-07,
                3.4663266242575825e-07,
                1.637377057618436e-07,
                1.8553912395160867e-07,
                7.338209805090567e-07
            ],
            [
                1.067702488159652e-06,
                1.855391460719133e-07,
                4.4508515805199415e-07,
                1.3709568799592562e-06,
                4.450852641656969e-07,
                4.450849458218309e-07,
                3.2887494572095624e-06,
                1.9947301970451086e-06,
                7.338213304196583e-07,
                5.043472278280699e-07
            ],
            [
                7.338211554758494e-07,
                3.059022998576899e-07,
                1.1253514863909295e-07,
                7.734424996918514e-08,
                5.715002426410745e-07,
                1.855390354818069e-07,
                2.3823699518764604e-07,
                6.47594875389178e-07,
                3.466327863961242e-07,
                2.102433660979124e-07
            ],
            [
                5.71500651413193e-07,
                3.927860597945825e-07,
                1.4449796927932878e-07,
                1.8553910183269882e-07,
                2.2603245673155757e-06,
                6.475948753930064e-07,
                6.475950297993789e-07,
                5.715005832872586e-07,
                3.4663253846718004e-07,
                8.315283250260307e-07
            ],
            [
                5.715003107655392e-07,
                3.9278615343901467e-07,
                1.5534975693601474e-06,
                1.209865539274514e-06,
                1.5534983101549167e-06,
                3.4663262110803996e-07,
                7.338207180761315e-07,
                7.338213304316717e-07,
                2.6995771309523475e-07,
                2.260325375354421e-06
            ],
            [
                8.315278294038928e-07,
                2.1024344128488479e-07,
                8.315280276546789e-07,
                3.0590219045271286e-07,
                3.466324971415162e-07,
                1.6373764720990908e-07,
                1.3709568799243436e-06,
                4.4508521110762794e-07,
                1.0677026154376365e-06,
                9.422449308566668e-07
            ],
            [
                0.9999996940978095,
                0.9999997300421903,
                0.9999994284997573,
                0.999999554915001,
                0.9999994284994167,
                0.9999994956523514,
                0.9999989322968754,
                0.9999986290432835,
                0.9999986290423029,
                0.9999997897567091
            ],
            [
                0.9999986290429567,
                0.9999989322972573,
                0.9999987901344607,
                0.9999962733593833,
                0.9999945777803847,
                0.999998790134028,
                0.9999952149055054,
                0.9999962733620488,
                0.9999967112517191,
                0.9999687980812002
            ],
            [
                0.999998005270041,
                0.9999991684717742,
                0.9999995549150542,
                0.9999986290424664,
                0.9999986290429567,
                0.9999980052705163,
                0.9999989322971299,
                0.9999994956526519,
                0.9999989322973847,
                0.9999991684722697
            ],
            [
                1.0677033791583005e-06,
                3.9278638755456876e-07,
                1.0677031245905116e-06,
                8.315281267861397e-07,
                7.338212429504183e-07,
                1.3709570433786157e-06,
                1.2098653950480359e-06,
                5.7150044702099e-07,
                1.067703251864202e-06,
                3.9278605979208185e-07
            ],
            [
                3.05902226923399e-07,
                3.466327863983311e-07,
                8.315282259051341e-07,
                2.1024329090929374e-07,
                2.6995790618252024e-07,
                5.715006513952608e-07,
                2.382368247909451e-07,
                1.3709573702248741e-06,
                9.422444815726566e-07,
                2.6995790618252024e-07
            ],
            [
                0.9999938558268634,
                0.9999977396762412,
                0.9999984465020603,
                0.9999945777784454,
                0.999991060299435,
                0.9999990577555185,
                0.9999984465022455,
                0.9999957771665557,
                0.9999974387184001,
                0.9999945777823237
            ],
            [
                0.9999994284994849,
                0.9999910603068932,
                0.9999930377429218,
                0.9999921107402369,
                0.9999945777784451,
                0.999993037740431,
                0.9999977396762412,
                0.999933947855328,
                0.9999986290423029,
                0.999933947823881
            ],
            [
                2.1024341622297196e-07,
                5.715003789033962e-07,
                5.71500651413193e-07,
                8.315282259117513e-07,
                2.3823699519290042e-07,
                2.102433410343832e-07,
                5.715003107655392e-07,
                1.0677024881887838e-06,
                8.315280276607289e-07,
                1.8553910183607374e-07
            ],
            [
                4.4508521110762794e-07,
                8.315277302649045e-07,
                1.637376862478556e-07,
                1.8553905760024476e-07,
                1.1253510839355284e-07,
                5.04347588540266e-07,
                4.4508505193123265e-07,
                2.382368531882742e-07,
                8.3152792852928e-07,
                2.1024339116010604e-07
            ],
            [
                3.288748281220719e-06,
                7.338210679909462e-07,
                7.338213304316717e-07,
                8.315277302788957e-07,
                1.3709576970949014e-06,
                8.315277302588544e-07,
                1.760344052714248e-06,
                1.370957860567974e-06,
                3.7266379512518984e-06,
                3.288750241473551e-06
            ],
            [
                1.067703379154416e-06,
                2.699578739999358e-07,
                3.4663266242969896e-07,
                5.715006514074756e-07,
                5.715006514151423e-07,
                3.9278615343901467e-07,
                1.3709573702248741e-06,
                4.450849458179853e-07,
                3.059021904580685e-07,
                2.6995780963588326e-07
            ],
            [
                0.999998005270992,
                0.9999998555020306,
                0.9999994284992805,
                0.9999990577549568,
                0.999999266179107,
                0.9999996533674201,
                0.9999997300422225,
                0.9999994956526519,
                0.9999996533674202,
                0.9999992661788445
            ],
            [
                4.450848927621807e-07,
                1.2098661161789477e-06,
                1.8553910183548312e-07,
                3.4663262110945863e-07,
                2.3823699518764604e-07,
                7.338212429504183e-07,
                5.043475284430694e-07,
                7.338208055579897e-07,
                7.338213304316717e-07,
                1.067702488159652e-06
            ],
            [
                0.9999982396559474,
                0.9999989322973846,
                0.9999987901347491,
                0.9999977396765106,
                0.9999984465026159,
                0.9999967112521114,
                0.9999994284996891,
                0.9999994956527721,
                0.9999990577550691,
                0.999998239656367
            ],
            [
                0.9999945777797378,
                0.9999885212277699,
                0.9999151889384531,
                0.9997694931751202,
                0.9999957771650453,
                0.9999852610162727,
                0.9996200155622891,
                0.999933947831744,
                0.9999952149055052,
                0.9999832985801487
            ],
            [
                0.9999962733598275,
                0.9999984465020603,
                0.9999982396563669,
                0.9999930377429204,
                0.999996273360716,
                0.9999974387177893,
                0.9999952149066462,
                0.9999987901347492,
                0.999998005269803,
                0.9999991684722698
            ],
            [
                7.338210679949506e-07,
                2.102433660979124e-07,
                3.059021539909339e-07,
                5.715003107416295e-07,
                3.0590226338671677e-07,
                3.0590226338490835e-07,
                5.715005151485975e-07,
                2.3823699519143784e-07,
                1.7603427936183298e-06,
                2.1024331597152624e-07
            ],
            [
                0.9999982396572065,
                0.9999957771670591,
                0.9999989322975118,
                0.9999989322970028,
                0.9999992661787571,
                0.999999352404893,
                0.999999352404893,
                0.9999984465022455,
                0.999999266178932,
                0.9999991684719723
            ],
            [
                8.31528126775552e-07,
                1.370957370247318e-06,
                NaN,
                3.466327863945479e-07,
                5.043474081957179e-07,
                3.9278605979208185e-07,
                9.42244256915735e-07,
                NaN,
                2.699577130905084e-07,
                2.902311293034278e-06
            ],
            [
                0.9999977396751634,
                0.9999991684722698,
                0.999999266178932,
                0.9999990577556307,
                0.9999974387168735,
                0.9999977396748939,
                0.9999994284992804,
                0.9999992661786696,
                0.9999990577549568,
                0.9999967112521109
            ],
            [
                2.3823682478975334e-07,
                2.26032348933062e-06,
                1.855391681891831e-07,
                2.3823685319076597e-07,
                3.4663257978039603e-07,
                5.715004470243685e-07,
                5.715003788933905e-07,
                2.3823690998803445e-07,
                2.3823699519035448e-07,
                4.450849988798682e-07
            ],
            [
                5.043474081957179e-07,
                5.04347348075149e-07,
                3.927863875584984e-07,
                3.927862470890063e-07,
                9.42244256915735e-07,
                3.927862939126708e-07,
                1.6373772528636992e-07,
                3.9278615342936924e-07,
                1.9947290080343035e-06,
                3.059022998576899e-07
            ],
            [
                0.9999957771670591,
                0.9999992661791945,
                0.9999990577552937,
                0.9999977396759717,
                0.999915188948618,
                0.9999938558246659,
                0.9999987901347491,
                0.9999980052702785,
                0.999998790134028,
                0.9999970976887068
            ],
            [
                0.9999987901346049,
                0.999999266178757,
                0.9999996940978095,
                0.999996273360272,
                0.9999251537639369,
                0.9999977396757023,
                0.9999967112501505,
                0.999995214906076,
                0.9999957771665555,
                0.9999957771675625
            ],
            [
                9.931189774187203e-08,
                3.927862939136532e-07,
                1.4449800372960563e-07,
                1.8553910183607374e-07,
                2.382369383923073e-07,
                3.466325384661554e-07,
                1.6373772528677946e-07,
                3.9278624708775595e-07,
                3.927862002606139e-07,
                2.699577130944368e-07
            ],
            [
                7.338208930315157e-07,
                5.04347528431602e-07,
                5.043475885634304e-07,
                5.04347227811786e-07,
                2.6995790618252024e-07,
                7.338212429504183e-07,
                3.9278638754242273e-07,
                9.422442569097361e-07,
                3.0590229985101266e-07,
                3.927863874713325e-07
            ],
            [
                5.422218318452962e-06,
                2.1024329090561285e-07,
                5.422221552756645e-06,
                5.043472879240838e-07,
                3.92786293909545e-07,
                3.0590215390051364e-07,
                1.0677026154376365e-06,
                2.6995777744140237e-07,
                7.338211554531576e-07,
                3.4663262110945863e-07
            ],
            [
                2.699577774585891e-07,
                4.450851049917114e-07,
                1.6373770576683237e-07,
                3.4663274507287414e-07,
                4.450851049941403e-07,
                4.450851049959619e-07,
                3.4663270375278157e-07,
                4.450852111100568e-07,
                3.0590222692437275e-07,
                3.05902226923399e-07
            ],
            [
                2.3823690999160957e-07,
                2.382368247924618e-07,
                3.9278629390507954e-07,
                7.338213304196583e-07,
                3.4663262110630603e-07,
                3.059021904543821e-07,
                1.6373762769034363e-07,
                3.466327863879275e-07,
                2.3823685318675746e-07,
                1.994729721469003e-06
            ],
            [
                0.9995694428609079,
                0.9998766054546218,
                0.9999546021205518,
                0.9999485577986598,
                0.9999038975851725,
                0.999968798092358,
                0.9999687980998132,
                0.999903897550844,
                0.9999982396572065,
                0.9998204719484429
            ],
            [
                0.22270014398423357,
                0.9999832985741748,
                0.29421498454004374,
                0.9999599363221695,
                0.32082130082460697,
                0.9999756997592735,
                0.9999485577741759,
                0.9998204719914653,
                0.9999339478238508,
                0.5
            ],
            [
                3.9278605979011705e-07,
                1.4449802095609418e-07,
                5.043476486883855e-07,
                2.38237023590304e-07,
                8.315281267834927e-07,
                3.4663249714451116e-07,
                1.4449803818107344e-07,
                8.764253719973308e-08,
                3.92786340734912e-07,
                2.699578096399958e-07
            ],
            [
                6.475946437966953e-07,
                1.3709578605542582e-06,
                3.05902263389638e-07,
                2.6995768091310296e-07,
                3.059021904571643e-07,
                2.5612812946890944e-06,
                9.422448185435711e-07,
                2.699578418185828e-07,
                3.059021175255426e-07,
                1.8553914607128047e-07
            ],
            [
                0.9999832985841305,
                0.9999599363030408,
                0.9999921107402369,
                0.9999991684721706,
                0.9999869928699864,
                0.9999921107392962,
                0.9999945777816769,
                0.9999992661788446,
                0.9999993524050473,
                0.9999987901338838
            ],
            [
                0.9999989322970027,
                0.9999995549150542,
                0.9999980052698029,
                0.9999996940977001,
                0.9999990577554062,
                0.9999986290429567,
                0.9999986290429567,
                0.9999994284993485,
                0.999998446502801,
                0.9999992661786696
            ],
            [
                3.927862470861484e-07,
                6.475951069985296e-07,
                1.6373764720849438e-07,
                7.338210679949506e-07,
                3.927862939075802e-07,
                2.2603240279591663e-06,
                1.5534981249291695e-06,
                1.2098656834834034e-06,
                1.3709575336860625e-06,
                5.715006514040971e-07
            ],
            [
                1.2098659719441482e-06,
                9.4224425692559e-07,
                1.855391018347238e-07,
                6.475947981975644e-07,
                1.8553912395338048e-07,
                2.260324028372372e-06,
                3.466327450756327e-07,
                7.338210679979539e-07,
                2.699578418198104e-07,
                3.9278634073625165e-07
            ],
            [
                4.450852641681257e-07,
                3.0590215397952704e-07,
                3.0590229985101266e-07,
                1.760344052693435e-06,
                1.994729008105057e-06,
                2.3823702358900394e-07,
                7.338210679949506e-07,
                1.0677031245710902e-06,
                4.450849988733914e-07,
                1.2098659719441482e-06
            ],
            [
                1.2751902768414384e-07,
                2.2603234893861252e-06,
                3.9278638755456876e-07,
                1.9947292458603553e-06,
                3.0590215398829087e-07,
                1.0677024881683915e-06,
                5.043473480345541e-07,
                3.0590226338671677e-07,
                3.9278634072866033e-07,
                2.1024329090427435e-07
            ],
            [
                8.3152792852928e-07,
                5.043476486883855e-07,
                1.275190428866973e-07,
                9.422445938861406e-07,
                5.043476486626983e-07,
                8.315277302588544e-07,
                1.670141586907437e-05,
                2.6995790618350237e-07,
                7.338209805040511e-07,
                2.3823702359138736e-07
            ],
            [
                1.8553919030118224e-07,
                5.715002426410745e-07,
                7.338213304343413e-07,
                1.067703378938839e-06,
                5.715006514074756e-07,
                6.475949525919915e-07,
                1.0677032518501217e-06,
                7.338213304243302e-07,
                8.315282258756395e-07,
                5.043472278255469e-07
            ],
            [
                5.715003107689177e-07,
                1.2098661161927025e-06,
                8.31528424151477e-07,
                3.9278634073312583e-07,
                3.4663266243111764e-07,
                2.6995768091310296e-07,
                5.043472278227948e-07,
                2.699577774560111e-07,
                1.5534981249496567e-06,
                2.3823685319244518e-07
            ],
            [
                1.444979520533721e-07,
                1.4449795205389775e-07,
                3.059023363207381e-07,
                1.275190884913241e-07,
                2.3823702359138736e-07,
                1.6373766672888118e-07,
                1.855391460719133e-07,
                3.0590226338838606e-07,
                5.043474081785165e-07,
                8.315280276505193e-07
            ],
            [
                4.450849988798682e-07,
                2.3823699519143784e-07,
                1.994729483535857e-06,
                3.9278638755992735e-07,
                3.059023363231725e-07,
                1.6373766672649848e-07,
                5.043475885657239e-07,
                3.4663249714451116e-07,
                9.422448185264317e-07,
                5.71500378896509e-07
            ],
            [
                4.450849988780466e-07,
                3.0590215398968196e-07,
                1.2098662604049616e-06,
                5.043474683050556e-07,
                2.699577774579753e-07,
                1.444979692787374e-07,
                7.338208055613267e-07,
                3.927862470861484e-07,
                3.4663270375278157e-07,
                8.315280276546789e-07
            ],
            [
                3.0590226338282174e-07,
                1.8553907971758842e-07,
                4.450850519360903e-07,
                1.4449803818107344e-07,
                2.3823699519143784e-07,
                5.71500242637956e-07,
                3.059021539909339e-07,
                2.382368815882068e-07,
                2.1024344128086927e-07,
                5.04347588554027e-07
            ],
            [
                9.42244818532859e-07,
                1.6373774480479287e-07,
                5.715003107689177e-07,
                2.6995774527577444e-07,
                4.450852641681257e-07,
                5.715005832676369e-07,
                2.3823693839154895e-07,
                2.2603242977802297e-06,
                7.338208930315157e-07,
                2.561282515914161e-06
            ],
            [
                8.315278294001114e-07,
                3.2887482809933958e-06,
                2.902311639073834e-06,
                5.043472278280699e-07,
                9.4224425692559e-07,
                1.8553903548267175e-07,
                3.4663257978780455e-07,
                2.6995774527718623e-07,
                1.5534981248712412e-06,
                5.715004470272272e-07
            ],
            [
                9.422447062094932e-07,
                1.2098662604192665e-06,
                8.315283250343497e-07,
                2.1024341622368903e-07,
                1.7603425837062577e-06,
                2.3823688159069855e-07,
                2.3823685319244518e-07,
                3.4663266242969896e-07,
                2.699577774585891e-07,
                2.102433660979124e-07
            ],
            [
                1.7603427936079236e-06,
                1.275190580875709e-07,
                2.1024341622368903e-07,
                3.4663278639738526e-07,
                1.8553914607043678e-07,
                5.043473480730849e-07,
                5.04347528431602e-07,
                8.939693105076969e-06,
                1.5534979397140412e-06,
                2.6995768091310296e-07
            ],
            [
                0.9999984465020603,
                0.9999977396757023,
                0.9999977396748939,
                0.9999962733616046,
                0.9999898700114365,
                0.9999869928653338,
                0.9999910603036967,
                0.9999962733616047,
                0.999999352404893,
                0.999999352405279
            ],
            [
                3.466327037548308e-07,
                6.475951069896949e-07,
                2.3823690999063455e-07,
                1.7603438428660665e-06,
                9.422450431912e-07,
                3.4663249714325014e-07,
                3.466327037512053e-07,
                1.3709575337016483e-06,
                2.699578096373564e-07,
                5.715004470243685e-07
            ],
            [
                2.3823696679040834e-07,
                1.8553914606950867e-07,
                7.338208930421943e-07,
                8.315280276580819e-07,
                3.9278605979011705e-07,
                8.3152792852928e-07,
                2.699577130944368e-07,
                4.222833947498071e-06,
                7.33821067986608e-07,
                3.927860597715407e-07
            ],
            [
                0.9999982396561572,
                0.9999962733607162,
                0.9999938558268633,
                0.9999852610127595,
                0.9999945777823237,
                0.9999952149066461,
                0.9999417087136441,
                0.9999930377429207,
                0.9999038975965325,
                0.9999945777829697
            ],
            [
                0.9999938558253988,
                0.9999646437366552,
                0.999991060299434,
                0.9999982396561572,
                0.9999994284993485,
                0.9999151889688097,
                0.999999266179107,
                0.9999990577550691,
                0.9999987901341723,
                0.9999970976887068
            ],
            [
                0.9999970976883609,
                0.9999785550541542,
                0.9999987901341723,
                0.9999898700054015,
                0.9999962733602719,
                0.9999962733593833,
                0.9999885212277724,
                0.9999885212291424,
                0.9999970976890532,
                0.9999945777816768
            ],
            [
                5.043475284430694e-07,
                1.209866116170145e-06,
                1.2098652508287273e-06,
                5.04347408197782e-07,
                1.3709576971242028e-06,
                6.475950297993789e-07,
                1.553498495308628e-06,
                1.209865250822125e-06,
                3.9278610661822475e-07,
                4.4508510499737865e-07
            ],
            [
                3.059021904571643e-07,
                3.05902117523595e-07,
                5.715007195431641e-07,
                5.04347648686092e-07,
                5.715003107715166e-07,
                3.4663257978465195e-07,
                5.715004470295662e-07,
                1.27519073289925e-07,
                8.315281267513512e-07,
                1.3709573702248741e-06
            ],
            [
                6.47594566597747e-07,
                1.0677024881941248e-06,
                1.4449798650551755e-07,
                1.4449795205429202e-07,
                2.3823690999236795e-07,
                6.475951069985296e-07,
                2.102433159721477e-07,
                1.1478772230407462e-05,
                5.715003789017068e-07,
                3.9278615343901467e-07
            ],
            [
                0.9999646437493069,
                0.9999990577556308,
                0.9999930377445807,
                0.9999989322972572,
                0.9999599363173919,
                0.9999994956524114,
                0.9999785550464821,
                0.9999995549150542,
                0.9999996940978825,
                0.9999785550515924
            ],
            [
                0.9999986290426298,
                0.999998005270992,
                0.9999984465020603,
                0.9999996533672962,
                0.9999994284997574,
                0.9999984465015047,
                0.9999885212305079,
                0.9999982396567867,
                0.9999994284996891,
                0.9999994284993485
            ],
            [
                0.9999991684721706,
                0.9999980052702786,
                0.9999991684717742,
                0.9999982396574163,
                0.9999991684720715,
                0.9999974387168733,
                0.9999967112521109,
                0.9999938558268633,
                0.9999992661786696,
                0.999999352405279
            ],
            [
                0.9999994284995529,
                0.999985261018029,
                0.9999986290426297,
                0.999999266179282,
                0.9999990577549569,
                0.9999991684720715,
                0.9999990577549568,
                0.9999989322975119,
                0.9999967112509348,
                0.9999977396746245
            ],
            [
                0.9999938558232019,
                0.99999862904312,
                0.999998629042303,
                0.999991060300501,
                0.99999893229713,
                0.999999057755743,
                0.9999993524053562,
                0.9999810748427396,
                0.9999687980849129,
                0.9999869928653341
            ],
            [
                0.9998911031037506,
                0.5,
                0.02931222831345362,
                0.999972464312192,
                0.5,
                0.9997040428661479,
                0.9997694932851432,
                0.999975699747687,
                0.99979657310026,
                0.999738809753899
            ],
            [
                2.3823702359138736e-07,
                1.6373772528320538e-07,
                2.699577452655852e-07,
                3.9278615343222713e-07,
                5.715003107619008e-07,
                2.1024336609638268e-07,
                4.4508521110762794e-07,
                4.4508494579673306e-07,
                3.4663278639044955e-07,
                3.4663262110630603e-07
            ],
            [
                0.9999980052695652,
                0.9999869928653372,
                0.999996273358939,
                0.9999980052707542,
                0.9996646498908519,
                0.9999869928746379,
                0.9999982396567867,
                0.9999962733602719,
                0.999959936298279,
                0.9999962733593832
            ],
            [
                0.9999993524054334,
                0.9999991684719723,
                0.9999980052695652,
                0.9999982396569966,
                0.9999957771655488,
                0.9999967112497589,
                0.9999990577552939,
                0.9999982396572065,
                0.9999970976890531,
                0.9999986290427931
            ],
            [
                0.9999986290426298,
                0.9999986290421394,
                0.9999687980960721,
                0.9999990577554061,
                0.999997438717484,
                0.9999977396765106,
                0.9999982396574163,
                0.9999986290424664,
                0.9999980052695652,
                0.999999428499553
            ],
            [
                0.9999974387184003,
                0.9999995549151073,
                0.9999986290421394,
                0.9999977396762411,
                0.9999986290427932,
                0.999998239656367,
                0.9999977396748939,
                0.9999996533673788,
                0.999998790134028,
                0.9999987901340283
            ],
            [
                3.4663257978638593e-07,
                5.043474081993875e-07,
                5.715005832872586e-07,
                3.9278615344178325e-07,
                9.422443692527585e-07,
                2.3823699519143784e-07,
                2.382368531929327e-07,
                8.315277302701984e-07,
                5.715002426460124e-07,
                5.043472278299047e-07
            ],
            [
                0.9999832985701967,
                0.9999910603026306,
                0.9999546021259605,
                0.9999885212346123,
                0.9999970976887069,
                0.9999982396574163,
                0.9999945777810304,
                0.9999546021422488,
                0.9999885212359801,
                0.9999952149055056
            ],
            [
                0.999925153746088,
                0.9999756997621728,
                0.999988521231877,
                0.9998415638399517,
                0.9999546021313694,
                0.9999546021151431,
                0.999664649851708,
                0.7310585903489892,
                0.9999756997650627,
                0.999972464302351
            ],
            [
                0.9999952149072168,
                0.9999930377420904,
                0.9999952149037941,
                0.9999986290424663,
                0.9999977396748938,
                0.9999921107345933,
                0.9999977396754327,
                0.9999957771655489,
                0.9999990577554061,
                0.9999962733616046
            ],
            [
                0.9999987901344607,
                0.999999352405279,
                0.9999977396762411,
                0.9999987901338838,
                0.9999991684720715,
                0.9999995549148419,
                0.9999997897567091,
                0.9999996533674201,
                0.9999984465026159,
                0.9999991684722698
            ],
            [
                0.9997388097536861,
                0.9999687980774782,
                0.9999832985761674,
                0.9999646437410106,
                0.9999339478632563,
                0.9997694933127227,
                0.9998601778594738,
                0.9999546021314398,
                0.9998911030654155,
                0.9999724643090512
            ],
            [
                3.0590222691880844e-07,
                3.05902226922147e-07,
                6.475947209953583e-07,
                1.2751899728286965e-07,
                1.7603427935967163e-06,
                1.0677027427525368e-06,
                3.4663257978638593e-07,
                2.1024331597152624e-07,
                9.422448185388577e-07,
                1.3709578604831862e-06
            ],
            [
                0.9998415637647566,
                0.9998601779260412,
                0.999925153746088,
                0.9999785550541502,
                0.99999893229713,
                0.9998601779429858,
                0.9999724643023485,
                0.9999251537550087,
                0.9999417087484261,
                0.9999251537461851
            ],
            [
                9.422444815409489e-07,
                1.8925143720384422e-05,
                6.475951069808602e-07,
                1.3709576971316842e-06,
                5.04347588540266e-07,
                2.5612819051373276e-06,
                1.0677029972993568e-06,
                1.2098659719601033e-06,
                6.475947209985977e-07,
                6.475951069896949e-07
            ],
            [
                2.699578096393206e-07,
                1.2098653950480359e-06,
                3.9278615343901467e-07,
                5.04347287945184e-07,
                2.1024339115914997e-07,
                3.927862002606139e-07,
                2.6995780963846126e-07,
                4.450852111120808e-07,
                3.466325384661554e-07,
                1.4449802095504282e-07
            ],
            [
                0.24508501313237172,
                0.9999852610162758,
                0.9995121429431802,
                0.09534945847239203,
                0.9998204720559609,
                0.015906393023865786,
                NaN,
                0.9984988174082263,
                0.9988304898888848,
                0.999373665715171
            ],
            [
                1.8553919030624466e-07,
                3.92786293909545e-07,
                1.2098656835136636e-06,
                3.4663253846718004e-07,
                1.8553905759809327e-07,
                7.338210679816025e-07,
                7.338208055579897e-07,
                3.927861534406222e-07,
                4.4508505193386385e-07,
                3.4663253846473677e-07
            ],
            [
                5.71500378868701e-07,
                3.466325797827604e-07,
                4.450849458125204e-07,
                1.2098653949192932e-06,
                5.715002426254813e-07,
                2.699578096302362e-07,
                1.7603427935342762e-06,
                2.5612822106421996e-06,
                3.466325384589045e-07,
                1.2098658276730537e-06
            ],
            [
                2.6995771309210433e-07,
                7.338212429537553e-07,
                1.637376276909393e-07,
                3.4663257978780455e-07,
                1.553498495308628e-06,
                5.715005151574337e-07,
                8.315282259009745e-07,
                4.450851049941403e-07,
                8.315283250343497e-07,
                1.553498310118888e-06
            ],
            [
                0.9999982396574163,
                0.9999994956527121,
                0.9999992661791944,
                0.9999995549147358,
                0.9999992661786696,
                0.9999996072137529,
                0.9999990577554061,
                0.9999982396572065,
                0.9999993524050474,
                0.9999987901341723
            ],
            [
                0.9999599363173673,
                0.9999885212318748,
                0.9999756997650834,
                0.9999646437535161,
                0.9998766053664693,
                0.99995993630782,
                0.9998911030907348,
                0.9999546021476033,
                0.9999785550439215,
                0.9999599363078219
            ],
            [
                3.4663266243111764e-07,
                2.3823699519143784e-07,
                2.699577130944368e-07,
                2.6995768091383957e-07,
                5.715006514105942e-07,
                1.994729008105057e-06,
                2.3823682479292225e-07,
                6.475951069961737e-07,
                4.450850519360903e-07,
                6.475951069961737e-07
            ],
            [
                3.9278615344178325e-07,
                2.102434412871794e-07,
                1.2098653950480359e-06,
                1.855391460719133e-07,
                5.715004470295662e-07,
                2.1024326584639497e-07,
                5.715005151550947e-07,
                2.6995768091383957e-07,
                1.637377643243723e-07,
                1.4449805540585765e-07
            ],
            [
                0.999999266178757,
                0.9999687980886387,
                0.999994577780384,
                0.9999945777823233,
                0.9999921107345936,
                0.999993855824666,
                0.9990889487350275,
                0.9999992661787571,
                0.9999930377445806,
                0.9999984465015046
            ],
            [
                1.7603434230537046e-06,
                1.8553905759893702e-07,
                3.0590226338490835e-07,
                9.422447062030659e-07,
                1.7603425837062577e-06,
                1.0677029972993568e-06,
                5.715002426202836e-07,
                7.338209805133949e-07,
                4.450852111100568e-07,
                1.0677026154619133e-06
            ],
            [
                0.9999485577740932,
                0.9986749777017122,
                0.0758581727088564,
                0.999704042936482,
                0.22270013882530884,
                0.9998911030518237,
                0.9999417087275401,
                0.9999417087414922,
                0.9999869928747971,
                0.9993736657560142
            ],
            [
                1.9947290080343035e-06,
                5.043473480730849e-07,
                6.144173868312501e-06,
                1.3709575336654889e-06,
                5.715005832827105e-07,
                8.315277302701984e-07,
                1.7603434230729168e-06,
                9.422442568951678e-07,
                1.2098659719524008e-06,
                3.4663266242969896e-07
            ],
            [
                0.9999991684719723,
                0.999996273360272,
                0.9999996072137529,
                0.9999982396561574,
                0.9999957771655492,
                0.9999938558268634,
                0.9999962733598275,
                0.9999992661790196,
                0.9999992661790195,
                0.9999977396757023
            ],
            [
                0.9999898700053986,
                0.999925153781771,
                0.9999852610110074,
                0.9999898700126439,
                0.9999151889788636,
                0.999985261011009,
                0.9999756997621856,
                0.9999987901338838,
                0.9999852610233012,
                0.9992903296275656
            ],
            [
                0.999999266179107,
                0.9999994284997574,
                0.9999982396561572,
                0.9999991684717742,
                0.999996273358939,
                0.9999990577554061,
                0.9999974387180947,
                0.999998446502801,
                0.9999962733593833,
                0.9999986290429567
            ],
            [
                0.9999990577554061,
                0.999999554915001,
                0.9999997617631752,
                0.9999997617631468,
                0.9999997300420937,
                0.9999986290423029,
                0.9999996072139402,
                0.9999996940976636,
                0.999998790134605,
                0.9999987901341724
            ],
            [
                0.9999967112521108,
                0.9999974387187053,
                0.9999967112501507,
                0.9999986290426298,
                0.9999962733611603,
                0.9999990577549568,
                0.9999921107355342,
                0.9999832985781574,
                0.9999921107364745,
                0.9999984465026159
            ],
            [
                2.1024344128660572e-07,
                7.338209804600024e-07,
                4.450851580497677e-07,
                2.1024344128488479e-07,
                1.444979520533721e-07,
                2.699576809121209e-07,
                5.043473480405171e-07,
                5.715003107715166e-07,
                3.059022269206168e-07,
                1.8553912395160867e-07
            ],
            [
                6.47594952559303e-07,
                3.466327037319744e-07,
                1.0677029970871782e-06,
                8.315281267248819e-07,
                1.0677027427340866e-06,
                6.475946437027523e-07,
                7.338208929998139e-07,
                5.715005831829134e-07,
                1.994729483608425e-06,
                3.9278638752956223e-07
            ],
            [
                3.0590237279032884e-07,
                1.2751904288617538e-07,
                2.3823688159237777e-07,
                3.4663257978780455e-07,
                3.4663257978780455e-07,
                2.382369667914917e-07,
                3.466325797896173e-07,
                2.699578096399958e-07,
                4.450852641717689e-07,
                1.8553903548231313e-07
            ],
            [
                3.0590226339061185e-07,
                2.1024339116082313e-07,
                1.6373766672821107e-07,
                3.4663270375278157e-07,
                4.4508526417014975e-07,
                1.4449802095504282e-07,
                3.0590226338671677e-07,
                2.102433410343832e-07,
                2.1024344128584085e-07,
                3.466325797778739e-07
            ],
            [
                9.422444815628016e-07,
                3.4663253846718004e-07,
                1.3709572068422585e-06,
                3.9278634073312583e-07,
                4.450852641717689e-07,
                3.059023727894942e-07,
                5.715006514040971e-07,
                8.315283250343497e-07,
                2.6995774527577444e-07,
                1.0677027426952437e-06
            ],
            [
                3.9278634073312583e-07,
                6.475951069961737e-07,
                5.04347468318358e-07,
                1.444980726319581e-07,
                1.8553907971682908e-07,
                9.422443692390473e-07,
                1.1253521571574156e-07,
                4.4508489275469177e-07,
                3.059021904571643e-07,
                7.338211554641698e-07
            ],
            [
                2.3823690999063455e-07,
                3.466327037548308e-07,
                5.715004470295662e-07,
                2.1024326584505647e-07,
                5.043476486883855e-07,
                1.855391239505118e-07,
                6.475947982002148e-07,
                2.6995790618252024e-07,
                4.450851580555361e-07,
                2.699577452746696e-07
            ],
            [
                1.444980209556342e-07,
                3.466325384661554e-07,
                5.715007195410849e-07,
                2.3823699519035448e-07,
                3.466327450756327e-07,
                3.466327863879275e-07,
                2.3823696679230424e-07,
                1.0677031245783732e-06,
                1.6373766672821107e-07,
                7.338213304316717e-07
            ],
            [
                1.7603434231097403e-06,
                3.927861534222245e-07,
                1.2098662603862553e-06,
                9.422444815563743e-07,
                4.450848927621807e-07,
                2.6995784182073116e-07,
                1.7603432132912532e-06,
                6.475951069961737e-07,
                1.0677033791437343e-06,
                4.450852641717689e-07
            ],
            [
                3.466324971396247e-07,
                5.043475284447896e-07,
                3.9278610661366994e-07,
                6.475950297971703e-07,
                1.3709570434054234e-06,
                3.0590222692437275e-07,
                5.71500378896509e-07,
                9.422447062202052e-07,
                5.715002426410745e-07,
                1.7603434231705793e-06
            ],
            [
                9.42244256915735e-07,
                2.699578418198104e-07,
                4.450848927637999e-07,
                2.3823699519143784e-07,
                3.059023363221292e-07,
                1.5534973841450852e-06,
                3.05902263389638e-07,
                2.3823685319244518e-07,
                1.637377643237766e-07,
                2.1024339116010604e-07
            ],
            [
                3.9278605979011705e-07,
                1.444980726319581e-07,
                2.3823690999160957e-07,
                1.444980209564556e-07,
                3.927862002556126e-07,
                7.338212429420757e-07,
                5.043474081867732e-07,
                1.637377448031548e-07,
                2.1024326584505647e-07,
                5.043474081993875e-07
            ],
            [
                1.0677032518413822e-06,
                9.422448185264317e-07,
                2.3823702359290413e-07,
                9.422447062202052e-07,
                4.450849458218309e-07,
                9.931194509683815e-08,
                2.6995777745711594e-07,
                1.2098653950480359e-06,
                8.315282258900085e-07,
                9.422447062202052e-07
            ]
        ]
    },
    {
        "q_id": "8732_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            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,
            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": [
            [
                0.005220126027259149,
                0.03732689015525377,
                0.46879062662624377,
                0.6513548646660542,
                0.009708475021981636,
                0.03308597505175204,
                0.06754669489377622,
                0.3208212943308302,
                0.9994472212860898,
                0.060086655644158424
            ],
            [
                6.14417679836736e-06,
                7.889266345957247e-06,
                6.962259566635186e-06,
                6.962257907702715e-06,
                2.4300243591756525e-05,
                3.7266392832104296e-06,
                2.5612819048205203e-06,
                4.222831933864508e-06,
                1.9947294835866542e-06,
                2.5612831266165976e-06
            ],
            [
                1.012998975391288e-05,
                4.222831933726245e-06,
                4.785096204650886e-06,
                3.2887486729337966e-06,
                6.144176064364297e-06,
                5.422219615069953e-06,
                8.939699491123385e-06,
                6.144176065582494e-06,
                8.939693096068342e-06,
                8.939699499627926e-06
            ],
            [
                3.2887498488809053e-06,
                1.760343003035712e-06,
                2.9023116384112864e-06,
                3.7266397271876744e-06,
                2.1444958600728787e-05,
                1.0129988561906404e-05,
                2.260324836341129e-06,
                7.484625372354849e-05,
                1.0129992186202796e-05,
                5.422221554374162e-06
            ],
            [
                2.2603253749309368e-06,
                3.288747887820713e-06,
                1.7603425834212764e-06,
                3.288749065077638e-06,
                6.962257064546644e-06,
                4.222833947428939e-06,
                4.785093923420688e-06,
                3.2887490645272776e-06,
                4.785095633999427e-06,
                3.726637950241874e-06
            ],
            [
                3.7266406165827946e-06,
                3.2887486729337966e-06,
                6.144173865328478e-06,
                3.726641060244989e-06,
                6.962253758916883e-06,
                5.422218967797024e-06,
                7.889261642363733e-06,
                1.8925154985774363e-05,
                7.889261639780667e-06,
                1.6701417854810315e-05
            ],
            [
                1.3007134657464394e-05,
                9.610239954721475e-05,
                1.8925157247225074e-05,
                1.1478764015736973e-05,
                1.4738985474764149e-05,
                2.4300243590165296e-05,
                1.8925154973863657e-05,
                1.6701417845878833e-05,
                2.7535700923478902e-05,
                3.2887494570719725e-06
            ],
            [
                1.0129995807165349e-05,
                6.144175333155351e-06,
                6.1441738616627104e-06,
                4.785096205077381e-06,
                6.962258738131379e-06,
                2.9023130228444433e-06,
                6.962257076628275e-06,
                6.144175332596544e-06,
                5.422220260656402e-06,
                2.9023119843875324e-06
            ],
            [
                4.7850933535006355e-06,
                2.902311638759718e-06,
                6.144173868044274e-06,
                4.785095064436034e-06,
                3.726637950723161e-06,
                4.222834450505264e-06,
                1.5534979396984994e-06,
                4.785093351568349e-06,
                2.561282821069686e-06,
                2.561281905058126e-06
            ],
            [
                1.0129993391236997e-05,
                1.4738981951974817e-05,
                2.1444940681867538e-05,
                2.75356844906435e-05,
                7.88926540454376e-06,
                3.535625487947387e-05,
                4.785092782501357e-06,
                4.785096776068365e-06,
                5.4222215550004564e-06,
                2.144495094975719e-05
            ],
            [
                2.1444940737257882e-05,
                0.00026119033360345797,
                0.00010889690835016822,
                6.605214442935156e-05,
                6.605212881496996e-05,
                5.1442225785164145e-05,
                0.00017952794173786783,
                2.144494580992165e-05,
                1.6701423822135842e-05,
                0.00010889690879065533
            ],
            [
                1.0129988556065312e-05,
                3.7266410589163644e-06,
                3.535624645507245e-05,
                6.9622545849505825e-06,
                2.4300246501849726e-05,
                1.3007126887061138e-05,
                6.962259568775433e-06,
                6.144173135628569e-06,
                5.422218321441422e-06,
                7.889264464508026e-06
            ],
            [
                8.93970056424046e-06,
                1.0129988554775483e-05,
                6.96225375833433e-06,
                1.4738987221038477e-05,
                1.4738985479214553e-05,
                1.0129987349373336e-05,
                1.4738983718463215e-05,
                1.4738988993050295e-05,
                1.4738987239295859e-05,
                1.0129992185539456e-05
            ],
            [
                7.88926634644516e-06,
                1.4738983726184394e-05,
                6.96225707894582e-06,
                2.260324297492425e-06,
                1.1478768112422929e-05,
                5.422217029943586e-06,
                1.147876675124548e-05,
                1.0129989771473008e-05,
                1.30071253611406e-05,
                6.14417679836736e-06
            ],
            [
                1.892515048449202e-05,
                1.4738981966291175e-05,
                6.962255418063657e-06,
                1.6701429795417824e-05,
                1.0129988552896015e-05,
                3.2887494564079503e-06,
                4.0063691962493854e-05,
                5.4222196143006464e-06,
                4.785095064044355e-06,
                2.4300249384892373e-05
            ],
            [
                6.144173866379033e-06,
                6.1441753313895225e-06,
                1.9947306721859212e-06,
                1.3007125354586914e-05,
                2.56128221029278e-06,
                6.475946437333795e-07,
                6.96225458545715e-06,
                6.96225458545715e-06,
                4.785092778253809e-06,
                3.7266388390502134e-06
            ],
            [
                3.2887494567070593e-06,
                7.889266341623432e-06,
                1.0129989769962063e-05,
                5.422220907909759e-06,
                1.0129990977262395e-05,
                6.9622562478334885e-06,
                6.962258733787562e-06,
                8.939698432690187e-06,
                4.222835453355155e-06,
                6.9622562489985925e-06
            ],
            [
                1.6701429788430605e-05,
                5.422219615286937e-06,
                3.2887502412970765e-06,
                2.561283126048207e-06,
                6.962258738131379e-06,
                1.5534973838144677e-06,
                7.889261642363733e-06,
                2.260325375572331e-06,
                3.535626269421476e-05,
                2.561282209081457e-06
            ],
            [
                1.3007133107528522e-05,
                6.96225375863827e-06,
                4.7850967744320136e-06,
                1.0677031242428688e-06,
                8.939699499432793e-06,
                3.288748280449018e-06,
                1.6701419835959236e-05,
                1.1478773586115126e-05,
                5.422218321993744e-06,
                1.4738978451920916e-05
            ],
            [
                8.939697367703906e-06,
                6.144174595777273e-06,
                2.1444956049650475e-05,
                6.144173867284299e-06,
                1.5534979394696104e-06,
                6.96225873459807e-06,
                1.147877222485351e-05,
                1.0129988557686814e-05,
                1.9947294833780224e-06,
                5.4222209070122355e-06
            ],
            [
                1.0129992183991656e-05,
                5.1442237637243264e-05,
                2.7535704167133664e-05,
                3.53562633082504e-05,
                6.962256244819412e-06,
                6.962258736902953e-06,
                7.88925976080083e-06,
                3.7266397272757976e-06,
                2.902313022305958e-06,
                8.939700562110258e-06
            ],
            [
                2.2603240281236263e-06,
                5.422217676200406e-06,
                8.93969736547614e-06,
                4.222833442816421e-06,
                8.939694167314623e-06,
                7.88926634305847e-06,
                2.561282515564741e-06,
                7.889259757385442e-06,
                3.7266401719851935e-06,
                6.144177528436518e-06
            ],
            [
                7.889263523668778e-06,
                3.535626325448691e-05,
                4.0063701703217896e-05,
                1.670141586150995e-05,
                1.4738983724575818e-05,
                3.5356250638847714e-05,
                1.89251527371985e-05,
                1.67014158650947e-05,
                6.605214451056634e-05,
                1.6701423825538316e-05
            ],
            [
                0.0001233945595223613,
                1.892515499864894e-05,
                6.605215211303957e-05,
                2.9023119835956434e-06,
                1.6701429797422853e-05,
                6.962257908044647e-06,
                2.4300234907624647e-05,
                1.473897669245728e-05,
                2.144495860338128e-05,
                1.4738980200124708e-05
            ],
            [
                1.0129987351289655e-05,
                1.89251482218717e-05,
                3.535623794449717e-05,
                0.9996200155291136,
                1.8925143719695944e-05,
                2.7535684477821552e-05,
                7.889266344981421e-06,
                3.5356254894393866e-05,
                2.7535691001590016e-05,
                1.3007128458384476e-05
            ],
            [
                0.9994472213559051,
                0.9978172837326448,
                0.9998601778611258,
                0.9996200155303406,
                0.9999646437451205,
                0.9924227577166485,
                0.9953904288440594,
                0.9796676476590934,
                0.9999038975512032,
                0.998830489847136
            ],
            [
                3.726641060536473e-06,
                7.889262584006375e-06,
                6.962253756687988e-06,
                8.315279285012978e-07,
                1.7603440524340693e-06,
                5.422218967649081e-06,
                1.1478772226690907e-05,
                1.1478768118310953e-05,
                2.9023123280039903e-06,
                3.7266392833663395e-06
            ],
            [
                2.2603237586397375e-06,
                6.144172402765906e-06,
                3.2887478885505384e-06,
                8.9396941718352e-06,
                3.7266397278791014e-06,
                7.889259761489647e-06,
                4.222835457003754e-06,
                1.2098658276862581e-06,
                3.288747889038086e-06,
                4.785096203884934e-06
            ],
            [
                3.1201900191715896e-05,
                6.962256247998122e-06,
                4.539786854257018e-05,
                4.006370157496225e-05,
                1.1478766747236611e-05,
                3.2887490644495094e-06,
                2.7535691022025e-05,
                1.012998734896796e-05,
                6.962257076628275e-06,
                1.4738980172564383e-05
            ],
            [
                0.9997040429059132,
                0.9990889486221761,
                0.9997040427646766,
                0.9988304897001311,
                0.9982992772151973,
                0.9991959142004607,
                0.9997965731017547,
                0.9988304895789644,
                0.9998204720143622,
                0.9996200154828161
            ],
            [
                1.3007123803563812e-05,
                7.889262574994342e-06,
                1.8925155001402863e-05,
                4.5397890240179425e-05,
                3.120190017071685e-05,
                8.93969523358515e-06,
                8.939694167932546e-06,
                2.1444958616409722e-05,
                2.4300243593170955e-05,
                1.3007128453983806e-05
            ],
            [
                8.939693103158165e-06,
                1.1478773580769965e-05,
                4.222831932543332e-06,
                2.1444945830751543e-05,
                6.96225458545715e-06,
                1.4738981962698681e-05,
                4.222835456105047e-06,
                1.147877222702498e-05,
                1.6701421824277888e-05,
                1.6701429796754513e-05
            ],
            [
                7.889260703117714e-06,
                6.962257906765564e-06,
                3.7266383950934104e-06,
                1.3709578604831862e-06,
                7.889264463675704e-06,
                5.4222202617511845e-06,
                3.726637950851956e-06,
                4.222831933296096e-06,
                5.422218321441422e-06,
                1.5534981249023245e-06
            ],
            [
                1.012999459934851e-05,
                1.473897669245728e-05,
                1.1478773594675732e-05,
                4.222832436587256e-06,
                2.4300243461452534e-05,
                7.88926258381982e-06,
                1.3007133109421283e-05,
                6.962257077033528e-06,
                6.962257077033528e-06,
                5.422218969384951e-06
            ],
            [
                2.561281293754979e-06,
                3.288748280891699e-06,
                1.147876401460948e-05,
                2.2603253754921562e-06,
                4.785093922654737e-06,
                8.939694162111085e-06,
                2.9023119844508833e-06,
                6.962257907348116e-06,
                2.260324567177841e-06,
                8.939693100686484e-06
            ],
            [
                1.4738978450955768e-05,
                2.9023116377197043e-06,
                3.288748280837859e-06,
                8.93969310367852e-06,
                4.785094494019719e-06,
                6.144176797730321e-06,
                2.2603240282243575e-06,
                3.2887482803712492e-06,
                6.144177530425867e-06,
                5.422221553910605e-06
            ],
            [
                6.144175332596544e-06,
                1.0129994600159262e-05,
                1.3007133114318805e-05,
                6.9622562478334885e-06,
                1.3007126904521862e-05,
                6.962259568509485e-06,
                2.260324028255194e-06,
                6.9622579075254155e-06,
                5.4222202617511845e-06,
                1.14787708580381e-05
            ],
            [
                1.9947294833417385e-06,
                4.78509563374701e-06,
                6.144172400295984e-06,
                4.785094492383368e-06,
                1.9947292455918548e-06,
                5.42222155426567e-06,
                6.962253757840428e-06,
                5.422218321855664e-06,
                1.5534979396448094e-06,
                8.939697366793286e-06
            ],
            [
                1.147876400863794e-05,
                3.726637945218865e-06,
                1.7603427931932593e-06,
                4.222831933564939e-06,
                1.3709578604308174e-06,
                2.56128159959988e-06,
                4.222835454952857e-06,
                1.0129989768616954e-05,
                6.962257907880012e-06,
                3.288749064371741e-06
            ],
            [
                6.9622537576631295e-06,
                1.0129989768616954e-05,
                3.2887478887419687e-06,
                1.0677032518093368e-06,
                7.889264462958184e-06,
                1.4738983715996728e-05,
                5.422217029736466e-06,
                1.6701421835335913e-05,
                7.88926258381982e-06,
                1.4738980207899506e-05
            ],
            [
                1.3007130012010681e-05,
                4.785093923420688e-06,
                8.939698431942181e-06,
                1.7603440525925705e-06,
                8.9396973679153e-06,
                3.726637950411341e-06,
                2.902311984915459e-06,
                4.785095064148803e-06,
                7.889264465397747e-06,
                1.9947299591826594e-06
            ],
            [
                2.2603253753174176e-06,
                6.962255416100709e-06,
                1.3007134632243331e-05,
                6.144174600985344e-06,
                7.889261641674914e-06,
                7.889260702342794e-06,
                7.889263523008662e-06,
                5.422218968822766e-06,
                3.726640171686931e-06,
                5.422220908116881e-06
            ],
            [
                2.5612812940671274e-06,
                1.7603438426491283e-06,
                4.2228354568040404e-06,
                4.2228339475595195e-06,
                5.422220908018252e-06,
                1.7603427932316836e-06,
                3.7266401716055872e-06,
                3.726640615840528e-06,
                3.288748672879957e-06,
                5.422219615069953e-06
            ],
            [
                4.222831932543332e-06,
                3.7266401719851935e-06,
                3.2887494563241995e-06,
                3.2887494561507166e-06,
                1.0129994594944656e-05,
                1.3007123797838208e-05,
                8.939695232316787e-06,
                6.144174599700092e-06,
                5.422218968477564e-06,
                1.1478773587200861e-05
            ],
            [
                2.4300249404340734e-05,
                1.4738987238035806e-05,
                4.006368735141308e-05,
                5.422217676299034e-06,
                1.1478768118310953e-05,
                6.9622570777680525e-06,
                2.1444940700278978e-05,
                1.0129992181043471e-05,
                1.0129990978441666e-05,
                8.4811051118468e-05
            ],
            [
                0.924141827813457,
                0.2942149721629888,
                0.9992903295284549,
                0.9993736659209173,
                0.9997694933191212,
                0.18242552380635635,
                0.9994472214496462,
                0.9998766054705328,
                0.9997965730106448,
                0.9971990733138151
            ],
            [
                1.9947304343125304e-06,
                4.785094494463623e-06,
                1.14787735942999e-05,
                1.3007126902392506e-05,
                4.222833443553821e-06,
                4.785096775389454e-06,
                2.4300234928664224e-05,
                1.4738987237553233e-05,
                1.670142183825232e-05,
                3.726640172385136e-06
            ],
            [
                3.726638838711279e-06,
                1.8925150466660388e-05,
                6.144176796221545e-06,
                2.2603242974060834e-06,
                1.4738985458142157e-05,
                8.939695232316787e-06,
                2.9023109466489728e-06,
                7.889264460776929e-06,
                3.7266406165319545e-06,
                1.3007123805078022e-05
            ],
            [
                2.5612831262578596e-06,
                6.96225956837018e-06,
                3.7266410608245674e-06,
                3.2887502411564953e-06,
                1.8925143714394646e-05,
                7.889263525534328e-06,
                2.260325375391425e-06,
                8.939699499627926e-06,
                2.9023119847359636e-06,
                2.9023112926251358e-06
            ],
            [
                2.753569108924008e-05,
                6.605217603921075e-05,
                6.962255413517216e-06,
                4.7850950646797465e-06,
                3.1201922511884416e-05,
                1.9947297213492663e-06,
                4.0063692054313215e-05,
                1.0129995805027913e-05,
                1.5534981248528732e-06,
                1.6701419835959236e-05
            ],
            [
                1.670142578341747e-05,
                4.539786839525728e-05,
                2.430023777599125e-05,
                2.4300231932115665e-05,
                7.889260701237816e-06,
                1.0129989770441144e-05,
                1.1478766741849697e-05,
                4.0063682500145096e-05,
                4.006369191206607e-05,
                3.288748280658394e-06
            ],
            [
                3.535626741099656e-05,
                1.4738985454496043e-05,
                2.144494327998681e-05,
                7.889261643181705e-06,
                1.473898543980435e-05,
                2.7535691060090174e-05,
                2.4300249375698603e-05,
                2.1444943281001e-05,
                2.561283430765865e-06,
                1.0129989757856078e-05
            ],
            [
                5.422217675874929e-06,
                6.9622570747539755e-06,
                2.4300249409733237e-05,
                6.96225458885115e-06,
                3.7266406161591266e-06,
                5.422218322664422e-06,
                4.785093923916815e-06,
                6.144173133762157e-06,
                1.0129992185060374e-05,
                3.7266410605974813e-06
            ],
            [
                0.053403334131154334,
                0.9988304900003963,
                0.9964063970534219,
                0.0008040859196819181,
                0.005220126022422906,
                0.033085982083187186,
                0.0009110512667738496,
                0.0953494616857507,
                0.08509904558710156,
                0.9998204720152111
            ],
            [
                0.9982992773845863,
                0.9999251537819083,
                0.9997388096703332,
                0.9999646437451953,
                0.9999724643187865,
                0.9993736657656694,
                0.9914225133745455,
                0.999860177943238,
                0.9993736657230045,
                0.9984988177336656
            ],
            [
                0.9997388096162996,
                0.007577241632036805,
                0.9996646498269748,
                0.00359360262477218,
                0.009708476875447522,
                0.9980732654526367,
                0.1645164608483867,
                0.001169510137905165,
                0.7057850340255386,
                0.0028009274002308146
            ],
            [
                2.5612828209345766e-06,
                2.9023112924403614e-06,
                1.1478772226690907e-05,
                2.2603237587774727e-06,
                3.726640615921872e-06,
                7.88926446135094e-06,
                4.78509449410676e-06,
                2.5612831262112703e-06,
                2.5612828209345766e-06,
                5.4222215541571775e-06
            ],
            [
                2.43002435793803e-05,
                4.785094492522632e-06,
                2.902312676334868e-06,
                1.0129993390942177e-05,
                1.7603425833860538e-06,
                6.144173136243255e-06,
                6.962254588433232e-06,
                1.1478765385746131e-05,
                6.962258738701267e-06,
                1.5534981248528732e-06
            ],
            [
                1.994729245749689e-06,
                3.7266410600755218e-06,
                2.902312330849511e-06,
                4.222831933795376e-06,
                2.2603234891147668e-06,
                4.785093923324944e-06,
                1.7603432131119386e-06,
                4.22283294007051e-06,
                2.902312330891746e-06,
                7.889266345770692e-06
            ],
            [
                5.422217675085898e-06,
                7.889264463446097e-06,
                2.902311984873224e-06,
                2.4300237781295346e-05,
                1.3007131559390956e-05,
                4.7850933527085725e-06,
                8.939697367703906e-06,
                4.222832436049568e-06,
                1.0129988557318292e-05,
                1.6701425816409292e-05
            ],
            [
                8.939699499823059e-06,
                1.8925145972677006e-05,
                1.8925141465200488e-05,
                5.422217676397663e-06,
                1.6701427783220165e-05,
                3.120189989194045e-05,
                1.0129990976451642e-05,
                2.144495601735242e-05,
                1.8925148215055747e-05,
                2.1444948367551967e-05
            ],
            [
                6.9622579086271995e-06,
                6.9622579075254155e-06,
                2.4300237791019522e-05,
                3.288749065029781e-06,
                1.67014178590634e-05,
                4.222834954057889e-06,
                8.939695230918335e-06,
                2.7535684498857565e-05,
                8.939700557166892e-06,
                6.60521522946916e-05
            ],
            [
                3.1201922487820644e-05,
                3.120191503554163e-05,
                1.8925157235383214e-05,
                1.0129993391236997e-05,
                1.1478769469800468e-05,
                3.120191133766637e-05,
                1.6701423819158677e-05,
                6.144175332283612e-06,
                1.012998855982425e-05,
                1.3007125339823377e-05
            ],
            [
                2.1444948398445745e-05,
                5.4222215529144515e-06,
                4.785096775580942e-06,
                1.1478773596283455e-05,
                6.144175333635923e-06,
                8.939696301384342e-06,
                5.422220906864292e-06,
                2.4300237812059105e-05,
                7.88926070097951e-06,
                1.8925143712742298e-05
            ],
            [
                0.9959298625445915,
                0.08509904964767095,
                0.9995694429931518,
                0.9991959139943148,
                0.9999339478649093,
                0.5926665999540698,
                0.9980732648911727,
                0.025957354513420506,
                0.9999038975990432,
                0.29421495978593415
            ],
            [
                0.9997040429771514,
                0.999903897597073,
                0.9999339478793599,
                0.9997965730530269,
                0.9999251537826124,
                0.9999151889899189,
                0.9999038975635213,
                0.9968273174410112,
                0.9989677687397241,
                0.9986749772987212
            ],
            [
                6.14417313533799e-06,
                1.67014238214675e-05,
                2.5612825157045092e-06,
                4.222832437386106e-06,
                4.785093352482268e-06,
                1.4738987235622935e-05,
                1.8925143721072897e-05,
                6.144176796780352e-06,
                1.4738978447095178e-05,
                1.8925157255968775e-05
            ],
            [
                2.7535681197606525e-05,
                8.93969843377968e-06,
                5.422220261948442e-06,
                2.1444950948742995e-05,
                2.4300243591756525e-05,
                1.3007128457958606e-05,
                2.430023492769181e-05,
                1.0129989764415789e-05,
                2.1444945849006956e-05,
                2.43002523073625e-05
            ],
            [
                0.9940889316007159,
                0.9992903297487606,
                0.9989677687577307,
                0.9964063966507476,
                0.9980732656066589,
                0.9999151889494887,
                0.9964063976620186,
                0.9997388096647475,
                0.9959298623765959,
                0.9993736657930682
            ],
            [
                2.144494839454502e-05,
                1.0129993385746e-05,
                3.535625066302841e-05,
                2.9023126767360923e-06,
                1.6701427797619914e-05,
                1.0129993389984017e-05,
                1.67014158650947e-05,
                4.539787917023896e-05,
                1.4738976688274975e-05,
                3.120191130543e-05
            ],
            [
                0.9975273773114025,
                0.0031726826075882293,
                0.047425869138458816,
                0.994779874233898,
                0.9890130599499976,
                0.9991959141750199,
                0.0004305570274901695,
                0.998498817636819,
                0.0017007225114479216,
                0.00010889690892692112
            ],
            [
                0.7772998663336157,
                0.9959298618065432,
                0.7772998611746912,
                0.9999251537466108,
                0.999860177933483,
                0.7310585844894971,
                0.9998601779627662,
                0.9982992778051929,
                0.06754669817865512,
                0.4687906266262437
            ],
            [
                4.7850967754851966e-06,
                5.422218323019487e-06,
                3.726640616630245e-06,
                1.3007125355533295e-05,
                6.96225541788636e-06,
                1.3007123809644304e-05,
                6.962258738283349e-06,
                5.422221554038823e-06,
                2.9023126767360923e-06,
                5.422217028109087e-06
            ],
            [
                7.889260702141888e-06,
                1.8925149892881225e-05,
                2.4300246368982074e-05,
                1.670142777884556e-05,
                4.5397879346287815e-05,
                1.3007133108001712e-05,
                1.0129994587353076e-05,
                1.300713309797007e-05,
                2.561282515289864e-06,
                2.2603242977308917e-06
            ],
            [
                1.1478768116055965e-05,
                1.3007131561047124e-05,
                1.8925152736303473e-05,
                1.8925152605216877e-05,
                2.144494322779506e-05,
                1.300713155082621e-05,
                3.120190746725888e-05,
                8.9396930985075e-06,
                4.785096205173126e-06,
                6.9622537584863015e-06
            ],
            [
                8.939695236398313e-06,
                1.1478769489719528e-05,
                6.962257862744856e-06,
                1.3007128454504315e-05,
                4.785096773526798e-06,
                1.1478773593548236e-05,
                8.939695230918335e-06,
                3.2887478884069663e-06,
                1.0129987345393286e-05,
                3.2887490637376303e-06
            ],
            [
                4.785094493636744e-06,
                2.9023126759653203e-06,
                8.939699498814873e-06,
                3.28874867137843e-06,
                1.4738980197336504e-05,
                4.2228349543420954e-06,
                6.144177526670688e-06,
                3.288749848749297e-06,
                5.422218967649081e-06,
                7.889265405677441e-06
            ],
            [
                0.00013982205538476137,
                0.02931223371923813,
                0.06008665354025421,
                0.05340333187132989,
                0.0003353501059576478,
                0.0010322310360345588,
                0.00023050673690969093,
                0.002182716445852275,
                0.017986209304104488,
                0.01798620933700384
            ],
            [
                3.288748671797183e-06,
                3.2887478889034873e-06,
                4.222833946315156e-06,
                4.785092781578734e-06,
                1.2098658276290391e-06,
                4.222835456696504e-06,
                2.5612825153504304e-06,
                1.4738980168060362e-05,
                4.2228334437304904e-06,
                3.288748672168078e-06
            ],
            [
                0.9996200154413385,
                0.16451645470385745,
                0.5312093733737563,
                0.5621765008857981,
                0.9997965730360564,
                0.9998204719542468,
                0.999860177963942,
                0.9982992776956929,
                0.5312093733737562,
                0.9999546021374848
            ],
            [
                6.144176066353646e-06,
                3.535624219155282e-05,
                0.00013982205590760068,
                3.120191135264947e-05,
                2.1444940732342966e-05,
                5.82912652794486e-05,
                4.006370636560259e-05,
                2.7535684497254823e-05,
                7.484620898327916e-05,
                4.539788480710582e-05
            ],
            [
                1.8925154994724604e-05,
                1.3007125350754073e-05,
                3.726641060244989e-06,
                3.7266401704599874e-06,
                8.939700557589678e-06,
                1.3007130009739366e-05,
                1.3007128453415979e-05,
                2.430023202246208e-05,
                3.535625066302841e-05,
                1.8925150490206403e-05
            ],
            [
                6.144176054842241e-06,
                1.0129988562901417e-05,
                5.422220904073088e-06,
                1.0129990976451642e-05,
                1.3709567163491442e-06,
                8.939696300636336e-06,
                6.14417679000762e-06,
                3.7266410598992754e-06,
                2.1444950957402623e-05,
                1.9947301960400456e-06
            ],
            [
                2.4300246467284693e-05,
                5.144220131787343e-05,
                3.120190015664183e-05,
                7.484622642044772e-05,
                1.6701429802769596e-05,
                1.012999097276641e-05,
                5.422217673162632e-06,
                2.4300246500523706e-05,
                4.785093923324944e-06,
                2.1444953506061874e-05
            ],
            [
                0.9997040429979813,
                0.9999339478563708,
                0.9994472212935183,
                0.9998911031303382,
                0.9999339478406392,
                0.9997694932631573,
                0.9999485577927315,
                0.9998766054148069,
                0.9999339478408159,
                0.999664649887037
            ],
            [
                3.7266401719174067e-06,
                1.1478765382927399e-05,
                2.902313368860448e-06,
                2.2603245671202796e-06,
                2.90231233035854e-06,
                7.889264465067689e-06,
                6.144175332887123e-06,
                1.473898898859989e-05,
                6.962255418063657e-06,
                1.9947301968056346e-06
            ],
            [
                0.0008040857658674861,
                0.0006263341365765649,
                0.0021827166192784336,
                0.004609572617378228,
                0.0002611902723350569,
                0.000295957014297884,
                0.00029595709315682396,
                0.0002034270630859672,
                0.07585817949893017,
                0.0008040861261552746
            ],
            [
                0.998967768832998,
                6.1441767989541075e-06,
                1.1478766749115769e-05,
                4.222833946937338e-06,
                2.144494839142443e-05,
                1.3007125355533295e-05,
                6.144173867608406e-06,
                7.889264465067689e-06,
                8.939695236593446e-06,
                6.9622579086271995e-06
            ],
            [
                5.422218968714274e-06,
                5.422218321993744e-06,
                1.473898196763166e-05,
                4.7850967757637256e-06,
                4.785095634930755e-06,
                3.288747888478753e-06,
                2.561282821069686e-06,
                3.2887506328937356e-06,
                2.5612825157464395e-06,
                5.422217030209884e-06
            ],
            [
                0.9996200155663351,
                0.9998911031318276,
                0.9997965729580045,
                0.999447221304838,
                0.9990889487371468,
                0.9999646437369178,
                0.9997694932351955,
                0.9998766054265344,
                0.9996200154391164,
                0.9999151889488297
            ],
            [
                1.0129994585694721e-05,
                1.8925148220012804e-05,
                1.0129989765963588e-05,
                7.889266342800164e-06,
                3.7266388378775e-06,
                1.760342792677731e-06,
                1.1478764005840086e-05,
                1.4738987226400411e-05,
                5.144220743759563e-05,
                1.0129989769188164e-05
            ],
            [
                2.9023126767360923e-06,
                7.88926068579682e-06,
                6.962254588116627e-06,
                8.93969523387785e-06,
                3.7266401712327585e-06,
                1.1478770853110533e-05,
                8.939698425080008e-06,
                5.422220907426478e-06,
                6.962259565292781e-06,
                3.726639727994339e-06
            ],
            [
                1.0129995802853624e-05,
                1.1478766753082876e-05,
                2.5612812943280275e-06,
                5.422218320464995e-06,
                1.8925143716804326e-05,
                1.4738988987366645e-05,
                5.144223795836889e-05,
                8.939693102572767e-06,
                1.3007125353545894e-05,
                2.90231198483099e-06
            ],
            [
                6.144173868781898e-06,
                3.726637950973972e-06,
                1.4738983711868037e-05,
                7.889263524960312e-06,
                3.726637950329997e-06,
                2.144494329192304e-05,
                1.6701429797422853e-05,
                7.88926164299515e-06,
                2.902310946400847e-06,
                5.422221553654169e-06
            ],
            [
                7.889262584006375e-06,
                3.2887494551038347e-06,
                8.939696296928812e-06,
                1.55349756893204e-06,
                1.1478773583860136e-05,
                7.889262581595514e-06,
                4.785093921175058e-06,
                6.9622570739434675e-06,
                2.9023112924403614e-06,
                2.902311292783513e-06
            ],
            [
                4.7850933527085725e-06,
                8.939695235487695e-06,
                1.1478772226690907e-05,
                1.1478769481785311e-05,
                6.144176798132662e-06,
                6.962257076830902e-06,
                3.2887486729876365e-06,
                8.939698428202134e-06,
                1.8925155000025902e-05,
                5.422217026609926e-06
            ],
            [
                0.9998415638020499,
                0.5926665999540698,
                0.5621765008857981,
                0.9997388096759037,
                0.0850990438468576,
                0.9999546021159592,
                0.6224593312018546,
                0.8175744828610095,
                0.999925153756578,
                0.9995121429515532
            ],
            [
                0.08509904210661366,
                0.00317268323717103,
                8.481101067591067e-05,
                0.002182716210560666,
                0.0013250221120430729,
                0.00015843629067854092,
                0.0011695100272095776,
                0.0004305571680759946,
                0.987568346231158,
                0.0008040860120454177
            ],
            [
                0.9998204719784549,
                0.9995121428545396,
                0.9997965729606267,
                0.9999485577816721,
                0.9980732656263593,
                0.9998766054511065,
                0.9996200155135484,
                0.999933947848131,
                0.9998415637651623,
                0.9996200154319861
            ],
            [
                1.670142979323052e-05,
                2.4300249394528152e-05,
                6.9622562453259804e-06,
                1.1478773591084453e-05,
                1.30071330853832e-05,
                1.012999460108057e-05,
                1.14787708580381e-05,
                1.6701417845088975e-05,
                1.0129990967938758e-05,
                1.3007131467260758e-05
            ],
            [
                6.962257063178913e-06,
                8.939696293806686e-06,
                1.892515496381185e-05,
                3.5356250514085596e-05,
                1.9947299590810645e-06,
                5.422221553654169e-06,
                1.6701427792273175e-05,
                7.889260696071684e-06,
                1.0129989759440728e-05,
                1.892514145136205e-05
            ],
            [
                1.012998976043574e-05,
                8.939697366289195e-06,
                3.2887502409830123e-06,
                3.535625429322045e-05,
                3.120190010329292e-05,
                2.561283126502453e-06,
                6.962257077932685e-06,
                6.962256246035174e-06,
                2.4300237770687153e-05,
                5.4222215541571775e-06
            ],
            [
                0.02297736986821033,
                0.00048785720469609646,
                0.0052201262859981525,
                0.029312229744396484,
                0.9982992773490087,
                0.0179862135481215,
                0.014063626617097633,
                0.006692851540337667,
                0.9996200155292794,
                0.00669284951881785
            ],
            [
                4.222833945954137e-06,
                4.006370168310508e-05,
                2.902311638759718e-06,
                6.962258737092915e-06,
                1.0129992185539456e-05,
                8.9396941702904e-06,
                2.4300246465693457e-05,
                7.88926540454376e-06,
                5.422220907426478e-06,
                6.144174600325954e-06
            ],
            [
                6.14417606400666e-06,
                1.670141982216708e-05,
                4.539787393897876e-05,
                1.0677029971065997e-06,
                1.892515273885085e-05,
                8.939696302457574e-06,
                2.5612834317116285e-06,
                4.2228324356808684e-06,
                7.338211554231243e-07,
                1.147877359392407e-05
            ],
            [
                3.120192241222406e-05,
                6.605212857036454e-05,
                2.144494327998681e-05,
                1.4738985438624722e-05,
                8.93969842042934e-06,
                2.430023491664161e-05,
                8.939693101044227e-06,
                4.006368731905769e-05,
                1.3007134658505415e-05,
                4.539785768204387e-05
            ],
            [
                1.553497198801472e-06,
                2.9023112928785396e-06,
                2.260323758676741e-06,
                1.9947294834796172e-06,
                1.7603434230312906e-06,
                1.9947301954885306e-06,
                1.370957043323753e-06,
                3.7266397276079535e-06,
                3.726640616477725e-06,
                3.7266383951544193e-06
            ],
            [
                0.20181322466072713,
                0.04208773076923105,
                0.0013250221852161063,
                0.003593602769001252,
                0.07585818211049714,
                0.0002611904319429955,
                4.006370164200498e-05,
                0.00669285106978476,
                0.022977371791713528,
                9.610243747578487e-05
            ],
            [
                0.1645164608483867,
                0.022977368362860108,
                0.012431651253373898,
                0.9978172836403537,
                0.9984988174057833,
                0.001169510121450415,
                0.029312231175339418,
                8.481105024228644e-05,
                0.9994472214194496,
                0.0059110690915643435
            ],
            [
                8.939694169591174e-06,
                3.726640171131078e-06,
                1.3709573702111586e-06,
                1.9947294833018263e-06,
                6.144173134164498e-06,
                2.5612822098455215e-06,
                8.93969629205049e-06,
                3.28874828059259e-06,
                1.1478765380839446e-05,
                1.0129995804696242e-05
            ],
            [
                0.9997965730763906,
                0.9997965730563123,
                0.9999251538000996,
                0.9996200153972519,
                0.9996200154441464,
                0.998498817990178,
                0.9986749774113308,
                0.9995121429559526,
                0.9998204719928471,
                0.9999251537843102
            ],
            [
                1.1478765384054893e-05,
                1.6701421834728333e-05,
                3.288748280891699e-06,
                6.962257908196617e-06,
                2.2603240274082256e-06,
                7.889266346603015e-06,
                2.430023491549239e-05,
                3.7266388391993445e-06,
                7.889264463675704e-06,
                8.939698432917844e-06
            ],
            [
                0.0035936022512772685,
                0.010986943521150141,
                0.00048785716325666563,
                0.0021827162323657064,
                0.0004878570272445308,
                0.0675466977093867,
                0.022977371206299495,
                0.1192029188930649,
                0.11920293297380237,
                0.02931222751848539
            ],
            [
                5.4222215550004564e-06,
                1.4738988991495334e-05,
                3.2887498483604557e-06,
                7.889266346746518e-06,
                8.939698434820389e-06,
                4.7850927830148924e-06,
                8.939698431682001e-06,
                3.2887502407138142e-06,
                3.726637951126493e-06,
                2.561283126304449e-06
            ],
            [
                4.785095064601411e-06,
                2.7535700899738242e-05,
                6.962256248606003e-06,
                8.939693102865466e-06,
                1.89251572481201e-05,
                1.1478770854906172e-05,
                1.3007134655902864e-05,
                2.1444956049650475e-05,
                2.430025230320762e-05,
                2.4300246465693457e-05
            ],
            [
                1.670142979323052e-05,
                2.5612831263929686e-06,
                7.889266342800164e-06,
                3.7266388391247794e-06,
                8.939694167314623e-06,
                1.4738988995409548e-05,
                2.9023133684671433e-06,
                8.939695234983602e-06,
                1.1478765366390824e-05,
                1.0129994600859455e-05
            ],
            [
                7.88925976126004e-06,
                6.1441745989959955e-06,
                1.1478765381674627e-05,
                7.889259759222289e-06,
                3.726640170337971e-06,
                6.144174596805476e-06,
                8.93969629829474e-06,
                1.5534981245279071e-06,
                3.120191092404195e-05,
                1.4738980185754733e-05
            ],
            [
                4.222831933649433e-06,
                1.0677031244759254e-06,
                6.144175333401224e-06,
                1.2098662604049616e-06,
                1.0129988561077228e-05,
                4.7850967744320136e-06,
                5.422220262037209e-06,
                8.939698432917844e-06,
                1.3007133108948093e-05,
                1.9947304346245714e-06
            ],
            [
                3.7266397276757403e-06,
                6.962254586166343e-06,
                6.962255419279419e-06,
                6.962257908487893e-06,
                1.0129990974903845e-05,
                4.785092781953005e-06,
                1.0677032518093368e-06,
                1.994729483680993e-06,
                4.222834954211514e-06,
                6.1441775309064404e-06
            ],
            [
                2.561282821239737e-06,
                2.2603248365014775e-06,
                5.422218322940583e-06,
                6.144172404218801e-06,
                5.422217676299034e-06,
                4.785094492661896e-06,
                6.962256248314727e-06,
                1.0129995809044816e-05,
                6.96225873895455e-06,
                2.561282210530385e-06
            ],
            [
                0.9986749776020428,
                0.9994472213042591,
                0.9999869928669095,
                0.9999251537475778,
                0.9995694428773665,
                0.9989677692024918,
                0.9997694932938623,
                0.999991060299451,
                0.9999485577810622,
                0.9999151889704591
            ],
            [
                2.5612834317908303e-06,
                3.2887502411564953e-06,
                5.422217676200406e-06,
                1.3007131552624333e-05,
                5.144223196402427e-05,
                1.147877086020957e-05,
                8.939696302457574e-06,
                7.889264464508026e-06,
                2.902311292920774e-06,
                1.1478770859624945e-05
            ],
            [
                1.3007133113017532e-05,
                2.7535694353228506e-05,
                1.1478768094508301e-05,
                2.144494072680393e-05,
                2.144494839938192e-05,
                1.3007133112307748e-05,
                1.300712687816516e-05,
                3.726639283291774e-06,
                4.006371119588617e-05,
                6.144172402765906e-06
            ],
            [
                1.1478772226690907e-05,
                6.605212866263221e-05,
                3.120190762537599e-05,
                2.430024361951464e-05,
                5.829127932776453e-05,
                7.484621817070943e-05,
                0.0002034269963754405,
                1.1478770855323762e-05,
                2.4300249391876106e-05,
                4.006371124165013e-05
            ],
            [
                8.939697365736316e-06,
                3.2887478883351803e-06,
                2.902313367469363e-06,
                1.6701415852639228e-05,
                9.422448184912962e-07,
                2.9023130224960116e-06,
                1.7603438424506017e-06,
                1.0129994596824126e-05,
                4.222832939870796e-06,
                6.962258735585878e-06
            ]
        ]
    },
    {
        "q_id": "8211_mmlu_math",
        "cot_ids": [
            0,
            1,
            4,
            5,
            6,
            7,
            9,
            11,
            17,
            18,
            19,
            20,
            21,
            22,
            25,
            26,
            28,
            29,
            32,
            33,
            34,
            36,
            37,
            38,
            40,
            44,
            48,
            49,
            50,
            51,
            52,
            53,
            56,
            61,
            62,
            64,
            66,
            67,
            69,
            71,
            76,
            77,
            78,
            81,
            82,
            83,
            84,
            85,
            86,
            91,
            93,
            95,
            96,
            97,
            102,
            103,
            107,
            108,
            109,
            112,
            113,
            114,
            115,
            117,
            118,
            119,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.8925154961195625e-05,
                1.4738976686988113e-05,
                1.3007130007988564e-05,
                8.481107145513842e-05,
                7.889264462211963e-06,
                8.939699500636112e-06,
                7.889261643727018e-06,
                2.144494328864643e-05,
                4.785093352238557e-06,
                4.785096205260165e-06
            ],
            [
                1.3007134662054344e-05,
                2.9023133687786197e-06,
                6.144175333926503e-06,
                3.726637951079042e-06,
                6.144176798691468e-06,
                7.889261644057078e-06,
                4.222834450950777e-06,
                8.939700563248534e-06,
                3.288750241410738e-06,
                3.2887494564857185e-06
            ],
            [
                2.5612812944538183e-06,
                4.222833947359807e-06,
                6.962259569117366e-06,
                1.994730672439908e-06,
                1.012998977108606e-05,
                1.012998856312253e-05,
                1.670142182257665e-05,
                2.1444945792602412e-05,
                1.0129994587353076e-05,
                3.7266392817462323e-06
            ],
            [
                1.0129993393945642e-05,
                6.144175329936627e-06,
                3.535625067794842e-05,
                6.14417313680765e-06,
                1.012999580884213e-05,
                3.2887486732358968e-06,
                1.7603440526662173e-06,
                2.5612828212676906e-06,
                4.785093353274332e-06,
                3.7266388396128453e-06
            ],
            [
                8.939696301384342e-06,
                1.2098661161602417e-06,
                4.785093353626844e-06,
                3.2887482811220126e-06,
                2.561283431942246e-06,
                1.760344052650207e-06,
                3.726638395527247e-06,
                1.3007123801954964e-05,
                1.4738983726559732e-05,
                5.422221554038823e-06
            ],
            [
                5.4222202621161125e-06,
                1.4738988988010078e-05,
                2.753568778267916e-05,
                1.012998735462479e-05,
                5.422221553910605e-06,
                2.1444948404530884e-05,
                3.7266383950934104e-06,
                1.0129992185299915e-05,
                6.9622562489985925e-06,
                1.670142778431382e-05
            ],
            [
                4.0063711217164954e-05,
                1.892515048042999e-05,
                7.484620921906373e-05,
                3.535626754334737e-05,
                4.5397863181173815e-05,
                3.1201922514835635e-05,
                7.48462003659803e-05,
                0.0002611903065562918,
                1.3007131561047124e-05,
                1.147876812106705e-05
            ],
            [
                2.1444940741392653e-05,
                1.4738976699106073e-05,
                7.889261644358435e-06,
                2.7535700931292276e-05,
                1.3007125361448172e-05,
                4.539787397828422e-05,
                1.0677032518209896e-06,
                3.2887494569044713e-06,
                2.4300234931404677e-05,
                6.9622537584863015e-06
            ],
            [
                1.8925150493166868e-05,
                2.144494073569759e-05,
                1.4738978449883382e-05,
                7.88925976316864e-06,
                1.4738981968060613e-05,
                6.144177528034176e-06,
                2.561283126304449e-06,
                3.535625067177463e-05,
                1.8925150483734688e-05,
                2.7535681227157105e-05
            ],
            [
                4.006369215691771e-05,
                1.8925155005051806e-05,
                2.7535684529910724e-05,
                5.1442232005568484e-05,
                2.1444950962395557e-05,
                7.484625390487944e-05,
                2.753569764776963e-05,
                8.939694169330997e-06,
                6.962259568509485e-06,
                2.5612812945260317e-06
            ],
            [
                6.605215242107913e-05,
                6.605216821327387e-05,
                0.0003799844808578411,
                1.147877222702498e-05,
                3.120191134788212e-05,
                0.9890130571467676,
                7.889260702744606e-06,
                3.535623802655717e-05,
                4.539787936115123e-05,
                6.962257078553231e-06
            ],
            [
                1.473898899256772e-05,
                2.4300243615448162e-05,
                6.96225458885115e-06,
                6.605214458361157e-05,
                3.535623805163821e-05,
                1.1478766754941153e-05,
                3.1201907623673364e-05,
                1.473898899664279e-05,
                6.14417313680765e-06,
                3.120192251336002e-05
            ],
            [
                1.8925141457627214e-05,
                2.1444956065331412e-05,
                2.7535700927485757e-05,
                2.1444948408977715e-05,
                4.0063682591672956e-05,
                4.006371123902672e-05,
                1.670142780594382e-05,
                7.889264462211963e-06,
                5.42221702873045e-06,
                4.006371117985421e-05
            ],
            [
                6.962253759157502e-06,
                2.5612822103393692e-06,
                1.012999580884213e-05,
                1.3007123810306773e-05,
                1.6701417845088975e-05,
                4.222834449076551e-06,
                1.5534983100920427e-06,
                5.422218969384951e-06,
                1.2098652506548698e-06,
                2.2603242966454563e-06
            ],
            [
                1.4738980205754734e-05,
                8.939695231633822e-06,
                3.535625908948878e-05,
                2.902311638759718e-06,
                6.14417753110761e-06,
                1.4738981968864903e-05,
                4.2228354541079185e-06,
                1.0129993391236997e-05,
                6.144177531459659e-06,
                4.7850933535006355e-06
            ],
            [
                2.753570421481532e-05,
                1.4738985479697128e-05,
                1.0129987351289655e-05,
                1.8925141464512013e-05,
                2.2603248362013377e-06,
                7.889266346287306e-06,
                7.88925976126004e-06,
                6.962254588433232e-06,
                2.260324028306588e-06,
                1.0129995803627524e-05
            ],
            [
                5.829126539607611e-05,
                1.6701425818232042e-05,
                2.7535691080725503e-05,
                6.605213660534067e-05,
                8.939696302831578e-06,
                6.605212886590941e-05,
                2.4300234931404677e-05,
                0.0001398220565931915,
                1.1478766754064213e-05,
                5.1442201347440924e-05
            ],
            [
                2.753569108573408e-05,
                3.120191134459038e-05,
                2.144494839454502e-05,
                1.6701425817016872e-05,
                5.1442225836439433e-05,
                2.753568116675371e-05,
                1.4738983716586539e-05,
                5.144220742112766e-05,
                5.144219520488886e-05,
                1.30071346612026e-05
            ],
            [
                1.6701415858046724e-05,
                1.4738987239295859e-05,
                3.535625068579429e-05,
                1.8925141455974863e-05,
                2.1444950894600863e-05,
                2.144495351862222e-05,
                3.120190762537599e-05,
                5.829127234919691e-05,
                7.48462538460694e-05,
                2.430024650299895e-05
            ],
            [
                3.2887494571676872e-06,
                1.6701421836551084e-05,
                5.422218322940583e-06,
                1.3007123807302014e-05,
                1.1478765386038447e-05,
                1.4738978443234588e-05,
                1.1478772227964558e-05,
                1.1478773593548236e-05,
                1.8925150485318196e-05,
                2.43002436174814e-05
            ],
            [
                4.785093353100252e-06,
                4.785093923916815e-06,
                1.6701417849645853e-05,
                2.7535687799708318e-05,
                2.144494328404357e-05,
                4.785092781709294e-06,
                8.93969523387785e-06,
                4.785093921819153e-06,
                1.8925150491445666e-05,
                1.670142581883963e-05
            ],
            [
                8.93969630226244e-06,
                4.785096200855943e-06,
                3.2887478886821466e-06,
                2.260325105488003e-06,
                1.5534975693347152e-06,
                1.6701415855069562e-05,
                7.889264463675704e-06,
                1.5534984952111384e-06,
                1.3007131562845248e-05,
                1.3007130010922344e-05
            ],
            [
                1.4738987234550548e-05,
                1.6701415828396637e-05,
                6.962254585203866e-06,
                1.01299933928585e-05,
                6.962253756687988e-06,
                2.144494837847401e-05,
                2.7535691071008866e-05,
                8.93970056424046e-06,
                2.7535684505068197e-05,
                1.760343632710514e-06
            ],
            [
                4.539786321684599e-05,
                1.4738980209829803e-05,
                2.1444948401176257e-05,
                3.535626333989112e-05,
                3.53562591336057e-05,
                4.0063696941289896e-05,
                2.7535681246690542e-05,
                1.0129987355988324e-05,
                1.6701417858577338e-05,
                6.962255419380732e-06
            ],
            [
                2.1444953507076064e-05,
                NaN,
                4.785096205973894e-06,
                1.4738976682752188e-05,
                6.96225707894582e-06,
                7.889265406151004e-06,
                4.785092783371756e-06,
                4.785096775842062e-06,
                1.147876949187012e-05,
                2.9023112930949896e-06
            ],
            [
                2.144495861531752e-05,
                1.6701421835335913e-05,
                8.939694170062744e-06,
                8.93969523617066e-06,
                1.670142781520948e-05,
                1.8925150482908516e-05,
                1.3007125360478133e-05,
                1.1478764015361142e-05,
                1.6701429792440666e-05,
                2.9023123308072772e-06
            ],
            [
                2.7535681222849733e-05,
                1.5534973840984598e-06,
                1.3007126906982452e-05,
                7.889261642363733e-06,
                5.422217676101776e-06,
                3.5356246203490305e-05,
                4.785093352482268e-06,
                6.9622562492265485e-06,
                6.1441724029223715e-06,
                1.3007123801954964e-05
            ],
            [
                2.753568123266654e-05,
                3.535624215245212e-05,
                1.8925145966893773e-05,
                1.1478769487464542e-05,
                3.7266388391993445e-06,
                1.3007125360146898e-05,
                5.829128634789482e-05,
                3.5356250699942575e-05,
                2.4300232029003796e-05,
                4.006371123377989e-05
            ],
            [
                2.1444945848226808e-05,
                1.892514597494899e-05,
                1.892515500560259e-05,
                1.670142184171555e-05,
                0.0001795279016357384,
                1.3007131562845248e-05,
                2.1444953524161264e-05,
                3.120191135264947e-05,
                2.7535681231364308e-05,
                6.1441767987808774e-06
            ],
            [
                3.726638395415398e-06,
                1.147876401460948e-05,
                5.422221554926484e-06,
                2.561281599776919e-06,
                4.222832437443716e-06,
                1.0129990974240505e-05,
                1.3709576967482697e-06,
                3.2887486718928972e-06,
                1.0129989767363975e-05,
                5.422218969769604e-06
            ],
            [
                1.147876949310201e-05,
                4.539786316234683e-05,
                8.9396994983433e-06,
                2.1444953517842076e-05,
                1.4738983725406915e-05,
                1.3007123811229494e-05,
                2.5612828211442287e-06,
                2.430024360006628e-05,
                8.939698433373153e-06,
                1.300712536203966e-05
            ],
            [
                4.7850933535659155e-06,
                2.7535681215036362e-05,
                2.902313022659669e-06,
                5.422219615967477e-06,
                6.144177531459659e-06,
                1.3709578605455302e-06,
                6.962257079376403e-06,
                1.7603434231385591e-06,
                5.422218321993744e-06,
                7.88925976397226e-06
            ],
            [
                5.829124463044478e-05,
                1.012999097799944e-05,
                8.939693104410264e-06,
                1.3007131564643372e-05,
                3.28875024125221e-06,
                8.93970056424046e-06,
                5.422218968595919e-06,
                2.430023492353693e-05,
                1.1478770850103883e-05,
                2.14449458497871e-05
            ],
            [
                8.939699496164318e-06,
                1.8925150479534963e-05,
                7.889263524257144e-06,
                4.222831934052698e-06,
                2.9023130229209922e-06,
                5.14422135082889e-05,
                6.144173865775523e-06,
                1.1478768123280277e-05,
                3.1201900183543295e-05,
                1.0129992183991656e-05
            ],
            [
                3.7266383952696564e-06,
                2.26032429753354e-06,
                3.7266401724291984e-06,
                1.7603425835173373e-06,
                1.1478765366390824e-05,
                1.4738978441143436e-05,
                6.144172403201774e-06,
                6.144174596313726e-06,
                2.9023130227599746e-06,
                7.889260702744606e-06
            ],
            [
                4.5397890270732005e-05,
                7.484622717027548e-05,
                4.5397852378781204e-05,
                3.12019225102953e-05,
                6.605215247874642e-05,
                1.4738981964307261e-05,
                7.484625360483934e-05,
                3.535625490931388e-05,
                5.144222583232244e-05,
                0.00017952798509195494
            ],
            [
                8.939696303010449e-06,
                5.144220748250827e-05,
                8.481103122976564e-05,
                3.5356259104666025e-05,
                4.006369212660275e-05,
                3.535626332111248e-05,
                2.4300249402042293e-05,
                5.144220745705777e-05,
                1.6701427807280505e-05,
                1.4738976699106073e-05
            ],
            [
                2.1444945844014022e-05,
                4.222833444106873e-06,
                1.300712535865635e-05,
                4.006371126992468e-05,
                1.4738978455701077e-05,
                2.7535687809124434e-05,
                3.120192623972722e-05,
                6.605212888657352e-05,
                1.4738980211116665e-05,
                1.8925143724239906e-05
            ],
            [
                1.1478768121735194e-05,
                2.7535704222728874e-05,
                4.539786320396437e-05,
                4.785093353274332e-06,
                3.5356267545276676e-05,
                1.0129987355122296e-05,
                6.144176796422715e-06,
                7.484621829540844e-05,
                0.00015843625365725506,
                0.0001233946334266641
            ],
            [
                6.144172403592939e-06,
                6.144173136131494e-06,
                8.939693105272102e-06,
                4.785093352482268e-06,
                4.785093922524176e-06,
                8.939696301839653e-06,
                7.889262584350785e-06,
                3.2887478886821466e-06,
                1.6701415858046724e-05,
                3.7266397280485686e-06
            ],
            [
                5.8291293208140155e-05,
                5.144222588434628e-05,
                3.120191136899467e-05,
                3.535623803273096e-05,
                1.1478765388314311e-05,
                4.0063682625048554e-05,
                4.539785779269366e-05,
                1.8925145979561802e-05,
                8.48110210734667e-05,
                2.4300252316291068e-05
            ],
            [
                1.3007126910649678e-05,
                4.539789024909747e-05,
                1.3007128452280321e-05,
                3.1201926235527406e-05,
                1.4738978454172926e-05,
                1.3007131561047124e-05,
                1.147876401711502e-05,
                1.8925148232267744e-05,
                1.1478772224060087e-05,
                NaN
            ],
            [
                6.962256247998122e-06,
                7.889263523869684e-06,
                1.209866116137134e-06,
                5.422218323019487e-06,
                1.067702615348298e-06,
                1.1478768122695653e-05,
                1.0129989767695646e-05,
                6.144173136885882e-06,
                1.1478770854029233e-05,
                6.475949525434003e-07
            ],
            [
                2.753568780802255e-05,
                2.144495863482118e-05,
                6.962257076830902e-06,
                6.9622570777680525e-06,
                2.7535697643963113e-05,
                3.1201918798457626e-05,
                2.144494327998681e-05,
                5.829127242214212e-05,
                7.889261643899223e-06,
                6.962257077223492e-06
            ],
            [
                1.994730434798734e-06,
                3.726638395415398e-06,
                2.902311292831027e-06,
                6.144172402609439e-06,
                1.5534983099027147e-06,
                1.1478769483831504e-05,
                3.288749848749297e-06,
                1.2098655392222467e-06,
                1.7603434231241496e-06,
                2.9023133686360798e-06
            ],
            [
                6.962256249327861e-06,
                8.939694170940841e-06,
                2.561281905058126e-06,
                8.93969736547614e-06,
                4.785096200855943e-06,
                6.144174600605357e-06,
                6.144175330584843e-06,
                7.889260703462123e-06,
                4.222834451065997e-06,
                1.0129992185539456e-05
            ],
            [
                1.6701423824262386e-05,
                4.785096205582214e-06,
                1.147876400863794e-05,
                1.3007128456539035e-05,
                8.939697367264857e-06,
                1.8925157255968775e-05,
                2.144495351940237e-05,
                5.422217030288788e-06,
                0.00010889688264030119,
                6.605212876547221e-05
            ],
            [
                3.535624225110421e-05,
                6.144172403592939e-06,
                1.3007126911974612e-05,
                3.726639727994339e-06,
                5.4222215529144515e-06,
                1.4738987238893715e-05,
                4.785096204972935e-06,
                5.422217675874929e-06,
                1.1478770860982112e-05,
                7.889260703763482e-06
            ],
            [
                6.605216823009351e-05,
                5.144219522921654e-05,
                1.3007125360478133e-05,
                1.3007123801954964e-05,
                5.8291258521838744e-05,
                4.539786858319682e-05,
                1.6701417843448496e-05,
                4.0063677837180203e-05,
                2.430024362393472e-05,
                3.2887482812506295e-06
            ],
            [
                8.481102027318002e-05,
                7.889259762307618e-06,
                2.1444948408977715e-05,
                1.0129987352616339e-05,
                7.889260701697028e-06,
                1.3007126910294786e-05,
                7.889260704050487e-06,
                5.422220908481809e-06,
                1.4738976698006875e-05,
                1.1478768123280277e-05
            ],
            [
                8.939696301384342e-06,
                1.3007131563176482e-05,
                1.8925148211888738e-05,
                4.006368738595465e-05,
                2.9023126769050284e-06,
                3.1201903906162046e-05,
                2.7535687806920664e-05,
                5.1442195212374294e-05,
                7.484621810808764e-05,
                1.67014218359435e-05
            ],
            [
                1.3007123806024402e-05,
                7.8892654060075e-06,
                2.5612831266165976e-06,
                3.12019262448351e-05,
                1.3007125361755747e-05,
                2.902311639073834e-06,
                6.962256248606003e-06,
                1.89251482270353e-05,
                6.1441753327418334e-06,
                2.5612822104232297e-06
            ],
            [
                1.8925148231579266e-05,
                7.889260701697028e-06,
                1.4738981964307261e-05,
                7.484623475949104e-05,
                7.88926164064169e-06,
                2.75357009146638e-05,
                1.760343842833246e-06,
                2.9023112929973233e-06,
                2.5612831259923004e-06,
                7.889266345397582e-06
            ],
            [
                3.5356254902111115e-05,
                4.0063682603624035e-05,
                7.889264463890957e-06,
                1.300712690556288e-05,
                1.4738978453743973e-05,
                6.144176796947993e-06,
                1.3709578604981489e-06,
                2.7535700939406174e-05,
                6.144177531459659e-06,
                2.430023783150746e-05
            ],
            [
                3.535625907765566e-05,
                5.4222202609325635e-06,
                1.300713311155064e-05,
                1.6701415866735174e-05,
                6.144176062330242e-06,
                1.4738980205754734e-05,
                1.3007123808910861e-05,
                1.892515274194901e-05,
                4.539788474963394e-05,
                5.1442201347440924e-05
            ],
            [
                3.2887478889513447e-06,
                1.0129992183070348e-05,
                2.902313368897403e-06,
                2.5612819052072116e-06,
                6.144174600180663e-06,
                NaN,
                8.939696297644297e-06,
                2.5612834318583854e-06,
                4.222833444283541e-06,
                5.422219612623952e-06
            ],
            [
                7.889263525778283e-06,
                6.962253756232077e-06,
                4.222834450589758e-06,
                5.422219615582823e-06,
                7.889264464895484e-06,
                4.222833946645451e-06,
                4.222831934052698e-06,
                1.7603440526133836e-06,
                3.7266392835086923e-06,
                1.147876401711502e-05
            ],
            [
                6.605212100345552e-05,
                2.1444956072586775e-05,
                6.144176065940129e-06,
                1.6701417857058377e-05,
                3.535624646150348e-05,
                1.0129990974903845e-05,
                0.00013982204061099143,
                3.12019076269651e-05,
                2.1444945841205498e-05,
                1.3007128461838766e-05
            ],
            [
                7.889266343316778e-06,
                3.535624646754865e-05,
                6.9622562472889285e-06,
                NaN,
                1.4738987235622935e-05,
                1.670141785420273e-05,
                3.120190018853766e-05,
                2.7535691091443854e-05,
                3.7266383954560706e-06,
                1.012999339309804e-05
            ],
            [
                2.4300249417247375e-05,
                4.785095064436034e-06,
                2.753569761591508e-05,
                NaN,
                1.3007125360146898e-05,
                1.1478768116974664e-05,
                1.67014238321306e-05,
                3.2887478887419687e-06,
                1.3007133114011233e-05,
                3.5356250651195314e-05
            ],
            [
                7.889266345397582e-06,
                3.1201915049389656e-05,
                6.144176064364297e-06,
                5.1442207381454816e-05,
                4.006369202458123e-05,
                7.88926352407059e-06,
                1.012998856078241e-05,
                2.1444940732342966e-05,
                1.892514821904893e-05,
                6.144175332283612e-06
            ],
            [
                2.9023112930659533e-06,
                4.785096205173126e-06,
                6.1441775309064404e-06,
                1.2098658277082653e-06,
                3.7266397264555753e-06,
                4.785094493932679e-06,
                2.260324028255194e-06,
                4.2228329408924035e-06,
                3.7266392838544054e-06,
                2.9023130230133794e-06
            ],
            [
                1.300712846217e-05,
                7.484624501203951e-05,
                3.535625070624499e-05,
                4.5397890231261374e-05,
                4.006370642360913e-05,
                1.4738978454172926e-05,
                3.2887498493325602e-06,
                5.8291279365509446e-05,
                2.1444940736477737e-05,
                4.006368736948546e-05
            ],
            [
                6.144177530425867e-06,
                3.7266379507909478e-06,
                4.222833443968609e-06,
                1.0129995808639442e-05,
                3.28875024125221e-06,
                6.962257909121104e-06,
                1.0129990977004428e-05,
                5.829129324249228e-05,
                6.144175333926503e-06,
                7.889261644982674e-06
            ],
            [
                4.785094494463623e-06,
                7.889265406567165e-06,
                5.8291293278964903e-05,
                2.4300252298610736e-05,
                1.8925145980181433e-05,
                1.670141587031992e-05,
                2.430024941371131e-05,
                4.539786858616951e-05,
                1.3007126913583456e-05,
                3.120190392409636e-05
            ],
            [
                8.481108150469728e-05,
                3.1201922508819695e-05,
                1.8925157240615665e-05,
                2.7535694350223355e-05,
                3.288747889038086e-06,
                5.14422074125194e-05,
                4.7850967754851966e-06,
                5.422221553654169e-06,
                8.939700562695657e-06,
                1.3007134641707146e-05
            ],
            [
                1.0129995804364571e-05,
                1.6701425817016872e-05,
                0.00012339455980783077,
                2.4300237828943813e-05,
                2.4300243625614346e-05,
                2.9023116388072315e-06,
                3.120190015232851e-05,
                3.5356254910985954e-05,
                1.3007133104831333e-05,
                2.430023200831783e-05
            ],
            [
                2.1444958623509054e-05,
                6.144177527609484e-06,
                1.1478764012939119e-05,
                1.0129987354108855e-05,
                1.300713000155317e-05,
                2.561282210590951e-06,
                2.1444943287710254e-05,
                3.288748280891699e-06,
                6.962257078553231e-06,
                1.4738988983291576e-05
            ],
            [
                5.422217676101776e-06,
                1.994729245842213e-06,
                8.939697368305565e-06,
                7.889262584666493e-06,
                1.3709576970026324e-06,
                3.2887498491620677e-06,
                1.7603425836870455e-06,
                4.222834953712232e-06,
                1.2098656834922064e-06,
                2.561283431942246e-06
            ],
            [
                7.484626284672882e-05,
                0.00017952798649721472,
                0.0002611904309550401,
                5.422219615395428e-06,
                4.539786318711917e-05,
                6.605216815416487e-05,
                0.00017952800766230892,
                2.7535704217219437e-05,
                0.00020342694756489505,
                0.0001233945892201689
            ],
            [
                4.006369212106443e-05,
                7.484624486991525e-05,
                1.6701419845680582e-05,
                1.8925157257345735e-05,
                6.60521524508739e-05,
                4.0063687367153544e-05,
                3.535625489632318e-05,
                7.8892625830162e-06,
                1.4738988995409548e-05,
                2.1444956070870452e-05
            ],
            [
                3.5356259128846735e-05,
                2.753570093009022e-05,
                2.430023492769181e-05,
                7.889265405677441e-06,
                2.430024360271833e-05,
                1.2098662602267027e-06,
                2.4300252306390083e-05,
                1.4738983723235332e-05,
                2.144494328404357e-05,
                8.4811031131658e-05
            ],
            [
                3.7266401697956756e-06,
                6.605213661206851e-05,
                1.012999097799944e-05,
                3.726640172385136e-06,
                2.7535700911558485e-05,
                7.889259759222289e-06,
                1.1478769487046951e-05,
                1.1478765375828365e-05,
                8.939698431389304e-06,
                2.4300234892861585e-05
            ]
        ]
    },
    {
        "q_id": "8855_mmlu_math",
        "cot_ids": [
            0,
            3,
            5,
            6,
            7,
            8,
            9,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            36,
            37,
            38,
            39,
            40,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            68,
            71,
            73,
            74,
            75,
            76,
            78,
            79,
            80,
            83,
            84,
            85,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                6.144177530548804e-06,
                1.3007125356006484e-05,
                1.1478768123280277e-05,
                0.00013982202373365993,
                5.4222170296279735e-06,
                1.892514372640862e-05,
                0.00023050663167558885,
                1.3007123803043302e-05,
                6.962254589104433e-06,
                0.00023050676939880138
            ],
            [
                0.0008040861043621611,
                1.4738983719053027e-05,
                2.260324836152e-06,
                4.0063682540662206e-05,
                0.00023050676882199219,
                1.0129994598482479e-05,
                2.1444948400318094e-05,
                1.3007126905042372e-05,
                NaN,
                3.53562380286151e-05
            ],
            [
                3.53562633126235e-05,
                6.962256248606003e-06,
                2.7535694358938284e-05,
                8.939698432202356e-06,
                9.610244900370157e-05,
                7.889261643181705e-06,
                3.535625488178903e-05,
                9.610243725904215e-05,
                7.889266342800164e-06,
                1.3007128458810347e-05
            ],
            [
                8.481108054830155e-05,
                0.0001584362355984317,
                9.610244913374722e-05,
                8.481107148352178e-05,
                2.4300231997886442e-05,
                2.4300243616508983e-05,
                0.00015843623564914578,
                2.144494581132591e-05,
                4.222833946645451e-06,
                9.610240331853667e-05
            ],
            [
                2.430024649530801e-05,
                8.481107159026786e-05,
                2.144495096161541e-05,
                1.3007131563507714e-05,
                8.93969416907082e-06,
                1.670142780594382e-05,
                7.484623609796368e-05,
                1.3007133114011233e-05,
                1.892514597343433e-05,
                8.939698433373153e-06
            ],
            [
                4.006371126117997e-05,
                0.00015843623521577093,
                3.12019038974219e-05,
                5.144223203551027e-05,
                4.006369215691771e-05,
                1.3007125352457558e-05,
                5.82912445833697e-05,
                1.892514370627059e-05,
                0.00033535013645709215,
                5.829129321831856e-05
            ],
            [
                0.00017952792282171864,
                1.4738988974605243e-05,
                0.000487857050376809,
                0.00015843627317065276,
                8.939700562988356e-06,
                0.00010889688299997942,
                3.5356246441695886e-05,
                7.484626283311537e-05,
                2.1444948367551967e-05,
                5.829126548725762e-05
            ],
            [
                6.962257908753841e-06,
                4.222833443553821e-06,
                2.4300243598740258e-05,
                1.1478769492642663e-05,
                6.962259568889411e-06,
                3.2887506334201674e-06,
                2.9023126767360923e-06,
                1.0129992185539456e-05,
                3.726641060956752e-06,
                4.7850933529174686e-06
            ],
            [
                3.2887482811220126e-06,
                3.288749065125496e-06,
                6.962257907880012e-06,
                6.962253759271479e-06,
                8.315281267248819e-07,
                1.7603438427660027e-06,
                2.7535697649071857e-05,
                4.222835457794923e-06,
                7.889263525663481e-06,
                3.120190762197074e-05
            ],
            [
                1.0129988562164371e-05,
                6.144172403335888e-06,
                2.7535687801010546e-05,
                2.1444958632714784e-05,
                7.889259763326495e-06,
                3.535624635706345e-05,
                0.00010889696114208605,
                2.1444940737257882e-05,
                5.422220262037209e-06,
                9.610244921065592e-05
            ],
            [
                3.120191134288775e-05,
                0.00017952792332844784,
                7.48462180835835e-05,
                6.605212890675706e-05,
                6.605212097077738e-05,
                4.006371124165013e-05,
                4.006367779782906e-05,
                0.00010889690883660543,
                2.1444940731484803e-05,
                6.605216805420816e-05
            ],
            [
                0.9999962733611628,
                0.9999885212305076,
                0.9999957771680661,
                0.9999869928715515,
                0.9999930377462414,
                0.9999977396754328,
                0.9999945777816769,
                0.999986992868442,
                0.9999885212277733,
                0.9999938558246669
            ],
            [
                8.481108156331507e-05,
                2.43002465110435e-05,
                1.0129993382466144e-05,
                5.4222215550004564e-06,
                6.962253759157502e-06,
                3.726640172385136e-06,
                5.144222581173747e-05,
                1.3007130010543792e-05,
                2.144494328950459e-05,
                1.8925157257345735e-05
            ],
            [
                2.1444953502863275e-05,
                7.889262584809997e-06,
                1.8925148227861472e-05,
                1.3007126910294786e-05,
                6.962254589433702e-06,
                7.889260701237816e-06,
                4.222834954057889e-06,
                1.1478768123551712e-05,
                1.4738980211920955e-05,
                1.4738980206290928e-05
            ],
            [
                0.00020342697146110656,
                2.4300249358548683e-05,
                4.539787397465094e-05,
                5.829127242638312e-05,
                1.892514596944115e-05,
                2.7535681216639104e-05,
                4.539786314550164e-05,
                4.0063687392367425e-05,
                3.120191130088966e-05,
                4.006371124922888e-05
            ],
            [
                8.939697368305565e-06,
                1.6701417848916754e-05,
                2.4300249391876106e-05,
                0.0001398220737675486,
                3.1201911328358685e-05,
                1.6701423824262386e-05,
                1.1478765386038447e-05,
                5.144221363404434e-05,
                0.00012339452992869436,
                1.0129992182443859e-05
            ],
            [
                4.222834450589758e-06,
                1.3007133110320344e-05,
                1.3709573701637772e-06,
                2.4300252288444548e-05,
                4.539786857361818e-05,
                2.4300246523066122e-05,
                8.939693103418341e-06,
                4.785094494185095e-06,
                2.561282210530385e-06,
                6.144176065314267e-06
            ],
            [
                0.9998911031056378,
                0.9999898700114536,
                0.9999910603006379,
                0.7057850340255386,
                0.9999417087206214,
                0.9999869928762741,
                0.9999724643155534,
                0.9999724643155167,
                0.7057850216484838,
                0.2689414096510108
            ],
            [
                3.535626740765242e-05,
                0.0002959571669783861,
                5.829126537996031e-05,
                3.535624641674347e-05,
                7.484624467551543e-05,
                7.484623608435025e-05,
                0.00010889692191970729,
                1.8925145971093502e-05,
                0.00010889688167534942,
                7.484622702869579e-05
            ],
            [
                4.5397884843438604e-05,
                2.430025230532926e-05,
                3.120192250393883e-05,
                7.88926070328992e-06,
                5.42222090821551e-06,
                5.82912515784739e-05,
                7.48462003365753e-05,
                6.605213672211696e-05,
                3.535625488616215e-05,
                1.1478772225646932e-05
            ],
            [
                1.6701419845680582e-05,
                2.902310946944611e-06,
                9.610239195213367e-05,
                3.120190020068305e-05,
                1.0129988561648438e-05,
                5.144223809160982e-05,
                0.0002611902718106809,
                1.6701415866735174e-05,
                1.6701419844465412e-05,
                1.8925154999337424e-05
            ],
            [
                0.999998446502801,
                0.9999967112497589,
                0.9999962733593837,
                0.9999991684719723,
                0.999999428499553,
                0.999983298574179,
                0.9999930377412639,
                0.9999977396759717,
                0.9999984465018755,
                0.9999885212359866
            ],
            [
                4.222832939978334e-06,
                2.5612825155181522e-06,
                7.88926634455091e-06,
                4.7850927808475986e-06,
                2.2603248365343694e-06,
                1.4738976698006875e-05,
                3.2887490645272776e-06,
                1.4738988997044936e-05,
                1.1478764016446877e-05,
                4.5397879417962496e-05
            ],
            [
                6.144173868670137e-06,
                6.144176065940129e-06,
                6.9622562489985925e-06,
                1.4738985484549675e-05,
                6.962257909412379e-06,
                4.785093924047376e-06,
                6.962258739454786e-06,
                4.7850967754851966e-06,
                1.3007130012341915e-05,
                4.785092783210732e-06
            ],
            [
                0.00029595709368209107,
                3.535625068579429e-05,
                4.006369693006752e-05,
                1.1478765386623071e-05,
                5.144219514537961e-05,
                0.00015843627169533376,
                5.144223195579028e-05,
                1.3007134605366103e-05,
                1.6701419846834993e-05,
                3.535625487947387e-05
            ],
            [
                3.120190760119872e-05,
                7.484626281841286e-05,
                5.829127231654119e-05,
                0.000139822073027029,
                1.6701423822135842e-05,
                0.00010889692138256647,
                3.120191506210258e-05,
                1.0129992177321387e-05,
                4.006371097260469e-05,
                1.6701423829123058e-05
            ],
            [
                8.939700565834043e-06,
                1.6701419848475466e-05,
                1.670141785809127e-05,
                4.006367782348017e-05,
                8.481104094612394e-05,
                4.5397890270732005e-05,
                1.3007125361755747e-05,
                3.120191878631223e-05,
                3.120190020068305e-05,
                4.785096204972935e-06
            ],
            [
                0.9999785550541518,
                0.9999957771675629,
                0.9999339478485848,
                0.9999832985761893,
                0.9999921107383558,
                0.9999977396754336,
                0.9999962733620517,
                0.9999974387174845,
                0.9998911031302559,
                0.9999957771670707
            ],
            [
                0.99986017786067,
                0.9626731130574597,
                0.9999646437451273,
                0.9999251537639369,
                0.9999967112505428,
                0.9999832985781667,
                0.9999910603028486,
                0.99982047201408,
                0.9999832985781679,
                0.9999687980813396
            ],
            [
                4.785095634930755e-06,
                4.539788481668446e-05,
                1.7603427931932593e-06,
                6.144175333926503e-06,
                2.7535694370357833e-05,
                6.475945665741875e-07,
                1.0129993389652346e-05,
                3.2887490648622804e-06,
                NaN,
                8.93969843377968e-06
            ],
            [
                0.9999910603026352,
                0.9999967112505427,
                0.9999982396561572,
                0.9999994284994167,
                0.9999938558232032,
                0.9999952149066478,
                0.9999986290429567,
                0.9999980052700408,
                0.999995777168066,
                0.9999970976869772
            ],
            [
                2.1444945846588504e-05,
                0.00010889694719068081,
                1.892515723083925e-05,
                NaN,
                5.8291258498513246e-05,
                1.0129987331831636e-05,
                3.535626332509972e-05,
                2.7535684425131356e-05,
                4.5397863134932104e-05,
                3.120192245603829e-05
            ],
            [
                5.829126543170052e-05,
                1.4738983726184394e-05,
                8.939697366793286e-06,
                4.539786320660675e-05,
                0.00010889693465105476,
                6.144175334015912e-06,
                8.939698434657777e-06,
                1.012998977108606e-05,
                3.1201922508819695e-05,
                2.9023123305485934e-06
            ],
            [
                2.1444958627955892e-05,
                2.430024649256756e-05,
                4.785095064819011e-06,
                8.939696300636336e-06,
                1.0129993387404356e-05,
                1.473898723508674e-05,
                1.4738988997044936e-05,
                4.539787938592359e-05,
                3.288748672879957e-06,
                7.88926258343236e-06
            ],
            [
                3.1201915063805214e-05,
                1.0129993393742954e-05,
                1.892515274614874e-05,
                3.726641060956752e-06,
                3.1201915071864306e-05,
                1.892514597832254e-05,
                1.4738987233478162e-05,
                4.22283545795623e-06,
                3.7266410608245674e-06,
                2.2603251061849014e-06
            ],
            [
                4.785094494019719e-06,
                1.1478769490387674e-05,
                1.012999097799944e-05,
                2.1444956070870452e-05,
                7.889259763728304e-06,
                1.994730196992497e-06,
                1.6701425816409292e-05,
                7.889260704179641e-06,
                1.670142582254589e-05,
                1.1478773597118638e-05
            ],
            [
                1.892515274194901e-05,
                1.0129989770441144e-05,
                1.8925152740434357e-05,
                4.2228344494606135e-06,
                7.889265405333033e-06,
                6.962259567914269e-06,
                4.222832939978334e-06,
                0.00010889689327853829,
                2.4300252300909177e-05,
                4.785095064436034e-06
            ],
            [
                1.8925155002022494e-05,
                1.6701417858577338e-05,
                0.00037998443733508946,
                1.8925154994724604e-05,
                4.539785230908836e-05,
                0.0003353500616817478,
                5.829127937441555e-05,
                3.5356259114569826e-05,
                7.484625370612328e-05,
                2.430024362393472e-05
            ],
            [
                7.889261643554814e-06,
                0.00012339453041524914,
                1.3007131559390956e-05,
                1.6701419847381817e-05,
                2.753568450797317e-05,
                7.889266345584138e-06,
                1.6701415864001047e-05,
                3.120191508185304e-05,
                4.785093923603471e-06,
                4.006368258380272e-05
            ],
            [
                6.605216816041215e-05,
                0.0035936019995017024,
                6.605212874576922e-05,
                8.481106147345398e-05,
                0.00029595697891556015,
                0.0001795280276624502,
                4.0063711140794525e-05,
                0.00012339460357982713,
                0.0002305067648044492,
                0.0004305570783686052
            ],
            [
                5.42222090821551e-06,
                0.0004305571302741351,
                2.753569762613258e-05,
                4.539789027320923e-05,
                5.1442207475397105e-05,
                6.962257079059797e-06,
                1.0129990976156825e-05,
                0.00017952794425061798,
                7.484624503872184e-05,
                3.535625491265802e-05
            ],
            [
                4.785096769888526e-06,
                3.9278638753849313e-07,
                4.7850933527085725e-06,
                3.288750633139005e-06,
                2.2603237583724906e-06,
                2.260324567054496e-06,
                3.535624646150348e-05,
                1.0129987351621326e-05,
                2.561281904391899e-06,
                1.1478764018012839e-05
            ],
            [
                4.7850956351657615e-06,
                1.6701425823457267e-05,
                3.288749065029781e-06,
                2.7535704202894907e-05,
                1.6701425823457267e-05,
                5.422220262195015e-06,
                1.892514823426434e-05,
                8.939693103418341e-06,
                0.0001088968831679349,
                3.2887490652810324e-06
            ],
            [
                0.00029595716630673294,
                2.561281293126023e-06,
                1.1478768072793603e-05,
                4.539787403938935e-05,
                0.0002959569931752648,
                0.0001088969608251887,
                6.60521761026448e-05,
                5.144221359250013e-05,
                2.43002465110435e-05,
                2.4300246517938825e-05
            ],
            [
                0.9998415638213143,
                0.99998699287154,
                0.999997097686977,
                0.999978555056705,
                0.9999546021097508,
                0.9999687980841329,
                0.9998911030784781,
                0.9999599363078364,
                0.9995694428647407,
                0.9999785550439318
            ],
            [
                0.9999938558276017,
                0.9999810748450029,
                0.9997040428335985,
                0.9991959140032004,
                0.9947798741589362,
                NaN,
                0.9999417087277005,
                0.9999151889490827,
                5.8291286090041897e-05,
                0.9999417087345585
            ],
            [
                0.00012339463351284362,
                3.120190019636974e-05,
                5.829129314282872e-05,
                0.00012339457442243326,
                1.0129990978220553e-05,
                4.539785235863304e-05,
                4.222835457364773e-06,
                2.430025228428967e-05,
                1.8925152716750642e-05,
                4.5397890240179425e-05
            ],
            [
                3.535624221779145e-05,
                4.0063687383622725e-05,
                5.1442232001825764e-05,
                1.892514822620912e-05,
                3.7266383937647876e-06,
                6.962259567914269e-06,
                8.93969417167259e-06,
                6.605216035706259e-05,
                0.00017952798686028367,
                2.4300252299759956e-05
            ],
            [
                2.9023133686835932e-06,
                6.962259567217739e-06,
                1.3007130010117919e-05,
                5.422217029391264e-06,
                5.422218969601935e-06,
                2.7535694366751658e-05,
                3.535625068579429e-05,
                4.222835457526079e-06,
                2.753568123266654e-05,
                1.4738981963234875e-05
            ],
            [
                1.4738988990959142e-05,
                3.120192623972722e-05,
                2.7535700932494338e-05,
                7.889263525534328e-06,
                2.7535700919171523e-05,
                1.0129995809247506e-05,
                2.144494839142443e-05,
                6.962254588433232e-06,
                5.4222202617511845e-06,
                5.422217676200406e-06
            ],
            [
                3.726639283752725e-06,
                1.012998856312253e-05,
                1.2098659719122375e-06,
                6.144173135025058e-06,
                1.8925155000025902e-05,
                5.1442207485876726e-05,
                4.222833443461647e-06,
                8.93969310367852e-06,
                6.962259567407701e-06,
                4.7850944943330625e-06
            ],
            [
                5.422218322763051e-06,
                1.3007123808532309e-05,
                9.610238052909926e-05,
                1.6701427815999337e-05,
                2.1444945847446664e-05,
                5.422220261652556e-06,
                1.892514595381266e-05,
                8.939696302831578e-06,
                1.892514597343433e-05,
                1.670142382796865e-05
            ],
            [
                5.1442207268424645e-05,
                0.0004878572281689812,
                0.0002959571285219396,
                2.7535684446568053e-05,
                1.67014218283487e-05,
                3.535625489632318e-05,
                3.12019225022362e-05,
                0.00017952800843023904,
                4.006370130096154e-05,
                6.605214437024256e-05
            ],
            [
                0.00013982207297616917,
                8.481101071663458e-05,
                7.484620039429623e-05,
                7.484623587361431e-05,
                8.481104105225297e-05,
                9.610238050882334e-05,
                5.829127930740772e-05,
                6.605216805420816e-05,
                6.962258738283349e-06,
                0.00015843615943512485
            ],
            [
                0.9999967112513267,
                0.9999852610145218,
                0.9999938558224687,
                0.9999810748449987,
                0.9999967112493671,
                0.9999832985721898,
                0.999992110733654,
                0.9999952149037962,
                0.9999869928669087,
                0.9999967112493676
            ],
            [
                1.8925150470928963e-05,
                5.8291251536063904e-05,
                0.00015843617845981184,
                3.120192231846612e-05,
                5.144221974590828e-05,
                3.535625487510076e-05,
                1.8925141420724705e-05,
                3.53562380286151e-05,
                5.1442237953129084e-05,
                3.1201922394743764e-05
            ],
            [
                4.222834953712232e-06,
                3.535625908948878e-05,
                1.4738976697631541e-05,
                5.422220907160179e-06,
                4.5397857701531434e-05,
                1.1478768122069266e-05,
                6.605214458361157e-05,
                6.605213659188498e-05,
                3.535623776597164e-05,
                5.829127220797157e-05
            ],
            [
                0.9999646437577614,
                0.9999852610197949,
                0.9999869928684474,
                0.9999485577740902,
                0.9999832985821401,
                0.9999687980923947,
                0.9999869928653375,
                0.9999832985741823,
                0.9998601779265763,
                0.9999921107383558
            ],
            [
                3.535626755428014e-05,
                1.1478766752748805e-05,
                3.535624646947797e-05,
                1.3007128453415979e-05,
                7.889263522520747e-06,
                NaN,
                4.006368739659403e-05,
                2.4300243611116483e-05,
                3.120191507912884e-05,
                1.3007133114886634e-05
            ],
            [
                1.1478772227651366e-05,
                1.670142183983204e-05,
                1.6701421833391647e-05,
                1.1478769487464542e-05,
                5.144221971259806e-05,
                1.4738981963771067e-05,
                2.4300252291096595e-05,
                0.00010889688304276053,
                2.144494073483943e-05,
                1.4738976694977387e-05
            ],
            [
                0.0019267349494324192,
                0.0006263342297763055,
                0.00017952790107154517,
                0.00012339461788023868,
                0.0005527785901656292,
                0.00015843615937519005,
                0.008577484059411694,
                0.0008040860317808097,
                8.481101059939908e-05,
                0.0007096702362551936
            ],
            [
                0.9999832985701924,
                0.9999990577554061,
                0.9999952149066466,
                0.9999990577550691,
                0.999998446502801,
                0.9999945777829696,
                0.9999967112505427,
                0.9999994956523514,
                0.9999930377429208,
                0.9999990577552939
            ],
            [
                3.120192251336002e-05,
                4.78509506425325e-06,
                6.144172403067661e-06,
                4.539786861787811e-05,
                3.5356246476937965e-05,
                3.535626334490732e-05,
                1.1478773596847203e-05,
                1.1478764017720528e-05,
                8.939693105662367e-06,
                4.7850956342431385e-06
            ],
            [
                7.889264465699106e-06,
                8.93969736955767e-06,
                8.9396941702904e-06,
                4.785092782936557e-06,
                1.670142980222277e-05,
                7.88926634687567e-06,
                1.0129987355122296e-05,
                1.3007131561047124e-05,
                7.889266344766165e-06,
                4.006370650070828e-05
            ],
            [
                8.939699499432793e-06,
                1.1478765380839446e-05,
                5.422220907909759e-06,
                1.9947304347098384e-06,
                1.1478772225646932e-05,
                6.962258735104638e-06,
                1.4738976699427788e-05,
                8.939693103158165e-06,
                1.147876675341695e-05,
                3.5356246478738656e-05
            ],
            [
                4.222835457364773e-06,
                0.00012339455908248694,
                4.785095063339331e-06,
                3.5356259112640515e-05,
                1.670142383167491e-05,
                2.1444953517061932e-05,
                2.430024941371131e-05,
                6.144173869072478e-06,
                3.7266388388875246e-06,
                2.1444958632714784e-05
            ],
            [
                0.00015843625243089628,
                1.4738978447095178e-05,
                6.605212098759701e-05,
                2.7535697553608395e-05,
                4.5397852355660356e-05,
                9.610241446330415e-05,
                0.00023050663167558885,
                0.0004878571609008625,
                3.120191134288775e-05,
                0.00020342689803812633
            ],
            [
                3.7266388394569345e-06,
                1.1478770858706246e-05,
                1.3007133113017532e-05,
                8.939695237504067e-06,
                1.4738985478678359e-05,
                6.14417313533799e-06,
                6.144177530001174e-06,
                6.962259567749634e-06,
                6.9622562484666964e-06,
                3.1201900207380036e-05
            ],
            [
                0.9998601779263891,
                0.9999546021313821,
                0.9999977396765105,
                0.9999417087345128,
                0.9999898700078145,
                0.9999852610127649,
                0.9999910603004994,
                0.9999785550592651,
                0.9999724642990595,
                0.9999785550413696
            ],
            [
                0.9999687980998082,
                0.9999724642957987,
                0.9999785550413929,
                0.999860177893019,
                0.9999646437366535,
                0.9999832985821464,
                0.9999852610110034,
                0.999948557768061,
                0.9999898700041931,
                0.9999417087276351
            ],
            [
                0.9999885212360026,
                0.9999810748495391,
                0.9999938558224808,
                0.9999993524049703,
                0.9999485577865725,
                0.9997694932321975,
                0.999994577779093,
                0.9999898700102369,
                0.999925153781868,
                0.999968798077524
            ],
            [
                3.7266392835764795e-06,
                1.3007128458384476e-05,
                4.539789016454115e-05,
                1.670141586084161e-05,
                7.484626237407027e-05,
                4.222834450666572e-06,
                3.120192248986379e-05,
                5.144221362768171e-05,
                2.7535687790192025e-05,
                0.00013982207313078314
            ],
            [
                4.539786318711917e-05,
                0.9770226311353565,
                1.300712380997554e-05,
                8.48110109406161e-05,
                5.144223200893693e-05,
                0.00010889688295561384,
                3.7266410598992754e-06,
                2.144494073483943e-05,
                3.120192623110058e-05,
                1.670142581883963e-05
            ],
            [
                2.753569765708558e-05,
                4.222831934052698e-06,
                6.962254587027508e-06,
                1.6701423833011596e-05,
                8.939699497855469e-06,
                2.7535681246690542e-05,
                1.4738976697229395e-05,
                1.670141785809127e-05,
                4.22283193320392e-06,
                2.2603251057881422e-06
            ],
            [
                3.120190020862863e-05,
                0.00012339453070430936,
                7.889260699343567e-06,
                7.48462093285157e-05,
                6.605213589795517e-05,
                6.605214456631139e-05,
                4.539785774447017e-05,
                1.6701415868193372e-05,
                5.8291251603919903e-05,
                3.1201922517673344e-05
            ],
            [
                0.9999724642958329,
                0.9999962733611607,
                0.9999724642990824,
                0.9999546021422833,
                0.9999910603058285,
                0.9999852610145177,
                0.9999485577987787,
                0.9999756997650858,
                0.9999910603058293,
                0.7981867705385762
            ],
            [
                0.00010889689607832474,
                1.892514822620912e-05,
                1.3007130000938025e-05,
                6.605213652748982e-05,
                0.0001398221061693531,
                0.00015843621558481343,
                0.00017952800766230892,
                5.829129318184594e-05,
                0.00015843621647461487,
                0.00010889688307128128
            ],
            [
                4.2228334437304904e-06,
                1.892514597632595e-05,
                0.00012339453009207622,
                1.0129995806612563e-05,
                4.006367780307588e-05,
                3.1201918794144304e-05,
                2.753569765908901e-05,
                1.892515725920463e-05,
                4.785093923690512e-06,
                3.1201903920010065e-05
            ],
            [
                0.9999832985761665,
                0.9999810748450044,
                0.9999921107336531,
                0.9999832985781607,
                0.9999962733616046,
                0.9999885212359813,
                0.9999785550413659,
                0.9999885212277736,
                0.9999417087138464,
                0.9999885212305063
            ],
            [
                0.9999687980850124,
                0.9999982396563688,
                0.9999938558239349,
                0.9999810748495214,
                0.9999869928699899,
                0.9999986290432835,
                0.9999996533674615,
                0.999999607213753,
                0.9999996940976273,
                0.9999982396572066
            ],
            [
                5.144220131787343e-05,
                7.484620039429623e-05,
                4.539789026296999e-05,
                1.0129990977004428e-05,
                0.00020342689869516837,
                1.0129993389984017e-05,
                4.0063706492255065e-05,
                8.939696302457574e-06,
                1.6701429794688725e-05,
                3.7266388390502134e-06
            ],
            [
                0.9994472213413375,
                0.9998911030944037,
                0.9999832985841328,
                0.9999785550515988,
                0.8670357563664174,
                0.9999151889286653,
                0.9999646437451655,
                0.9999724643091307,
                0.9998911031057169,
                0.9998601778602204
            ],
            [
                0.9997694933135142,
                0.9999151889690362,
                0.9999810748472538,
                0.9999546021314433,
                0.9999869928715388,
                0.999959936303095,
                0.9998415637092224,
                0.999981074842751,
                0.9999724643187757,
                0.9999038976196576
            ],
            [
                0.99997569976805,
                0.9999921107345939,
                0.9999687980924401,
                0.9999599363030566,
                0.999941708706696,
                0.99997246431547,
                0.9999832985801475,
                0.9999646437535306,
                0.9999921107355341,
                0.9999599363078577
            ],
            [
                7.484620035127781e-05,
                1.6701419849447602e-05,
                2.43002436174814e-05,
                9.610243767994252e-05,
                8.939700565996655e-06,
                0.00020342699550530334,
                8.939700565102295e-06,
                2.430023782328611e-05,
                2.7535691088138193e-05,
                9.610244921065592e-05
            ],
            [
                0.9999962733616048,
                0.9999756997563752,
                0.9999724642958079,
                0.9999930377437508,
                0.9999921107402371,
                0.9999724643122112,
                0.9999724643023379,
                0.999989870007814,
                0.9999785550414021,
                0.9999993524048931
            ],
            [
                6.144172403592939e-06,
                5.1442225848041874e-05,
                6.962253759157502e-06,
                6.144175333926503e-06,
                5.422217030209884e-06,
                1.0129988561906404e-05,
                1.300712380997554e-05,
                1.1478766755233466e-05,
                3.2887494573561262e-06,
                1.0129992184802409e-05
            ],
            [
                4.006369215458579e-05,
                9.610243751354004e-05,
                4.0063706476368846e-05,
                0.0001233946329706308,
                4.006368258642613e-05,
                3.120191133766637e-05,
                3.120192250053358e-05,
                0.00010889696084103356,
                1.8925157244540003e-05,
                3.1201918752486736e-05
            ],
            [
                0.9999938558261329,
                0.9999970976866313,
                0.9999987901343166,
                0.9999930377404317,
                0.9999967112513268,
                0.9999982396561572,
                0.9999957771650461,
                0.9999952149049355,
                0.9999986290432834,
                0.9999967112509347
            ],
            [
                3.535624645944555e-05,
                1.1478770859332632e-05,
                1.4738983715996728e-05,
                4.785096204285318e-06,
                0.00010889688308554166,
                3.120192623836512e-05,
                1.6701415855069562e-05,
                5.829127239415151e-05,
                3.120191132631554e-05,
                0.0001584362915683428
            ],
            [
                0.9999898700041988,
                0.9999984465022456,
                0.9999417087207189,
                0.9999810748519853,
                0.999841563802716,
                0.9995121428426186,
                0.9999038975738676,
                0.9999938558246664,
                0.9999910603036973,
                0.9998204719499423
            ],
            [
                6.144173868781898e-06,
                5.144222587049821e-05,
                6.9622562487453084e-06,
                1.3007125360478133e-05,
                5.42221767672807e-06,
                2.430023492769181e-05,
                2.1444950966608343e-05,
                1.4738980205754734e-05,
                6.962258739454786e-06,
                3.2887486731252264e-06
            ],
            [
                3.7266392839425286e-06,
                1.3007131562514014e-05,
                1.147876675466972e-05,
                7.484620933559467e-05,
                4.539785237316614e-05,
                1.1478770859917257e-05,
                1.670142781025767e-05,
                3.288749065125496e-06,
                1.6701423831188846e-05,
                2.430023493052066e-05
            ],
            [
                5.1442225851784594e-05,
                2.4300240725599276e-05,
                1.473898196763166e-05,
                1.6701423830702777e-05,
                8.939695231633822e-06,
                3.2887502411564953e-06,
                0.0001398221401234088,
                5.422221554374162e-06,
                5.42222155351609e-06,
                1.6701429800582296e-05
            ],
            [
                8.93969523678858e-06,
                2.7535697646567574e-05,
                3.53562420932866e-05,
                6.144172402285332e-06,
                7.889262580217877e-06,
                3.7266388388875246e-06,
                4.222834954514924e-06,
                1.892514147046736e-05,
                1.4738980207363312e-05,
                1.8925143726890553e-05
            ],
            [
                1.0129990975235516e-05,
                2.144494073054863e-05,
                5.144221970062134e-05,
                5.422218968595919e-06,
                1.3007130012980722e-05,
                3.5356246483883486e-05,
                1.892515500560259e-05,
                1.1478766754377407e-05,
                5.8291244542232006e-05,
                1.1478769491598686e-05
            ],
            [
                0.9999417087484042,
                0.9999832985841309,
                0.9998766053810748,
                0.9999952149055057,
                0.9999869928668863,
                0.9999785550413632,
                0.9999957771675625,
                0.999978555056703,
                0.9999785550413645,
                0.9999038975736865
            ],
            [
                1.4738976684950577e-05,
                7.484623604187633e-05,
                2.7535697639856078e-05,
                5.829126546520442e-05,
                7.889264464508026e-06,
                6.144174599532449e-06,
                2.7535681210027785e-05,
                3.7266392836374875e-06,
                7.889266346287306e-06,
                2.144494073569759e-05
            ],
            [
                3.120191506868607e-05,
                2.2603251060142746e-06,
                3.535624226936835e-05,
                1.300713000155317e-05,
                2.7535690999185903e-05,
                2.4300243607668818e-05,
                1.1478764013398468e-05,
                7.889262584809997e-06,
                8.939699497042417e-06,
                2.144494328404357e-05
            ],
            [
                1.1478765383679059e-05,
                3.7266388391247794e-06,
                3.1201918760886355e-05,
                2.4300243625614346e-05,
                4.222833444283541e-06,
                6.962255419051463e-06,
                8.939695236593446e-06,
                3.120191507776674e-05,
                8.481103102244385e-05,
                5.8291265401165313e-05
            ],
            [
                5.144221975938208e-05,
                0.0001233945893961187,
                6.9622562489985925e-06,
                2.4300252313904224e-05,
                0.00012339460405022358,
                2.430023782222529e-05,
                2.1444945848226808e-05,
                3.120190389923804e-05,
                1.892514823426434e-05,
                5.829125150595281e-05
            ],
            [
                0.9999993524049703,
                0.9999980052700408,
                0.9999962733611609,
                0.9999984465015048,
                0.9999970976880149,
                0.9999938558268638,
                0.999981074842751,
                0.9999974387180951,
                0.9999910603047647,
                0.9999957771675626
            ],
            [
                0.9999485577618847,
                0.9999885212359826,
                0.9999885212359814,
                0.999997097687323,
                0.9999417087415676,
                0.9999687980960955,
                0.9999785550516085,
                0.999986992868442,
                0.9999996533672962,
                0.9999546021151962
            ],
            [
                2.7535691069506297e-05,
                4.006368737181739e-05,
                4.785093353274332e-06,
                1.6701421838799146e-05,
                1.6701425814404263e-05,
                7.88926258343236e-06,
                7.889265405505236e-06,
                1.8925148230890784e-05,
                7.889265404113251e-06,
                3.1201911346293e-05
            ],
            [
                1.892515499864894e-05,
                2.430024069660355e-05,
                6.605214457207814e-05,
                7.889266345584138e-06,
                2.4300240718880753e-05,
                0.00015843629168590728,
                7.48462180835835e-05,
                1.0129993391808207e-05,
                4.5397884843438604e-05,
                7.88926164421493e-06
            ]
        ]
    },
    {
        "q_id": "8636_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            7,
            9,
            10,
            12,
            13,
            14,
            15,
            16,
            17,
            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,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            64,
            65,
            66,
            67,
            68,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            81,
            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,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124
        ],
        "rewards": [
            [
                2.9023112926779284e-06,
                6.1441767990323395e-06,
                3.7266388397721442e-06,
                2.561281294616881e-06,
                6.144172404380855e-06,
                5.422219615395428e-06,
                1.1478773597390071e-05,
                1.0129988564430787e-05,
                1.7603430034439723e-06,
                1.0129995810076682e-05
            ],
            [
                9.610243782956492e-05,
                2.753569109925723e-05,
                4.785092783210732e-06,
                1.1478770861859053e-05,
                1.670141587141357e-05,
                4.78509563555309e-06,
                0.00012339463333689376,
                8.481108169906156e-05,
                2.144494841326852e-05,
                1.1478770861859053e-05
            ],
            [
                6.9622562492265485e-06,
                1.9947304347570075e-06,
                7.889259764079887e-06,
                1.1478765388523107e-05,
                2.1444950966608343e-05,
                2.430023783530873e-05,
                8.315280276338815e-07,
                1.4738983728490028e-05,
                6.962257079376403e-06,
                2.260324028255194e-06
            ],
            [
                1.4738989000181669e-05,
                3.288750241500471e-06,
                6.962254589781966e-06,
                1.4738976701170414e-05,
                6.14417533430649e-06,
                2.1444940743225995e-05,
                1.9947299592824403e-06,
                1.4738988999940381e-05,
                3.7266397283231055e-06,
                1.6701425821573757e-05
            ],
            [
                1.14787681240737e-05,
                7.889260701697028e-06,
                1.7603430034311638e-06,
                9.422443691996268e-07,
                7.889260704631679e-06,
                1.0677026154473471e-06,
                6.144173869072478e-06,
                1.1478768122987964e-05,
                4.2228349547223175e-06,
                1.370957533676711e-06
            ],
            [
                6.1441775312976045e-06,
                1.1478772230198667e-05,
                7.338210679949506e-07,
                2.1444948410928083e-05,
                6.144177531459659e-06,
                4.222833947897496e-06,
                8.939695237959376e-06,
                6.962259568775433e-06,
                1.8925150494750372e-05,
                1.3007131563815288e-05
            ],
            [
                1.994729959270648e-06,
                3.726640172537657e-06,
                1.4738988999672284e-05,
                3.726640616670918e-06,
                1.0129989771657269e-05,
                3.2887482812506295e-06,
                6.475945665853783e-07,
                4.222831934248571e-06,
                9.42244256915735e-07,
                3.288750241500471e-06
            ],
            [
                0.9999756997651352,
                0.11920292358664392,
                0.43782349911420193,
                0.012431652522541893,
                0.10669059465574898,
                NaN,
                0.9980732651067588,
                0.9999151889387117,
                0.0021827165396646688,
                NaN
            ],
            [
                6.962254589781966e-06,
                3.288750633518874e-06,
                6.144176066521288e-06,
                5.1442201272586515e-05,
                6.962257909007124e-06,
                6.962253759157502e-06,
                2.7535704228438656e-05,
                1.0129990979381404e-05,
                1.6701417861189946e-05,
                3.726640616748873e-06
            ],
            [
                0.9999986290427931,
                0.9999990577555183,
                0.9999990577549569,
                0.9999991684717741,
                0.999998005269803,
                0.9999994284994167,
                0.9999986290427932,
                0.9999977396746244,
                0.9999984465024306,
                0.9999992661791944
            ],
            [
                2.26032402841657e-06,
                2.1444948412137308e-05,
                6.962256249606473e-06,
                1.8925141472360678e-05,
                7.889261645269683e-06,
                3.2887498494282754e-06,
                8.93969310662177e-06,
                2.144495608222158e-05,
                1.892514147143123e-05,
                8.939698434966738e-06
            ],
            [
                4.78509563535725e-06,
                1.892514823488397e-05,
                2.1444956079218013e-05,
                2.4300252317086683e-05,
                1.7603425836005905e-06,
                6.144172404218801e-06,
                6.144176066051891e-06,
                1.8925145983348442e-05,
                1.3007128464346676e-05,
                8.939697368663308e-06
            ],
            [
                5.8291286359769625e-05,
                2.4300246523066122e-05,
                3.120191509274984e-05,
                6.962254589528684e-06,
                3.288749457409966e-06,
                1.0677032518578904e-06,
                1.2098653950205268e-06,
                1.4738985484227961e-05,
                6.962258739530771e-06,
                2.2603248367656408e-06
            ],
            [
                1.209865539274514e-06,
                8.939696303758459e-06,
                7.889264466545779e-06,
                1.7603436329978976e-06,
                3.288750241410738e-06,
                6.144175334094145e-06,
                1.3007130014636887e-05,
                4.22283545795623e-06,
                4.785093924251918e-06,
                1.7603440526662173e-06
            ],
            [
                0.9999994956523514,
                0.9999992661792819,
                0.9999993524051246,
                0.9999967112513269,
                0.9999984465022456,
                0.9999994284996893,
                0.9999970976890531,
                0.9999992661790196,
                0.9999962733620489,
                0.9999996072137529
            ],
            [
                0.22270013366638425,
                8.315280275416164e-07,
                9.422443692390473e-07,
                0.9999251537564452,
                0.34864513533394575,
                0.9999485577867293,
                NaN,
                0.9999251537372333,
                0.08509904268669496,
                0.999512142826866
            ],
            [
                0.7057850154599563,
                0.999985261019976,
                0.9999910603016338,
                0.7057850278370112,
                0.999964643749551,
                0.999991060304765,
                0.7057850216484838,
                0.9999945777784567,
                0.962673113860638,
                0.999997739675972
            ],
            [
                1.4738981971250963e-05,
                1.6701417859519093e-05,
                1.6701417859944398e-05,
                7.889264465842609e-06,
                8.93969736955767e-06,
                6.144177531532303e-06,
                1.47389819699641e-05,
                3.726641061085547e-06,
                8.939693106987645e-06,
                7.889266346746518e-06
            ],
            [
                0.22270013366638425,
                0.3486451488696663,
                0.8519527982093666,
                0.8807970732843033,
                0.9989677690111426,
                0.2942149783515162,
                0.9999910603054606,
                0.9046505261034854,
                0.5926665999540698,
                0.1192029235866439
            ],
            [
                0.9999546021477249,
                0.9669140194661122,
                0.9999810748562825,
                0.9999339478258658,
                0.9999957771670611,
                0.999983298572614,
                0.9999962733593833,
                0.9999869928764377,
                4.222831934052698e-06,
                0.9999869928766917
            ],
            [
                1.994729721323867e-06,
                8.939700565834043e-06,
                9.422444815323792e-07,
                1.2098656834195822e-06,
                5.715003107353922e-07,
                1.6701419848475466e-05,
                5.715005832676369e-07,
                4.2228324375512536e-06,
                1.7603440525925705e-06,
                1.2098653950205268e-06
            ],
            [
                1.3007126912542439e-05,
                1.5534981249291695e-06,
                3.7266383955611403e-06,
                2.260324836696773e-06,
                1.4738987242968784e-05,
                1.1478768124553928e-05,
                6.962258738574625e-06,
                3.288749457409966e-06,
                2.260323489490968e-06,
                1.3007133115903994e-05
            ],
            [
                0.9999962733593832,
                0.9999996072136125,
                0.9999977396748938,
                0.9999984465020603,
                0.9999991684722698,
                0.9999980052695652,
                0.9999970976887068,
                0.9999977396751634,
                0.9999984465026158,
                0.9999994956523514
            ],
            [
                3.1201918796982014e-05,
                1.0129989771288745e-05,
                4.785095635413826e-06,
                6.962257079173776e-06,
                1.892515726357648e-05,
                4.785093353687772e-06,
                3.726637951170554e-06,
                2.4300252313904224e-05,
                1.6701421842961097e-05,
                1.1478764019328247e-05
            ],
            [
                0.8175744695262775,
                1.067703379136937e-06,
                1.2098652507957165e-06,
                7.889262584508638e-06,
                1.760342793515064e-06,
                0.8807970889295664,
                0.9465966671870766,
                6.475948753847607e-07,
                0.9999756997681383,
                8.315283250150648e-07
            ],
            [
                1.1478764020372226e-05,
                3.726641061027928e-06,
                5.1442207526298114e-05,
                1.3007133115903994e-05,
                1.147876675686207e-05,
                6.962253759828703e-06,
                1.3007123812980299e-05,
                4.785096205973894e-06,
                9.422450431954847e-07,
                4.006370173834246e-05
            ],
            [
                0.9999970976887078,
                0.9999986290427934,
                0.9999977396746246,
                0.9999852610215476,
                0.999996711249367,
                0.9999970976876692,
                0.9999977396754328,
                0.9999982396569966,
                0.9999945777810327,
                0.9999980052702792
            ],
            [
                0.9999910603058286,
                0.9999952149037944,
                0.9999756997653465,
                0.9999957771655488,
                0.9999687980998352,
                0.9998601779594093,
                0.9999938558261344,
                0.9999977396754328,
                0.9999938558239349,
                0.9999921107355334
            ],
            [
                0.9999987901338839,
                0.9999687980792193,
                0.9999756997563856,
                0.9999982396572066,
                0.9999991684722699,
                0.9999967112497594,
                0.9999910603047628,
                0.9999869928668885,
                0.9999952149072173,
                0.9999982396569974
            ],
            [
                0.999991060301566,
                0.9999993524049702,
                0.9999974387177893,
                0.9999952149043645,
                0.9999989322967482,
                0.9999938558268632,
                0.9999957771650453,
                0.9999952149060758,
                0.9999967112513266,
                0.9999952149032236
            ],
            [
                7.889264465986113e-06,
                1.3007123810638006e-05,
                1.3007128464559612e-05,
                7.889260704423598e-06,
                1.0129995809929273e-05,
                3.726640172337686e-06,
                5.422219615582823e-06,
                8.939696302831578e-06,
                6.605215254025824e-05,
                4.785095635017795e-06
            ],
            [
                0.9998766054001061,
                0.8354835452961425,
                0.8519528019683105,
                0.320821300824607,
                0.9999945777829822,
                0.6224593241981982,
                0.9999687980863495,
                0.8670357649558006,
                0.731058584489497,
                0.9999724643089206
            ],
            [
                0.9999952149061312,
                0.9999756997622509,
                0.9999646437341345,
                0.9999724643153589,
                0.9999810748451506,
                0.9999832985841371,
                0.9999546021104644,
                1.3007134663876127e-05,
                0.939913354875362,
                0.9579122729855218
            ],
            [
                1.7603438427852151e-06,
                1.473898548194914e-05,
                7.338207180601138e-07,
                1.1478764020560142e-05,
                3.726639728262097e-06,
                1.0129987353832463e-05,
                2.4300249412738893e-05,
                9.422443692390473e-07,
                5.422217676925328e-06,
                3.7266388398585725e-06
            ],
            [
                0.999996273359384,
                0.9999898700041914,
                0.9999991684722698,
                0.9999898700078236,
                0.999998932297512,
                0.9999974387165685,
                0.9999921107392997,
                0.9999957771665555,
                0.9997965730034855,
                0.9999952149066462
            ],
            [
                0.9999974387171787,
                0.9999974387187053,
                0.9999974387168733,
                0.9999977396759716,
                0.9999898700114452,
                0.9999945777784449,
                0.9999967112517187,
                0.9999986290423029,
                0.999995777164542,
                0.9999952149072169
            ],
            [
                1.0129992186774007e-05,
                2.430024361951464e-05,
                1.0129992186589747e-05,
                8.939697368663308e-06,
                1.4738988998787566e-05,
                1.9947304348703948e-06,
                1.6701417858577338e-05,
                1.4738976697631541e-05,
                5.422220262505697e-06,
                2.144495096457996e-05
            ],
            [
                1.3007128463873485e-05,
                4.222832940942332e-06,
                1.7603438427660027e-06,
                5.043474081957179e-07,
                1.3709568799592562e-06,
                8.939699500636112e-06,
                1.0129990979547237e-05,
                4.222834954561012e-06,
                1.14787708624228e-05,
                1.2098658277082653e-06
            ],
            [
                1.7603438427660027e-06,
                2.4300252313904224e-05,
                2.4300249419722622e-05,
                1.300712536258383e-05,
                1.6701417861189946e-05,
                2.4300237832303074e-05,
                8.939698434966738e-06,
                1.760344052650207e-06,
                1.1478764019787597e-05,
                1.1478768124553928e-05
            ],
            [
                1.0129988564845378e-05,
                1.1478769492642663e-05,
                3.120191878472311e-05,
                8.93969417167259e-06,
                2.5612831266165976e-06,
                8.939695238333382e-06,
                1.892515274546026e-05,
                1.670142781636389e-05,
                1.300712846361323e-05,
                8.93969417214416e-06
            ],
            [
                1.300713311614059e-05,
                1.0129993394811673e-05,
                0.9999997617630616,
                0.9999646437619342,
                0.9999994284993485,
                5.422217030663578e-06,
                0.9999996533674614,
                0.999997438716568,
                0.999999057755743,
                0.9999785550439172
            ],
            [
                0.6791786926816161,
                0.9579122767402745,
                0.9996200154336001,
                0.9999957771646641,
                0.9399133443558416,
                0.999978555049332,
                0.9998601778704655,
                0.5,
                0.8670357477770337,
                0.5926665999540698
            ],
            [
                1.3007134665413997e-05,
                3.535624226936835e-05,
                1.553497198908852e-06,
                3.288748280658394e-06,
                4.222832940942332e-06,
                9.61024376337973e-05,
                1.7603434229832599e-06,
                1.6701425823457267e-05,
                8.315283249636384e-07,
                1.0677033788961119e-06
            ],
            [
                1.0129988564430787e-05,
                5.1442232055908106e-05,
                3.726638395527247e-06,
                6.962256249682458e-06,
                2.75356976629957e-05,
                1.0129990978847043e-05,
                6.144175334172377e-06,
                8.939697369785323e-06,
                1.3007125363057018e-05,
                2.144494073569759e-05
            ],
            [
                0.9999921107346041,
                0.9999869928731052,
                0.9999910603068937,
                0.9999945777784469,
                0.9525741273273217,
                0.9999785550515924,
                0.9999810748472753,
                0.9999898700114359,
                0.9999756997535074,
                0.9999785550413804
            ],
            [
                1.473898197154587e-05,
                5.1442213617576366e-05,
                2.7535684533717236e-05,
                1.0129994600638342e-05,
                8.93969736929749e-06,
                2.7535694382378416e-05,
                6.144173868983067e-06,
                4.5397890270732005e-05,
                1.0129995806612563e-05,
                4.222834953712232e-06
            ],
            [
                1.6701423833011596e-05,
                1.8925150497435443e-05,
                3.535626756842843e-05,
                4.539789028295303e-05,
                1.8925150495232307e-05,
                0.00010889694818890738,
                1.473898197063434e-05,
                1.147876812574406e-05,
                2.7535694382378416e-05,
                2.1444948412137308e-05
            ],
            [
                6.962257079629686e-06,
                3.2887506334560605e-06,
                7.889262585541864e-06,
                8.31528126775552e-07,
                4.222832437186393e-06,
                4.785095065171522e-06,
                1.5534971989696065e-06,
                6.962256249517824e-06,
                3.7266392838544054e-06,
                6.144173136885882e-06
            ],
            [
                0.9149009538328171,
                0.3208213138121609,
                0.9998766054550277,
                0.9996200155603765,
                NaN,
                NaN,
                0.9399133536130195,
                0.6791787121629466,
                NaN,
                0.9999646437514469
            ],
            [
                1.8925145979561802e-05,
                1.0129993394314164e-05,
                7.88925976316864e-06,
                1.012998735687278e-05,
                2.260324297702111e-06,
                0.00023050671126180846,
                5.422220908634683e-06,
                1.9947290080905435e-06,
                2.5612834318257725e-06,
                2.4300232039788792e-05
            ],
            [
                1.670141587141357e-05,
                1.3007128464346676e-05,
                4.7850939242083995e-06,
                4.006368741175151e-05,
                4.006367783922064e-05,
                0.979667644505429,
                3.535626335815526e-05,
                7.88925976397226e-06,
                4.5397868633071815e-05,
                4.006369219233375e-05
            ],
            [
                6.962254589528684e-06,
                4.785095065132354e-06,
                5.422217676866151e-06,
                1.5534984952111384e-06,
                2.260323489435463e-06,
                1.1478768125577027e-05,
                3.288749457383046e-06,
                1.0129992187105678e-05,
                4.78509563546605e-06,
                1.4738983728490028e-05
            ],
            [
                1.3007130012980722e-05,
                1.670142980687079e-05,
                1.0129988564430787e-05,
                8.481104130646901e-05,
                5.144220740840241e-05,
                1.6701417862648148e-05,
                4.785096205778054e-06,
                3.7266388396975786e-06,
                7.889262585642319e-06,
                2.4300243613326524e-05
            ],
            [
                5.14422381473764e-05,
                9.610243775685123e-05,
                2.1444956081636468e-05,
                4.222832437497486e-06,
                1.670142980608093e-05,
                1.6701427812931038e-05,
                3.120192252800261e-05,
                6.962258739530771e-06,
                8.939693104865575e-06,
                2.1444940743225995e-05
            ],
            [
                2.430023493936082e-05,
                6.962257079629686e-06,
                6.962259569313662e-06,
                6.144176799099397e-06,
                1.0129990979694647e-05,
                1.1478764019787597e-05,
                6.962253758916883e-06,
                5.144220139740624e-05,
                1.3709572068478697e-06,
                4.539785782390681e-05
            ],
            [
                0.9999995549149481,
                0.9999982396569966,
                0.9999996072138465,
                0.9999994284994849,
                0.9999977396762411,
                0.9999992661787571,
                0.9999986290432834,
                0.9999982396567867,
                0.9999995549147359,
                0.999999352404893
            ],
            [
                1.3007128463873485e-05,
                6.962253759752719e-06,
                1.2098658276730537e-06,
                1.3007128463069061e-05,
                3.2887482811579057e-06,
                7.889262585642319e-06,
                1.473897845457507e-05,
                1.9947292458603553e-06,
                9.422447062030659e-07,
                4.785092782692845e-06
            ],
            [
                1.6701425822059825e-05,
                1.8925157260443894e-05,
                2.43002465110435e-05,
                1.6701417862648148e-05,
                6.962254589851619e-06,
                1.0129988564716393e-05,
                1.1478766757237902e-05,
                1.3007126913583456e-05,
                8.93969310662177e-06,
                8.939693106873817e-06
            ],
            [
                1.012998735687278e-05,
                8.481102115121237e-05,
                5.82912932959289e-05,
                4.006369218184011e-05,
                3.535626757125808e-05,
                2.1444958637356654e-05,
                9.61023804983358e-05,
                2.4300249422639878e-05,
                NaN,
                5.42222090821551e-06
            ],
            [
                0.9999417087087165,
                0.9999930377420908,
                0.9999251537818069,
                0.9999898700102289,
                0.9999885212333849,
                0.9999724643187513,
                0.999841563805752,
                0.999988521226404,
                0.9999756997505892,
                0.9999151889688598
            ],
            [
                1.30071253611406e-05,
                6.1441746018123775e-06,
                1.2098656835076114e-06,
                1.6701421843720577e-05,
                2.4300240728958537e-05,
                2.4300246520590875e-05,
                2.9023112929973233e-06,
                2.2603245672867952e-06,
                6.144172404520556e-06,
                5.4222215550004564e-06
            ],
            [
                0.9999991684722697,
                0.9999980052700408,
                0.9999980052707542,
                0.999998790134028,
                0.9999986290423029,
                0.999997097686977,
                0.9999986290429566,
                0.9999852610162777,
                0.9999990577552937,
                0.9999984465020603
            ],
            [
                5.4222196154940574e-06,
                7.484622696171771e-05,
                8.939699500766203e-06,
                8.939700565834043e-06,
                3.7266410608245674e-06,
                1.5534984953298217e-06,
                2.902311984683171e-06,
                2.4300252310279753e-05,
                5.4222215550004564e-06,
                4.785096205778054e-06
            ],
            [
                4.00636874062132e-05,
                4.222831933726245e-06,
                6.144172403928222e-06,
                2.1444945853375776e-05,
                2.1444948409679848e-05,
                1.1478770860481005e-05,
                2.1444950969026795e-05,
                4.5397863219323224e-05,
                1.4738980213341866e-05,
                1.8925145981283003e-05
            ],
            [
                0.9999987901341723,
                0.9999994284994849,
                0.999999057755743,
                0.99999862904312,
                0.9999991684716749,
                0.9999980052693274,
                0.999999266178932,
                0.9999982396559474,
                0.9999921107374158,
                0.9999987901347491
            ],
            [
                2.4300249419722622e-05,
                7.889263525103816e-06,
                4.006369218184011e-05,
                0.0001398220405906475,
                2.1444945853999886e-05,
                2.753568781222975e-05,
                1.4738978456049602e-05,
                5.8291244687274174e-05,
                2.753568124458694e-05,
                0.00010889689615913351
            ],
            [
                0.9999785550439516,
                0.9999687980928318,
                0.999941708734573,
                0.9999785550440398,
                0.9999852610215888,
                0.9999724642990984,
                0.9999930377412614,
                0.7772998714925403,
                0.7057850278370112,
                0.9999885212305096
            ],
            [
                6.962253759043525e-06,
                3.5356246483883486e-05,
                8.939694170518055e-06,
                2.7535681252300143e-05,
                1.473898021457511e-05,
                1.370957370247318e-06,
                2.9023133690188264e-06,
                3.2887486732000038e-06,
                2.1444943300075563e-05,
                8.939700566801578e-06
            ],
            [
                3.288748673295719e-06,
                6.962255419728997e-06,
                1.0129988564578197e-05,
                1.6701419848961534e-05,
                4.785093923768848e-06,
                4.785092783267308e-06,
                4.785095065045315e-06,
                6.962259569560613e-06,
                1.9947301970106386e-06,
                2.430023783309869e-05
            ],
            [
                6.605217616367606e-05,
                1.8925155007633607e-05,
                1.892514823488397e-05,
                0.00010889692206231105,
                3.120191136400031e-05,
                1.89251482406672e-05,
                8.939693105662367e-06,
                3.1201926246083686e-05,
                1.670141587068447e-05,
                2.7535684533717236e-05
            ],
            [
                6.962253759670401e-06,
                2.1444940744318203e-05,
                1.4738978457336465e-05,
                7.889261645090304e-06,
                5.1442232053101066e-05,
                1.14787708624228e-05,
                1.6701427816728442e-05,
                4.785094494672519e-06,
                1.7603440527046419e-06,
                3.7266383955611403e-06
            ],
            [
                2.4300249416363357e-05,
                2.4300252317882297e-05,
                1.4738980213985297e-05,
                1.6701419850389357e-05,
                7.889262585642319e-06,
                1.3007131565376817e-05,
                3.726640172537657e-06,
                8.939700566289352e-06,
                1.4738980213985297e-05,
                0.000179528029994973
            ],
            [
                1.0129989770662257e-05,
                5.422220908402905e-06,
                1.4738985482753428e-05,
                1.0129990976451642e-05,
                1.0129992187105678e-05,
                7.338211554398095e-07,
                1.0677033791437343e-06,
                1.5534973841592143e-06,
                1.0129987355785634e-05,
                1.0677028699625768e-06
            ],
            [
                4.222831934202483e-06,
                3.2887494572873306e-06,
                2.902312331081799e-06,
                6.962257909501028e-06,
                4.222833947820683e-06,
                1.3709575336860625e-06,
                2.2603248367173307e-06,
                1.0677031245783732e-06,
                6.9622545892184106e-06,
                1.209866116137134e-06
            ],
            [
                0.9999885212332453,
                0.9999980052709929,
                0.9999938558232038,
                0.9999810748427385,
                0.9999977396757023,
                0.9999974387187055,
                0.999994577782324,
                0.9999945777816769,
                0.9999898700114386,
                0.9999980052698031
            ],
            [
                8.939695234463248e-06,
                2.4300232039788792e-05,
                2.9023126765777146e-06,
                6.144172403067661e-06,
                5.422217676575195e-06,
                3.288749849000549e-06,
                8.939700560549195e-06,
                6.144177529531776e-06,
                5.829129317633263e-05,
                2.1444956078515887e-05
            ],
            [
                2.9023112931688987e-06,
                2.9023116391675407e-06,
                4.222832941034507e-06,
                3.7266406167827664e-06,
                1.8925152752138513e-05,
                2.144494585801764e-05,
                1.473898197154587e-05,
                0.9999997617629764,
                2.1444956079842134e-05,
                3.120192252686752e-05
            ],
            [
                5.715003107689177e-07,
                7.338209805170655e-07,
                2.561281905376098e-06,
                6.144172404129392e-06,
                3.2887506333812835e-06,
                1.7603434231097403e-06,
                4.222831934248571e-06,
                1.0129993394664264e-05,
                6.1441767990323395e-06,
                3.726639284050988e-06
            ],
            [
                6.144177531532303e-06,
                1.1478772230762415e-05,
                5.4222215552470286e-06,
                4.785096205930373e-06,
                1.012998977213635e-05,
                3.120190393260949e-05,
                1.3007128464559612e-05,
                1.3007125363293615e-05,
                2.4300246523773334e-05,
                2.4300234940642642e-05
            ],
            [
                0.9999967112497584,
                0.9999938558268646,
                0.9999957771670593,
                0.9999952149055075,
                0.9999921107355344,
                0.9999993524048929,
                0.9999977396746244,
                0.9999986290424663,
                0.999988521227774,
                0.999993037740433
            ],
            [
                3.726641061085547e-06,
                8.939699500896292e-06,
                2.902312331081799e-06,
                1.9947301970451086e-06,
                4.222835458175145e-06,
                1.6701419852090592e-05,
                2.1444956081636468e-05,
                3.2887490653408545e-06,
                6.962257909501028e-06,
                6.9622587396067566e-06
            ],
            [
                8.93969310662177e-06,
                3.535626333989112e-05,
                8.939698432917844e-06,
                NaN,
                1.4738981968060613e-05,
                1.4738976700661033e-05,
                4.0063706492255065e-05,
                3.120190393374457e-05,
                9.610238062768217e-05,
                3.535624227425594e-05
            ],
            [
                4.785094494628999e-06,
                3.7266392839832006e-06,
                1.3007133115667397e-05,
                1.473898372822193e-05,
                5.043473471134824e-07,
                1.5534973841705173e-06,
                7.889260704531226e-06,
                1.3007128463069061e-05,
                3.12019002122609e-05,
                4.00636874062132e-05
            ],
            [
                3.726639284017094e-06,
                1.3709572068272963e-06,
                1.994729008105057e-06,
                2.902313023063532e-06,
                3.288747889178668e-06,
                7.889266347456862e-06,
                1.4738983729053029e-05,
                4.222834451169694e-06,
                1.1478766756653273e-05,
                2.1444948412722418e-05
            ],
            [
                0.9999962733607158,
                0.9999977396765105,
                0.999995777164542,
                0.9999986290432834,
                0.9999970976890528,
                0.9999974387177893,
                0.9999984465026158,
                0.9999974387171788,
                0.999999352405279,
                0.9999952149043646
            ],
            [
                0.9999994284993485,
                0.999999266178757,
                0.9999994956527722,
                0.999999495652652,
                0.9999982396563669,
                0.9999994956524716,
                0.999996273360716,
                0.9999962733607162,
                0.9999980052705163,
                0.9999984465028011
            ],
            [
                0.9999970976890534,
                0.9999986290429567,
                0.9999974387174841,
                0.9999982396563671,
                0.9999852610197955,
                0.9999970976869776,
                0.9999724643027272,
                0.9999724643155167,
                0.9999930377429255,
                0.9999938558261334
            ],
            [
                6.144172404520556e-06,
                4.78509392429544e-06,
                1.4738988999377379e-05,
                1.7603432132784448e-06,
                1.0129988564716393e-05,
                1.7603425837606927e-06,
                2.2603242978665707e-06,
                1.4738976700366126e-05,
                1.147876538789672e-05,
                6.144175334418252e-06
            ],
            [
                1.6701419853518415e-05,
                4.785093353626844e-06,
                1.892515500663531e-05,
                1.670142383495587e-05,
                2.7535691100960147e-05,
                2.4300246523066122e-05,
                3.120191508707442e-05,
                3.5356250691324983e-05,
                1.0129989771288745e-05,
                8.93969310662177e-06
            ],
            [
                0.9999994956525317,
                0.9999938558224688,
                0.9999986290427931,
                0.999999266178757,
                0.999997438716568,
                0.9999996940977366,
                0.9999994956525917,
                0.9999995549148419,
                0.9999996072139402,
                0.9999989322967482
            ],
            [
                0.9999986290426297,
                0.9999989322967481,
                0.9999982396565769,
                0.9999962733607161,
                0.9999977396748937,
                0.9999994284992805,
                0.9999989322966208,
                0.9999996072137529,
                0.9999995549150011,
                0.9999990577555183
            ],
            [
                1.3709568799679844e-06,
                2.4300234937946394e-05,
                1.3007130010922344e-05,
                2.144494074201677e-05,
                5.422217030614265e-06,
                2.1444950970626095e-05,
                4.539785780805251e-05,
                4.5397879445707534e-05,
                1.0129994601872894e-05,
                6.144176798870286e-06
            ],
            [
                0.999998446502801,
                0.9999990577551814,
                0.9999987901343166,
                0.9999992661792819,
                0.99999862904312,
                0.9999977396748938,
                0.9999987901343165,
                0.9999962733593831,
                0.9999974387180947,
                0.9999967112513266
            ],
            [
                0.9999339478636408,
                NaN,
                0.6791787056691698,
                NaN,
                0.9998204720557494,
                0.999985261018038,
                0.9999852610154806,
                0.9999599362987166,
                0.9999038975971584,
                0.9999810748443173
            ],
            [
                1.0129988564430787e-05,
                1.1478772229989872e-05,
                5.422218968595919e-06,
                1.892515726099468e-05,
                6.962254589104433e-06,
                6.144177531208195e-06,
                2.753568780802255e-05,
                2.1444945853375776e-05,
                2.561282821069686e-06,
                1.670142582300158e-05
            ],
            [
                2.144495863411905e-05,
                1.4738985485166298e-05,
                8.939697369671496e-06,
                1.1478773598329648e-05,
                4.785093353787868e-06,
                5.422221555192784e-06,
                1.6701419853518415e-05,
                7.889261644875049e-06,
                2.9023112931688987e-06,
                6.605216829977486e-05
            ],
            [
                5.144220136765162e-05,
                1.8925150493717652e-05,
                1.4738980212644815e-05,
                9.610243757506701e-05,
                2.4300237832303074e-05,
                2.1444958635523312e-05,
                8.481107159890629e-05,
                5.829125859054295e-05,
                3.535626333281696e-05,
                3.5356246471407274e-05
            ],
            [
                0.999998446502801,
                0.9999967112497584,
                0.9999952149037942,
                0.9999910603036961,
                0.9999982396567867,
                0.9999967112517187,
                0.9999974387177893,
                0.9999989322968754,
                0.9999869928668841,
                0.9999977396746244
            ],
            [
                0.9999810748565502,
                NaN,
                0.9999967112501505,
                0.9999984465026159,
                0.8807970795424088,
                0.9999687980961919,
                0.7772998663336158,
                0.8670357546485407,
                0.9999687980744039,
                NaN
            ],
            [
                0.946596674343187,
                0.9706877668107408,
                0.999972464306051,
                0.9999599363245327,
                0.9149009509324104,
                0.962673116671762,
                0.7310585903489892,
                0.999941708752241,
                0.9999885212278269,
                0.9998766054030973
            ],
            [
                1.6701427817427163e-05,
                1.8925141472360678e-05,
                1.4738988999672284e-05,
                7.889260704308795e-06,
                1.6701419852090592e-05,
                7.88926634755014e-06,
                1.8925152752586028e-05,
                2.1444958632714784e-05,
                1.4738981233261554e-05,
                1.0129995809431767e-05
            ],
            [
                1.4738988999940381e-05,
                1.892515049702235e-05,
                5.422217030495909e-06,
                1.8925143729954285e-05,
                6.605215256332514e-05,
                2.753570094621784e-05,
                4.22283344433731e-06,
                3.1201915085825835e-05,
                1.6701429808298613e-05,
                2.4300232042706045e-05
            ],
            [
                2.144495863482118e-05,
                3.726638839833152e-06,
                7.889263525663481e-06,
                5.144220138000259e-05,
                1.5534977545603963e-06,
                2.1444953523537147e-05,
                5.422217030614265e-06,
                3.535624649468763e-05,
                3.535623806861614e-05,
                1.670142980893658e-05
            ],
            [
                0.9999982396561571,
                0.9999989322971299,
                0.9999938558224692,
                0.9999977396754327,
                0.9999977396754327,
                0.9999970976883608,
                0.9999990577556308,
                0.9999962733616043,
                0.9999898700053989,
                0.9999930377462404
            ],
            [
                0.9999977396757022,
                0.9999990577550691,
                0.9999991684719723,
                0.9999994284997573,
                0.999999653367379,
                0.9999990577550691,
                0.999999266178932,
                0.9999992661786696,
                0.9999991684717742,
                0.9999990577555183
            ],
            [
                0.999664649970408,
                0.5,
                0.9999599362990792,
                0.9999898700078441,
                NaN,
                0.37754066879814546,
                0.9999687980964781,
                0.7981867729389246,
                0.7549149923816048,
                0.9999945777784462
            ],
            [
                7.889265406904397e-06,
                NaN,
                1.4738985485997396e-05,
                1.6701417861584877e-05,
                1.3007123812317831e-05,
                1.7603427935967163e-06,
                6.1441746018123775e-06,
                1.4738976694977387e-05,
                1.1478773599102191e-05,
                7.889265406438011e-06
            ],
            [
                3.2887490652810324e-06,
                2.561283432005142e-06,
                1.0677031245710902e-06,
                3.726641061058432e-06,
                2.9023109471452223e-06,
                3.288747889229516e-06,
                2.5612812946681295e-06,
                1.2098658277181688e-06,
                1.7603434231097403e-06,
                1.7603436330091044e-06
            ],
            [
                3.7266406160845606e-06,
                7.889261643899223e-06,
                6.144176798870286e-06,
                7.889261644982674e-06,
                1.3709576971061233e-06,
                3.288748673265808e-06,
                1.4738980214280206e-05,
                2.260324567227179e-06,
                3.120190021453107e-05,
                3.726637951079042e-06
            ],
            [
                4.006370651207639e-05,
                2.7535684526905577e-05,
                2.144494329952946e-05,
                5.829125856806564e-05,
                2.9023112929973233e-06,
                7.889261644982674e-06,
                3.2887490653109436e-06,
                6.962253759486771e-06,
                2.1444956071728615e-05,
                3.535623804803683e-05
            ]
        ]
    },
    {
        "q_id": "7887_mmlu_math",
        "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,
            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,
            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,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                2.9023109470554753e-06,
                3.7266401721817755e-06,
                1.994729959270648e-06,
                3.7266392833663395e-06,
                1.5534975692866768e-06,
                2.561283431942246e-06,
                1.5534979396815448e-06,
                2.2603245671490605e-06,
                1.1478772229989872e-05,
                3.726637950851956e-06
            ],
            [
                3.2887498494551953e-06,
                6.962255414631664e-06,
                6.962254589104433e-06,
                6.144176798255599e-06,
                6.962258737814774e-06,
                8.939697369151141e-06,
                1.5534981249023245e-06,
                1.473898899664279e-05,
                8.939698434332555e-06,
                6.144173136455602e-06
            ],
            [
                7.889265405505236e-06,
                2.902313022952668e-06,
                1.3709576970824327e-06,
                5.422220262333096e-06,
                8.315277302649045e-07,
                6.144177530794679e-06,
                7.338209804920378e-07,
                8.939698434657777e-06,
                1.1478769492141554e-05,
                1.4738985474174337e-05
            ],
            [
                1.0677032518413822e-06,
                5.04347528440776e-07,
                5.71500651413193e-07,
                5.71500242637956e-07,
                2.5612831265630198e-06,
                1.99472995920443e-06,
                6.475948753965404e-07,
                1.7603430034311638e-06,
                1.760344052650207e-06,
                2.5612831266165976e-06
            ],
            [
                1.6701415866735174e-05,
                8.939699498814873e-06,
                1.14787681240737e-05,
                1.4738981968864903e-05,
                3.1201900154598675e-05,
                2.144495863201265e-05,
                3.12019076363863e-05,
                2.144494073796001e-05,
                3.120191506039996e-05,
                1.892515499389843e-05
            ],
            [
                1.473897669245728e-05,
                5.422220262037209e-06,
                3.2887482810801374e-06,
                4.785093924103951e-06,
                2.260324567087388e-06,
                1.3007134661628471e-05,
                1.0129994600859455e-05,
                1.473897670007122e-05,
                5.422218323019487e-06,
                1.892515048820981e-05
            ],
            [
                1.9947304347098384e-06,
                1.1478766751997141e-05,
                1.1478772224477678e-05,
                5.422217029272909e-06,
                2.260323758806253e-06,
                8.315283250150648e-07,
                1.2098653950315304e-06,
                7.338212429240558e-07,
                1.5534983100016177e-06,
                7.338210679622478e-07
            ],
            [
                0.9997388096601193,
                0.9994472214551452,
                0.9996200154254085,
                0.9991959141503273,
                0.9975273766521303,
                0.9971990735420756,
                0.9998766054104226,
                0.9953904273911682,
                0.9995694429104336,
                0.998674977383294
            ],
            [
                1.3709570433661467e-06,
                1.7603436328770204e-06,
                2.902311639073834e-06,
                3.28874828059259e-06,
                4.222833947674739e-06,
                8.939695235959266e-06,
                1.3007125360809367e-05,
                NaN,
                2.5612815998491325e-06,
                2.9023112926779284e-06
            ],
            [
                1.3709573702248741e-06,
                2.561282210590951e-06,
                9.422444815726566e-07,
                2.561282515820982e-06,
                1.7603438428460541e-06,
                4.785093923516432e-06,
                4.222833444283541e-06,
                2.382369667892166e-07,
                3.0590215398829087e-07,
                1.0677033791291683e-06
            ],
            [
                1.012998856312253e-05,
                4.22283193338827e-06,
                4.222835458044565e-06,
                7.88926352407059e-06,
                7.889262584350785e-06,
                6.962255418215627e-06,
                1.1478770861211786e-05,
                3.7266392835764795e-06,
                1.1478768119939555e-05,
                2.5612819053166966e-06
            ],
            [
                4.539789028064095e-05,
                7.88925976126004e-06,
                2.902312677007974e-06,
                6.144173136019732e-06,
                7.88925976359915e-06,
                8.939697367703906e-06,
                1.0129994601688632e-05,
                1.5534983100425914e-06,
                2.9023133690425823e-06,
                7.889266346746518e-06
            ],
            [
                1.3007133107528522e-05,
                1.0129990975862006e-05,
                2.561282210618905e-06,
                1.370957043323753e-06,
                6.962255417544426e-06,
                1.892514371095225e-05,
                4.785092782936557e-06,
                1.6701415866188347e-05,
                1.5534975693347152e-06,
                2.4300237825230942e-05
            ],
            [
                5.422220262037209e-06,
                1.8925141465820123e-05,
                1.3007126911643378e-05,
                1.0129990979381404e-05,
                1.8925148231579266e-05,
                2.1444948407573453e-05,
                6.962257909323729e-06,
                2.561281905058126e-06,
                1.300712845966209e-05,
                1.0129990978644356e-05
            ],
            [
                3.7266392835764795e-06,
                1.3007130009313495e-05,
                3.7266406163624873e-06,
                3.2887478887958082e-06,
                6.9622545892184106e-06,
                8.315283250082584e-07,
                6.1441767990323395e-06,
                7.889266347004826e-06,
                4.785096776068365e-06,
                5.422217030495909e-06
            ],
            [
                1.3007123810306773e-05,
                5.829127918738738e-05,
                4.222834450820197e-06,
                4.539786317820113e-05,
                7.484625377419046e-05,
                0.9997694932066167,
                2.430023782328611e-05,
                1.6701415862117537e-05,
                3.5356238024242e-05,
                1.8925145961179394e-05
            ],
            [
                4.222834954057889e-06,
                2.260323758882316e-06,
                1.3709578604981489e-06,
                1.0677028699043128e-06,
                1.7603436328994344e-06,
                2.561283431942246e-06,
                9.422444815323792e-07,
                2.5612828212909852e-06,
                1.067702742683591e-06,
                1.370957370196196e-06
            ],
            [
                0.9990889489925723,
                0.9989677691649183,
                0.9997694931753952,
                0.9995694429116361,
                0.9947798737357649,
                0.9990889487778368,
                0.9988304896007226,
                0.9982992776723697,
                0.9980732655838241,
                0.9984988179191573
            ],
            [
                2.902313368583287e-06,
                7.889260702744606e-06,
                3.726639283752725e-06,
                1.0129987353242826e-05,
                6.144176065828368e-06,
                3.2887490649221017e-06,
                2.9023133682084594e-06,
                1.9947292457750883e-06,
                8.939696301611998e-06,
                2.561283126502453e-06
            ],
            [
                3.726637950411341e-06,
                5.043475284274736e-07,
                6.962259568889411e-06,
                2.5612819052374947e-06,
                1.4738978454172926e-05,
                5.422221555192784e-06,
                1.0129989770662257e-05,
                2.5612825159421147e-06,
                1.670141785651155e-05,
                1.4738980209829803e-05
            ],
            [
                9.42244930849811e-07,
                1.5534973841309562e-06,
                1.9947292458930106e-06,
                7.338212429307298e-07,
                1.7603436329394601e-06,
                3.927862002606139e-07,
                6.475951069896949e-07,
                6.475950297868629e-07,
                3.927862002606139e-07,
                9.422443692261927e-07
            ],
            [
                4.539786857692116e-05,
                3.7266388397382506e-06,
                7.889264464895484e-06,
                6.144174601499446e-06,
                1.670142780910326e-05,
                3.7266392836374875e-06,
                0.00020342697245850854,
                1.1478768122987964e-05,
                1.3007133114886634e-05,
                1.1478769491598686e-05
            ],
            [
                5.8291244568526206e-05,
                1.2098652506746763e-06,
                1.0129989769464556e-05,
                0.9999038975852738,
                1.14787667504103e-05,
                6.144174601499446e-06,
                7.889262582800945e-06,
                4.006370648569653e-05,
                6.1441746016670885e-06,
                7.889263524960312e-06
            ],
            [
                3.1201907620154606e-05,
                1.1478769492141554e-05,
                1.300712536203966e-05,
                7.889261642578988e-06,
                5.42222090821551e-06,
                6.144173869312763e-06,
                6.962257909323729e-06,
                1.473898724181597e-05,
                7.889263523453522e-06,
                1.473898899664279e-05
            ],
            [
                2.7535694358938284e-05,
                1.1478765386038447e-05,
                7.8892654060075e-06,
                1.0129990974572174e-05,
                1.4738981968462759e-05,
                1.0677033790757595e-06,
                4.539785230182181e-05,
                2.430024643227764e-05,
                3.2887482809933958e-06,
                3.535625904858737e-05
            ],
            [
                1.1478769491598686e-05,
                2.2603245666515692e-06,
                1.4738983718463215e-05,
                2.1444940738662144e-05,
                4.222833443154396e-06,
                2.902311984783477e-06,
                4.222833946937338e-06,
                1.3007134655335035e-05,
                1.994729245842213e-06,
                6.962255418215627e-06
            ],
            [
                2.2603234893861252e-06,
                2.9023109467598367e-06,
                1.5534975693205863e-06,
                3.2887494569044713e-06,
                9.422448185101494e-07,
                1.1478766755233466e-05,
                6.962253759271479e-06,
                2.902313368897403e-06,
                4.7850967744320136e-06,
                2.902312330759764e-06
            ],
            [
                1.5534973840984598e-06,
                6.144175333021237e-06,
                3.28874906467085e-06,
                2.7535697651475977e-05,
                2.5612834317535587e-06,
                1.9947299592407137e-06,
                1.9947304347570075e-06,
                8.939695237162584e-06,
                4.222833947674739e-06,
                1.9947290079889487e-06
            ],
            [
                8.939694168517944e-06,
                6.9622579059043994e-06,
                6.962257908753841e-06,
                9.422444815679433e-07,
                4.222833443968609e-06,
                6.144176066353646e-06,
                6.962255419475714e-06,
                4.785096205260165e-06,
                2.561283431942246e-06,
                4.222832437497486e-06
            ],
            [
                5.422218969217281e-06,
                2.260325375615501e-06,
                8.939696300636336e-06,
                2.2603245672497918e-06,
                1.3007134659451795e-05,
                6.9622554185195676e-06,
                1.994729483630195e-06,
                6.144174600985344e-06,
                1.5534975692683091e-06,
                2.902311984915459e-06
            ],
            [
                0.9996200155152066,
                0.9995694429623517,
                0.9995694430135433,
                0.9995121428823267,
                0.9997388097221476,
                0.9982992775686017,
                0.9992903297087612,
                0.9978172837539427,
                0.9997040430071777,
                0.9996646498498932
            ],
            [
                1.67014218359435e-05,
                3.2887506330851655e-06,
                9.422445938797133e-07,
                4.785095634756674e-06,
                3.2887502413389517e-06,
                3.1201907631845964e-05,
                2.5612812945260317e-06,
                1.0677029972920738e-06,
                8.315281267513512e-07,
                3.2887490652451393e-06
            ],
            [
                6.962256249517824e-06,
                1.0129988563343644e-05,
                7.889264465067689e-06,
                4.785092783149804e-06,
                8.939697367037201e-06,
                3.535623804803683e-05,
                2.7535704220525098e-05,
                1.147876948662936e-05,
                1.1478764007009336e-05,
                1.8925155003330605e-05
            ],
            [
                3.726639727994339e-06,
                1.9947306725868575e-06,
                6.475947981860793e-07,
                1.7603430033607189e-06,
                2.9023126769762986e-06,
                3.726639728224814e-06,
                5.42221767672807e-06,
                1.5534981249397663e-06,
                4.785096205077381e-06,
                1.994729008105057e-06
            ],
            [
                6.9622562478334885e-06,
                1.5534979396815448e-06,
                1.1478769478987456e-05,
                7.889264463890957e-06,
                4.222833947282995e-06,
                6.144174600985344e-06,
                3.726638394957837e-06,
                5.422221554758815e-06,
                8.93969629982328e-06,
                1.1478765372362364e-05
            ],
            [
                2.561282515662579e-06,
                2.9023123307122503e-06,
                4.4508526415598164e-07,
                6.962253756232077e-06,
                3.7266406165319545e-06,
                1.3007131562514014e-05,
                4.222832940715735e-06,
                1.4738981964307261e-05,
                7.889264465397747e-06,
                4.785093353626844e-06
            ],
            [
                4.785095065093186e-06,
                4.5397890187331725e-05,
                6.144173135896795e-06,
                6.144177529855884e-06,
                6.144176796601534e-06,
                1.473897669838221e-05,
                6.144173868781898e-06,
                3.726637950973972e-06,
                7.889259763857458e-06,
                4.222831934156396e-06
            ],
            [
                7.889263524788109e-06,
                6.962258737814774e-06,
                1.8925145971093502e-05,
                3.7266397280485686e-06,
                4.785092783210732e-06,
                1.2098652508056196e-06,
                6.144174601309452e-06,
                3.2887494571676872e-06,
                4.785095064523075e-06,
                1.01299933920846e-05
            ],
            [
                0.9998911030779519,
                0.9998766054400665,
                0.9999938558275957,
                0.9997694933124477,
                0.9999810748585306,
                0.9998601779594948,
                0.9999599363126035,
                0.9999785550566994,
                0.999769493257899,
                0.9999417087275825
            ],
            [
                7.3382115538308e-07,
                1.5534973841592143e-06,
                5.043475885576967e-07,
                8.315280276338815e-07,
                1.3709576971160984e-06,
                2.9023109469023766e-06,
                1.7603440526133836e-06,
                2.5612819052654485e-06,
                9.422444815323792e-07,
                1.3709568799243436e-06
            ],
            [
                1.0129988556912918e-05,
                5.4222183221120994e-06,
                1.473898724181597e-05,
                7.889261641904523e-06,
                0.00020342689969552968,
                6.962255419279419e-06,
                3.2887494569044713e-06,
                5.1442207158762935e-05,
                1.012999097799944e-05,
                1.1478765379920747e-05
            ],
            [
                1.3709576971160984e-06,
                1.994730434798734e-06,
                2.2603251060985603e-06,
                8.315278293951957e-07,
                4.785093353013212e-06,
                1.553498495308628e-06,
                5.422217030209884e-06,
                6.14417753110761e-06,
                1.3709567164962755e-06,
                1.0677024880528344e-06
            ],
            [
                6.962257079173776e-06,
                8.93969310367852e-06,
                1.7603425835461557e-06,
                7.889262584666493e-06,
                4.222833444168322e-06,
                3.7266383950934104e-06,
                4.222831933864508e-06,
                1.4738981970956057e-05,
                7.889265405677441e-06,
                7.889260704308795e-06
            ],
            [
                8.939696303010449e-06,
                1.9947304348332037e-06,
                1.0677031245429291e-06,
                1.994729721396435e-06,
                2.2603248367173307e-06,
                2.561281294369958e-06,
                4.2228319339950885e-06,
                2.561282515914161e-06,
                8.939698433974813e-06,
                1.300713156215912e-05
            ],
            [
                1.0677032518578904e-06,
                8.315277302444853e-07,
                1.7603434230729168e-06,
                1.7603434231097403e-06,
                1.2098656834922064e-06,
                1.0677033790883835e-06,
                7.338212429367364e-07,
                6.475947981754775e-07,
                1.7603430034311638e-06,
                1.3709575336654889e-06
            ],
            [
                3.288748281220719e-06,
                2.144494074076854e-05,
                4.7850950649408664e-06,
                7.889262584809997e-06,
                2.9023130228444433e-06,
                3.1201915058697335e-05,
                1.8925152747938785e-05,
                4.5397863120399e-05,
                7.889265406904397e-06,
                1.300713466316634e-05
            ],
            [
                6.144172403335888e-06,
                3.726638395493353e-06,
                4.222832939548183e-06,
                6.9622595675850006e-06,
                7.889264466344872e-06,
                1.300713001414004e-05,
                1.067703251784089e-06,
                3.2887498485279564e-06,
                6.962257907880012e-06,
                1.1478764016112805e-05
            ],
            [
                3.726640616477725e-06,
                4.7850933534310035e-06,
                1.0677031245710902e-06,
                2.5612828207295832e-06,
                2.5612819051722694e-06,
                8.939695235487695e-06,
                1.5534977545102382e-06,
                3.2887478886163427e-06,
                8.315277302649045e-07,
                1.3007131561804229e-05
            ],
            [
                5.422217030495909e-06,
                2.902312677060767e-06,
                3.288750241410738e-06,
                8.315281267248819e-07,
                7.8892625849535e-06,
                3.2887486729876365e-06,
                8.939693105076969e-06,
                5.422221555069497e-06,
                5.422217030362759e-06,
                1.2098658276862581e-06
            ],
            [
                1.6701429804288556e-05,
                2.9023112930949896e-06,
                6.1441753337365085e-06,
                6.144176797115634e-06,
                6.144173869312763e-06,
                5.422218323093458e-06,
                4.222831934286977e-06,
                1.7603425836870455e-06,
                4.78509563546605e-06,
                1.3709572067680694e-06
            ],
            [
                2.7535694356133476e-05,
                2.1444958628814052e-05,
                4.539787944042276e-05,
                0.00010889689563466869,
                5.829124465207388e-05,
                6.962257907702715e-06,
                0.00012339454526145543,
                4.006369208491967e-05,
                4.539786316895279e-05,
                0.0001088968960910006
            ],
            [
                1.3709567164663505e-06,
                2.561282821239737e-06,
                2.5612812945889277e-06,
                1.7603434231385591e-06,
                8.939696302051047e-06,
                1.760343632854606e-06,
                3.2887494572514376e-06,
                4.7850944942634305e-06,
                1.5534983100595462e-06,
                1.209865683500459e-06
            ],
            [
                6.144177530146464e-06,
                8.93969417150998e-06,
                2.902313368860448e-06,
                3.7266406155693803e-06,
                2.561283431124603e-06,
                8.939696302051047e-06,
                1.8925157236484784e-05,
                7.88926164421493e-06,
                1.3709567164326847e-06,
                5.422220908703723e-06
            ],
            [
                7.889263524615903e-06,
                3.726640616477725e-06,
                1.0677033789602024e-06,
                2.561282515662579e-06,
                8.31528424146183e-07,
                7.338211554398095e-07,
                1.4738983727578497e-05,
                4.78509563466093e-06,
                2.144495349826041e-05,
                4.785093353013212e-06
            ],
            [
                0.9995694430191672,
                0.9999038976196813,
                0.9996646500138839,
                0.9984988180657358,
                0.9993736659125737,
                0.9997040429711238,
                0.9994472214713208,
                0.9986749776222232,
                0.9995694429151432,
                0.9997694933412077
            ],
            [
                1.1478765382927399e-05,
                5.422220908762902e-06,
                2.561281294281438e-06,
                3.1201918760886355e-05,
                1.3709576970949014e-06,
                3.2887478891128633e-06,
                2.902311638596061e-06,
                4.222834450420771e-06,
                1.7603432127148856e-06,
                4.7850933535006355e-06
            ],
            [
                4.222833443461647e-06,
                1.4738983725406915e-05,
                1.0129990978644356e-05,
                2.9023112930949896e-06,
                4.222833947774596e-06,
                7.88925976080083e-06,
                3.2887482809455384e-06,
                3.2887482809933958e-06,
                2.260324297702111e-06,
                1.994729721436347e-06
            ],
            [
                6.144173136556186e-06,
                4.785093353013212e-06,
                1.7603430033158905e-06,
                6.144174600180663e-06,
                6.144177531381426e-06,
                1.994730434778778e-06,
                1.3709567164663505e-06,
                1.553498310118888e-06,
                9.422450431654909e-07,
                6.96225956921868e-06
            ],
            [
                2.7535681231364308e-05,
                1.0129992185760567e-05,
                1.3007125360146898e-05,
                4.222834450666572e-06,
                1.1478766754941153e-05,
                1.1478769490387674e-05,
                6.1441775296994185e-06,
                4.7850944942634305e-06,
                6.962253757840428e-06,
                3.288748672879957e-06
            ],
            [
                6.144175333401224e-06,
                3.7266379512518984e-06,
                4.539787939583253e-05,
                1.4738987236641703e-05,
                4.2228344508893285e-06,
                6.962254587420098e-06,
                4.539786853134004e-05,
                1.8925148220012804e-05,
                2.4300252300909177e-05,
                5.829125851250855e-05
            ],
            [
                1.6701423833436905e-05,
                3.7266388397382506e-06,
                3.5356250701614645e-05,
                5.422217675874929e-06,
                7.889262584666493e-06,
                8.939699500489763e-06,
                1.0129990978220553e-05,
                2.9023112929973233e-06,
                3.7266388396128453e-06,
                3.7266379512518984e-06
            ],
            [
                1.4738978454950406e-05,
                3.5356254910985954e-05,
                2.561282515886208e-06,
                1.1478765387416494e-05,
                5.422219615967477e-06,
                7.889261644982674e-06,
                1.5534979397140412e-06,
                6.962258739068529e-06,
                3.535624646549072e-05,
                1.1478764018576587e-05
            ],
            [
                4.222835457733473e-06,
                2.902311292920774e-06,
                1.370956879949281e-06,
                3.0590211750425905e-07,
                1.3709570433786157e-06,
                3.288747889038086e-06,
                1.0677028700130727e-06,
                1.9947301969707264e-06,
                4.7850933535659155e-06,
                9.42244256886598e-07
            ],
            [
                4.222833947728508e-06,
                2.26032537546132e-06,
                6.962257078819179e-06,
                0.9996646498124666,
                6.144174600471243e-06,
                4.785094494019719e-06,
                1.8925141469400216e-05,
                4.7850956351657615e-06,
                2.5612819053166966e-06,
                4.785094494576774e-06
            ],
            [
                0.9998911030519014,
                0.9999151889788864,
                0.999841563839848,
                0.9998911031038012,
                0.9998601778760521,
                0.9978172840384224,
                0.9999546021476239,
                0.9998766053811251,
                0.9989677689328742,
                0.9994472213893174
            ],
            [
                9.422444815006715e-07,
                1.7603425835173373e-06,
                2.902313368897403e-06,
                2.260324567054496e-06,
                3.726638395320497e-06,
                2.2603242978007868e-06,
                1.3709567164139816e-06,
                9.422445938111562e-07,
                1.0677031245710902e-06,
                2.4300243623139103e-05
            ],
            [
                6.9622562489985925e-06,
                6.962257906968191e-06,
                2.902310946332217e-06,
                6.1441775290176756e-06,
                7.889266345957247e-06,
                1.7603430031766016e-06,
                1.5534979396024226e-06,
                1.4738980209829803e-05,
                4.222832939432965e-06,
                2.260323758806253e-06
            ],
            [
                0.9996646497711177,
                0.9998204719488529,
                0.9999151889182053,
                0.999738809566689,
                0.9999151889688264,
                0.9999646437408591,
                0.9999485577618268,
                0.9998204719912641,
                0.9997694931751202,
                0.9968273169498629
            ],
            [
                7.889262584666493e-06,
                5.422217675874929e-06,
                8.939695237162584e-06,
                2.902311984873224e-06,
                1.1478765386894505e-05,
                1.147877086020957e-05,
                1.2098653949192932e-06,
                6.962259567914269e-06,
                2.902313368963394e-06,
                3.726640616748873e-06
            ],
            [
                0.99951214282627,
                0.9991959140476753,
                0.9968273170419073,
                0.9998415637645907,
                0.9989677688043076,
                0.9997694933398595,
                0.9984988174494078,
                0.9993736658227624,
                0.9998766054105698,
                0.9998415637836636
            ],
            [
                6.962259569117366e-06,
                5.422220908634683e-06,
                2.902311985079115e-06,
                1.5534984953199313e-06,
                6.9622562478334885e-06,
                7.889259763010786e-06,
                4.7850950648799385e-06,
                1.1478770861650256e-05,
                4.7850950649408664e-06,
                6.9622545877746946e-06
            ],
            [
                0.9995121428247089,
                0.9995694429619885,
                0.9971990729684977,
                0.9947798739993402,
                0.9996200155614821,
                0.9980732651535474,
                0.999512142880567,
                0.9996646498899543,
                0.9971990726251314,
                0.9989677689230306
            ],
            [
                0.9997040429717438,
                0.9996646500107031,
                0.9994472213207883,
                0.8175744695262775,
                0.9875683497185115,
                0.9997388095975285,
                0.9994472214524439,
                0.9989677690494364,
                0.9994472212557325,
                0.9997040429712185
            ],
            [
                6.1441760661636525e-06,
                3.726638395320497e-06,
                1.0129993393540266e-05,
                3.2887498492936755e-06,
                4.7850933535006355e-06,
                1.0129995808639442e-05,
                5.71500719517695e-07,
                3.7266397280960194e-06,
                2.4300232032009452e-05,
                3.726637950973972e-06
            ],
            [
                1.300713466420736e-05,
                1.9947290080343035e-06,
                6.1441738684354385e-06,
                1.8925141465200488e-05,
                2.561282821106957e-06,
                5.422221555069497e-06,
                1.4738987232298539e-05,
                1.5534977545102382e-06,
                3.2887482812506295e-06,
                4.785093923768848e-06
            ],
            [
                0.9992903296338813,
                0.9940889322765782,
                0.9997388097858935,
                0.9933071506050118,
                0.9998204720773533,
                0.9947798733803012,
                0.9993736657594027,
                0.9971990726895127,
                0.9996200154256959,
                0.9940889322601605
            ],
            [
                1.2098656834481918e-06,
                6.1441760661636525e-06,
                7.338209805040511e-07,
                9.422448185264317e-07,
                4.785095634565186e-06,
                2.5612831265630198e-06,
                1.5534981248712412e-06,
                2.260324567087388e-06,
                1.7603434230729168e-06,
                5.422220261544064e-06
            ],
            [
                7.484625383027781e-05,
                2.902312676941983e-06,
                1.6701419853518415e-05,
                6.9622579095833456e-06,
                6.962258738283349e-06,
                6.962259563418482e-06,
                2.7535691093547457e-05,
                8.939698434332555e-06,
                2.430023783309869e-05,
                1.8925145981833788e-05
            ],
            [
                2.1444945853999886e-05,
                5.422217676866151e-06,
                6.144174601309452e-06,
                2.1444953515423628e-05,
                7.889262585082652e-06,
                1.0129987355785634e-05,
                4.2228319341064674e-06,
                4.785095065045315e-06,
                3.12019225022362e-05,
                6.144173136556186e-06
            ],
            [
                1.7603430033991435e-06,
                1.994729721469003e-06,
                6.962255418658875e-06,
                3.726641060773727e-06,
                6.144175334015912e-06,
                6.1441731363550164e-06,
                6.9622562484666964e-06,
                5.422217676299034e-06,
                6.962257909007124e-06,
                5.422219615750493e-06
            ],
            [
                1.8925141463066202e-05,
                7.889265406151004e-06,
                1.3007134662054344e-05,
                1.670142779591868e-05,
                2.561282515820982e-06,
                7.889260702342794e-06,
                3.2887498492936755e-06,
                4.0063706471413514e-05,
                3.7266388396128453e-06,
                1.670142980222277e-05
            ],
            [
                6.14417753110761e-06,
                1.209866116149238e-06,
                6.144176065940129e-06,
                1.3007130012673148e-05,
                6.144177530794679e-06,
                4.7850927830148924e-06,
                6.144176066264237e-06,
                5.422218968595919e-06,
                2.561281905293402e-06,
                1.7603425836870455e-06
            ],
            [
                0.00033535021173980174,
                3.535624215245212e-05,
                3.1201915053248934e-05,
                4.7850967754851966e-06,
                5.422221554670048e-06,
                4.785096775998733e-06,
                1.3007126894017035e-05,
                1.0129993394314164e-05,
                3.5356267533443565e-05,
                3.120190755988168e-05
            ],
            [
                1.0677024881683915e-06,
                5.422220261198862e-06,
                4.222833947674739e-06,
                1.3709572068079696e-06,
                1.209865971934245e-06,
                1.9947290080905435e-06,
                2.561281599914358e-06,
                1.9947292457750883e-06,
                2.5612828213352452e-06,
                3.726637951170554e-06
            ],
            [
                4.7850950646797465e-06,
                4.785094493932679e-06,
                5.422220262037209e-06,
                2.2603234888228504e-06,
                2.2603253753174176e-06,
                1.7603434229832599e-06,
                9.422447061876404e-07,
                3.726641060658489e-06,
                6.962257908196617e-06,
                1.2098656834195822e-06
            ],
            [
                0.00015843627113056323,
                1.1478770859332632e-05,
                2.1444958616409722e-05,
                7.889263522779056e-06,
                3.5356246444011064e-05,
                0.00012339461826445564,
                5.829129305079897e-05,
                1.6701423823533284e-05,
                2.430023491664161e-05,
                2.1444940727740105e-05
            ],
            [
                1.3007134658505415e-05,
                3.120192623110058e-05,
                3.535625065376772e-05,
                4.006369687905675e-05,
                4.785093923982095e-06,
                4.785093924103951e-06,
                3.288748672760313e-06,
                6.9622537576631295e-06,
                1.8925152747938785e-05,
                1.8925143716804326e-05
            ],
            [
                1.5534977545243671e-06,
                1.4738985481091229e-05,
                3.2887494572514376e-06,
                7.889263525663481e-06,
                2.5612819052654485e-06,
                1.1478764001538906e-05,
                7.889260703619978e-06,
                6.144174600985344e-06,
                3.288748280449018e-06,
                7.88926540454376e-06
            ],
            [
                0.9933071483544071,
                0.9993736658250942,
                0.9997040428662339,
                0.9995694430134556,
                0.9947798743886578,
                0.9998415637455751,
                0.9996646498900617,
                0.9998415638210192,
                0.9996646499700762,
                0.9991959139682193
            ],
            [
                4.22283545795623e-06,
                2.5612822098455215e-06,
                2.260324567054496e-06,
                6.144173868983067e-06,
                2.5612815995532906e-06,
                3.4663253846111126e-07,
                5.422219615750493e-06,
                2.2603242976404388e-06,
                3.2887490649221017e-06,
                3.7266392838544054e-06
            ],
            [
                3.2887490653647836e-06,
                6.144177531007026e-06,
                5.422220908116881e-06,
                5.4222196154940574e-06,
                1.670141985166528e-05,
                3.120190017071685e-05,
                1.0129994602057158e-05,
                4.785093353352668e-06,
                1.892515500450102e-05,
                6.9622562487453084e-06
            ],
            [
                2.2603251060985603e-06,
                2.56128159999123e-06,
                2.7535704156916166e-05,
                7.889265404959923e-06,
                1.3007123808153756e-05,
                4.22283545795623e-06,
                1.1478769492642663e-05,
                6.144172403067661e-06,
                4.22283394762097e-06,
                4.785092783210732e-06
            ],
            [
                6.144177531459659e-06,
                2.561281294644835e-06,
                2.7535697639856078e-05,
                1.14787681240737e-05,
                2.7535684521195802e-05,
                3.726639727994339e-06,
                1.0129995809431767e-05,
                5.829129305079897e-05,
                4.006367783499403e-05,
                3.120191508321514e-05
            ],
            [
                7.889260702744606e-06,
                7.889265402362503e-06,
                1.2098652507285942e-06,
                4.78509506425325e-06,
                7.889260699917581e-06,
                1.6701419849933667e-05,
                1.8925150482151187e-05,
                4.222834451065997e-06,
                6.144172403067661e-06,
                2.430024072091399e-05
            ],
            [
                0.9996646498510153,
                0.9998601779094202,
                0.9992903295355962,
                0.9995121428842284,
                0.9997388095978781,
                0.9999038975392628,
                0.9989677691831648,
                0.9978172837980599,
                0.9986749775373426,
                0.9995121428234033
            ],
            [
                2.1444945852673643e-05,
                4.5397857748103446e-05,
                2.7535681242383173e-05,
                3.7266388384265735e-06,
                2.4300252293748645e-05,
                1.3007125360478133e-05,
                2.4300240719941574e-05,
                1.0677033790621648e-06,
                6.144174599867732e-06,
                5.42221702886853e-06
            ],
            [
                0.9994472212561827,
                0.9991959141635154,
                0.9998415637644547,
                0.9995121427687655,
                0.99937366589851,
                0.999569442963003,
                0.9997388096606815,
                0.999088948981605,
                0.9989677690556786,
                0.9982992776974717
            ],
            [
                1.3007130007988564e-05,
                7.889261644875049e-06,
                6.1441767989541075e-06,
                6.144172403827636e-06,
                1.1478765377958073e-05,
                2.902312330891746e-06,
                1.8925155002710973e-05,
                1.4738978449883382e-05,
                1.3007126912258525e-05,
                6.96225956837018e-06
            ],
            [
                0.9924227592854065,
                0.9980732657342642,
                0.9999546021421996,
                0.9982992773045367,
                0.9992903294533685,
                0.997817283583052,
                0.9840936056349263,
                0.9986749775840192,
                0.9992903294598493,
                0.9999417087206625
            ],
            [
                2.1444958627955892e-05,
                6.144176065012512e-06,
                6.962257076628275e-06,
                2.5612831262112703e-06,
                3.288748279234635e-06,
                2.5612825157045092e-06,
                1.2098661160436029e-06,
                1.994729483535857e-06,
                6.144175333837093e-06,
                4.785092782858221e-06
            ],
            [
                1.7603427935678977e-06,
                8.9396941718352e-06,
                3.2887482811220126e-06,
                1.7603427935518875e-06,
                1.209865539274514e-06,
                2.2603242977802297e-06,
                1.5534981247680996e-06,
                1.5534971989809095e-06,
                1.7603440527046419e-06,
                3.2887482800422294e-06
            ],
            [
                4.785092783210732e-06,
                4.78509449306228e-06,
                1.3709572067181944e-06,
                1.6701419848961534e-05,
                3.7266406162947e-06,
                2.902313022802209e-06,
                2.561281294558644e-06,
                6.475948753930064e-07,
                2.5612815999679353e-06,
                2.561283431669698e-06
            ],
            [
                1.209865827698362e-06,
                7.33821330394297e-07,
                1.0677027426418351e-06,
                9.422445938728576e-07,
                1.76034258364702e-06,
                1.7603434231385591e-06,
                1.5534971989427613e-06,
                1.2098656834041774e-06,
                5.71500719517695e-07,
                1.9947297214182054e-06
            ],
            [
                4.785096205930373e-06,
                1.994730434816876e-06,
                1.5534983100228109e-06,
                9.422442568300383e-07,
                5.715002426254813e-07,
                2.561282821209454e-06,
                4.785096775920397e-06,
                4.222833443968609e-06,
                1.5534973841154145e-06,
                4.222834450236421e-06
            ],
            [
                0.9996646500107031,
                0.9995694429607108,
                0.9971990733833987,
                0.9988304900133154,
                0.9999417087275438,
                0.9998601778760724,
                0.9968273167193841,
                0.9975273764384985,
                0.9998601778759504,
                0.9986749773936152
            ],
            [
                1.1478766749115769e-05,
                6.962256248314727e-06,
                2.260324836250676e-06,
                9.422450431654909e-07,
                3.7266388382164344e-06,
                3.288748672760313e-06,
                6.144176798691468e-06,
                6.962259565039499e-06,
                4.785092782936557e-06,
                5.422221554038823e-06
            ],
            [
                3.535624225110421e-05,
                4.539786852010991e-05,
                0.0001398220563124451,
                0.00010889686984082694,
                7.484622706027895e-05,
                3.120192622145237e-05,
                2.144494840531103e-05,
                2.4300237825230942e-05,
                7.48462092936653e-05,
                2.7535700939406174e-05
            ],
            [
                0.9999810748495086,
                0.7772998663336158,
                0.9999038975510453,
                0.9999038976081353,
                0.9875683494783986,
                0.9995121427660125,
                0.9998415637835808,
                0.9997965731025479,
                0.9986749775123867,
                0.9999339478396271
            ],
            [
                3.7266397281434697e-06,
                1.5534979397267575e-06,
                1.99472924590571e-06,
                4.222834450420771e-06,
                2.5612812946890944e-06,
                2.2603251060142746e-06,
                6.144174601097106e-06,
                4.7850962047640385e-06,
                1.553498310118888e-06,
                2.9023116388547446e-06
            ],
            [
                1.0129992185299915e-05,
                1.3007125361755747e-05,
                0.994088929953472,
                1.9947290080125335e-06,
                5.422217029943586e-06,
                2.561283431888668e-06,
                2.753570420970657e-05,
                5.422220908116881e-06,
                1.7603430033991435e-06,
                7.889264465067689e-06
            ],
            [
                1.670142780910326e-05,
                6.96225541916544e-06,
                6.144175333401224e-06,
                6.962253758916883e-06,
                1.4738988989189704e-05,
                5.4222202621161125e-06,
                1.670141785596473e-05,
                6.962258739271155e-06,
                1.0129995806612563e-05,
                2.9023109471452223e-06
            ],
            [
                6.962255415872755e-06,
                4.785096205512581e-06,
                4.785095632554564e-06,
                3.7266383950256237e-06,
                1.067702488159652e-06,
                1.3709578605243332e-06,
                6.1441775309064404e-06,
                2.9023126766305067e-06,
                1.370957370083977e-06,
                2.260324836250676e-06
            ],
            [
                0.9933071497227253,
                0.9975273769277843,
                0.9902915225067305,
                0.9991959142454031,
                0.9997040427955382,
                0.9980732653122708,
                0.9992903295368345,
                0.974042641483562,
                0.9940889311629102,
                0.9988304897417439
            ],
            [
                1.5534973840984598e-06,
                6.9622554185195676e-06,
                3.2887486732358968e-06,
                8.315281267706361e-07,
                6.475947209826952e-07,
                2.902311984783477e-06,
                7.338210679622478e-07,
                8.315280276096808e-07,
                6.96225873895455e-06,
                1.2098655392574583e-06
            ],
            [
                1.6701423831188846e-05,
                7.889263524615903e-06,
                3.7266388393349185e-06,
                6.9622537584863015e-06,
                2.1444940737257882e-05,
                4.2228344508893285e-06,
                5.422220261849814e-06,
                4.785092782936557e-06,
                1.370957370196196e-06,
                4.785093923982095e-06
            ],
            [
                0.9991959140520712,
                0.9997694933674324,
                0.9997040428300853,
                0.9993736657476342,
                0.9859363755007278,
                0.9997388097217372,
                0.9994472213197593,
                0.9978172840156032,
                0.9997040429360429,
                0.9997388096596329
            ],
            [
                0.9999646437493199,
                0.9999599363079912,
                0.9999869928684425,
                0.9999885212291464,
                0.9999852610198116,
                0.9997040429090992,
                0.9989677690848492,
                0.9999546021314468,
                0.9999599363126939,
                3.7266392839425286e-06
            ],
            [
                2.9023109468548636e-06,
                7.338208930078229e-07,
                1.9947297213492663e-06,
                4.222835457449267e-06,
                2.2603242976733308e-06,
                4.222832940715735e-06,
                2.7535691056684346e-05,
                2.902311292831027e-06,
                6.14417460073947e-06,
                6.9622570786798724e-06
            ],
            [
                0.999933947871222,
                0.99994170874838,
                0.9999724642990556,
                0.9971990727421882,
                0.999841563802165,
                0.9964063979879929,
                0.9998601779093368,
                0.9999485578047611,
                0.9998415637454438,
                0.9990889489974996
            ],
            [
                0.9980732657949328,
                0.9947798732908305,
                0.9993736658973441,
                0.9991959142466659,
                0.998674977386683,
                0.9998204719911963,
                0.9940889320412577,
                0.9982992772877362,
                0.9994472212555717,
                0.9996646498109543
            ],
            [
                3.2887490648622804e-06,
                1.892514146884943e-05,
                6.144174600180663e-06,
                5.829129322807287e-05,
                9.61024605302213e-05,
                1.3007123810306773e-05,
                2.4300246497960055e-05,
                5.829127204384482e-05,
                5.8291286228722664e-05,
                5.144219518617526e-05
            ],
            [
                1.14787681240737e-05,
                4.785096205260165e-06,
                4.222833444283541e-06,
                6.475950297421001e-07,
                6.144173136131494e-06,
                1.3007133113703658e-05,
                8.93969417150998e-06,
                1.5534975688557435e-06,
                1.5534981248881956e-06,
                1.0129993393540266e-05
            ]
        ]
    },
    {
        "q_id": "7802_mmlu_math",
        "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": [
            [
                0.002800927256511175,
                0.022977372000789975,
                0.9999957771680658,
                0.0031726821466306087,
                0.0004305570358697047,
                0.004070138603064188,
                0.9999980052700408,
                0.0008040859055117214,
                0.00857748358421866,
                0.0010322311320693372
            ],
            [
                0.0001584362920800941,
                0.0006263340768602412,
                0.004070138516234965,
                0.020332353453964554,
                0.0002034270212542617,
                0.0017007225877421481,
                0.0017007225835914258,
                0.0004305571371005144,
                0.0009110513935064438,
                0.9999977396757029
            ],
            [
                1.2098662604192665e-06,
                6.144172404028807e-06,
                2.5612812947077304e-06,
                9.422443692489024e-07,
                1.2098662604247682e-06,
                2.902311985146426e-06,
                2.5612834320214477e-06,
                1.3709570433786157e-06,
                1.5534983100920427e-06,
                1.5534979397394734e-06
            ],
            [
                0.000379984570070101,
                0.000911051129338941,
                0.000709670522896136,
                0.00020342689946467704,
                0.0003799844761153313,
                0.00280092749452651,
                0.0011695102997328853,
                0.0010322310930552074,
                0.0003353499817841547,
                4.539786862564012e-05
            ],
            [
                0.002472623618929369,
                0.0007096704360452392,
                0.00023050677027072224,
                0.00033535010608448483,
                0.0021827167871265713,
                0.0009110511955132641,
                0.00029595716409372186,
                0.0011695105135086981,
                0.0009110512618995194,
                0.0002034269472748494
            ],
            [
                0.9999980052693276,
                0.0059110697099648965,
                0.0008040861103950187,
                0.00048785717302047643,
                0.0013250222756425762,
                0.0009110513420080797,
                0.00023050676917076054,
                0.0015011825509411,
                0.0031726823469188955,
                0.00048785711358611953
            ],
            [
                0.0019267348934650951,
                0.999972464312199,
                0.9997694932351218,
                0.00043055702468446577,
                0.000626334020277299,
                0.9999852610127639,
                0.0019267346534772277,
                0.0003353502231649008,
                0.004609572284067848,
                NaN
            ],
            [
                0.0007096705436594463,
                0.001700722751003898,
                0.014063626152209092,
                0.00015843619804005064,
                0.00015843625426351888,
                0.00026119039998644155,
                0.020332355420367123,
                0.004609572506274765,
                0.0019267347869033145,
                0.001325022146395886
            ],
            [
                0.0035936021137177687,
                0.996827316459451,
                0.2942149783515162,
                5.8291272448012225e-05,
                0.985936374235198,
                0.3486451217982255,
                0.01798620996209156,
                0.00043055707586351217,
                0.00033535002913340374,
                0.9971990736474267
            ],
            [
                0.0003799845261272566,
                0.0015011819543315234,
                0.00029595706130497397,
                0.00026119040133918027,
                0.005220125700812761,
                0.0005527787221427441,
                0.0006263342142187248,
                0.00048785716847916905,
                0.00013982209045161867,
                0.004609571465748237
            ],
            [
                0.9999546021313795,
                0.00020342694831072675,
                0.00026119040013843466,
                0.0006263340734718228,
                0.0015011823773152994,
                0.0007096702620545249,
                0.0011695103235310814,
                8.481105123878872e-05,
                0.0024726233467211125,
                0.00023050674165159843
            ],
            [
                0.0013250222497624277,
                0.0052201256282691216,
                0.00037998443528995137,
                0.003172682591388439,
                9.610246072738731e-05,
                0.0006263343010059837,
                0.005911068664703822,
                0.0013250226613800917,
                8.93970050952194e-06,
                0.0011695101663270065
            ],
            [
                0.002182715953971139,
                0.9999952149037947,
                0.00048785716180912395,
                0.0005527785959862567,
                0.0024726229263489275,
                0.00010889690897128673,
                0.0011695104933822204,
                0.000379984478525278,
                0.9999724643187635,
                0.999989870009023
            ],
            [
                0.005911068700275531,
                0.000552778662778765,
                0.001926734468561223,
                0.0008040861216189398,
                0.00317268309358196,
                0.0017007224881248166,
                0.001700722078191653,
                0.9999991684721706,
                0.004609571720004184,
                0.9999852610162737
            ],
            [
                0.0013250225287442959,
                0.0013250226043821291,
                0.0011695104459218115,
                0.0006263342434028521,
                0.0005527785326025212,
                0.00037998443844056953,
                0.0017007222481735702,
                0.00020342694765960385,
                0.0009110510747676453,
                0.0005527786013245117
            ],
            [
                0.006692851320539922,
                0.999994577781032,
                0.0017007221333369478,
                0.0003799845734970903,
                0.001325022602071401,
                0.0007096702362551936,
                0.003172682387418367,
                0.00043055703605758664,
                0.0010322312152594715,
                0.0007096703521251574
            ],
            [
                0.0009110512729197442,
                0.0019267343637904201,
                0.008577484772201294,
                0.000911051208970653,
                0.00043055702501012774,
                0.9999962733602719,
                0.005911069362456614,
                0.0006263340910697381,
                0.007577241421935267,
                0.00017952805118096838
            ],
            [
                0.00048785716271738537,
                0.0001398221402841261,
                0.0006263342221979056,
                0.00023050668607671747,
                8.481103099344347e-05,
                6.60521288918597e-05,
                0.9992903296290516,
                9.610244912256048e-05,
                0.9998766054695488,
                0.9999599363221586
            ],
            [
                0.0006263342850476204,
                0.9999938558246658,
                0.9999687980849524,
                0.0008040858381214495,
                0.0005527785833480987,
                0.0035936023613248724,
                0.002472623296184562,
                0.0031726824529538762,
                0.0015011823549795197,
                0.9999921107355341
            ],
            [
                0.0009110510411771602,
                0.00020342699589597716,
                0.0040701382425341655,
                0.003172682904338937,
                0.9999869928684378,
                0.0059110684676912835,
                0.0031726830545551876,
                0.00757724072159685,
                0.9999984465020603,
                0.0003353500209377781
            ],
            [
                0.0001584362914162005,
                0.0004305570343541236,
                0.0008040857869590955,
                0.002472623117583806,
                0.0009110513410544062,
                0.0035936027089752787,
                0.000203427044428327,
                0.00029595702517349335,
                0.0009110510747676453,
                0.0007096704280371249
            ],
            [
                0.00029595706149441455,
                0.0006263341694041499,
                0.0024726225886729618,
                0.00037998456406734225,
                0.0002959571668836658,
                0.002472622594990029,
                0.0017007225410959365,
                0.0006263341583280279,
                0.0008040860278524377,
                0.0013250225136475396
            ],
            [
                0.00026119024631385,
                0.00037998447986290894,
                0.0009110512980331417,
                0.00029595706130497397,
                0.999995777164542,
                0.00020342692393505483,
                0.0015011822361461961,
                0.0019267346234787463,
                0.000804085802298448,
                0.0017007224015526167
            ],
            [
                0.0017007223643937743,
                0.0004305570249099241,
                0.007577241709074037,
                0.001501182286750694,
                0.9999962733602719,
                0.9999977396746245,
                0.000911051033123921,
                0.00048785716884815027,
                0.00023050679691796684,
                0.000911051258826572
            ],
            [
                0.00026119027604368705,
                0.00048785711381318486,
                0.0017007227729434323,
                0.0046095717285506025,
                0.0013250226924978994,
                0.00023050663201764992,
                0.0003353501492091,
                0.00013982212345967678,
                0.0003353502244430289,
                0.00029595713312879083
            ],
            [
                0.00015843629194178295,
                0.0001398220234122257,
                3.1201903930339314e-05,
                3.120190764716959e-05,
                0.00029595705964306356,
                0.0003353500675747937,
                0.00012339461875639704,
                0.00013982207349493977,
                6.605216040319643e-05,
                0.00043055708418042097
            ],
            [
                0.00037998457290013086,
                0.0011695104646883914,
                0.00026119036977781217,
                0.9999938558232011,
                0.0010322311778059037,
                0.00037998457260165114,
                0.00023050663172924555,
                0.00012339457458581518,
                0.9999810748585323,
                0.00280092638053688
            ],
            [
                0.0007096704253539936,
                0.00037998443829685713,
                0.0017007221908540847,
                0.0009110510078515854,
                0.0015011825382027241,
                0.0009110511084111137,
                0.0006263341568706434,
                0.008577485754267061,
                0.0005527786699821945,
                0.00017952796506569833
            ],
            [
                0.0019267342885703597,
                0.000626334093875203,
                0.000552778705645603,
                0.0011695102612478037,
                0.0002034269243375671,
                0.0007096703617431496,
                0.010986941092358602,
                0.0003799844364396507,
                0.000804085789110346,
                0.0013250223640664217
            ],
            [
                0.001032231274440913,
                0.0007096703832494759,
                0.0002305066850974836,
                0.0013250223728471873,
                0.0019267343320009892,
                0.000295957167271158,
                0.00043055707784253567,
                0.00020342699674539676,
                0.00015843625362498245,
                0.0006263341547938705
            ],
            [
                0.0006263340711400079,
                0.00857748345750052,
                9.610242636527403e-05,
                0.9999687980886797,
                0.001032230985976434,
                0.0008040859150052856,
                0.9999945777803841,
                0.001700722028580655,
                0.0002611902761956801,
                0.0005527785348535924
            ],
            [
                0.004070137313839177,
                0.001032231107100294,
                0.0002959570264220788,
                0.0017007221309651068,
                0.0028009272252960513,
                0.0002611903388092208,
                0.00669285015963647,
                0.004070137551675678,
                0.00023050662727574473,
                0.9999930377404312
            ],
            [
                1.7603440526806268e-06,
                2.2603242978213447e-06,
                1.1478765388314311e-05,
                1.994729245822257e-06,
                3.7266388397721442e-06,
                2.2603242978377903e-06,
                2.561283432005142e-06,
                5.422220261948442e-06,
                1.1478768124783601e-05,
                2.561281905376098e-06
            ],
            [
                0.0013250225162663646,
                0.0035936032600470957,
                0.0015011822570859881,
                0.003172682731295717,
                0.0008040857988377404,
                0.0007096704229185362,
                0.002182716769885372,
                0.00017952800821866645,
                0.00010889696098363736,
                0.0019267345813913255
            ],
            [
                0.0004878571720554486,
                0.003172682542789071,
                0.0005527786526167845,
                0.0004305569794550197,
                0.00043055701864719233,
                0.0008040861215721733,
                0.00043055708019732304,
                0.001169510332642391,
                0.004609571833244232,
                0.0015011821598904557
            ],
            [
                0.9999724642957716,
                0.0002959572366236608,
                0.0008040859065405806,
                0.0035936033084013595,
                0.9998415637079199,
                0.0005527786021284658,
                0.00013982205683325005,
                0.00026119030663228837,
                0.0007096704212673785,
                0.0015011823966846092
            ],
            [
                0.0004878570516540514,
                0.0006263342144373325,
                0.0008040858135691311,
                0.0019267343991617588,
                0.9999967112509348,
                0.9999785550439309,
                0.0035936026389449785,
                0.0004305569807451424,
                0.004070137893329724,
                0.0011695100145625392
            ],
            [
                0.00033535018777734076,
                7.484621820719341e-05,
                0.0008040858847942396,
                0.003172683335842498,
                0.00080408609557009,
                0.999964643736673,
                0.00023050668672059728,
                0.9999646437620174,
                0.009708476320303113,
                0.00037998447844789435
            ],
            [
                0.00026119033798085854,
                8.481104126512805e-05,
                0.0007096705200066098,
                0.0011695100044993047,
                0.0003353501437843744,
                0.0021827165143099674,
                0.0002611904291083236,
                0.00037998443311215577,
                0.999981074842739,
                0.00026119020984312656
            ],
            [
                0.00017952790156782624,
                0.00033535010959689676,
                0.00037998448193015685,
                0.00048785711381318486,
                0.001501182420416376,
                0.0006263341648133887,
                0.00013982212394793165,
                4.006370650653807e-05,
                0.00033535022830668334,
                0.00033535018765050364
            ],
            [
                0.0003799845701474846,
                0.00026119039983444844,
                0.00037998457130823904,
                0.0005527787146498905,
                0.0017007224748820371,
                0.0028009269762253835,
                0.0007096705194699835,
                0.0009110510713768076,
                0.0005527785777525786,
                0.0019267343973708051
            ],
            [
                0.0005527786693711892,
                0.02297736915735049,
                0.00017952796487763384,
                0.001700722552955143,
                0.00048785722479138344,
                0.0013250224930050362,
                0.00407013841430501,
                0.9999339478711234,
                0.9999980052695652,
                0.0031726826716510347
            ],
            [
                6.605214462205646e-05,
                0.00043055713170203836,
                0.000709670418254016,
                0.022977370411809042,
                0.0001795279440024774,
                0.0005527786590162596,
                0.9999921107345938,
                0.00048785722198144924,
                0.0002611903690254463,
                0.000139822139856903
            ],
            [
                0.00970847745745379,
                0.0052201258072101,
                0.0010322310390356454,
                0.00037998448055936144,
                0.001325022247143603,
                0.00013982210704821174,
                0.0046095730895679725,
                0.0008040858203034811,
                0.005220125427565059,
                0.003593602864042378
            ],
            [
                0.0003353502658699926,
                0.0005527785403847958,
                0.00043055698229829963,
                0.005911069105245771,
                0.0013250226854116657,
                0.000626334085604547,
                0.0021827160386558215,
                0.00026119027449335807,
                0.004070137215684434,
                0.0004878570537544056
            ],
            [
                0.9999921107383568,
                0.014063628282948357,
                0.00012339458908910424,
                0.0009110513895857862,
                0.00017952796543137923,
                8.48110512764275e-05,
                0.0009110512782179293,
                0.00037998443374227933,
                0.00012339460383297942,
                0.0006263340676787204
            ],
            [
                0.0004878570563372735,
                0.008577485469151182,
                0.0008040861186726605,
                0.005220125674213427,
                0.0035936033017318052,
                0.0006263342264243209,
                0.00460957240585433,
                0.009708476705322619,
                0.0007096702744382043,
                0.00522012612640213
            ],
            [
                0.0009110512641247571,
                0.0028009266575710376,
                0.00012339460388863702,
                0.0004305569843023736,
                0.0019267344305034522,
                0.005220124842379764,
                0.0003799844352236226,
                0.00023050679489242738,
                0.00013982202288328333,
                0.0003353502652553203
            ],
            [
                0.00020342701912923257,
                0.00023050679605275296,
                0.0015011824111679666,
                0.0017007225529551426,
                0.999975699759268,
                0.0005527786037042157,
                0.00407013694009613,
                0.9999952149032248,
                0.0007096702826527116,
                0.00043055707826840145
            ],
            [
                0.000911051258826572,
                0.9999957771660523,
                0.00043055702871766494,
                0.0004305571281949077,
                0.0028009266120489905,
                0.0003799844383742407,
                0.0015011823270597953,
                5.8291244621538684e-05,
                0.00015843623477548052,
                0.00020342702037820512
            ],
            [
                0.0005527785890079353,
                0.00029595713181992836,
                0.0002959570266115192,
                0.0002034270457128155,
                0.0010322311541573375,
                0.0007096704133005432,
                0.0011695102351377842,
                7.484622715666203e-05,
                0.00048785710160842286,
                9.610239198289712e-05
            ],
            [
                0.0004305571341820806,
                0.0007096702708056582,
                0.0002959570266115192,
                0.0013250225047127247,
                0.0007096703742093884,
                0.00010889688312673828,
                0.0006263343039207533,
                0.001032231163520729,
                0.0009110510062091485,
                0.00010889693518502668
            ],
            [
                0.00020342689987606823,
                0.00048785705063225746,
                0.000379984477574565,
                0.00020342697316290525,
                0.02297736991002562,
                0.0015011822291662654,
                0.0002611903706517724,
                0.0006263342494874331,
                0.005911068577142693,
                0.0007096704363341918
            ],
            [
                7.48462628538078e-05,
                0.9999945777823231,
                0.00037998447986290894,
                0.006692852345230872,
                0.0002959570939834738,
                0.0013250221604142985,
                0.0015011822939051229,
                0.0006263340772974565,
                0.0013250225498489458,
                0.0005527787266448879
            ],
            [
                0.00048785705290291064,
                0.001926734614523976,
                0.0004305570850572035,
                0.000911051309000385,
                0.0002611902444747344,
                0.0002305067422082863,
                0.0004878570493550151,
                0.004070138080201287,
                0.0006263342345128058,
                0.0007096703444059965
            ],
            [
                1.5534979397677313e-06,
                2.2603245673155757e-06,
                8.939696304116203e-06,
                4.2228349547223175e-06,
                6.144173869446876e-06,
                0.2942149783515162,
                8.93969736929749e-06,
                6.144175334418252e-06,
                7.889263526093993e-06,
                2.9023126771227976e-06
            ],
            [
                0.000626334148272075,
                0.0035936031399951347,
                0.0019267350962906852,
                0.004070137949957469,
                0.0013250226532155187,
                0.005911069882350904,
                0.9999810748517598,
                0.0005527787211458407,
                0.004070137004274226,
                0.001700722239279167
            ],
            [
                0.001032231128227946,
                0.0024726229125662342,
                0.0004305570700266456,
                0.00017952800863658765,
                0.0035936021103829927,
                0.0001233945306055621,
                0.0001795280298591486,
                0.0004305571345828956,
                0.00015843629196944517,
                0.0004305571380524498
            ],
            [
                0.00023050679617348047,
                0.0003799845239494604,
                0.00015843615949275445,
                0.0017007220386609774,
                0.00020342697281662618,
                0.0005527785936708688,
                0.0010322311527168157,
                0.04742587704837889,
                0.0013250223192383043,
                0.00026119039457548677
            ],
            [
                0.00026119027604368705,
                0.00026119039872489876,
                0.00023050668637182906,
                0.0006263342379740942,
                0.0017007226434804191,
                0.9997040428348902,
                0.00015843627235231176,
                0.0024726236585546238,
                0.0015011821267357874,
                0.00017952805093282765
            ],
            [
                0.00013982204002712035,
                0.008577483481260173,
                0.999997097686977,
                0.0004878572180645712,
                0.0024726226219811335,
                0.0013250224440176043,
                0.003593602911562942,
                0.007577240588532559,
                0.0002611903995988591,
                0.0005527786693711892
            ],
            [
                2.7535691098355687e-05,
                0.00048785711551617493,
                0.0007096705444024673,
                0.00026119027293542937,
                7.484620037305929e-05,
                0.00029595723963748977,
                9.610238053958679e-05,
                0.00015843629218613268,
                0.0003353502663578278,
                0.0002611903385128343
            ],
            [
                0.9997694933459899,
                0.00015843619788790842,
                0.001700722243627542,
                0.0011695101948848389,
                0.00015843623527340056,
                0.0004305570337779522,
                0.001700722128988573,
                0.0002959571654111954,
                0.000430557035393737,
                0.01798621062007865
            ],
            [
                0.0007096705296658833,
                0.0017007225650120025,
                0.0017007226624551504,
                0.0009110510833507033,
                0.0021827160645176116,
                0.0010322311243865546,
                0.0001584362732789965,
                0.005911069113454627,
                0.004609572907956527,
                0.0007096704412876647
            ],
            [
                9.610242621495249e-05,
                0.0017007221420336969,
                0.0015011825882837373,
                0.00033535026311860204,
                0.0015011819473515944,
                0.0006263342345128058,
                0.0003799845683344967,
                0.0013250226301082361,
                0.00012339455989760105,
                0.0003799844300389213
            ],
            [
                0.0001398220569024194,
                0.00023050671463547068,
                6.605212099816935e-05,
                0.0009110513982748108,
                0.0013250225127232483,
                0.9999930377412607,
                0.00013982214035329548,
                0.00012339453034163755,
                0.0005527785949893535,
                0.0001795280503346778
            ],
            [
                0.00029595713124299565,
                0.0002959570230638145,
                0.001032230997740693,
                0.00013982209011187473,
                0.000552778765813541,
                9.610244917849409e-05,
                0.00048785710898804636,
                0.9999546021313694,
                0.0009110510122490776,
                0.00033535010584056737
            ],
            [
                0.0013250222234201337,
                0.0001795279649925621,
                0.0011695102532244123,
                0.0015011825392497139,
                0.9990889488890987,
                7.48462271838889e-05,
                0.0013250226923438508,
                0.0008040857877073565,
                0.5621765008857981,
                6.605215250517728e-05
            ],
            [
                0.0035936024255193095,
                0.0004305570811242075,
                0.0004305570329011698,
                0.0010322311233061632,
                0.0003799844369592262,
                0.0003353502261699653,
                0.01590639188675485,
                0.0006263341488914634,
                0.0040701378687910345,
                0.00020342706909405917
            ],
            [
                0.002472622970568403,
                0.002472623155486216,
                0.0013250221208238367,
                0.000626334164230435,
                0.004609572170827789,
                0.00020342706880993266,
                0.0015011824551415351,
                0.0007096703576152559,
                0.0001584362730899713,
                0.0019267342115593482
            ],
            [
                0.0007096704212673785,
                0.0024726225955643078,
                0.002472622970568403,
                0.00037998448289192457,
                0.0009110509842216873,
                0.0005527787246510813,
                0.0003353501465162505,
                0.0015011819370561983,
                0.0005527786398178344,
                0.0004878571633701983
            ],
            [
                0.0015011822504550538,
                0.999820472056068,
                0.060086648070103596,
                0.017986211541260618,
                0.0059110677480483185,
                0.0011695100412165125,
                0.020332354418614848,
                0.005911069532106325,
                0.0013250221346882008,
                0.0013250224142862391
            ],
            [
                3.726639283806955e-06,
                5.422220908703723e-06,
                4.222834451254188e-06,
                1.473898021151881e-05,
                3.2887486732358968e-06,
                4.222832437386106e-06,
                6.96225873895455e-06,
                2.2603234895053587e-06,
                3.059022998558814e-07,
                1.0677027427340866e-06
            ],
            [
                0.0005527785157838042,
                0.001169510216099229,
                0.0003799845251212695,
                0.0017007226581067742,
                0.0028009268520152153,
                0.0006263342365531442,
                0.00012339455958160968,
                0.001700722523109474,
                0.00522012523895161,
                0.00669285039800863
            ],
            [
                0.000487857093462454,
                0.0004305570820135155,
                0.00043055703113507946,
                0.0001795280301307974,
                0.00015843629174353693,
                0.0001398220898168875,
                0.000552778650044131,
                0.00043055698664463504,
                0.0002034269972307794,
                0.0009110511727840525
            ],
            [
                0.00043055703231247304,
                0.00013982205708144615,
                0.00026119040140757717,
                0.002182716057418297,
                0.01243165083031793,
                0.004609573044699262,
                0.008577487298644907,
                0.00013982205641619924,
                0.00026119027671245645,
                0.00017952794348530013
            ],
            [
                0.001926735105693197,
                0.00037998451770349687,
                0.000911051251197186,
                0.0015011824411816724,
                0.00012339461851940337,
                0.0007096704218452838,
                0.000626334067241505,
                0.000430557028016239,
                0.009708474207173075,
                0.008577486205700558
            ],
            [
                0.00026119030819781683,
                0.0019267346051214669,
                5.8291258498513246e-05,
                8.481105139057794e-05,
                0.9998415638020614,
                0.9984988175500934,
                0.0035936017919119285,
                0.0011695104153241279,
                0.9998766054425675,
                0.004609572660110329
            ],
            [
                0.0008040858229691614,
                0.0021827164123840704,
                0.0002611903693294325,
                0.0001398220400515331,
                0.00010889687024170175,
                0.000552778733269471,
                0.00020342692237827937,
                0.00015843627317065276,
                0.00033535018572843333,
                0.0006263340979923137
            ],
            [
                0.00037998443829685713,
                0.00460957249559174,
                0.01798620578387407,
                0.0040701368702552605,
                0.003172682622315311,
                0.0035936023438172984,
                0.005220126856674878,
                0.00010889690913765778,
                0.014063623801939484,
                0.0008040858084716022
            ],
            [
                0.001325022650596693,
                0.999997438717484,
                0.0046095711473941705,
                0.9999869928746399,
                0.000487857060736664,
                0.0003353501474724072,
                0.003593601963652865,
                0.003593602509722404,
                0.9999977396762412,
                0.0009110512566013345
            ],
            [
                0.0006263340966442332,
                0.0008040861133880642,
                0.0015011820797957583,
                0.000552778605119175,
                0.000709670462422483,
                0.0005527787254871938,
                0.00017952798686028367,
                0.0013250221946130645,
                0.00037998456548235716,
                0.0010322311287081199
            ],
            [
                0.0010322312404686044,
                0.001926734681237017,
                0.0008040860590923485,
                0.0003799844820738693,
                0.0003799845743814746,
                0.0008040858029999429,
                0.00017952794348530013,
                0.0021827165158312496,
                0.0004305571778959613,
                8.481101099738277e-05
            ],
            [
                0.0017007221950048061,
                0.00017952796304139312,
                0.0021827161152270045,
                0.0007096702832306167,
                0.0009110513887380765,
                0.00043055708619702085,
                0.00017952800800186987,
                0.001032230916231185,
                0.0004878571038506931,
                0.9999339478397309
            ],
            [
                0.0006263342332740288,
                0.00023050663004576857,
                0.0001398220567376335,
                0.00026119027729003003,
                0.00048785705063225746,
                0.0009110513703003905,
                0.0013250227028191526,
                0.0006263341402928952,
                0.000626334173156915,
                0.0015011825355852495
            ],
            [
                0.00020342699656189845,
                0.00020342701994017684,
                0.0001795280507499871,
                0.0005527786663483215,
                0.00017952790114468135,
                8.4811010852998e-05,
                0.0005527786389174057,
                0.00029595720137047445,
                2.4300246515109972e-05,
                0.0002611903351689866
            ],
            [
                0.0007096704999863216,
                0.0009110513030664175,
                0.9999885212359846,
                0.0021827160153295015,
                0.0019267349601781458,
                0.0017007223926582128,
                0.00020342706918876805,
                0.001325022213715078,
                0.0031726831716355043,
                0.0007096703663663905
            ],
            [
                0.00023050674058517224,
                9.610246044492253e-05,
                0.0031726828211309194,
                0.00970847490558041,
                0.0002611903374412831,
                0.0019267342621537916,
                0.002472622742579689,
                0.0010322309932990852,
                0.9999977396746245,
                0.0011695104189958499
            ],
            [
                0.003593602140395974,
                0.009708478666236147,
                0.0009110510930463799,
                0.005220126716423813,
                0.0003353500245770261,
                0.003593602884051036,
                0.003593602604763523,
                0.0019267342093206563,
                0.0004305571137906215,
                0.000552778636023171
            ],
            [
                0.0003353501447990712,
                0.0019267342218573322,
                0.00029595716561785793,
                0.00026119024248362586,
                0.000335350266484665,
                0.00012339461898800447,
                0.0009110512790656388,
                0.9999810748585295,
                0.00023050679623384424,
                0.00013982214002779226
            ],
            [
                0.0010322309463620923,
                0.0031726821267490514,
                0.003172682949256541,
                0.00043055712934725055,
                0.0008040860722804548,
                0.0015011821682663724,
                0.00033535026575291224,
                0.000709670415529606,
                0.0010322312135788627,
                0.0013250223400348533
            ],
            [
                0.00026119043324253675,
                0.0003353501815232948,
                0.0019267345607953542,
                0.0006263340635616098,
                0.0004878570909363522,
                0.002800926455323093,
                0.0015011825167394334,
                0.000911051403784924,
                0.00460957214946174,
                0.0017007225100643475
            ],
            [
                0.00020342702066233158,
                0.00010889689617180939,
                0.0007096702628801035,
                0.00023050679646188508,
                0.9999687980998051,
                0.0007096704239917886,
                0.0021827163495044145,
                0.00037998452235756875,
                0.0006263342297763055,
                0.00037998443620749985
            ],
            [
                0.0013250222224958428,
                0.0035936027698349462,
                0.0002611902766440596,
                0.0006263342355329748,
                0.003593602922400965,
                0.0005527785192568852,
                0.009708475165244687,
                0.0024726229676970087,
                0.0017007222319659913,
                0.001501182211716439
            ],
            [
                0.9993736657479986,
                0.001169510207939848,
                0.00020342697136639773,
                0.0031726828248126904,
                0.000911051056541893,
                0.0010322311165837286,
                0.00026119036793109603,
                0.00043055703113507946,
                0.9980732651262354,
                0.0031726830501370624
            ],
            [
                0.007577242038233127,
                0.00015843623443200788,
                0.00037998447955337454,
                0.0003353501481748897,
                0.0004305570859214607,
                0.001169510193524942,
                1.8925145977014425e-05,
                0.0004878571063200286,
                0.002182716374859114,
                9.610242635548565e-05
            ],
            [
                0.0001584361598062595,
                0.0019267347081013294,
                0.9999938558239334,
                0.000261190240956096,
                0.003593602040352704,
                0.00048785717361652303,
                0.007577242948673239,
                0.0009110510614162221,
                0.0024726236005524396,
                0.000487857040840066
            ],
            [
                7.484626290608339e-05,
                0.0017007227670138283,
                0.0011695103074842977,
                0.00020342697165644344,
                0.00026119024581227305,
                0.00048785710226123574,
                0.000430557028016239,
                0.00012339458929198511,
                0.0013250224859188038,
                0.0002959570613996943
            ],
            [
                0.020332352674823966,
                0.001032230850327331,
                0.0013250225019398514,
                0.0013250224192157918,
                0.00023050665953679899,
                0.00015843629177119916,
                0.0005527786701429852,
                0.0009110511477766222,
                0.0021827166213068097,
                0.0015011820565874914
            ],
            [
                0.0010322308509275483,
                0.0002034269966980424,
                0.0004305570852450855,
                0.0010322310942556421,
                0.008577484542524638,
                0.000804086098609902,
                0.0009110510281436283,
                0.0004305570749115768,
                0.0003353502254382126,
                0.0008040861124059713
            ],
            [
                0.0008040858542558305,
                0.010986944512906837,
                0.0007096704410399911,
                0.0008040859069147113,
                0.003593602052024418,
                0.012431651539222537,
                0.00522012641657672,
                0.0006263340210788604,
                0.005220126929218535,
                0.025957354372137545
            ],
            [
                0.0010322310982170766,
                0.0008040861133880642,
                0.00026119027543571494,
                0.00015843621574156602,
                0.9999989322967482,
                0.0002305066315012048,
                0.0052201267938037105,
                0.0003799844790006344,
                0.0003353501880115016,
                0.0028009263077016125
            ],
            [
                0.0003353500681601955,
                0.0003353502244430289,
                0.00015843629194178295,
                6.605214458937832e-05,
                0.0010322309993012581,
                0.0009110510751915001,
                0.0024726232467965703,
                0.00029595702651679897,
                0.0002034270689046415,
                0.0005527786481146411
            ],
            [
                0.9999810748427455,
                0.0015011819279822905,
                0.00033535022568213015,
                0.00020342697281662618,
                0.0003799845681797294,
                0.0002959571681150299,
                0.0013250226171681583,
                0.0004305571354596783,
                0.002800926627656549,
                0.000626334306835523
            ],
            [
                0.9999417087208643,
                0.012431649080924477,
                0.0006263342221979056,
                0.0011695104535372352,
                NaN,
                0.000108896934971121,
                0.0035936028698782367,
                0.00317268338812365,
                0.006692850088434397,
                0.0005527785316377764
            ],
            [
                0.0021827163596462944,
                0.002800926795437811,
                0.005220126479447883,
                0.0028009270802757903,
                0.0046095729549618415,
                0.0005527786204264609,
                0.0005527786685672351,
                0.0008040861137154286,
                0.00048785711247917594,
                0.0010322310266711683
            ],
            [
                0.00460957298701092,
                0.001700722638143776,
                0.004609571878112931,
                0.0010322311529569026,
                0.9999930377445814,
                0.9999910603036976,
                0.0006263341501666749,
                0.005911067879389994,
                0.025957354843080743,
                0.0005527785290329655
            ],
            [
                0.0009110511256302121,
                0.0015011823324692418,
                0.000626334016888881,
                0.00026119043274095945,
                0.00026119040051841743,
                0.002472622619684018,
                0.00026119043118302983,
                0.0010322312482714314,
                0.0013250221681167234,
                0.0010322307993088677
            ],
            [
                0.9999991684722697,
                0.00043055707846880896,
                0.002800927554355505,
                0.0002959570570597831,
                0.0009110513804729068,
                0.004609572243472355,
                0.010986944300387538,
                0.00013982210700345504,
                0.0075772406970850085,
                0.003593602704806809
            ],
            [
                0.0009110510977617638,
                0.002800926775278046,
                0.0008040858206308455,
                0.0011695104535372352,
                0.002800926378585935,
                0.001325022565715945,
                0.00460957162172037,
                0.0010322308167151667,
                0.0004305571333929763,
                0.0009110510862647044
            ],
            [
                0.0031726826664965563,
                0.0005527785235339204,
                0.014063623943988735,
                9.610243765756909e-05,
                0.0005527787224964839,
                0.0013250222047802651,
                2.1444956070012293e-05,
                0.0007096702806300439,
                0.00010889696088381469,
                0.00029595716839058
            ],
            [
                0.0011695101077154582,
                0.0008040858890032087,
                0.022977369910025615,
                0.0002959570613996943,
                0.000179527964164556,
                0.00017952800803843798,
                0.00020342694784902143,
                0.0011695101984205705,
                5.829126551609642e-05,
                0.005911067783620021
            ],
            [
                0.02033235360237229,
                0.005220125446910029,
                0.0021827164788133856,
                0.0009110511865593322,
                0.0015011825729278863,
                0.0019267345890028801,
                0.0010322308536885475,
                0.037326890958432175,
                0.0017007221129786488,
                0.0010322311537972072
            ],
            [
                0.00048785709317862233,
                0.0007096704389347652,
                0.0004305570290182761,
                0.0004878571131036056,
                0.00043055712714276846,
                0.00015843621639162822,
                0.0003353502229112265,
                7.484624498426811e-05,
                0.0003799844722682603,
                0.0004878570448420921
            ],
            [
                1.670142383015595e-05,
                6.9622587396067566e-06,
                7.338208055613267e-07,
                4.7850927830148924e-06,
                8.93969630388855e-06,
                7.889263525778283e-06,
                1.2098652508056196e-06,
                1.2098658277264215e-06,
                9.422449308716635e-07,
                1.300712691308661e-05
            ],
            [
                0.0015011823537580315,
                0.0031726832747250955,
                0.001325022359599015,
                0.00037998443397443016,
                0.00029595720328210286,
                0.001169510302588669,
                0.0028009266777308008,
                0.0009110510530450917,
                0.00037998443271418294,
                0.00012339463371033836
            ],
            [
                0.9999990577550691,
                0.001926734250512592,
                0.0003799844254511792,
                0.9999957771680661,
                0.00017952792253962202,
                0.0035936031024788977,
                0.9999930377420914,
                0.0002959572398097085,
                0.0021827166167429635,
                0.0008040861030059375
            ],
            [
                0.00020342697160908904,
                0.001169510331282494,
                0.0031726825280619896,
                0.0021827167409810095,
                0.0008040858192746222,
                0.001032230921032923,
                0.0001398221404407745,
                0.0017007223659750016,
                0.0007096703691733583,
                0.0021827165036609926
            ],
            [
                0.999996711249759,
                0.00037998442828120806,
                6.605215252536083e-05,
                0.0017007226814298815,
                0.9999898700114365,
                0.0004878571070863742,
                0.002800926451421204,
                0.00015843627335967802,
                0.00033535014391121145,
                0.00020342697165644344
            ],
            [
                0.00012339463339075595,
                0.014063629780922819,
                0.002800926580833873,
                0.9999485577680016,
                0.0004305571286207735,
                0.0004878570415212619,
                0.0002959570230638145,
                0.0010322312755213043,
                0.9999339478318099,
                0.9998415637648419
            ],
            [
                0.002472623510964909,
                0.0015011822206158507,
                0.0006263341688211962,
                0.0011695100236738464,
                0.0015011820764802915,
                0.00026119043186699893,
                0.001032230807831952,
                0.0011695101535439774,
                0.00048785717435448545,
                0.00023050665953679899
            ],
            [
                0.003172683072964042,
                0.0011695101090753552,
                0.0017007224369325793,
                0.0011695101627912752,
                0.00017952805162239774,
                0.0005527785378764593,
                0.0002305066319572862,
                0.00048785711199666207,
                0.002800927103687132,
                0.022977372209866422
            ],
            [
                0.00013982207342373593,
                0.0010322312459906048,
                0.0006263340097841332,
                0.0001233945595618602,
                0.00020342694789637583,
                0.00020342694798812497,
                0.00012339457472406142,
                0.00013982205641619924,
                0.0010322310005016929,
                0.000335350143013595
            ],
            [
                0.001169510487534663,
                0.005911068038094522,
                0.001325022721459028,
                0.025957354419231863,
                0.008577486174021013,
                0.00043055697955522346,
                0.0003799844335875122,
                0.0024726229160119077,
                0.00013982205718926903,
                0.0017007222936338533
            ],
            [
                0.9978172834927894,
                0.9997388095976653,
                0.9998601779886069,
                0.00023050679713930062,
                3.5356254919217684e-05,
                0.9991959140594134,
                0.991422513968537,
                0.001926734738995289,
                0.9991959139649924,
                0.9820137897747135
            ],
            [
                0.0003799845691304426,
                0.00023050679557654998,
                0.0001233946038509335,
                0.000552778583187308,
                0.004609571536256187,
                5.144222590680261e-05,
                0.0007096702401766919,
                0.0008040859940403802,
                0.0006263340849851588,
                0.0004878572172698423
            ],
            [
                0.009708475612941737,
                0.0019267346516862736,
                0.0035936029324052945,
                0.00043055703530605884,
                0.002182716451430309,
                0.008577484035652042,
                0.001501182258307476,
                0.0009110511732079073,
                0.012431652808390557,
                0.004070138112290343
            ],
            [
                0.00048785717216898124,
                0.9999485577679709,
                0.0001584361974821959,
                0.0013250222938203,
                0.002472623113563854,
                0.0010322308847798005,
                0.00037998448407478843,
                0.0004305570736339794,
                0.004070136807964758,
                0.001700722720762919
            ]
        ]
    },
    {
        "q_id": "9043_mmlu_math",
        "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": [
            [
                0.9999989322972572,
                0.999999266178932,
                0.9999977396746245,
                0.9999984465022455,
                0.9999977396757023,
                0.9999990577555185,
                0.9999990577557432,
                0.9999982396569966,
                0.999998005270992,
                0.9999982396574163
            ],
            [
                0.9999989322968754,
                0.9999977396754328,
                0.9999980052700408,
                0.9999990577551815,
                0.999998239656367,
                0.9999991684717742,
                0.999999266178757,
                0.9999993524053562,
                0.9999984465020603,
                0.9999974387171787
            ],
            [
                0.9999974387165682,
                0.9999986290429567,
                0.9999991684719725,
                0.9999986290424663,
                0.9999984465016899,
                0.9999986290431201,
                0.9999982396572065,
                0.9999982396561572,
                0.9999986290426298,
                0.9999990577550693
            ],
            [
                0.9999967112497585,
                0.9999970976873229,
                0.9999974387168734,
                0.9999982396559474,
                0.9999952149072167,
                0.9999957771650456,
                0.9999967112505427,
                0.9999980052702786,
                0.9999974387187053,
                0.9999986290432834
            ],
            [
                0.9999986290426297,
                0.9999987901338838,
                0.9999990577549568,
                0.9999991684722697,
                0.9999990577554061,
                0.9999989322967482,
                0.9999977396757024,
                0.9999993524052789,
                0.9999967112497585,
                0.9999987901340281
            ],
            [
                0.9999989322970027,
                0.9999987901338838,
                0.9999991684718732,
                0.999999057755743,
                0.9999967112521109,
                0.9999967112517189,
                0.9999984465022455,
                0.9999991684719723,
                0.9999984465028011,
                0.9999957771660524
            ],
            [
                0.9999974387184,
                0.9999982396565769,
                0.9999957771655489,
                0.9999982396561572,
                0.9999967112493666,
                0.999993855827596,
                0.9999945777810306,
                0.9999980052702786,
                0.9999945777810306,
                0.9999984465022455
            ],
            [
                0.9999967112509348,
                0.9999980052705164,
                0.9999987901346049,
                0.99999893229713,
                0.9999984465020603,
                0.9999991684721706,
                0.9999989322972572,
                0.9999991684715759,
                0.9999990577550691,
                0.9999987901338839
            ],
            [
                0.9999974387165681,
                0.9999987901343166,
                0.999997097688707,
                0.9999967112509348,
                0.999999057755743,
                0.9999991684722697,
                0.9999987901344607,
                0.9999986290424664,
                0.9999982396559474,
                0.9999974387177893
            ],
            [
                0.9999991684717742,
                0.9999990577550691,
                0.9999989322972572,
                0.9999974387165681,
                0.9999977396751634,
                0.9999980052709919,
                0.9999990577554061,
                0.9999980052705164,
                0.9999989322966208,
                0.999998005270992
            ],
            [
                0.9999989322970028,
                0.999999352405279,
                0.9999982396574163,
                0.9999989322970027,
                0.9999991684722698,
                0.9999974387177895,
                0.9999970976883612,
                0.9999982396559474,
                0.9999991684717741,
                0.9999974387184001
            ],
            [
                0.9999987901344607,
                0.9999987901338838,
                0.9999990577557432,
                0.9999989322970027,
                0.9999980052695652,
                0.9999989322967482,
                0.9999991684718732,
                0.9999980052695652,
                0.9999977396757023,
                0.9999987901338838
            ],
            [
                0.9999992661792819,
                0.9999989322973845,
                0.9999984465015048,
                0.9999987901341723,
                0.9999984465024307,
                0.999996273360272,
                0.9999982396561572,
                0.9999986290424663,
                0.9999980052705164,
                0.9999989322973846
            ],
            [
                0.9999986290421394,
                0.9999977396762411,
                0.9999967112513268,
                0.9999986290427931,
                0.9999990577551815,
                0.9999982396561572,
                0.9999987901344607,
                0.9999977396757023,
                0.9999989322968754,
                0.9999982396565769
            ],
            [
                0.9999991684721706,
                0.9999974387180948,
                0.999998005269803,
                0.9999974387177893,
                0.999998005269803,
                0.9999980052693275,
                0.999997097687669,
                0.999996273360272,
                0.9999977396754328,
                0.9999989322973845
            ],
            [
                0.9999974387171788,
                0.9999982396572065,
                0.9999986290432835,
                0.9999982396565769,
                0.9999977396751635,
                0.9999980052705164,
                0.9999970976869772,
                0.9999980052705164,
                0.9999989322975118,
                0.9999987901343165
            ],
            [
                0.9999989322972573,
                0.9999990577556307,
                0.9999990577549568,
                0.9999987901344608,
                0.9999980052695653,
                0.9999986290432835,
                0.999998790134605,
                0.9999987901338839,
                0.9999987901337396,
                0.9999980052705164
            ],
            [
                0.9999986290427932,
                0.9999974387177893,
                0.9999989322967482,
                0.9999989322973846,
                0.99999893229713,
                0.99999862904312,
                0.9999984465024306,
                0.9999974387177893,
                0.9999974387171787,
                0.9999974387184
            ],
            [
                0.9999945777810305,
                0.9999982396572065,
                0.999997097687669,
                0.9999987901344607,
                0.9999982396574163,
                0.9999980052702785,
                0.9999977396759717,
                0.9999984465018751,
                0.9999945777803844,
                0.9999957771665557
            ],
            [
                0.9999986290429566,
                0.9999957771660523,
                0.9999970976866313,
                0.9999982396567867,
                0.9999982396569966,
                0.9999957771680666,
                0.9999982396569966,
                0.999997097687323,
                0.9999989322966208,
                0.9999984465018751
            ],
            [
                0.9999987901346049,
                0.9999974387187054,
                0.9999982396569966,
                0.9999989322970028,
                0.999996711252111,
                0.9999987901344607,
                0.9999982396574163,
                0.9999987901343165,
                0.9999982396569966,
                0.9999986290432835
            ],
            [
                0.9999962733611603,
                0.999997438716568,
                0.9999991684718732,
                0.9999989322970028,
                0.9999984465015047,
                0.9999977396759717,
                0.9999987901343165,
                0.9999980052707541,
                0.9999986290432834,
                0.9999974387165681
            ],
            [
                0.9999987901344607,
                0.999997097686977,
                0.9999982396567867,
                0.999999352404893,
                0.9999986290426297,
                0.9999986290424664,
                0.9999982396569965,
                0.9999989322970028,
                0.9999952149072169,
                0.9999984465018751
            ],
            [
                0.9999984465024306,
                0.9999982396561572,
                0.9999974387168734,
                0.9999982396567867,
                0.9999984465028011,
                0.9999974387180947,
                0.9999989322967482,
                0.9999984465022456,
                0.9999938558261318,
                0.9999982396574163
            ],
            [
                0.9999987901341723,
                0.999998239656367,
                0.99999893229713,
                0.9999980052695652,
                0.9999984465015047,
                0.9999984465018751,
                0.9999974387184001,
                0.999999266179107,
                0.9999982396561572,
                0.9999989322975118
            ],
            [
                0.9999980052705164,
                0.9999982396567867,
                0.9999991684715759,
                0.9999974387184,
                0.9999984465024306,
                0.9999970976890529,
                0.999997097686631,
                0.9999986290424664,
                0.9999994956527721,
                0.9999982396565769
            ],
            [
                0.999996273360272,
                0.9999989322975118,
                0.9999982396565769,
                0.999996273360272,
                0.999998446502801,
                0.999999057755069,
                0.9999980052693275,
                0.9999991684718732,
                0.9999974387180948,
                0.9999984465020603
            ],
            [
                0.9999987901338838,
                0.9999982396574163,
                0.9999980052702786,
                0.999997097686977,
                0.9999991684718732,
                0.9999984465020603,
                0.9999991684715758,
                0.9999962733593832,
                0.9999984465028011,
                0.9999980052705164
            ],
            [
                0.9999982396572065,
                0.9999980052709919,
                0.9999994284996211,
                0.9999986290424663,
                0.9999970976890531,
                0.9999986290426297,
                0.9999984465028011,
                0.9999984465026158,
                0.9999977396757023,
                0.9999989322973846
            ],
            [
                0.999998005269803,
                0.9999984465020603,
                0.9999977396751634,
                0.9999962733607163,
                0.9999986290421394,
                0.9999987901338838,
                0.999998446502801,
                0.9999977396754327,
                0.9999974387180947,
                0.9999982396569966
            ],
            [
                0.9999962733607161,
                0.999997097688707,
                0.9999910602994339,
                0.9999977396746245,
                0.9999962733598274,
                0.9999962733593832,
                0.9999980052709919,
                0.9999957771650455,
                0.9999952149043646,
                0.9999962733598275
            ],
            [
                0.9999987901344608,
                0.9999986290426298,
                0.9999990577557432,
                0.99999893229713,
                0.9999987901343166,
                0.9999982396574163,
                0.9999990577556307,
                0.999997097687669,
                0.9999984465015047,
                0.9999977396751635
            ],
            [
                0.9999977396746244,
                0.999997097686977,
                0.9999967112497585,
                0.9999957771650453,
                0.9999967112501507,
                0.9999945777829697,
                0.9999986290424664,
                0.9999986290426297,
                0.9999970976873229,
                0.9999977396759716
            ],
            [
                0.9999986290426298,
                0.9999974387168734,
                0.9999984465018751,
                0.9999987901338838,
                0.999998005269803,
                0.9999989322967482,
                0.9999962733607162,
                0.9999986290427932,
                0.9999962733593835,
                0.999997438717484
            ],
            [
                0.999997097689053,
                0.9999980052707542,
                0.9999987901337396,
                0.999999352405279,
                0.9999984465024306,
                0.9999986290421395,
                0.9999984465016899,
                0.9999977396751634,
                0.9999992661788446,
                0.9999952149066464
            ],
            [
                0.9999989322970027,
                0.9999990577551815,
                0.9999974387187054,
                0.999998629042303,
                0.9999977396762411,
                0.999997438717484,
                0.9999977396757023,
                0.9999986290429566,
                0.999995777165549,
                0.99999893229713
            ],
            [
                0.9999987901341723,
                0.9999987901343166,
                0.9999974387165681,
                0.9999982396569966,
                0.9999987901347491,
                0.9999984465026158,
                0.9999945777803844,
                0.9999987901338838,
                0.9999984465015046,
                0.9999986290424664
            ],
            [
                0.999998005270992,
                0.9999991684717741,
                0.9999986290431201,
                0.9999991684716749,
                0.9999986290424664,
                0.9999991684721706,
                0.9999989322973846,
                0.999999266178757,
                0.999998446502801,
                0.9999986290424663
            ],
            [
                0.99999862904312,
                0.9999974387165681,
                0.9999982396565769,
                0.9999977396751635,
                0.999997438717484,
                0.9999980052695652,
                0.9999977396754328,
                0.9999989322966208,
                0.9999987901343165,
                0.999999168471675
            ],
            [
                0.9999984465028011,
                0.9999967112513268,
                0.9999967112501507,
                0.9999970976869772,
                0.9999982396574163,
                0.999999168471675,
                0.9999991684718732,
                0.9999987901341724,
                0.9999991684722697,
                0.999999495652712
            ],
            [
                0.9999984465015047,
                0.999998790134028,
                0.9999938558268635,
                0.9999986290426298,
                0.9999980052709919,
                0.9999980052702785,
                0.9999986290426297,
                0.9999984465016899,
                0.9999982396572065,
                0.9999974387171787
            ],
            [
                0.9999977396754327,
                0.9999989322975118,
                0.999997438716568,
                0.9999977396746245,
                0.9999990577556307,
                0.9999974387177895,
                0.9999986290427932,
                0.999997097686631,
                0.9999986290421394,
                0.9999970976887069
            ],
            [
                0.9999982396572065,
                0.9999982396559474,
                0.9999977396746245,
                0.9999982396572065,
                0.9999982396569966,
                0.9999984465018751,
                0.9999967112497586,
                0.9999986290427931,
                0.9999987901343165,
                0.9999982396574163
            ],
            [
                0.9999980052693275,
                0.9999980052693275,
                0.9999980052693275,
                0.9999984465020603,
                0.9999980052702786,
                0.9999982396574163,
                0.99999862904312,
                0.9999987901338838,
                0.9999967112521109,
                0.9999984465028011
            ],
            [
                0.9999992661792819,
                0.999998790134605,
                0.9999984465018752,
                0.999998239656367,
                0.9999990577557432,
                0.9999987901347492,
                0.9999982396559474,
                0.9999987901341724,
                0.9999990577554061,
                0.9999982396559474
            ],
            [
                0.9999980052709919,
                0.999998005270992,
                0.9999982396559474,
                0.9999974387187054,
                0.9999986290431201,
                0.9999989322966208,
                0.9999984465022455,
                0.9999970976887069,
                0.99999893229713,
                0.9999977396757023
            ],
            [
                0.9999974387171787,
                0.9999992661789321,
                0.9999990577555185,
                0.9999986290429567,
                0.9999986290432835,
                0.9999974387184001,
                0.9999982396572065,
                0.9999986290429566,
                0.9999982396561572,
                0.9999987901338839
            ],
            [
                0.9999962733611607,
                0.9999986290424663,
                0.9999980052702786,
                0.9999977396748939,
                0.99999862904312,
                0.9999990577549568,
                0.9999974387171787,
                0.9999993524052019,
                0.9999986290432835,
                0.9999980052693275
            ],
            [
                0.9999989322968754,
                0.9999993524050474,
                0.999998239656577,
                0.9999974387168735,
                0.99999893229713,
                0.9999984465026158,
                0.9999982396567867,
                0.9999987901337396,
                0.9999989322970027,
                0.9999991684722698
            ],
            [
                0.9999980052698031,
                0.9999977396757023,
                0.999998005269803,
                0.9999980052693275,
                0.999999057755743,
                0.9999986290432834,
                0.9999991684721706,
                0.9999984465026158,
                0.999999266178757,
                0.9999987901347491
            ],
            [
                0.9999987901343166,
                0.999998629042303,
                0.9999987901343166,
                0.9999990577551815,
                0.9999989322968754,
                0.9999994284992805,
                0.9999984465028011,
                0.9999993524049703,
                0.9999989322967482,
                0.9999989322967481
            ],
            [
                0.9999982396572065,
                0.9999986290426297,
                0.9999974387177896,
                0.9999990577550693,
                0.9999982396559474,
                0.9999982396572065,
                0.9999970976880151,
                0.9999980052695652,
                0.9999977396757023,
                0.9999974387168734
            ],
            [
                0.9999930377437508,
                0.9999962733611603,
                0.999998446502801,
                0.9999962733616046,
                0.9999984465024306,
                0.9999957771670591,
                0.9999974387171787,
                0.9999952149060758,
                0.9999990577552937,
                0.9999962733620489
            ],
            [
                0.9999989322973846,
                0.9999977396765106,
                0.9999952149049356,
                0.9999974387180948,
                0.9999982396559474,
                0.9999987901343165,
                0.999996711250935,
                0.9999989322970028,
                0.9999984465022455,
                0.9999974387187054
            ],
            [
                0.9999980052707541,
                0.9999898700126462,
                0.9999957771665557,
                0.9999987901347492,
                0.9999982396561572,
                0.9999977396746245,
                0.9999982396574163,
                0.9999987901341723,
                0.9999930377404317,
                0.9999974387171787
            ],
            [
                0.9999980052693275,
                0.9999984465020603,
                0.999998446502801,
                0.9999974387184,
                0.9999992661791945,
                0.9999994284996211,
                0.9999970976887069,
                0.9999991684721706,
                0.9999967112517191,
                0.9999989322968754
            ],
            [
                0.9999984465028011,
                0.9999980052705164,
                0.9999986290423029,
                0.9999977396748938,
                0.9999977396748938,
                0.9999952149032243,
                0.9999982396567868,
                0.9999974387187053,
                0.9999986290423029,
                0.9999962733598275
            ],
            [
                0.9999982396559474,
                0.9999990577551815,
                0.9999967112493665,
                0.9999970976880149,
                0.999997097686977,
                0.9999982396567868,
                0.9999980052693274,
                0.9999967112517189,
                0.9999991684715759,
                0.9999986290421394
            ],
            [
                0.9999970976869771,
                0.9999987901343165,
                0.9999984465020603,
                0.9999977396746245,
                0.9999987901337396,
                0.9999974387165681,
                0.9999987901344607,
                0.9999982396567868,
                0.9999967112497586,
                0.9999986290427931
            ],
            [
                0.9999991684720715,
                0.9999984465022455,
                0.9999986290421395,
                0.9999986290424663,
                0.9999991684720715,
                0.9999982396565769,
                0.9999984465026158,
                0.9999967112513269,
                0.9999980052709919,
                0.9999990577554061
            ],
            [
                0.9999980052695652,
                0.99999893229713,
                0.999996711250935,
                0.999997097687669,
                0.999998239656577,
                0.9999989322968754,
                0.99999862904312,
                0.9999991684721706,
                0.9999990577557432,
                0.9999974387184001
            ],
            [
                0.9999989322970027,
                0.9999989322971299,
                0.9999982396572065,
                0.9999984465016899,
                0.9999994956526519,
                0.9999977396751634,
                0.999999057755743,
                0.9999980052693275,
                0.999997438717484,
                0.9999984465018751
            ],
            [
                0.9999984465020603,
                0.9999986290429567,
                0.9999974387171787,
                0.9999982396567867,
                0.9999967112497586,
                0.9999980052693275,
                0.999999168471675,
                0.9999986290427931,
                0.9999980052707541,
                0.9999989322967482
            ],
            [
                0.9999977396765105,
                0.999999266179107,
                0.9999980052695654,
                0.9999986290429567,
                0.9999990577554061,
                0.9999990577549568,
                0.9999984465024307,
                0.9999980052693275,
                0.9999987901343166,
                0.9999990577557432
            ],
            [
                0.9999980052702786,
                0.9999982396567867,
                0.9999977396754328,
                0.9999980052693275,
                0.9999974387184,
                0.9999992661790195,
                0.9999980052709919,
                0.9999987901337396,
                0.9999977396765105,
                0.9999987901337396
            ],
            [
                0.9999980052705163,
                0.9999967112493668,
                0.9999982396565769,
                0.9999980052698031,
                0.9999990577550691,
                0.9999967112521111,
                0.9999980052700408,
                0.9999982396574163,
                0.9999986290423029,
                0.9999980052698031
            ],
            [
                1.9947306725451314e-06,
                9.422444815679433e-07,
                1.2098656834834034e-06,
                1.994729721396435e-06,
                6.962258736700326e-06,
                1.3709578605243332e-06,
                6.9622554171645e-06,
                4.222831934156396e-06,
                3.2887482812506295e-06,
                1.3709573702566696e-06
            ],
            [
                0.9999977396762412,
                0.9999952149037944,
                0.9999980052702785,
                0.9999977396754327,
                0.9999986290424664,
                0.9999980052695652,
                0.9999982396567867,
                0.9999967112505427,
                0.9999974387177893,
                0.9999984465026158
            ],
            [
                0.9999980052709919,
                0.9999970976873229,
                0.999997097686977,
                0.9999977396765105,
                0.999993037741261,
                0.9999989322970027,
                0.999996273358939,
                0.9999980052702786,
                0.9999987901347491,
                0.9999987901341724
            ],
            [
                1.553498495338299e-06,
                4.22283193393364e-06,
                4.7850950647493785e-06,
                3.2887482810801374e-06,
                1.0129993393319151e-05,
                2.2603237588597026e-06,
                2.260323758923431e-06,
                3.7266388397382506e-06,
                1.0129993393540266e-05,
                6.962258738283349e-06
            ],
            [
                0.999999266178757,
                0.9999992661786696,
                0.9999991684716749,
                0.9999991684719723,
                0.999999266178932,
                0.9999994284996891,
                0.999998629042303,
                0.9999982396569966,
                0.9999993524054335,
                0.9999991684715758
            ],
            [
                0.9999986290423029,
                0.9999982396559474,
                0.9999990577551815,
                0.9999990577557432,
                0.9999977396748939,
                0.9999957771670596,
                0.9999987901341723,
                0.9999986290424663,
                0.9999967112517191,
                0.9999977396759717
            ],
            [
                0.9999984465018751,
                0.9999977396751634,
                0.999998446502801,
                0.9999970976876689,
                0.9999989322975119,
                0.999997097687669,
                0.9999989322972572,
                0.9999967112517191,
                0.9999980052702786,
                0.9999974387177893
            ],
            [
                0.9999982396569966,
                0.9999989322973845,
                0.9999984465024307,
                0.9999986290424663,
                0.9999984465018751,
                0.9999984465015047,
                0.9999982396559474,
                0.9999987901343166,
                0.9999982396572065,
                0.9999974387171787
            ],
            [
                0.9999967112509349,
                0.999995214906076,
                0.9999984465022455,
                0.9999984465020603,
                0.9999967112509348,
                0.9999982396559474,
                0.9999974387177893,
                0.9999945777823231,
                0.9999982396574163,
                0.9999982396572065
            ],
            [
                0.9999980052709919,
                0.9999986290427931,
                0.9999984465022455,
                0.9999980052705165,
                0.999998790134605,
                0.9999980052695652,
                0.99999862904312,
                0.9999977396762412,
                0.9999984465022455,
                0.9999982396569966
            ],
            [
                0.9999982396561572,
                0.9999987901346049,
                0.9999980052702786,
                0.9999987901341723,
                0.9999970976887069,
                0.9999980052709919,
                0.9999982396569966,
                0.9999980052693274,
                0.9999967112505427,
                0.9999974387177893
            ],
            [
                0.9999984465020604,
                0.9999994284995529,
                0.9999987901338838,
                0.9999987901344607,
                0.9999994284996211,
                0.9999994284993485,
                0.9999989322968754,
                0.9999986290423029,
                0.9999986290421394,
                0.9999989322975118
            ],
            [
                0.9999977396762412,
                0.9999986290426298,
                0.9999982396559474,
                0.9999967112513267,
                0.9999970976873229,
                0.9999984465016899,
                0.9999989322966208,
                0.9999986290421394,
                0.9999980052707541,
                0.9999982396569966
            ],
            [
                0.9999974387168733,
                0.9999977396751634,
                0.9999994284992805,
                0.9999982396559474,
                0.9999962733611604,
                0.999998239656367,
                0.999998790134028,
                0.9999984465016899,
                0.9999984465024306,
                0.9999967112509348
            ],
            [
                0.9999987901343166,
                0.9999977396746245,
                0.9999986290424663,
                0.9999977396765106,
                0.9999957771680662,
                0.9999982396569966,
                0.999998629042303,
                0.9999970976866311,
                0.9999980052707541,
                0.9999982396574164
            ],
            [
                0.9999982396565769,
                0.9999987901337396,
                0.9999987901344608,
                0.9999990577551815,
                0.9999974387177893,
                0.9999980052705164,
                0.9999986290426298,
                0.999998005269803,
                0.9999986290426298,
                0.9999984465015047
            ],
            [
                0.9999980052707541,
                0.9999986290421394,
                0.999997097686977,
                0.9999962733593833,
                0.9999921107364748,
                0.9999930377420914,
                0.9999986290426298,
                0.999997438716568,
                0.9999987901347491,
                0.9999977396765106
            ],
            [
                0.9999987901346049,
                0.999998790134028,
                0.9999957771660526,
                0.9999987901341723,
                0.9999989322968754,
                0.9999990577550691,
                0.9999970976873229,
                0.9999984465022455,
                0.9999989322973845,
                0.9999986290427931
            ],
            [
                0.9999982396569966,
                0.9999974387174841,
                0.999998446502801,
                0.9999967112513272,
                0.9999986290429567,
                0.9999970976869771,
                0.9999982396561572,
                0.999997097688707,
                0.9999987901346049,
                0.999998005269803
            ],
            [
                0.9999970976890529,
                0.9999967112497586,
                0.9999987901343165,
                0.9999980052693274,
                0.9999982396567867,
                0.9999991684719723,
                0.9999974387168734,
                0.9999974387165681,
                0.9999986290427931,
                0.999997438717484
            ],
            [
                0.9999989322966208,
                0.9999990577556308,
                0.999998239656367,
                0.9999986290424664,
                0.9999974387168734,
                0.9999991684716749,
                0.9999991684722697,
                0.9999987901347491,
                0.9999989322968754,
                0.9999986290421395
            ],
            [
                0.9999974387187053,
                0.9999982396561572,
                0.9999987901347491,
                0.999998005269803,
                0.9999977396757023,
                0.9999980052702786,
                0.9999991684717741,
                0.999997438716568,
                0.9999977396757022,
                0.9999980052698031
            ],
            [
                0.9999977396757023,
                0.9999986290423029,
                0.999996711249367,
                0.9999984465024307,
                0.9999984465018751,
                0.9999987901337396,
                0.9999987901344607,
                0.999998446502801,
                0.9999984465022455,
                0.9999970976883609
            ],
            [
                0.9999989322966208,
                0.9999977396759717,
                0.9999982396574163,
                0.9999984465018751,
                0.9999945777810305,
                0.9999974387184,
                0.9999967112505427,
                0.9999974387165681,
                0.9999952149066464,
                0.9999974387177893
            ],
            [
                0.9999989322973846,
                0.9999987901344607,
                0.9999977396759717,
                0.9999994284993485,
                0.9999982396572065,
                0.9999982396559474,
                0.9999987901337396,
                0.9999990577551815,
                0.999997097688707,
                0.9999992661788445
            ],
            [
                0.9999982396569966,
                0.999998790134028,
                0.9999987901341724,
                0.999999266178757,
                0.9999993524049703,
                0.9999990577554061,
                0.99999893229713,
                0.9999991684722698,
                0.9999991684717741,
                0.9999986290429566
            ],
            [
                0.9999982396561572,
                0.9999991684717742,
                0.999998790134605,
                0.9999952149066468,
                0.9999974387184001,
                0.9999987901343165,
                0.9999989322966208,
                0.9999990577554061,
                0.99999844650169,
                0.9999989322966208
            ],
            [
                0.9999974387174841,
                0.9999977396746244,
                0.9999987901346049,
                0.9999977396765107,
                0.9999991684718733,
                0.9999980052695652,
                0.9999980052707541,
                0.999996711252111,
                0.9999982396565769,
                0.9999982396567867
            ],
            [
                0.9999980052693275,
                0.9999989322970027,
                0.9999986290424663,
                0.9999962733616046,
                0.9999980052700408,
                0.9999982396574163,
                0.9999984465015047,
                0.9999962733611603,
                0.9999980052705164,
                0.9999984465020603
            ],
            [
                0.9999974387165681,
                0.9999989322968754,
                0.9999982396565769,
                0.9999984465018751,
                0.9999980052705164,
                0.9999989322973845,
                0.9999980052705164,
                0.9999967112497586,
                0.999997097687323,
                0.999997097687323
            ],
            [
                0.9999986290429566,
                0.9999990577556308,
                0.9999989322966208,
                0.9999992661791071,
                0.9999982396574163,
                0.9999987901343165,
                0.9999986290431201,
                0.9999987901343166,
                0.9999991684722698,
                0.9999982396561572
            ],
            [
                0.9999977396754328,
                0.99999893229713,
                0.9999989322972572,
                0.9999980052707541,
                0.9999987901341723,
                0.9999987901337396,
                0.999998005269803,
                0.9999989322975119,
                0.9999984465022455,
                0.99999844650169
            ],
            [
                0.9999980052705164,
                0.9999986290421395,
                0.9999977396751634,
                0.999998790134028,
                0.9999977396759717,
                0.9999967112497585,
                0.9999980052702785,
                0.9999970976887069,
                0.9999986290424663,
                0.9999974387184
            ],
            [
                0.9999970976880149,
                0.9999984465022455,
                0.9999938558268635,
                0.9999982396559474,
                0.9999984465026158,
                0.9999980052705164,
                0.9999980052709919,
                0.9999980052695652,
                0.9999984465016899,
                0.9999990577556307
            ],
            [
                0.999997097688361,
                0.9999974387184,
                0.999997097689053,
                0.9999987901344608,
                0.9999987901346049,
                0.9999974387180947,
                0.9999977396762411,
                0.999997438717484,
                0.9999986290426298,
                0.999999168471675
            ],
            [
                0.9999995549151073,
                0.9999982396559474,
                0.9999990577555185,
                0.9999987901341724,
                0.9999990577557432,
                0.999996711250543,
                0.9999982396574163,
                0.9999993524054335,
                0.9999986290427932,
                0.9999984465024306
            ],
            [
                1.1478768123280277e-05,
                8.481104103127398e-05,
                3.7266383953679482e-06,
                3.2887490652810324e-06,
                5.422220908481809e-06,
                2.144494327452579e-05,
                1.30071346612026e-05,
                3.726639728224814e-06,
                5.422217676486429e-06,
                6.144172404218801e-06
            ],
            [
                0.9999957771655489,
                0.999997097686631,
                0.9999977396748939,
                0.999998446502801,
                0.9999984465020603,
                0.999995777168066,
                0.999993855827596,
                0.9999987901347492,
                0.9999982396572065,
                0.9999977396748938
            ],
            [
                0.9999987901343166,
                0.9999970976883609,
                0.9999991684722698,
                0.9999967112501508,
                0.9999986290429566,
                0.999997097686977,
                0.9999980052707542,
                0.9999982396572065,
                0.9999984465024306,
                0.9999984465018751
            ],
            [
                0.999995777166556,
                0.9999982396561572,
                0.9999980052707541,
                0.9999986290424664,
                0.999998005269803,
                0.9999977396748939,
                0.9999977396757022,
                0.9999982396563669,
                0.99999862904312,
                0.9999982396559474
            ],
            [
                0.9999984465016899,
                0.999997097686631,
                0.9999991684722698,
                0.999998790134028,
                0.9999991684717742,
                0.9999982396574163,
                0.9999974387165681,
                0.9999982396565769,
                0.9999987901337396,
                0.9999986290424663
            ],
            [
                0.9999980052707542,
                0.9999990577550693,
                0.9999987901338838,
                0.9999989322970027,
                0.9999987901340281,
                0.9999986290426297,
                0.9999986290426298,
                0.9999987901346049,
                0.999998239656577,
                0.9999989322968754
            ],
            [
                0.9999990577555185,
                0.9999992661787571,
                0.9999980052695652,
                0.9999987901341724,
                0.9999989322966208,
                0.9999984465020603,
                0.9999986290423029,
                0.9999982396567868,
                0.9999987901337396,
                0.9999987901346049
            ],
            [
                0.999997438716568,
                0.9999980052709919,
                0.9999980052702786,
                0.9999962733598275,
                0.9999967112517189,
                0.9999980052707541,
                0.9999984465015047,
                0.9999952149072169,
                0.9999957771665557,
                0.9999989322970028
            ],
            [
                0.999997438717484,
                0.9999987901340281,
                0.999998629042303,
                0.9999974387180947,
                0.9999982396559474,
                0.9999989322966208,
                0.9999970976873233,
                0.9999987901340281,
                0.9999991684718732,
                0.999998005269803
            ],
            [
                0.999996273362049,
                0.9999962733611605,
                0.9999962733593835,
                0.999997097687669,
                0.999993855822469,
                0.9999957771660523,
                0.9999980052695653,
                0.9999982396567867,
                0.9999974387180947,
                0.9999987901338838
            ],
            [
                0.9999986290432834,
                0.9999990577550693,
                0.999998790134028,
                0.9999984465016899,
                0.9999991684720715,
                0.9999986290426298,
                0.999999266178757,
                0.9999980052700408,
                0.999998446502801,
                0.999999168471675
            ],
            [
                0.9999990577552939,
                0.9999986290429566,
                0.9999945777810307,
                0.9999967112497586,
                0.9999991684720715,
                0.999997438717484,
                0.9999967112505427,
                0.9999974387184,
                0.9999952149032239,
                0.9999980052705164
            ],
            [
                0.9999991684719725,
                0.9999989322973846,
                0.9999989322966208,
                0.9999991684719725,
                0.9999980052700408,
                0.9999984465024306,
                0.9999994284996212,
                0.9999994284994849,
                0.9999991684719725,
                0.9999980052695653
            ],
            [
                0.9999977396748938,
                0.9999984465024306,
                0.999998790134028,
                0.9999984465015047,
                0.9999982396572065,
                0.9999987901344608,
                0.99999862904312,
                0.9999962733607161,
                0.9999986290432835,
                0.9999986290421394
            ],
            [
                0.9999977396751634,
                0.9999992661789321,
                0.9999990577549568,
                0.9999974387180949,
                0.9999982396565769,
                0.999998005270992,
                0.9999980052709919,
                0.9999974387174841,
                0.9999991684722697,
                0.9999974387184001
            ],
            [
                0.9999980052695653,
                0.9999986290421394,
                0.999999057755069,
                0.9999996072136125,
                0.99999844650169,
                0.9999984465026158,
                0.9999986290432834,
                0.9999989322967481,
                0.999998005269803,
                0.9999982396565769
            ],
            [
                0.9999989322972572,
                0.9999980052693274,
                0.9999990577552939,
                0.9999990577556308,
                0.99999893229713,
                0.9999982396567868,
                0.9999992661787571,
                0.9999991684720715,
                0.999999266179107,
                0.9999994284994167
            ],
            [
                0.9999977396757023,
                0.9999977396746245,
                0.9999980052705164,
                0.9999980052702785,
                0.9999991684722698,
                0.9999982396569966,
                0.9999957771660524,
                0.9999982396561572,
                0.9999989322967481,
                0.9999974387171787
            ],
            [
                0.9999982396569966,
                0.9999986290426297,
                0.9999987901346049,
                0.9999989322970028,
                0.9999982396572065,
                0.9999982396561572,
                0.9999980052705163,
                0.9999977396762412,
                0.9999989322967482,
                0.9999984465016899
            ],
            [
                0.9999991684716749,
                0.999999168471675,
                0.9999989322970027,
                0.9999982396567868,
                0.9999992661788446,
                0.9999987901337396,
                0.9999991684715758,
                0.9999989322972572,
                0.9999989322968754,
                0.9999987901344607
            ],
            [
                0.9999987901338838,
                0.999998790134605,
                0.9999987901338838,
                0.9999986290426297,
                0.999996711250935,
                0.9999984465015047,
                0.999998005269803,
                0.9999984465018751,
                0.9999984465015047,
                0.9999970976890531
            ],
            [
                0.9999974387187053,
                0.9999984465015047,
                0.9999970976873229,
                0.9999962733616046,
                0.9999952149072169,
                0.9999974387180948,
                0.999998629042303,
                0.9999957771655493,
                0.9999986290421394,
                0.9999967112521109
            ],
            [
                0.9999980052705164,
                0.9999967112517189,
                0.9999987901344607,
                0.999998446502801,
                0.9999987901347491,
                0.9999970976890531,
                0.9999986290429566,
                0.9999986290421395,
                0.9999982396561572,
                0.9999982396572064
            ],
            [
                0.9999990577556307,
                0.9999974387184,
                0.9999980052702786,
                0.9999970976883609,
                0.9999962733607162,
                0.9999952149043647,
                0.9999962733611603,
                0.999997097687669,
                0.9999970976880149,
                0.9999967112493665
            ],
            [
                0.9999984465016899,
                0.9999970976887069,
                0.9999977396762411,
                0.999997097689053,
                0.9999977396762411,
                0.9999977396757023,
                0.9999962733616047,
                0.9999977396748938,
                0.9999967112505427,
                0.9999977396765105
            ],
            [
                0.999998790134605,
                0.9999987901344607,
                0.9999962733598278,
                0.999998629042303,
                0.9999991684715759,
                0.9999987901347491,
                0.9999984465024306,
                0.999998790134605,
                0.9999989322973845,
                0.9999980052695652
            ]
        ]
    },
    {
        "q_id": "8905_mmlu_math",
        "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,
            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": [
            [
                0.999820472076904,
                0.9999687980960746,
                0.9999038975736655,
                0.9999785550464778,
                0.9999810748517634,
                0.9999938558239334,
                0.999903897596715,
                0.9997694932873096,
                0.9999885212277707,
                0.9999785550439183
            ],
            [
                0.9999756997621677,
                0.9999967112509347,
                0.9998766054692311,
                0.9999910603047619,
                0.9999898700126446,
                0.9999885212277698,
                0.999996711249759,
                0.9999885212305063,
                0.9999967112513267,
                0.9999970976876692
            ],
            [
                0.9998204719487146,
                0.9999921107336531,
                0.9999832985781592,
                0.9999646437577242,
                0.9999910603058282,
                0.9999832985721862,
                0.9999546021259605,
                0.9999952149049349,
                0.9999785550413627,
                0.9999957771665557
            ],
            [
                0.9988304894973705,
                0.99408893027909,
                0.7310585903489892,
                0.9980732652619002,
                0.962673113726775,
                0.5,
                0.9999038975393034,
                0.6513548714339145,
                0.9324533022906133,
                0.0758581847220642
            ],
            [
                0.99994855779862,
                0.9999756997563729,
                0.9999038976194506,
                0.999998005269803,
                0.9999869928715388,
                0.999972464315468,
                0.9999417087344882,
                0.9999885212277699,
                0.9997694933675934,
                0.9998415638399263
            ],
            [
                0.9989677689297531,
                0.9999151889688344,
                0.9933071493852894,
                0.9993736659000402,
                0.9998415638021374,
                0.9982992772086748,
                0.9997040429358706,
                0.9998204720127244,
                0.999964643736671,
                0.9997040428304383
            ],
            [
                0.999876605454525,
                0.9990889489884927,
                0.999954602131393,
                0.9997694931750665,
                0.9999151889385265,
                0.9998415637268017,
                0.9959298622954295,
                0.9999599362984696,
                0.9999339478474597,
                0.9996200154251874
            ],
            [
                0.9998415637830782,
                0.9996646497708933,
                0.9999599363125974,
                0.9959298624634251,
                0.9999339478474549,
                0.9999832985761661,
                0.9999687980774743,
                0.9999485578047429,
                0.9996200154695172,
                0.9997965730996415
            ],
            [
                0.9999339478239027,
                0.9999910602994334,
                0.9999756997505781,
                0.9999417087275172,
                0.9999832985741752,
                0.9999485577802313,
                0.9999151889688264,
                0.9997388096300018,
                0.9999485578047843,
                0.9999852610162724
            ],
            [
                0.9999810748472509,
                0.9999898700041906,
                0.9999756997505882,
                0.9999930377420911,
                0.9999869928715369,
                0.9999339478711452,
                0.9999910603068937,
                0.9999785550490333,
                0.9999852610145151,
                0.9999599363126054
            ],
            [
                0.9998601778932509,
                0.9997040428313339,
                0.9998601779425421,
                0.9999417087344838,
                0.9998601778593273,
                0.9995694430129921,
                0.999972464315468,
                0.9997965730753606,
                0.9998601779260412,
                0.9989677691680393
            ],
            [
                0.9999945777829695,
                0.9997040427600956,
                0.9999832985701931,
                0.9999832985781574,
                0.9999810748449914,
                0.9999957771645418,
                0.9999151889181905,
                0.9999974387184,
                0.9999646437619356,
                0.9999546021151652
            ],
            [
                0.9999339478789965,
                0.9993736659696304,
                0.9986749778523717,
                0.9997388095674719,
                0.9995694428619476,
                0.9998204719913973,
                0.9999930377462403,
                0.999925153745984,
                0.9998204720340828,
                0.9999785550515862
            ],
            [
                0.9997694933127764,
                0.9999869928730875,
                0.9999485578047517,
                0.9999546021097148,
                0.9998204719916403,
                0.9998911030389356,
                0.9999251537906513,
                0.9999417087553606,
                0.9999599362934916,
                0.9999417087484042
            ],
            [
                0.9999251537370814,
                0.999933947863201,
                0.9999687980997901,
                0.999991060306894,
                0.9999646437450873,
                0.9999992661791944,
                0.9999546021314075,
                0.9999599363173987,
                0.9999546021205374,
                0.9996200154702357
            ],
            [
                0.9959298627371258,
                0.9996200155598238,
                0.9978172840085039,
                0.9046505395995927,
                0.999903897573697,
                0.9998911030648799,
                0.9995694429100579,
                0.9999417087483918,
                0.9999339478474645,
                0.9999687980886323
            ],
            [
                0.9999339478789471,
                0.9999930377462404,
                0.9999687980811924,
                0.9999938558268633,
                0.999959936307828,
                0.9999485577618298,
                0.9999485578047517,
                0.9999921107355335,
                0.9999038975736046,
                0.999989870006605
            ],
            [
                0.9997694932572485,
                0.9989677688058682,
                0.9999251537727529,
                0.9933071485680133,
                0.9999646437619356,
                0.9997388097844571,
                0.9924227589702542,
                0.9999251537995719,
                0.9999151889486347,
                0.9993736657528445
            ],
            [
                5.829127939137956e-05,
                2.144495862967221e-05,
                1.3007131564903626e-05,
                5.422220908402905e-06,
                4.7850950649408664e-06,
                8.939699498587217e-06,
                2.144494583184375e-05,
                2.4300232034838305e-05,
                4.2228349546493465e-06,
                7.88926258381982e-06
            ],
            [
                0.9995121427666085,
                0.9995694430145703,
                0.9999687980997901,
                0.9999687980737704,
                0.9984988175710332,
                0.999860177926084,
                0.9999687980960721,
                0.9999952149032243,
                0.9999810748562796,
                0.9999646437577359
            ],
            [
                2.902312677060767e-06,
                2.260325375615501e-06,
                2.2603237589676295e-06,
                4.78509563555309e-06,
                2.144494074201677e-05,
                1.670141587031992e-05,
                1.994729483680993e-06,
                6.144172404218801e-06,
                1.5534975693707442e-06,
                1.3007131564643372e-05
            ],
            [
                0.9997388096918782,
                0.9997694933131654,
                0.9991959139541894,
                0.9996200154698709,
                0.99829927797557,
                0.9997388096599749,
                0.999978555041362,
                0.9999869928730862,
                0.9999485577618208,
                0.999738809691445
            ],
            [
                0.9999599363030566,
                0.9999785550490299,
                0.9999646437408634,
                0.9998911031037632,
                0.9999151889384686,
                0.9998766054693118,
                0.9998766053809797,
                0.999993855826863,
                0.9999785550464785,
                0.9999885212359801
            ],
            [
                0.9997040429361289,
                0.9999485577740995,
                0.9975273764534298,
                0.9997965729794797,
                0.9964063980355135,
                0.99991518895867,
                0.9997040429724672,
                0.9999038975506866,
                0.9992903296502691,
                0.9991959142469933
            ],
            [
                0.9999251537638258,
                0.9999967112517191,
                0.9998204720553445,
                0.9999810748540158,
                0.9998766054692957,
                0.9999970976890528,
                0.9999485577740842,
                0.9998601778594107,
                0.9998601778593477,
                0.9999910603004992
            ],
            [
                0.999820471969804,
                0.9999646437619387,
                0.9980732651280264,
                0.999975699756372,
                0.9999151889283289,
                0.9992903296205894,
                0.998674977700942,
                0.9978172831875187,
                0.9991959142396977,
                0.9999546021421849
            ],
            [
                0.9999599362934992,
                0.9999756997505781,
                0.9991959139513366,
                0.9999485577740932,
                0.9999646437408619,
                0.9998911031037379,
                0.9999810748495068,
                0.9999339478474597,
                0.9999898700126462,
                0.9998911031037632
            ],
            [
                0.9988304898909246,
                0.9999646437535052,
                0.9999885212305066,
                0.9998911031298519,
                0.9980732656147181,
                0.9991959140536613,
                0.9999485577618125,
                0.9999785550541448,
                0.998967769172721,
                0.9999417087414129
            ],
            [
                0.9999599362983339,
                0.9998766053663525,
                0.999512142825901,
                0.999925153739876,
                0.9999339478711028,
                0.9999898700053974,
                0.9994472213952024,
                0.9999599363221412,
                0.9999810748450013,
                0.9998601779594297
            ],
            [
                0.9991959142485832,
                0.9998911031037759,
                0.9999546021476186,
                0.9999038975965528,
                0.9999910603058275,
                0.9997040429013149,
                0.9999646437535268,
                0.9989677689412771,
                0.9997965729539469,
                0.9999417087275172
            ],
            [
                0.9999810748449934,
                0.9999945777810305,
                0.9999938558268633,
                0.9999832985821387,
                0.9999785550541473,
                0.9998415637457365,
                0.9999967112513267,
                0.9998601779093998,
                0.999972464315468,
                0.9999885212332431
            ],
            [
                0.999992110740236,
                0.9998911030648276,
                0.9999724643121839,
                0.9998204719915698,
                0.9999910603058276,
                0.9999785550592579,
                0.9999756997505788,
                0.9999962733607158,
                0.9999785550439222,
                0.9999687980774697
            ],
            [
                0.9995121428855623,
                0.9998204720339496,
                0.9999546021476033,
                0.9995121428860448,
                0.999954602125951,
                0.9999417087205802,
                0.9999930377445804,
                0.999986992876188,
                0.9999599363030427,
                0.9997694933399669
            ],
            [
                0.9999724643121858,
                0.9999417087275647,
                0.9999852610197881,
                0.9998601779425829,
                0.9996646497699858,
                0.9995121429425842,
                0.9999910603004991,
                0.9995694429619008,
                0.9997040429730182,
                0.9999546021097148
            ],
            [
                0.9999885212277692,
                0.9986749773746673,
                0.9999910603005002,
                0.9999724643056221,
                0.999988521231875,
                0.9999810748472474,
                0.9997694933401279,
                0.9998911030648022,
                0.9999810748562717,
                0.9997694933675396
            ],
            [
                0.9999810748562752,
                0.9999546021367783,
                0.9999930377420906,
                0.9999339478631961,
                0.9999251537906008,
                0.9999930377462406,
                0.9999852610197864,
                0.9999339478317002,
                0.9997965730267956,
                0.9998204720344249
            ],
            [
                0.9999785550592636,
                0.9999930377437504,
                0.9999910603026312,
                0.9999974387168733,
                0.9999898700090204,
                0.9999832985701952,
                0.9999982396561571,
                0.9999967112513267,
                0.9999970976883609,
                0.9999984465024306
            ],
            [
                0.9999038975964927,
                0.9999756997621669,
                0.999933947878971,
                0.9999687980886298,
                0.9999957771645422,
                0.9999785550439235,
                0.9999785550592568,
                0.9999687980737564,
                0.9999785550541436,
                0.9999646437366505
            ],
            [
                0.9999982396565769,
                0.9999151889384605,
                0.9999930377445806,
                0.9999756997534754,
                0.9999921107383549,
                0.9999832985781563,
                0.9999038976080912,
                0.9999869928699874,
                0.999997097686977,
                0.999997438717484
            ],
            [
                0.9999546021151381,
                0.9998766054251126,
                0.9999898700078131,
                0.9999938558232008,
                0.999903897539223,
                0.9999646437535129,
                0.9997040427962616,
                0.9998911030647778,
                0.9999724642957772,
                0.9997965730028551
            ],
            [
                0.9997040429022191,
                0.9999756997650677,
                0.9999646437492984,
                0.9999724643187513,
                0.9999945777790912,
                0.9998601778592866,
                0.9999952149072167,
                0.9999938558224687,
                0.9999869928653333,
                0.999915188928401
            ],
            [
                0.9999869928653361,
                0.9998415637834425,
                0.9998204719697047,
                0.9999852610162742,
                0.9997388097843127,
                0.9995694428631875,
                0.9997965730753162,
                0.9999546021205351,
                0.9995694429621763,
                0.9999724642990531
            ],
            [
                0.9993736658981092,
                0.9996200154250436,
                0.9995121429410231,
                1.4738978457041559e-05,
                0.9998766054545734,
                0.9997040428297409,
                0.9994472214657896,
                0.053403333754516925,
                0.9992903294596016,
                0.9997040428309721
            ],
            [
                0.9993736657546297,
                0.999860177859368,
                0.9997388096593592,
                0.9997388097223529,
                0.9986749775606039,
                0.9997388097536861,
                0.9997694932575167,
                0.9999938558253981,
                0.9996646498904032,
                0.9996200155154941
            ],
            [
                0.999769493367325,
                0.9999810748517602,
                0.9999417087205958,
                0.9999485577679742,
                0.998299277700239,
                0.9999852610197864,
                0.9998601778594738,
                0.9999910603068939,
                0.9997965730753606,
                0.9999810748517622
            ],
            [
                0.9997388095975969,
                0.9999417087136283,
                0.9999785550490452,
                0.9999910603026305,
                0.9999546021313743,
                0.9998766053664531,
                0.9998204720986045,
                0.9999974387177893,
                0.9999151889891026,
                0.9995121428824402
            ],
            [
                0.9999952149060758,
                0.9999832985741748,
                0.9999974387180947,
                0.9999885212346117,
                0.999993855825398,
                0.9999785550515873,
                0.9999852610215424,
                0.999994577782323,
                0.999997097686977,
                0.9999339478238761
            ],
            [
                0.9999898700114356,
                0.9999962733616046,
                0.9999885212305059,
                0.9999832985721833,
                0.9999832985721836,
                0.9999996072137998,
                0.9999962733598274,
                0.999975699765066,
                0.9999724643023389,
                0.9999952149060757
            ],
            [
                0.9999987901346049,
                0.9999869928684358,
                0.9999646437450794,
                0.9999832985701956,
                0.9999832985841333,
                0.9999938558232009,
                0.9999852610180288,
                0.999997438717484,
                0.9999962733620487,
                0.9999952149055052
            ],
            [
                0.9999852610110006,
                0.9999151889687629,
                0.9999251537638694,
                0.9990889486727209,
                0.9999785550490321,
                0.9999952149066466,
                0.9997965730507836,
                0.9999832985741745,
                0.999891103038858,
                0.9999869928715365
            ],
            [
                0.9999417087553479,
                0.9999810748427375,
                0.999876605410471,
                0.9999852610145165,
                0.9999885212359799,
                0.999975699762166,
                0.9999885212359798,
                0.999972464315473,
                0.9999417087136283,
                0.9999417087136648
            ],
            [
                0.9994472212601381,
                0.9999930377454103,
                0.9999251537905887,
                0.9996646499732083,
                0.9999930377462403,
                0.9999885212264011,
                0.9999832985701927,
                0.9999151889890187,
                0.999981074842736,
                0.9994472214616412
            ],
            [
                0.9997040428305244,
                0.999891103064853,
                0.9990889486584158,
                0.9999810748562722,
                0.9999417087275647,
                0.9998601779092554,
                0.9992903294551022,
                0.9999945777790912,
                0.9995694429098825,
                0.9999339478789813
            ],
            [
                0.9993736657538281,
                0.9999251537370814,
                0.9995121427654164,
                0.9998601778929518,
                0.999964643732444,
                0.9999599363126097,
                0.9999687980886276,
                0.9999952149072167,
                0.9998911030647413,
                0.9999546021151652
            ],
            [
                0.999876605366322,
                0.999954602131396,
                0.9999038976195017,
                0.9999930377462406,
                0.9999687980960662,
                0.9999756997534802,
                0.9999970976883609,
                0.9999546021205622,
                0.9999724643056332,
                0.9999852610232993
            ],
            [
                0.9999898700114376,
                0.9999885212318768,
                0.999996273358939,
                0.9999687980998007,
                0.9999869928715361,
                0.9999921107345933,
                0.9999898700066059,
                0.9999938558239334,
                0.9999251537906579,
                0.9999687980812105
            ],
            [
                0.9999952149032239,
                0.9999724642957752,
                0.9999938558261307,
                0.9999417087484003,
                0.9999724643089016,
                0.9999687980997901,
                0.9999957771650453,
                0.9999885212264015,
                0.9999910603015646,
                0.9999646437619434
            ],
            [
                0.9997040427609136,
                0.9998204720766716,
                0.9997388097856731,
                0.9998911030777198,
                0.9991959139589127,
                0.9991959142517634,
                0.9978172837377158,
                0.999841563726562,
                0.9999885212277696,
                0.9996200154693735
            ],
            [
                0.9998911031167924,
                0.9996646498100469,
                0.9998415637646436,
                0.9999646437492894,
                0.999876605439966,
                0.9999151889283214,
                0.9999599363221504,
                0.9999852610110004,
                0.9999646437492894,
                0.999985261021543
            ],
            [
                0.9997040429725532,
                0.9998911030777935,
                0.9999646437366446,
                0.9999038975850487,
                0.9999785550566983,
                0.9982992779220059,
                0.999620015423684,
                0.9999810748517607,
                0.9997388096912398,
                0.9998766054398044
            ],
            [
                0.9996646498500006,
                0.9994472213894782,
                0.999968798081195,
                0.9999599363221742,
                0.9996646497705518,
                0.9999339478474549,
                0.9996646500128009,
                0.9999038975392727,
                0.9999417087136174,
                0.9998601779760934
            ],
            [
                0.9999810748585277,
                0.9999921107355337,
                0.9997388096283755,
                0.9999910602994336,
                0.999195914056514,
                0.9999885212291378,
                0.9995121429387809,
                0.9999038976079275,
                0.9999485577740932,
                0.9968273173062583
            ],
            [
                0.9999898700078128,
                0.9999938558275954,
                0.998967768816432,
                0.9997965729788819,
                0.9999646437324302,
                0.9997388096916577,
                0.9998601778593477,
                0.9998601779094832,
                0.9999151889384377,
                0.9999417087275244
            ],
            [
                0.9999885212359795,
                0.9988304894737082,
                0.9992903296260383,
                0.999664649732569,
                0.9998415638404773,
                0.9997965729540741,
                0.997527377155773,
                0.999941708734492,
                0.999664649850908,
                0.9999885212318752
            ],
            [
                0.999891103090875,
                0.9999687980997926,
                0.9997965730023874,
                0.9999970976866309,
                0.9998601778760724,
                0.9997040429363098,
                0.9999251537817575,
                0.9998415637266933,
                0.9999687980849105,
                0.9999151889889952
            ],
            [
                0.9999646437366521,
                0.9999832985701939,
                0.99994855779862,
                0.9999546021151239,
                0.9999599362887301,
                0.9999852610197877,
                0.9999832985821392,
                0.9999910603068934,
                0.9994472212566329,
                0.9999599363030465
            ],
            [
                0.9996646499318398,
                0.9999151889182053,
                0.9999339478395777,
                0.9999038976079472,
                0.9999832985701935,
                0.994088930815402,
                0.9997388096285122,
                0.9994472213860052,
                0.9999687980960696,
                0.9999945777810303
            ],
            [
                0.9999885212305084,
                0.9999898700090202,
                0.9999687980923594,
                0.9999957771650453,
                0.9999898700102279,
                0.9999339478711133,
                0.9999756997563752,
                0.9999989322975118,
                0.9999974387184,
                0.999981074844992
            ],
            [
                0.999975699759271,
                0.999664649850225,
                0.9999339478317386,
                0.999738809784176,
                0.9998204719485109,
                0.9999646437535178,
                0.9998601779260005,
                0.9998415637078668,
                0.9995694429123752,
                0.9999785550413609
            ],
            [
                0.9994472213942698,
                0.9971990735394745,
                0.9998204719699032,
                0.999664649811647,
                0.9324533046369554,
                0.9933071478683754,
                0.9996200155148418,
                0.9796676462863219,
                0.9978172838700672,
                0.997527376725638
            ],
            [
                0.9993736659004411,
                0.9998415637644547,
                0.9999852610215436,
                0.9998911030907847,
                0.9990889487655981,
                0.9998204720340488,
                0.999915188928337,
                0.9995694429099702,
                0.9999339478238412,
                0.9991959140511358
            ],
            [
                0.9999038975621306,
                0.9998911030777808,
                0.9995121427709511,
                0.999876605395702,
                0.9999756997679586,
                0.999841563783258,
                0.9999599363125902,
                0.9997965730265855,
                0.9999810748472479,
                0.9999038975735655
            ],
            [
                0.9998911030777935,
                0.9999038975621508,
                0.9999687980811902,
                0.9997965729786599,
                0.9999724642957734,
                0.9999251537549547,
                0.9998415638209155,
                0.9999885212277693,
                0.9999898700066052,
                0.9998415637267211
            ],
            [
                0.9999724642957725,
                0.9999251537459781,
                0.9999832985721853,
                0.9999785550592579,
                0.9999339478317094,
                0.9998911030778569,
                0.9999852610110012,
                0.9999930377437504,
                0.9999599362982855,
                0.9999832985821384
            ],
            [
                0.9999546021476033,
                0.999983298578157,
                0.9999945777829696,
                0.9997965730996001,
                0.9999417087414205,
                0.9999910603068931,
                0.9999974387177893,
                0.9999980052700408,
                0.9998911030908354,
                0.9995121427642527
            ],
            [
                0.9999546021205374,
                0.9997694933127764,
                0.9999599363221466,
                0.9982992772780512,
                0.9999485577741123,
                0.9626731094431571,
                0.9999038975965423,
                0.99979657309939,
                0.9999151889688264,
                0.9820137907616943
            ],
            [
                0.9999910603058275,
                0.9999885212332428,
                0.9999810748540162,
                0.9996646498498932,
                0.999959936298279,
                0.999841563783258,
                0.9999485577679873,
                0.9999756997650643,
                0.9999546021151535,
                0.9999417087275647
            ],
            [
                0.9999485577802684,
                0.9999785550490472,
                0.9999945777829699,
                0.9999485577863757,
                0.9999785550515903,
                0.9999898700102287,
                0.9999852610215424,
                0.9999945777797377,
                0.9998766054251933,
                0.9998911030649464
            ],
            [
                0.9999810748449934,
                0.9999485577924913,
                0.99998987000419,
                0.9999646437619328,
                0.9999869928668845,
                0.999983298578157,
                0.9999957771670588,
                0.9999485577863757,
                0.9999910603004988,
                0.9999038975850585
            ],
            [
                0.9998204719482784,
                0.9998911030649053,
                0.9998766054250983,
                0.9992903297092566,
                0.9998601779426847,
                0.9995121428828092,
                0.9997388096281096,
                0.9999785550567073,
                0.9998415638400854,
                0.9999038975965528
            ],
            [
                0.9999417087344801,
                0.9998911031037506,
                0.9999885212264009,
                0.9997388097532681,
                0.9999485577618298,
                0.999948557780225,
                0.9999687980811988,
                0.9999038975393356,
                0.9999756997621738,
                0.9999251537995654
            ],
            [
                0.999512142880567,
                0.9996646497329202,
                0.999948557780219,
                0.9999599362934845,
                0.9999339478632202,
                0.9982992775122704,
                0.999925153745984,
                0.9999810748495044,
                0.9989677689401968,
                0.9992903294581156
            ],
            [
                0.9999724642957707,
                0.9999785550592561,
                0.9999646437324375,
                0.9999885212264013,
                0.9999724642990531,
                0.9996200154242477,
                0.9999962733607162,
                0.9999546021151215,
                0.9999339478789965,
                0.9999485577864269
            ],
            [
                0.9999646437492881,
                0.9999869928715357,
                0.999903897550667,
                0.9999687980737552,
                0.9999756997650613,
                0.9991959140610036,
                0.9999339478395777,
                0.9999921107402358,
                0.999915188958662,
                0.999820471969804
            ],
            [
                0.9999546021151283,
                0.9999151889586856,
                0.9999251537638889,
                0.9999417087206043,
                0.9999251537817047,
                0.9999646437577306,
                0.999891103129683,
                0.9998415637077608,
                0.9999646437408634,
                0.9998766054251449
            ],
            [
                0.9999339478474694,
                0.9998911030778442,
                0.9999417087414095,
                0.9999810748472489,
                0.9999646437450808,
                0.9997965730265855,
                0.9999756997650613,
                0.9998766053957971,
                0.9998601779592853,
                0.9992903296318586
            ],
            [
                0.9999687980811913,
                0.999993037740431,
                0.9999339478474645,
                0.9995694428599811,
                0.999925153745996,
                0.9999417087206002,
                0.9995694429619008,
                0.9998601779093775,
                0.9994472213914721,
                0.9997965729548229
            ],
            [
                0.9999646437450794,
                0.9999724643187504,
                0.9998766054399983,
                0.9999417087275282,
                0.9999251537906008,
                0.9999485577924853,
                0.9999151889586466,
                0.9999646437577242,
                0.9998601779095931,
                0.9999417087345258
            ],
            [
                0.9989677689302332,
                0.9975273770489571,
                0.9995121427666085,
                0.9840936079966184,
                0.9980732656397915,
                0.9990889488142884,
                0.9947798733948098,
                0.9959298631995857,
                0.6513548782017745,
                0.9993736658235275
            ],
            [
                0.999992110740236,
                0.9999646437408665,
                0.9999938558239333,
                0.9999756997534747,
                0.9999810748449929,
                0.9998204719703159,
                0.9999885212264029,
                0.9998204719912301,
                0.999978555056703,
                0.9999339478711082
            ],
            [
                0.9999038975735655,
                0.9999687980886505,
                0.9999785550566999,
                0.9996200154271773,
                0.9890130583308034,
                0.9998911030778569,
                0.9989677690587997,
                0.9991959140467399,
                0.9999485577925467,
                0.9990889489864794
            ],
            [
                0.9999810748427375,
                0.9999599362982653,
                0.9999810748562717,
                0.9998911030780216,
                0.9999599363078477,
                0.9999339478632303,
                0.9999938558232011,
                0.9999984465026158,
                0.9999930377429205,
                0.9999785550464753
            ],
            [
                0.9999810748449929,
                0.999994577782323,
                0.9999885212264035,
                0.99995460213136,
                0.999981074844992,
                0.9999810748562757,
                0.9999785550413712,
                0.9999485577986424,
                0.9999646437408728,
                0.9999810748449924
            ],
            [
                0.9964063970734305,
                0.9982992775644509,
                0.999820472076609,
                0.9997388096289302,
                0.9971990729984124,
                0.9997694933119682,
                0.9995121428248224,
                0.9989677689157079,
                0.9984988177750217,
                0.9999724643056319
            ],
            [
                0.9999938558253982,
                0.9999952149055054,
                0.9997040427620245,
                0.9999852610110015,
                0.9999910603036963,
                0.9999832985821404,
                0.9999756997650643,
                0.9999646437366568,
                0.9999921107336527,
                0.9999980052707541
            ],
            [
                0.9999687980960733,
                0.9999957771665555,
                0.9997388096917338,
                0.9998204719912641,
                0.9999546021097371,
                0.9999785550567005,
                0.9999417087205921,
                0.9999930377404308,
                0.9995694429103334,
                0.9999251537816921
            ],
            [
                0.999903897596573,
                0.9998766053809959,
                0.9998911030907467,
                0.9982992772976188,
                0.9999151889384297,
                0.9999485578047547,
                0.9999151889586547,
                0.9998204720124266,
                0.9999885212346111,
                0.999796573075402
            ],
            [
                0.9999987901341723,
                0.9999910602994335,
                0.9999832985781555,
                0.9999810748495063,
                0.9999952149043645,
                0.9999485577679526,
                0.9999546021313821,
                0.9999945777803839,
                0.9999485577924853,
                0.9999646437619342
            ],
            [
                0.999512142881617,
                0.9999038975392328,
                0.9998204719486806,
                0.9999038975623201,
                0.9999832985781563,
                0.9999599363173749,
                0.9996646497713518,
                0.9999885212359795,
                0.999941708741406,
                0.9999869928653335
            ],
            [
                0.9999485577740842,
                0.9996646498512495,
                0.9999885212264013,
                0.9999251537995099,
                0.9999599363030427,
                0.999954602136796,
                0.999964643732436,
                0.9998911030519267,
                0.9998204719913294,
                0.9998911030907103
            ],
            [
                0.9999151889182442,
                0.9999417087414205,
                0.9999785550439207,
                0.9999687980774782,
                0.9999885212291378,
                0.999959936288716,
                0.9999599362982833,
                0.9999885212277696,
                0.9999967112493664,
                0.9999038975621809
            ],
            [
                0.9997694931750665,
                0.9999151889182362,
                0.99997246431547,
                0.9999038975736445,
                0.9999251537816801,
                0.9998911030778062,
                0.9999599363221447,
                0.9999417087205764,
                0.9999967112505427,
                0.9999599363030408
            ],
            [
                0.999991060304762,
                0.9999986290423029,
                0.9999974387187053,
                0.9999984465020603,
                0.9999980052709918,
                0.9999970976866309,
                0.9999980052709919,
                0.999997097688361,
                0.9999952149072167,
                0.9999910603026306
            ],
            [
                0.9998204720340488,
                0.9999724643187544,
                0.9992903296198464,
                0.999738809722216,
                0.9999810748540218,
                0.9997040428661479,
                0.9998911030388326,
                0.999978555041368,
                0.9998911030518111,
                0.9997040427599234
            ],
            [
                0.9999869928653331,
                0.9999687980737515,
                0.9999724642990565,
                0.9999687980737526,
                0.9999687980997866,
                0.999997097686631,
                0.9999038975737291,
                0.9999724643089064,
                0.999988521233244,
                0.9999646437324458
            ],
            [
                0.9996646498901787,
                0.9999687980811962,
                0.9999921107345932,
                0.9999485577863566,
                0.9999646437366552,
                0.9999938558246657,
                0.9998601778760724,
                0.9998911030909019,
                0.9999038976079563,
                0.9999898700078126
            ],
            [
                0.9999646437577242,
                0.996406397004234,
                0.9998766053810425,
                0.9997694933396449,
                0.9998204720767369,
                0.9996200155610399,
                0.9975273763379997,
                0.9990889489772076,
                0.10669060317692274,
                0.9990889489852608
            ],
            [
                0.9998601778592866,
                0.9999724643187523,
                0.9998601779426236,
                0.9999417087344801,
                0.9999251537817047,
                0.9999417087136402,
                0.9999724643023361,
                0.9998766053810263,
                0.9998766054693118,
                0.9999687980997913
            ],
            [
                0.9999546021259791,
                0.9997965730762041,
                0.9999687980811937,
                0.9998766053959319,
                0.9999852610180304,
                0.9992903294560929,
                0.9999151889586775,
                0.9999962733616045,
                0.9999945777784447,
                0.9999930377420913
            ],
            [
                1.7603440527046419e-06,
                3.726641061058432e-06,
                7.889262585441413e-06,
                8.939700566565793e-06,
                6.1441767990323395e-06,
                3.288748673295719e-06,
                6.962259569560613e-06,
                5.422217676925328e-06,
                5.4222215552470286e-06,
                5.422217676979575e-06
            ],
            [
                0.999981074849503,
                0.9998601779427884,
                0.9999151889789265,
                0.9999546021205397,
                0.9998204720341847,
                0.9999898700126436,
                0.9998911030518111,
                0.9998766053959498,
                0.9999724643187504,
                0.9999151889485612
            ],
            [
                0.9999546021097218,
                0.9999724643089007,
                0.9996646498514739,
                0.9999756997650636,
                0.9999687980923607,
                0.9999417087345085,
                0.9999898700114355,
                0.9999646437366654,
                0.9999417087414566,
                0.9999869928715361
            ],
            [
                0.9999930377437501,
                0.9999885212346111,
                0.9999339478317142,
                0.9999957771665555,
                0.9999785550541442,
                0.9999930377429204,
                0.9999885212291383,
                0.9999785550592574,
                0.9999869928653338,
                0.9992903294543592
            ],
            [
                0.999915188978879,
                0.9999599363221718,
                0.9999599363078128,
                0.9999785550515891,
                0.9999599363125955,
                0.9999756997592703,
                0.9999251537728095,
                0.9999756997534754,
                0.9999945777823229,
                0.9999599362982708
            ],
            [
                0.04208772776542873,
                0.99539042755996,
                0.9875683484950792,
                0.9997388097262362,
                0.2689414213699951,
                0.999569443020545,
                0.40733340004593027,
                0.8670357477770336,
                0.37754067580180184,
                0.002472623170417469
            ],
            [
                0.9998766054105537,
                0.9999646437492907,
                0.999975699762166,
                0.9999339478631961,
                0.9999852610127608,
                0.999860177942705,
                0.9999852610110079,
                0.9997965729791543,
                0.9998204720980979,
                0.9999339478396116
            ],
            [
                0.9999546021205351,
                0.9999339478554895,
                0.9999930377429203,
                0.987568348769494,
                0.9995694428602566,
                0.9999810748540162,
                0.9999724643154672,
                0.9999785550541426,
                0.9995694430172133,
                0.9999724643023389
            ],
            [
                0.9982992774855872,
                0.9999485577924977,
                0.9997040429002644,
                0.9999910602994353,
                0.9994472212587553,
                0.999796572978571,
                0.9998601779095057,
                0.9989677688100697,
                0.9999810748427396,
                0.9998911030647897
            ],
            [
                0.9999756997592674,
                0.9999417087344724,
                0.9999756997505774,
                0.9997965729795745,
                0.9999151889889872,
                0.9999810748540182,
                0.9999251537817111,
                0.9992903294467226,
                0.9999810748450007,
                0.9995121428813901
            ],
            [
                0.9997965730025976,
                0.9997965729538639,
                0.9999687980774675,
                0.9996646500109276,
                0.9998911031037379,
                0.9998601779259395,
                0.9999417087344652,
                0.9997965729785296,
                0.9999869928746377,
                0.9996200155601777
            ],
            [
                0.9998766053810425,
                0.9998601778925937,
                0.99996879809608,
                0.9998766053958816,
                0.9999546021259631,
                0.9999485577618268,
                0.9999785550490321,
                0.9998415637832303,
                0.9999724642957742,
                0.9999485578047708
            ],
            [
                0.9999546021259709,
                0.9999921107336528,
                0.9999646437619467,
                0.9999339478238862,
                0.9999869928668843,
                0.9999938558275955,
                0.999981074842744,
                0.9999910603068932,
                0.9999810748449955,
                0.9999869928653358
            ],
            [
                0.9999151889687703,
                0.9999687980960662,
                0.9999810748517638,
                0.9999869928653335,
                0.9999485577802159,
                0.9999599362934953,
                0.9998766054397883,
                0.9999810748427365,
                0.9999151889485612,
                0.9999832985841293
            ],
            [
                0.9999724642990546,
                0.9999852610233015,
                0.9999756997505795,
                0.9999038975850585,
                0.9999151889587182,
                0.9999251537906317,
                0.9997388097531315,
                0.9999785550567005,
                0.999512142766495,
                0.9999546021259557
            ],
            [
                0.9999785550515873,
                0.999985261011,
                0.9999038975735851,
                0.9999339478474597,
                0.999933947855328,
                0.9995121428801128,
                0.9999930377412605,
                0.9999852610197874,
                0.9999938558232008,
                0.9999832985801471
            ],
            [
                0.9999546021259487,
                0.9999945777797374,
                0.9999898700078126,
                0.9999930377454104,
                0.9999485577618298,
                0.9999930377462405,
                0.9997040429365767,
                0.9997694932850358,
                0.9999885212346123,
                0.9997040427953574
            ],
            [
                0.9999546021422073,
                0.9999869928684358,
                0.9999151889485539,
                0.9997040427966318,
                0.9999910603036961,
                0.9999930377429204,
                0.9999986290427931,
                0.9999921107392957,
                0.9999724643121964,
                0.9997040429384109
            ]
        ]
    },
    {
        "q_id": "8482_mmlu_math",
        "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,
            58,
            59,
            60,
            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,
            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": [
            [
                0.9999996940977366,
                0.9999996072137998,
                0.9999997617630616,
                0.9999996072138465,
                0.999999694097773,
                0.9999996940976272,
                0.9999996940977366,
                0.9999997300421903,
                0.9999995549147359,
                0.9999994284996893
            ],
            [
                0.9999992661786696,
                0.9999993524050473,
                0.9999994284997573,
                0.999999495652712,
                0.9999994956524114,
                0.9999998724808963,
                0.9999998874647574,
                0.999999730042319,
                0.9999994956524716,
                0.999999266178932
            ],
            [
                0.9999991684715759,
                0.9999987901338838,
                0.9999995549151073,
                0.9999980052700408,
                0.9999989322973845,
                0.9999993524050474,
                0.9999997300421903,
                0.9999995549148419,
                0.9999996940978095,
                0.9999994956526519
            ],
            [
                3.120191133017482e-05,
                0.00010889688265614603,
                1.6701415863393463e-05,
                3.1201926214528354e-05,
                0.00012339453007232675,
                3.120190763332158e-05,
                3.5356254890278004e-05,
                3.12019225022362e-05,
                4.5397868567012224e-05,
                5.1442219708855337e-05
            ],
            [
                0.9999996533673375,
                0.9999998555019962,
                0.9999996940977366,
                0.9999996940978095,
                0.9999998362622357,
                0.9999996940977001,
                0.9999997300421903,
                0.9999997617631468,
                0.9999997300421903,
                0.9999996533674615
            ],
            [
                0.9999997300420937,
                0.9999990577549568,
                0.9999997897565587,
                0.999999814460876,
                0.999999730042126,
                0.9999998362622747,
                0.9999997897565587,
                0.9999989322973846,
                0.9999990577549568,
                0.9999977396754327
            ],
            [
                0.9999992661792819,
                0.9999984465020603,
                0.999999266178757,
                0.9999996072136592,
                0.9999999123575881,
                0.9999996072137998,
                0.9999997897566089,
                0.9999996072138934,
                0.9999998874647574,
                0.999999554914789
            ],
            [
                0.9999984465022455,
                0.9999987901343165,
                0.9999987901338839,
                0.9999984465020603,
                0.9999992661791945,
                0.9999996940976271,
                0.9999994956525918,
                0.9999994284992805,
                0.9999996940976272,
                0.99999862904312
            ],
            [
                0.9999996940976636,
                0.9999996940978095,
                0.9999998874647842,
                0.9999995549149481,
                0.9999997617630048,
                0.9999993524054335,
                0.9999996940977002,
                0.9999998555019963,
                0.9999996072138934,
                0.9999994956524716
            ],
            [
                0.999999554914895,
                0.9999996072136125,
                0.999999352404893,
                0.999999352404893,
                0.999999554914895,
                0.9999992661790196,
                0.9999996072138465,
                0.9999977396751633,
                0.9999996940977366,
                0.999999789756634
            ],
            [
                0.9999982396559474,
                0.9999994956525318,
                0.9999986290431201,
                0.9999991684719723,
                0.999999266178757,
                0.999999855502048,
                0.9999989322966208,
                0.9999989322973845,
                0.9999996072136125,
                0.9999992661791071
            ],
            [
                0.9999996072136125,
                0.9999994284994849,
                0.9999995549147889,
                0.9999993524053563,
                0.999999730042126,
                0.9999977396759716,
                0.9999967112501507,
                0.9999997897565838,
                0.9999984465018751,
                0.9999967112513267
            ],
            [
                0.9999996072139402,
                0.9999995549147359,
                0.9999999006879838,
                0.9999994956527121,
                0.9999992661791944,
                0.9999992661791944,
                0.999999266179107,
                0.999999653367379,
                0.9999994956524716,
                0.9999996533672135
            ],
            [
                0.9999995549150011,
                0.9999995549148419,
                0.9999996533674615,
                0.9999993524052019,
                0.9999986290431201,
                0.9999989322968754,
                0.9999997617630332,
                0.9999996533672962,
                0.9999994284994167,
                0.999999730042319
            ],
            [
                0.9999997300422868,
                0.9999996072137998,
                0.9999997897567091,
                0.9999990577554062,
                0.9999998144608317,
                0.9999997300422868,
                0.9999995549150011,
                0.9999997300422225,
                0.9999993524050474,
                0.99999893229713
            ],
            [
                0.9999996940976271,
                0.9999998724809875,
                0.9999998555020135,
                0.9999993524053562,
                0.9999994956524115,
                0.9999994956524115,
                0.9999998144608317,
                0.9999998724808963,
                0.999999814460876,
                0.9999994284996891
            ],
            [
                5.422217676866151e-06,
                1.4738980213985297e-05,
                1.3007130011655787e-05,
                6.962253759157502e-06,
                1.1478770861859053e-05,
                2.4300252313020203e-05,
                7.88926164421493e-06,
                1.370956716519966e-06,
                2.5612822104977725e-06,
                6.9622579086271995e-06
            ],
            [
                0.999999057755743,
                0.9999996072138934,
                0.9999992661788445,
                0.999999730042319,
                0.9999993524051246,
                0.9999999123574941,
                0.9999994284994848,
                0.9999991684717742,
                0.9999994284994849,
                0.9999997300420937
            ],
            [
                0.9999998362622357,
                0.9999996940978825,
                0.9999997617631752,
                0.9999998362623332,
                0.9999991684715759,
                0.9999997617630049,
                0.999999653367379,
                0.9999996533673375,
                0.9999996072136125,
                0.999999653367379
            ],
            [
                0.9999994956527721,
                0.9999997300421581,
                0.9999994284997574,
                0.999999814460876,
                0.99999976176309,
                0.9999994956523514,
                0.999999266179107,
                0.9999997617631469,
                0.9999996072137061,
                0.999999730042126
            ],
            [
                0.9999996940978095,
                0.9999998144608319,
                0.9999995549148419,
                0.9999996533675028,
                0.9999996072137061,
                0.9999998724810027,
                0.9999990577552939,
                0.999999789756684,
                0.9999997300422547,
                0.9999996072138465
            ],
            [
                0.999999266178757,
                0.9999977396746244,
                0.9999987901346049,
                0.9999998874647709,
                0.9999984465024306,
                0.9999994956525317,
                0.9999998144608983,
                0.999999814460876,
                0.9999998555019962,
                0.9999996072137998
            ],
            [
                0.9999995549150011,
                0.9999997897566089,
                0.9999999006880075,
                0.9999997897566589,
                0.9999998144608317,
                0.9999999006880668,
                0.9999997617630616,
                0.9999997300421581,
                0.9999996072139402,
                0.9999994284995529
            ],
            [
                0.9999993524051246,
                0.9999997300421581,
                0.9999994284996891,
                0.9999982396569966,
                0.9999989322972572,
                0.9999984465024306,
                0.999997097688361,
                0.9999996072138934,
                0.9999992661787571,
                0.9999993524053562
            ],
            [
                0.9999997617630616,
                0.9999996940977366,
                0.9999992661791944,
                0.9999986290421394,
                0.9999996072138465,
                0.9999990577556308,
                0.9999996533675028,
                0.9999996072137998,
                0.9999997897566338,
                0.9999997617631752
            ],
            [
                0.0005527785221511195,
                0.0001233945450100987,
                0.0002611903988844915,
                3.53562675293277e-05,
                0.00015843615881503027,
                0.0002305066852249182,
                0.0002959571608560093,
                0.00013982209003863654,
                4.53978686205205e-05,
                0.00017952800719214757
            ],
            [
                0.9999989322968754,
                0.9999996072137061,
                0.999999352404893,
                0.9999994284995529,
                0.9999994284995529,
                0.9999994956523514,
                0.9999994284996212,
                0.9999994956527722,
                0.9999989322966208,
                0.9999993524052019
            ],
            [
                0.9999993524053563,
                0.9999995549147358,
                0.9999999006880549,
                0.999999789756684,
                0.9999998144609423,
                0.999999554914895,
                0.9999995549150011,
                0.9999992661786695,
                0.9999997300422225,
                0.999999855501979
            ],
            [
                0.9999998874647574,
                0.9999993524053562,
                0.9999995549149481,
                0.9999994956523514,
                0.999999730042126,
                0.9999998874647709,
                0.9999992661790196,
                0.9999993524054334,
                0.9999994956523512,
                0.999999653367379
            ],
            [
                0.9999998555020135,
                0.999999730042319,
                0.9999996533673375,
                0.9999998144608538,
                0.9999998362622942,
                0.9999997617630616,
                0.9999998724809419,
                0.9999996533673375,
                0.9999998362623528,
                0.9999998362622357
            ],
            [
                0.9999997300422547,
                0.9999995549148419,
                0.9999999006881022,
                0.9999989322973845,
                0.9999994956527121,
                0.9999996940976636,
                0.9999997617630049,
                0.9999998555020306,
                0.9999991684720715,
                0.9999998144608538
            ],
            [
                0.9999996940978095,
                0.9999996533672962,
                0.9999996533672549,
                0.9999997897567091,
                0.9999994284994167,
                0.9999994956524115,
                0.9999998144608319,
                0.9999996533675028,
                0.9999994284996211,
                0.9999996072137998
            ],
            [
                0.9999997300421903,
                0.9999997617631468,
                0.9999999123575045,
                0.9999996940978095,
                0.999999789756684,
                0.9999996940976636,
                0.9999996940976636,
                0.9999996072138465,
                0.9999996533672962,
                0.9999998555019618
            ],
            [
                0.9999992661790196,
                0.9999990577550691,
                0.9999996072139402,
                0.9999996940978095,
                0.9999993524052019,
                0.999999554914789,
                0.999999694097846,
                0.9999996533672962,
                0.999999814460876,
                0.9999994956524716
            ],
            [
                0.9999994956527121,
                0.9999998555020307,
                0.9999987901340281,
                0.9999994956526519,
                0.9999992661786695,
                0.9999989322973846,
                0.9999992661790195,
                0.9999990577554061,
                0.9999977396765106,
                0.9999996533672962
            ],
            [
                0.9999998144608317,
                0.999999730042126,
                0.9999996533672136,
                0.9999994956524716,
                0.9999990577554061,
                0.9999996533672549,
                0.9999991684715759,
                0.999999352404893,
                0.9999996533674201,
                0.9999984465015047
            ],
            [
                0.9999998362623723,
                0.99999976176309,
                0.9999997897567091,
                0.9999994956527721,
                0.9999999123575045,
                0.9999994284993485,
                0.999999855502048,
                0.999999730042319,
                0.999999694097846,
                0.9999987901346049
            ],
            [
                0.9999996940977366,
                0.9999998874648647,
                0.999999730042126,
                0.999999814460876,
                0.9999998362623137,
                0.9999997897566589,
                0.9999997897565587,
                0.9999997300420937,
                0.9999998724809571,
                0.9999989322972573
            ],
            [
                0.9999996072138465,
                0.9999996072137998,
                0.999999554914842,
                0.9999993524050474,
                0.9999993524054335,
                0.9999996072137998,
                0.9999997617630899,
                0.999999352405279,
                0.9999994284994167,
                0.9999991684719723
            ],
            [
                0.9999998144609423,
                0.9999987901338838,
                0.9999998144608538,
                0.9999994956523514,
                0.9999994284996211,
                0.9999999226558145,
                0.9999984465020603,
                0.9999984465016899,
                0.9999995549150541,
                0.9999997300420937
            ],
            [
                8.48110816558695e-05,
                0.00015843629205243188,
                0.00043055708241433044,
                0.00017952796391380334,
                0.00033535022653096336,
                0.0002611902138101439,
                0.0002959571971080597,
                0.0004305571331925688,
                0.0002959570630702156,
                0.0004878571660665995
            ],
            [
                0.9999980052705163,
                0.9999998724808963,
                0.999999554914895,
                0.9999990577554061,
                0.9999991684717741,
                0.9999994956525918,
                0.99999893229713,
                0.9999994284996891,
                0.9999977396762411,
                0.9999989322968754
            ],
            [
                2.9023109470554753e-06,
                4.222833444383398e-06,
                3.2887498493983645e-06,
                6.144173136729416e-06,
                2.56128282131428e-06,
                6.144173868178388e-06,
                6.144176066353646e-06,
                2.430024072648329e-05,
                3.7266410609160796e-06,
                3.2887478887958082e-06
            ],
            [
                0.9999993524052019,
                0.9999996533674202,
                0.9999996940976272,
                0.9999989322973845,
                0.9999997300422225,
                0.9999998144608098,
                0.9999991684719725,
                0.9999994956525918,
                0.999999352404893,
                0.9999986290424663
            ],
            [
                0.999999266179107,
                0.9999998555019446,
                0.9999994956527722,
                0.9999986290427931,
                0.9999997897566089,
                0.9999993524053563,
                0.9999995549147358,
                0.9999996072137529,
                0.9999996533673375,
                0.9999996072138465
            ],
            [
                0.9999989322975118,
                0.9999986290421394,
                0.9999996072136125,
                0.999999352405279,
                0.9999996533674201,
                0.9999990577556308,
                0.9999996940977002,
                0.9999990577549568,
                0.99999862904312,
                0.999999352404893
            ],
            [
                0.9999997617631752,
                0.9999998724808963,
                0.9999997617630049,
                0.9999998362622357,
                0.9999992661788446,
                0.999999730042126,
                0.9999997300421581,
                0.9999999468421439,
                0.9999998724809723,
                0.9999996533674614
            ],
            [
                0.9999994284997573,
                0.9999998362623722,
                0.9999996533673375,
                0.9999992661790195,
                0.9999998724810027,
                0.9999998555019446,
                0.9999994284996893,
                0.9999996072136592,
                0.9999999317439872,
                0.9999994956525317
            ],
            [
                0.9999994284992805,
                0.999999789756684,
                0.999999554914789,
                0.9999993524053562,
                0.9999995549150011,
                0.9999993524052018,
                0.9999996072138934,
                0.9999993524049702,
                0.9999994956524114,
                0.999999352405279
            ],
            [
                0.9999987901341723,
                0.999999352404893,
                0.9999997897566089,
                0.9999974387171787,
                0.9999997617630049,
                0.9999997617630617,
                0.9999982396559474,
                0.9999997897566589,
                0.9999998555019618,
                0.9999999468421565
            ],
            [
                0.999999352404893,
                0.9999994956524716,
                0.9999997897565587,
                0.9999997617630332,
                0.9999994956524715,
                0.9999996940977366,
                0.9999996940978095,
                0.9999995549148419,
                0.999999730042319,
                0.9999997300421903
            ],
            [
                0.9999989322970028,
                0.9999996072137061,
                0.9999991684717742,
                0.9999998724809875,
                0.9999990577551814,
                0.9999987901343166,
                0.9999995549148419,
                0.9999996533672962,
                0.9999994956524114,
                0.9999980052700407
            ],
            [
                4.222832436955956e-06,
                2.2603253754921562e-06,
                4.222832940834793e-06,
                5.422218969384951e-06,
                8.939699499432793e-06,
                2.9023126769050284e-06,
                1.3709575336654889e-06,
                2.902312330965655e-06,
                2.260323489435463e-06,
                1.4738976694494812e-05
            ],
            [
                0.9999994284994167,
                0.9999998874647976,
                0.999997097686977,
                0.999999266178757,
                0.9999997300421903,
                0.9999995549147889,
                0.9999974387187053,
                0.999998239656367,
                0.9999996940977002,
                0.9999999317439953
            ],
            [
                0.999999653367379,
                0.9999987901338838,
                0.9999996072137998,
                0.9999997897565587,
                0.9999998724809267,
                0.9999998362622746,
                0.9999994284996211,
                0.9999991684719723,
                0.999999855501979,
                0.9999994284994849
            ],
            [
                0.9999996533673375,
                0.999997438716568,
                0.9999994284997573,
                0.9999984465020603,
                0.9999997300422547,
                0.9999996533672962,
                0.9999996072138934,
                0.9999993524054334,
                0.9999987901344607,
                0.999999266178757
            ],
            [
                0.9999998874648379,
                0.9999996533674201,
                0.9999994956527121,
                0.9999995549147359,
                0.999999730042126,
                0.9999990577554061,
                0.9999997300422869,
                0.9999993524051246,
                0.999999495652652,
                0.9999998144609645
            ],
            [
                0.9999996533673375,
                0.9999977396746244,
                0.9999982396561572,
                0.9999982396559474,
                0.9999993524054335,
                0.9999989322968754,
                0.9999992661791944,
                0.9999977396751633,
                0.9999998144608317,
                0.9999996533672135
            ],
            [
                0.9999996940977366,
                0.9999999123575045,
                0.9999994284994167,
                0.9999997617630049,
                0.9999998362622552,
                0.999999730042126,
                0.9999997897566089,
                0.9999998724808963,
                0.9999991684722697,
                0.9999996940976272
            ],
            [
                0.999998790134028,
                0.9999999226557961,
                0.9999998555019618,
                0.9999998144608983,
                0.9999995549149481,
                0.9999999123575464,
                0.9999998144608097,
                0.9999998144608098,
                0.999999789756634,
                0.9999998874647842
            ],
            [
                0.9999998724808964,
                0.9999994956524114,
                0.9999997300421903,
                0.9999998362622552,
                0.9999997617630049,
                0.9999993524054335,
                0.9999999006879721,
                0.9999998144608319,
                0.9999996533673375,
                0.9999996533672549
            ],
            [
                0.999999168471675,
                0.9999994956524716,
                0.9999997300420937,
                0.9999996072136125,
                0.999999266178932,
                0.9999998362622552,
                0.9999991684720715,
                0.9999989322967482,
                0.9999974387187053,
                0.9999998362622747
            ],
            [
                0.9999998362623332,
                0.9999999468421947,
                0.9999999468421122,
                0.9999998874648782,
                0.999999855501979,
                0.9999994284996893,
                0.9999997897566589,
                0.9999993524051246,
                0.9999996533674615,
                0.9999996533672135
            ],
            [
                3.5356259106723956e-05,
                2.430024649256756e-05,
                1.0129995809431767e-05,
                8.93969630226244e-06,
                8.939697368305565e-06,
                6.605212878421408e-05,
                4.539786860136322e-05,
                4.785094494185095e-06,
                7.889265406681968e-06,
                8.939699500164542e-06
            ],
            [
                0.9999998144608317,
                0.9999997617631752,
                0.9999996072137061,
                0.9999998362622746,
                0.9999998144609423,
                0.9999998144608098,
                0.9999997617631752,
                0.9999998362622357,
                0.9999998555019446,
                0.9999997897566089
            ],
            [
                0.9999996072138934,
                0.9999997617631752,
                0.999999653367379,
                0.9999996072136125,
                0.999999057755069,
                0.9999997617630049,
                0.9999962733598275,
                0.9999996533672549,
                0.9999996072138465,
                0.9999996072137061
            ],
            [
                0.999999352404893,
                0.9999995549151073,
                0.9999996940978825,
                0.9999997617631183,
                0.9999994284994167,
                0.9999996533673375,
                0.9999996533672549,
                0.9999994956527121,
                0.9999998555020135,
                0.9999990577554061
            ],
            [
                0.9999989322970027,
                0.9999994956527721,
                0.9999986290421394,
                0.9999986290431201,
                0.9999996072136125,
                0.9999980052705163,
                0.999999554914895,
                0.9999994956527722,
                0.999996711251719,
                0.9999987901341724
            ],
            [
                0.9999993524052018,
                0.9999996533674201,
                0.9999997300422225,
                0.9999994284993485,
                0.9999996072138934,
                0.9999994956524114,
                0.99999992265575,
                0.9999994284994167,
                0.9999996533674615,
                0.9999997617631469
            ],
            [
                0.9999994284995529,
                0.9999997897565838,
                0.9999993524049702,
                0.9999994956523514,
                0.9999999006881496,
                0.9999995549149481,
                0.999999900688043,
                0.9999997300421903,
                0.9999990577550691,
                0.9999997897565587
            ],
            [
                2.4300234925658572e-05,
                2.9023126769050284e-06,
                4.0063692064806855e-05,
                2.4300249406550775e-05,
                2.7535691091443854e-05,
                1.4738978456398127e-05,
                2.4300240729754152e-05,
                1.47389819699641e-05,
                3.5356242260622145e-05,
                5.4222202623972055e-06
            ],
            [
                0.9999996072136125,
                0.9999989322966208,
                0.9999996072136592,
                0.9999990577557432,
                0.9999992661787571,
                0.9999990577549569,
                0.9999994956526519,
                0.9999994956524716,
                0.999999554914895,
                0.9999992661791945
            ],
            [
                0.9999998144609423,
                0.9999991684721706,
                0.9999996072137998,
                0.9999993524053563,
                0.9999996533673788,
                0.9999994956523514,
                0.9999993524049702,
                0.9999997617630616,
                0.9999996072138465,
                0.9999996072136125
            ],
            [
                0.9999994956524114,
                0.9999998724809419,
                0.999999266178932,
                0.9999997617630049,
                0.9999997617631183,
                0.9999998874649051,
                0.9999997300422869,
                0.9999996533672135,
                0.9999990577556308,
                0.9999996072137998
            ],
            [
                2.1444943284979742e-05,
                0.00010889694793538952,
                3.2887506333394084e-06,
                2.7535697654881812e-05,
                4.5397857790051276e-05,
                5.4222183222304545e-06,
                1.012998977022003e-05,
                3.2887506333812835e-06,
                2.1444958618516124e-05,
                1.4738987237124277e-05
            ],
            [
                0.9999986290426298,
                0.9999995549147889,
                0.9999997617631183,
                0.9999992661792819,
                0.9999998144609423,
                0.9999998362622943,
                0.9999991684717741,
                0.9999990577552939,
                0.9999993524053562,
                0.9999997300421581
            ],
            [
                0.9999982396569966,
                0.999999730042319,
                0.9999991684721706,
                0.9999995549147359,
                0.9999993524050474,
                0.9999996072137061,
                0.9999997617630332,
                0.9999974387187054,
                0.9999997897566338,
                0.9999998555020135
            ],
            [
                0.9999998874649318,
                0.999999266179107,
                0.9999996940976636,
                0.9999994284995529,
                0.9999990577551815,
                0.9999996072137061,
                0.9999991684720715,
                0.9999997897567091,
                0.9999990577556308,
                0.9999994956524114
            ],
            [
                0.999998790134605,
                0.9999994284996211,
                0.9999990577556308,
                0.9999994956527721,
                0.9999994284994167,
                0.999999266178932,
                0.9999996533672135,
                0.9999998144608097,
                0.9999999006880312,
                0.9999977396765106
            ],
            [
                0.9999994956525317,
                0.9999998362623528,
                0.9999996533672136,
                0.9999995549147359,
                0.999999495652712,
                0.9999997300420937,
                0.9999996533674615,
                0.9999990577552937,
                0.9999997617629763,
                0.9999998724809723
            ],
            [
                0.9999994284993485,
                0.9999994284993485,
                0.9999993524050473,
                0.9999989322970027,
                0.9999997300422869,
                0.9999994956525918,
                0.9999998724808963,
                0.9999996072137529,
                0.9999996533674614,
                0.9999997300421903
            ],
            [
                0.9999997617630333,
                0.9999980052702786,
                0.9999982396569966,
                0.999999057755069,
                0.9999987901343165,
                0.9999980052693274,
                0.9999986290424664,
                0.9999993524049702,
                0.9999996940977366,
                0.9999986290432834
            ],
            [
                0.000295957061968016,
                0.0001795279227538065,
                0.00026119040118718716,
                0.0009110512919932106,
                0.0005527786040257974,
                0.0011695104731197534,
                0.000911050987135688,
                0.0005527785966294199,
                0.0008040860222872443,
                5.829124467582348e-05
            ],
            [
                0.999999789756684,
                0.9999996072137061,
                0.9999996072136592,
                0.9999996940977366,
                0.9999994956525918,
                0.9999996533674614,
                0.9999997300421903,
                0.9999996533674201,
                0.9999992661792819,
                0.9999996533672136
            ],
            [
                0.9999989322975118,
                0.9999989322968754,
                0.9999994284994167,
                0.9999993524049702,
                0.9999991684717741,
                0.9999994956525918,
                0.9999991684715759,
                0.9999998724809571,
                0.9999986290424663,
                0.9999992661787571
            ],
            [
                0.999999887464744,
                0.9999996940977002,
                0.9999997617629764,
                0.9999997897567091,
                0.9999998724809267,
                0.999999912357515,
                0.9999996533673375,
                0.9999990577551815,
                0.9999997300420937,
                0.9999996072137529
            ],
            [
                0.9999996072138465,
                0.9999996533672962,
                0.9999994956524716,
                0.999999168471675,
                0.999999266178932,
                0.9999990577552937,
                0.999998790134605,
                0.9999996533675028,
                0.9999994956525918,
                0.9999998144609645
            ],
            [
                2.9023109471188266e-06,
                1.0677031245783732e-06,
                3.2887490649221017e-06,
                3.726641060773727e-06,
                1.3007131553239479e-05,
                4.785095634843714e-06,
                1.3709576969826825e-06,
                7.338207180714596e-07,
                1.7603438426203097e-06,
                1.9947297214182054e-06
            ],
            [
                0.9999993524054334,
                0.9999993524052018,
                0.9999994956526519,
                0.9999999006879721,
                0.9999997897566089,
                0.9999990577551815,
                0.9999993524054335,
                0.9999997300420937,
                0.9999994284997573,
                0.9999993524052018
            ],
            [
                0.9999996533674202,
                0.9999994956524716,
                0.9999996072137998,
                0.9999997897566589,
                0.9999997617630332,
                0.9999995549150011,
                0.999999266179107,
                0.9999996072137529,
                0.9999997617630899,
                0.9999997897566338
            ],
            [
                7.484624503218738e-05,
                0.00020342694789637583,
                5.8291251569143705e-05,
                0.00013982212390520934,
                0.00010889690872727589,
                2.7535681235270997e-05,
                0.00020342694707359326,
                0.00029595720299794193,
                8.481107090659926e-05,
                9.610239191997185e-05
            ],
            [
                0.999999789756684,
                0.999998629042303,
                0.9999993524054335,
                0.9999996940977002,
                0.9999992661791071,
                0.9999987901338838,
                0.9999974387177893,
                0.9999990577555185,
                0.9999995549147358,
                0.9999997897566338
            ],
            [
                1.5534984952492866e-06,
                7.889264465239894e-06,
                1.370956716529941e-06,
                2.144494074076854e-05,
                3.288749065167371e-06,
                7.338212429504183e-07,
                7.338208055369664e-07,
                4.222835457733473e-06,
                5.422217676299034e-06,
                1.5534971989427613e-06
            ],
            [
                0.9999998362623722,
                0.9999982396565769,
                0.9999997897565838,
                0.9999991684715759,
                0.9999994284993485,
                0.9999977396746244,
                0.9999987901337396,
                0.9999996533672962,
                0.9999996940978095,
                0.9999994284994849
            ],
            [
                0.9999993524053563,
                0.9999986290431201,
                0.9999998362622357,
                0.9999994284994849,
                0.9999994284994848,
                0.9999994956527722,
                0.9999962733611601,
                0.9999990577556307,
                0.9999994956525918,
                0.9999982396561572
            ],
            [
                0.9999982396574163,
                0.9999996533675028,
                0.999999814460876,
                0.9999992661791945,
                0.9999996533674201,
                0.9999998874648379,
                0.9999995549151073,
                0.9999994284996891,
                0.9999998362623722,
                0.999999554914895
            ],
            [
                7.889265406151004e-06,
                3.726637951126493e-06,
                3.288749065167371e-06,
                6.962259567217739e-06,
                1.0129990978847043e-05,
                1.473898196763166e-05,
                1.3007130011655787e-05,
                7.889264465067689e-06,
                1.4738981964843453e-05,
                6.962256249327861e-06
            ],
            [
                0.9999997617630332,
                0.9999997300420937,
                0.999999887464744,
                0.999999814460876,
                0.9999998144608317,
                0.9999997897565587,
                0.9999996533672135,
                0.9999991684715759,
                0.9999997300422547,
                0.9999998874647709
            ],
            [
                0.9999995549148419,
                0.9999996533672962,
                0.9999998144609645,
                0.9999996533674202,
                0.9999999317439302,
                0.999999789756684,
                0.999999789756684,
                0.9999997300421581,
                0.9999999226557869,
                0.9999998362622552
            ],
            [
                0.9999998555019618,
                0.9999994284994848,
                0.9999991684719725,
                0.9999996072139402,
                0.9999998144608981,
                0.9999996072138465,
                0.9999996533674615,
                0.9999990577551815,
                0.999999730042319,
                0.9999997300422869
            ],
            [
                0.9999994956523514,
                0.9999995549150011,
                0.9999986290432835,
                0.9999996533672136,
                0.9999996940976636,
                0.9999995549150011,
                0.9999987901344607,
                0.9999997300422225,
                0.9999991684722697,
                0.999997097687669
            ],
            [
                0.9999993524050474,
                0.9999996940976636,
                0.999998790134605,
                0.9999997897565587,
                0.9999991684719723,
                0.9999991684720715,
                0.9999995549150542,
                0.9999991684718733,
                0.9999994956525318,
                0.9999996072137061
            ],
            [
                0.9999984465018751,
                0.99999862904312,
                0.9999996940977366,
                0.9999991684715759,
                0.9999995549148419,
                0.999999694097846,
                0.999999730042319,
                0.9999996072136125,
                0.9999996940977731,
                0.9999994284992805
            ],
            [
                0.9999997300421903,
                0.999999266178757,
                0.9999994284994849,
                0.9999996533674202,
                0.9999997300421903,
                0.9999997300422225,
                0.9999997617630049,
                0.9999997897567091,
                0.9999996072138934,
                0.9999995549150542
            ],
            [
                0.9999996072136125,
                0.9999998362622942,
                0.9999997617630049,
                0.9999997617631752,
                0.9999996940977366,
                0.9999996940977001,
                0.9999998874647709,
                0.999999814460876,
                0.9999997617630899,
                0.9999998144608981
            ],
            [
                0.9999994284997573,
                0.9999992661786696,
                0.9999989322973845,
                0.9999990577552937,
                0.9999994956525918,
                0.9999997617629764,
                0.999999057755743,
                0.9999998144609423,
                0.9999998144608319,
                0.9999996940976636
            ],
            [
                0.9999994284994167,
                0.9999998144609645,
                0.9999994284993485,
                0.9999984465016899,
                0.9999987901338838,
                0.9999995549147889,
                0.9999998362622747,
                0.9999993524049702,
                0.9999991684720715,
                0.9999998555019962
            ],
            [
                0.9999996072136592,
                0.9999996072138934,
                0.9999996533673375,
                0.9999998362623528,
                0.9999990577550691,
                0.9999974387184001,
                0.9999997897566589,
                0.9999994284994167,
                0.9999993524051246,
                0.9999996533672962
            ],
            [
                0.9999998724809875,
                0.9999997617631184,
                0.9999997617630333,
                0.9999996533674202,
                0.9999997617630616,
                0.9999999006879721,
                0.9999998362623332,
                0.9999994284993485,
                0.9999996072138465,
                0.9999996533673788
            ],
            [
                0.9999995549150011,
                0.9999996072137061,
                0.9999995549149481,
                0.9999984465022455,
                0.999999352405279,
                0.9999990577555185,
                0.9999990577554061,
                0.9999989322967482,
                0.9999996533672962,
                0.9999996940978825
            ],
            [
                0.9999997617630616,
                0.9999994284992805,
                0.9999982396567867,
                0.9999991684719723,
                0.9999984465020603,
                0.9999992661790195,
                0.9999991684721706,
                0.9999996072136592,
                0.9999989322967481,
                0.9999992661791944
            ],
            [
                0.9999987901340281,
                0.9999997300422869,
                0.9999999226558145,
                0.999999730042126,
                0.9999998144608097,
                0.999999057755743,
                0.9999996533675028,
                0.9999997300421581,
                0.9999990577552937,
                0.9999996940978095
            ],
            [
                0.9999989322968754,
                0.9999997897565587,
                0.999999694097773,
                0.999999694097846,
                0.9999991684718732,
                0.9999997617630616,
                0.9999997617630616,
                0.9999997300420937,
                0.9999996533672549,
                0.999999730042319
            ],
            [
                0.9999996940977731,
                0.99999992265575,
                0.9999994956525918,
                0.999999694097846,
                0.9999974387180947,
                0.9999994284994849,
                0.999999694097846,
                0.9999989322972572,
                0.999999730042126,
                0.999999352404893
            ],
            [
                0.9999987901347491,
                0.9999990577549568,
                0.9999992661790196,
                0.9999994956526519,
                0.9999957771660523,
                0.999998790134028,
                0.9999986290431201,
                0.9999989322966208,
                0.9999992661790196,
                0.9999974387187053
            ],
            [
                1.892515726099468e-05,
                2.1444940739364273e-05,
                1.3007130010922344e-05,
                4.539785227903126e-05,
                1.30071346612026e-05,
                4.00636969277356e-05,
                1.6701417854810315e-05,
                7.889261641158302e-06,
                6.6052121039017e-05,
                1.0129994594539281e-05
            ],
            [
                0.9999989322975118,
                0.9999986290423029,
                0.9999995549147359,
                0.9999995549150011,
                0.9999997617630332,
                0.9999998362623528,
                0.9999998555019618,
                0.9999984465016899,
                0.9999996940976636,
                0.9999996533673788
            ],
            [
                0.9999957771675624,
                0.9999993524054334,
                0.9999991684715759,
                0.9999989322967482,
                0.9999957771645419,
                0.9999952149072167,
                0.9999957771655488,
                0.9999996072136592,
                0.9999977396751633,
                0.9999980052693274
            ],
            [
                0.9999957771680665,
                0.9999993524049702,
                0.9999977396762411,
                0.9999990577556307,
                0.9999938558268634,
                0.9999984465016899,
                0.9999990577552937,
                0.9999994956525317,
                0.9999996072137529,
                0.999999814460876
            ],
            [
                0.9999999226557592,
                0.9999996533674614,
                0.9999997617631752,
                0.9999992661788445,
                0.9999998874647306,
                0.9999997617630048,
                0.9999996940978095,
                0.9999994956524715,
                0.9999996533672549,
                0.9999996940978095
            ],
            [
                0.9999992661789321,
                0.9999996533675028,
                0.9999992661790195,
                0.9999992661791944,
                0.9999997300422547,
                0.9999991684721706,
                0.9999994284993485,
                0.9999996072137529,
                0.9999992661791944,
                0.9999989322967481
            ],
            [
                0.999999057755743,
                0.9999990577556307,
                0.9999998144608097,
                0.9999996072138934,
                0.999999168471675,
                0.9999991684719723,
                0.9999993524050474,
                0.9999987901341723,
                0.9999996533672549,
                0.9999994956524716
            ],
            [
                0.9999996072139402,
                0.9999997897566089,
                0.9999996533673375,
                0.999999900688043,
                0.9999999586006344,
                0.9999999317439139,
                0.9999997617631469,
                0.9999998874648514,
                0.9999998555020307,
                0.9999997617630332
            ],
            [
                0.9999996533675028,
                0.9999996940977001,
                0.9999990577554061,
                0.9999994956524115,
                0.9999994956527121,
                0.9999996940977002,
                0.9999998362623528,
                0.9999996533672962,
                0.9999991684716749,
                0.9999994956524115
            ],
            [
                8.315278293899016e-07,
                3.7266406165319545e-06,
                0.999988521233246,
                5.422217029844958e-06,
                4.222834954057889e-06,
                2.56128282131428e-06,
                6.962259568889411e-06,
                1.7603436329714805e-06,
                3.2887486731252264e-06,
                2.902311984873224e-06
            ]
        ]
    },
    {
        "q_id": "8143_mmlu_math",
        "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,
            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": [
            [
                0.9999756997679662,
                0.9999724642957877,
                0.9999724643187565,
                0.9999599363221504,
                0.9999599363173919,
                0.9999974387168733,
                0.9999832985761703,
                0.999997097686977,
                0.9999852610180315,
                0.9999967112493665
            ],
            [
                0.9999724642990576,
                0.9999756997621654,
                0.999738809629637,
                0.9999852610145146,
                0.9999885212318744,
                0.9999038975965026,
                0.9999974387171787,
                0.9999785550464741,
                0.9999852610232997,
                0.9999921107336524
            ],
            [
                0.9999930377462405,
                0.9999921107345942,
                0.9999756997621748,
                0.9999599363078364,
                0.9999687980774866,
                0.9999599362935143,
                0.9998601778930637,
                0.999983298574179,
                0.99995993631745,
                0.9999785550439251
            ],
            [
                0.9999885212264016,
                0.9999546021259874,
                0.9999339478711735,
                0.9999898700066064,
                0.9999785550439243,
                0.9999687980997993,
                0.9999987901337396,
                0.9999869928730875,
                0.9999974387177893,
                0.999992110738355
            ],
            [
                0.9999339478632563,
                0.9999417087206172,
                0.9999687980960938,
                0.9999910603058276,
                0.9998601778769086,
                0.9999938558246658,
                0.9999417087484351,
                0.9999869928761891,
                0.9999785550592614,
                0.9999952149060758
            ],
            [
                0.9999910603047625,
                0.9999687980923714,
                0.9997694933128299,
                0.999933947839643,
                0.9999646437535114,
                0.9999885212359798,
                0.9998766053957809,
                0.9999952149043645,
                0.9999038975393034,
                0.9997694931758981
            ],
            [
                0.9999898700078128,
                0.9999785550490375,
                0.999975699753477,
                0.9999962733598275,
                0.9999724643056231,
                0.9999646437408634,
                0.9999546021151483,
                0.9998766053959319,
                0.9995694429666103,
                0.9999724643023379
            ],
            [
                0.9999151889891291,
                0.9999339478395968,
                0.9999151889486693,
                0.9999852610215433,
                0.9999967112505427,
                0.9999938558224684,
                0.9998601778928643,
                0.999933947831781,
                0.9999599363221545,
                0.999989870006605
            ],
            [
                0.9999339478632457,
                0.9999785550541448,
                0.9999417087484088,
                0.9999687980886323,
                0.999981074858529,
                0.9999885212291401,
                0.9999852610145148,
                0.9999646437535068,
                0.9999687980737588,
                0.9999546021476109
            ],
            [
                0.9999967112521109,
                0.9999810748495079,
                0.999997097686977,
                0.999978555054151,
                0.9999151889688097,
                0.9999687980886414,
                0.9999852610180315,
                0.9999687980997966,
                0.9999599363126054,
                0.9999869928746379
            ],
            [
                0.9999687980737629,
                0.999796573003077,
                0.9999987901343165,
                0.9999546021313743,
                0.9999852610110026,
                0.9999974387184,
                0.9999251537638889,
                0.9999980052702786,
                0.9999785550413632,
                0.9999756997476907
            ],
            [
                0.9999810748540182,
                0.9998204719921104,
                0.9999151889891654,
                0.9999938558275957,
                0.9999945777816768,
                0.9998415638401937,
                0.9999038975739906,
                0.9999756997476854,
                0.9999967112509347,
                0.9999852610127589
            ],
            [
                0.9998911030648799,
                0.9999251537906715,
                0.9999687980849155,
                0.9998911030651303,
                0.9999756997592761,
                0.9999339478475212,
                0.9999930377404307,
                0.9999417087345216,
                0.9999687980737588,
                0.9999756997476907
            ],
            [
                0.999972464299064,
                0.9999810748427413,
                0.9997694932857603,
                0.999964643732436,
                0.9999957771670589,
                0.9999810748427375,
                0.9999910603004992,
                0.9999885212332433,
                0.9999785550515903,
                0.9999724642990595
            ],
            [
                0.9999910603068942,
                0.9999810748585355,
                0.9999756997650724,
                0.9999945777810305,
                0.9999945777823234,
                0.9999938558224687,
                0.9999962733616047,
                0.9999952149032237,
                0.999991060304762,
                0.9999982396559473
            ],
            [
                0.9999687980811937,
                0.9998911031037379,
                0.9999869928684351,
                0.9999898700090208,
                0.9999938558224684,
                0.9999898700114356,
                0.9999930377445803,
                0.9998601779596922,
                0.9999687980849209,
                0.9999599363221565
            ],
            [
                0.9999417087483837,
                0.9999810748495074,
                0.9999977396751634,
                0.9999810748517634,
                0.9999646437577306,
                0.9999038976197051,
                0.999986992866886,
                0.9999832985821414,
                0.9999852610180298,
                0.9999599363125974
            ],
            [
                0.9999898700053977,
                0.9999151889485933,
                0.9998204720133566,
                0.9998766054546218,
                0.9996200155627424,
                0.999975699753474,
                0.9994472214012481,
                0.9997694933404632,
                0.9999417087483609,
                0.9999885212359796
            ],
            [
                0.999948557780244,
                0.9999885212346115,
                0.9999646437408665,
                0.9999910603015647,
                0.999975699767961,
                0.9999930377429204,
                0.9999810748517634,
                0.9999852610127629,
                0.9999885212318748,
                0.9999646437324424
            ],
            [
                0.999981074847252,
                0.9999869928761874,
                0.999993855825398,
                0.9999898700041912,
                0.9999687980811924,
                0.9999724643089074,
                0.99998987000419,
                0.9999687980997926,
                0.9999832985761654,
                0.9999724643056213
            ],
            [
                0.9999599363126164,
                0.9999910603004992,
                0.9999724643089085,
                0.9999832985741761,
                0.9999785550592636,
                0.9999885212332446,
                0.9999921107402361,
                0.999981074842739,
                0.9999869928684356,
                0.9999986290427931
            ],
            [
                1.1478769491598686e-05,
                3.7266383954560706e-06,
                3.726639283901856e-06,
                3.288747889178668e-06,
                1.300713466316634e-05,
                1.147877359392407e-05,
                1.760342583722268e-06,
                2.5612812946890944e-06,
                2.5612822106654943e-06,
                8.939697368663308e-06
            ],
            [
                0.99996879808864,
                0.9996646500116203,
                0.9999251537906921,
                0.9999810748427375,
                0.9999417087136648,
                0.999933947831719,
                0.9997040427972863,
                0.9999885212264018,
                0.9999938558253983,
                0.9999930377445807
            ],
            [
                0.9999485577802993,
                0.9998911030522437,
                0.9999546021205596,
                0.9999945777790915,
                0.9999417087484398,
                0.9999869928668849,
                0.9999546021421896,
                0.9998204720562874,
                0.9998601778764243,
                0.9999339478790639
            ],
            [
                0.9997388095691286,
                0.9999485578047611,
                0.9999687980849181,
                0.9998204720346757,
                0.9999646437366552,
                0.9995694430202444,
                0.9999930377412606,
                0.9999970976883609,
                0.9999810748517645,
                0.9999151889688949
            ],
            [
                0.9999485577925108,
                0.9999756997476837,
                0.9999930377437505,
                0.9999852610180329,
                0.9999885212264011,
                0.99995993630782,
                0.9999885212305073,
                0.9999251537461021,
                0.9999869928715358,
                0.9999724642990576
            ],
            [
                0.9999852610145151,
                0.9999339478632202,
                0.9999785550490328,
                0.9999251537460401,
                0.9999885212359796,
                0.9999938558275955,
                0.9999921107355336,
                0.9999810748427375,
                0.9999151889890027,
                0.9998911030519679
            ],
            [
                0.9999151889689492,
                0.9995694429106089,
                0.9999756997534777,
                0.9999910603004994,
                0.9999251537728369,
                0.9999938558246658,
                0.9999938558253981,
                0.9999852610233032,
                0.999972464302344,
                0.9999898700053974
            ],
            [
                0.9999885212305063,
                0.9999930377412605,
                0.9999756997592703,
                0.9999869928746379,
                0.9999687980811974,
                0.9999921107355337,
                0.999992110736474,
                0.9999957771670588,
                0.9999869928730867,
                0.9999921107392953
            ],
            [
                0.9999251537638889,
                0.9999038975737075,
                0.9999945777784451,
                0.9999687980886335,
                0.999991060300499,
                0.9997965729784852,
                0.9999810748585316,
                0.9999546021367987,
                0.9999852610162715,
                0.9998911030908354
            ],
            [
                0.9999546021205518,
                0.9999930377412607,
                0.9999952149043647,
                0.9999687980886374,
                0.9999417087483918,
                0.9999546021205493,
                0.9999921107374146,
                0.9998601779429633,
                0.999996273360716,
                0.9999485577741262
            ],
            [
                0.9999339478633428,
                0.9998415638028636,
                0.9999852610215495,
                0.9999339478318906,
                0.9999756997476829,
                0.9999945777829694,
                0.9999339478790639,
                0.9999885212277702,
                0.9999810748472499,
                0.9999646437408728
            ],
            [
                0.9999885212346117,
                0.9999952149060758,
                0.9999869928699867,
                0.9999599363078477,
                0.9999251537817503,
                0.9998601779597145,
                0.9999898700126435,
                0.9999910603047619,
                0.9999810748562746,
                0.999995214906076
            ],
            [
                0.9999646437577306,
                0.9999832985781574,
                0.9999921107345934,
                0.9999852610197855,
                0.9999810748472546,
                0.9999980052707541,
                0.9999952149032236,
                0.9999952149060758,
                0.9999852610197867,
                0.999993855826131
            ],
            [
                0.9999646437492968,
                0.9999852610232999,
                0.9999967112521108,
                0.9999952149049349,
                0.9999756997505811,
                0.9999785550439235,
                0.9999980052698029,
                0.9999952149072169,
                0.9999945777784448,
                0.9999945777823231
            ],
            [
                0.9997694932025857,
                0.9998415637265365,
                0.9986749775442747,
                0.9999251537995921,
                0.9998415637265896,
                0.9914225163445024,
                0.9999687980997866,
                0.9982992779303075,
                0.9998911030907974,
                0.9999832985841309
            ],
            [
                0.9999151889688855,
                0.9999898700126442,
                0.9999945777790913,
                0.9998415637268294,
                0.9999756997679602,
                0.9999417087205619,
                0.9999546021259655,
                0.999995777164542,
                0.9999962733589389,
                0.9998766054105537
            ],
            [
                0.99979657295416,
                0.9996646499715593,
                0.9997388097231431,
                0.9998204720135393,
                0.9999646437408649,
                0.9999810748495058,
                0.9999417087275562,
                0.999933947831719,
                0.9999724642957752,
                0.9999869928715355
            ],
            [
                0.9999810748495038,
                0.9999810748562722,
                0.9999785550567023,
                0.9997388097851638,
                0.9999546021151381,
                0.9999339478711399,
                0.9999546021097396,
                0.9997040429032524,
                0.999941708727552,
                0.9999810748517612
            ],
            [
                0.9999785550464791,
                0.9999952149060758,
                0.9999957771675622,
                0.9999339478239027,
                0.9997694933412077,
                0.9999785550439251,
                0.9999785550490361,
                0.9999974387187053,
                0.9999945777810302,
                0.9999832985841314
            ],
            [
                0.9999910603058276,
                0.9999921107336528,
                0.999992110737415,
                0.9999485577863757,
                0.9999967112501504,
                0.9999921107364745,
                0.9999938558224682,
                0.9999785550541473,
                0.9999485577679873,
                0.9999885212291393
            ],
            [
                0.9998415638213696,
                0.9999599362982728,
                0.9999952149032237,
                0.9999417087206043,
                0.9999785550490328,
                0.9999151889890513,
                0.9999921107374153,
                0.9999938558246659,
                0.9998415637645629,
                0.9999756997592744
            ],
            [
                0.9999898700041912,
                0.9999810748427385,
                0.9999898700078138,
                0.999983298578157,
                0.9999785550439235,
                0.999998005269803,
                0.9999485577925318,
                0.9999930377404306,
                0.9999938558261307,
                0.9999832985821404
            ],
            [
                0.9999756997679652,
                0.999997097686977,
                0.9999852610197864,
                0.9999810748495068,
                0.9999938558253981,
                0.9999898700126437,
                0.9999970976866309,
                0.999997097686977,
                0.9999417087414608,
                0.9999687980774836
            ],
            [
                0.9525741310298373,
                0.9997694932296756,
                0.9988304898649506,
                0.999195914143967,
                0.9820137880968465,
                0.9924227573699808,
                0.0009110512380047056,
                0.00048785717540466276,
                0.9968273171464695,
                0.9995121427651894
            ],
            [
                0.9999921107345933,
                0.9999852610180315,
                0.9999921107355337,
                0.9999930377404314,
                0.9999756997650677,
                0.9999945777790912,
                0.9999952149049349,
                0.9999967112497585,
                0.9999785550490361,
                0.9999930377445811
            ],
            [
                0.9999756997650627,
                0.999933947863251,
                0.9998204719483437,
                0.9999251537639581,
                0.9994472213342948,
                0.9999724643187554,
                0.99995993630783,
                0.9999724642957971,
                0.9999251537728434,
                0.9999910603068934
            ],
            [
                0.9999810748427379,
                0.999972464305637,
                0.9999810748517651,
                0.9999785550592722,
                0.9998766054110851,
                0.9999546021476354,
                0.9999970976883609,
                0.9999987901341723,
                0.9999869928761891,
                0.9999687980849237
            ],
            [
                0.9999756997621748,
                0.9999646437535161,
                0.999991060304762,
                0.9999967112497584,
                0.9999785550439229,
                0.9999756997592719,
                0.9999687980849181,
                0.99998526101803,
                0.9999930377462402,
                0.9999869928730869
            ],
            [
                0.9999251537728369,
                0.999991060304763,
                0.999959936298309,
                0.9999599363078385,
                0.9999339478475049,
                0.9999646437535178,
                0.9998601779096359,
                0.9999910603047625,
                0.9999687980849129,
                0.999975699767967
            ],
            [
                0.9999646437408712,
                0.9999546021259734,
                0.9999785550464746,
                0.9999646437535161,
                0.9999339478632303,
                0.9999724642990617,
                0.9999251537549879,
                0.9999485578047674,
                0.99997855505926,
                0.9999785550490354
            ],
            [
                0.9999810748472489,
                0.9999898700102282,
                0.9999921107383549,
                0.9999646437535082,
                0.9999885212264015,
                0.9999724642990617,
                0.9999151889284265,
                0.9999646437577411,
                0.9999898700053982,
                0.9999832985841317
            ],
            [
                0.9999957771645419,
                0.9999832985741748,
                0.9999417087345085,
                0.9999724642990556,
                0.9999417087136911,
                0.9999646437366552,
                0.9999869928668857,
                0.9999339478474795,
                0.9999869928699859,
                0.999964643732436
            ],
            [
                0.9999546021314016,
                0.9999952149060758,
                0.9999724643154851,
                0.999972464315472,
                0.9999885212332433,
                0.9999785550464758,
                0.9999417087484261,
                0.9999852610180308,
                0.9999952149072169,
                0.9999810748585306
            ],
            [
                0.9999485577618773,
                0.9999852610215454,
                0.9999687980774782,
                0.9999724643121898,
                0.9999339478553833,
                0.999964643736646,
                0.9999251537907204,
                0.9998415638399794,
                0.9999977396765105,
                0.9999724642990687
            ],
            [
                0.9999967112493665,
                0.9998766054547727,
                0.9999962733616046,
                0.9999599362887323,
                0.9999339478711341,
                0.9999910603068932,
                0.9999038976195017,
                0.999933947879035,
                0.9999151889587349,
                0.9999038975737515
            ],
            [
                0.9999967112505427,
                0.9999417087553785,
                0.9999832985821396,
                0.9999930377454104,
                0.9999869928761891,
                0.9999251537728645,
                0.9999885212264021,
                0.9999785550592586,
                0.9999930377445807,
                0.9999687980811988
            ],
            [
                0.9999885212318752,
                0.9999885212305071,
                0.9999599362983018,
                0.9999898700078138,
                0.9999967112509348,
                0.9999869928653345,
                0.9999251537907733,
                0.9999910603068943,
                0.9999957771655487,
                0.9999869928668857
            ],
            [
                0.999820471970073,
                0.9999756997621788,
                0.9999038976080479,
                0.9999756997563752,
                0.9999952149049349,
                0.9999921107374146,
                0.9999945777816768,
                0.999992110734593,
                0.999989870011436,
                0.9997694932030821
            ],
            [
                0.9999687980886445,
                0.9999980052695652,
                0.9999945777784448,
                0.9999852610197874,
                0.999948557798626,
                0.9999962733607161,
                0.9999546021476268,
                0.999964643749305,
                0.9999869928761882,
                0.9999724643154672
            ],
            [
                0.9997965730760205,
                0.9999885212277696,
                0.9999910602994336,
                0.9999945777790911,
                0.9999485578047809,
                0.9999938558232011,
                0.9999869928730883,
                0.9999898700114355,
                0.9999724643121888,
                0.9999885212359796
            ],
            [
                0.9999852610197877,
                0.9999938558253983,
                0.9999546021476443,
                0.9999599362935313,
                0.9999687980998007,
                0.999941708713745,
                0.9999756997650677,
                0.9999599362982922,
                0.999978555046477,
                0.9999832985781563
            ],
            [
                0.9999417087206676,
                0.999978555056705,
                0.999989870009021,
                0.9999938558232011,
                0.9999687980923667,
                0.9999687980774756,
                0.9999339478475102,
                0.9999910603068933,
                0.9999687980849222,
                0.9999810748517663
            ],
            [
                0.9999546021476239,
                0.9999910603004999,
                0.9999417087484839,
                0.9999756997563826,
                0.9999921107402366,
                0.9999756997650743,
                0.9999687980886445,
                0.9999952149055054,
                0.9999885212359817,
                0.9998415637272235
            ],
            [
                0.9999930377437503,
                0.999992110738355,
                0.9999339478317487,
                0.9999952149032236,
                0.9999962733589389,
                0.9999785550413688,
                0.9999599363030504,
                0.9999832985841314,
                0.9999967112501505,
                0.9999646437535129
            ],
            [
                0.9999038975967626,
                0.9999546021097478,
                0.9999785550515903,
                0.9999832985701939,
                0.9999910603004993,
                0.9999832985741766,
                0.9998766054400162,
                0.9998204720559244,
                0.9999546021151456,
                0.999985261021544
            ],
            [
                0.9999967112517189,
                0.9999962733611601,
                0.9999910603005008,
                0.9999785550464791,
                0.9999952149032237,
                0.9999986290424663,
                0.9999910603068948,
                0.9999921107336541,
                0.9999962733602717,
                0.9999869928761882
            ],
            [
                0.9999546021421996,
                0.999925153755067,
                0.9999785550541453,
                0.9999417087136822,
                0.9999852610180279,
                0.9999417087136402,
                0.9999938558232008,
                0.9997388096000895,
                0.9999687980998051,
                0.9999869928761898
            ],
            [
                0.9999852610197894,
                0.9999952149043646,
                0.9999869928715369,
                0.9999832985801483,
                0.9999546021476212,
                0.9999756997679837,
                0.9999952149066464,
                0.9999938558253983,
                0.999988521234613,
                0.9999756997534777
            ],
            [
                0.9999910603058276,
                0.9999756997592695,
                0.9999967112505425,
                0.9999785550515903,
                0.9999687980997993,
                0.9999898700126436,
                0.99999303774624,
                0.9999869928653338,
                0.9999546021313874,
                0.9999910603036969
            ],
            [
                0.9999756997563796,
                0.999988521229139,
                0.9999910603068932,
                0.9999930377445804,
                0.9999970976876689,
                0.9999885212332436,
                0.9999485577679679,
                0.9999910603026305,
                0.9999599363126013,
                0.9999687980886323
            ],
            [
                0.999992110736474,
                0.9998415637835254,
                0.9999339478238921,
                0.999925153772803,
                0.999933947879035,
                0.9997388097857415,
                0.999769493313863,
                0.9999921107364742,
                0.9999938558261307,
                0.9999810748449955
            ],
            [
                0.9999251537906448,
                0.9999151889486779,
                0.999981074844995,
                0.9999646437408697,
                0.9999938558246656,
                0.9999485577679709,
                0.9999687980849142,
                0.9999599363078321,
                0.9999756997476916,
                0.9999646437493086
            ],
            [
                0.999933947831781,
                0.9999646437619403,
                0.9999785550515903,
                0.9999962733593833,
                0.9998911031300373,
                0.9998601779095057,
                0.9999810748540204,
                0.9999756997592719,
                0.9999417087206086,
                0.999997097686631
            ],
            [
                0.999978555054148,
                0.9999938558224687,
                0.9999898700090224,
                0.9999869928684354,
                0.9999785550439195,
                0.9999756997505803,
                0.9999869928715373,
                0.999972464302344,
                0.9998204720777556,
                0.9999785550592643
            ],
            [
                0.9999785550439222,
                0.9999832985781607,
                0.9999869928715366,
                0.9999832985701949,
                0.9999756997534762,
                0.9999785550439243,
                0.9999869928668857,
                0.9999938558224687,
                0.9999938558261307,
                0.999948557767984
            ],
            [
                0.9999962733598274,
                0.9999921107374146,
                0.9999785550592561,
                0.9999980052693274,
                0.999985261016272,
                0.9999967112509347,
                0.9999599363173769,
                0.9999898700126435,
                0.9999945777797374,
                0.9999921107383554
            ],
            [
                0.9999724643154663,
                0.9999980052702785,
                0.9999546021368069,
                0.9999869928746385,
                0.9999756997534794,
                0.9999724642990586,
                0.9999885212305066,
                0.9999898700126439,
                0.9999930377420907,
                0.9999599363078239
            ],
            [
                0.9999885212277709,
                0.9999151889587429,
                0.9999646437324408,
                0.9999832985801516,
                0.999891103077925,
                0.999985261021544,
                0.9995694430155098,
                0.9997965729546424,
                0.9999417087136692,
                0.9997040428660531
            ],
            [
                0.9999962733611603,
                0.9999898700090215,
                0.9999938558246657,
                0.9999984465026158,
                0.9999898700114378,
                0.9999885212277699,
                0.9999417087345216,
                0.9999974387187053,
                0.9999962733602719,
                0.9999756997476862
            ],
            [
                0.9999967112517187,
                0.9999910603068934,
                0.999978555054148,
                0.9999646437493511,
                0.9999945777797377,
                0.9999962733589389,
                0.9998601779431668,
                0.9999869928668851,
                0.9999599362935166,
                0.9999417087067253
            ],
            [
                0.9999546021205493,
                0.9999832985801506,
                0.9999599362887323,
                0.9999417087136692,
                0.9999930377429206,
                0.9999910603047618,
                0.9999967112501505,
                0.9999417087344962,
                0.999933947839665,
                0.9998911031038679
            ],
            [
                0.9999869928746369,
                0.9997388097858174,
                0.9999930377437505,
                0.9998911031167164,
                0.9999599363221524,
                0.9999869928684351,
                0.9999832985701927,
                0.999933947839643,
                0.9999339478239084,
                0.9999945777829694
            ],
            [
                0.9999952149072169,
                0.9999038976195234,
                0.9999938558224686,
                0.9999038975622648,
                0.9999921107374153,
                0.9999957771665555,
                0.9999938558275956,
                0.9999885212291383,
                0.9999898700090203,
                0.9999921107355337
            ],
            [
                0.9999251537460951,
                0.9999957771675624,
                0.9999339478318275,
                0.9999869928730869,
                0.9999832985701935,
                0.9999952149072167,
                0.9999885212264018,
                0.999989870006606,
                0.9998415637839841,
                0.999860177859783
            ],
            [
                0.9999599363030699,
                0.9999546021097218,
                0.9999417087206625,
                0.9999724643089074,
                0.9999038976195891,
                0.9999930377462403,
                0.9999970976880149,
                0.9999724643023389,
                0.999993037743751,
                0.9999898700066057
            ],
            [
                0.9999832985841293,
                0.9999938558268632,
                0.9999938558261307,
                0.999986992873088,
                0.9999756997563761,
                0.9999945777823231,
                0.9999869928653365,
                0.9999898700090203,
                0.9994472213235218,
                0.9999724643121942
            ],
            [
                0.9999921107374156,
                0.9999930377437507,
                0.9999970976869769,
                0.9999756997476862,
                0.9999546021476324,
                0.9999687980811962,
                0.9999921107402373,
                0.9999832985801487,
                0.9998766053959157,
                0.999992110733653
            ],
            [
                0.9999898700066056,
                0.9999646437535114,
                0.9998601778928846,
                0.9999885212346119,
                0.9999339478238608,
                0.9999967112513267,
                0.9998766054546381,
                0.9991959140523986,
                0.9999485577863824,
                0.9999251537995218
            ],
            [
                0.9999938558232011,
                0.9999852610233037,
                0.9999724643187576,
                0.9999952149032237,
                0.9999852610215443,
                0.9999962733607162,
                0.9999756997505835,
                0.99998526101803,
                0.9999930377437511,
                0.9999910603068939
            ],
            [
                0.9999832985821401,
                0.9999885212318752,
                0.999959936298279,
                0.9999970976890528,
                0.9999646437492907,
                0.9999910603004999,
                0.9999952149072167,
                0.999997097686977,
                0.9999599363030746,
                0.9999724643089085
            ],
            [
                0.9999417087414243,
                0.9999485577863757,
                0.9999251537727649,
                0.9999151889891383,
                0.9999810748449939,
                0.9999417087136733,
                0.9999785550592579,
                0.9997965730029439,
                0.9999687980774823,
                0.9998204720985366
            ],
            [
                0.9997388096284439,
                0.9997694932023174,
                0.999447221330468,
                0.9999756997534754,
                0.9999339478395914,
                0.9999251537728434,
                0.9999485577679526,
                0.9998766054693118,
                0.9999546021097193,
                0.9998204719698691
            ],
            [
                0.9999869928653343,
                0.9998766053664352,
                0.9999910603026309,
                0.9999785550490375,
                0.999941708748449,
                0.9999930377429206,
                0.999903897585194,
                0.9999646437619537,
                0.9998911030520361,
                0.9999339478239136
            ],
            [
                0.9999038975851613,
                0.9999810748517622,
                0.9999646437408763,
                0.9999785550439207,
                0.9999485577863694,
                0.9997388095673958,
                0.9996646498928325,
                0.9999938558224684,
                0.9998911030778981,
                0.9999599362887345
            ],
            [
                0.9999930377420907,
                0.9999945777803839,
                0.9999962733616046,
                0.9999339478633125,
                0.9999938558239335,
                0.9999852610180308,
                0.999972464315468,
                0.9999938558232011,
                0.9999151889487513,
                0.9998911031171347
            ],
            [
                0.9999987901341723,
                0.9999910603004991,
                0.9999938558275956,
                0.999996273358939,
                0.9999546021097598,
                0.9999910603015663,
                0.9999869928715386,
                0.9999921107402364,
                0.9999885212264016,
                0.9999977396765106
            ],
            [
                0.9999970976890528,
                0.9999756997534945,
                0.999993855827596,
                0.9999898700102282,
                0.9999974387168733,
                0.9999785550592643,
                0.9999962733611604,
                0.9999785550567132,
                0.9999756997534868,
                0.9999785550490369
            ],
            [
                0.9999930377462404,
                0.9999898700078133,
                0.999978555046477,
                0.9999151889891291,
                0.9999339478711452,
                0.9999921107392962,
                0.9999852610110006,
                0.9999952149066462,
                0.9999921107392968,
                0.9999038975965836
            ],
            [
                0.9999151889890594,
                0.9999810748517612,
                0.9999930377454104,
                0.9999485578047843,
                0.9999038975965626,
                0.9998766053667745,
                0.9999599363030566,
                0.999972464312192,
                0.9999930377445806,
                0.999972464312199
            ],
            [
                0.9999810748472484,
                0.9999869928746372,
                0.9999251537907063,
                0.9999151889183269,
                0.9999599363030898,
                0.9999485577679709,
                0.9999546021476109,
                0.9999957771665554,
                0.999997097686977,
                0.9998601778760948
            ],
            [
                0.9999921107374143,
                0.9999339478789965,
                0.9999869928684356,
                0.9999930377404308,
                0.9999852610145155,
                0.9999810748449944,
                0.9999957771670589,
                0.9999485577679742,
                0.9999599362887411,
                0.9999957771665554
            ],
            [
                0.9999974387187053,
                0.999998005269803,
                0.9999957771650453,
                0.9999724643121931,
                0.9999945777829696,
                0.9999756997592761,
                0.9999952149072167,
                0.9999967112517189,
                0.999988521229139,
                0.9999599363078259
            ],
            [
                0.999925153737126,
                0.9999038975738438,
                0.9997694933424284,
                0.999941708748413,
                0.9999485577863929,
                0.9999785550515903,
                0.9999952149032236,
                0.9999930377429209,
                0.9997965730281482,
                0.9999885212305093
            ],
            [
                0.9999646437324424,
                0.9999921107345939,
                0.9999151889890266,
                0.9999339478475265,
                0.9999599363221565,
                0.9999756997505845,
                0.9998766054549343,
                0.9999869928684356,
                0.9999599362982748,
                0.9997040428664148
            ],
            [
                0.9999810748449934,
                0.9999885212332431,
                0.9998911030519141,
                0.9999724643089045,
                0.999975699767961,
                0.9999898700078128,
                0.9999251537995529,
                0.9999687980849105,
                0.9999646437450794,
                0.9999898700090208
            ],
            [
                0.9999417087136822,
                0.9999885212332433,
                0.9999251537461239,
                0.9999599363078239,
                0.9998766054694967,
                0.9999417087275694,
                0.9999646437535286,
                0.9999599362935055,
                0.9999724642957742,
                0.9997694932860486
            ],
            [
                0.9997694933403491,
                0.9999967112497585,
                0.9999957771645421,
                0.9997388097536861,
                0.9999910603004993,
                0.9999785550541502,
                0.9999832985781584,
                0.9998601778600699,
                0.9999810748562752,
                0.9999898700066059
            ],
            [
                0.9999910602994334,
                0.9999938558232012,
                0.9999038975966262,
                0.999738809660978,
                0.999933947863225,
                0.9999810748472499,
                0.9999785550464765,
                0.9999038976080695,
                0.9999417087066845,
                0.9999687980997966
            ],
            [
                0.9999930377454103,
                0.999447221461802,
                0.9999967112521109,
                0.99995993630783,
                0.9999251537370629,
                0.999972464295789,
                0.9999938558275954,
                0.9999646437366535,
                0.9999724643056263,
                0.9998766053958636
            ],
            [
                0.9999832985761661,
                0.9997388096917338,
                0.9999599363030652,
                0.9997694933678146,
                0.9999938558253981,
                0.9999910602994334,
                0.9998766054546542,
                0.9999852610215451,
                0.9999151889789025,
                0.9999339478474997
            ],
            [
                0.9999832985741748,
                0.9998766054105033,
                0.9999930377445805,
                0.9999785550567081,
                0.9999832985821381,
                0.9999756997476926,
                0.9994472213875166,
                0.9998601779762216,
                0.9999485577741123,
                0.9999724643089064
            ],
            [
                0.999903897539346,
                0.9999810748449934,
                0.999891103090875,
                0.9998766054693442,
                0.9999038975852054,
                0.9999251537460537,
                0.9999910603036963,
                0.9999038976081689,
                0.9999898700053983,
                0.9999852610215436
            ],
            [
                0.9999599363221608,
                0.9999687980886347,
                0.9999785550567011,
                0.9999485577863566,
                0.9999687980737675,
                0.9999646437492984,
                0.9999869928699852,
                0.9999339478632726,
                0.9999646437450943,
                0.9999930377445803
            ],
            [
                0.9999898700114356,
                0.9998766054548427,
                0.9991959139760291,
                0.9999869928699862,
                0.9999038975392935,
                0.9999251537460276,
                0.9999885212318748,
                0.9999885212264013,
                0.9999485577925007,
                0.9999646437535082
            ],
            [
                0.9998766053961293,
                0.9999038975509236,
                0.9998601779428311,
                0.9998766054399821,
                0.9999885212332451,
                0.999925153781771,
                0.9999724642957795,
                0.9999785550515903,
                0.9999898700066059,
                0.9999945777790912
            ],
            [
                0.9999724643089097,
                0.9999724643187565,
                0.9999885212318764,
                0.9999417087484003,
                0.9999756997563787,
                0.9999646437366552,
                0.9999724643121931,
                0.9999485577802758,
                0.999996273358939,
                0.9999921107345936
            ],
            [
                0.9999546021368043,
                0.9999921107374145,
                0.9999546021097453,
                0.9999869928730867,
                0.9999724643023389,
                0.9997965729788819,
                0.9997694931760726,
                0.999985261021544,
                0.9999898700041906,
                0.9991959140594134
            ],
            [
                0.9998601779433112,
                0.9999251537549951,
                0.9997965730762514,
                0.9999646437366602,
                0.999993855823201,
                0.9999930377454104,
                0.9999339478789965,
                0.999978555059262,
                0.9999756997592781,
                0.9999785550464758
            ],
            [
                0.9999151889790481,
                0.9997965731008195,
                0.9999687980737645,
                0.9999957771665555,
                0.9999832985841286,
                0.9999687980774823,
                0.9999810748495074,
                0.9999921107345933,
                0.9999945777829696,
                0.9999921107345932
            ],
            [
                0.9999151889587515,
                0.9999852610127603,
                0.9999938558224685,
                0.9999151889285257,
                0.9999756997592695,
                0.9999898700126436,
                0.9999962733620488,
                0.9999546021367987,
                0.9999485577741718,
                0.9999921107402359
            ],
            [
                0.999993037740431,
                0.9999982396567867,
                0.9999910603026325,
                0.9999977396757022,
                0.999991060306894,
                0.9999038975623201,
                0.9999910603005013,
                0.999968798092365,
                0.9999974387168734,
                0.9999646437324408
            ],
            [
                0.9999930377437503,
                0.999948557780225,
                0.9999910603015648,
                0.9999417087275736,
                0.999994577782323,
                0.9997965730758843,
                0.9999546021259992,
                0.9999885212264009,
                0.9999785550464765,
                0.9999810748540172
            ],
            [
                0.9999852610145158,
                0.9999038975737187,
                0.9998766054548085,
                0.9997965730031214,
                0.9998911031167798,
                0.9999151889688264,
                0.9999546021313821,
                0.9999417087136911,
                0.9998766053664531,
                0.9999756997476862
            ],
            [
                0.999978555043919,
                0.9998204720344616,
                0.9998415637266403,
                0.9999810748495079,
                0.999954602136796,
                0.9999038975736242,
                0.9999599363030566,
                0.9999485577618425,
                0.9999646437366602,
                0.9998601779594093
            ],
            [
                0.9999687980960708,
                0.9999417087345,
                0.9999810748449944,
                0.9999724642957716,
                0.9999832985701927,
                0.9999869928699864,
                0.9999756997650621,
                0.999989870010228,
                0.9998601778927992,
                0.9999251537995338
            ],
            [
                0.999992110738355,
                0.9999910603004993,
                0.9999962733611603,
                0.9999756997505828,
                0.9999251537908125,
                0.9998601779095707,
                0.9999546021421996,
                0.9999417087345488,
                0.9999687980849105,
                0.9999852610127582
            ]
        ]
    },
    {
        "q_id": "7693_mmlu_math",
        "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,
            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": [
            [
                1.370957370247318e-06,
                8.315283250150648e-07,
                1.9947290080905435e-06,
                1.2098656834922064e-06,
                4.785094494576774e-06,
                2.2603245672867952e-06,
                1.5534973841705173e-06,
                2.260323758882316e-06,
                9.422450431860582e-07,
                5.715004470025379e-07
            ],
            [
                1.4738981969615573e-05,
                4.22283193393364e-06,
                4.222833444106873e-06,
                2.5612828213690224e-06,
                0.00023050665925510163,
                1.473897845457507e-05,
                7.484624507084954e-05,
                0.00017952802996101694,
                3.7266406167827664e-06,
                6.605217610793098e-05
            ],
            [
                6.144174601588856e-06,
                0.0001398221232419965,
                0.9964063968033137,
                5.829125853074485e-05,
                3.2887478887419687e-06,
                1.670142781478417e-05,
                0.994779873815563,
                6.475948753847607e-07,
                4.539786861523573e-05,
                0.0001795280291695786
            ],
            [
                1.7603440527222532e-06,
                4.222832941072913e-06,
                8.31528424162821e-07,
                4.450848927650143e-07,
                3.7266397283231055e-06,
                6.962255419475714e-06,
                4.222835458002318e-06,
                5.715002426439334e-07,
                5.043473480777865e-07,
                8.315278294097538e-07
            ],
            [
                5.42222090882208e-06,
                1.892514372737249e-05,
                2.1444953522913026e-05,
                1.1478764019996392e-05,
                2.2603242978665707e-06,
                5.42221767672807e-06,
                5.422220908314139e-06,
                2.902311639073834e-06,
                1.892515049571424e-05,
                1.1478772227651366e-05
            ],
            [
                6.962257909323729e-06,
                6.144173869072478e-06,
                0.9706877715275527,
                3.120190392795564e-05,
                1.0129987355564522e-05,
                2.4300243621371074e-05,
                4.539785779797843e-05,
                0.00043055698645675316,
                1.2098662604247682e-06,
                5.8291272294063885e-05
            ],
            [
                6.962256249112569e-06,
                2.9023119850527192e-06,
                4.222834954561012e-06,
                1.6701415869924985e-05,
                7.889264466344872e-06,
                9.422448184561605e-07,
                6.144177531459659e-06,
                3.120191137126484e-05,
                1.067703251864202e-06,
                1.4738981970956057e-05
            ],
            [
                4.539785237316614e-05,
                0.9999151889687937,
                4.539786317522845e-05,
                7.48462624165442e-05,
                1.3007131559390956e-05,
                6.962254586824882e-06,
                6.9622579092224155e-06,
                8.481106106004433e-05,
                3.1201922508819695e-05,
                7.889261644760245e-06
            ],
            [
                4.222833947932061e-06,
                6.962253759904688e-06,
                4.2228324377740105e-06,
                1.8925143723620274e-05,
                9.610241487022105e-05,
                4.222834451169694e-06,
                1.4738989000181669e-05,
                2.561282516042282e-06,
                3.7266397283231055e-06,
                0.0002034270698221334
            ],
            [
                6.475945665800774e-07,
                6.475946437966953e-07,
                6.962257909412379e-06,
                4.78509392429544e-06,
                1.2098652508347793e-06,
                1.5534984953453635e-06,
                3.726639728348526e-06,
                1.9947306726594253e-06,
                1.2098655392574583e-06,
                1.5534983100595462e-06
            ],
            [
                3.726638395611981e-06,
                1.3709576971242028e-06,
                3.2887498494282754e-06,
                4.222833947774596e-06,
                4.222834954753043e-06,
                4.785093353687772e-06,
                1.0677029973192638e-06,
                1.3007128464559612e-05,
                4.22283344433731e-06,
                3.288749457383046e-06
            ],
            [
                1.1478766756444477e-05,
                1.9947297215043796e-06,
                2.9023133690637e-06,
                1.2098658277489788e-06,
                4.222833444467892e-06,
                1.8925155007633607e-05,
                1.3709573702722555e-06,
                2.7535681250497054e-05,
                2.902313023101807e-06,
                5.422221555133606e-06
            ],
            [
                3.059021904543821e-07,
                8.939700564468113e-06,
                3.288748673265808e-06,
                4.222835457906302e-06,
                4.006370647374544e-05,
                3.288750241473551e-06,
                5.422221553910605e-06,
                1.7603434231705793e-06,
                4.785095635413826e-06,
                2.260324297570543e-06
            ],
            [
                6.962257079553702e-06,
                8.315280276546789e-07,
                1.99472924590571e-06,
                1.0129990979694647e-05,
                1.2098653950656417e-06,
                5.04347468323289e-07,
                1.670141985166528e-05,
                1.7603427936183298e-06,
                1.9947304348595095e-06,
                1.2098662604247682e-06
            ],
            [
                6.962257079705671e-06,
                4.006369695353247e-05,
                1.5534981249397663e-06,
                1.5534979397592542e-06,
                4.785095635413826e-06,
                1.0129989771288745e-05,
                4.222834954561012e-06,
                1.3709572068179446e-06,
                0.9997040429024946,
                5.422218969217281e-06
            ],
            [
                3.2887490649221017e-06,
                4.5397874046655906e-05,
                5.422217676866151e-06,
                6.60521210438226e-05,
                5.144223203214182e-05,
                1.670142781636389e-05,
                2.4300252319959737e-05,
                5.8291279387562654e-05,
                2.1444956081636468e-05,
                1.8925141468298646e-05
            ],
            [
                3.120191137012976e-05,
                1.473898899908247e-05,
                1.147876812574406e-05,
                1.0129990979842057e-05,
                5.144221976237626e-05,
                4.785093353352668e-06,
                3.535625913206225e-05,
                4.222832437639588e-06,
                8.481102114380802e-05,
                9.610239186473745e-05
            ],
            [
                3.288748673035494e-06,
                2.260325375650449e-06,
                7.889264466445326e-06,
                1.8925145980732218e-05,
                2.4300243627117176e-05,
                2.5612825159677387e-06,
                2.5612831267086116e-06,
                4.785094494672519e-06,
                1.473898021457511e-05,
                1.473898372822193e-05
            ],
            [
                2.4300240706150922e-05,
                4.785095064819011e-06,
                4.222831934052698e-06,
                3.5356246490314526e-05,
                6.962254588977791e-06,
                2.2603251061232293e-06,
                4.222833947428939e-06,
                2.9023109470871505e-06,
                7.889262582571338e-06,
                1.5534979397677313e-06
            ],
            [
                6.962254589104433e-06,
                1.1478766755985128e-05,
                3.7266406168403854e-06,
                1.5534975693707442e-06,
                3.726641060956752e-06,
                1.8925157261545463e-05,
                1.3007131562845248e-05,
                1.1478768124783601e-05,
                3.7266406168624155e-06,
                1.1478764019787597e-05
            ],
            [
                3.1201907609144296e-05,
                2.260324297853209e-06,
                1.0129993391531815e-05,
                3.9278605979208185e-07,
                0.000261190400374024,
                1.8925145981283003e-05,
                4.5397890204837524e-05,
                1.147877359872636e-05,
                1.14787681240737e-05,
                1.2098659719716573e-06
            ],
            [
                7.484625402740036e-05,
                4.0063687374440786e-05,
                6.144177529855884e-06,
                3.5356242260622145e-05,
                1.4738985485461206e-05,
                2.1444940736477737e-05,
                8.939695237341456e-06,
                1.0129994598777299e-05,
                2.260323758882316e-06,
                8.481102108148808e-05
            ],
            [
                1.3709576971379186e-06,
                6.96225458885115e-06,
                1.553498495338299e-06,
                1.9947304348332037e-06,
                2.260323489435463e-06,
                7.338210680002898e-07,
                7.338208055664991e-07,
                1.553498495295912e-06,
                5.422217676654099e-06,
                3.7266397280485686e-06
            ],
            [
                2.902311985146426e-06,
                4.785092783210732e-06,
                1.0677028700266676e-06,
                4.00636778083227e-05,
                3.7266383953679482e-06,
                2.2603242978213447e-06,
                8.939693106020111e-06,
                1.9947306726049992e-06,
                2.260325375634003e-06,
                1.0129990978644356e-05
            ],
            [
                1.2098658277451275e-06,
                2.902310947190096e-06,
                1.760344052714248e-06,
                2.3823688159291947e-07,
                8.315281267706361e-07,
                1.0677024881683915e-06,
                6.825609419823202e-08,
                7.338207180864763e-07,
                1.4738983726559732e-05,
                3.9278634073312583e-07
            ],
            [
                0.0002611904026083228,
                1.7603436329714805e-06,
                5.422220262505697e-06,
                4.0063692183734794e-05,
                9.610243787850682e-05,
                0.00015843627322597727,
                5.422218969818919e-06,
                4.0063687408107886e-05,
                9.61024149988683e-05,
                3.72664017246987e-06
            ],
            [
                0.00010889696116743783,
                1.3007125362820425e-05,
                4.539785781036459e-05,
                8.939699499432793e-06,
                2.902311984683171e-06,
                1.300712536203966e-05,
                1.147876538789672e-05,
                8.939699501132077e-06,
                8.939694172290508e-06,
                0.00015843625368722246
            ],
            [
                7.889264466344872e-06,
                5.422221555069497e-06,
                1.99472924590571e-06,
                1.994730672668496e-06,
                1.9947297215043796e-06,
                3.72664061671159e-06,
                7.889262585211807e-06,
                1.067703379154416e-06,
                9.422445939002803e-07,
                2.2603234895289998e-06
            ],
            [
                0.4073334000459302,
                3.53562675670136e-05,
                4.5397868612593344e-05,
                1.6701419850845044e-05,
                0.0019267346252697006,
                3.5356259136692605e-05,
                3.535624227734284e-05,
                0.3775406687981454,
                0.00013982212402930744,
                0.6791786861878392
            ],
            [
                5.422218968349347e-06,
                2.5612831264675113e-06,
                1.2098656835136636e-06,
                2.7535704221626983e-05,
                1.3007125361448172e-05,
                0.9997040429725532,
                2.9023126771227976e-06,
                5.8291251620035695e-05,
                0.8933094167058151,
                2.561282821239737e-06
            ],
            [
                1.8925155007633607e-05,
                1.3007131564903626e-05,
                3.2887478891128633e-06,
                2.144495352533148e-05,
                6.475949526003845e-07,
                1.012999097799944e-05,
                1.6701419852819694e-05,
                0.00010889696107712208,
                1.3007131564903626e-05,
                1.3007130015299356e-05
            ],
            [
                1.3709570434122812e-06,
                3.535624649751729e-05,
                3.120191507912884e-05,
                0.0005527786801120172,
                0.0001088969092152976,
                0.0006263341725739613,
                1.0129990978441666e-05,
                0.0003799844364396507,
                0.0005527786126441852,
                0.9964063978487661
            ],
            [
                1.3007126913346863e-05,
                0.00013982214069303955,
                1.4738983724146862e-05,
                3.535624649468763e-05,
                2.260324836776948e-06,
                1.4738978457336465e-05,
                1.3007130012010681e-05,
                3.120190018002454e-05,
                1.473898021366358e-05,
                5.829125856424875e-05
            ],
            [
                8.315282259117513e-07,
                1.5534981249496567e-06,
                5.71500515159253e-07,
                6.475946437966953e-07,
                9.422448185435711e-07,
                4.450850518520938e-07,
                2.9023116391675407e-06,
                1.8925143727854426e-05,
                7.889266347356409e-06,
                1.209865250822125e-06
            ],
            [
                2.561283431888668e-06,
                1.7603430033399058e-06,
                2.9023133689924295e-06,
                1.9947290080905435e-06,
                1.5534975693601474e-06,
                3.7266406167827664e-06,
                4.785093353274332e-06,
                5.4222170304318e-06,
                9.422442568763144e-07,
                3.2887502412970765e-06
            ],
            [
                4.785093924251918e-06,
                4.7850939242083995e-06,
                2.5612825160562587e-06,
                4.222834954514924e-06,
                6.144172404587612e-06,
                1.9947301970287804e-06,
                5.144220138599094e-05,
                2.9023112930949896e-06,
                3.5356238071317175e-05,
                8.939699500164542e-06
            ],
            [
                2.561283432005142e-06,
                2.4300240730549767e-05,
                3.7266392840781026e-06,
                6.1441767987808774e-06,
                8.939700566289352e-06,
                1.012998977213635e-05,
                6.144173136645595e-06,
                1.892514598551715e-05,
                4.2228324377164004e-06,
                1.4738988997044936e-05
            ],
            [
                1.7603427936335396e-06,
                2.9023123310290063e-06,
                2.2603234894560207e-06,
                5.043473480678099e-07,
                1.0677032518413822e-06,
                7.338207180838067e-07,
                3.9278638755671223e-07,
                7.338211554688417e-07,
                1.370956716519966e-06,
                1.0677024881941248e-06
            ],
            [
                1.8925141465820123e-05,
                5.422221553654169e-06,
                1.2098653950551882e-06,
                8.939699501229642e-06,
                1.0129993393742954e-05,
                5.422219616085833e-06,
                6.962254589433702e-06,
                8.481105146894064e-05,
                6.144173869312763e-06,
                3.5356242271040426e-05
            ],
            [
                7.484626290608339e-05,
                4.53978794604058e-05,
                1.473898197154587e-05,
                1.0677027427600627e-06,
                1.4738987241172537e-05,
                2.561283126639892e-06,
                3.1201900207380036e-05,
                5.1442213646395314e-05,
                0.0002611903095201565,
                6.962256249327861e-06
            ],
            [
                1.2098658277181688e-06,
                2.9023126771227976e-06,
                1.1478769493728398e-05,
                2.2603240280866228e-06,
                1.4738988999672284e-05,
                1.012999460108057e-05,
                1.3007126911974612e-05,
                1.7603436330179102e-06,
                3.12019150894581e-05,
                1.3709567165579959e-06
            ],
            [
                0.0021827161162411924,
                0.004609573194261633,
                0.9999485577680016,
                5.144219520863158e-05,
                0.9859363746096915,
                0.0004305570338656305,
                0.9978172840014047,
                7.889265406567165e-06,
                0.009708478102137695,
                5.8291279387562654e-05
            ],
            [
                5.71500378896509e-07,
                1.1253517547010071e-07,
                1.7603432133032607e-06,
                1.7603425836870455e-06,
                4.450851580555361e-07,
                1.2098662604126641e-06,
                4.450848927650143e-07,
                1.7603432133032607e-06,
                1.8553919030776337e-07,
                3.4663257978638593e-07
            ],
            [
                1.6373764721039308e-07,
                8.9396973679153e-06,
                2.5612834317116285e-06,
                1.0129989771288745e-05,
                1.9947299592933255e-06,
                6.9622537584863015e-06,
                1.0677024881683915e-06,
                3.288749849477628e-06,
                0.00017952790139543387,
                4.785092783149804e-06
            ],
            [
                3.535623804983752e-05,
                1.4738985483504099e-05,
                4.222833444283541e-06,
                4.0063706508432764e-05,
                9.610243738349442e-05,
                2.430024941459533e-05,
                4.539786320660675e-05,
                2.7535687809124434e-05,
                4.00636826326273e-05,
                0.0002959572029032216
            ],
            [
                3.7266406162947e-06,
                8.31527928532683e-07,
                1.2098653950315304e-06,
                2.2603251061664e-06,
                4.450849458200093e-07,
                2.2603234894745224e-06,
                1.6701419850389357e-05,
                7.889263524788109e-06,
                2.9023133690188264e-06,
                1.2098652507957165e-06
            ],
            [
                3.7266410609940346e-06,
                6.605216823537969e-05,
                5.829125856424875e-05,
                2.4300246515109972e-05,
                2.753569109925723e-05,
                7.889265406567165e-06,
                5.8291251608160896e-05,
                6.144176066521288e-06,
                0.0001233946336636578,
                0.00010889694805897948
            ],
            [
                4.450851049890802e-07,
                1.300712846411008e-05,
                6.144176799166453e-06,
                2.5612825159677387e-06,
                2.902311985079115e-06,
                3.7266406167827664e-06,
                4.006369218184011e-05,
                1.7603430034655858e-06,
                1.3709572067356507e-06,
                2.699578739984626e-07
            ],
            [
                1.8925141467679015e-05,
                1.7603438428660665e-06,
                4.785096205717126e-06,
                8.481102099695511e-05,
                2.7535697664698622e-05,
                0.0024726235592043484,
                0.00013982204071474552,
                0.00017952790186820695,
                6.962257079705671e-06,
                1.6701417861949427e-05
            ],
            [
                8.939698435226916e-06,
                1.892514598469098e-05,
                1.9947306726358406e-06,
                1.1478769494083349e-05,
                4.222834451327159e-06,
                2.2603240283888175e-06,
                4.539786864000808e-05,
                1.4738988999377379e-05,
                3.120190393260949e-05,
                1.7603432132464244e-06
            ],
            [
                3.2887490652451393e-06,
                6.962256249606473e-06,
                5.422219616085833e-06,
                3.726641060956752e-06,
                5.715007195228928e-07,
                1.3007131564903626e-05,
                6.144175334094145e-06,
                2.1444943298944354e-05,
                4.785094494463623e-06,
                6.475946437657736e-07
            ],
            [
                9.422445937837332e-07,
                1.20986611609532e-06,
                2.2603245671490605e-06,
                6.47594643788744e-07,
                3.059021904506262e-07,
                1.760343632920248e-06,
                1.9947292458603553e-06,
                3.2887502412970765e-06,
                3.2887486732000038e-06,
                1.3709573702248741e-06
            ],
            [
                2.1444943296369872e-05,
                1.9947290081177566e-06,
                1.1478765388314311e-05,
                1.5534979397740895e-06,
                2.2603234895053587e-06,
                6.962256249429175e-06,
                1.3709568799823232e-06,
                6.144173136645595e-06,
                1.2098661162023305e-06,
                8.939694169835089e-06
            ],
            [
                2.5612825160096693e-06,
                5.422218323399208e-06,
                5.422217677078203e-06,
                5.422218323399208e-06,
                1.5534971989992774e-06,
                2.3823699519290042e-07,
                3.7266406167827664e-06,
                2.2603245673155757e-06,
                5.043474081993875e-07,
                1.7603432133136672e-06
            ],
            [
                1.0677033790475986e-06,
                3.2887490652451393e-06,
                5.422217676979575e-06,
                2.1444940745371397e-05,
                1.9947306726594253e-06,
                6.9622570784012604e-06,
                2.260325375615501e-06,
                8.939700562695657e-06,
                6.962257079275089e-06,
                8.315280276456036e-07
            ],
            [
                1.3709572068478697e-06,
                9.422449308748773e-07,
                8.939694172542558e-06,
                4.222835458148261e-06,
                4.222834451254188e-06,
                1.0129993394811673e-05,
                7.338208930443633e-07,
                2.5612825160271407e-06,
                2.2603242978665707e-06,
                3.2887478892683997e-06
            ],
            [
                1.2098662604291696e-06,
                1.670141587141357e-05,
                1.9947297214944016e-06,
                1.7603434231705793e-06,
                1.147876812538911e-05,
                8.93969736955767e-06,
                1.0677033791495609e-06,
                5.715003789017068e-07,
                4.785096205973894e-06,
                8.315281267800897e-07
            ],
            [
                3.2887482809455384e-06,
                6.47594952595231e-07,
                1.3709567165530083e-06,
                1.0129987357158383e-05,
                2.5612825160096693e-06,
                8.315280275673297e-07,
                5.422219616085833e-06,
                1.7603436330179102e-06,
                9.422445939002803e-07,
                8.315281267834927e-07
            ],
            [
                1.0677032516821266e-06,
                4.785093353687772e-06,
                8.315278293301564e-07,
                1.0677032508392387e-06,
                8.31528424146183e-07,
                9.422443691996268e-07,
                1.637377252820885e-07,
                2.5612825156159896e-06,
                4.2228324375512536e-06,
                1.2098655392464547e-06
            ],
            [
                2.902312331125353e-06,
                1.6701429804744246e-05,
                6.605213668174985e-05,
                6.9622595694023114e-06,
                7.338211554758494e-07,
                1.300712536258383e-05,
                3.288749065077638e-06,
                5.422221555296344e-06,
                1.89251527491092e-05,
                1.99472924590571e-06
            ],
            [
                0.9991959139649924,
                2.7535691098355687e-05,
                6.962255419279419e-06,
                0.00010889693439595244,
                3.726639283806955e-06,
                1.1478766756653273e-05,
                1.0129993394664264e-05,
                0.00023050682235793918,
                1.0677032518501217e-06,
                0.0001584362543718626
            ],
            [
                6.47594566560052e-07,
                9.422445938642879e-07,
                7.484626286742124e-05,
                1.012999097799944e-05,
                4.222832941142044e-06,
                2.902313368820854e-06,
                6.144175334094145e-06,
                6.962257079173776e-06,
                7.889263525534328e-06,
                4.785094494628999e-06
            ],
            [
                0.9998766054418422,
                0.9324533079218341,
                0.9999151889891205,
                0.0021827160842942746,
                0.9998911030391447,
                0.9984988174282936,
                0.9998415637842584,
                0.999975699767958,
                0.2227001491431584,
                0.9992903294618719
            ],
            [
                0.0008040860133548748,
                0.00010889696078082307,
                3.120190764966677e-05,
                0.9986749776744457,
                1.6701421842566163e-05,
                0.0007096705111729157,
                5.144221359250013e-05,
                0.0007096703451902962,
                9.610241456817964e-05,
                0.0005527787269664695
            ],
            [
                2.753568780802255e-05,
                0.07585818054355695,
                5.144223204748698e-05,
                4.785093924251918e-06,
                0.0011695102548562883,
                1.1478765388314311e-05,
                4.539789027568648e-05,
                3.53562633540394e-05,
                1.1478768125577027e-05,
                0.000139822090473997
            ],
            [
                6.9622579092224155e-06,
                4.78509392429544e-06,
                1.2098655392811161e-06,
                4.785096205930373e-06,
                6.144173137126169e-06,
                7.338209805133949e-07,
                7.889265406681968e-06,
                4.450852111135988e-07,
                1.7603432133136672e-06,
                1.300712846411008e-05
            ],
            [
                0.0002611904024031321,
                9.610243774636368e-05,
                0.9997388097537545,
                8.48110614210065e-05,
                5.144220139179215e-05,
                0.0009110510106596227,
                0.0019267347573525696,
                0.0002959571685714096,
                3.535626335686906e-05,
                0.9997040428654331
            ],
            [
                2.4300234937239182e-05,
                0.9947798755179202,
                1.3007126910294786e-05,
                2.7535704219423216e-05,
                1.760344052693435e-06,
                1.0129987354882753e-05,
                0.00013982214083137844,
                0.0006263341634288735,
                0.0007096705403984095,
                0.0002611902154060705
            ],
            [
                4.7850944945245504e-06,
                6.1441746018123775e-06,
                1.0129994602057158e-05,
                6.144176799227922e-06,
                1.670141587068447e-05,
                6.1441767989541075e-06,
                7.88926164518358e-06,
                9.422443692489024e-07,
                7.8892625849535e-06,
                6.962253759752719e-06
            ],
            [
                0.0001584362732789965,
                3.120192625073753e-05,
                6.962255419570695e-06,
                1.1478766757404937e-05,
                3.120191137012976e-05,
                2.430024362932722e-05,
                2.144495352474637e-05,
                3.726641061058432e-06,
                1.6701417859944398e-05,
                1.0129987355988324e-05
            ],
            [
                6.475950297993789e-07,
                7.338208930391909e-07,
                2.260325375664839e-06,
                2.561281600049467e-06,
                1.3709575336860625e-06,
                7.338208055436404e-07,
                9.422450431954847e-07,
                6.475947982022763e-07,
                5.04347287955046e-07,
                3.466327037548308e-07
            ],
            [
                8.315278294072958e-07,
                3.726639284050988e-06,
                1.3007125360478133e-05,
                1.209865827740176e-06,
                7.338207180864763e-07,
                1.5534979397677313e-06,
                1.7603434231241496e-06,
                2.902310947208574e-06,
                1.3709575337078829e-06,
                1.3709573702566696e-06
            ],
            [
                0.00029595709712646536,
                2.9023133690637e-06,
                0.00033534998941389107,
                1.147876675686207e-05,
                3.726641060956752e-06,
                0.00317268334836052,
                0.00023050666014043624,
                3.120192252686752e-05,
                3.5356242272712497e-05,
                4.006369696096547e-05
            ],
            [
                1.760344052714248e-06,
                7.338213304343413e-07,
                1.1253520230052635e-07,
                5.715007195447234e-07,
                2.561281600049467e-06,
                2.3823696679230424e-07,
                1.2098652508287273e-06,
                4.785095065132354e-06,
                1.6373776432481905e-07,
                3.46632497145457e-07
            ],
            [
                3.288749065406658e-06,
                3.2887482812745586e-06,
                7.338211554783522e-07,
                1.892514372737249e-05,
                4.22283344433731e-06,
                3.726639284050988e-06,
                0.09534946361376596,
                7.889259764273619e-06,
                3.120192625073753e-05,
                3.12019150894581e-05
            ],
            [
                2.2603237589028734e-06,
                2.561281905376098e-06,
                6.14417533430649e-06,
                1.3709576971379186e-06,
                1.553498495338299e-06,
                2.902310947190096e-06,
                1.553497384180408e-06,
                1.5534984953453635e-06,
                2.902312331125353e-06,
                2.382368815916736e-07
            ],
            [
                1.5534981249697903e-06,
                4.7850950649408664e-06,
                6.605216038349344e-05,
                2.902310947208574e-06,
                1.4738987239295859e-05,
                1.0129993394129904e-05,
                2.902312677084523e-06,
                1.6701417858577338e-05,
                1.3709568799879344e-06,
                3.7266401725935817e-06
            ],
            [
                1.1478770861859053e-05,
                0.00020342702111811778,
                3.535624227734284e-05,
                7.889261643727018e-06,
                8.939696304002375e-06,
                4.785092783454444e-06,
                2.7535700942411318e-05,
                4.0063692152253866e-05,
                0.00012339457482280874,
                5.8291272486605336e-05
            ],
            [
                5.422220261948442e-06,
                3.2887478888496478e-06,
                2.902311293147782e-06,
                1.1478770861441461e-05,
                7.889260701467423e-06,
                7.338207180801359e-07,
                6.962254589528684e-06,
                1.5534973841895917e-06,
                3.535624645738762e-05,
                5.422217675756574e-06
            ],
            [
                1.0129994597155795e-05,
                1.4738983721733992e-05,
                7.889265405146477e-06,
                1.6701415838482526e-05,
                6.144176797864436e-06,
                4.222833947674739e-06,
                6.144174600180663e-06,
                1.2098658276598493e-06,
                4.450852641596248e-07,
                2.753570094040789e-05
            ],
            [
                8.48110814738458e-05,
                2.9023133690637e-06,
                2.561281905376098e-06,
                4.7850967763512445e-06,
                1.2098661161927025e-06,
                2.9023116391675407e-06,
                2.9023126771227976e-06,
                2.4300234936443568e-05,
                1.0129995810343862e-05,
                2.902311985079115e-06
            ],
            [
                1.3007126912542439e-05,
                2.260324836776948e-06,
                2.902310947208574e-06,
                9.422447062202052e-07,
                1.7603430034655858e-06,
                3.726639284050988e-06,
                7.889261644875049e-06,
                3.535624228313077e-05,
                4.222835457664342e-06,
                3.2887482812506295e-06
            ],
            [
                7.889264465397747e-06,
                8.939694172542558e-06,
                5.422217676575195e-06,
                1.2098662604247682e-06,
                1.7603438428460541e-06,
                3.288747889178668e-06,
                9.422443691524936e-07,
                6.9622570780973205e-06,
                2.90231163910023e-06,
                4.7850967757637256e-06
            ],
            [
                4.006367780569929e-05,
                0.0003799844246662885,
                1.0129992186939844e-05,
                0.003172682479462622,
                0.00013982210726385758,
                0.00010889692199259365,
                1.4738985483128763e-05,
                0.0001398220566664297,
                2.4300232031037035e-05,
                0.00013982202357701158
            ],
            [
                1.473898372500477e-05,
                2.430024071781994e-05,
                4.785096776394765e-06,
                6.962257909121104e-06,
                4.222834450820197e-06,
                2.260324028331257e-06,
                1.6701429804744246e-05,
                4.22283545808297e-06,
                3.2887506330851655e-06,
                5.4222215550004564e-06
            ],
            [
                3.726640616748873e-06,
                7.889261644631091e-06,
                6.962256249112569e-06,
                1.1478769492893215e-05,
                7.889259764273619e-06,
                1.1478764020727177e-05,
                5.422219616140078e-06,
                3.535625070920327e-05,
                3.726639728262097e-06,
                6.144175333401224e-06
            ],
            [
                1.8925148238808306e-05,
                0.00015843623549239316,
                7.338210679979539e-07,
                1.0129995806022926e-05,
                1.0129989771823107e-05,
                5.422218969306048e-06,
                5.42221961567159e-06,
                1.5534975693036317e-06,
                6.144176799099397e-06,
                3.726638839806038e-06
            ],
            [
                1.994729721482609e-06,
                5.715007195384861e-07,
                1.1253517547010071e-07,
                4.4508499888219586e-07,
                3.05902190458764e-07,
                6.144176799227922e-06,
                1.3709573702647743e-06,
                2.1024329090867228e-07,
                0.0008040857517440585,
                5.043474081993875e-07
            ],
            [
                2.4300234937946394e-05,
                2.260324028404236e-06,
                2.902310947190096e-06,
                2.9023133690821773e-06,
                5.715004470295662e-07,
                1.1478770862067849e-05,
                3.2887478890769702e-06,
                4.785095635655362e-06,
                2.902310947190096e-06,
                2.902310947208574e-06
            ],
            [
                4.785092783454444e-06,
                3.7266397282926013e-06,
                1.9947297215043796e-06,
                1.9947306726594253e-06,
                3.12019262448351e-05,
                2.2603237589676295e-06,
                1.9947301970813926e-06,
                3.7266379513162962e-06,
                8.93969310662177e-06,
                6.962255419728997e-06
            ],
            [
                3.288750633488963e-06,
                1.3007130015299356e-05,
                1.147876675686207e-05,
                1.3709567165617364e-06,
                1.5534983101393749e-06,
                1.9947299591354906e-06,
                4.222833444467892e-06,
                5.71500515159253e-07,
                2.2603234895289998e-06,
                5.422217030707961e-06
            ],
            [
                6.9622579095833456e-06,
                2.7535687799708318e-05,
                1.8925150494750372e-05,
                6.605212892117389e-05,
                5.4222170304318e-06,
                3.5356254925134237e-05,
                8.481108177187105e-05,
                7.484621826927065e-05,
                9.610243785962923e-05,
                4.539786862811735e-05
            ],
            [
                0.00017952803029535388,
                1.6701427817730953e-05,
                4.7850944942634305e-06,
                8.315277302747361e-07,
                4.785095635624897e-06,
                2.1444958639072976e-05,
                3.288749065406658e-06,
                1.7603434231385591e-06,
                2.902312331081799e-06,
                8.315279285149107e-07
            ],
            [
                1.0129990979381404e-05,
                4.222834451254188e-06,
                0.00010889690911072151,
                4.222832941111319e-06,
                4.78509563546605e-06,
                1.8925155007633607e-05,
                7.484620041444411e-05,
                2.144494329496561e-05,
                3.2887486731252264e-06,
                1.9947306725451314e-06
            ],
            [
                0.00043055709048073,
                5.829127247176183e-05,
                0.004070137680031891,
                0.0003799845740166661,
                0.9890130554061335,
                0.001325022300752483,
                8.481103123717e-05,
                8.481106149875219e-05,
                4.5397852408342864e-05,
                0.00010889689590403128
            ],
            [
                6.144176799227922e-06,
                1.9947297215125433e-06,
                4.78509563550957e-06,
                1.670141985166528e-05,
                5.422219616140078e-06,
                2.561282210729555e-06,
                1.3709576971425944e-06,
                2.561282821352716e-06,
                1.994730434879465e-06,
                5.4222183234485234e-06
            ],
            [
                7.889263524443698e-06,
                4.222833947774596e-06,
                1.0129992185060374e-05,
                7.889262585642319e-06,
                1.3007128463873485e-05,
                2.2603242976733308e-06,
                8.939696303758459e-06,
                8.93969417150998e-06,
                2.902312677007974e-06,
                6.9622579096593295e-06
            ],
            [
                0.9999646437492937,
                0.9997040427590537,
                0.999997097686977,
                0.0011695100737180418,
                0.9999852610145148,
                0.9999970976876689,
                0.9999546021259487,
                0.9999756997650636,
                0.9999898700114355,
                0.9999952149055052
            ],
            [
                1.1478772227964558e-05,
                4.785093353687772e-06,
                6.962257908880483e-06,
                2.5612825157464395e-06,
                1.0129994601688632e-05,
                4.7850956351657615e-06,
                6.962255419279419e-06,
                7.889260703763482e-06,
                4.7850950646797465e-06,
                5.422218969217281e-06
            ],
            [
                1.0129987354882753e-05,
                2.4300246523773334e-05,
                1.300713466619476e-05,
                3.535625070778844e-05,
                1.8925152752999112e-05,
                8.481108174040254e-05,
                2.902311984873224e-06,
                5.422217677078203e-06,
                5.422217030555087e-06,
                1.1478766756214804e-05
            ],
            [
                1.1478772229551402e-05,
                1.1478769491014062e-05,
                3.059023363221292e-07,
                4.539789026032761e-05,
                3.535625490931388e-05,
                1.4738978456398127e-05,
                8.939695237813028e-06,
                1.2098658277181688e-06,
                2.2603242978778778e-06,
                1.1478764019996392e-05
            ],
            [
                4.222832941111319e-06,
                7.889262585642319e-06,
                2.75356976629957e-05,
                1.3709573702778664e-06,
                1.8925145983795953e-05,
                1.7603427936079236e-06,
                1.0129990978441666e-05,
                4.785093353874907e-06,
                4.450850519403407e-07,
                8.939699500327152e-06
            ],
            [
                3.5356246490314526e-05,
                1.8925155003330605e-05,
                1.670142183983204e-05,
                8.939693106020111e-06,
                4.0063706508432764e-05,
                8.939695237666677e-06,
                0.0001398220572747136,
                1.300712846115264e-05,
                4.0063692178050736e-05,
                1.6701419852819694e-05
            ],
            [
                7.338208930421943e-07,
                1.9947290081286418e-06,
                6.475948753991907e-07,
                6.962257909323729e-06,
                1.1478764020372226e-05,
                2.1444950969026795e-05,
                1.0677031245905116e-06,
                1.3709575337016483e-06,
                1.3007123812767362e-05,
                7.889264466545779e-06
            ],
            [
                2.902311984989368e-06,
                1.670141785809127e-05,
                5.829127245607013e-05,
                4.222834954687752e-06,
                2.430023202688216e-05,
                6.962253759670401e-06,
                4.5397852408342864e-05,
                1.4738976693529666e-05,
                5.1442232055908106e-05,
                8.93969736955767e-06
            ],
            [
                2.2603242977308917e-06,
                7.889266346129453e-06,
                2.430025231213619e-05,
                8.939698431389304e-06,
                4.222833947121688e-06,
                6.96225541788636e-06,
                6.962259568775433e-06,
                5.422220907909759e-06,
                6.605212101402784e-05,
                0.00048785711381318486
            ],
            [
                3.4663253846718004e-07,
                5.043472278299047e-07,
                1.99472924590571e-06,
                7.338208930421943e-07,
                1.0677031245990084e-06,
                1.2098653950656417e-06,
                3.7266388397721442e-06,
                1.2098652508287273e-06,
                3.726638839833152e-06,
                2.9023126771227976e-06
            ],
            [
                7.338208055536515e-07,
                3.288750633569722e-06,
                6.962257909323729e-06,
                1.0129992186589747e-05,
                1.0677031245905116e-06,
                8.939693106873817e-06,
                1.994729483630195e-06,
                4.785096776251149e-06,
                3.726641061085547e-06,
                3.726640172503764e-06
            ],
            [
                3.466325797888292e-07,
                8.315277302819205e-07,
                1.3709576970949014e-06,
                9.422442569290178e-07,
                1.76034300345598e-06,
                4.450848927599543e-07,
                1.9947306726594253e-06,
                3.7266388397382506e-06,
                2.5612825160562587e-06,
                1.2098659719757836e-06
            ],
            [
                2.1444950965906214e-05,
                5.422218969601935e-06,
                7.889266347004826e-06,
                2.4300232034838305e-05,
                1.1478769491598686e-05,
                3.120191502237466e-05,
                1.3007128464559612e-05,
                3.1201922508819695e-05,
                7.484625401596508e-05,
                1.3007131562845248e-05
            ],
            [
                3.288750241473551e-06,
                1.3709576971425944e-06,
                3.466327863983311e-07,
                5.715006514151423e-07,
                6.475948753991907e-07,
                2.561283432005142e-06,
                3.9278615344178325e-07,
                1.0677031245953668e-06,
                1.5534983101549167e-06,
                1.7603430034439723e-06
            ],
            [
                6.475945665800774e-07,
                5.043472879383035e-07,
                7.889261644358435e-06,
                2.260323489490968e-06,
                1.7603432133032607e-06,
                3.288748673319648e-06,
                2.2603251060985603e-06,
                8.939694172542558e-06,
                6.962256249327861e-06,
                2.2603251061458426e-06
            ],
            [
                6.825598842065202e-08,
                9.422445939032799e-07,
                5.715003788993679e-07,
                1.2751902768478173e-07,
                1.444980381819277e-07,
                2.902313368963394e-06,
                5.04347528446051e-07,
                1.9947297215043796e-06,
                1.5534983101301911e-06,
                1.5534979397740895e-06
            ],
            [
                3.2887498493983645e-06,
                1.1478765387416494e-05,
                6.9622587396067566e-06,
                3.7266401725681614e-06,
                7.484620938079124e-05,
                1.1478770859917257e-05,
                1.8925145981833788e-05,
                6.1441731370702875e-06,
                0.0001398221072211353,
                1.370957860567974e-06
            ],
            [
                1.0129992186939844e-05,
                8.939697367264857e-06,
                1.9947292458603553e-06,
                1.5534973841895917e-06,
                7.338211554725124e-07,
                1.6701421841259862e-05,
                6.962257909412379e-06,
                1.5534981249023245e-06,
                2.1444943297072005e-05,
                3.288748281295496e-06
            ],
            [
                3.927860597945825e-07,
                6.475948754012522e-07,
                7.338207180884785e-07,
                1.760343003481596e-06,
                6.825601283086733e-08,
                1.5534983101393749e-06,
                9.422444815726566e-07,
                7.73441946488886e-08,
                5.043474081993875e-07,
                3.059022998576899e-07
            ],
            [
                5.422217030614265e-06,
                2.1444958631232504e-05,
                5.422220262555012e-06,
                3.120192252437034e-05,
                6.144172403201774e-06,
                2.26032429745131e-06,
                4.222833444467892e-06,
                1.8925143723620274e-05,
                5.043475284447896e-07,
                4.222834954514924e-06
            ],
            [
                8.31527928532683e-07,
                1.275191036933194e-07,
                3.9278638755671223e-07,
                5.043475885674441e-07,
                2.902312677104321e-06,
                3.9278634073098236e-07,
                4.2228319341064674e-06,
                2.382368247924618e-07,
                3.059022998569248e-07,
                8.315277302701984e-07
            ],
            [
                4.785093353787868e-06,
                4.22283193338827e-06,
                4.785096205512581e-06,
                1.8925152747938785e-05,
                1.3007133110320344e-05,
                6.962256247998122e-06,
                6.605215218800707e-05,
                2.9023133686835932e-06,
                4.222832940715735e-06,
                2.902311984952413e-06
            ],
            [
                5.829125855619084e-05,
                8.93969630348202e-06,
                2.2603234895053587e-06,
                6.1441767990323395e-06,
                2.9023133690980155e-06,
                3.288748281295496e-06,
                3.5356254910985954e-05,
                4.785096776133645e-06,
                4.222833947897496e-06,
                6.1441724044534996e-06
            ],
            [
                1.6701427813872793e-05,
                1.300712536203966e-05,
                6.1441738691562974e-06,
                8.93969523617066e-06,
                1.3007134664822509e-05,
                1.012999339449843e-05,
                3.5356238036718197e-05,
                7.484625399799535e-05,
                6.144173869558639e-06,
                1.3709572068422585e-06
            ],
            [
                1.473898899664279e-05,
                1.5534979397740895e-06,
                2.4300249417247375e-05,
                6.1441724046434924e-06,
                4.222833947674739e-06,
                6.9622570780973205e-06,
                1.7603425837494853e-06,
                5.422218969661113e-06,
                2.561283126679493e-06,
                3.7266410608245674e-06
            ],
            [
                1.7603440527222532e-06,
                5.715005832872586e-07,
                1.5534979397500702e-06,
                4.222833444168322e-06,
                1.2098653950656417e-06,
                7.338213304316717e-07,
                6.962257909722651e-06,
                4.222832437747125e-06,
                7.338213304343413e-07,
                2.2603251062270446e-06
            ],
            [
                2.7535704227537108e-05,
                4.222831934248571e-06,
                1.3007125360146898e-05,
                1.0129990979547237e-05,
                1.3007133115667397e-05,
                1.670142781520948e-05,
                2.7535694373763664e-05,
                3.4663253846718004e-07,
                2.2603242978377903e-06,
                6.962258739454786e-06
            ],
            [
                2.902313023101807e-06,
                4.785096206013061e-06,
                1.2098656835136636e-06,
                1.5534981249496567e-06,
                2.2603240283888175e-06,
                1.7603430034655858e-06,
                1.4738983723664288e-05,
                2.430024651705481e-05,
                8.315278293899016e-07,
                1.3709572068179446e-06
            ],
            [
                1.9947290081286418e-06,
                1.3709567165579959e-06,
                5.715006514151423e-07,
                3.1201918809808464e-05,
                1.5534979397677313e-06,
                6.962258739530771e-06,
                3.726640172503764e-06,
                2.4300243626409964e-05,
                7.338207180864763e-07,
                4.450848927637999e-07
            ],
            [
                0.9933071476269075,
                0.000804086028179802,
                0.0003799845741603785,
                0.0009110510020765653,
                0.9998766053809959,
                0.001926735025100244,
                6.962257907880012e-06,
                0.9999970976866313,
                0.9999910603026306,
                0.9999921107355337
            ]
        ]
    },
    {
        "q_id": "7711_mmlu_math",
        "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,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            86,
            87,
            89,
            90,
            91,
            92,
            93,
            94,
            96,
            97,
            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,
            85,
            95
        ],
        "rewards": [
            [
                5.422218969029887e-06,
                3.7266392839425286e-06,
                1.0677032518209896e-06,
                1.370957533322598e-06,
                2.902313023039776e-06,
                6.475945665741875e-07,
                5.04347348070562e-07,
                5.715004469900632e-07,
                1.7603440524340693e-06,
                9.422450431569214e-07
            ],
            [
                3.726641060956752e-06,
                9.422448184912962e-07,
                2.2603251060738913e-06,
                6.962259568648793e-06,
                2.260323489192885e-06,
                1.553497754476329e-06,
                1.994729959019382e-06,
                3.726639283129085e-06,
                1.3007130013572209e-05,
                1.5534979395006942e-06
            ],
            [
                5.422221555069497e-06,
                1.012999097799944e-05,
                3.288750633545794e-06,
                6.962257079376403e-06,
                1.3709573702647743e-06,
                1.5534981249397663e-06,
                7.33821067986608e-07,
                2.9023109471689794e-06,
                8.939696302831578e-06,
                3.2887502411026557e-06
            ],
            [
                0.9999997897567342,
                0.9999998724809874,
                0.9999998362622747,
                0.9999998555019274,
                0.9999998724809723,
                0.9999998144608097,
                0.9999998874648648,
                0.9999998362622552,
                0.9999998144609424,
                0.9999997897566589
            ],
            [
                0.9998911031037886,
                0.9999785550592574,
                0.9999785550566999,
                0.9999546021151456,
                0.9999810748472494,
                0.9999832985841286,
                0.9999417087344962,
                0.9999756997535574,
                0.9998766053809636,
                0.9999546021313769
            ],
            [
                4.450848927621807e-07,
                8.315278293951957e-07,
                4.222832940339353e-06,
                7.338208930391909e-07,
                1.994730196992497e-06,
                6.475950297906914e-07,
                3.288749849209925e-06,
                2.5612819052654485e-06,
                2.5612831266608576e-06,
                1.5534979397500702e-06
            ],
            [
                0.9999994956525917,
                0.9999991684722697,
                0.9999982396561574,
                0.9999995549149481,
                0.9999993524051246,
                0.9999990577556307,
                0.9999980052707542,
                0.9999990577554062,
                0.9999996940976636,
                0.9999986290424664
            ],
            [
                0.9999994956526519,
                0.9999993524052789,
                0.9999994284995529,
                0.9999992661792819,
                0.9999998874648648,
                0.9999992661790196,
                0.9999996533672136,
                0.9999989322967482,
                0.9999994956525918,
                0.999999428499553
            ],
            [
                0.9999996072136593,
                0.9999984465018752,
                0.9999952149049363,
                0.9999991684717742,
                0.9999996533672962,
                0.9999992661786696,
                0.9999989322966208,
                0.9999996072139402,
                0.9999995549147889,
                0.9999993524053562
            ],
            [
                0.9999785550515862,
                0.9971990730588917,
                0.9999417087275282,
                0.9999599362982616,
                0.9999898700114355,
                0.9999417087136441,
                0.9998204719697386,
                0.9998415638400323,
                0.999981074858529,
                0.999986992873086
            ],
            [
                1.0677028699955933e-06,
                1.0677033791291683e-06,
                1.2098652507583041e-06,
                5.04347287945184e-07,
                6.475948753794598e-07,
                5.715003788801361e-07,
                2.699579061739269e-07,
                4.4508521110175827e-07,
                5.715003788933905e-07,
                2.5612831264675113e-06
            ],
            [
                1.7603438428660665e-06,
                3.2887494573232236e-06,
                2.2603245672867952e-06,
                2.2603245671490605e-06,
                4.7850944942634305e-06,
                2.3823690999160957e-07,
                2.260324028351814e-06,
                2.699579061812927e-07,
                1.0677033791495609e-06,
                6.962257077932685e-06
            ],
            [
                0.9999970976880149,
                0.9999962733598275,
                0.9999938558261308,
                0.9999945777823231,
                0.9999832985781602,
                0.999993855825398,
                0.9999921107345932,
                0.9999885212346119,
                0.9999945777816768,
                0.9999980052705163
            ],
            [
                0.999999694097773,
                0.9999997617629763,
                0.9999998144608317,
                0.9999996940976636,
                0.9999998144608317,
                0.9999998362622942,
                0.9999998144609645,
                0.9999995549149481,
                0.9999996940976636,
                0.999999653367379
            ],
            [
                5.422219616026655e-06,
                4.785096205717126e-06,
                1.6701415866735174e-05,
                1.0677028700130727e-06,
                2.561282210590951e-06,
                3.726638395527247e-06,
                5.422218968822766e-06,
                3.535625913206225e-05,
                8.939698435340743e-06,
                2.561282821352716e-06
            ],
            [
                3.2887490653408545e-06,
                3.059021539845349e-07,
                1.0129988561906404e-05,
                6.1441724044534996e-06,
                1.553498310118888e-06,
                4.785095065045315e-06,
                1.7603434231505666e-06,
                6.144173136455602e-06,
                5.422218969661113e-06,
                8.939694172542558e-06
            ],
            [
                6.475947209985977e-07,
                4.7850950649408664e-06,
                7.338211554725124e-07,
                1.3709578605542582e-06,
                5.422217676925328e-06,
                1.2098655392811161e-06,
                8.315280276505193e-07,
                4.222833947820683e-06,
                4.4508505193791187e-07,
                3.726640616670918e-06
            ],
            [
                0.9999984465022456,
                0.9999990577555185,
                0.9999986290427932,
                0.9999996940978095,
                0.9999990577551815,
                0.9999995549148419,
                0.9999980052695652,
                0.9999995549150542,
                0.9999994956525318,
                0.9999996072138465
            ],
            [
                3.059021175247079e-07,
                1.0677028699625768e-06,
                5.715003788993679e-07,
                1.209865683518615e-06,
                6.475951069808602e-07,
                1.9947297215043796e-06,
                7.338211554531576e-07,
                6.475947981975644e-07,
                1.3709570434054234e-06,
                4.4508505193791187e-07
            ],
            [
                0.9999994956523514,
                0.9999982396569966,
                0.9999987901341724,
                0.9999994284997573,
                0.999998446502801,
                0.9999970976883612,
                0.9999993524053563,
                0.9999994284994167,
                0.999999266179107,
                0.9999991684717742
            ],
            [
                3.4663257978638593e-07,
                2.2603248366762157e-06,
                2.382369667929001e-07,
                4.4508526417014975e-07,
                3.059023363221292e-07,
                4.450849988780466e-07,
                8.31528325021115e-07,
                6.47594566594213e-07,
                5.715002426460124e-07,
                7.338213304196583e-07
            ],
            [
                0.9999994284996891,
                0.9999993524052018,
                0.999998790134605,
                0.9999997300421903,
                0.9999997897567091,
                0.9999994956523514,
                0.9999993524053562,
                0.9999986290429566,
                0.9999986290429567,
                0.9999977396757022
            ],
            [
                3.4663266243111764e-07,
                4.450852111148132e-07,
                5.04347648686092e-07,
                3.059022998576899e-07,
                2.3823693839290317e-07,
                1.7603436329978976e-06,
                4.450849988811838e-07,
                9.422443692527585e-07,
                8.315278294038928e-07,
                7.338210679979539e-07
            ],
            [
                5.715005832827105e-07,
                6.475949525919915e-07,
                9.422448185264317e-07,
                1.5534984952492866e-06,
                1.209865827698362e-06,
                1.7603425837366772e-06,
                1.0677033791437343e-06,
                1.7603432132784448e-06,
                3.4663278639265633e-07,
                6.475946437928669e-07
            ],
            [
                0.9999989322968754,
                0.9999977396748939,
                0.9999987901344607,
                0.9999987901338838,
                0.9999982396569966,
                0.9999984465022455,
                0.9999982396567868,
                0.9999982396572065,
                0.9999986290426298,
                0.9999982396569966
            ],
            [
                1.3709575335121232e-06,
                1.3709575336093795e-06,
                1.370957206783032e-06,
                1.760343842700361e-06,
                6.96225873895455e-06,
                1.3709570433536782e-06,
                2.5612831265630198e-06,
                2.260324567054496e-06,
                8.93969843377968e-06,
                5.422219615069953e-06
            ],
            [
                4.222834954280646e-06,
                2.561282821176841e-06,
                1.5534979396448094e-06,
                6.475945665900901e-07,
                3.2887478888496478e-06,
                3.2887486729876365e-06,
                8.315283250150648e-07,
                1.209865827698362e-06,
                8.315279284937352e-07,
                6.475951069808602e-07
            ],
            [
                0.9999990577549568,
                0.9999993524053562,
                0.9999989322968754,
                0.9999974387187053,
                0.9999996533674614,
                0.9999992661791944,
                0.9999930377420909,
                0.9999990577557432,
                0.999997097686977,
                0.9999990577550693
            ],
            [
                0.999999730042126,
                0.9999998144608317,
                0.9999997300420939,
                0.9999997300420937,
                0.9999997300422547,
                0.9999994956524716,
                0.999999554914895,
                0.9999995549151073,
                0.9999996072137061,
                0.9999996072137998
            ],
            [
                0.999999814460876,
                0.999999814460854,
                0.9999997617630616,
                0.9999996940976636,
                0.9999997617631468,
                0.999999730042126,
                0.9999997617630048,
                0.999999789756684,
                0.9999997617631752,
                0.9999996072137061
            ],
            [
                0.9999991684718732,
                0.9999989322970027,
                0.9999952149066469,
                0.9999991684722698,
                0.9999993524050474,
                0.9999980052700408,
                0.9999995549151073,
                0.9999987901347491,
                0.9999984465028011,
                0.9999990577555185
            ],
            [
                1.3709568799243436e-06,
                5.715007195275709e-07,
                1.9947301969471416e-06,
                7.338213304196583e-07,
                2.260324836696773e-06,
                3.0590237278532086e-07,
                4.222834450950777e-06,
                8.3152792848466e-07,
                1.5534983100595462e-06,
                5.715005151485975e-07
            ],
            [
                0.9999990577555185,
                0.9999990577552937,
                0.9999990577551815,
                0.9999992661791071,
                0.9999987901343165,
                0.9999993524049703,
                0.9999986290421394,
                0.9999974387180949,
                0.9999984465022455,
                0.9999989322975119
            ],
            [
                3.927862470861484e-07,
                9.42244930862237e-07,
                2.2603251060985603e-06,
                6.475948753991907e-07,
                2.6995780963846126e-07,
                2.6995768091383957e-07,
                1.7603434231505666e-06,
                6.47594798194325e-07,
                9.422445938964242e-07,
                2.561281294616881e-06
            ],
            [
                0.9999996533675028,
                0.9999994956525918,
                0.9999990577555185,
                0.999999352405279,
                0.9999984465018752,
                0.9999974387180948,
                0.999999554914895,
                0.9999993524053562,
                0.9999990577554061,
                0.999999554914895
            ],
            [
                0.9999967112497585,
                0.9999991684718733,
                0.9999980052709919,
                0.9999962733616046,
                0.9999986290427931,
                0.999988521234612,
                0.9999990577556307,
                0.9999485577863694,
                0.9999910603015656,
                0.9999990577554061
            ],
            [
                0.999975699762171,
                0.9999417087483762,
                0.9999417087136402,
                0.9999785550541436,
                0.9933071486515983,
                0.9999869928653341,
                0.9997694932029144,
                0.9999885212264013,
                0.9999339478396017,
                0.9999485577740995
            ],
            [
                3.927861534349064e-07,
                6.475951069855719e-07,
                1.760342793583908e-06,
                1.370956716519966e-06,
                8.315279285149107e-07,
                1.9947301969471416e-06,
                7.338208055436404e-07,
                4.222834451169694e-06,
                1.3709572067955008e-06,
                2.902311293034278e-06
            ],
            [
                0.9999995549147889,
                0.999999730042319,
                0.9999997617630616,
                0.9999996940977731,
                0.9999998362622357,
                0.9999998144608981,
                0.9999997897567091,
                0.9999996533672135,
                0.9999996533673375,
                0.9999998362622943
            ],
            [
                1.5534973841705173e-06,
                2.902312677007974e-06,
                4.222831934052698e-06,
                9.422445938861406e-07,
                7.338209805133949e-07,
                5.715007195275709e-07,
                6.475947981860793e-07,
                3.927862470840049e-07,
                5.71500515151976e-07,
                2.5612825160271407e-06
            ],
            [
                0.9999993524050474,
                0.999998790134028,
                0.9999990577554062,
                0.999998790134028,
                0.999998005269803,
                0.9999992661789321,
                0.9999993524049702,
                0.9999992661787571,
                0.9999992661787571,
                0.9999990577551815
            ],
            [
                1.3709568799592562e-06,
                5.043472879481655e-07,
                3.2887482811579057e-06,
                4.450852111135988e-07,
                2.9023130230133794e-06,
                7.338207180864763e-07,
                4.450852111135988e-07,
                1.7603425836246058e-06,
                1.3709572068179446e-06,
                1.370957533676711e-06
            ],
            [
                9.422450431260706e-07,
                7.338213304316717e-07,
                9.422450431800595e-07,
                3.2887482811579057e-06,
                5.715007195410849e-07,
                9.422444815679433e-07,
                1.5534979396815448e-06,
                3.726639283901856e-06,
                1.0677033791437343e-06,
                1.2098653950606901e-06
            ],
            [
                3.726637951126493e-06,
                6.475948753965404e-07,
                1.7603434230729168e-06,
                2.2603245672497918e-06,
                2.561282210618905e-06,
                5.71500378896509e-07,
                5.04347528438253e-07,
                0.999088949016626,
                3.9278605979208185e-07,
                7.8892625849535e-06
            ],
            [
                1.0677024881941248e-06,
                1.5534983101061718e-06,
                4.450851049917114e-07,
                1.9947304348703948e-06,
                2.2603248367173307e-06,
                1.370956879949281e-06,
                3.288749065209246e-06,
                6.475950297906914e-07,
                1.5534984953199313e-06,
                7.338211554725124e-07
            ],
            [
                9.422448185478557e-07,
                5.043475885634304e-07,
                1.3709575337016483e-06,
                1.209865539274514e-06,
                6.144175333926503e-06,
                3.927861066170637e-07,
                2.260323489410794e-06,
                2.561283126639892e-06,
                1.7603430034311638e-06,
                4.7850950647493785e-06
            ],
            [
                0.9999898700066062,
                0.9999967112497586,
                0.9999921107336531,
                0.9999910603068942,
                0.9999989322970027,
                0.9999952149072168,
                0.9999952149049353,
                0.9999962733598278,
                0.9999938558232011,
                0.9999962733602719
            ],
            [
                0.999999057755069,
                0.9999984465022456,
                0.9999996072139402,
                0.999997097688017,
                0.9999977396757022,
                0.9999990577554062,
                0.9999974387187054,
                0.999992110740236,
                0.9999967112523602,
                0.9999974387168734
            ],
            [
                0.9999980052709919,
                0.9999852610145158,
                0.9999832985701952,
                0.9999910603026313,
                0.9999810748585355,
                0.9999898700066053,
                0.9999910602994343,
                0.9999810748449955,
                0.9999921107402373,
                0.999993037742092
            ],
            [
                0.9999994956524716,
                0.9999992661786696,
                0.9999982396572065,
                0.9999995549151073,
                0.9999987901341723,
                0.9999995549148419,
                0.9999982396567868,
                0.9999994956525918,
                0.9999998144608538,
                0.9999994956524715
            ],
            [
                0.9999991684716749,
                0.9999994284997574,
                0.9999994956524114,
                0.9999998144608981,
                0.99999976176309,
                0.9999994956527721,
                0.9999991684718733,
                0.9999994284994849,
                0.9999996072136125,
                0.9999992661787571
            ],
            [
                0.9999996072137061,
                0.9999996072136125,
                0.9999996533672549,
                0.9999994284992805,
                0.9999996533675028,
                0.999999554914895,
                0.9999996072136592,
                0.9999994284995529,
                0.9999994284996211,
                0.9999996533672136
            ],
            [
                1.9947306725215466e-06,
                1.9947301970451086e-06,
                1.3709572068422585e-06,
                1.7603425837702984e-06,
                2.2603234893861252e-06,
                4.222833444283541e-06,
                3.2887494573232236e-06,
                7.338210679949506e-07,
                1.3709578604981489e-06,
                1.9947292458930106e-06
            ],
            [
                0.9999994284993485,
                0.9999994284994167,
                0.9999995549147359,
                0.9999994956527721,
                0.9999994284996891,
                0.999999352404893,
                0.9999996533674202,
                0.9999996072138934,
                0.9999996072137998,
                0.9999992661789321
            ],
            [
                0.9999996940978461,
                0.9999997300421903,
                0.9999998144608317,
                0.999999730042319,
                0.9999996072139402,
                0.999999554914842,
                0.9999995549150011,
                0.9999996533675028,
                0.999999554914895,
                0.9999997617630332
            ],
            [
                0.9999996940978095,
                0.9999996940976636,
                0.9999992661786696,
                0.999999730042126,
                0.9999997617629763,
                0.9999998144608097,
                0.9999997300421903,
                0.9999997300421581,
                0.999999730042126,
                0.9999994956524114
            ],
            [
                0.999996711250935,
                0.9999945777823236,
                0.9999898700053997,
                0.9999952149043646,
                0.999996273360272,
                0.9999945777784455,
                0.9999952149037947,
                0.9999982396559474,
                0.9999989322972572,
                0.9999957771675627
            ],
            [
                0.9999962733593835,
                0.9999984465018751,
                0.9999986290421394,
                0.9999984465015047,
                0.999998005269803,
                0.9999992661792819,
                0.9999996533672135,
                0.9999989322970028,
                0.9999989322971299,
                0.999998790134605
            ],
            [
                1.670142780910326e-05,
                6.962256247098965e-06,
                3.120190018853766e-05,
                1.8925157262061825e-05,
                5.422221554926484e-06,
                4.785093353187292e-06,
                3.2887482811908074e-06,
                1.670142781560441e-05,
                1.0129994599624903e-05,
                7.889266345584138e-06
            ],
            [
                0.9999987901341724,
                0.9999977396762412,
                0.9999982396567868,
                0.9999987901338838,
                0.999999694097773,
                0.9999977396751634,
                0.9999980052693274,
                0.9999997617629763,
                0.9999986290423029,
                0.9999989322975118
            ],
            [
                0.9999994284995529,
                0.9999996072136592,
                0.9999997617631753,
                0.9999989322972573,
                0.9999996072136592,
                0.9999996940978095,
                0.999999694097846,
                0.9999990577550693,
                0.9999993524050473,
                0.9999995549149481
            ],
            [
                0.9999251537727355,
                0.9999852610215436,
                0.999999057755069,
                0.9999852610180293,
                0.9999810748540172,
                0.999975699762166,
                0.9999885212277702,
                0.9999945777803838,
                0.9999546021151405,
                0.9999938558253981
            ],
            [
                1.994730434816876e-06,
                3.059023727894942e-07,
                8.315280276580819e-07,
                5.715005832762133e-07,
                2.260324567302214e-06,
                1.067702488159652e-06,
                1.553498495338299e-06,
                7.338213304283347e-07,
                8.315283250150648e-07,
                2.2603242977308917e-06
            ],
            [
                2.260323758923431e-06,
                2.9023126770343703e-06,
                1.2098655392871682e-06,
                6.144172404028807e-06,
                2.561283126639892e-06,
                3.7266388396128453e-06,
                6.1441724044534996e-06,
                6.475948754012522e-07,
                1.76034363298589e-06,
                3.7266383954560706e-06
            ],
            [
                3.059021539909339e-07,
                3.4663278639738526e-07,
                3.05902263389638e-07,
                1.275190124842887e-07,
                2.3823685319174098e-07,
                2.3823688159069855e-07,
                4.4508521110762794e-07,
                1.4449795205264928e-07,
                2.1024326584582131e-07,
                2.6995780963846126e-07
            ],
            [
                0.9999869928761874,
                0.9999974387184,
                0.9999485577802103,
                0.9999945777803838,
                0.9999938558246657,
                0.9999810748495038,
                0.9999952149066461,
                0.9999910603036959,
                0.9999646437450749,
                0.9999417087275205
            ],
            [
                0.9999967112521109,
                0.9999945777784448,
                0.999999352405279,
                0.9999992661788446,
                0.9859363697800156,
                0.999996273358939,
                0.9999986290421394,
                0.9999994284996893,
                0.9999980052709919,
                0.9999989322967482
            ],
            [
                0.9999986290432835,
                0.9999993524052018,
                0.9999974387174841,
                0.9999977396757023,
                0.9999967112513272,
                0.9999996072139402,
                0.9999991684722697,
                0.9999995549147359,
                0.9999980052705164,
                0.9999980052695653
            ],
            [
                0.9999997897566089,
                0.9999997897565587,
                0.9999999397642796,
                0.9999998724809723,
                0.9999997897565838,
                0.9999996072138934,
                0.999999694097846,
                0.9999998362623138,
                0.9999996940978825,
                0.9999997300422869
            ],
            [
                1.3709570433979422e-06,
                1.209865250822125e-06,
                3.2887494573232236e-06,
                1.2098655392811161e-06,
                1.9947290079889487e-06,
                5.71500651413193e-07,
                1.3709568798220997e-06,
                4.450851580497677e-07,
                3.2887486729337966e-06,
                1.9947306725451314e-06
            ],
            [
                0.9999994956523514,
                0.9999994956527722,
                0.9999910603005044,
                0.9999996940976636,
                0.9999994956525318,
                0.9999977396759717,
                0.999999352404893,
                0.999999352404893,
                0.9999994956527721,
                0.9999996533672549
            ],
            [
                0.9999996940976272,
                0.9999998362622357,
                0.9999994956523512,
                0.999999168471675,
                0.9999996940976271,
                0.9999994284993485,
                0.9999991684719723,
                0.9999996533673788,
                0.9999994284997574,
                0.9999994284994167
            ],
            [
                0.9999997617630332,
                0.9999998362622357,
                0.9999998555019274,
                0.9999998144609202,
                0.999999554914895,
                0.9999997617630332,
                0.9999996533673375,
                0.9999998144609424,
                0.9999996533674201,
                0.9999998555019618
            ],
            [
                0.9999993524054335,
                0.9999996072136592,
                0.999999266179107,
                0.9999996940976271,
                0.999991060306899,
                0.9999994284992805,
                0.9999989322967482,
                0.9999992661790195,
                0.9999996072138934,
                0.9999991684719725
            ],
            [
                0.9999995549148419,
                0.9999997300421903,
                0.999999352404893,
                0.9999995549150542,
                0.9999994284994848,
                0.999999495652652,
                0.9999997300422225,
                0.9999996940978461,
                0.9999996072137061,
                0.9999991684717741
            ],
            [
                0.8519528076067262,
                0.9626731121204183,
                0.6224593312018546,
                0.9997388097528578,
                0.9997040428324447,
                0.9998911030389086,
                0.9995121429391215,
                0.2942149659744614,
                0.9995694428592421,
                0.3775406617944891
            ],
            [
                1.2098656834922064e-06,
                1.5534975693707442e-06,
                1.5534981249291695e-06,
                1.0677029972993568e-06,
                3.0590211752206485e-07,
                1.209865250822125e-06,
                1.0677029973114952e-06,
                7.338210679979539e-07,
                2.5612819053586272e-06,
                1.0677027427471959e-06
            ],
            [
                8.315278293838516e-07,
                6.96225956921868e-06,
                3.2887482811908074e-06,
                4.222834451012227e-06,
                1.5534973841450852e-06,
                2.902313022984344e-06,
                6.144177531459659e-06,
                1.3709578604981489e-06,
                1.2098652507957165e-06,
                1.0677033791291683e-06
            ],
            [
                0.9999038975736865,
                0.9999687980887508,
                0.9997388096300779,
                0.9998204719917813,
                0.9998911030395266,
                0.99998107485853,
                0.9997965730269643,
                0.9999251537817503,
                0.9999687980737704,
                0.9999724643089074
            ],
            [
                6.475946437966953e-07,
                7.338213304143191e-07,
                9.422444815726566e-07,
                6.475947209953583e-07,
                6.475951069932288e-07,
                6.475947209953583e-07,
                3.927862470861484e-07,
                2.260324028331257e-06,
                7.338212429464139e-07,
                8.315280276399315e-07
            ],
            [
                0.999991060303696,
                0.9999992661791945,
                0.9999898700114366,
                0.9999986290421394,
                0.9999982396565767,
                0.9999986290421395,
                0.9999921107355342,
                0.9999724642957807,
                0.9999977396759716,
                0.9999970976873229
            ],
            [
                0.9999991684718733,
                0.999999057755743,
                0.9999967112505427,
                0.9999994956524115,
                0.9999984465028011,
                0.9999987901346049,
                0.9999991684717741,
                0.9999991684719723,
                0.9999980052702785,
                0.9999993524050474
            ],
            [
                5.71500242637956e-07,
                3.2887486729337966e-06,
                5.715005832624392e-07,
                1.3709575336530204e-06,
                5.043476486764593e-07,
                1.0677033791291683e-06,
                2.561282210562998e-06,
                9.422444815220956e-07,
                1.0677032518209896e-06,
                5.4222196154940574e-06
            ],
            [
                0.9999921107383551,
                0.9999967112501508,
                0.9999957771650455,
                0.9999251537729087,
                0.9999962733598274,
                0.9999984465026159,
                0.9999930377445808,
                0.9999957771680659,
                0.999995214903795,
                0.9999974387184
            ],
            [
                0.9999996940978825,
                0.9999998362623528,
                0.9999996533674202,
                0.9999996533672135,
                0.9999998362623528,
                0.9999996533672136,
                0.9999994284992805,
                0.9999997617631752,
                0.9999996533675028,
                0.9999998144608097
            ],
            [
                4.4508494582314646e-07,
                7.889265406438011e-06,
                6.475951069961737e-07,
                1.7603438427660027e-06,
                4.450849458179853e-07,
                1.2098658277181688e-06,
                9.422447062202052e-07,
                2.561282210701601e-06,
                2.3823690999063455e-07,
                1.0677031245953668e-06
            ],
            [
                0.9999998144608319,
                0.9999986290429567,
                0.946596676038055,
                0.9999987901346049,
                0.9999989322967482,
                0.9999991684718733,
                0.9999989322973846,
                0.9999996533674201,
                0.9999992661789321,
                0.9999984465022455
            ],
            [
                1.370957206783032e-06,
                1.9947292458603553e-06,
                3.927862002625787e-07,
                2.2603251061849014e-06,
                2.561282821176841e-06,
                7.338209804773549e-07,
                6.475948753965404e-07,
                1.0677028700266676e-06,
                1.0677028700130727e-06,
                1.9947299592407137e-06
            ],
            [
                0.9999998362623528,
                0.9999998555019446,
                0.9999997617630048,
                0.9999998362622552,
                0.9999998724809571,
                0.9999996072137998,
                0.9999998144608538,
                0.9999998362622357,
                0.9999998362623332,
                0.999999730042126
            ],
            [
                3.0590226338671677e-07,
                5.715003788993679e-07,
                1.9947299592407137e-06,
                7.338212429420757e-07,
                3.288747889229516e-06,
                1.5534973841592143e-06,
                3.059023727869902e-07,
                4.4508505192819656e-07,
                5.043473480643696e-07,
                2.6995771309333195e-07
            ],
            [
                3.7266383954560706e-06,
                4.450852641717689e-07,
                1.99472995920443e-06,
                1.553497754577351e-06,
                8.315277302701984e-07,
                5.715005832853093e-07,
                2.902311639126627e-06,
                5.715003789017068e-07,
                8.31528325021115e-07,
                1.994730434847717e-06
            ],
            [
                3.7266397280960194e-06,
                1.9947301970587145e-06,
                2.56128282131428e-06,
                3.7266392839832006e-06,
                1.5534973841705173e-06,
                2.902312330965655e-06,
                1.5534971989696065e-06,
                4.222832436955956e-06,
                6.475948753965404e-07,
                9.422448185388577e-07
            ],
            [
                0.9999885212291427,
                0.9999982396567867,
                0.9999994956525318,
                0.9999986290421394,
                0.9999970976887073,
                0.9999989322967481,
                0.999995777166556,
                0.999999352404893,
                0.9999990577550691,
                0.9999993524051246
            ],
            [
                1.3709568799823232e-06,
                1.2098656835076114e-06,
                1.994729008074216e-06,
                2.2603251061232293e-06,
                1.2098656835076114e-06,
                1.067703379154416e-06,
                2.2603248367656408e-06,
                1.0677024881941248e-06,
                1.9947306726358406e-06,
                4.222834451012227e-06
            ],
            [
                6.144173134868593e-06,
                7.889265406294507e-06,
                6.144175333289463e-06,
                1.5534973841450852e-06,
                6.144172404129392e-06,
                3.2887502414436403e-06,
                3.726639727994339e-06,
                3.7266392835764795e-06,
                7.889259761704902e-06,
                1.3007126909916233e-05
            ],
            [
                0.9999996072137998,
                0.9999995549150542,
                0.9999994956524715,
                0.9999995549147359,
                0.999999168471675,
                0.9999994284997573,
                0.9999996533675028,
                0.9999996072136125,
                0.9999996072136592,
                0.9999994956527721
            ],
            [
                0.9999992661792819,
                0.9999984465022455,
                0.9995121428867828,
                0.999989870011436,
                0.9999687980811913,
                0.999995777164542,
                0.9999756997505803,
                0.9999938558239334,
                0.9999970976887068,
                0.9999832985741735
            ],
            [
                0.9999930377462406,
                0.9999898700102293,
                0.9999339478398399,
                0.9999869928761891,
                0.9975273773027884,
                0.9995121427740732,
                0.9999980052707568,
                0.9999687980997901,
                0.9998204719495138,
                0.9999938558268632
            ],
            [
                1.0677033791204289e-06,
                1.0677026154473471e-06,
                5.422219615829396e-06,
                9.422449308420983e-07,
                1.5534979397267575e-06,
                6.144175333837093e-06,
                1.5534983100425914e-06,
                2.561283126535066e-06,
                4.222835457526079e-06,
                9.422443691233569e-07
            ],
            [
                0.9924227574120011,
                0.9999151889182053,
                0.9993736658201027,
                0.9996646498897299,
                0.9953904286474917,
                0.9999687980849942,
                0.9991959139516638,
                0.9998204720980013,
                0.9999485577925075,
                0.99979657295416
            ],
            [
                7.338207180838067e-07,
                1.2098661161789477e-06,
                2.561283431986506e-06,
                9.422445938917108e-07,
                2.561281294616881e-06,
                9.422449308673789e-07,
                9.422442569028803e-07,
                1.3709568799592562e-06,
                1.5534975693869924e-06,
                1.0677026154730804e-06
            ],
            [
                0.9999997300422869,
                0.9999998144608317,
                0.9999997897566089,
                0.9999999006881259,
                0.9999994956523514,
                0.9999997300422869,
                0.9999997300422547,
                0.9999998144608097,
                0.9999998555019962,
                0.9999996072136592
            ],
            [
                9.422445938917108e-07,
                3.927861534370498e-07,
                7.338210679909462e-07,
                4.4508526417014975e-07,
                5.043475885606781e-07,
                8.315282258956806e-07,
                1.0677029973056687e-06,
                4.4508505193386385e-07,
                1.3709568799592562e-06,
                1.9947294835866542e-06
            ],
            [
                1.2098658276598493e-06,
                3.288749849209925e-06,
                1.0677032518413822e-06,
                5.04347468309184e-07,
                1.0677031244040661e-06,
                2.699578418172324e-07,
                1.5534979397394734e-06,
                1.553498495281783e-06,
                7.338207180454308e-07,
                9.422449308420983e-07
            ],
            [
                0.999999789756684,
                0.9999996940977731,
                0.9999995549151073,
                0.9999997300422869,
                0.9999996533672135,
                0.9999996072137998,
                0.9999997617631752,
                0.9999997300423191,
                0.9999995549148419,
                0.9999996533674202
            ],
            [
                0.9999996533674615,
                0.999999057755743,
                0.9999982396569966,
                0.9999993524054335,
                0.9999996072137061,
                0.9999994284994167,
                0.9999990577551814,
                0.9999995549149481,
                0.9999987901337396,
                0.9999989322966208
            ],
            [
                1.370957697068717e-06,
                1.3709568799679844e-06,
                2.260325375520937e-06,
                6.475945666009864e-07,
                1.370956879949281e-06,
                7.338210679909462e-07,
                4.450849458200093e-07,
                2.6995774527577444e-07,
                3.9278615343901467e-07,
                4.4508505193791187e-07
            ],
            [
                0.9999996940977731,
                0.9999994284994168,
                0.9999997897565838,
                0.9999996940977366,
                0.9999996072139402,
                0.9999993524052018,
                0.9999996940978825,
                0.9999996940977366,
                0.9999996940976272,
                0.999999789756684
            ],
            [
                0.9999957771665556,
                0.9999970976866309,
                0.9999986290421394,
                0.9999962733620488,
                0.9999989322967482,
                0.9999984465020603,
                0.9999921107355346,
                0.9999977396765105,
                0.9999957771650453,
                0.9999962733593836
            ],
            [
                1.9947301970287804e-06,
                8.315281267706361e-07,
                2.9023123310580418e-06,
                2.5612819051373276e-06,
                1.3709573702248741e-06,
                1.2098661161861e-06,
                2.260324836651547e-06,
                4.785095064523075e-06,
                2.9023130229209922e-06,
                1.209866116170145e-06
            ],
            [
                0.999997438716568,
                0.9999938558246657,
                0.9999994284993486,
                0.9999957771670589,
                0.9999945777797388,
                0.9999994956524716,
                0.9999945777797379,
                0.9999994956525317,
                0.9999990577556308,
                0.9999986290421394
            ],
            [
                0.9999990577555185,
                0.9999996533672135,
                0.9999952149072169,
                0.999999266179107,
                0.9999993524053562,
                0.9999989322968754,
                0.9999994956524716,
                0.9999997617629763,
                0.9999997300422225,
                0.9999984465026159
            ],
            [
                2.6995780963846126e-07,
                1.7603436329394601e-06,
                3.7266401724291984e-06,
                7.338208055579897e-07,
                4.22283294098842e-06,
                5.42222090882208e-06,
                8.315280276399315e-07,
                4.785092782936557e-06,
                1.5534977545603963e-06,
                1.370957370236096e-06
            ],
            [
                0.9999991684719725,
                0.9999990577555185,
                0.9999990577549568,
                0.9999987901346049,
                0.9999987901337396,
                0.9999991684719723,
                0.999999168471675,
                0.9999991684719723,
                0.9999994284994167,
                0.9999990577551815
            ],
            [
                0.9999982396567867,
                0.9999984465022455,
                0.9999962733598277,
                0.9999785550490369,
                0.9999957771645421,
                0.9999938558232014,
                0.999997097687323,
                0.9999977396748939,
                0.9999910603068948,
                0.999995777165549
            ],
            [
                0.9999996940977366,
                0.9999989322971301,
                0.9999994284994848,
                0.999999730042126,
                0.9999994284996891,
                0.9999994956527722,
                0.9999989322972573,
                0.9999992661787571,
                0.9999996072139402,
                0.9999989322970028
            ],
            [
                0.9999967112493665,
                0.9999986290432835,
                0.9999987901337396,
                0.999998239656367,
                0.9999957771680658,
                0.9999987901341723,
                0.9999977396751634,
                0.9999970976873229,
                0.9999989322966208,
                0.999999554914789
            ],
            [
                3.288749065077638e-06,
                1.2098662603961589e-06,
                1.2098655392662613e-06,
                2.260324028306588e-06,
                1.9947294837154625e-06,
                4.7850950646797465e-06,
                4.222832437677995e-06,
                1.0677028700130727e-06,
                2.9023126766832993e-06,
                1.0677028700053041e-06
            ],
            [
                4.450852641681257e-07,
                5.04347348051526e-07,
                1.2098652507957165e-06,
                5.715004470243685e-07,
                3.4663270374947136e-07,
                2.3823699519035448e-07,
                6.47594566594213e-07,
                5.043474081867732e-07,
                3.4663262110945863e-07,
                1.4449807262959252e-07
            ],
            [
                0.9999987901347492,
                0.9999989322971299,
                0.9999980052705164,
                0.9999990577556308,
                0.9999957771645427,
                0.9999989322970027,
                0.9999994956527121,
                0.9999994956525917,
                0.999999352404893,
                0.9999989322967481
            ],
            [
                0.9999996533673375,
                0.9999998362623722,
                0.9999996072139402,
                0.999999789756684,
                0.9999996940977001,
                0.9999998555019962,
                0.9999998362623722,
                0.9999998362623722,
                0.9999998362623138,
                0.9999998362622552
            ],
            [
                3.927862470861484e-07,
                4.785093353739995e-06,
                2.5612828212909852e-06,
                3.4663262110803996e-07,
                3.0590215398829087e-07,
                5.422218968931258e-06,
                9.422448185510695e-07,
                1.7603436330091044e-06,
                9.422447062240614e-07,
                1.3709567165386693e-06
            ],
            [
                0.9999990577551815,
                0.9999987901347492,
                0.9999989322975118,
                0.9999996940978095,
                0.9999980052693274,
                0.9999984465024306,
                0.999998005270992,
                0.9999990577555185,
                0.9999991684715758,
                0.9999987901344607
            ],
            [
                9.422444815628016e-07,
                3.7266379512112265e-06,
                6.9622537593854575e-06,
                3.2887482810382622e-06,
                2.5612828213352452e-06,
                4.785093923916815e-06,
                2.260323489490968e-06,
                1.7603427936079236e-06,
                2.2603234893861252e-06,
                5.422220908560712e-06
            ]
        ]
    },
    {
        "q_id": "8858_mmlu_math",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            8,
            10,
            12,
            13,
            14,
            16,
            18,
            19,
            23,
            25,
            26,
            27,
            28,
            31,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            69,
            71,
            72,
            74,
            75,
            76,
            77,
            79,
            80,
            81,
            82,
            83,
            84,
            86,
            87,
            89,
            91,
            92,
            94,
            95,
            96,
            99,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            114,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            126
        ],
        "rewards": [
            [
                4.78509563546605e-06,
                5.4222202621161125e-06,
                3.120190021339598e-05,
                2.260323758923431e-06,
                5.422217030495909e-06,
                1.473898197063434e-05,
                4.785095064819011e-06,
                0.0002305067666556042,
                1.6701423833436905e-05,
                1.0129995809929273e-05
            ],
            [
                6.962253758916883e-06,
                1.760342793583908e-06,
                NaN,
                6.144176797730321e-06,
                NaN,
                0.00010889693298417507,
                3.726639283291774e-06,
                6.962257077223492e-06,
                1.0129994601872894e-05,
                1.2098655392222467e-06
            ],
            [
                NaN,
                8.93970056529743e-06,
                1.0677024881004167e-06,
                2.561283124235882e-06,
                4.785096776068365e-06,
                8.939698434332555e-06,
                1.5534979397500702e-06,
                6.1441767989541075e-06,
                1.99472900790731e-06,
                1.5534977544932838e-06
            ],
            [
                1.8925148231579266e-05,
                NaN,
                NaN,
                2.2603234892298883e-06,
                NaN,
                7.889266346603015e-06,
                NaN,
                1.0129989766700635e-05,
                NaN,
                3.466325797715686e-07
            ],
            [
                4.22283394762097e-06,
                1.4738978454950406e-05,
                7.88925976359915e-06,
                6.96225707894582e-06,
                1.4738980213341866e-05,
                1.0129993394129904e-05,
                6.962258734344787e-06,
                NaN,
                2.561282821106957e-06,
                4.0063706483364614e-05
            ],
            [
                3.2887494571676872e-06,
                8.315281265690903e-07,
                NaN,
                6.962259569117366e-06,
                5.422218969128516e-06,
                NaN,
                2.56128251465159e-06,
                NaN,
                2.561282210460501e-06,
                1.1478764018305152e-05
            ],
            [
                NaN,
                6.144177531208195e-06,
                2.7535681238877168e-05,
                NaN,
                4.539787401825028e-05,
                2.753569435172593e-05,
                3.5356254898252494e-05,
                NaN,
                6.962254588116627e-06,
                1.6701423829123058e-05
            ],
            [
                1.5534981249023245e-06,
                1.2098662603631479e-06,
                3.28875024125221e-06,
                1.5534975692471157e-06,
                4.2228324370327694e-06,
                7.889266346603015e-06,
                NaN,
                3.28874867308036e-06,
                9.42245043087507e-07,
                8.93969950000193e-06
            ],
            [
                5.04347588554027e-07,
                1.4738988987366645e-05,
                3.288749849000549e-06,
                2.9023123299942713e-06,
                0.00015843622972481943,
                1.3709568798956654e-06,
                3.2887502412970765e-06,
                7.88926164421493e-06,
                3.288749456838667e-06,
                NaN
            ],
            [
                2.1444958627955892e-05,
                0.9999251537732049,
                0.999993855822469,
                0.9999599363033733,
                NaN,
                0.9999038975744157,
                0.9995694429491624,
                NaN,
                0.9999869928715455,
                NaN
            ],
            [
                2.260324566088294e-06,
                NaN,
                2.902312330965655e-06,
                NaN,
                NaN,
                NaN,
                2.9023112930659533e-06,
                1.7603432131855856e-06,
                2.5612819052072116e-06,
                1.30071315640992e-05
            ],
            [
                3.726639283440905e-06,
                3.7266410605974813e-06,
                NaN,
                1.760344052650207e-06,
                NaN,
                1.4738983721251418e-05,
                3.7266388392671313e-06,
                1.7603430034151537e-06,
                3.2887478883351803e-06,
                6.144174600471243e-06
            ],
            [
                3.288749848677511e-06,
                3.535623804803683e-05,
                6.60521524508739e-05,
                2.7535697654881812e-05,
                8.939698434495167e-06,
                2.902312330891746e-06,
                5.422218321589366e-06,
                1.1478765382509808e-05,
                2.7535694365549603e-05,
                7.338208052926959e-07
            ],
            [
                NaN,
                2.430023202582134e-05,
                1.2098658277082653e-06,
                3.7266388393349185e-06,
                2.430024650299895e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                8.939695224056166e-06,
                8.315280276096808e-07,
                1.4738981968864903e-05,
                2.5612815998491325e-06,
                7.338212429006964e-07,
                2.260324567087388e-06,
                1.4738980211116665e-05,
                1.5534973838144677e-06,
                6.962257078553231e-06,
                2.7535697606699305e-05
            ],
            [
                2.9023116387069255e-06,
                4.222832935899587e-06,
                2.260324567227179e-06,
                4.222835457449267e-06,
                5.422220907554695e-06,
                6.9622579059043994e-06,
                3.2887486732000038e-06,
                NaN,
                NaN,
                6.1441753335241615e-06
            ],
            [
                NaN,
                0.9999038976081689,
                0.9999339478398543,
                0.9999599363222444,
                0.9999339478397501,
                NaN,
                NaN,
                0.43782349911420193,
                NaN,
                1.0129988563343644e-05
            ],
            [
                7.889260703763482e-06,
                2.2603234894745224e-06,
                2.5612812944538183e-06,
                4.006371125185228e-05,
                1.3709570433075437e-06,
                4.785093353274332e-06,
                NaN,
                5.144220750533887e-05,
                2.2603237580929087e-06,
                1.1478772227964558e-05
            ],
            [
                3.726640616423495e-06,
                9.422445937528824e-07,
                3.726639728262097e-06,
                1.5534971989427613e-06,
                NaN,
                NaN,
                8.939694170940841e-06,
                NaN,
                1.0677024878858105e-06,
                1.300713311155064e-05
            ],
            [
                NaN,
                1.5534979396815448e-06,
                1.6701417857058377e-05,
                5.4222170132161045e-06,
                NaN,
                4.785095057968966e-06,
                2.4300246507772637e-05,
                NaN,
                NaN,
                0.010986940667320136
            ],
            [
                8.315280271468437e-07,
                2.7535687805818776e-05,
                NaN,
                NaN,
                NaN,
                0.9978172837732123,
                NaN,
                NaN,
                NaN,
                1.1478773596575768e-05
            ],
            [
                NaN,
                6.962258738435319e-06,
                4.222833443553821e-06,
                5.422217029006611e-06,
                NaN,
                1.9947292458004866e-06,
                4.785095633999427e-06,
                6.144175332440078e-06,
                1.2098661155572414e-06,
                4.222832940646604e-06
            ],
            [
                1.3709570431803621e-06,
                5.8291265334581605e-05,
                3.7266410607194972e-06,
                6.144176797730321e-06,
                9.422443692176231e-07,
                3.2887506333812835e-06,
                2.5612819040145253e-06,
                3.726638839395927e-06,
                3.2887494569044713e-06,
                2.90231094680735e-06
            ],
            [
                5.4222202621161125e-06,
                1.760342583722268e-06,
                2.5612831265630198e-06,
                1.3709576971160984e-06,
                3.288749064802458e-06,
                2.260324028306588e-06,
                7.338208055613267e-07,
                2.2603248367173307e-06,
                4.222833947674739e-06,
                2.561282515853595e-06
            ],
            [
                6.9622579075254155e-06,
                1.1478765384430723e-05,
                0.02033235104233902,
                1.9947297200031353e-06,
                NaN,
                3.535624218589351e-05,
                2.1444950944374182e-05,
                4.539788485169606e-05,
                3.288747889038086e-06,
                NaN
            ],
            [
                0.9999646437325495,
                NaN,
                0.9999646437451367,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999724643089597,
                NaN,
                0.9999339478792175
            ],
            [
                2.753568124458694e-05,
                1.0129995807165349e-05,
                8.939699500327152e-06,
                NaN,
                2.4300252310279753e-05,
                6.144173868558375e-06,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                3.288750241473551e-06,
                1.6701427806612162e-05,
                4.785093923603471e-06,
                3.7266401722360055e-06,
                0.00017952791773353084,
                2.902310946944611e-06,
                1.76034258364702e-06,
                4.222833444229772e-06,
                NaN
            ],
            [
                NaN,
                6.144172403928222e-06,
                NaN,
                2.9023126769050284e-06,
                5.422220261544064e-06,
                7.33821330386288e-07,
                5.422217676486429e-06,
                4.785094492226697e-06,
                4.0063701710213663e-05,
                1.0677028697159255e-06
            ],
            [
                2.7535700939406174e-05,
                1.0129987350552609e-05,
                3.120192251631124e-05,
                0.0006263340999962171,
                5.1442207475397105e-05,
                1.892514821904893e-05,
                NaN,
                7.889265400267349e-06,
                NaN,
                7.889259761489647e-06
            ],
            [
                4.785094494628999e-06,
                3.2887506332466845e-06,
                6.144176065828368e-06,
                4.222832940162684e-06,
                2.902312677084523e-06,
                3.2887482807780376e-06,
                1.0677028700320085e-06,
                4.785096205651846e-06,
                9.422448185264317e-07,
                1.2098661159071575e-06
            ],
            [
                NaN,
                8.939694171135975e-06,
                3.288749848749297e-06,
                6.962258738827909e-06,
                5.144219519029225e-05,
                2.9023133687311063e-06,
                4.222832940339353e-06,
                2.2603234892298883e-06,
                6.962254589104433e-06,
                NaN
            ],
            [
                NaN,
                5.4222183186699456e-06,
                1.147876675124548e-05,
                2.1444956072586775e-05,
                NaN,
                1.0129990870169556e-05,
                NaN,
                3.5356250918726455e-05,
                9.422448182367774e-07,
                NaN
            ],
            [
                4.222835457852533e-06,
                5.4222202624563834e-06,
                5.422218322763051e-06,
                NaN,
                6.605216027536722e-05,
                2.5612825160271407e-06,
                2.5612828213352452e-06,
                4.222832940834793e-06,
                1.994729008105057e-06,
                8.315281267581578e-07
            ],
            [
                0.9994472214592935,
                1.9947301947265702e-06,
                1.7603425836005905e-06,
                1.3007130012010681e-05,
                0.9997694933151574,
                6.962259569003389e-06,
                NaN,
                1.6701419847381817e-05,
                1.0677026153784014e-06,
                NaN
            ],
            [
                8.939700565996655e-06,
                3.288749064371741e-06,
                NaN,
                1.2098655391617266e-06,
                1.1478769464371791e-05,
                1.4738983716586539e-05,
                3.288749065125496e-06,
                1.0129995809044816e-05,
                NaN,
                NaN
            ],
            [
                5.1442219756013625e-05,
                4.785093353187292e-06,
                7.889264465397747e-06,
                4.2228319341064674e-06,
                6.144173868178388e-06,
                1.3007126908733257e-05,
                0.0007096705034537529,
                2.753569437476538e-05,
                2.9023112926251358e-06,
                NaN
            ],
            [
                NaN,
                0.14804719803168948,
                0.9999485577794102,
                0.9998204720180948,
                0.40733340004593027,
                NaN,
                0.9993736657957644,
                0.9999910602994424,
                0.9999810748449961,
                0.6224593312018545
            ],
            [
                0.9999339478400403,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9986749775639929,
                0.9993736658746089,
                NaN,
                0.9998766054698882,
                0.9999810748540237
            ],
            [
                8.939695237162584e-06,
                2.9023130195343465e-06,
                1.0,
                5.715002425776618e-07,
                1.6701417842658638e-05,
                4.785096776068365e-06,
                NaN,
                7.88926446470893e-06,
                4.222833945262824e-06,
                1.3007133112662637e-05
            ],
            [
                4.222832437497486e-06,
                7.889259762307618e-06,
                NaN,
                1.3709570427539306e-06,
                1.0,
                8.93969736654937e-06,
                1.6701417843448496e-05,
                2.1444950958338794e-05,
                NaN,
                2.430023493564795e-05
            ],
            [
                5.1442238107329257e-05,
                NaN,
                4.006370171677219e-05,
                2.260324567177841e-06,
                8.93969523617066e-06,
                1.3007128456065844e-05,
                1.0129988562901417e-05,
                3.120192622145237e-05,
                3.535625067794842e-05,
                5.422218969306048e-06
            ],
            [
                1.1478764018827141e-05,
                1.0129995808418327e-05,
                5.422219614833243e-06,
                2.7535687805818776e-05,
                1.012999339309804e-05,
                1.3007123809289414e-05,
                1.0129987355122296e-05,
                2.260324567227179e-06,
                2.1444945851269378e-05,
                8.315281267581578e-07
            ],
            [
                NaN,
                NaN,
                NaN,
                4.785093924103951e-06,
                NaN,
                6.144175334094145e-06,
                NaN,
                1.2098653948576728e-06,
                1.3007123810638006e-05,
                NaN
            ],
            [
                4.2228324375512536e-06,
                NaN,
                NaN,
                0.8807970826714614,
                0.679178699175393,
                6.962257077932685e-06,
                NaN,
                0.00033535028752987685,
                1.7603425831394971e-06,
                0.9992903294768563
            ],
            [
                8.939696302457574e-06,
                NaN,
                6.962259569003389e-06,
                1.5534983100765009e-06,
                8.939696302831578e-06,
                2.2603251060142746e-06,
                5.422217676797111e-06,
                NaN,
                6.962258739169842e-06,
                2.4300237746995527e-05
            ],
            [
                4.78509563546605e-06,
                8.939695236593446e-06,
                0.0019267347945148702,
                NaN,
                3.7266379504926854e-06,
                8.315282257281667e-07,
                1.8925145978942173e-05,
                1.6701419845073e-05,
                1.4738988997044936e-05,
                NaN
            ],
            [
                3.12019187926687e-05,
                1.8925157257345735e-05,
                1.3007133110746217e-05,
                3.120190019932095e-05,
                NaN,
                1.4738980212296288e-05,
                1.0129995807441742e-05,
                1.1478770859624945e-05,
                7.889261644982674e-06,
                1.012999218369684e-05
            ],
            [
                0.9999852610215495,
                NaN,
                NaN,
                0.999985261018048,
                0.9999832985821429,
                0.9999251537818603,
                NaN,
                0.9997388096654315,
                0.9999599362935121,
                NaN
            ],
            [
                2.90231233035854e-06,
                NaN,
                3.535625069312567e-05,
                7.338209804773549e-07,
                2.260324028004393e-06,
                NaN,
                4.785096776194573e-06,
                4.222832437324657e-06,
                3.726640172290235e-06,
                NaN
            ],
            [
                7.338212428346234e-07,
                1.2098658276444443e-06,
                2.2603245668941476e-06,
                1.4738981963771067e-05,
                NaN,
                3.2887498488809053e-06,
                NaN,
                6.475946437966953e-07,
                3.726638394957837e-06,
                6.144176065582494e-06
            ],
            [
                0.0002611903843995483,
                0.9999546021423262,
                4.539789021177379e-05,
                5.829127931249693e-05,
                4.222831932420432e-06,
                3.7266410586723317e-06,
                0.00029595720155991504,
                6.144173864881432e-06,
                NaN,
                1.8925148215055747e-05
            ],
            [
                1.3709570433536782e-06,
                3.120191879561992e-05,
                4.222832940646604e-06,
                NaN,
                NaN,
                3.2887494564857185e-06,
                NaN,
                NaN,
                1.0129990976156825e-05,
                4.785096205512581e-06
            ],
            [
                3.2887506334201674e-06,
                1.1478770094098141e-05,
                5.422220908481809e-06,
                0.003172682714359573,
                5.422217676299034e-06,
                5.42221702914469e-06,
                1.3709575334098791e-06,
                2.902311291368672e-06,
                4.222835457733473e-06,
                7.88926540262081e-06
            ],
            [
                3.288748280891699e-06,
                NaN,
                6.9622587329010695e-06,
                4.785095063339331e-06,
                6.962253759157502e-06,
                NaN,
                4.7850939242083995e-06,
                3.2887506317631033e-06,
                3.2887490648622804e-06,
                3.726637951028202e-06
            ],
            [
                NaN,
                1.8925150492616083e-05,
                NaN,
                6.9622579092224155e-06,
                3.2887506326006084e-06,
                4.006368740446426e-05,
                NaN,
                NaN,
                2.1444953517061932e-05,
                9.422442568660309e-07
            ],
            [
                NaN,
                0.999968798099866,
                NaN,
                0.9997694932058788,
                NaN,
                NaN,
                0.9999599362935468,
                NaN,
                0.999986992874653,
                NaN
            ],
            [
                2.561281293950654e-06,
                4.006368740052914e-05,
                3.7266410607194972e-06,
                2.561281905100056e-06,
                NaN,
                2.144495607789177e-05,
                3.535626755762428e-05,
                NaN,
                6.144173135483279e-06,
                8.939694162111085e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                0.04742587115801276,
                0.9999339478711677,
                0.999959936303167,
                0.9988304895184489,
                NaN,
                NaN,
                NaN
            ],
            [
                2.144495347391985e-05,
                4.785096204285318e-06,
                2.902311984102453e-06,
                2.144494585197151e-05,
                NaN,
                2.4300243621371074e-05,
                1.0129988563914856e-05,
                1.4738981966291175e-05,
                NaN,
                NaN
            ],
            [
                9.422447061576466e-07,
                1.4738978439695717e-05,
                NaN,
                4.539787877057832e-05,
                1.0129993384382464e-05,
                NaN,
                NaN,
                NaN,
                1.1478769488633793e-05,
                NaN
            ],
            [
                1.2098653950315304e-06,
                2.2603245671202796e-06,
                1.99473067167069e-06,
                2.902310946400847e-06,
                6.9622570780973205e-06,
                NaN,
                5.829129323316207e-05,
                1.3007130011300897e-05,
                3.726639728184142e-06,
                8.939693101044227e-06
            ],
            [
                2.561283126535066e-06,
                NaN,
                2.5612831264675113e-06,
                1.994730672468935e-06,
                NaN,
                NaN,
                3.0590211543432996e-07,
                7.889266347133978e-06,
                7.889263523668778e-06,
                NaN
            ],
            [
                7.889261641674914e-06,
                0.0001795279778723677,
                6.962254588433232e-06,
                8.939698429568063e-06,
                5.829125100084977e-05,
                2.753568117757223e-05,
                1.0129989769722525e-05,
                0.9996200154333569,
                0.10669060317692272,
                0.9997965730768226
            ],
            [
                2.902311292155282e-06,
                1.0129993385746e-05,
                NaN,
                4.7850944937411915e-06,
                NaN,
                NaN,
                2.430023203572232e-05,
                NaN,
                4.539786858947248e-05,
                3.1201918807538294e-05
            ],
            [
                1.47389819699641e-05,
                NaN,
                NaN,
                1.1478764018012839e-05,
                5.144223199845732e-05,
                2.1444953520182517e-05,
                NaN,
                7.889266343575084e-06,
                3.120191509059319e-05,
                6.60521198251207e-05
            ],
            [
                5.422220254975367e-06,
                6.144174600985344e-06,
                1.0129994601301684e-05,
                3.7266410605974813e-06,
                9.610240241940429e-05,
                4.785095064148803e-06,
                6.962256248314727e-06,
                NaN,
                1.1478768116515313e-05,
                4.222831933864508e-06
            ],
            [
                0.9999687980961421,
                NaN,
                0.9999038975454309,
                0.10669060033653141,
                0.9999485577620361,
                NaN,
                0.9998415637088005,
                NaN,
                NaN,
                0.9999869928653509
            ],
            [
                NaN,
                0.9999599363222226,
                6.475949525163072e-07,
                6.962258738283349e-06,
                8.315284239011517e-07,
                1.6701419850845044e-05,
                NaN,
                6.144176797585032e-06,
                1.3007133114602719e-05,
                NaN
            ],
            [
                0.3208213138121609,
                0.9890130586141624,
                0.9999151889691954,
                NaN,
                0.9998415637086137,
                0.9999687980812412,
                0.9992903295613129,
                0.9998766054566812,
                0.9999599363222021,
                0.9996646498526447
            ],
            [
                NaN,
                1.9947290080343035e-06,
                6.4759464375046e-07,
                1.7603436322590265e-06,
                8.315280275900177e-07,
                6.962259568078904e-06,
                2.260325374873376e-06,
                3.2887494564079503e-06,
                4.785093924103951e-06,
                7.338209804920378e-07
            ],
            [
                1.147876402018431e-05,
                1.300713156215912e-05,
                5.422219615967477e-06,
                3.12019225022362e-05,
                1.4738983728490028e-05,
                6.144176066051891e-06,
                NaN,
                8.93969417199781e-06,
                1.892515725376564e-05,
                2.1444953524161264e-05
            ],
            [
                NaN,
                1.3007123809644304e-05,
                4.785092783267308e-06,
                NaN,
                1.0129992187400498e-05,
                1.0129993393945642e-05,
                7.889264466115267e-06,
                1.0677032518413822e-06,
                1.0129990977004428e-05,
                1.5534975691524517e-06
            ],
            [
                6.605212099816935e-05,
                NaN,
                NaN,
                NaN,
                4.222832940339353e-06,
                1.1478764016446877e-05,
                3.726638839395927e-06,
                NaN,
                NaN,
                4.222834954514924e-06
            ],
            [
                NaN,
                4.222833444283541e-06,
                2.4300252308334918e-05,
                1.7603425835173373e-06,
                2.75356976629957e-05,
                NaN,
                1.3007130012010681e-05,
                5.829127229957719e-05,
                6.605214460571739e-05,
                1.473898196763166e-05
            ],
            [
                7.889266346287306e-06,
                0.9999724643023546,
                1.4738976679695888e-05,
                2.753568774621674e-05,
                NaN,
                NaN,
                NaN,
                0.00015843618265294257,
                0.0028009266211534,
                NaN
            ],
            [
                3.120192243379064e-05,
                0.00015843625383705955,
                1.0129989750153945e-05,
                8.481103099344347e-05,
                8.939698434657777e-06,
                NaN,
                0.004070138257634899,
                0.9999885212305073,
                NaN,
                8.93970056424046e-06
            ],
            [
                2.260324567087388e-06,
                1.0129989771473008e-05,
                3.288747889038086e-06,
                5.422219615967477e-06,
                1.5534981245957261e-06,
                1.3709567164962755e-06,
                1.8925152735477297e-05,
                1.473898899256772e-05,
                0.0002959571622854249,
                5.422218962559821e-06
            ],
            [
                3.535626334645077e-05,
                6.9622570761976915e-06,
                1.3007134665934505e-05,
                2.902312677060767e-06,
                6.962257079553702e-06,
                0.029312229585402833,
                NaN,
                NaN,
                NaN,
                2.260324567087388e-06
            ],
            [
                1.0129987348120356e-05,
                0.9999038976206601,
                0.9999151889586775,
                0.9999251537461169,
                0.9999885212291413,
                0.9999785550567105,
                0.9997694931772665,
                0.9992903295476083,
                0.999738809598372,
                7.889261644057078e-06
            ],
            [
                NaN,
                0.00029595719521365314,
                NaN,
                NaN,
                1.8925155000714377e-05,
                NaN,
                3.2887482802097306e-06,
                3.2887490652810324e-06,
                NaN,
                1.760343632710514e-06
            ],
            [
                NaN,
                NaN,
                4.785095064523075e-06,
                1.7603430033607189e-06,
                5.422219614833243e-06,
                NaN,
                3.7266406162269133e-06,
                NaN,
                NaN,
                4.785093353187292e-06
            ],
            [
                NaN,
                0.9998204719914653,
                NaN,
                0.9999852610233131,
                4.222832434666943e-06,
                NaN,
                NaN,
                NaN,
                1.0,
                0.9998766053673472
            ],
            [
                NaN,
                5.422218967649081e-06,
                2.4300252308334918e-05,
                0.00037998450091125186,
                1.4738987227794512e-05,
                1.6701415860173268e-05,
                0.000804086069100344,
                2.902310945682868e-06,
                2.753568442272724e-05,
                1.6701425802374098e-05
            ],
            [
                1.3007134658978603e-05,
                3.288747889038086e-06,
                NaN,
                NaN,
                NaN,
                4.539787389438853e-05,
                7.889264465986113e-06,
                NaN,
                1.3709573700615334e-06,
                NaN
            ],
            [
                0.9990889486077651,
                0.9999485577865359,
                0.9999546021479823,
                NaN,
                0.999915188928401,
                0.9999724643122055,
                NaN,
                0.7057850340255386,
                0.9999898700102309,
                0.9999724643187952
            ],
            [
                NaN,
                5.422219616026655e-06,
                1.9947299591826594e-06,
                7.889266345957247e-06,
                2.7535684479824982e-05,
                NaN,
                7.889262585441413e-06,
                3.7266388395111645e-06,
                6.144173136455602e-06,
                8.939697367703906e-06
            ],
            [
                6.144173135181524e-06,
                6.962257079553702e-06,
                6.144173868670137e-06,
                8.315277301416325e-07,
                6.144175332115971e-06,
                4.22283294007051e-06,
                3.2887494572514376e-06,
                NaN,
                2.260324567268294e-06,
                NaN
            ],
            [
                1.3709570430407122e-06,
                4.785095634121282e-06,
                1.2098655391947376e-06,
                3.5356242238628006e-05,
                1.760344052491706e-06,
                9.422445938454347e-07,
                9.422444813378479e-07,
                6.144173136243255e-06,
                8.939700544971085e-06,
                NaN
            ],
            [
                NaN,
                0.9996200155156709,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999646437580106,
                0.9999756997679876,
                0.9999485577836738
            ]
        ]
    },
    {
        "q_id": "8910_mmlu_math",
        "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,
            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,
            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,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999869928684356,
                0.9999967112517189,
                0.9999930377429208,
                0.9999977396754327,
                0.9999957771670589,
                0.9999977396757056,
                0.9999970976869769,
                0.9999982396567867,
                0.9999962733620488,
                0.999997097686631
            ],
            [
                0.9999930377412624,
                0.9999921107355355,
                0.9999885212291404,
                0.9999930377429223,
                0.9999832985841344,
                0.9999930377445809,
                0.9999869928761915,
                0.9999996533674202,
                0.9999938558246669,
                0.9999852610180356
            ],
            [
                4.222833444283541e-06,
                1.9947290081177566e-06,
                4.222832941072913e-06,
                6.962259568889411e-06,
                3.288747889178668e-06,
                2.260325375634003e-06,
                1.0129993394314164e-05,
                6.962257909412379e-06,
                2.9023123311055552e-06,
                4.785096776303374e-06
            ],
            [
                2.9023133689317184e-06,
                3.2887486733420804e-06,
                1.3709572068354007e-06,
                4.222835458002318e-06,
                4.785093353687772e-06,
                3.288748673295719e-06,
                1.7603430034655858e-06,
                6.144173869379821e-06,
                2.9023112931873767e-06,
                4.222833947728508e-06
            ],
            [
                1.0129993393742954e-05,
                4.22283294098842e-06,
                5.422217676866151e-06,
                3.726637951170554e-06,
                7.889264465699106e-06,
                1.0129989770662257e-05,
                1.4738978453315019e-05,
                4.2228319339950885e-06,
                3.726640616630245e-06,
                2.2603242978007868e-06
            ],
            [
                0.9999982396574164,
                0.9999962733598277,
                0.9999724643187647,
                0.9999599362887388,
                0.9999910602994345,
                0.9999756997593048,
                0.9999938558246659,
                0.9999151889183892,
                0.9999756997563867,
                0.9999785550490417
            ],
            [
                0.9999724643056332,
                0.9997694933128299,
                0.9998766053816746,
                0.9999832985781659,
                0.9999852610127625,
                0.9999687980849209,
                0.9999852610110046,
                0.9999417087414523,
                0.9999869928746399,
                0.9999910603015673
            ],
            [
                0.9999997617631469,
                0.9999251537996058,
                0.9999646437450943,
                0.9998415638403066,
                0.9999810748472509,
                0.9998911030651905,
                0.9995121429466146,
                0.999972464302351,
                0.9999339478474842,
                0.9999724642957784
            ],
            [
                0.9999599363221765,
                0.9999417087137098,
                0.9997388095690449,
                0.9999251537639511,
                0.999860177926322,
                0.9999687980960889,
                0.9998204719926486,
                0.9993736659793219,
                0.9999485577803418,
                0.9993736658369718
            ],
            [
                0.9999852610127591,
                0.9999785550439229,
                0.9999687980923503,
                0.9999967112509347,
                0.9999832985801496,
                0.9999339478395914,
                0.9999724643089064,
                0.999972464295784,
                0.9999852610197857,
                0.9999599363030631
            ],
            [
                0.9991959139643376,
                0.9998204720350075,
                0.9999852610180362,
                0.9999038976083912,
                0.9998911031168464,
                0.9999417087137878,
                0.9998601778929518,
                0.9998911030520361,
                0.9997965729792904,
                0.9998204719704229
            ],
            [
                0.9999785550567105,
                0.999993855826864,
                0.9998766054551228,
                0.9998204720995318,
                0.9999852610197937,
                0.9999921107402371,
                0.9999952149049355,
                0.999985261012762,
                0.9999038975508887,
                0.9999251537818217
            ],
            [
                0.999994577779092,
                0.9999724642990628,
                0.9999885212359829,
                0.9999485577741557,
                0.9997694931767165,
                0.9999885212318768,
                0.9999810748540223,
                0.9999832985821457,
                0.9999724643154851,
                0.9999785550464855
            ],
            [
                0.9999952149049353,
                0.999981074854021,
                0.9999930377462418,
                0.9999987901347491,
                0.9999869928684375,
                0.9999970976887068,
                0.9999930377412609,
                0.9999962733598275,
                0.9999339478633067,
                0.9999898700066059
            ],
            [
                0.9997694932867596,
                0.9999687980886505,
                0.9996200154744918,
                0.9999339478790581,
                0.9999724643089193,
                0.9997694933683847,
                0.9997965730519172,
                0.9999485577802952,
                0.9999756997476967,
                0.999933947824102
            ],
            [
                0.9964063977887401,
                0.9999952149055056,
                0.9999646437366636,
                0.9999832985822427,
                0.999986992869988,
                0.9999974387177893,
                0.9996646498524105,
                0.9999990577554061,
                0.9999952149032237,
                0.9999992661786696
            ],
            [
                0.999964643757745,
                0.9999417087415413,
                0.9993736659152335,
                0.9999339478239792,
                0.9995694428723312,
                0.9999485577864075,
                0.9999151889486606,
                0.9999038975397089,
                0.99989110306594,
                0.9999151889486779
            ],
            [
                0.9999987901338838,
                0.9999980052693274,
                0.9999910603005013,
                0.9999962733616047,
                0.9999952149066462,
                0.9999967112505427,
                0.9999989322972573,
                0.9999986290421394,
                0.9999921107355343,
                0.9999962733607161
            ],
            [
                0.9991959142501733,
                0.9989677690656423,
                0.9998766053665733,
                0.9997040430082713,
                0.9999599363173874,
                0.9999251537372034,
                0.9994472213315935,
                0.9997388096292799,
                0.9999151889183269,
                0.9995121428836323
            ],
            [
                0.9997388097866459,
                0.999996711249367,
                0.9996646498207793,
                0.9999785550490417,
                0.9999038975394824,
                0.9999251537642266,
                0.9999984465028011,
                0.9998204720559609,
                0.9999938558253987,
                0.9999832985761737
            ],
            [
                0.999978555054151,
                0.9999251537818217,
                0.9999852610162746,
                0.9999938558253987,
                0.9999646437493142,
                0.9999599362935143,
                0.9999756997650704,
                0.9999417087206578,
                0.9999546021368217,
                0.9999785550464821
            ],
            [
                0.9999756997650704,
                0.999925153746088,
                0.9999646437409038,
                0.9999151889284886,
                0.9999687980886678,
                0.9999687980737948,
                0.9993736659061248,
                0.9999339478476496,
                0.9999546021097687,
                0.9998415638215102
            ],
            [
                0.9999687980849252,
                0.9999417087206002,
                0.999959936317401,
                0.9995694429644184,
                0.9999339478711182,
                0.9999546021260055,
                0.9997388097536177,
                0.9995694429662221,
                0.9995694428667071,
                0.9999546021476443
            ],
            [
                0.9999885212277791,
                0.9999869928699862,
                0.9999687980960759,
                0.9999984465020604,
                0.9999910603068948,
                0.9999952149049351,
                0.9999885212264104,
                0.9999962733589395,
                0.9999785550490482,
                0.9999646437366985
            ],
            [
                0.9999921107364755,
                0.9999885212332462,
                0.9999646437408973,
                0.9999952149066472,
                0.9999930377412621,
                0.9999921107383567,
                0.9998415637647267,
                0.9999852610162742,
                0.9999952149037952,
                0.9999910603005008
            ],
            [
                2.5612822107167428e-06,
                1.7603434231385591e-06,
                3.726639284050988e-06,
                1.99473067264854e-06,
                1.3007128462477575e-05,
                3.288750241473551e-06,
                1.9947299592933255e-06,
                1.7603427936183298e-06,
                3.7266406168403854e-06,
                2.561282821352716e-06
            ],
            [
                0.9999921107355342,
                0.9999756997650809,
                0.9999869928668866,
                0.9999992661792819,
                0.9999921107402387,
                0.9998601778769086,
                0.9999151889385525,
                0.9999930377420918,
                0.999997438717484,
                0.9999938558268644
            ],
            [
                2.144494074076854e-05,
                1.5534975693869924e-06,
                3.72664061681327e-06,
                2.144494329769612e-05,
                6.962257079465052e-06,
                5.422218323019487e-06,
                2.144495607789177e-05,
                1.0129990978441666e-05,
                4.222834451327159e-06,
                3.7266383953679482e-06
            ],
            [
                0.9989677690488362,
                0.9997388096921669,
                0.9999485577619212,
                0.999769493202693,
                0.9999485577741026,
                0.9999546021422621,
                0.9999339478790124,
                0.9999546021259874,
                0.9999151889790573,
                0.9998415637645353
            ],
            [
                0.9999945777823239,
                0.9998601778929518,
                0.9999810748495139,
                0.999988521229141,
                0.999995777165549,
                0.9999339478791137,
                0.9999339478397501,
                0.9999938558275999,
                0.9999898700078197,
                0.9999930377420913
            ],
            [
                5.422219616026655e-06,
                8.939697369151141e-06,
                6.962257079275089e-06,
                4.222831934248571e-06,
                3.7266388397721442e-06,
                2.260325375664839e-06,
                6.144172404302622e-06,
                4.785096205882502e-06,
                6.962257909323729e-06,
                7.889260703763482e-06
            ],
            [
                0.9999962733607165,
                0.9999938558261322,
                0.9999885212277724,
                0.9999898700078172,
                0.9999910603058312,
                0.9999930377462427,
                0.9999970976890532,
                0.9999885212291455,
                0.9999852610162822,
                0.9999938558224721
            ],
            [
                0.9999967112505427,
                0.999993855825399,
                0.9999938558232019,
                0.9999485577680656,
                0.9999930377462409,
                0.9999984465018751,
                0.9999869928761944,
                0.999994577778449,
                0.9999938558239341,
                0.9999962733598277
            ],
            [
                0.9999485577802911,
                0.9999599363221943,
                0.9999852610110069,
                0.9999785550490482,
                0.9999687980849544,
                0.9999756997650822,
                0.9999687980886571,
                0.9999756997622222,
                0.9999885212291416,
                0.9999546021151928
            ],
            [
                0.9997694931755629,
                0.9999546021426348,
                0.9999417087066884,
                0.9999724643023361,
                0.9989677691816041,
                0.9996200155162237,
                0.995929863207136,
                0.9525741251394715,
                0.999959936298309,
                0.9999151889789265
            ],
            [
                0.999997438717484,
                0.9999938558232014,
                0.999997097687323,
                0.9999910603005008,
                0.9999952149072168,
                0.9999785550592586,
                0.9999982396567868,
                0.9999984465018751,
                0.9999832985741774,
                0.9999970976866309
            ],
            [
                6.962257909501028e-06,
                3.288748673319648e-06,
                1.3709570434122812e-06,
                5.422221555133606e-06,
                6.962256249517824e-06,
                5.422218969601935e-06,
                4.785093924156175e-06,
                7.889266346746518e-06,
                7.889260704631679e-06,
                3.726639728262097e-06
            ],
            [
                0.9999038975628276,
                0.9999852610145189,
                0.999915188938561,
                0.9999810748472673,
                0.9999898700053994,
                0.9998766053958636,
                0.9999810748585384,
                0.9999869928668863,
                0.9999485578048138,
                0.9999869928684372
            ],
            [
                4.7850956352353935e-06,
                1.5534979397394734e-06,
                1.670142383015595e-05,
                8.93969630333567e-06,
                2.5612812946890944e-06,
                7.889260704531226e-06,
                2.9023109471689794e-06,
                3.288748673295719e-06,
                1.553497384180408e-06,
                2.1444948407573453e-05
            ],
            [
                0.9999485577618885,
                0.9999810748495231,
                0.9999724643122142,
                0.9999687980849485,
                0.9999810748472526,
                0.9999810748540218,
                0.9999756997650798,
                0.9999832985841434,
                0.9999599362888268,
                0.9999724643154851
            ],
            [
                1.300712380997554e-05,
                3.1201907643310305e-05,
                2.144495607336692e-05,
                8.939698433584547e-06,
                1.0129995808639442e-05,
                4.0063677837180203e-05,
                1.1478770858706246e-05,
                3.7266410609160796e-06,
                1.8925150491445666e-05,
                4.785096776068365e-06
            ],
            [
                1.3709570434054234e-06,
                4.222832437639588e-06,
                2.902313022984344e-06,
                1.0677028700363782e-06,
                5.715007195353674e-07,
                1.3709572068422585e-06,
                1.7603436330179102e-06,
                1.2098656835136636e-06,
                3.2887490653408545e-06,
                4.785092783415276e-06
            ],
            [
                0.9999832985721891,
                0.9999687980961026,
                0.9999994956527722,
                0.9999785550541648,
                0.9997965730768226,
                0.9999546021314231,
                0.9999599362935444,
                0.9999885212359829,
                0.9999339478711341,
                0.9999810748517651
            ],
            [
                1.1478769492642663e-05,
                3.726638395527247e-06,
                1.8925148236674017e-05,
                4.5397874031792504e-05,
                5.4222183234485234e-06,
                5.829126550803852e-05,
                6.144174601410037e-06,
                1.1478772229989872e-05,
                4.5397879448184774e-05,
                4.5397868633071815e-05
            ],
            [
                0.9999945777810302,
                0.9999987901341723,
                0.9999687980849412,
                0.9999869928715366,
                0.999964643736649,
                0.9999977396748938,
                0.9999982396561572,
                0.9999989322967482,
                0.9999952149072168,
                0.999997438716568
            ],
            [
                0.9999952149055125,
                0.9046505357435622,
                0.9998204720130326,
                0.9999785550442745,
                0.9999832985722106,
                0.9914225128914324,
                0.997817283242792,
                0.9149009515124917,
                0.9998415638404773,
                0.9995694430029968
            ],
            [
                0.9999038975852388,
                0.9999646437324774,
                0.999972464295789,
                0.9999832985701989,
                0.9998601778931329,
                0.999664650012918,
                0.9999832985741794,
                0.9999832985841411,
                0.9999417087137394,
                0.9998911030914043
            ],
            [
                0.99997246431548,
                0.9997040429022191,
                0.9999832985761689,
                0.9989677691774027,
                0.9999852610197902,
                0.9999832985801532,
                0.9999957771660521,
                0.9999885212332462,
                0.9999977396757023,
                0.9999646437450979
            ],
            [
                0.999988521226408,
                0.9999930377412614,
                0.9999910603005089,
                0.9999930377445835,
                0.9999938558261312,
                0.999994577779092,
                0.9999885212305162,
                0.9999417087206438,
                0.9999756997563835,
                0.9999869928699956
            ],
            [
                4.785092783319532e-06,
                6.962257909412379e-06,
                5.422220908703723e-06,
                2.4300246516082393e-05,
                6.144172404520556e-06,
                2.26032402841657e-06,
                7.889259763857458e-06,
                6.144177531532303e-06,
                4.222832941142044e-06,
                7.889264466115267e-06
            ],
            [
                0.999769493314527,
                0.99997246431876,
                0.9995121428874073,
                0.9999251537818445,
                0.9998766053813154,
                0.9998204720135393,
                0.9998766054550079,
                0.9998204719705692,
                0.9999832985781624,
                0.9999151889891938
            ],
            [
                0.9999038975969373,
                0.9999921107402365,
                0.9998415638411204,
                0.9998911030392049,
                0.9998766054553652,
                0.9999687980774866,
                0.999991060304763,
                0.9999687980774961,
                0.9999546021476804,
                0.9999724643056611
            ],
            [
                0.9999930377437519,
                0.9999756997679721,
                0.9999945777810305,
                0.999988521231877,
                0.9998415638407447,
                0.9999910602994336,
                0.9999952149060762,
                0.9999756997621809,
                0.9999962733598279,
                0.999986992876194
            ],
            [
                0.9990889487015431,
                0.995390428570574,
                0.9999646437450999,
                0.9999869928684372,
                0.9993736659021899,
                0.9993736658292114,
                0.9999417087275694,
                0.9998415637835808,
                0.9993736659115535,
                0.999569442912851
            ],
            [
                0.9998601779267207,
                0.9999339478712346,
                0.9998766054256547,
                0.999925153746154,
                0.9990889487729095,
                0.998830489977686,
                0.9999546021097687,
                0.9998601779264115,
                0.9986749777354489,
                0.9999151889386154
            ],
            [
                0.9999930377445808,
                0.9999898700066077,
                0.999959936312614,
                0.9999930377412614,
                0.9999485578047914,
                0.9999967112497589,
                0.9999921107364762,
                0.9999852610127629,
                0.9999962733620492,
                0.9999417087137394
            ],
            [
                0.9989677691738014,
                0.9992903296243045,
                0.9999251537907281,
                0.9998204720772462,
                0.9999251537639581,
                0.9999417087206531,
                0.999975699767971,
                0.9997388096288542,
                0.9999599362935339,
                0.9999417087414828
            ],
            [
                0.9999852610233055,
                0.9999339478396944,
                0.9999885212305069,
                0.9999485577986746,
                0.9999869928668873,
                0.9999417087206043,
                0.9999646437619992,
                0.9999485578048678,
                0.9999785550490354,
                0.9999756997477003
            ],
            [
                0.9999957771675625,
                0.9999970976890529,
                0.9999952149032237,
                0.999993855824666,
                0.999995777166052,
                0.9999993524053562,
                0.9999885212264016,
                0.9999945777790913,
                0.9999921107402363,
                0.9999970976869772
            ],
            [
                1.7603440525925705e-06,
                2.9023119850210436e-06,
                1.9947306723745965e-06,
                1.9947294836483373e-06,
                1.5534983101478522e-06,
                4.7850933534310035e-06,
                4.222832940834793e-06,
                1.5534984953199313e-06,
                1.0677027427413698e-06,
                5.422217676797111e-06
            ],
            [
                0.9999869928684416,
                0.999985261014518,
                0.9997694933131654,
                0.9999687980737768,
                0.9999910603036991,
                0.9999810748540223,
                0.9999687980737768,
                0.9999724642990753,
                0.9999869928730883,
                0.9999646437451138
            ],
            [
                0.9999251537639369,
                0.99979657295416,
                0.9999756997563761,
                0.9999599363078128,
                0.9999910603047628,
                0.99995993629351,
                0.9999546021313719,
                0.9999646437493017,
                0.999996273358939,
                0.9999832985781653
            ],
            [
                0.9999151889891562,
                0.9999756997592832,
                0.9998204719496654,
                0.9999687980774731,
                0.9999417087345632,
                0.9999646437578114,
                0.9999599362888137,
                0.9999724643089181,
                0.9999885212359839,
                0.9999646437493261
            ],
            [
                0.9999898700041936,
                0.9999921107336545,
                0.9999952149055061,
                0.9999852610145198,
                0.9999898700066098,
                0.9999938558246667,
                0.9999970976866313,
                0.9999785550490452,
                0.9999930377412617,
                0.9999952149066472
            ],
            [
                0.9999251537639581,
                0.9999724642990838,
                0.9997694932038869,
                0.9998911031174453,
                0.9999687980923697,
                0.9999339478398184,
                0.9998911031299643,
                0.9999038975741514,
                0.9998415637653767,
                0.9999756997592926
            ],
            [
                0.9999930377420932,
                0.9999687980775394,
                0.9999869928761901,
                0.9999546021151737,
                0.9999724643187728,
                0.9999646437535583,
                0.9999832985821445,
                0.9999724643154826,
                0.999986992876201,
                0.9999687980923779
            ],
            [
                1.3007126912542439e-05,
                1.1478768123280277e-05,
                2.144494329348333e-05,
                6.144172403715875e-06,
                7.889262585082652e-06,
                6.962258739530771e-06,
                4.785092783267308e-06,
                1.0129992186589747e-05,
                7.889266346129453e-06,
                6.962257079465052e-06
            ],
            [
                0.9999724642957943,
                0.9998415637458471,
                0.9999852610197911,
                0.9999910602994353,
                0.999997438717484,
                0.9999898700041947,
                0.9999910602994353,
                0.9999921107364752,
                0.9999885212359829,
                0.9999957771680664
            ],
            [
                0.9993736658351866,
                0.9999546021205397,
                0.9998601779763558,
                0.9999339478397636,
                0.9999952149072167,
                0.9997388096960351,
                0.9998911030519679,
                0.9999785550439243,
                0.999290329472398,
                0.999620015518302
            ],
            [
                0.9995121427749531,
                0.9999485577741262,
                0.9995121429486014,
                0.999981074854021,
                0.9999987901341723,
                0.9999785550541638,
                0.9999832985741856,
                0.9999945777810312,
                0.9999599362935236,
                0.9999852610110069
            ],
            [
                0.9999599363078904,
                0.9999930377437508,
                0.9999852610145177,
                0.9999599362887558,
                0.9999898700053983,
                0.9999687980923553,
                0.9999962733598275,
                0.9998204719915358,
                0.9975273764919065,
                0.9997965730762514
            ],
            [
                0.9998911030650574,
                0.9999417087554217,
                0.9999810748562864,
                0.9999898700041926,
                0.9999885212264047,
                0.9999967112501507,
                0.999915188928498,
                0.999993037741261,
                0.9999997897567342,
                0.9999984465022456
            ],
            [
                0.9999417087276458,
                0.999964643749322,
                0.999964643732451,
                0.9998601779773609,
                0.9997040427610945,
                0.9999945777829701,
                0.9999785550541487,
                0.99993394782408,
                0.9999251537906645,
                0.9999921107392965
            ],
            [
                2.4300252315495453e-05,
                1.1478770861211786e-05,
                8.939698434966738e-06,
                1.8925155005051806e-05,
                2.1444956079218013e-05,
                2.1444953524161264e-05,
                6.144175334094145e-06,
                1.0129995809044816e-05,
                8.939696303758459e-06,
                1.4738976699427788e-05
            ],
            [
                0.9999957771650453,
                0.9999832985701977,
                0.999995777168066,
                0.9999921107336528,
                0.9999945777829695,
                0.9999970976880149,
                0.9999724643089085,
                0.9999974387180947,
                0.9999938558224686,
                0.9999724642957828
            ],
            [
                4.78509506499309e-06,
                5.422218322940583e-06,
                5.42221767672807e-06,
                3.288750241374845e-06,
                6.1441767989541075e-06,
                5.4222215552470286e-06,
                1.0129989771657269e-05,
                6.9622579086271995e-06,
                5.42221961567159e-06,
                3.726639284017094e-06
            ],
            [
                0.9999938558246673,
                0.9999869928715396,
                0.9999930377437526,
                0.9999785550413756,
                0.9995121428829227,
                0.9999756997505934,
                0.9999417087206256,
                0.9999810748540244,
                0.9999646437408781,
                0.9999810748450007
            ],
            [
                0.9999885212332453,
                0.9999852610162758,
                0.9999546021476569,
                0.9999785550567105,
                0.9999810748450104,
                0.9999852610180356,
                0.9999930377429218,
                0.9999785550490384,
                0.9999756997563856,
                0.9999724642957877
            ],
            [
                0.9999756997650686,
                0.9999910603068956,
                0.9999852610145189,
                0.9999930377445809,
                0.9999898700114366,
                0.9999885212291424,
                0.9999687980774852,
                0.9999957771660523,
                0.9999967112509351,
                0.9999910603015663
            ],
            [
                4.785096776303374e-06,
                2.902312677104321e-06,
                1.473898372500477e-05,
                2.753568453191415e-05,
                1.1478773598914277e-05,
                8.939694172420599e-06,
                8.939696303010449e-06,
                9.610242629256036e-05,
                1.8925143727854426e-05,
                2.260324297853209e-06
            ],
            [
                1.7603430034439723e-06,
                2.9023112930949896e-06,
                4.785092783371756e-06,
                6.144176798590883e-06,
                1.5534975693792215e-06,
                2.9023119851266288e-06,
                1.370957860567974e-06,
                2.9023119851266288e-06,
                1.5534979397592542e-06,
                1.9947304348332037e-06
            ],
            [
                0.9999724643056297,
                0.9999687980849237,
                0.9998601778928216,
                0.999841563840392,
                0.9997040428316094,
                0.9999957771655488,
                0.999981074842739,
                0.999373665831361,
                0.9999869928684368,
                0.9999038975852054
            ],
            [
                2.561282821352716e-06,
                1.1478766757404937e-05,
                8.939695237666677e-06,
                2.260324567268294e-06,
                2.5612819053399912e-06,
                4.785092783371756e-06,
                5.422220262333096e-06,
                4.222834451065997e-06,
                2.2603248367512505e-06,
                2.5612822106421996e-06
            ],
            [
                0.99994855779869,
                0.999991060300499,
                0.9999945777816769,
                0.9999945777784456,
                0.9999945777829699,
                0.9999885212332462,
                0.9999885212277702,
                0.9999967112505427,
                0.9999977396754327,
                0.9999852610197869
            ],
            [
                0.9999687980774769,
                0.9999869928668845,
                0.9999910603004989,
                0.9999485577924824,
                0.9999945777797375,
                0.9999724643121888,
                0.9998911031298644,
                0.9999151889890266,
                0.9999898700126436,
                0.9999869928684346
            ],
            [
                0.9999646437366768,
                0.9999038976196464,
                0.9999546021476354,
                0.9997388097540433,
                0.9999646437577469,
                0.9990889486859663,
                0.9999546021260055,
                0.9999724642990713,
                0.9999724643154878,
                0.9999852610110046
            ],
            [
                0.9997694932584088,
                0.9999724642958031,
                0.9999251537996416,
                0.9999785550439327,
                0.9999724643089275,
                0.9997388096610463,
                0.999975699767989,
                0.9999251537462094,
                0.999972464302386,
                0.9999599363222136
            ],
            [
                1.67014218359435e-05,
                1.3007131563815288e-05,
                3.726639728224814e-06,
                3.726640616748873e-06,
                2.7535697658087296e-05,
                8.93969310418261e-06,
                1.994729483666479e-06,
                3.120191508820951e-05,
                1.6701427811412077e-05,
                5.829127935617924e-05
            ],
            [
                0.9999930377454109,
                0.9999970976883612,
                0.999997438717484,
                0.9999945777784448,
                0.9999921107364749,
                0.9999646437408874,
                0.9999885212318759,
                0.9999962733616046,
                0.9999945777816768,
                0.9999832985841344
            ],
            [
                0.9999832985781628,
                0.9999724642990738,
                0.9999938558224694,
                0.9999938558253989,
                0.999983298574185,
                0.9999967112521111,
                0.9999910603047634,
                0.9999982396565769,
                0.9999952149049353,
                0.9999885212277752
            ],
            [
                0.999997097686977,
                0.9999785550490375,
                0.9999898700041916,
                0.9999952149066464,
                0.9999974387187053,
                0.9999995549148419,
                0.9999251537640033,
                0.9999967112513267,
                0.9999885212291387,
                0.9999687980812203
            ],
            [
                0.9999687980886571,
                0.9999724642990699,
                0.999954602136831,
                0.9999852610215463,
                0.9999724643023485,
                0.9999832985761699,
                0.9999151889386432,
                0.9999898700078157,
                0.9999724642957902,
                0.9999038976080801
            ],
            [
                0.9999995549147358,
                0.9999952149060767,
                0.999988521231878,
                0.9999038975508663,
                0.9999885212277744,
                0.9999339478790639,
                0.999992110740237,
                0.9995694428624236,
                0.9999785550515996,
                0.9999930377404322
            ],
            [
                0.9999785550541495,
                0.9999898700041923,
                0.9997965730521511,
                0.9999724643023429,
                0.9999885212264037,
                0.999985261023306,
                0.9999930377445818,
                0.9999599363126381,
                0.9999687980886642,
                0.9998911031172932
            ],
            [
                0.9999885212291427,
                0.9999785550567266,
                0.9999599363221943,
                0.9999785550464899,
                0.9999687980998164,
                0.9996200155172518,
                0.9999869928730912,
                0.9999930377454107,
                0.9999724643155044,
                0.999978555056716
            ],
            [
                0.9998601778600699,
                0.999891103104096,
                0.9999756997563835,
                0.9999785550541617,
                0.9999921107364751,
                0.9999852610233045,
                0.9999724643187674,
                0.9999646437367106,
                0.9999910603058285,
                0.9999869928653401
            ],
            [
                2.14449458497871e-05,
                1.300713466316634e-05,
                0.0004878571555364432,
                1.8925141469400216e-05,
                4.0063692167994334e-05,
                1.3007123810306773e-05,
                4.0063692159249626e-05,
                2.4300249410794055e-05,
                1.3007130012673148e-05,
                9.610246059873997e-05
            ],
            [
                0.9999646437535114,
                0.9999485578047674,
                0.9999724643023409,
                0.9999869928715355,
                0.9999989322975118,
                0.999996273358939,
                0.9999945777784451,
                0.9999980052695652,
                0.999998005269803,
                0.9999599363030427
            ],
            [
                1.7603432132784448e-06,
                4.785095635413826e-06,
                1.553497199007048e-06,
                6.144174601309452e-06,
                5.422218969384951e-06,
                2.4300243591756525e-05,
                6.1441731363550164e-06,
                5.422220262264056e-06,
                5.422219615750493e-06,
                2.902313022984344e-06
            ],
            [
                0.999972464302386,
                0.9999885212332473,
                0.9999151889793035,
                0.9999938558232012,
                0.9999869928653464,
                0.9999251537638759,
                0.9999724643187915,
                0.999941708713636,
                0.9999921107345942,
                0.9997040428344854
            ],
            [
                0.999983298574177,
                0.9999967112517187,
                0.9999724643121909,
                0.9997694933143458,
                0.9999785550541518,
                0.9999921107383555,
                0.9999962733620487,
                0.9997040429375756,
                0.9999852610215443,
                0.9999910603004997
            ],
            [
                0.9999756997592754,
                0.999978555056703,
                0.9999898700126437,
                0.9999977396765105,
                0.9999417087414281,
                0.999992110734593,
                0.999985261016273,
                0.9999417087484088,
                0.9999785550567114,
                0.9997965730514673
            ],
            [
                0.9988304897586067,
                0.9997965730028551,
                0.9997040427983367,
                0.9995694430167372,
                0.9999756997650743,
                0.9999485577802613,
                0.9994472213315935,
                0.9996646498927155,
                0.9999417087067868,
                0.9996200155200596
            ],
            [
                0.9999984465026158,
                0.9999957771655488,
                0.9999724643187635,
                0.9999930377429205,
                0.9999982396565769,
                0.9999898700041918,
                0.9999967112521109,
                0.9999810748427379,
                0.9999910602994333,
                0.9999945777797379
            ],
            [
                0.9999869928761923,
                0.9999898700053996,
                0.999991060304766,
                0.9999869928668892,
                0.9999339478791008,
                0.999972464312199,
                0.9996646498129349,
                0.9999724643187743,
                0.9999869928684425,
                0.9999910603047655
            ],
            [
                1.012998856312253e-05,
                6.962258738574625e-06,
                1.0129990979215566e-05,
                6.962257908880483e-06,
                7.889265406567165e-06,
                1.3007130012673148e-05,
                6.962259569003389e-06,
                4.006368261266023e-05,
                6.962254589104433e-06,
                1.1478772229781076e-05
            ],
            [
                0.9999756997534981,
                0.9999646437493306,
                0.9999251537639369,
                0.9999724643023645,
                0.9999724642958001,
                0.9998601778768068,
                0.9999599362983198,
                0.9997694932854182,
                0.9995694429288711,
                0.9999485578048138
            ],
            [
                0.9999724643056397,
                0.9991959141727283,
                0.9999724643122028,
                0.9998204720563633,
                0.9999038975509473,
                0.9999599363126164,
                0.9999724642957943,
                0.9999417087067525,
                0.9998766053813334,
                0.9999852610233002
            ],
            [
                1.4738981971250963e-05,
                1.012998977213635e-05,
                8.93969630348202e-06,
                2.56128282131428e-06,
                8.939695238211425e-06,
                6.144176799099397e-06,
                4.785093353787868e-06,
                4.222833444467892e-06,
                7.889264466445326e-06,
                3.726638395611981e-06
            ],
            [
                0.9999921107402369,
                0.9999151889487513,
                0.9999756997621758,
                0.9999885212346133,
                0.9999869928761926,
                0.99996879809982,
                0.9999852610145198,
                0.9999852610110037,
                0.9999930377429213,
                0.9999832985701983
            ],
            [
                2.1444950939693305e-05,
                6.60521524508739e-05,
                1.3007128460797749e-05,
                4.006370650464339e-05,
                2.4300249411766472e-05,
                2.4300237832303074e-05,
                7.889265406567165e-06,
                0.0001088969610644462,
                4.539785778740889e-05,
                0.00010889689603554361
            ],
            [
                1.9947301970451086e-06,
                4.785096775920397e-06,
                3.2887478891128633e-06,
                3.726640616670918e-06,
                6.962254588281262e-06,
                4.222834451254188e-06,
                3.2887478891128633e-06,
                3.726641061058432e-06,
                3.2887490653109436e-06,
                1.4738980212644815e-05
            ],
            [
                0.9999957771675625,
                0.9999910603004997,
                0.9999885212318764,
                0.9999930377412607,
                0.9999921107374157,
                0.9999945777790913,
                0.999995214903224,
                0.9999986290429566,
                0.9999970976883608,
                0.9999967112521108
            ],
            [
                0.9995694430149461,
                0.999975699756396,
                0.9999756997534971,
                0.9999646437493586,
                0.9999687980774995,
                0.9998766054695668,
                0.9996200155644005,
                0.9999756997592889,
                0.9999945777810306,
                0.9999151889588132
            ],
            [
                0.999986992876196,
                0.9999938558239337,
                0.9997965730274498,
                0.9999485578047742,
                0.9875683501644353,
                0.999959936298269,
                0.9999898700102285,
                0.9998415638399794,
                0.9999962733589416,
                0.9999921107392955
            ],
            [
                0.9999785550413688,
                0.999988521229139,
                0.9999852610197889,
                0.999954602147616,
                0.9998911030911317,
                0.999993855824667,
                0.9999898700102325,
                0.999992110738356,
                0.9999957771680661,
                0.9995121428928001
            ],
            [
                0.9999417087553565,
                0.9999852610127575,
                0.9999756997505863,
                0.9999417087275134,
                0.9999910602994336,
                0.9999869928684351,
                0.9999546021151431,
                0.9999417087553318,
                0.9999646437492984,
                0.9999810748540229
            ],
            [
                0.9999930377404321,
                0.9999945777823236,
                0.9999756997679731,
                0.9999898700053986,
                0.9999417087345395,
                0.9999885212305113,
                0.9999646437408835,
                0.9997965730762041,
                0.9999952149060765,
                0.9999599363030545
            ],
            [
                4.222832437639588e-06,
                1.1478772230198667e-05,
                2.1444943298320236e-05,
                1.7603425837606927e-06,
                3.7266406168403854e-06,
                7.889261644631091e-06,
                4.785094494750855e-06,
                2.1444945853999886e-05,
                1.147877359926923e-05,
                1.473897670007122e-05
            ],
            [
                0.9999832985741811,
                0.9999832985741794,
                0.9999485577925504,
                0.9999251537907886,
                0.9999921107402385,
                0.9999646437535655,
                0.999995777165046,
                0.9999417087207524,
                0.9999251537906851,
                0.9999898700102318
            ],
            [
                0.9999724643154964,
                0.999903897619545,
                0.9999646437535384,
                0.9999832985761709,
                0.9999785550490434,
                0.9999974387165684,
                0.9999832985741818,
                0.9999724643154851,
                0.9999832985801526,
                0.9999810748585416
            ],
            [
                0.999986992876197,
                0.9999938558246676,
                0.999989870012645,
                0.9999485577925392,
                0.9997694933404095,
                0.9999930377445825,
                0.9999869928730921,
                0.9999910603058296,
                0.9999952149043653,
                0.9999546021259963
            ],
            [
                0.9999832985841371,
                0.9999339478712945,
                0.999964643736669,
                0.999959936317406,
                0.9999785550592685,
                0.9999885212305106,
                0.9999952149072177,
                0.9999967112493666,
                0.9998415637846757,
                0.9999785550541569
            ],
            [
                0.9999832985781653,
                0.9999852610180403,
                0.9999910602994345,
                0.9999962733589393,
                0.9999898700041934,
                0.9999967112517191,
                0.9999967112513268,
                0.9999810748450022,
                0.9999869928761944,
                0.9997388097541877
            ],
            [
                0.9999038975395677,
                0.999738809754332,
                0.9999952149037942,
                0.9996646497746887,
                0.999975699762171,
                0.9999898700066077,
                0.9999869928761915,
                0.9999687980886323,
                0.9999945777790917,
                0.9998415637078946
            ]
        ]
    },
    {
        "q_id": "8258_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            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,
            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,
            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": [
            [
                5.4222183231674305e-06,
                7.889262585642319e-06,
                8.939695238211425e-06,
                9.422448185388577e-07,
                1.994730197071414e-06,
                8.93969630362837e-06,
                1.3007125363293615e-05,
                1.3007133115903994e-05,
                7.889263525663481e-06,
                8.939698435340743e-06
            ],
            [
                1.1478765386623071e-05,
                4.785094494628999e-06,
                2.9023112931688987e-06,
                2.2603240283888175e-06,
                2.1444956063303036e-05,
                1.3007126912542439e-05,
                6.962253759581752e-06,
                6.962258739068529e-06,
                2.90231094702116e-06,
                1.1478766756653273e-05
            ],
            [
                4.7850950647493785e-06,
                5.4222183231674305e-06,
                2.5612819053166966e-06,
                3.288747889178668e-06,
                4.222833444383398e-06,
                3.288749457409966e-06,
                1.0129995809597604e-05,
                1.6701417851711638e-05,
                2.5612831266608576e-06,
                1.6701415863393463e-05
            ],
            [
                0.9999962733589403,
                0.9999485578048216,
                0.7981867801399695,
                0.9999898700114389,
                0.9999962733589393,
                0.9999756997476992,
                0.9999967112501511,
                0.999964643736646,
                0.9999945777803856,
                0.9999885212346988
            ],
            [
                4.785096205582214e-06,
                4.785096775998733e-06,
                6.962256249429175e-06,
                2.561282210618905e-06,
                1.300712845966209e-05,
                6.962257076830902e-06,
                5.422217676397663e-06,
                4.222831934052698e-06,
                1.300712846361323e-05,
                4.222831934248571e-06
            ],
            [
                7.889266346287306e-06,
                7.88926258381982e-06,
                2.1444948392516633e-05,
                1.670141785420273e-05,
                1.3007123807302014e-05,
                1.1478764020372226e-05,
                7.889266346603015e-06,
                1.3007130013856124e-05,
                1.994729959224386e-06,
                3.1201918798457626e-05
            ],
            [
                6.962257908880483e-06,
                1.4738988993532872e-05,
                3.726640172503764e-06,
                1.0129987355988324e-05,
                6.144176066443055e-06,
                1.1478765388523107e-05,
                9.422449308241022e-07,
                2.144495607492721e-05,
                6.144173868781898e-06,
                1.4738981969240237e-05
            ],
            [
                1.994730196992497e-06,
                6.144172403928222e-06,
                1.994729245842213e-06,
                0.00010889688308554166,
                1.1478773598329648e-05,
                2.260324567302214e-06,
                9.422450431912e-07,
                6.962254589528684e-06,
                2.1444950968441685e-05,
                2.9023109471188266e-06
            ],
            [
                1.5534983100228109e-06,
                6.962255419570695e-06,
                2.9023109471452223e-06,
                6.144173136885882e-06,
                1.994729245917502e-06,
                2.5612812946681295e-06,
                2.260325375615501e-06,
                1.5534975693707442e-06,
                2.260324567227179e-06,
                7.338211554641698e-07
            ],
            [
                1.0129990979031306e-05,
                1.9947292459265734e-06,
                4.785093353787868e-06,
                8.93969310662177e-06,
                8.93969310584124e-06,
                6.962256249429175e-06,
                6.962253759581752e-06,
                6.962256249517824e-06,
                4.785095635017795e-06,
                2.902310947190096e-06
            ],
            [
                2.430023783309869e-05,
                1.6701427815999337e-05,
                8.939699500636112e-06,
                1.3007131564643372e-05,
                1.7603438428460541e-06,
                1.0129988563343644e-05,
                4.785094494019719e-06,
                6.605214464752619e-05,
                3.2887482810382622e-06,
                8.93969630333567e-06
            ],
            [
                3.726640172537657e-06,
                4.222832941034507e-06,
                5.4222215550004564e-06,
                6.962257079553702e-06,
                4.222832941072913e-06,
                3.726639283752725e-06,
                1.0129987355988324e-05,
                4.222835457364773e-06,
                4.2228344511197656e-06,
                7.889266347356409e-06
            ],
            [
                2.7535684514885004e-05,
                8.93969310662177e-06,
                5.422220908560712e-06,
                1.0129993389652346e-05,
                5.422221554374162e-06,
                1.6701425817016872e-05,
                0.9990889488691775,
                1.4738988987366645e-05,
                4.0063711283916205e-05,
                1.8925150491445666e-05
            ],
            [
                0.999769493367761,
                0.9982992779176576,
                0.0002959571333096205,
                0.9997040429031577,
                0.9999485577679644,
                0.9998601778929518,
                0.9999687980812043,
                0.999876605439948,
                0.9999785550465029,
                0.9991959141538348
            ],
            [
                0.9997040427580979,
                0.9999810748427564,
                0.9997388096858593,
                0.9998766054809785,
                0.9996200155173292,
                0.9999646437493017,
                0.9997694933127227,
                0.9999885212305084,
                0.8175744850834648,
                0.9999952149037946
            ],
            [
                7.889264466445326e-06,
                5.14422075117015e-05,
                6.9622579092224155e-06,
                3.2887482811908074e-06,
                1.0129990978441666e-05,
                6.1441738684354385e-06,
                7.889263525103816e-06,
                6.144172404380855e-06,
                4.785092783267308e-06,
                4.222834451254188e-06
            ],
            [
                4.006367783499403e-05,
                1.300713466420736e-05,
                3.120191879981973e-05,
                6.962255419051463e-06,
                5.14422074608005e-05,
                7.889259763857458e-06,
                5.422221554581283e-06,
                4.7850944937411915e-06,
                3.120192251903545e-05,
                5.144223815748175e-05
            ],
            [
                1.4738985482351282e-05,
                1.6701427815999337e-05,
                8.939698435226916e-06,
                2.430024651882284e-05,
                3.535624228313077e-05,
                2.1444943297072005e-05,
                7.88926258532661e-06,
                1.1478768123280277e-05,
                7.48462447582851e-05,
                1.3007131561804229e-05
            ],
            [
                4.539787945792856e-05,
                4.785095634460739e-06,
                7.8892625849535e-06,
                7.889263523453522e-06,
                2.753569437686898e-05,
                1.892515726357648e-05,
                8.939699500636112e-06,
                1.0129992185539456e-05,
                1.1478770861859053e-05,
                1.2098658277082653e-06
            ],
            [
                6.144177531208195e-06,
                8.939698434657777e-06,
                1.553497754188098e-06,
                5.422220907426478e-06,
                2.75357009372024e-05,
                3.120191502691499e-05,
                1.300712536258383e-05,
                1.8925148237775583e-05,
                1.012999218369684e-05,
                1.670142781432848e-05
            ],
            [
                0.9998415637645076,
                0.9999810748427396,
                0.999948557792614,
                0.9998415638216255,
                0.9999810748562764,
                0.9999869928653384,
                0.9999810748495187,
                0.9999832985702075,
                0.9999869928669048,
                0.9999417087417208
            ],
            [
                1.0129990979031306e-05,
                1.0129993394314164e-05,
                1.012998735687278e-05,
                8.315279285205827e-07,
                1.1478770862067849e-05,
                1.892515500560259e-05,
                1.0129992187400498e-05,
                3.120190761663585e-05,
                5.4222183231674305e-06,
                4.222832437497486e-06
            ],
            [
                1.0129988564430787e-05,
                1.012998977213635e-05,
                1.8925145981833788e-05,
                1.4738976699427788e-05,
                1.3007134665934505e-05,
                1.89251482355036e-05,
                2.4300249421932663e-05,
                1.3007128463873485e-05,
                7.889260704050487e-06,
                6.962256249429175e-06
            ],
            [
                0.9999989322970029,
                0.9999898700041916,
                0.9999251537908708,
                0.9999982396569972,
                0.9999994956526519,
                0.9999785550491542,
                0.999992110740238,
                0.9999756997506137,
                0.9999962733593838,
                0.9999885212360181
            ],
            [
                4.78509563546605e-06,
                4.22283545795623e-06,
                2.1444948404530884e-05,
                1.1478766756653273e-05,
                4.785093924156175e-06,
                4.78509563550957e-06,
                2.5612822106654943e-06,
                5.422219615582823e-06,
                3.2887498493325602e-06,
                8.939694170729447e-06
            ],
            [
                3.288749457383046e-06,
                2.5612819053586272e-06,
                2.2603234894745224e-06,
                1.1478773598099973e-05,
                2.260325375677174e-06,
                2.144495096161541e-05,
                8.93969630317306e-06,
                1.670141586949968e-05,
                5.144221357303798e-05,
                3.726638395493353e-06
            ],
            [
                0.999941708714167,
                0.9999852610127649,
                0.9998766053968708,
                0.9999485577743488,
                0.9999885212332581,
                0.9999930377437632,
                0.9995121428818442,
                0.9999724643056468,
                0.9999038975851088,
                0.9999898700114399
            ],
            [
                5.4222202623972055e-06,
                6.144173869072478e-06,
                3.2887494573561262e-06,
                1.1478772229551402e-05,
                5.422217030288788e-06,
                4.785092783210732e-06,
                3.2887478892055875e-06,
                3.72664017246987e-06,
                2.9023109467598367e-06,
                1.6701423834226767e-05
            ],
            [
                7.889261644760245e-06,
                6.1441767990323395e-06,
                6.962255419380732e-06,
                1.0677026152337119e-06,
                1.0129987356375273e-05,
                3.726639284050988e-06,
                0.000911051248654057,
                6.9622595694023114e-06,
                4.0063682398706585e-05,
                8.939700566565793e-06
            ],
            [
                3.288749065209246e-06,
                1.4738988998117324e-05,
                1.4738978455325741e-05,
                2.902310946944611e-06,
                7.889265404759017e-06,
                1.1478766756444477e-05,
                4.7850950648799385e-06,
                0.0008040858087989665,
                7.889265406294507e-06,
                1.0129995808639442e-05
            ],
            [
                2.9023119851266288e-06,
                3.2887502413389517e-06,
                3.2887478892055875e-06,
                1.0129987355988324e-05,
                6.962256249429175e-06,
                2.9023116391675407e-06,
                8.939696301839653e-06,
                3.7266379513162962e-06,
                3.726638839656906e-06,
                2.9023116390421582e-06
            ],
            [
                NaN,
                1.8925141468298646e-05,
                8.939694172656384e-06,
                8.939700565834043e-06,
                2.2603251062013478e-06,
                1.0129988564578197e-05,
                1.0129987356541108e-05,
                8.93969310662177e-06,
                2.9023123311055552e-06,
                2.753569765908901e-05
            ],
            [
                1.3007123810638006e-05,
                5.422218322851817e-06,
                3.2887482811220126e-06,
                1.01299946023704e-05,
                6.962254589104433e-06,
                6.9622562489985925e-06,
                6.962257908880483e-06,
                3.726639284103523e-06,
                3.726639284050988e-06,
                3.726637950973972e-06
            ],
            [
                0.9999962733616059,
                0.9992903296267812,
                0.9998766054252419,
                0.2018132246607271,
                0.9999038975856611,
                0.9992903296338813,
                0.13296422989056964,
                0.9999724643027549,
                0.999972464315532,
                0.9998204720130326
            ],
            [
                6.144172404129392e-06,
                4.0063696888092954e-05,
                1.0129993394314164e-05,
                6.962258738827909e-06,
                6.962253759904688e-06,
                1.1478765388711023e-05,
                5.422220908703723e-06,
                1.7603440527046419e-06,
                8.93969736955767e-06,
                6.144174601410037e-06
            ],
            [
                1.8925157254522964e-05,
                1.0129988562901417e-05,
                4.0063711012247355e-05,
                1.4738981947899752e-05,
                1.300713466316634e-05,
                1.670142980222277e-05,
                1.8925148238808306e-05,
                5.422217028582506e-06,
                1.0129988563546333e-05,
                6.144177530548804e-06
            ],
            [
                2.7535694369155778e-05,
                2.4300252297461515e-05,
                1.3007126913583456e-05,
                6.962254588977791e-06,
                6.962254589617333e-06,
                2.4300240732671408e-05,
                4.785095635017795e-06,
                4.785093353352668e-06,
                2.7535684470208522e-05,
                1.8925150495232307e-05
            ],
            [
                6.962257909501028e-06,
                2.5612816000331606e-06,
                2.4300252279869583e-05,
                8.939693102865466e-06,
                1.7603436328770204e-06,
                6.962255419728997e-06,
                7.338211554725124e-07,
                4.785096776251149e-06,
                6.962258739271155e-06,
                7.889260704732132e-06
            ],
            [
                1.0129995809597604e-05,
                1.8925148239772175e-05,
                2.4300246514137558e-05,
                1.5534977545603963e-06,
                8.939700566143004e-06,
                1.3007133114011233e-05,
                1.994729483630195e-06,
                1.47389819699641e-05,
                7.889260704631679e-06,
                6.144175334015912e-06
            ],
            [
                1.3007123811229494e-05,
                5.422218969720291e-06,
                1.6701429806475863e-05,
                2.7535681250497054e-05,
                1.4738980215111302e-05,
                1.300712691308661e-05,
                4.5397874048967995e-05,
                3.120190021339598e-05,
                5.8291258493848154e-05,
                2.144494584573034e-05
            ],
            [
                6.962254589104433e-06,
                2.9023119851266288e-06,
                1.3007126912826352e-05,
                7.889259763728304e-06,
                1.3007125360478133e-05,
                5.422218969128516e-06,
                3.7266406168403854e-06,
                6.144177531599359e-06,
                3.2887498494551953e-06,
                1.760344052693435e-06
            ],
            [
                0.9999898700102764,
                0.9999869928654934,
                0.9999910603068951,
                0.9997040427695332,
                0.9999599362982876,
                0.914900959053549,
                0.9999974387187054,
                0.9999687980751767,
                0.999981074844998,
                0.9999546021316517
            ],
            [
                1.3709573702566696e-06,
                3.1201911303159835e-05,
                1.4738985481091229e-05,
                2.753568123767511e-05,
                7.889262584666493e-06,
                6.962257078819179e-06,
                2.7535684525803696e-05,
                4.78509563546605e-06,
                5.42221767672807e-06,
                4.785095635017795e-06
            ],
            [
                2.902310947190096e-06,
                4.785092783267308e-06,
                1.300712691403299e-05,
                5.422218322763051e-06,
                2.2603240283888175e-06,
                5.422219615967477e-06,
                3.288749065209246e-06,
                8.939694171135975e-06,
                2.2603248365343694e-06,
                1.0129993394664264e-05
            ],
            [
                7.889260704308795e-06,
                8.939698433584547e-06,
                2.144495608046625e-05,
                3.726639283901856e-06,
                5.4222176759932836e-06,
                6.144172404380855e-06,
                8.93970056529743e-06,
                1.300712381094558e-05,
                1.1478772228256871e-05,
                6.962256249429175e-06
            ],
            [
                1.9947306723419413e-06,
                2.9023133690637e-06,
                1.9947304348332037e-06,
                2.561283432005142e-06,
                1.0677031245783732e-06,
                8.315282258756395e-07,
                4.785096776303374e-06,
                1.9947290080905435e-06,
                5.715003788853339e-07,
                3.2887478890769702e-06
            ],
            [
                1.0129990978220553e-05,
                1.1478764017428212e-05,
                2.144495096457996e-05,
                4.222833443645997e-06,
                2.1444956074147067e-05,
                3.120191877064807e-05,
                8.9396941718352e-06,
                4.7850944942634305e-06,
                1.4738983723664288e-05,
                3.7266401722360055e-06
            ],
            [
                4.7850962047640385e-06,
                2.7535700936100516e-05,
                3.2887498492518007e-06,
                4.222834451169694e-06,
                8.939699498099386e-06,
                1.0677024880353552e-06,
                1.0129989771473008e-05,
                2.4300249420429837e-05,
                8.939698434153684e-06,
                6.475947981813674e-07
            ],
            [
                6.144177531381426e-06,
                1.892514372640862e-05,
                9.422448184561605e-07,
                6.1441731363550164e-06,
                1.8925145981833788e-05,
                1.5534973841705173e-06,
                3.12019076363863e-05,
                7.889259763326495e-06,
                5.422220908762902e-06,
                3.7266388396128453e-06
            ],
            [
                0.9999485577802874,
                0.9996200154787036,
                0.999512142895752,
                0.5,
                0.9999485577806115,
                0.9998911031051971,
                0.999933947847887,
                0.9992903297654785,
                0.9996646498940424,
                0.9997965729809772
            ],
            [
                2.4300243618542217e-05,
                7.889259763728304e-06,
                8.93969630333567e-06,
                1.3007133113017532e-05,
                1.8925150495232307e-05,
                2.144495096387783e-05,
                4.222833444168322e-06,
                1.1478766756444477e-05,
                2.7535697658087296e-05,
                7.889263525663481e-06
            ],
            [
                1.6701415868193372e-05,
                1.012998977198894e-05,
                1.6701415867707307e-05,
                6.14417606659952e-06,
                2.902312677007974e-06,
                4.222833444383398e-06,
                6.962257077590752e-06,
                8.939693105272102e-06,
                6.962256249429175e-06,
                7.889261644760245e-06
            ],
            [
                6.1441760661636525e-06,
                4.22283394762097e-06,
                7.338208055489796e-07,
                1.2098653950205268e-06,
                2.902311985146426e-06,
                6.475947209953583e-07,
                1.1478769494083349e-05,
                6.144175334094145e-06,
                2.2603248365960415e-06,
                1.5534979397677313e-06
            ],
            [
                4.222833937520116e-06,
                3.2887486731641103e-06,
                8.939697369004791e-06,
                1.0129995806888955e-05,
                7.889264465239894e-06,
                1.0129992186774007e-05,
                7.889263525534328e-06,
                1.6701425816409292e-05,
                1.1478769491306371e-05,
                1.0129995807939249e-05
            ],
            [
                1.275190732889102e-07,
                3.466327450744504e-07,
                6.962258738827909e-06,
                2.561282821352716e-06,
                2.5612834319655406e-06,
                2.561281905293402e-06,
                2.2603248367512505e-06,
                1.1478773592378984e-05,
                1.670142183934597e-05,
                2.561283431986506e-06
            ],
            [
                1.7603430033991435e-06,
                5.144222591859218e-05,
                1.4738988999672284e-05,
                4.5397857812676685e-05,
                4.0063687398634466e-05,
                3.288749065209246e-06,
                5.144221360709674e-05,
                1.1478768124783601e-05,
                5.422219616085833e-06,
                8.939697369004791e-06
            ],
            [
                1.4738987242432592e-05,
                2.260324836651547e-06,
                2.561281294616881e-06,
                8.939697368110433e-06,
                3.5356263289471766e-05,
                6.144175333289463e-06,
                4.785093923916815e-06,
                2.26032402841657e-06,
                2.1444953502863275e-05,
                6.144176066264237e-06
            ],
            [
                1.5534981248881956e-06,
                3.2887482812506295e-06,
                8.93969736942758e-06,
                2.2603240283888175e-06,
                1.67014238321306e-05,
                6.144173869072478e-06,
                6.1441738691562974e-06,
                1.0129989771288745e-05,
                5.422220908876325e-06,
                7.889263526093993e-06
            ],
            [
                6.144173869379821e-06,
                3.2887498492518007e-06,
                3.288748281220719e-06,
                2.260323489490968e-06,
                8.939698434495167e-06,
                4.785094494402695e-06,
                4.7850944943330625e-06,
                2.9023123310580418e-06,
                6.144172404520556e-06,
                6.1441775312976045e-06
            ],
            [
                3.7266397282926013e-06,
                1.892514147143123e-05,
                6.144173136885882e-06,
                1.5534981249496567e-06,
                1.8925150492616083e-05,
                1.5534977545497995e-06,
                4.7850967763512445e-06,
                1.2098652507439992e-06,
                8.939697369004791e-06,
                2.902311639183378e-06
            ],
            [
                3.120192251631124e-05,
                2.260324028404236e-06,
                2.1444948407573453e-05,
                1.4738981969615573e-05,
                4.785094494185095e-06,
                6.144173136645595e-06,
                8.939693106182721e-06,
                3.288750633569722e-06,
                8.93969310367852e-06,
                6.14417606400666e-06
            ],
            [
                0.9999724643056438,
                0.9999930377412629,
                0.9999967112501507,
                0.9996646498506738,
                0.9999977396751636,
                0.999998005270993,
                0.9999994284996211,
                0.9998766054254141,
                0.9999930377462413,
                0.9999724643023473
            ],
            [
                7.889260703619978e-06,
                6.962259569484628e-06,
                4.222834954607099e-06,
                1.1478772225981004e-05,
                1.1478766753082876e-05,
                4.222833947820683e-06,
                4.2228339475595195e-06,
                3.7266388397382506e-06,
                1.0129987355122296e-05,
                1.1478769492392108e-05
            ],
            [
                7.88925976418034e-06,
                1.2098658277181688e-06,
                1.012999218752948e-05,
                6.14417753110761e-06,
                1.0129995809247506e-05,
                1.9947301970287804e-06,
                8.939698435096828e-06,
                1.1478764019996392e-05,
                5.4222170304318e-06,
                1.8925141471913163e-05
            ],
            [
                2.5612812945260317e-06,
                3.288748280837859e-06,
                6.144177531007026e-06,
                3.288750241204353e-06,
                4.22283294098842e-06,
                1.5534973841895917e-06,
                4.22283294007051e-06,
                1.5534981249496567e-06,
                2.561283431888668e-06,
                1.7603425836678333e-06
            ],
            [
                1.300713466420736e-05,
                6.144176798870286e-06,
                8.939694171135975e-06,
                4.222835457852533e-06,
                6.962258738701267e-06,
                7.889263523453522e-06,
                1.6701419850845044e-05,
                3.7266406165827946e-06,
                1.670142183983204e-05,
                8.939697367264857e-06
            ],
            [
                6.962254588281262e-06,
                6.144176799099397e-06,
                1.1478768124783601e-05,
                6.144177531381426e-06,
                1.3007130013572209e-05,
                1.670141785651155e-05,
                1.1478769492141554e-05,
                6.962255419380732e-06,
                7.88925976359915e-06,
                1.6701417859519093e-05
            ],
            [
                3.535623803273096e-05,
                5.422220908876325e-06,
                1.6701423830702777e-05,
                1.0129993393742954e-05,
                1.1478765386894505e-05,
                4.539786316895279e-05,
                3.2887482811579057e-06,
                1.8925145982350146e-05,
                4.7850933535006355e-06,
                1.3007134665674251e-05
            ],
            [
                2.430024072471526e-05,
                4.785096776068365e-06,
                7.889262575797963e-06,
                2.2603251060738913e-06,
                1.3007131564643372e-05,
                1.8925150491445666e-05,
                1.300713001414004e-05,
                5.422218969029887e-06,
                1.3007133114318805e-05,
                4.785093352813021e-06
            ],
            [
                1.4738981968864903e-05,
                8.93969417214416e-06,
                1.4738976700366126e-05,
                6.962259568648793e-06,
                1.89251527491092e-05,
                1.5534983100228109e-06,
                2.753570093009022e-05,
                1.1478773597640625e-05,
                2.2603242976404388e-06,
                1.0129995809044816e-05
            ],
            [
                0.9999921107345958,
                0.999991060303697,
                0.9999945777803857,
                0.9999930377437505,
                0.9999980052695652,
                0.9999910602994336,
                0.9999980052698044,
                0.9999869928746405,
                0.9999251537551883,
                0.9999921107336559
            ],
            [
                1.370957533676711e-06,
                7.889263525663481e-06,
                1.4738988992031526e-05,
                8.939693106873817e-06,
                7.889261644760245e-06,
                8.939696302457574e-06,
                2.9023116389365734e-06,
                6.9622579092224155e-06,
                1.892515274614874e-05,
                2.144494328864643e-05
            ],
            [
                2.144494329348333e-05,
                6.144173869502757e-06,
                1.3007133114886634e-05,
                1.6701423827421826e-05,
                2.144494074076854e-05,
                6.9622537593854575e-06,
                2.144495351940237e-05,
                6.9622537593854575e-06,
                1.9947297214544894e-06,
                8.939700565996655e-06
            ],
            [
                3.726638395493353e-06,
                6.144176065828368e-06,
                1.2098655392662613e-06,
                1.4738976690741464e-05,
                5.422220908762902e-06,
                6.962257079376403e-06,
                8.939695238089467e-06,
                4.222832941111319e-06,
                5.422220262264056e-06,
                6.9622595694023114e-06
            ],
            [
                4.785096205260165e-06,
                7.889263525534328e-06,
                1.892514147046736e-05,
                7.889266347248781e-06,
                1.3007130013288297e-05,
                1.300712691308661e-05,
                3.535625070624499e-05,
                8.939696303010449e-06,
                2.4300249419722622e-05,
                8.9396941718352e-06
            ],
            [
                0.9999724643023497,
                0.9999852610233104,
                0.9999930377420924,
                0.9999938558275956,
                0.9999938558239376,
                0.999769493314775,
                0.9999756997564082,
                0.9998601778716985,
                0.9997388096772565,
                0.9999945777816773
            ],
            [
                1.8925148238291944e-05,
                3.1201900204769344e-05,
                2.4300243626409964e-05,
                2.144494329769612e-05,
                2.1444950969026795e-05,
                2.4300249418927004e-05,
                4.222832940834793e-06,
                2.1444945855248125e-05,
                3.120190392409636e-05,
                4.5397884856980825e-05
            ],
            [
                3.7266401724291984e-06,
                6.9622537593854575e-06,
                3.726638839656906e-06,
                3.2887490653109436e-06,
                2.5612812947240366e-06,
                1.0129993394664264e-05,
                4.785096205582214e-06,
                1.0129993394811673e-05,
                8.93969736427282e-06,
                1.3709568799679844e-06
            ],
            [
                6.9622587393661365e-06,
                1.3007134664822509e-05,
                8.93969417199781e-06,
                3.5356254907513187e-05,
                1.892515049199645e-05,
                2.7535704227537108e-05,
                2.1444956071728615e-05,
                3.535623803067304e-05,
                2.753569109034197e-05,
                1.892515048449202e-05
            ],
            [
                2.4300232034838305e-05,
                8.939694170518055e-06,
                6.144173869240119e-06,
                6.962256249327861e-06,
                3.1201903929204235e-05,
                1.012999218340202e-05,
                2.1444950968441685e-05,
                4.5397890268254766e-05,
                7.48462091951041e-05,
                6.144172403827636e-06
            ],
            [
                5.422221554847581e-06,
                1.8925143711847272e-05,
                1.6701415868193372e-05,
                1.670142581883963e-05,
                4.2228324370327694e-06,
                5.715006513999389e-07,
                1.4738983726908257e-05,
                2.1444956079218013e-05,
                3.535623800597785e-05,
                5.829128633941282e-05
            ],
            [
                1.892515725665725e-05,
                7.88926164518358e-06,
                1.8925145979561802e-05,
                6.144175333926503e-06,
                6.605217603296344e-05,
                3.5356237968677856e-05,
                7.889259763469998e-06,
                4.785096205717126e-06,
                1.3007133108474901e-05,
                6.144174601410037e-06
            ],
            [
                4.222832941072913e-06,
                6.144173136243255e-06,
                5.422218323290717e-06,
                2.9023112931213857e-06,
                2.9023112930949896e-06,
                1.760344052650207e-06,
                6.1441760654483806e-06,
                1.0129994601688632e-05,
                7.889259761905808e-06,
                7.889263525893087e-06
            ],
            [
                7.88926258532661e-06,
                4.539787944306515e-05,
                2.902311639126627e-06,
                3.726639728224814e-06,
                4.7850967763512445e-06,
                4.78509563546605e-06,
                3.2887490653109436e-06,
                5.422217030288788e-06,
                2.4300252313020203e-05,
                1.0129992186202796e-05
            ],
            [
                0.9999938558246665,
                0.9999970976880248,
                0.9999852610215458,
                0.999992110735535,
                0.9999339478796193,
                0.9999885212264037,
                0.9999832985821483,
                0.9999938558265,
                0.2942149721629888,
                0.9999832985821424
            ],
            [
                6.962255419279419e-06,
                1.6701423833436905e-05,
                4.222834953804408e-06,
                6.962254588116627e-06,
                6.144172403592939e-06,
                6.144173136645595e-06,
                7.338210678941723e-07,
                7.889259763010786e-06,
                7.88926258417858e-06,
                7.8892654060075e-06
            ],
            [
                4.785096205973894e-06,
                4.222833444467892e-06,
                6.962256249517824e-06,
                4.222835458002318e-06,
                8.939698434657777e-06,
                5.422217030614265e-06,
                7.889260704308795e-06,
                4.785096205882502e-06,
                1.3007131565376817e-05,
                1.4738981971250963e-05
            ],
            [
                8.939699500896292e-06,
                3.288749065167371e-06,
                7.889262585211807e-06,
                3.5356250681935664e-05,
                1.0129988562164371e-05,
                8.939699500636112e-06,
                7.338211554725124e-07,
                1.7603438428188364e-06,
                1.0129988562901417e-05,
                1.300712846361323e-05
            ],
            [
                6.144173868983067e-06,
                6.96225707894582e-06,
                1.6701419852090592e-05,
                4.222834954687752e-06,
                1.892515274194901e-05,
                4.78509563535725e-06,
                8.93969950000193e-06,
                1.3709570432052998e-06,
                3.7266388397382506e-06,
                4.785093353274332e-06
            ],
            [
                8.939695237813028e-06,
                7.338209805200689e-07,
                7.889265407004852e-06,
                7.889262584508638e-06,
                6.144177531208195e-06,
                8.9397005654763e-06,
                1.7603425837606927e-06,
                6.962254589528684e-06,
                1.994729721436347e-06,
                1.8925145980181433e-05
            ],
            [
                0.37754066879814546,
                0.999985261021549,
                0.9999756997595121,
                0.9986749773233691,
                0.9999910603047638,
                0.37754066879814546,
                0.9999945777823259,
                0.9999599363030631,
                0.9999938558232024,
                0.9999885212305103
            ],
            [
                8.939696300376156e-06,
                1.6701421841259862e-05,
                8.939696302831578e-06,
                2.1444945853375776e-05,
                1.0129992186774007e-05,
                7.889259761030436e-06,
                3.2887506333812835e-06,
                8.939699498814873e-06,
                1.0677031245312763e-06,
                6.144174601410037e-06
            ],
            [
                0.6513548782017745,
                0.9999810748562817,
                0.999664649920444,
                0.9999251537462939,
                0.9994472212687887,
                0.8354835411997897,
                0.40733340004593027,
                0.9999646437368962,
                0.999796572931628,
                0.9996200155718846
            ],
            [
                2.5612822106654943e-06,
                6.962257079465052e-06,
                1.2098662604247682e-06,
                6.144176798870286e-06,
                2.902313023039776e-06,
                7.889266347636241e-06,
                3.726638395493353e-06,
                3.288748673265808e-06,
                2.2603251062147097e-06,
                4.785094494402695e-06
            ],
            [
                0.9999810748585343,
                0.9999646437619778,
                0.9996200155165111,
                0.9999687980960674,
                0.9999832985761751,
                0.5312093733737563,
                0.9999599363173673,
                0.9999930377439556,
                0.9999646437619467,
                0.9999756997534859
            ],
            [
                0.9999910603015654,
                0.9999962733589396,
                0.9999970976869776,
                0.9999910602994433,
                0.9999974387180947,
                0.9999930377404416,
                0.999998932297512,
                0.9999989322966208,
                0.999981074851795,
                0.9999986290429568
            ],
            [
                1.0677029973056687e-06,
                1.7603436329554703e-06,
                2.9023123310580418e-06,
                1.9947301970287804e-06,
                2.2603253755476615e-06,
                1.3007123808153756e-05,
                2.5612816000145246e-06,
                1.0129990979381404e-05,
                3.5356242236570075e-05,
                1.1478768122987964e-05
            ],
            [
                1.3007133115903994e-05,
                4.785094494628999e-06,
                2.260325375615501e-06,
                1.670142183983204e-05,
                1.147876812538911e-05,
                1.4738985478678359e-05,
                1.670142183825232e-05,
                2.4300237832303074e-05,
                2.1444943284979742e-05,
                6.962253759271479e-06
            ],
            [
                8.939695236593446e-06,
                1.2098653950606901e-06,
                1.7603440526662173e-06,
                1.9947290081286418e-06,
                4.222834954607099e-06,
                6.144176799099397e-06,
                2.9023109471452223e-06,
                5.422218322940583e-06,
                3.2887486733420804e-06,
                4.2228334445370225e-06
            ],
            [
                5.422220908703723e-06,
                1.0129988563914856e-05,
                6.144176066795103e-06,
                1.0129988564578197e-05,
                3.726641061058432e-06,
                1.1478773598099973e-05,
                6.1441767987808774e-06,
                8.939696304002375e-06,
                1.4738983727900215e-05,
                6.475951069561228e-07
            ],
            [
                1.370957860466977e-06,
                1.9947299588742466e-06,
                5.422217029844958e-06,
                1.0129988563730593e-05,
                6.144174601309452e-06,
                3.2887478892504536e-06,
                8.93969950000193e-06,
                1.300713466316634e-05,
                1.012998856312253e-05,
                6.1441746018123775e-06
            ],
            [
                1.7603425837366772e-06,
                5.1442219536690144e-05,
                1.1478764019328247e-05,
                6.962259568775433e-06,
                8.93969630317306e-06,
                1.1478770858372173e-05,
                8.939697369671496e-06,
                7.889261644358435e-06,
                4.785096205717126e-06,
                5.422218969661113e-06
            ],
            [
                1.7603432132912532e-06,
                7.889262585082652e-06,
                7.88926258532661e-06,
                1.1478772229050293e-05,
                8.93969630348202e-06,
                1.0129988561372045e-05,
                4.785095065093186e-06,
                6.144172404218801e-06,
                7.338208055229508e-07,
                5.422219616026655e-06
            ],
            [
                2.144495607640949e-05,
                1.4738985483879434e-05,
                9.422447062030659e-07,
                1.8925150493166868e-05,
                3.5356259128846735e-05,
                1.670141786036971e-05,
                3.5356238040705445e-05,
                1.0129992186774007e-05,
                2.753570422573402e-05,
                1.4738978454950406e-05
            ],
            [
                1.670142182342727e-05,
                6.9622595694023114e-06,
                2.753568448703733e-05,
                6.962258739530771e-06,
                3.2887502415243994e-06,
                2.5612828212676906e-06,
                8.939696304116203e-06,
                3.72664061681327e-06,
                5.422218969769604e-06,
                1.3007133115667397e-05
            ],
            [
                1.6701425824307884e-05,
                1.3007125363057018e-05,
                2.4300246525276163e-05,
                6.962255419804982e-06,
                7.889262582800945e-06,
                1.3007128462477575e-05,
                1.3007130014376633e-05,
                7.889262584508638e-06,
                1.4738978456719842e-05,
                1.892515725920463e-05
            ],
            [
                0.999997438716568,
                0.9999832985702,
                0.9999687980812608,
                0.9999852610163064,
                0.9999987901344656,
                0.9999646437450908,
                0.999964643732436,
                0.9999869928668892,
                0.9999785550414007,
                0.9999977396759717
            ],
            [
                6.962258738701267e-06,
                3.7266397283231055e-06,
                3.2887490653109436e-06,
                1.5534984953199313e-06,
                5.422218969029887e-06,
                7.338207180714596e-07,
                4.222831934156396e-06,
                3.7266397280960194e-06,
                2.5612831266608576e-06,
                1.5534973841450852e-06
            ],
            [
                1.8925155003330605e-05,
                1.1478768124324254e-05,
                7.484620048414485e-05,
                6.1441724044534996e-06,
                2.4300234907624647e-05,
                7.889266345584138e-06,
                5.1442201272586515e-05,
                1.0129989770662257e-05,
                2.56128159959988e-06,
                1.3007126906509262e-05
            ],
            [
                0.817574471748733,
                0.9995121428267525,
                0.9991959139643376,
                0.9997388095983036,
                0.9999038976086108,
                0.9999485577989097,
                0.9999251537921603,
                0.9994472214680407,
                0.9999646437412266,
                0.9999038975863729
            ],
            [
                4.785093353274332e-06,
                5.4222215552470286e-06,
                5.04347588554027e-07,
                7.338209804920378e-07,
                3.726639727994339e-06,
                2.9023112931873767e-06,
                8.93969310647542e-06,
                5.422217676979575e-06,
                6.475947981904966e-07,
                5.422218323290717e-06
            ],
            [
                0.08509904094645106,
                0.999738809629067,
                0.9990889488147122,
                0.07585817479810983,
                0.10669059252545564,
                0.9998766054111066,
                0.9988304895796443,
                0.9975273767761746,
                0.9988304897344005,
                0.9968273174130297
            ],
            [
                0.9999724643122239,
                0.9999910603015817,
                0.9999546021476443,
                0.9999921107364758,
                0.9999869928669071,
                0.9999599363078321,
                0.9999599362982833,
                0.9999986290423029,
                0.9999810748585398,
                0.999876605366419
            ],
            [
                5.422217676575195e-06,
                2.7535704220525098e-05,
                2.7535691096552598e-05,
                1.670142383167491e-05,
                1.67014178554179e-05,
                3.7266410609940346e-06,
                4.785093353352668e-06,
                2.4300240730549767e-05,
                5.829126548725762e-05,
                4.539787945313924e-05
            ],
            [
                6.144173136243255e-06,
                1.4738976695459959e-05,
                3.2887506330851655e-06,
                2.2603245672497918e-06,
                8.9396941718352e-06,
                1.067702487932422e-06,
                6.144175333635923e-06,
                1.9947299590520376e-06,
                6.962257079376403e-06,
                3.726639283901856e-06
            ],
            [
                8.31528325021115e-07,
                4.785093923916815e-06,
                1.9947297214182054e-06,
                1.147876675162131e-05,
                9.422445938728576e-07,
                2.5612831265630198e-06,
                7.338207180661203e-07,
                7.338209804987119e-07,
                5.422218323093458e-06,
                5.422219615395428e-06
            ],
            [
                2.9023130230133794e-06,
                1.3007133107008012e-05,
                6.962255418063657e-06,
                2.7535681187990065e-05,
                3.726639283806955e-06,
                5.422219614705025e-06,
                1.3007133109421283e-05,
                2.7535704181959054e-05,
                8.939695237504067e-06,
                4.222833444383398e-06
            ],
            [
                1.994729959270648e-06,
                7.88925976359915e-06,
                2.902313368860448e-06,
                2.2603251062013478e-06,
                1.7603440527046419e-06,
                5.422218322851817e-06,
                1.4738987234014356e-05,
                1.9947306726358406e-06,
                2.2603248367512505e-06,
                2.902313368897403e-06
            ],
            [
                6.47594875389178e-07,
                1.994729721436347e-06,
                6.14417606659952e-06,
                1.0129987356541108e-05,
                3.2887478892504536e-06,
                6.144175334239434e-06,
                1.3007131565376817e-05,
                1.994729483608425e-06,
                1.3007133114011233e-05,
                5.422221555296344e-06
            ],
            [
                6.962258739454786e-06,
                2.753570094040789e-05,
                6.144173869312763e-06,
                1.1478769492893215e-05,
                8.939694172420599e-06,
                6.9622579096593295e-06,
                1.0129988561077228e-05,
                1.0129987356541108e-05,
                1.670142183934597e-05,
                7.889260703117714e-06
            ],
            [
                4.785096776068365e-06,
                1.012999339449843e-05,
                6.1441760661636525e-06,
                1.147877086073156e-05,
                7.889262582112126e-06,
                1.76034363298589e-06,
                1.1478770859917257e-05,
                4.222833947774596e-06,
                1.9947301970287804e-06,
                3.2887490653872164e-06
            ],
            [
                6.9622595694023114e-06,
                1.89251482372248e-05,
                1.4738983723664288e-05,
                1.1478769493331685e-05,
                1.6701425825492673e-05,
                NaN,
                1.1478769491598686e-05,
                5.422219615750493e-06,
                5.422220908762902e-06,
                1.012999460108057e-05
            ],
            [
                8.93969630317306e-06,
                7.88926164299515e-06,
                2.5612831267086116e-06,
                6.962255419380732e-06,
                1.670142183132586e-05,
                1.0129988562901417e-05,
                1.3007123812554424e-05,
                2.430024362932722e-05,
                2.4300234934056724e-05,
                1.2098662603862553e-06
            ],
            [
                0.999997739675169,
                0.9999898700054091,
                0.9999921107345994,
                0.9999938558246677,
                0.9999974387184023,
                0.9999957771650463,
                0.9999810748427777,
                0.9999885212346412,
                0.9999986290424664,
                0.999996711251327
            ]
        ]
    },
    {
        "q_id": "7976_mmlu_math",
        "cot_ids": [
            0,
            1,
            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,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            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,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9579122722345712,
                0.9999785550465604,
                0.9999687980998835,
                0.9997694932352559,
                0.9992903294591062,
                0.9984988177628068,
                0.9999785550464995,
                0.999972464302517,
                0.9999832985841886,
                0.9999756997679662
            ],
            [
                0.9995694429127508,
                0.9997040428295686,
                0.9998766053811754,
                0.9999885212294153,
                0.9999546021208858,
                0.999860177892614,
                0.9991959139553117,
                0.9997694932869408,
                0.9995694430125411,
                0.9999151889789851
            ],
            [
                0.32082130731838393,
                0.9999251537378503,
                0.8519528076067262,
                0.9994472214580716,
                0.9995121427682832,
                0.9997040428305244,
                0.9999945777830478,
                0.962673116671762,
                0.7981867801399695,
                0.9993736659012061
            ],
            [
                0.9999251537816561,
                0.9997388097841076,
                0.997527376352931,
                0.9991959139485306,
                0.9989677690375521,
                0.9994472214519937,
                0.9995121428213029,
                0.9996646500107031,
                0.9998911030648404,
                0.9993736658212321
            ],
            [
                0.9999417087136911,
                0.8175744850834648,
                0.9999546021433369,
                0.9999485577936039,
                0.999954602142306,
                0.9999724643058386,
                0.9992903297047985,
                0.4378234991142019,
                0.9999724643056662,
                0.9999485577789474
            ],
            [
                3.2887498492936755e-06,
                6.1441731363550164e-06,
                1.473897669838221e-05,
                2.9023116390421582e-06,
                1.0129990979031306e-05,
                1.7603432132912532e-06,
                7.889266347356409e-06,
                4.785093924047376e-06,
                1.0129987357020188e-05,
                8.315284241257637e-07
            ],
            [
                2.1024341622368903e-07,
                3.059021175247079e-07,
                2.699576809107705e-07,
                5.71500583272315e-07,
                2.902312677007974e-06,
                1.5534971989907999e-06,
                3.059023727786437e-07,
                6.47594566597747e-07,
                5.715005832827105e-07,
                1.6373764720990908e-07
            ],
            [
                1.6701421841259862e-05,
                1.670141785809127e-05,
                3.726639728184142e-06,
                6.962257079553702e-06,
                2.9023130230846496e-06,
                1.47389854857293e-05,
                1.3709570433885908e-06,
                8.315282259051341e-07,
                7.889262585082652e-06,
                1.1478765388523107e-05
            ],
            [
                0.9999898700078182,
                0.999985261012766,
                0.9999785550490534,
                0.9998204719483776,
                0.9999599363078551,
                0.9998415638132762,
                0.7310585844894971,
                1.6701415871049018e-05,
                0.9999151889586547,
                0.999959936312614
            ],
            [
                1.7603427935518875e-06,
                4.785093923916815e-06,
                4.785096776303374e-06,
                2.2603237589542675e-06,
                4.7850927830148924e-06,
                6.144172404218801e-06,
                3.726641061058432e-06,
                6.962255419380732e-06,
                3.2887498491620677e-06,
                5.71500378896509e-07
            ],
            [
                4.222834954561012e-06,
                8.939693106020111e-06,
                3.2887478891487563e-06,
                7.889266347456862e-06,
                1.3709572067356507e-06,
                1.4738978456398127e-05,
                1.1478769493916314e-05,
                4.7850956351657615e-06,
                5.422217676979575e-06,
                1.6701419852819694e-05
            ],
            [
                0.9989677691805238,
                0.9964063980380146,
                0.9999646437619328,
                0.9999546021476009,
                0.9997965729781035,
                0.9989677691747617,
                0.9999339478553472,
                0.9998911031167418,
                0.9997694932028607,
                0.9999832985741761
            ],
            [
                8.315282258680767e-07,
                2.9023109471689794e-06,
                5.422221555192784e-06,
                2.260323758882316e-06,
                6.962256249682458e-06,
                5.422218323290717e-06,
                7.889259764359722e-06,
                6.144177531381426e-06,
                1.3709573702647743e-06,
                2.5612812947077304e-06
            ],
            [
                1.300712691403299e-05,
                6.96225375863827e-06,
                6.9622595694023114e-06,
                1.9947299591354906e-06,
                2.561283431986506e-06,
                8.939700566289352e-06,
                6.962256248871951e-06,
                1.0129988564578197e-05,
                2.902311639073834e-06,
                5.4222202621161125e-06
            ],
            [
                2.430024362393472e-05,
                1.300712380997554e-05,
                4.785096205778054e-06,
                2.144494585197151e-05,
                1.9947299591826594e-06,
                6.144173136645595e-06,
                5.422221555133606e-06,
                1.994729008105057e-06,
                1.994730434735237e-06,
                5.422220908402905e-06
            ],
            [
                7.889261644057078e-06,
                4.785093924251918e-06,
                8.315284241401329e-07,
                6.144177530146464e-06,
                1.1478764018012839e-05,
                4.785096776394765e-06,
                4.785095635296322e-06,
                2.9023112930949896e-06,
                6.962257079173776e-06,
                1.5534981249496567e-06
            ],
            [
                1.3709576971160984e-06,
                2.260323758923431e-06,
                1.2098656834723998e-06,
                2.2603245672025095e-06,
                6.144172403715875e-06,
                3.7266379512518984e-06,
                2.1444945854624007e-05,
                3.72664061671159e-06,
                3.535625070778844e-05,
                1.6701423834226767e-05
            ],
            [
                5.043474081739295e-07,
                1.209865827698362e-06,
                3.2887494573232236e-06,
                8.315279285251204e-07,
                4.450849988780466e-07,
                9.422443692090534e-07,
                7.338211554641698e-07,
                2.9023112931213857e-06,
                1.994729483608425e-06,
                5.043476486764593e-07
            ],
            [
                1.0129992185760567e-05,
                5.422217676575195e-06,
                4.78509563546605e-06,
                7.889264466344872e-06,
                8.939699500636112e-06,
                2.5612819053166966e-06,
                3.2887486731641103e-06,
                8.939696302831578e-06,
                1.1478773598329648e-05,
                1.760344052693435e-06
            ],
            [
                0.9989677688089893,
                0.9990889489048873,
                0.9998415638409615,
                0.9993736659654403,
                0.9996200154254749,
                0.9999852610127815,
                0.9997965730029439,
                0.4073334000459302,
                0.9997388096004012,
                0.9999724643122271
            ],
            [
                4.222834451065997e-06,
                7.338207180801359e-07,
                3.726639728224814e-06,
                1.8925150494750372e-05,
                7.88925976359915e-06,
                4.222833443891798e-06,
                1.0677026154619133e-06,
                1.0677024881941248e-06,
                1.5534973841592143e-06,
                6.144177531459659e-06
            ],
            [
                0.9999151889889952,
                4.450852111100568e-07,
                0.9995694428599811,
                0.9991959142505943,
                0.6224593312018546,
                0.9997040429712185,
                0.9995694429107091,
                0.9995694429662972,
                0.946596676038055,
                0.9999810748453962
            ],
            [
                0.9999339478789758,
                0.9998911030518618,
                0.9999485577742286,
                0.9999038975621306,
                0.9998766053957648,
                0.9999898700090265,
                0.9999339478317045,
                0.999860177892673,
                0.9046505293168444,
                0.9999921107336531
            ],
            [
                0.9999756997679917,
                0.9999546021317619,
                0.9999885212278448,
                0.9990889489946385,
                0.9996646500102446,
                0.9986749777827418,
                0.9999599363078385,
                0.9998415637646436,
                0.9999151889895141,
                0.9995121429446278
            ],
            [
                0.9999251537550157,
                0.9997694933122868,
                0.999972464315468,
                0.9990889487619954,
                0.9999974387180947,
                0.9997965729302667,
                0.9999251537727469,
                0.999841563745317,
                0.9999687980775371,
                0.999891103129733
            ],
            [
                1.9947304348595095e-06,
                2.561283126502453e-06,
                2.6995790617613663e-07,
                7.338212429367364e-07,
                3.466327863879275e-07,
                1.760342793515064e-06,
                1.7603430033399058e-06,
                1.3709573701812335e-06,
                6.475950297709604e-07,
                6.47594566594213e-07
            ],
            [
                6.962254589705982e-06,
                4.222834954403545e-06,
                4.785093924156175e-06,
                2.260324297853209e-06,
                4.7850967763512445e-06,
                4.450851049890802e-07,
                4.785093353739995e-06,
                1.6701423833011596e-05,
                1.994729959270648e-06,
                1.7603432133136672e-06
            ],
            [
                0.9999687980852325,
                0.9995694429188757,
                0.9999646437450749,
                0.9999938558232024,
                0.932453306514029,
                0.9999646437367428,
                0.9999785550439259,
                0.9999962733611704,
                0.9998415637266933,
                0.9989677688279561
            ],
            [
                0.9999832985761661,
                0.999964643736649,
                0.9999994284993486,
                0.9999962733616045,
                0.9999785550413615,
                0.9999921107355337,
                0.9999646437535129,
                0.9999852610127573,
                0.9999984465024306,
                0.9999992661786695
            ],
            [
                0.7057850154599563,
                0.9999885212346176,
                0.999891103064815,
                0.9996200154247563,
                0.9626731106479246,
                0.9399133451974033,
                0.952574131703022,
                0.46879062662624377,
                0.9998415637076571,
                0.9999910603047849
            ],
            [
                4.450848927621807e-07,
                1.994729483630195e-06,
                2.9023116391477434e-06,
                7.338207180714596e-07,
                2.699578096302362e-07,
                5.043474081831035e-07,
                3.288747889178668e-06,
                3.7266379512518984e-06,
                7.338208055489796e-07,
                2.9023116389365734e-06
            ],
            [
                1.994729483630195e-06,
                5.422221554482653e-06,
                5.422220261849814e-06,
                4.222833444283541e-06,
                0.9999992661788446,
                1.067702997240607e-06,
                7.88926634687567e-06,
                6.47594566560052e-07,
                1.1478765385746131e-05,
                2.2603245672867952e-06
            ],
            [
                3.059021175247079e-07,
                3.726640616670918e-06,
                4.222831933795376e-06,
                3.7266397283231055e-06,
                9.422448185264317e-07,
                2.5612834317908303e-06,
                1.76034300345598e-06,
                1.0677024881887838e-06,
                4.4508521110499674e-07,
                5.715003107655392e-07
            ],
            [
                3.466327450744504e-07,
                4.785094494463623e-06,
                2.5612825159677387e-06,
                7.338207180454308e-07,
                1.0677031245783732e-06,
                3.0590226338490835e-07,
                1.3709578605243332e-06,
                1.3709573702111586e-06,
                3.927862939075802e-07,
                6.962253759157502e-06
            ],
            [
                0.9999599363173831,
                0.9998911031041878,
                0.9999852610215433,
                0.9999687980811937,
                0.9999810748525334,
                0.9999785550413659,
                0.9999832985721836,
                0.9998766054399318,
                0.9999785550541431,
                0.999876605454541
            ],
            [
                3.2887482810801374e-06,
                6.962257909323729e-06,
                1.5534981249164537e-06,
                2.9023119851266288e-06,
                4.222832437324657e-06,
                2.902312330849511e-06,
                3.7266379512857925e-06,
                1.2098655392662613e-06,
                1.2098652508056196e-06,
                5.422217030555087e-06
            ],
            [
                0.999876605454525,
                0.998830489491251,
                0.9999546021205374,
                0.9997694931750665,
                0.9994472212621641,
                0.9706877700966099,
                0.999447221467719,
                0.9995694429187756,
                0.9999151889790031,
                0.9999546021259874
            ],
            [
                0.9999957771660534,
                0.9999687980887747,
                0.999983298570613,
                0.9998766054254681,
                0.7310585727705126,
                0.9770226313026177,
                0.9998911030394917,
                0.9999646437409352,
                0.9998911030519949,
                0.9998766054546381
            ],
            [
                2.5612831265909735e-06,
                3.535626755929635e-05,
                1.473898020838208e-05,
                9.42244930849811e-07,
                1.0677026154055912e-06,
                7.88925976359915e-06,
                2.430023493865361e-05,
                9.42244481511812e-07,
                1.5534971989427613e-06,
                3.120192625073753e-05
            ],
            [
                1.3709572068354007e-06,
                4.785093923847183e-06,
                1.3709572068079696e-06,
                5.422217676486429e-06,
                1.3007130014376633e-05,
                4.2228319341064674e-06,
                0.9999952149060767,
                1.0677024881683915e-06,
                7.88925976397226e-06,
                3.120191880504111e-05
            ],
            [
                0.9999599362982898,
                0.999992110738355,
                0.9998415637267211,
                0.9999646437408634,
                0.9997694932569868,
                0.9997040428650887,
                0.99951214282153,
                0.9994472212583051,
                0.9999151889282987,
                0.9999832985781563
            ],
            [
                5.422220908634683e-06,
                1.994729008105057e-06,
                2.9023112931688987e-06,
                3.288749065125496e-06,
                5.422217676866151e-06,
                1.7603434230312906e-06,
                2.9023112930949896e-06,
                1.5534971989809095e-06,
                5.043474081931949e-07,
                5.422217676925328e-06
            ],
            [
                1.0129992186939844e-05,
                6.144175333635923e-06,
                6.962257079173776e-06,
                1.4738988995409548e-05,
                1.8925148236674017e-05,
                2.902312676941983e-06,
                3.2887502413389517e-06,
                2.753568453191415e-05,
                3.5356246473207964e-05,
                2.4300249420429837e-05
            ],
            [
                5.422221555133606e-06,
                4.222833947932061e-06,
                6.475947981904966e-07,
                3.2887490649221017e-06,
                5.422220908925639e-06,
                6.962257079553702e-06,
                4.785093924047376e-06,
                4.222831934286977e-06,
                1.3709572068354007e-06,
                2.3823685318675746e-07
            ],
            [
                1.3709576970949014e-06,
                7.889264466344872e-06,
                2.260324028306588e-06,
                1.012999580884213e-05,
                6.962257909007124e-06,
                4.785095065045315e-06,
                1.0129988564099116e-05,
                2.561281905100056e-06,
                1.9947292458603553e-06,
                1.1478768123551712e-05
            ],
            [
                3.2887498494282754e-06,
                1.0677029973056687e-06,
                9.422450431912e-07,
                8.315280276399315e-07,
                1.209865539274514e-06,
                8.939693105272102e-06,
                8.31528424146183e-07,
                1.3709567162743315e-06,
                2.2603248367173307e-06,
                2.5612815999679353e-06
            ],
            [
                0.7981867729389246,
                0.9999339478482357,
                0.679178699175393,
                0.9579122677288676,
                0.9999251537997098,
                0.9999724642958001,
                0.5312093733737563,
                0.999972464312714,
                0.9999417087066884,
                0.9999756997680656
            ],
            [
                0.8807970795424088,
                0.9999646437495427,
                0.9579122684798184,
                0.9999989322971332,
                0.9995121427829856,
                0.9999546021367783,
                0.9998204720384944,
                0.9465966758497363,
                0.9999898700115881,
                0.9999687980963183
            ],
            [
                9.422450431800595e-07,
                3.2887498493983645e-06,
                4.78509506499309e-06,
                4.7850956351657615e-06,
                2.2603237589028734e-06,
                7.338212429464139e-07,
                2.430024072285883e-05,
                1.4738980213985297e-05,
                1.2098661161789477e-06,
                4.78509563546605e-06
            ],
            [
                5.422217676575195e-06,
                1.5534971988707037e-06,
                3.2887494573561262e-06,
                5.422220908634683e-06,
                5.422218322457301e-06,
                8.315278293762888e-07,
                6.144176066051891e-06,
                3.288747889178668e-06,
                1.0129988563914856e-05,
                3.2887494572514376e-06
            ],
            [
                0.9999151889486014,
                0.9999251537460276,
                0.8807970811069351,
                0.9579122681794381,
                0.9999687981004931,
                0.9998766054292347,
                0.9999599363180278,
                0.9999417087344724,
                0.9999599363078626,
                0.9998766053815704
            ],
            [
                1.5534977544141614e-06,
                1.7603436329394601e-06,
                2.9023112930949896e-06,
                3.2887502411564953e-06,
                3.7266388396975786e-06,
                1.9947294835630703e-06,
                2.2603234894560207e-06,
                2.7535684529910724e-05,
                3.726640172503764e-06,
                4.785093353352668e-06
            ],
            [
                0.9998204720131736,
                0.9999869928701857,
                0.22270014398423357,
                0.9998766053957325,
                0.9999756997505761,
                0.9995121427669491,
                0.9399133504571636,
                0.9997040430069108,
                0.999704042901401,
                0.9988304897193058
            ],
            [
                1.5534975693488444e-06,
                2.260325375572331e-06,
                1.3709576971061233e-06,
                2.699576809034048e-07,
                3.4663278639044955e-07,
                1.4449805540585765e-07,
                1.370956716519966e-06,
                2.38237023590304e-07,
                1.7603432132624344e-06,
                8.315280276456036e-07
            ],
            [
                2.2603245671202796e-06,
                1.20986611609532e-06,
                1.5534971989696065e-06,
                3.726637951126493e-06,
                8.315284240985381e-07,
                3.2887490642879904e-06,
                6.962259568775433e-06,
                8.315284240236674e-07,
                7.338208054381903e-07,
                4.222835457664342e-06
            ],
            [
                2.561282210562998e-06,
                2.4300249418927004e-05,
                6.475948753847607e-07,
                1.3007125361755747e-05,
                8.315280276505193e-07,
                1.8925141462377723e-05,
                6.144172404380855e-06,
                1.4738980212296288e-05,
                3.7266410605974813e-06,
                6.144173868781898e-06
            ],
            [
                1.0129992186774007e-05,
                1.20986611609532e-06,
                2.2603245671490605e-06,
                1.994729483508644e-06,
                1.1478769493728398e-05,
                3.5356246446326235e-05,
                2.902311985079115e-06,
                1.0129988564578197e-05,
                3.2887494571676872e-06,
                8.939700566435704e-06
            ],
            [
                9.422449308241022e-07,
                2.5612825160096693e-06,
                2.2603251061232293e-06,
                4.222832941072913e-06,
                1.99472924590571e-06,
                0.9999038976080479,
                6.144172403470001e-06,
                2.9023116390421582e-06,
                4.222835458002318e-06,
                4.785096205582214e-06
            ],
            [
                6.96225956921868e-06,
                2.5612815999423112e-06,
                1.370957533676711e-06,
                4.222833444283541e-06,
                3.288750241410738e-06,
                1.0677031245050577e-06,
                6.1441767989541075e-06,
                6.144173869379821e-06,
                4.222833947674739e-06,
                5.422219616026655e-06
            ],
            [
                0.9996200154699372,
                0.867035763237924,
                0.9997965730752333,
                0.9998601778767315,
                0.9998601778594738,
                8.315277302263348e-07,
                0.9999485577687456,
                0.9988304898895648,
                0.7057850340255386,
                0.9980732650075848
            ],
            [
                6.962255419570695e-06,
                1.670142184171555e-05,
                1.1478770860982112e-05,
                7.88925976316864e-06,
                6.475950297942253e-07,
                1.0677031245186523e-06,
                5.422218323231539e-06,
                1.5534979397140412e-06,
                1.012999460251781e-05,
                6.144174601879434e-06
            ],
            [
                5.422221555192784e-06,
                8.939696302457574e-06,
                2.260324297853209e-06,
                8.939698434153684e-06,
                4.22283394786293e-06,
                6.962257909007124e-06,
                6.144176799166453e-06,
                8.93969417214416e-06,
                1.7603425837062577e-06,
                1.0129992186939844e-05
            ],
            [
                6.9622545892184106e-06,
                3.7266397280485686e-06,
                1.9947299590810645e-06,
                2.9023133687786197e-06,
                3.288749065125496e-06,
                1.3709578605455302e-06,
                4.7850956351657615e-06,
                4.222835457906302e-06,
                3.2887486732000038e-06,
                2.2603234894560207e-06
            ],
            [
                1.9947299592933255e-06,
                2.5612815999679353e-06,
                4.222834954607099e-06,
                2.3823682479181176e-07,
                7.889264466639056e-06,
                3.2887482811579057e-06,
                3.726640616748873e-06,
                1.7603432132784448e-06,
                4.7850967763512445e-06,
                1.8925157258585e-05
            ],
            [
                0.9999339478813725,
                0.9999339478647902,
                0.0474258688018665,
                0.999876605425082,
                0.8670357718273068,
                0.9999646437577823,
                0.9999785550515996,
                0.9999756997505969,
                0.9999038975965026,
                0.999993037741267
            ],
            [
                0.9997694932847676,
                0.9999546021178478,
                0.9997965730753162,
                0.9999599362899514,
                0.7549149813536518,
                0.320821300824607,
                0.9999038975395789,
                0.9995121428425618,
                0.9626731161363099,
                0.999891103038808
            ],
            [
                3.7266410608720178e-06,
                1.5534977545497995e-06,
                1.994730434816876e-06,
                3.466327037512053e-07,
                2.5612822106421996e-06,
                3.0590226338838606e-07,
                4.2228334438149845e-06,
                5.043472278280699e-07,
                1.2098653950315304e-06,
                7.338208055229508e-07
            ],
            [
                0.9991959141442943,
                0.9997388096906166,
                0.9999599362982634,
                0.9996646500101373,
                0.9999852610110004,
                0.4378234991142019,
                0.8354835452961425,
                0.9994472212543818,
                0.9999251537638204,
                0.9998766054398994
            ],
            [
                9.422450431912e-07,
                2.902312331125353e-06,
                1.9947290080905435e-06,
                7.338212429167144e-07,
                4.78509563555309e-06,
                2.260323758939877e-06,
                6.144175334172377e-06,
                1.994730434778778e-06,
                6.475951069896949e-07,
                6.475949525834513e-07
            ],
            [
                9.422450431260706e-07,
                2.5612822106841303e-06,
                4.785093923116048e-06,
                2.2603245672867952e-06,
                9.422444814749625e-07,
                1.994729245842213e-06,
                5.422221554758815e-06,
                2.561283431888668e-06,
                9.422448185388577e-07,
                2.9023112930949896e-06
            ],
            [
                0.998830489636488,
                0.9982992776703933,
                0.9975273770483829,
                0.9971990723721589,
                0.43782349911420193,
                0.9996200155230666,
                0.9988304899144509,
                0.9999646437619967,
                0.9890130593427998,
                0.99781728397605
            ],
            [
                0.9890130551328943,
                0.9740426423783543,
                0.9796676449877543,
                0.9975273772620146,
                0.9968273171177516,
                0.9990889486604292,
                0.9465966658688456,
                0.997199072941835,
                0.9998911030518491,
                0.9859363701415957
            ],
            [
                0.9998911030412093,
                0.8519527982093668,
                0.9999885212333021,
                0.8670357512127872,
                0.9999485577871381,
                0.9999417087208381,
                0.9999038975749555,
                0.9996200155176277,
                0.9998204719721652,
                0.9997040428652609
            ],
            [
                3.726640172120768e-06,
                7.338211554531576e-07,
                4.450849458153541e-07,
                7.338207180714596e-07,
                1.5534973841309562e-06,
                7.338211554464836e-07,
                1.994729721482609e-06,
                6.962255419051463e-06,
                3.726638839656906e-06,
                1.300712536203966e-05
            ],
            [
                4.785096205973894e-06,
                2.902313368897403e-06,
                8.939698434966738e-06,
                1.300712846411008e-05,
                2.5612819052072116e-06,
                2.5612815999423112e-06,
                7.889259764079887e-06,
                1.6701425825492673e-05,
                7.338213304243302e-07,
                5.42221767672807e-06
            ],
            [
                5.043472278195839e-07,
                6.1441760667392215e-06,
                1.5534975693792215e-06,
                7.889262584666493e-06,
                3.288749065209246e-06,
                2.2603248367173307e-06,
                1.9947306726049992e-06,
                5.043475885674441e-07,
                3.2887498494551953e-06,
                5.422219615967477e-06
            ],
            [
                1.370957370247318e-06,
                1.5534973841592143e-06,
                2.902311984989368e-06,
                5.422217676575195e-06,
                4.7850933538313875e-06,
                6.962258739454786e-06,
                3.05902226923399e-07,
                1.3007130012341915e-05,
                3.7266392839832006e-06,
                3.726640172503764e-06
            ],
            [
                4.22283394786293e-06,
                4.222831934202483e-06,
                2.9023116390421582e-06,
                2.5612828213352452e-06,
                2.2603248367656408e-06,
                3.9278638755671223e-07,
                9.422450431732037e-07,
                9.42244256915735e-07,
                3.288748673319648e-06,
                1.994729008105057e-06
            ],
            [
                0.99997246431548,
                0.9999957771650598,
                0.9999417087205802,
                0.9999962733607166,
                0.9998601778594107,
                0.999876605395702,
                0.999981074845483,
                0.9999339478239252,
                0.9999417087276151,
                0.9999810748449934
            ],
            [
                3.7266379512112265e-06,
                7.338211554758494e-07,
                3.2887482812506295e-06,
                1.2098655392921197e-06,
                6.47594566594213e-07,
                3.466325797747213e-07,
                5.715002426410745e-07,
                2.5612819053166966e-06,
                3.059021539845349e-07,
                2.5612828212676906e-06
            ],
            [
                0.9525741286736911,
                0.32082129433083023,
                0.9626731098447463,
                0.987568351433603,
                0.9997965730515117,
                0.6224593312018546,
                0.999195913968874,
                0.9999151889788562,
                0.9706877713685591,
                0.9986749776727513
            ],
            [
                0.9999251537552057,
                0.9999898700116274,
                0.9999687980850651,
                0.9999599363082087,
                0.999968798077481,
                0.9999646437619387,
                0.9998415637673845,
                0.9859363749841851,
                0.9986749777052555,
                0.9706877672347239
            ],
            [
                1.5534971989696065e-06,
                3.059023363207381e-07,
                3.927862938991851e-07,
                3.927861066113479e-07,
                6.962256249112569e-06,
                1.2098656834834034e-06,
                3.466326624233938e-07,
                5.715005832762133e-07,
                0.9999992661786696,
                4.785092782779884e-06
            ],
            [
                0.9971990735869474,
                0.9999038975901302,
                0.9992903297006293,
                0.9999898700102311,
                0.9997040428863577,
                0.9999810748480125,
                0.9993736658227624,
                0.9999724642958389,
                0.9989677690411534,
                0.9998204720124919
            ],
            [
                0.9999724643023806,
                0.9994472213803454,
                0.6791786926816161,
                0.9999038975623201,
                0.9995121429654326,
                0.9995694429087928,
                0.999968798092389,
                0.9706877689306563,
                0.9999417087414875,
                0.9996646499755498
            ],
            [
                5.422218969661113e-06,
                6.96225956921868e-06,
                6.962256249606473e-06,
                2.902312677007974e-06,
                1.7603432132784448e-06,
                1.3709573702647743e-06,
                3.288748673319648e-06,
                4.7850950649408664e-06,
                9.422450431732037e-07,
                3.0590211752039556e-07
            ],
            [
                2.9023119850527192e-06,
                6.14417313680765e-06,
                3.7266410607194972e-06,
                3.2887486731641103e-06,
                7.338208930391909e-07,
                1.994729483630195e-06,
                5.715005832762133e-07,
                2.260325375520937e-06,
                1.0677031245623505e-06,
                5.422218323399208e-06
            ],
            [
                6.144172404587612e-06,
                6.962257909121104e-06,
                1.0129993394959082e-05,
                1.5534981249023245e-06,
                2.260325375634003e-06,
                7.338210679816025e-07,
                6.144173136885882e-06,
                2.9023130230133794e-06,
                4.222834451065997e-06,
                4.222834451254188e-06
            ],
            [
                0.9996646498099395,
                0.99994855779862,
                0.9999832985702398,
                0.9046505440982948,
                0.999975699753703,
                0.9999646437408817,
                0.9996200155615594,
                0.9999038976080912,
                0.9999151889390856,
                0.9999417087345535
            ],
            [
                5.043472278255469e-07,
                6.144177531532303e-06,
                1.7603427936183298e-06,
                2.2603251062013478e-06,
                8.315281267649641e-07,
                5.043476486883855e-07,
                3.927862939126708e-07,
                2.5612822106654943e-06,
                1.1478764019996392e-05,
                1.147876675686207e-05
            ],
            [
                2.5612819053586272e-06,
                1.8553919030708836e-07,
                3.7266383954560706e-06,
                2.2603234894560207e-06,
                5.715006514105942e-07,
                8.31528424151477e-07,
                3.7266410608245674e-06,
                2.5612812945260317e-06,
                5.71500583272315e-07,
                6.1441746018123775e-06
            ],
            [
                3.2887482811579057e-06,
                3.726639728262097e-06,
                0.9999151889829971,
                2.561282821352716e-06,
                6.144177531599359e-06,
                3.535625492217596e-05,
                4.22283394786293e-06,
                1.7603425836870455e-06,
                1.3709567165087443e-06,
                2.5612819053166966e-06
            ],
            [
                0.9999251537460276,
                0.4378234991142019,
                0.9984988180151313,
                0.9975273769099816,
                0.9995121429399445,
                0.9968273165058413,
                0.9998911030398118,
                0.999290329542077,
                0.9991959142415684,
                0.9989677691695998
            ],
            [
                7.338208055536515e-07,
                2.699578096373564e-07,
                3.0590215398968196e-07,
                1.3709568799243436e-06,
                6.475948753930064e-07,
                1.6373776432303203e-07,
                9.422445938917108e-07,
                1.8553907971758842e-07,
                1.9947290080343035e-06,
                6.475950297906914e-07
            ],
            [
                0.9999785550517147,
                0.8175744761936437,
                0.9998415637076825,
                0.9997040429034418,
                0.7549149868676283,
                0.9998601779440089,
                0.8807970811069351,
                0.9998204720347854,
                0.9995694429649821,
                0.9999885212306191
            ],
            [
                0.1066905854244781,
                0.9999832985761932,
                0.4687906266262437,
                0.9999485577620361,
                0.9324533112067127,
                0.9999038975851193,
                0.4073334000459302,
                0.9324533149608596,
                0.9968273170205529,
                0.9859363704515216
            ],
            [
                0.9988304897191698,
                0.9998911031191217,
                0.9997694933407449,
                0.9999869928668963,
                0.798186768138228,
                0.7549149868676283,
                0.9999687980923594,
                0.9999251537995338,
                0.9999485577863421,
                0.9997694932025321
            ],
            [
                0.9998415638406548,
                0.9999546021259533,
                0.999195914249846,
                0.8933094003735664,
                0.9999646437324686,
                0.9999339478632779,
                0.9999339478397065,
                0.9997694932303262,
                0.9997694933128299,
                0.9999151889287293
            ],
            [
                9.42244930849811e-07,
                1.5534975693601474e-06,
                6.144173868882483e-06,
                2.260325375650449e-06,
                1.3709576971160984e-06,
                1.2098659719232413e-06,
                1.370957533676711e-06,
                3.2887498494282754e-06,
                4.22283545795623e-06,
                3.9278605979011705e-07
            ],
            [
                0.9999810748562789,
                0.9999417087344962,
                0.9998766054694967,
                0.9998415637269954,
                0.9999832985782341,
                0.9999339478474997,
                0.9999546021151405,
                0.9999930377437575,
                0.9999599363221485,
                0.8175744806385542
            ],
            [
                0.9999646437577411,
                0.9998601779433112,
                0.9999038975621705,
                0.9999885212291876,
                0.9324533121452495,
                0.7057850340255385,
                0.9999785550592614,
                0.6224593241981982,
                0.9999339478352751,
                0.9525741303566527
            ],
            [
                7.338208930355202e-07,
                7.338211554591642e-07,
                2.902312677104321e-06,
                3.927862002582919e-07,
                2.902311293147782e-06,
                3.7266392838544054e-06,
                1.3709567165530083e-06,
                1.2098662603862553e-06,
                9.422445938964242e-07,
                7.338209805040511e-07
            ],
            [
                2.561282210530385e-06,
                3.726638395415398e-06,
                3.726639727994339e-06,
                7.889266347248781e-06,
                1.0129987355564522e-05,
                4.222834451169694e-06,
                1.0129990978847043e-05,
                8.315282258956806e-07,
                1.3007131564903626e-05,
                2.260323758676741e-06
            ],
            [
                0.9999485577804146,
                0.9999417087346539,
                0.999986992874655,
                0.9999546021206108,
                0.9999546021259533,
                0.9999485577741157,
                0.9999810748495079,
                0.9999151889284886,
                0.9999785550439243,
                0.9999251537657828
            ],
            [
                0.94659667246,
                0.9999957771645435,
                0.9986749775237862,
                0.9999724642957707,
                0.6224593312018546,
                0.9999756997534821,
                0.9999910603005039,
                0.9998601779108239,
                0.9999546021313795,
                0.9999485577986391
            ],
            [
                0.9998766054104872,
                0.9999785550492665,
                0.9997694933395409,
                0.999959936298269,
                0.9999599363125902,
                0.9999756997650677,
                0.9994472213869057,
                0.9998766053956859,
                0.9998415638287808,
                0.99962001555905
            ],
            [
                5.04347468309184e-07,
                3.7266401725681614e-06,
                2.9023133689317184e-06,
                1.3007134664822509e-05,
                1.760344052650207e-06,
                2.3823699519035448e-07,
                3.726637951028202e-06,
                2.260325375520937e-06,
                8.939695238333382e-06,
                5.715002426410745e-07
            ],
            [
                0.9999832985841499,
                0.9999251537906008,
                0.9998601778761151,
                0.9996646499339863,
                0.9999417087375297,
                0.9978172831327525,
                0.9999038975965836,
                0.9999485577679945,
                0.9999546021477497,
                0.8354835411997897
            ],
            [
                1.6373766672821107e-07,
                1.7603425837606927e-06,
                1.1253517546838634e-07,
                1.275190428866973e-07,
                3.4663249713741784e-07,
                8.315280276546789e-07,
                2.699578096373564e-07,
                5.043472879481655e-07,
                2.1024331597152624e-07,
                7.338212429504183e-07
            ],
            [
                5.043475284430694e-07,
                5.422220908634683e-06,
                2.902310947190096e-06,
                3.2887498494282754e-06,
                2.902311292920774e-06,
                2.2603248367173307e-06,
                2.699577774579753e-07,
                5.043474682903772e-07,
                1.0677033791437343e-06,
                4.4508510497875774e-07
            ],
            [
                0.9999417087344686,
                0.9999756997476845,
                0.9996200154239604,
                0.9997965729297074,
                0.9998601778758304,
                0.9999756997650652,
                0.9997694931749592,
                0.9990889486523759,
                0.9971990728332324,
                0.9999756997505795
            ],
            [
                0.9525741268224333,
                0.9998415638410236,
                0.999968798081203,
                0.9999038975739906,
                0.9999646437493915,
                0.9998766054549163,
                0.9999417087484839,
                0.9994472214093199,
                0.9999485577864349,
                0.9996646498117641
            ],
            [
                0.9999599363126209,
                0.9999485578048816,
                0.9999339478710649,
                0.9999646437548146,
                0.9999810748540158,
                0.9999869928715361,
                0.9999687980743507,
                0.9999977396754341,
                0.9997040428408489,
                0.9999785550546285
            ],
            [
                3.288750633518874e-06,
                3.288750633518874e-06,
                1.0129992186774007e-05,
                6.475946437928669e-07,
                5.715004470243685e-07,
                2.9023130228444433e-06,
                2.9023112930949896e-06,
                3.92786293909545e-07,
                1.7603432132624344e-06,
                1.8925157262061825e-05
            ],
            [
                1.300712846411008e-05,
                1.2098661161239298e-06,
                8.939699501132077e-06,
                1.147876812538911e-05,
                8.93969310675186e-06,
                1.147876538789672e-05,
                2.9023109469842055e-06,
                3.288748281220719e-06,
                7.889261644875049e-06,
                6.962257079376403e-06
            ],
            [
                4.222835458002318e-06,
                4.222833947198501e-06,
                1.3007130010922344e-05,
                1.3709576971160984e-06,
                0.9999998144609423,
                5.422218323399208e-06,
                6.144176798691468e-06,
                2.144495862967221e-05,
                1.994729483261914e-06,
                8.93969310584124e-06
            ],
            [
                1.994729008105057e-06,
                1.5534971989907999e-06,
                2.2603234894560207e-06,
                7.889266346129453e-06,
                8.939696301384342e-06,
                2.6995768090929735e-07,
                1.9947297213746646e-06,
                1.209866116137134e-06,
                3.288750241473551e-06,
                1.5534973840377051e-06
            ],
            [
                0.99991518895867,
                0.43782349911420193,
                0.9999599363173789,
                0.9993736658219973,
                0.999769493205235,
                0.9999417087415846,
                0.9999339478710932,
                0.8933094032139577,
                0.9999546021264765,
                0.9998766053764643
            ],
            [
                7.889260703619978e-06,
                4.222834954561012e-06,
                3.2887490653872164e-06,
                6.962257079705671e-06,
                1.5534979397592542e-06,
                8.315277302788957e-07,
                1.553498309846199e-06,
                1.0677032518501217e-06,
                1.994730434735237e-06,
                1.3709578604108674e-06
            ],
            [
                0.9998911030518111,
                0.9999646437451318,
                0.9997694932848749,
                0.8933093975331752,
                0.9998204720772462,
                0.9999756997564498,
                0.9997040428660531,
                0.999876605439966,
                0.9999945777811065,
                0.9999910603037392
            ],
            [
                4.4508499887035535e-07,
                1.3709568798607528e-06,
                2.5612819053399912e-06,
                6.144175332115971e-06,
                5.422220908402905e-06,
                3.2887502414436403e-06,
                6.144176798870286e-06,
                4.7850950649408664e-06,
                2.5612819052374947e-06,
                2.5612828213352452e-06
            ],
            [
                0.9999151889385698,
                0.9999785550593011,
                0.9997040427974756,
                0.9999485578047843,
                0.9978172838868014,
                0.9995121428795167,
                0.9999646437409905,
                0.9999756997679626,
                0.9999417087136692,
                0.9997388097217372
            ],
            [
                8.939700566435704e-06,
                1.1478764018827141e-05,
                7.889262585211807e-06,
                2.902311984915459e-06,
                5.422217030288788e-06,
                1.4738987240475486e-05,
                3.7266410609160796e-06,
                1.7603434230537046e-06,
                2.2603251060738913e-06,
                5.422218969029887e-06
            ],
            [
                1.2098656834723998e-06,
                1.7603427936079236e-06,
                8.93969736942758e-06,
                3.72664061671159e-06,
                3.927861534370498e-07,
                2.6995768090757867e-07,
                3.2887490653109436e-06,
                3.726640616670918e-06,
                3.2887478891128633e-06,
                6.475947981813674e-07
            ]
        ]
    },
    {
        "q_id": "8239_mmlu_math",
        "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": [
            [
                0.9999986290424664,
                0.999998790134605,
                0.9999994284994848,
                0.9999987901338839,
                0.9999989322975119,
                0.9999992661791944,
                0.9999977396762412,
                0.9999986290432835,
                0.999999057755743,
                0.9999952149037946
            ],
            [
                0.9999993524053562,
                0.9999984465020603,
                0.9999967112505428,
                0.99999893229713,
                0.9999984465026159,
                0.9999982396569966,
                0.9999990577556308,
                0.9999996072138465,
                0.9999987901341723,
                0.9999980052693275
            ],
            [
                0.9999980052707544,
                0.9999989322967482,
                0.9999984465020604,
                0.9999991684715759,
                0.9999984465026158,
                0.9999987901343165,
                0.9999980052700408,
                0.9999982396567869,
                0.9999974387184001,
                0.9999974387180948
            ],
            [
                0.9999974387171787,
                0.9999989322967482,
                0.9999987901340281,
                0.9999987901338838,
                0.9999974387187054,
                0.9999980052695653,
                0.9999980052702786,
                0.9999986290429567,
                0.9999967112521114,
                0.9999994284994848
            ],
            [
                0.999998790134028,
                0.9999986290429568,
                0.9999980052707543,
                0.9999989322966211,
                0.999997739674894,
                0.9999987901343166,
                0.9999984465018751,
                0.9999991684716751,
                0.9999990577551815,
                0.9999991684720715
            ],
            [
                0.9999990577551815,
                0.9999990577555186,
                0.9999980052698031,
                0.9999991684717742,
                0.9999989322971301,
                0.9999986290426298,
                0.9999974387187056,
                0.9999996072137998,
                0.9999989322967482,
                0.9999989322970028
            ],
            [
                0.999998790134028,
                0.999996273360272,
                0.9999974387174841,
                0.9999984465020603,
                0.99999844650169,
                0.9999986290429567,
                0.9999990577551815,
                0.9999987901344608,
                0.9999989322975118,
                0.9999984465018751
            ],
            [
                0.9999993524054334,
                0.9999980052693275,
                0.999996711251719,
                0.9999952149072171,
                0.999997097687323,
                0.9999995549151072,
                0.9999970976890531,
                0.999999554914895,
                0.999997097689053,
                0.9999977396746245
            ],
            [
                0.9999994956527121,
                0.9999992661788446,
                0.9999987901344609,
                0.9999991684717741,
                0.9999989322971301,
                0.9999987901347492,
                0.9999989322975119,
                0.9999991684717742,
                0.9999990577555186,
                0.9999986290423029
            ],
            [
                0.9999952149032242,
                0.9999991684719723,
                0.9999984465016899,
                0.9999982396559474,
                0.9999977396751634,
                0.9999977396748942,
                0.9999994284995529,
                0.9999970976873231,
                0.99999844650169,
                0.9999989322966208
            ],
            [
                0.9999977396751634,
                0.9999986290432835,
                0.9999980052707543,
                0.9999991684720715,
                0.9999982396559474,
                0.9999990577552937,
                0.9999986290424663,
                0.9999977396762412,
                0.9999993524052019,
                0.999998005270041
            ],
            [
                0.9999980052695653,
                0.9999986290432835,
                0.999997097688707,
                0.9999987901338838,
                0.9999990577556308,
                0.9999974387184001,
                0.9999993524052018,
                0.999997097688361,
                0.9999952149043648,
                0.9999957771655497
            ],
            [
                0.9999982396563671,
                0.9999996072139402,
                0.9999991684719725,
                0.9999987901337396,
                0.9999994284997573,
                0.9999986290426298,
                0.9999990577555185,
                0.999998790134605,
                0.9999987901338839,
                0.9999984465028011
            ],
            [
                0.9999994284992805,
                0.9999974387180949,
                0.9999996940977002,
                0.9999993524054335,
                0.9999990577556308,
                0.9999992661786695,
                0.9999990577551815,
                0.9999993524054335,
                0.9999994956526519,
                0.9999994284995529
            ],
            [
                0.9999987901337398,
                0.9999982396574163,
                0.9999980052709921,
                0.9999980052695653,
                0.9999977396759717,
                0.9999982396561572,
                0.9999980052698031,
                0.9999993524051246,
                0.9999992661787571,
                0.9999982396559474
            ],
            [
                0.9999991684718732,
                0.999997438717484,
                0.9999991684721706,
                0.9999977396754328,
                0.999995777168066,
                0.9999994284994848,
                0.9999977396754328,
                0.9999987901343166,
                0.9999982396559474,
                0.9999984465020603
            ],
            [
                0.9999991684717741,
                0.9999952149043652,
                0.9999980052709919,
                0.9999990577552937,
                0.9999991684718732,
                0.9999986290421394,
                0.99999893229713,
                0.9999990577551815,
                0.9999992661791945,
                0.9999980052698031
            ],
            [
                0.9999990577551815,
                0.9999987901343166,
                0.999998932296621,
                0.9999977396757023,
                0.9999984465020604,
                0.9999990577554062,
                0.9999996072136125,
                0.9999992661786695,
                0.9999989322975118,
                0.9999992661787571
            ],
            [
                0.9999962733593839,
                0.9999989322967481,
                0.9999990577555185,
                0.9999994956527722,
                0.9999992661790195,
                0.9999993524052018,
                0.9999993524050474,
                0.9999980052709919,
                0.9999989322975118,
                0.9999994956524716
            ],
            [
                0.9999977396765106,
                0.9999982396574163,
                0.999997097688361,
                0.9999967112505428,
                0.9999992661788445,
                0.999999057755743,
                0.999997097686977,
                0.99999844650169,
                0.9999991684720715,
                0.9999980052700408
            ],
            [
                0.9999982396572065,
                0.9999957771655492,
                0.9999984465026159,
                0.9999991684718732,
                0.9999994284992804,
                0.9999977396762413,
                0.9999980052707541,
                0.9999990577554062,
                0.9999980052702787,
                0.9999982396559474
            ],
            [
                0.9999986290421395,
                0.9999994284994848,
                0.9999990577554062,
                0.9999992661791944,
                0.9999982396574163,
                0.9999990577555185,
                0.9999977396757024,
                0.9999992661792819,
                0.9999957771675638,
                0.9999982396559474
            ],
            [
                0.9999984465015047,
                0.9999967112509348,
                0.9999724643023546,
                0.999997097687323,
                0.9999957771645424,
                0.9999980052705165,
                0.9999984465024306,
                0.9999982396572065,
                0.9999945777816776,
                0.9999977396748939
            ],
            [
                0.9999957771670596,
                0.9999982396572065,
                0.9999987901344608,
                0.9999989322973845,
                0.9999994284996891,
                0.999997097686631,
                0.999996273362049,
                0.9999982396561572,
                0.9999977396754328,
                0.999998790134028
            ],
            [
                0.999996711251327,
                0.9999980052695653,
                0.9999989322975119,
                0.9999974387187056,
                0.9999989322973847,
                0.9999974387187055,
                0.9999980052709921,
                0.9999974387174841,
                0.999999352404893,
                0.9999970976890532
            ],
            [
                0.9999869928761931,
                0.999959936303167,
                0.9999832985801532,
                0.9999869928715411,
                0.9997694932323182,
                0.999988521235985,
                0.9999756997679742,
                0.9999687980775028,
                0.9997388096006368,
                0.9999251537640834
            ],
            [
                0.9999970976880153,
                0.9999984465020604,
                0.9999990577550691,
                0.999998446502801,
                0.9999987901347492,
                0.9999984465028012,
                0.999997438717484,
                0.999998629042303,
                0.9999982396572065,
                0.9999986290432835
            ],
            [
                0.9999994956525918,
                0.9999986290429567,
                0.9999989322971301,
                0.9999989322975119,
                0.9999987901337397,
                0.999998932296621,
                0.9999980052707543,
                0.9999991684721707,
                0.9999993524051246,
                0.999998239656367
            ],
            [
                0.9999984465020604,
                0.999999168471675,
                0.999998790134028,
                0.99999844650169,
                0.9999986290421395,
                0.9999977396759717,
                0.9999986290432836,
                0.9999957771660528,
                0.9999989322972572,
                0.9999992661788445
            ],
            [
                0.9999984465015048,
                0.9999991684717741,
                0.9999991684719723,
                0.999999266178757,
                0.99999893229713,
                0.9999982396572065,
                0.9999986290429567,
                0.9999984465018751,
                0.9999984465020604,
                0.9999992661791944
            ],
            [
                0.9999986290424663,
                0.9999984465028011,
                0.9999980052698031,
                0.9999980052693276,
                0.9999989322968755,
                0.9999989322968755,
                0.9999982396563671,
                0.9999994956524115,
                0.9999986290424663,
                0.999997097688707
            ],
            [
                0.9999991684719725,
                0.9999980052698032,
                0.9999990577550693,
                0.9999982396567869,
                0.999998005270041,
                0.9999980052693275,
                0.999999168471675,
                0.9999982396567868,
                0.9999980052702787,
                0.999999266178757
            ],
            [
                0.9999977396746247,
                0.9999987901343166,
                0.9999987901337396,
                0.9999967112513273,
                0.9999984465015048,
                0.9999989322973847,
                0.9999977396754329,
                0.9999984465020604,
                0.9999992661790196,
                0.9999990577552939
            ],
            [
                0.9999987901343167,
                0.9999987901337396,
                0.9999987901344608,
                0.9999992661787571,
                0.9999984465020603,
                0.9999996072139402,
                0.999998239656367,
                0.9999986290426297,
                0.9999967112517194,
                0.9999986290427932
            ],
            [
                0.9999990577557432,
                0.9999977396751634,
                0.9999990577554062,
                0.9999990577552939,
                0.9999986290432836,
                0.9999982396574164,
                0.9999987901340281,
                0.9999987901340281,
                0.9999991684721706,
                0.9999990577554061
            ],
            [
                0.9999992661788446,
                0.9999982396567867,
                0.999996273360272,
                0.9999992661791944,
                0.9999991684716749,
                0.9999989322972572,
                0.9999991684721706,
                0.9999987901343166,
                0.999998932296621,
                0.9999987901347491
            ],
            [
                0.9999989322973846,
                0.9999982396567868,
                0.9999987901347492,
                0.9999980052695654,
                0.9999990577551815,
                0.9999994956526519,
                0.9999991684721706,
                0.9999987901343165,
                0.9999994956524114,
                0.999999352404893
            ],
            [
                0.9999990577549569,
                0.9999992661791944,
                0.9999986290421394,
                0.9999987901343167,
                0.9999993524054334,
                0.9999986290423031,
                0.9999996533672549,
                0.9999989322966208,
                0.9999993524053562,
                0.999999266178757
            ],
            [
                0.9999987901346051,
                0.9999974387171788,
                0.9999977396751635,
                0.9999990577552939,
                0.9999984465020604,
                0.9999991684721706,
                0.999998790134028,
                0.9999982396563671,
                0.9999967112493671,
                0.9999993524049702
            ],
            [
                0.9999980052707541,
                0.9999980052695652,
                0.9999987901338839,
                0.9999990577551815,
                0.9999982396572065,
                0.9999987901341724,
                0.9999987901338839,
                0.9999986290427932,
                0.9999962733611607,
                0.9999984465024307
            ],
            [
                0.9999993524052019,
                0.9999994956525917,
                0.9999993524054334,
                0.9999989322972572,
                0.9999990577550691,
                0.9999990577549569,
                0.9999991684718733,
                0.9999995549151072,
                0.9999994956524716,
                0.9999984465020603
            ],
            [
                0.9999986290429567,
                0.9999984465024306,
                0.9999984465026159,
                0.9999984465026158,
                0.9999992661790195,
                0.9999987901338839,
                0.9999992661790195,
                0.9999987901341724,
                0.9999991684718733,
                0.9999974387177893
            ],
            [
                0.9999970976890532,
                0.9999957771680664,
                0.9999986290431202,
                0.9999989322972573,
                0.9999980052702787,
                0.9999967112521115,
                0.9999957771660524,
                0.9999980052698033,
                0.999993855822469,
                0.9999938558232023
            ],
            [
                0.9999989322972573,
                0.9999987901337397,
                0.9999986290426298,
                0.9999980052695653,
                0.9999990577557432,
                0.9999982396559474,
                0.9999991684715759,
                0.9999987901340281,
                0.9999982396567867,
                0.9999984465024306
            ],
            [
                0.9999980052695655,
                0.9999962733593837,
                0.999997097688707,
                0.9999987901346049,
                0.9999991684715758,
                0.9999980052698031,
                0.9999982396569966,
                0.999998629042303,
                0.9999962733607165,
                0.9999967112501509
            ],
            [
                0.9999785550541518,
                0.9999785550490384,
                0.9999967112497589,
                0.99999457778297,
                0.999993037742922,
                0.9999952149072171,
                0.9999938558232017,
                0.9999945777790915,
                0.999978555059262,
                0.9999986290427931
            ],
            [
                0.9999987901338838,
                0.9999991684719723,
                0.999999352404893,
                0.999998629042303,
                0.999996273360272,
                0.999997438717484,
                0.9999996533673375,
                0.9999991684718732,
                0.999999168471675,
                0.9999991684720715
            ],
            [
                0.9999987901343166,
                0.9999986290432835,
                0.9999982396563671,
                0.9999986290421395,
                0.9999996533672549,
                0.9999980052705165,
                0.9999996533673375,
                0.9999987901344608,
                0.9999984465018751,
                0.999997097688707
            ],
            [
                0.9999991684722697,
                0.9999970976887069,
                0.999999057755743,
                0.9999991684717742,
                0.9999991684717742,
                0.9999986290423029,
                0.9999992661787571,
                0.9999990577549569,
                0.9999982396561572,
                0.9999980052705164
            ],
            [
                0.9999977396762413,
                0.9999987901341724,
                0.9999987901337396,
                0.9999991684716749,
                0.9999996072137061,
                0.9999986290431201,
                0.9999992661790195,
                0.9999986290424664,
                0.9999989322970027,
                0.9999990577552939
            ],
            [
                0.9999987901344607,
                0.9999967112509355,
                0.9999984465020605,
                0.9999984465028012,
                0.9999982396561574,
                0.9999980052693275,
                0.9999898700102333,
                0.9999989322972572,
                0.9999986290426299,
                0.9999945777790942
            ],
            [
                0.9999992661790196,
                0.9999987901341724,
                0.999999554914895,
                0.9999995549150011,
                0.999999168471675,
                0.9999993524050474,
                0.9999991684718732,
                0.9999994956524716,
                0.9999993524049702,
                0.9999991684720715
            ],
            [
                0.9999996533672962,
                0.9999986290423029,
                0.9999991684722697,
                0.9999987901338839,
                0.9999990577555185,
                0.9999990577554061,
                0.9999986290431201,
                0.9999991684721706,
                0.9999989322975118,
                0.9999986290421395
            ],
            [
                0.9999990577552939,
                0.9999984465020604,
                0.999998239656367,
                0.9999990577551815,
                0.9999991684716749,
                0.999999057755743,
                0.9999977396751634,
                0.9999987901344607,
                0.9999986290427932,
                0.9999987901340281
            ],
            [
                0.9999990577552937,
                0.9999989322973846,
                0.9999990577554062,
                0.9999989322972572,
                0.9999982396559474,
                0.9999977396748939,
                0.9999980052709919,
                0.9999982396559474,
                0.999999266178757,
                0.9999938558239344
            ],
            [
                0.9999987901344607,
                0.9999995549151072,
                0.9999994284996211,
                0.999998932296621,
                0.9999982396563671,
                0.9999990577551816,
                0.9999980052693275,
                0.999998629042303,
                0.9999989322972572,
                0.9999984465026158
            ],
            [
                0.9999977396765107,
                0.9999986290427932,
                0.999999352405279,
                0.9999994956526519,
                0.9999990577551815,
                0.9999987901341723,
                0.9999987901340281,
                0.9999982396572065,
                0.9999974387174841,
                0.9999990577550691
            ],
            [
                0.9999984465026159,
                0.9999980052709921,
                0.9999970976876695,
                0.9999984465018752,
                0.9999957771675627,
                0.9999984465028012,
                0.9999989322968755,
                0.9999974387171793,
                0.999998446502616,
                0.9999962733620492
            ],
            [
                0.9999987901337396,
                0.9999990577557432,
                0.9999987901341724,
                0.9999989322973846,
                0.9999984465024309,
                0.9999993524052019,
                0.9999986290427932,
                0.9999984465018752,
                0.9999982396565771,
                0.9999986290431201
            ],
            [
                0.9999967112501508,
                0.9999991684719723,
                0.9999986290423029,
                0.9999986290432835,
                0.9999980052709919,
                0.999999266178932,
                0.9999990577555185,
                0.999998629042303,
                0.9999994284994167,
                0.9999986290431201
            ],
            [
                0.9999967112517191,
                0.9999984465026159,
                0.999999057755743,
                0.999998005270992,
                0.9999986290421395,
                0.999998005270041,
                0.9999990577556308,
                0.9999989322975119,
                0.999998239656577,
                0.9999967112501511
            ],
            [
                0.999996273360272,
                0.9999986290427932,
                0.9999994284996891,
                0.9999982396565769,
                0.9999898700102293,
                0.9999970976880151,
                0.9999982396574163,
                0.9999977396746245,
                0.9999980052695653,
                0.9999984465020603
            ],
            [
                0.999997438718095,
                0.9999984465028012,
                0.9999984465015047,
                0.9999990577551815,
                0.999999352404893,
                0.9999992661790195,
                0.9999986290429567,
                0.9999982396561573,
                0.9999989322968754,
                0.9999993524052019
            ],
            [
                0.9999980052698031,
                0.9999977396746245,
                0.9999987901343166,
                0.9999986290424664,
                0.9999989322968755,
                0.9999989322972573,
                0.9999987901337396,
                0.9999977396746246,
                0.9999990577556308,
                0.9999980052695654
            ],
            [
                0.9999982396567868,
                0.9999986290427932,
                0.9999990577555185,
                0.9999984465022455,
                0.9999977396765107,
                0.9999977396748939,
                0.999998005270992,
                0.9999957771660526,
                0.9999989322967481,
                0.9999987901343165
            ],
            [
                0.99999893229713,
                0.9999990577551815,
                0.9999991684721706,
                0.9999987901347491,
                0.999998629042303,
                0.9999977396757024,
                0.9999987901337396,
                0.9999993524053563,
                0.9999993524049703,
                0.9999987901344607
            ],
            [
                0.9999991684715758,
                0.9999970976866313,
                0.9999982396569966,
                0.9999994956523514,
                0.9999984465022456,
                0.9999987901340281,
                0.999999352404893,
                0.9999990577557432,
                0.9999986290424664,
                0.9999993524054334
            ],
            [
                0.9999990577552937,
                0.9999974387184001,
                0.9999982396565769,
                0.9999952149055059,
                0.9999980052709919,
                0.9999987901347492,
                0.999995777166556,
                0.9999982396569966,
                0.9999982396565769,
                0.9999984465024307
            ],
            [
                0.9999991684717741,
                0.9999987901338838,
                0.9999991684716749,
                0.9999974387177895,
                0.9999989322968754,
                0.9999987901338839,
                0.999999554914895,
                0.9999962733611605,
                0.9999991684715759,
                0.9999994284996212
            ],
            [
                0.9999986290424664,
                0.9999980052695654,
                0.9999991684720715,
                0.9999990577550691,
                0.9999962733611607,
                0.9999991684717742,
                0.9999987901344608,
                0.9999984465024306,
                0.9999987901344607,
                0.999999554914895
            ],
            [
                0.99999893229713,
                0.9999986290427934,
                0.9999977396765106,
                0.9999987901340281,
                0.9999995549151073,
                0.9999977396751636,
                0.9999980052707541,
                0.9999991684721706,
                0.9999970976866321,
                0.9999980052702786
            ],
            [
                0.9999992661786696,
                0.9999992661788445,
                0.9999982396569966,
                0.9999982396565769,
                0.9999962733602723,
                0.9999977396751634,
                0.9999986290424664,
                0.9999989322966208,
                0.9999989322972572,
                0.9999989322967482
            ],
            [
                0.9999980052700408,
                0.9999994956524115,
                0.9999984465024306,
                0.9999982396561572,
                0.9999987901343166,
                0.9999980052695652,
                0.9999967112501508,
                0.9999987901340281,
                0.9999991684721706,
                0.9999984465022455
            ],
            [
                0.9999986290421394,
                0.9999982396561572,
                0.9999991684718733,
                0.9999986290431201,
                0.9999990577554062,
                0.9999987901337396,
                0.9999987901337397,
                0.9999990577549569,
                0.9999987901347492,
                0.9999986290424664
            ],
            [
                0.9999970976869772,
                0.9999962733607162,
                0.9999977396751634,
                0.9999987901341723,
                0.9999957771670592,
                0.9999970976869771,
                0.9999962733593835,
                0.9999991684719723,
                0.9999967112517189,
                0.9999992661786695
            ],
            [
                0.9999989322966208,
                0.9999989322972572,
                0.9999992661792819,
                0.9999991684718733,
                0.9999989322967482,
                0.9999991684717741,
                0.999998790134605,
                0.9999982396565769,
                0.9999982396569966,
                0.9999990577552939
            ],
            [
                0.999997097688361,
                0.9999980052707541,
                0.9999977396759716,
                0.9999980052693277,
                0.9997965729551455,
                0.9999885212291404,
                0.9999982396561572,
                0.9999785550490384,
                0.9982992776674284,
                0.9999974387168733
            ],
            [
                0.9999987901337396,
                0.999996273360272,
                0.9999987901341723,
                0.9999982396559474,
                0.999997097686631,
                0.9999984465026158,
                0.9999984465022455,
                0.999997097689053,
                0.9999987901344607,
                0.9999986290421395
            ],
            [
                0.9999989322967482,
                0.9999984465020603,
                0.9999987901344607,
                0.9999980052700409,
                0.9999987901347493,
                0.9999996533672963,
                0.9999984465020603,
                0.9999984465020603,
                0.9999974387165681,
                0.9999986290429567
            ],
            [
                0.9999980052698031,
                0.9999993524051247,
                0.9999977396746245,
                0.9999967112501507,
                0.9999977396759717,
                0.9999977396757023,
                0.999997097686631,
                0.9999994956525318,
                0.9999952149055059,
                0.9999980052693274
            ],
            [
                0.9999970976866311,
                0.9999990577550691,
                0.999998446502801,
                0.999998790134605,
                0.9999982396559474,
                0.9999984465020603,
                0.9999980052700409,
                0.9999984465016899,
                0.9999986290427932,
                0.9999984465026158
            ],
            [
                0.9999974387174844,
                0.9999986290421395,
                0.9999994956525918,
                0.9999989322970028,
                0.9999982396569966,
                0.9999991684722698,
                0.9999967112521111,
                0.9999977396759719,
                0.9999990577550691,
                0.9999930377404321
            ],
            [
                0.9999994956523514,
                0.9999980052705163,
                0.9999982396572065,
                0.9999994956527121,
                0.9999962733616047,
                0.9999974387187054,
                0.9999986290426298,
                0.9999984465018752,
                0.9999945777816779,
                0.9999970976873235
            ],
            [
                0.9999984465015048,
                0.9999994284994168,
                0.9999987901343166,
                0.999999352405279,
                0.9999993524050474,
                0.9999991684721706,
                0.9999991684717741,
                0.9999984465024307,
                0.9999991684717742,
                0.9999987901337396
            ],
            [
                0.9999967112517191,
                0.9999987901341724,
                0.999997097689053,
                0.9999982396561572,
                0.9999987901343165,
                0.9999984465026158,
                0.9999994956524715,
                0.99999893229713,
                0.9999989322968754,
                0.9999982396559474
            ],
            [
                0.9999984465028011,
                0.9999991684722697,
                0.9999980052693275,
                0.9999986290424664,
                0.9999986290432835,
                0.999999352405279,
                0.9999984465022455,
                0.999999266179107,
                0.9999980052695653,
                0.9999987901346049
            ],
            [
                0.9999974387187054,
                0.9999982396561573,
                0.9999987901347493,
                0.9999994284994849,
                0.9999993524052018,
                0.9999991684715758,
                0.999999266179107,
                0.9999984465020603,
                0.9999989322972573,
                0.999999266178757
            ],
            [
                0.9999967112493668,
                0.9999970976883611,
                0.9999989322972573,
                0.9999974387177893,
                0.9999957771655492,
                0.9999986290421395,
                0.9999992661789321,
                0.9999980052702786,
                0.9999980052695652,
                0.9999977396751634
            ],
            [
                0.9999977396754332,
                0.9999994956524715,
                0.9999974387171788,
                0.9999980052702786,
                0.9999986290432835,
                0.9999980052707543,
                0.9999930377437527,
                0.9999995549147889,
                0.9999974387168734,
                0.9999992661790195
            ],
            [
                0.9999984465016899,
                0.9999977396765108,
                0.9999977396762412,
                0.9999990577550693,
                0.999998790134028,
                0.999998239656577,
                0.9999990577557432,
                0.9999990577549569,
                0.9999986290427931,
                0.9999987901337396
            ],
            [
                0.9999967112513269,
                0.9999990577555185,
                0.9999977396757023,
                0.9999982396572065,
                0.9999987901343166,
                0.9999962733607163,
                0.9999987901338839,
                0.9999967112501513,
                0.9999987901344608,
                0.9999989322968754
            ],
            [
                0.9999991684720715,
                0.9999987901344608,
                0.9999984465018752,
                0.9999982396572065,
                0.999998790134028,
                0.9999991684715759,
                0.9999987901337396,
                0.9999987901337396,
                0.9999991684717741,
                0.9999991684715758
            ],
            [
                0.9999974387187058,
                0.9999980052702786,
                0.9999984465015047,
                0.9999967112513269,
                0.9999977396759717,
                0.9999989322970028,
                0.9999980052707542,
                0.999998790134605,
                0.9999987901343166,
                0.9999952149049361
            ],
            [
                0.9999986290426298,
                0.9999994284993485,
                0.9999993524052019,
                0.9999984465018752,
                0.9999992661786696,
                0.9999986290427932,
                0.9999992661792819,
                0.9999989322966208,
                0.9999996940976272,
                0.999998790134028
            ],
            [
                0.9999987901344608,
                0.9999989322967482,
                0.9999987901344608,
                0.9999982396561572,
                0.9999986290429567,
                0.9999990577555185,
                0.9999991684722698,
                0.999999168471675,
                0.9999982396559474,
                0.9999986290431201
            ],
            [
                0.9999993524053562,
                0.9999990577549569,
                0.9999994284996212,
                0.999999266179107,
                0.9999990577557432,
                0.9999982396574163,
                0.9999991684720716,
                0.9999987901338839,
                0.9999987901343165,
                0.9999996940976272
            ],
            [
                0.9999987901338839,
                0.9999974387174843,
                0.9999989322968754,
                0.9999990577557432,
                0.999999814460876,
                0.999997097688707,
                0.9999995549150011,
                0.999999266179107,
                0.999999653367379,
                0.9999989322972572
            ],
            [
                0.999999168471675,
                0.9999994956525318,
                0.9999996072136592,
                0.9999986290421395,
                0.9999992661788446,
                0.999998790134028,
                0.9999987901340281,
                0.9999992661790195,
                0.9999993524052019,
                0.9999980052705166
            ],
            [
                0.9999962733620491,
                0.9999957771680664,
                0.9999986290432835,
                0.9999980052707542,
                0.9999967112501509,
                0.9999990577549568,
                0.9999986290426297,
                0.9999977396746246,
                0.9999987901338839,
                0.9999974387174841
            ],
            [
                0.9999987901337397,
                0.9999982396567868,
                0.9999993524053562,
                0.999998239656367,
                0.9999989322968754,
                0.9999994956527722,
                0.9999996072136592,
                0.9999977396754328,
                0.999998446502801,
                0.9999982396561572
            ],
            [
                0.9999930377404312,
                0.9999967112493667,
                0.999991060302632,
                0.999996711250543,
                0.9999962733611605,
                0.9999930377412617,
                0.9999938558232017,
                0.999996711250935,
                0.9999938558253989,
                0.9999967112501508
            ],
            [
                0.9999987901344607,
                0.9999990577551815,
                0.9999982396574164,
                0.9999980052698032,
                0.999998239656577,
                0.99999844650169,
                0.999999168471675,
                0.9999987901343166,
                0.999999168471576,
                0.9999984465018752
            ],
            [
                0.9999982396559474,
                0.9999986290427932,
                0.9999986290432836,
                0.9999987901343166,
                0.9999982396561572,
                0.9999986290421395,
                0.9999990577550693,
                0.9999990577552939,
                0.9999980052698032,
                0.9999991684722697
            ],
            [
                0.999996711251327,
                0.999997739674894,
                0.9999980052695655,
                0.999999057755743,
                0.999997097688361,
                0.9999987901338838,
                0.9999982396567868,
                0.9999990577550693,
                0.9999991684721706,
                0.9999986290427932
            ],
            [
                0.9999962733593835,
                0.9999967112513268,
                0.9999982396567867,
                0.9999945777784452,
                0.999998239656577,
                0.9999980052700409,
                0.9999986290426298,
                0.9999967112493666,
                0.9999967112513268,
                0.9999980052693275
            ],
            [
                0.9999990577549569,
                0.9999957771675629,
                0.999997739674894,
                0.9999984465026159,
                0.9999980052700408,
                0.9999967112521111,
                0.9999986290432835,
                0.9999982396567868,
                0.9999987901347492,
                0.9999987901344608
            ],
            [
                0.99999844650169,
                0.9999994284994849,
                0.999999266179107,
                0.9999977396751634,
                0.9999991684720715,
                0.9999984465022456,
                0.9999986290427932,
                0.9999984465018751,
                0.999999168471675,
                0.9999994284994848
            ],
            [
                0.9999967112493666,
                0.9999987901338839,
                0.9999993524050474,
                0.9999982396574163,
                0.999997097689053,
                0.999999554914895,
                0.9999974387165682,
                0.9999967112497586,
                0.999994577782324,
                0.9999987901346051
            ],
            [
                0.999999266179107,
                0.9999989322967482,
                0.999998446502801,
                0.9999984465026159,
                0.9999996072139402,
                0.9999987901343165,
                0.9999987901344607,
                0.9999986290421395,
                0.9999993524051246,
                0.9999980052695654
            ],
            [
                0.999998239656577,
                0.999999266178932,
                0.9999990577555185,
                0.9999993524052789,
                0.9999993524050473,
                0.9999992661786696,
                0.9999987901344608,
                0.9999982396559474,
                0.9999993524051246,
                0.9999989322973846
            ],
            [
                0.9999989322972573,
                0.9999980052709919,
                0.9999990577555185,
                0.9999993524050474,
                0.9999986290424664,
                0.9999987901346049,
                0.9999984465024306,
                0.9999957771645429,
                0.9999997897565587,
                0.9999987901347491
            ],
            [
                0.9999992661789321,
                0.9999982396567868,
                0.999998932296621,
                0.9999987901343166,
                0.9999994956525318,
                0.9999982396569966,
                0.9999980052693275,
                0.9999989322966208,
                0.9999980052695652,
                0.9999970976880151
            ],
            [
                0.999998629042303,
                0.9999970976866311,
                0.9999994284993486,
                0.9999990577552937,
                0.9999986290427931,
                0.9999990577554061,
                0.9999992661786696,
                0.9999984465024307,
                0.9999992661790195,
                0.9999987901344608
            ],
            [
                0.9999984465018752,
                0.9999992661788445,
                0.9999991684717741,
                0.9999989322973846,
                0.9999990577550691,
                0.9999991684721706,
                0.99999893229713,
                0.9999986290427932,
                0.9999989322972572,
                0.9999987901341724
            ],
            [
                0.9999970976883614,
                0.9999991684722699,
                0.9999989322967482,
                0.9999991684720715,
                0.9999986290423031,
                0.99999893229713,
                0.9999982396559474,
                0.999998239656367,
                0.9999987901347492,
                0.9999982396559474
            ],
            [
                0.9999989322972572,
                0.9999986290431201,
                0.9999977396751634,
                0.99999862904312,
                0.9999993524050474,
                0.9999974387187054,
                0.9999977396757023,
                0.9999984465026158,
                0.9999989322973846,
                0.9999991684720715
            ],
            [
                0.9999990577552939,
                0.9999991684715759,
                0.9999992661791944,
                0.9999993524052018,
                0.9999980052695653,
                0.9999986290432835,
                0.9999991684720715,
                0.9999987901337396,
                0.9999991684722698,
                0.9999993524054334
            ],
            [
                0.9999930377412621,
                0.9999970976876691,
                0.9999962733616048,
                0.9999974387187054,
                0.9999990577555186,
                0.9999977396762411,
                0.9999980052693275,
                0.9999952149060761,
                0.99999862904312,
                0.9999852610180351
            ],
            [
                0.9999987901346049,
                0.9999982396569966,
                0.9999986290431201,
                0.9999990577555185,
                0.9999982396561575,
                0.9999952149049357,
                0.9999984465016899,
                0.9999986290421397,
                0.9999984465020603,
                0.9999986290424663
            ],
            [
                0.9999993524051246,
                0.999998239656577,
                0.9999980052705164,
                0.999996711250543,
                0.9999992661788445,
                0.999999266179107,
                0.9999984465026159,
                0.9999991684715758,
                0.999999168471675,
                0.9999991684718733
            ],
            [
                0.9999994284994168,
                0.9999982396567869,
                0.9999990577556308,
                0.9999986290429568,
                0.9999991684722698,
                0.9999984465022456,
                0.9999989322970029,
                0.9999984465018751,
                0.9999977396765108,
                0.9999982396572067
            ],
            [
                0.9999994956525318,
                0.9999993524052018,
                0.9999989322975118,
                0.9999982396563671,
                0.9999982396561572,
                0.9999990577555185,
                0.9999967112505428,
                0.9999980052702787,
                0.9999989322972573,
                0.9999990577549568
            ],
            [
                0.9999984465015047,
                0.9999974387171788,
                0.9999962733593835,
                0.9999974387168735,
                0.9999982396561572,
                0.9999974387168734,
                0.9999977396751634,
                0.9999980052705164,
                0.9999984465028011,
                0.9999987901347491
            ],
            [
                0.9999962733611605,
                0.9999980052705164,
                0.9999984465018751,
                0.9999977396762412,
                0.9999982396572065,
                0.9999977396751634,
                0.9999984465026158,
                0.9999986290424664,
                0.9999986290423029,
                0.9999967112505428
            ],
            [
                0.9999989322970028,
                0.999999554915001,
                0.9999987901341723,
                0.999998932296621,
                0.9999986290424664,
                0.9999974387174841,
                0.9999989322975119,
                0.9999993524054335,
                0.9999991684720715,
                0.9999986290427932
            ],
            [
                0.9999986290426298,
                0.9999994284992805,
                0.999997097688707,
                0.9999991684719723,
                0.999998005269803,
                0.9999980052693275,
                0.9999990577550691,
                0.9999991684720715,
                0.9999952149060765,
                0.9999938558224694
            ],
            [
                0.9999980052705164,
                0.9999987901338838,
                0.9999989322973845,
                0.9999998362623138,
                0.9999992661788445,
                0.9999986290421395,
                0.9999984465022456,
                0.9999986290423029,
                0.9999991684719725,
                0.9999977396751634
            ],
            [
                0.9999986290421395,
                0.9999990577557432,
                0.9999993524050473,
                0.9999957771675627,
                0.9999984465024306,
                0.9999989322970027,
                0.9999989322966208,
                0.9999992661792819,
                0.9999993524052018,
                0.9999987901347491
            ]
        ]
    },
    {
        "q_id": "7766_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            6,
            7,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            20,
            22,
            24,
            25,
            26,
            27,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            38,
            40,
            41,
            42,
            43,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            62,
            63,
            64,
            65,
            66,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            79,
            82,
            83,
            85,
            86,
            89,
            90,
            91,
            92,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            104,
            105,
            106,
            108,
            111,
            112,
            113,
            114,
            116,
            117,
            118,
            119,
            120,
            121,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999724642991018,
                0.9999546021121904,
                0.9999251537629317,
                0.9999599363127827,
                0.99996879809267,
                0.9999957771680663,
                0.9988304895096096,
                2.753568124458694e-05,
                6.962258739169842e-06,
                1.8925155001402863e-05
            ],
            [
                0.9999898700048415,
                0.9999546021477672,
                0.9997694932769472,
                0.9999785550465765,
                0.9999251537522327,
                0.999959936298309,
                0.9998415638058303,
                0.9999869928762956,
                0.9999151889398841,
                0.9999785550548669
            ],
            [
                6.962256248871951e-06,
                2.1444958631232504e-05,
                1.3007126909159127e-05,
                1.1478765388711023e-05,
                1.3007125360478133e-05,
                1.1478768124553928e-05,
                1.6701421837705495e-05,
                5.422217029736466e-06,
                1.3007126912258525e-05,
                2.1444940731484803e-05
            ],
            [
                1.0129990979215566e-05,
                6.144172404218801e-06,
                6.962259568648793e-06,
                2.753570422573402e-05,
                1.4738976700661033e-05,
                1.1478765388898939e-05,
                1.7603432133032607e-06,
                8.939700566435704e-06,
                4.78509563555309e-06,
                6.144176799099397e-06
            ],
            [
                2.430024651705481e-05,
                2.7535694322475846e-05,
                6.962257079553702e-06,
                1.6701427815999337e-05,
                4.785093923982095e-06,
                NaN,
                2.1444943291142893e-05,
                1.473898899742027e-05,
                8.939695235487695e-06,
                1.892514823488397e-05
            ],
            [
                0.9999687980960972,
                0.9999546021314331,
                0.7549149923816048,
                0.9999339478717382,
                NaN,
                0.9998601778983449,
                0.9999038975544585,
                0.9999339478658446,
                0.0003353501805866515,
                0.010986941132838454
            ],
            [
                6.144177531532303e-06,
                1.4738987242137685e-05,
                5.422218323093458e-06,
                7.889266347636241e-06,
                1.4738981968864903e-05,
                5.422217677078203e-06,
                2.2603251062270446e-06,
                1.300713466619476e-05,
                6.144176799227922e-06,
                4.785096205882502e-06
            ],
            [
                2.4300246524568948e-05,
                6.1441753337365085e-06,
                1.8925150493717652e-05,
                3.120191137012976e-05,
                4.222835458002318e-06,
                4.2228319341064674e-06,
                1.6701421842961097e-05,
                2.4300246525983375e-05,
                3.120190021339598e-05,
                6.9622595694023114e-06
            ],
            [
                4.4508505192495825e-07,
                6.962259568775433e-06,
                1.2098661161602417e-06,
                2.9023109471188266e-06,
                6.144172404218801e-06,
                4.222833947774596e-06,
                1.5534983100425914e-06,
                5.715003107353922e-07,
                5.715006513900631e-07,
                8.9396941718352e-06
            ],
            [
                7.889261644875049e-06,
                3.2887490652810324e-06,
                7.889261644631091e-06,
                1.3709576971061233e-06,
                1.0129987356706945e-05,
                5.422218323231539e-06,
                4.785096776194573e-06,
                1.473898021151881e-05,
                7.889262584809997e-06,
                1.0129987356375273e-05
            ],
            [
                3.7266401725935817e-06,
                8.939693103158165e-06,
                1.4738983726559732e-05,
                6.962256249606473e-06,
                3.288750241473551e-06,
                4.539787403691212e-05,
                6.144176799227922e-06,
                5.42222090882208e-06,
                6.962253758916883e-06,
                8.315284241257637e-07
            ],
            [
                1.1478768123823146e-05,
                2.1444945850567248e-05,
                3.535626333088765e-05,
                1.1478768124553928e-05,
                5.422220262264056e-06,
                NaN,
                NaN,
                7.889264465699106e-06,
                1.1478768124324254e-05,
                2.2603234894745224e-06
            ],
            [
                0.9999810748472743,
                0.9999546021478132,
                0.9998911031308865,
                0.5621765008857981,
                0.9989677690056205,
                0.999972464299172,
                0.9999885212319221,
                0.9999339478633246,
                0.9999756997650686,
                0.22270013366638422
            ],
            [
                0.679178699175393,
                0.9241418147556224,
                0.999989870008332,
                0.9999930377429291,
                0.9999952149060779,
                NaN,
                0.9999938558268658,
                2.902313022984344e-06,
                NaN,
                NaN
            ],
            [
                1.2098661161861e-06,
                5.422220262333096e-06,
                6.962255419380732e-06,
                4.785096776133645e-06,
                0.9999546021479174,
                2.5612825160271407e-06,
                1.994729721469003e-06,
                1.1478764019996392e-05,
                6.475948753452987e-07,
                3.7266379512518984e-06
            ],
            [
                2.430023783530873e-05,
                4.22283545808297e-06,
                1.1478764019996392e-05,
                4.2228329408924035e-06,
                1.8925153276897985e-05,
                2.4300243621371074e-05,
                2.561281600049467e-06,
                4.785095635413826e-06,
                6.144173136729416e-06,
                1.0129990979547237e-05
            ],
            [
                1.3007125361755747e-05,
                1.7603436329714805e-06,
                1.994729721469003e-06,
                7.889261644982674e-06,
                3.288748673265808e-06,
                8.939699500896292e-06,
                3.7266392839832006e-06,
                1.4738980213341866e-05,
                1.9947294836483373e-06,
                2.2603251061664e-06
            ],
            [
                1.892515726099468e-05,
                2.1444945856964448e-05,
                4.785094494672519e-06,
                5.422219616140078e-06,
                4.222832941142044e-06,
                8.93970056668775e-06,
                3.7266406168403854e-06,
                4.22283294025486e-06,
                3.2887498493983645e-06,
                1.473898724181597e-05
            ],
            [
                2.4300232040584407e-05,
                1.3709567164962755e-06,
                2.561282821239737e-06,
                1.1478770860982112e-05,
                4.785094494628999e-06,
                1.0129995809597604e-05,
                1.8925155002710973e-05,
                2.90231233114251e-06,
                1.0129990979381404e-05,
                9.422443692446175e-07
            ],
            [
                1.3007131564643372e-05,
                1.0129992186939844e-05,
                3.535626333461766e-05,
                1.3007123812767362e-05,
                2.1444956082767684e-05,
                1.8925152752138513e-05,
                1.0129994600638342e-05,
                3.535625489632318e-05,
                6.144175334418252e-06,
                1.4738987242968784e-05
            ],
            [
                NaN,
                0.9999251537372568,
                0.5926665999540698,
                0.9999852610240785,
                NaN,
                0.9999485577653134,
                NaN,
                0.9999945777811582,
                NaN,
                0.9999756997548592
            ],
            [
                7.889261645269683e-06,
                6.144173136729416e-06,
                0.9999251537467786,
                1.3007126912258525e-05,
                1.1478768124553928e-05,
                1.4738983727578497e-05,
                2.4300243628620005e-05,
                2.144495352474637e-05,
                1.3007126911643378e-05,
                6.144172404028807e-06
            ],
            [
                1.3007133114011233e-05,
                1.9947306726358406e-06,
                2.1444958627097733e-05,
                1.4738976698006875e-05,
                3.2887486731252264e-06,
                6.962254587420098e-06,
                8.939693105467234e-06,
                4.222834450743383e-06,
                1.0129990979215566e-05,
                7.88925976359915e-06
            ],
            [
                1.670141586907437e-05,
                1.300713001414004e-05,
                1.147877086073156e-05,
                4.006368261266023e-05,
                1.0129994600159262e-05,
                8.939698434657777e-06,
                2.7535681228559507e-05,
                4.539787945561647e-05,
                6.605216813542297e-05,
                1.6701421840318107e-05
            ],
            [
                NaN,
                4.0063696951637786e-05,
                3.726639283440905e-06,
                2.7535700933696396e-05,
                1.9947306723419413e-06,
                2.144495096457996e-05,
                1.4738978452886064e-05,
                4.006371123640331e-05,
                2.1444945850567248e-05,
                3.53562506982705e-05
            ],
            [
                4.006370650464339e-05,
                0.00010889696099789775,
                3.1201903930339314e-05,
                1.8925157261545463e-05,
                7.889261644631091e-06,
                5.144219525129858e-05,
                8.939695238211425e-06,
                1.1478769493331685e-05,
                1.6701429807630274e-05,
                1.1478765386330758e-05
            ],
            [
                2.4300249416363357e-05,
                2.7535694353228506e-05,
                NaN,
                1.3007130012341915e-05,
                5.829129328744691e-05,
                7.889260704050487e-06,
                4.006371126117997e-05,
                3.1201903906162046e-05,
                1.6701417850314193e-05,
                2.753569764115831e-05
            ],
            [
                4.222831934286977e-06,
                6.1441738691562974e-06,
                5.422218969463855e-06,
                2.56128282131428e-06,
                8.939695238333382e-06,
                1.6701421840804172e-05,
                1.7603438428564603e-06,
                2.7535681238877168e-05,
                2.902313023063532e-06,
                6.144173869446876e-06
            ],
            [
                0.9995694428585532,
                6.14417606659952e-06,
                0.8670357598021707,
                0.43782349911420193,
                0.32082130731838393,
                0.9999938558275973,
                0.9999687980886817,
                0.8933094138654242,
                0.34864513533394575,
                0.9999724643191686
            ],
            [
                1.3007125360146898e-05,
                2.7535684525803696e-05,
                1.473898197063434e-05,
                1.0129987355343409e-05,
                1.4738978456398127e-05,
                3.12019002122609e-05,
                3.535624227734284e-05,
                2.75356976629957e-05,
                1.3007123811513407e-05,
                1.0129988563343644e-05
            ],
            [
                4.5397879448184774e-05,
                1.4738978451920916e-05,
                3.535624222962456e-05,
                1.8925148238291944e-05,
                3.5356242258821454e-05,
                1.1478773595343877e-05,
                0.0001233945598437389,
                7.889263524257144e-06,
                7.889265406567165e-06,
                4.006370168019018e-05
            ],
            [
                3.288750633518874e-06,
                8.93969523678858e-06,
                1.0129993393540266e-05,
                6.144172404302622e-06,
                1.1478765386894505e-05,
                1.1478766755734576e-05,
                7.889262585211807e-06,
                1.0129990979547237e-05,
                1.3709568771338344e-06,
                5.422219615898437e-06
            ],
            [
                2.9023116391477434e-06,
                3.5356259031352186e-05,
                1.4738985483879434e-05,
                1.0129992186589747e-05,
                4.2228349546493465e-06,
                1.6701419850845044e-05,
                3.1201900209877224e-05,
                7.889263525893087e-06,
                1.8925145983348442e-05,
                1.4738987241494252e-05
            ],
            [
                2.7535684526905577e-05,
                0.651354857898194,
                0.320821300824607,
                0.9999962733590242,
                0.9999546021233809,
                0.9999869928746594,
                0.9241418163225626,
                0.3208212878370535,
                0.5,
                0.9999810748521629
            ],
            [
                0.9999756997565895,
                0.999948557768631,
                0.9999599362892745,
                0.9999724643024414,
                0.9999785550491432,
                0.999997097686985,
                0.9999785550518812,
                0.9999962733616065,
                0.9999832985822779,
                0.010986944553386703
            ],
            [
                1.473897845457507e-05,
                1.8925150489517924e-05,
                1.3007134663521234e-05,
                2.144495863614743e-05,
                1.6701429791650804e-05,
                6.962257908487893e-06,
                1.4738983723664288e-05,
                3.12019149849169e-05,
                1.147876673742324e-05,
                1.670142380269315e-05
            ],
            [
                0.9999646437639808,
                0.9999546021321821,
                0.14804719803168948,
                0.999664649890608,
                0.9999962733611967,
                0.2018132174596823,
                0.24508501864634824,
                0.798186787341014,
                0.9999852610180272,
                0.9999599362890426
            ],
            [
                1.3007133115667397e-05,
                1.0129993394664264e-05,
                4.78509563535725e-06,
                1.4738978453315019e-05,
                1.370957370236096e-06,
                3.288748281295496e-06,
                1.0129994601872894e-05,
                3.7266379512857925e-06,
                1.4738978457336465e-05,
                2.260325375650449e-06
            ],
            [
                1.5534983101061718e-06,
                4.7850944943330625e-06,
                4.22283545795623e-06,
                3.7266401724291984e-06,
                1.8925157240615665e-05,
                2.9023116391477434e-06,
                3.2887498491620677e-06,
                6.144174601410037e-06,
                2.4300246514137558e-05,
                0.11920291419948609
            ],
            [
                1.670142980380249e-05,
                3.2887506328937356e-06,
                2.14449432697669e-05,
                2.144495607640949e-05,
                2.753569437686898e-05,
                0.00020342701747182827,
                5.8291293278964903e-05,
                8.481102104878554e-05,
                3.120192621089609e-05,
                2.753568451618723e-05
            ],
            [
                0.000158436178074846,
                4.006368737677271e-05,
                1.300713466420736e-05,
                4.006369692044835e-05,
                1.6701417857058377e-05,
                0.9997388096148024,
                1.6701427812931038e-05,
                1.1478772229300848e-05,
                0.4073334000459302,
                2.1444956079842134e-05
            ],
            [
                NaN,
                0.9999885212319124,
                0.9999687980739141,
                0.9999417087559561,
                1.8925150490826034e-05,
                0.6513548782017745,
                0.9999967112521152,
                0.9999151889260132,
                NaN,
                0.999999266179112
            ],
            [
                8.93969630333567e-06,
                4.222834451292594e-06,
                7.889263526180094e-06,
                0.9999339478289221,
                1.7603440526806268e-06,
                1.012998856048759e-05,
                3.2887490653647836e-06,
                1.0677024881941248e-06,
                6.1441753337365085e-06,
                1.2098652507583041e-06
            ],
            [
                0.9998911030651763,
                0.9997694931809888,
                0.9998415638060425,
                2.753568452349975e-05,
                0.9978172835967436,
                0.9999756997535163,
                0.9999687980812332,
                0.9999921107364745,
                0.9999251537734042,
                0.9999852610145203
            ],
            [
                0.0003353502254382126,
                NaN,
                0.9999599363126873,
                5.144223204748698e-05,
                0.9989677687301207,
                5.1442195242316055e-05,
                0.9999832985761857,
                7.484621828887399e-05,
                0.00015843621571159862,
                6.605214456006411e-05
            ],
            [
                7.889260704050487e-06,
                4.785096775676685e-06,
                1.012999339449843e-05,
                4.785094494672519e-06,
                4.785093353626844e-06,
                8.93969736955767e-06,
                1.8925155003330605e-05,
                8.939693106987645e-06,
                2.7535687809124434e-05,
                1.670141785809127e-05
            ],
            [
                6.1441746017453204e-06,
                1.3007128463352975e-05,
                1.6701421842566163e-05,
                0.9999898700126476,
                1.8925141471913163e-05,
                6.962257079465052e-06,
                2.144495352474637e-05,
                4.785092783319532e-06,
                5.422218322851817e-06,
                3.1201903931474406e-05
            ],
            [
                6.962258739169842e-06,
                7.889263526180094e-06,
                4.4508521108475657e-07,
                4.222833947897496e-06,
                NaN,
                8.939693106987645e-06,
                7.889262585728421e-06,
                5.422217030121119e-06,
                4.4508505192495825e-07,
                5.422219615286937e-06
            ],
            [
                0.9999945777823389,
                0.9999810748472974,
                0.9999910603015684,
                0.9999957771650685,
                0.9999687980739276,
                0.9999546021098314,
                0.9999599363241992,
                0.9999945777797765,
                0.9999852610242775,
                0.9999852610199155
            ],
            [
                8.4811010852998e-05,
                0.00010889694808591575,
                8.481105143068482e-05,
                0.010986942165074799,
                4.539787943513799e-05,
                9.610238051931088e-05,
                1.0129992186202796e-05,
                4.5397890240179425e-05,
                8.481104130646901e-05,
                2.753569109454917e-05
            ],
            [
                0.3775406687981454,
                3.1201900209877224e-05,
                0.00043055698477834114,
                4.539788482296012e-05,
                4.00636778475281e-05,
                2.7535687797204028e-05,
                1.012998977108606e-05,
                0.9990889486935427,
                4.539787943778038e-05,
                4.539786857361818e-05
            ],
            [
                3.120192252800261e-05,
                8.93969630333567e-06,
                0.0004305570330514753,
                4.222832437186393e-06,
                1.3007134664822509e-05,
                0.9999852610132264,
                2.4300246520590875e-05,
                1.670141586907437e-05,
                0.9999756997642906,
                8.93969630333567e-06
            ],
            [
                2.9023123309973302e-06,
                1.6701415869924985e-05,
                7.889265406567165e-06,
                1.1478770861441461e-05,
                1.3007133114011233e-05,
                1.892514372737249e-05,
                NaN,
                6.144174601588856e-06,
                1.1478772230407462e-05,
                1.7603434231385591e-06
            ],
            [
                0.9999832985703382,
                0.14804719051380197,
                0.999985261023377,
                0.46879062662624377,
                0.9999852610163138,
                0.9999756997653465,
                0.46879062662624377,
                0.9999832985724126,
                0.999925153737113,
                0.9996200154093238
            ],
            [
                1.2098656835136636e-06,
                2.5612828213690224e-06,
                0.9998415637689381,
                1.012999581021488e-05,
                3.2887494573561262e-06,
                1.99472924590571e-06,
                6.1441767990323395e-06,
                3.726640616670918e-06,
                6.962255419804982e-06,
                3.726639284050988e-06
            ],
            [
                4.222832941111319e-06,
                1.1478765386623071e-05,
                7.88926352599354e-06,
                1.5534977544141614e-06,
                1.2098661161602417e-06,
                6.962254588977791e-06,
                1.6701425826191394e-05,
                1.8925152728867892e-05,
                3.535626334953767e-05,
                1.3007130012341915e-05
            ],
            [
                0.9999646437535943,
                2.1444953489522773e-05,
                0.5312093733737563,
                7.889263524960312e-06,
                0.3208212878370535,
                3.120191508446373e-05,
                NaN,
                0.8519528057272544,
                0.9998911030575421,
                0.3775406758018019
            ],
            [
                0.9669140237564794,
                0.9999687980775012,
                0.9999785550568071,
                0.9999869928762337,
                0.9999810748590325,
                3.535625912022914e-05,
                0.7981867873410141,
                0.9999646437590468,
                0.3775406687981454,
                0.1329642436335826
            ],
            [
                0.9997694931757841,
                0.9998204719943149,
                0.6791786926816161,
                0.9998415637089273,
                0.9999251537821353,
                0.999933947863362,
                0.9999251537479613,
                0.8354835391516132,
                0.9998766053665034,
                0.9859363735895196
            ],
            [
                6.1441767989541075e-06,
                1.0129995808639442e-05,
                6.144172402106516e-06,
                1.473898899846585e-05,
                6.144173868044274e-06,
                1.1478772227964558e-05,
                8.939698434495167e-06,
                8.939697368663308e-06,
                6.144173136556186e-06,
                7.889266346603015e-06
            ],
            [
                2.430024362393472e-05,
                4.006369696446335e-05,
                2.7535681250497054e-05,
                7.484626291261785e-05,
                1.4738983727900215e-05,
                5.144220748924517e-05,
                4.539789026561238e-05,
                3.120190393260949e-05,
                1.8925154994724604e-05,
                0.00015843625377712472
            ],
            [
                4.0063706496627415e-05,
                6.9622587393661365e-06,
                6.144177531599359e-06,
                2.1444958632714784e-05,
                2.4300252308334918e-05,
                2.1444956081636468e-05,
                1.0129992186589747e-05,
                1.1478772230198667e-05,
                1.1478769493540482e-05,
                2.7535697663897248e-05
            ],
            [
                3.12019262448351e-05,
                0.9997694932639757,
                0.5621765008857981,
                0.3208213138121609,
                0.9998601779599728,
                0.9999485577682174,
                0.9998415637346646,
                0.9998766054700713,
                0.6513548782017745,
                0.9999646437453373
            ],
            [
                0.00020342696840674793,
                6.144177531381426e-06,
                1.4738985483128763e-05,
                3.120192252686752e-05,
                1.4738987241172537e-05,
                1.6701425822059825e-05,
                4.222833444429485e-06,
                1.6701419853184244e-05,
                5.422220908876325e-06,
                1.1478772230407462e-05
            ],
            [
                4.006368740256958e-05,
                0.11920292202211756,
                0.09534946875514017,
                0.9997694931762068,
                0.9997694933673988,
                0.9995121429407677,
                0.1329642316084462,
                0.9998415638523951,
                0.5926665999540698,
                0.11920292202211756
            ],
            [
                2.1444950948742995e-05,
                0.00013982212280460153,
                2.1444940734059286e-05,
                2.753569765708558e-05,
                0.00012339454522734274,
                3.120191136263821e-05,
                9.610239172350516e-05,
                2.1444950969026795e-05,
                3.5356246483883486e-05,
                1.1478769492642663e-05
            ],
            [
                0.9999930377422195,
                0.9999687980961723,
                0.9999898700066673,
                0.9999910602994365,
                0.9999485577681516,
                0.9999038975859325,
                0.4687906266262437,
                0.9999957771670598,
                0.9999962733607168,
                0.9999885212319024
            ],
            [
                4.006369696446335e-05,
                7.484622725304513e-05,
                3.12019225291377e-05,
                7.484620920327215e-05,
                4.006370650653807e-05,
                2.1444958636771547e-05,
                1.3007126911974612e-05,
                4.0063687374440786e-05,
                1.6701427816728442e-05,
                3.12019224440064e-05
            ],
            [
                NaN,
                0.999993855823205,
                0.1824255326961778,
                0.9579122749379931,
                0.03732689028911683,
                0.9999546021206726,
                0.867035758084294,
                0.9999980052702803,
                0.9999869928701483,
                0.7549149923816048
            ],
            [
                1.670141785651155e-05,
                2.4300249418927004e-05,
                2.4300234904884198e-05,
                3.535626333641835e-05,
                1.0129994600398803e-05,
                8.939695235959266e-06,
                2.753569761230891e-05,
                1.1478769485293071e-05,
                4.539786858947248e-05,
                0.679178699175393
            ],
            [
                5.422218969661113e-06,
                4.78509563535725e-06,
                1.1478766755734576e-05,
                1.8925152752138513e-05,
                3.726640172537657e-06,
                1.3007125361755747e-05,
                1.4738976700366126e-05,
                3.2887482812506295e-06,
                6.9622587393661365e-06,
                1.8925157264023994e-05
            ],
            [
                4.006369690762278e-05,
                3.2887498492518007e-06,
                0.00023050671166423338,
                0.00026119043171500577,
                1.0129989769962063e-05,
                5.829126543678972e-05,
                7.889262582112126e-06,
                1.8925148211888738e-05,
                3.120191505506507e-05,
                1.8925152748558416e-05
            ],
            [
                0.0011695101592555436,
                2.430024072188641e-05,
                1.473898372822193e-05,
                5.144223203551027e-05,
                9.610238051931088e-05,
                2.7535697654881812e-05,
                1.30071315640992e-05,
                1.6701429807630274e-05,
                2.75356976629957e-05,
                6.605216031765658e-05
            ],
            [
                0.00013982207363327857,
                8.481108161082634e-05,
                NaN,
                0.0001584362346832731,
                5.422217025761715e-06,
                5.829127939986156e-05,
                5.144219520863158e-05,
                1.3007130012980722e-05,
                6.605216030564256e-05,
                1.1478772221888615e-05
            ],
            [
                6.962253759670401e-06,
                1.4738983727900215e-05,
                8.939700566289352e-06,
                1.3007130013572209e-05,
                1.892515500808112e-05,
                1.8925150490826034e-05,
                1.473898899846585e-05,
                3.120191136899467e-05,
                6.962253759670401e-06,
                1.300713311517055e-05
            ],
            [
                0.40733340004593027,
                0.18242551936144574,
                0.9999869928669095,
                0.9999151889188952,
                NaN,
                5.144220136091472e-05,
                0.9999852610180465,
                4.222834954461155e-06,
                2.753569437476538e-05,
                0.2689414096510108
            ],
            [
                0.9999646437577657,
                0.999983298576216,
                0.9999921107374152,
                0.9999962733616087,
                0.9999952149060803,
                0.9999898700042098,
                0.9999785550592722,
                0.9994472214095128,
                0.9999898700114423,
                0.9999910603069019
            ],
            [
                6.962253759670401e-06,
                1.9947306726213275e-06,
                1.760344052714248e-06,
                2.144494329192304e-05,
                1.5534983101393749e-06,
                1.3007123812554424e-05,
                2.2603251061849014e-06,
                8.939700565102295e-06,
                1.012999460150437e-05,
                2.9023119851055122e-06
            ],
            [
                7.889262585728421e-06,
                8.939694172542558e-06,
                5.4222183222304545e-06,
                1.4738978457604563e-05,
                1.6701427809710842e-05,
                1.0129989771473008e-05,
                1.1478770862067849e-05,
                8.939699500164542e-06,
                1.0129989771823107e-05,
                6.962258739530771e-06
            ],
            [
                0.9999885212265772,
                0.9999038975999102,
                0.9999898700102532,
                0.9999910603027673,
                0.9999810748472895,
                7.889261644875049e-06,
                NaN,
                0.9999687980867481,
                0.9995121428281716,
                0.9999599363032895
            ],
            [
                6.144173868882483e-06,
                2.4300249421932663e-05,
                2.144494329566774e-05,
                6.962253759486771e-06,
                2.4300243618542217e-05,
                6.144174601588856e-06,
                1.147877223059538e-05,
                5.422217677028889e-06,
                1.0129993394811673e-05,
                2.1444953523537147e-05
            ],
            [
                2.1444953520182517e-05,
                1.0129988562422337e-05,
                2.1444950968441685e-05,
                7.889264465239894e-06,
                0.00026119021044349896,
                6.144177530146464e-06,
                1.6701423825538316e-05,
                4.222834954134701e-06,
                4.222831932420432e-06,
                2.5612834309848352e-06
            ],
            [
                2.4300240723831244e-05,
                3.1201911375578156e-05,
                1.4738978456398127e-05,
                1.0129990979215566e-05,
                2.4300232042706045e-05,
                4.0063711285810896e-05,
                2.5612819053399912e-06,
                5.4222209089700225e-06,
                3.535626756251187e-05,
                6.1441724044534996e-06
            ],
            [
                5.8291258453558646e-05,
                2.2603248367656408e-06,
                1.1478766752372975e-05,
                1.300712846217e-05,
                7.88925976397226e-06,
                NaN,
                2.1444945842219688e-05,
                1.8925152748558416e-05,
                3.72664017246987e-06,
                4.539786319306454e-05
            ],
            [
                1.4738988995838502e-05,
                5.422218969532895e-06,
                1.0129994601301684e-05,
                6.144176799166453e-06,
                3.288749065209246e-06,
                2.1444958627955892e-05,
                6.144175333926503e-06,
                1.4738981971250963e-05,
                6.962254589433702e-06,
                1.300713466281145e-05
            ],
            [
                1.147876675124548e-05,
                8.481104136076758e-05,
                1.6701429804744246e-05,
                1.6701423834591316e-05,
                1.67014178576052e-05,
                1.892515725665725e-05,
                5.422220908634683e-06,
                0.8670357563664174,
                0.9997388097326655,
                2.902313022554084e-06
            ],
            [
                1.0129993394959082e-05,
                1.1478766756653273e-05,
                1.1478766754941153e-05,
                1.6701421843356024e-05,
                6.144173136729416e-06,
                2.144494329192304e-05,
                2.9023109471452223e-06,
                4.22283294098842e-06,
                1.3007133114011233e-05,
                1.147876675686207e-05
            ],
            [
                0.9999339478561506,
                2.4300243624818735e-05,
                0.0330859792229422,
                0.9999724643123791,
                0.037326887879581695,
                0.015906388329639098,
                0.04742587688008271,
                0.20181322706107543,
                1.1478772229989872e-05,
                1.3007125361448172e-05
            ],
            [
                1.8925152749659986e-05,
                4.222833444429485e-06,
                NaN,
                NaN,
                0.9999485577816842,
                0.999820472058398,
                1.3007125363293615e-05,
                0.9998415637357342,
                0.9999251537919468,
                1.3007133115667397e-05
            ],
            [
                7.889266346746518e-06,
                NaN,
                4.222833947359807e-06,
                5.144219519403497e-05,
                1.0,
                0.999704042995777,
                1.8925152747388e-05,
                4.0063687367153544e-05,
                6.605214443655996e-05,
                1.8925152746768368e-05
            ],
            [
                0.999876605454392,
                0.9999832985746082,
                0.9999810748537362,
                0.9998601778666573,
                0.9998601778720606,
                0.9999810748514477,
                0.9999599362936574,
                0.9998415637111702,
                0.46879062662624377,
                0.9998766054261539
            ],
            [
                0.00010889689626212509,
                4.0063687409856826e-05,
                5.829127936084435e-05,
                1.6701415868193372e-05,
                8.48110109233393e-05,
                3.120191508707442e-05,
                1.3007131562514014e-05,
                1.6701421842566163e-05,
                1.4738981971813965e-05,
                1.670142980726572e-05
            ],
            [
                0.9999952149038275,
                0.999992110740536,
                0.9999599362935444,
                0.990291525631656,
                6.1441760651689774e-06,
                0.9999599362891725,
                0.5926665999540698,
                0.9999151889590218,
                2.430023202688216e-05,
                0.14804719803168948
            ],
            [
                0.6513548714339145,
                2.7535700934898458e-05,
                0.9999756997506608,
                0.9999038975870594,
                0.9999957771680749,
                0.679178699175393,
                0.9999251537632279,
                0.9999810748519274,
                0.9998601779102075,
                0.9999785550517812
            ],
            [
                3.927862002625787e-07,
                1.0129987356541108e-05,
                8.939698435340743e-06,
                2.2603248367656408e-06,
                5.715002426343175e-07,
                1.5534981249574276e-06,
                2.260324028351814e-06,
                3.927862470861484e-07,
                5.422218969661113e-06,
                5.715007195353674e-07
            ],
            [
                3.726639283752725e-06,
                4.5397864199812656e-05,
                1.6701429801675944e-05,
                8.939696303758459e-06,
                4.7850944943330625e-06,
                6.962259568230874e-06,
                8.939693105076969e-06,
                8.93969310647542e-06,
                1.4738978453743973e-05,
                4.222831933795376e-06
            ],
            [
                6.144174601208867e-06,
                5.422218969661113e-06,
                4.006367785146321e-05,
                1.0129990978847043e-05,
                6.962253759752719e-06,
                3.7266392836374875e-06,
                6.9622545877746946e-06,
                1.1478766756214804e-05,
                1.1478773595009805e-05,
                2.430023203572232e-05
            ],
            [
                0.24508501313237172,
                0.9999485578074312,
                NaN,
                0.9999967112509524,
                0.999989870004242,
                0.9999852610133512,
                0.9999756997478382,
                0.999891103092198,
                0.5,
                0.9999646437367669
            ]
        ]
    },
    {
        "q_id": "8063_mmlu_math",
        "cot_ids": [
            0,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            12,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            30,
            31,
            33,
            35,
            36,
            38,
            39,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            52,
            54,
            57,
            58,
            59,
            63,
            65,
            67,
            68,
            69,
            71,
            73,
            74,
            75,
            76,
            77,
            83,
            90,
            91,
            94,
            95,
            97,
            98,
            99,
            100,
            102,
            104,
            105,
            106,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            119,
            120,
            122,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.3007123805078022e-05,
                3.535625909386188e-05,
                0.0001088969610644462,
                3.120191506868607e-05,
                3.120192248986379e-05,
                5.144222566240286e-05,
                1.1478769488257963e-05,
                0.00012339455982578483,
                2.144494327218535e-05,
                2.1444953495919973e-05
            ],
            [
                0.8670357563664174,
                0.9999957771676388,
                0.9999996533672962,
                0.9820137884587394,
                0.999997438716568,
                0.9999982396565843,
                0.9999974387165732,
                0.9999997300422547,
                0.9999952149066478,
                0.9999998144609424
            ],
            [
                7.484625401596508e-05,
                3.1201926243586504e-05,
                2.144495607789177e-05,
                1.6701417859944398e-05,
                3.2887482812506295e-06,
                3.7266406162947e-06,
                6.962258737979408e-06,
                4.222833947674739e-06,
                1.6701423834591316e-05,
                6.9622537593854575e-06
            ],
            [
                2.7535687806920664e-05,
                8.939697368305565e-06,
                1.1478765380839446e-05,
                6.144174601499446e-06,
                5.1442195248304415e-05,
                2.1444940741392653e-05,
                3.535624228030111e-05,
                5.1442238133528324e-05,
                6.605216818444021e-05,
                3.120191876292951e-05
            ],
            [
                8.939697366289195e-06,
                1.0129995806888955e-05,
                1.1478764012062179e-05,
                5.1442219765744705e-05,
                8.93969630226244e-06,
                4.006369217615605e-05,
                1.670142582254589e-05,
                3.53562506982705e-05,
                1.1478773587743728e-05,
                8.93970056152486e-06
            ],
            [
                0.9999994284994167,
                0.9999982396566405,
                0.9999910603047684,
                0.9999967112510089,
                0.9999910603015729,
                0.9999910602994343,
                0.9999967112497621,
                0.9999980052705164,
                0.9999962733616047,
                0.9999957771645431
            ],
            [
                0.9999984465015048,
                0.9999962733603129,
                0.9999967112505448,
                0.9999990577557493,
                0.9999930377404322,
                0.9999993524052798,
                0.9999992661791945,
                NaN,
                0.9999992661790197,
                0.9999995549149481
            ],
            [
                1.7603434230921292e-06,
                3.28874867308036e-06,
                2.902312677060767e-06,
                4.222833444506298e-06,
                3.7266379497470296e-06,
                1.067703251864202e-06,
                8.939696302831578e-06,
                4.785093923768848e-06,
                1.2098662603356388e-06,
                3.7266388397382506e-06
            ],
            [
                1.8925145978942173e-05,
                3.726638839656906e-06,
                3.726637951079042e-06,
                7.889260704531226e-06,
                2.5612825160271407e-06,
                3.726640172385136e-06,
                5.4222183231674305e-06,
                1.0129988563914856e-05,
                4.785093924103951e-06,
                8.939699500164542e-06
            ],
            [
                0.9999992661791944,
                0.9999990577549577,
                0.9999967112493668,
                0.9999977396757033,
                0.9999995549150011,
                0.999999352404893,
                0.9999980052705605,
                0.9999998362623332,
                0.9999996940976636,
                0.999999352405279
            ],
            [
                4.0063692167994334e-05,
                3.120191880867338e-05,
                1.7603436328770204e-06,
                3.726640172120768e-06,
                6.144173136019732e-06,
                1.6701417857058377e-05,
                1.300712846115264e-05,
                4.2228324375512536e-06,
                1.3007123810638006e-05,
                6.962258738574625e-06
            ],
            [
                3.7266406165827946e-06,
                3.7266401724291984e-06,
                3.288750633545794e-06,
                3.535625912022914e-05,
                5.422218322348809e-06,
                3.726638395320497e-06,
                6.962258738701267e-06,
                1.2098658276730537e-06,
                4.7850933535659155e-06,
                2.902311639126627e-06
            ],
            [
                9.422447062240614e-07,
                1.2098653950480359e-06,
                1.0677031245851707e-06,
                9.422445938861406e-07,
                1.0677027427525368e-06,
                1.5534983101301911e-06,
                2.5612819053586272e-06,
                8.315282258900085e-07,
                1.5534984953298217e-06,
                1.370956716529941e-06
            ],
            [
                1.8925157260443894e-05,
                2.2603234894745224e-06,
                1.0677031245312763e-06,
                1.30071315640992e-05,
                2.2603248355969475e-06,
                3.288748672760313e-06,
                6.962253757295868e-06,
                2.2603234894745224e-06,
                4.7850933535006355e-06,
                4.222833444168322e-06
            ],
            [
                0.9999997617631468,
                0.9999910602994395,
                0.9999995549149481,
                0.9999992661788445,
                0.9999996940977366,
                0.5,
                0.9999910603015888,
                0.9999990577550693,
                0.9998911030625047,
                0.9999885212319007
            ],
            [
                0.9999996072137061,
                0.999999887464811,
                0.999999855502048,
                0.999999855501979,
                0.9999999397642437,
                0.9999993524052789,
                0.9999987901343165,
                0.9999995549147889,
                0.9999997897565838,
                0.9999997300421581
            ],
            [
                2.7535687788789623e-05,
                1.8925155002710973e-05,
                4.539789022498571e-05,
                0.0003353502673139849,
                2.1444950959196957e-05,
                8.939694167932546e-06,
                5.144220122131125e-05,
                6.605213671635022e-05,
                4.0063687383622725e-05,
                1.300713001414004e-05
            ],
            [
                4.5397852394305204e-05,
                1.3007134665674251e-05,
                1.4738987240475486e-05,
                5.144221975264518e-05,
                7.48462180748709e-05,
                6.144176065828368e-06,
                3.2887502414436403e-06,
                1.67014178576052e-05,
                6.962258739068529e-06,
                7.889265404959923e-06
            ],
            [
                4.222832940942332e-06,
                1.9947306725669014e-06,
                2.5612825159677387e-06,
                6.144174601309452e-06,
                1.2098652507715085e-06,
                1.994729245842213e-06,
                2.7535681246690542e-05,
                1.9947297214182054e-06,
                7.889266347133978e-06,
                1.209865683500459e-06
            ],
            [
                0.5926665999540698,
                2.4300234920177672e-05,
                0.9998204719929699,
                0.9999756997476992,
                0.9996200155629855,
                0.05340332942318685,
                0.7310585727705126,
                0.998967769017865,
                0.7772998663336157,
                0.9999898700090285
            ],
            [
                1.0129993393540266e-05,
                3.2887482809933958e-06,
                1.1478772229300848e-05,
                3.5356259136692605e-05,
                8.93969630317306e-06,
                8.939695237162584e-06,
                3.288749065125496e-06,
                1.4738987234014356e-05,
                4.222835457906302e-06,
                2.1444956074147067e-05
            ],
            [
                0.9999998555019791,
                0.9999998874648915,
                0.9999995549151073,
                0.9999994956525918,
                0.9999996533674614,
                0.9999996533672135,
                0.9999994956526519,
                0.9999974387180948,
                0.999997438717484,
                0.9999998144609424
            ],
            [
                0.9999998144609202,
                0.999998932296621,
                0.9999993524051246,
                0.9999996533674615,
                0.9999982396565769,
                0.9999994284996891,
                0.9999996072138465,
                0.9999998724810027,
                0.9999998144608097,
                0.9999998144608097
            ],
            [
                7.889262582341733e-06,
                1.1478766754377407e-05,
                4.222832939870796e-06,
                2.561282821209454e-06,
                5.144221974590828e-05,
                2.5612812943280275e-06,
                1.0129994591922764e-05,
                6.144176064185479e-06,
                2.9023130222373278e-06,
                1.4738976698006875e-05
            ],
            [
                0.9999599362935166,
                0.9770226321389233,
                0.9999987901337445,
                0.9525741222784363,
                0.9999952149072371,
                0.7772998560157665,
                0.9525741318713181,
                0.982013791584178,
                0.9579122713334306,
                0.7772998560157665
            ],
            [
                2.5612815998141903e-06,
                1.1478770851648967e-05,
                1.0129988562164371e-05,
                4.539785238406597e-05,
                2.561281294558644e-06,
                4.222833947728508e-06,
                1.994730434816876e-06,
                NaN,
                3.5356237914914405e-05,
                7.88926634687567e-06
            ],
            [
                1.670142781432848e-05,
                1.892514147046736e-05,
                2.7535700932494338e-05,
                3.1201903930339314e-05,
                4.006370646383477e-05,
                5.144223201941656e-05,
                1.6701415863393463e-05,
                1.0129988561906404e-05,
                1.670142581883963e-05,
                1.3007128461507534e-05
            ],
            [
                0.9999984465018751,
                0.9999967112505427,
                0.9999986290424663,
                0.9999986290432835,
                0.99999743871749,
                0.9999999468421376,
                0.9999989322975118,
                0.9999962733616046,
                0.9999991684722697,
                0.9999998874648917
            ],
            [
                0.00010889689614645761,
                5.4222183221120994e-06,
                NaN,
                2.7535697661092444e-05,
                6.1441775309064404e-06,
                1.8925157255280296e-05,
                1.892515049423401e-05,
                2.144495863411905e-05,
                2.144494330062167e-05,
                1.670142383015595e-05
            ],
            [
                2.9023133690637e-06,
                1.3709572068354007e-06,
                6.9622562492265485e-06,
                1.5534981249023245e-06,
                3.2887494572873306e-06,
                1.7603436329978976e-06,
                1.8925141469950998e-05,
                1.6701427811412077e-05,
                7.484620038013827e-05,
                2.9023123310290063e-06
            ],
            [
                0.04208772325972563,
                0.999195914207008,
                0.9770226276646877,
                0.9999599363097902,
                0.8933094003735664,
                0.7310585844894971,
                NaN,
                0.9999599363079387,
                0.9999724643188024,
                0.22270014914315833
            ],
            [
                0.9999251537572249,
                0.9796676474735838,
                0.99142251582971,
                0.9999997300422225,
                0.9999974387175297,
                0.9964063968399962,
                0.9999997897566589,
                0.9999998362622552,
                0.9933071480819816,
                0.9999998874647709
            ],
            [
                3.726638395415398e-06,
                4.222831934286977e-06,
                4.222834451169694e-06,
                1.5534983100228109e-06,
                7.889261644760245e-06,
                9.422444815323792e-07,
                3.726640172537657e-06,
                3.5356242272712497e-05,
                1.994729483630195e-06,
                2.5612812946681295e-06
            ],
            [
                0.999999730042126,
                0.9999998874647306,
                0.9999999317440035,
                0.9999998555019446,
                0.9999998144609645,
                0.9999997897567341,
                0.9999999586006542,
                0.9999991684718875,
                0.9999999123574628,
                0.9999996533672549
            ],
            [
                0.9999945777797377,
                0.999996273362049,
                0.9999756997483684,
                0.9999687980744982,
                0.9999986290427931,
                0.9324533116759811,
                0.9998415638401131,
                0.9999967112493676,
                0.9999952149055472,
                0.9999546021205679
            ],
            [
                0.999997438716568,
                0.9999974387184224,
                0.9999970976890531,
                0.9984988173977564,
                0.9914225150694009,
                0.999989870011436,
                0.9999987901338838,
                0.9999984465022455,
                0.9999810748517658,
                0.9999952149072171
            ],
            [
                0.9999997300420937,
                0.9999990577554062,
                0.9999994956525318,
                0.9999997617630049,
                0.9999996940977366,
                0.9999994284993485,
                0.9999992661789321,
                0.9999992661788445,
                0.9999945777816778,
                0.9999993524054335
            ],
            [
                5.04347588554027e-07,
                1.209865971934245e-06,
                6.475945665853783e-07,
                7.338209804853638e-07,
                3.726640172120768e-06,
                4.222834954280646e-06,
                1.067702615417244e-06,
                1.0677033790757595e-06,
                1.3709578605455302e-06,
                2.902311984915459e-06
            ],
            [
                5.422217029943586e-06,
                6.962257907348116e-06,
                1.4738988998787566e-05,
                1.8925155003330605e-05,
                1.670142781636389e-05,
                1.7603425836246058e-06,
                3.288748281220719e-06,
                3.72664017246987e-06,
                1.7603434230921292e-06,
                3.2887502412970765e-06
            ],
            [
                0.9999898700078231,
                0.9999038975396431,
                0.9999687980775585,
                0.9999910603005054,
                0.999986992874644,
                0.9999970976869782,
                0.9998766054265597,
                0.9999417087277856,
                0.9999646437451547,
                0.999989870010234
            ],
            [
                0.9999756997679721,
                0.9999970976883609,
                0.999954602142202,
                0.999998446502801,
                0.9999977396762656,
                0.9999921107377154,
                0.9993736659831112,
                0.9999982396567868,
                0.9999997300422868,
                0.9984988176076779
            ],
            [
                1.3007128457958606e-05,
                6.144172403067661e-06,
                7.889264465842609e-06,
                1.6701423833011596e-05,
                1.473898899846585e-05,
                1.5534979397394734e-06,
                7.889261638546534e-06,
                5.422220908560712e-06,
                4.785096205260165e-06,
                5.1442219708855337e-05
            ],
            [
                0.00048785704782232424,
                1.670142382796865e-05,
                0.00017952802935764314,
                8.939693101694668e-06,
                4.539789026561238e-05,
                5.829127929171602e-05,
                2.1444953490927035e-05,
                1.147876401423365e-05,
                0.0003799845720710205,
                1.3007131559390956e-05
            ],
            [
                0.9999993524049703,
                0.9999938558268633,
                0.9999251537550597,
                0.9999991684720715,
                0.9999967112521111,
                0.9999970976880151,
                0.999996711251719,
                0.9999991684720715,
                0.9999910603058294,
                0.999999168471675
            ],
            [
                2.902313022659669e-06,
                1.553498495230919e-06,
                5.422218322940583e-06,
                1.7603440526662173e-06,
                4.222831933864508e-06,
                1.209866116137134e-06,
                1.3709576970387918e-06,
                8.31528325021115e-07,
                8.939694171331106e-06,
                1.0677033791204289e-06
            ],
            [
                6.962254588977791e-06,
                1.147876675548402e-05,
                6.144175332440078e-06,
                3.7266392836374875e-06,
                5.422217030121119e-06,
                2.2603248365960415e-06,
                2.4300232038993178e-05,
                5.422218969661113e-06,
                7.889259763857458e-06,
                1.8925157262061825e-05
            ],
            [
                0.9999957771651049,
                0.9999910603047643,
                0.9999970976876843,
                0.9999989322971305,
                0.9999970976873236,
                0.9999952149055061,
                0.9999984465018752,
                0.9999957771650456,
                0.9947798742024624,
                0.9999986290432857
            ],
            [
                4.785095633616451e-06,
                4.222832437186393e-06,
                6.962259568509485e-06,
                2.260324836696773e-06,
                2.9023116389365734e-06,
                5.42222090821551e-06,
                1.5534977545243671e-06,
                3.2887478887958082e-06,
                2.9023126765777146e-06,
                2.902312330759764e-06
            ],
            [
                4.785094493305991e-06,
                7.484620042805751e-05,
                1.473898020838208e-05,
                6.60521682190406e-05,
                2.1444958631232504e-05,
                1.0129993386593603e-05,
                1.473897670007122e-05,
                1.892515046321799e-05,
                1.0129988562164371e-05,
                1.1478772223642496e-05
            ],
            [
                0.9999987901341724,
                0.9999974387174846,
                0.9999832985721876,
                0.9999852610180398,
                0.9999977396762411,
                0.9241418152779358,
                0.9999898700114355,
                0.9999938558268652,
                0.999996273360716,
                0.9999938558246667
            ],
            [
                0.999997097687669,
                0.9999724642990628,
                0.9999995549151073,
                0.9999974387168733,
                0.999998629042305,
                0.9999910602995548,
                0.9999970976866317,
                0.9999339478327425,
                0.9999832985841337,
                0.999986992866886
            ],
            [
                0.9999980052695654,
                0.9999945777787829,
                0.9999945777803847,
                0.9999952149072342,
                0.9999910603015664,
                0.9999952149032266,
                0.9999930377412638,
                0.9999910603015673,
                0.9999810748450347,
                0.9399133485636498
            ],
            [
                8.9396941718352e-06,
                6.605212890195146e-05,
                3.5356246490314526e-05,
                5.14422013436982e-05,
                5.8291251611977796e-05,
                5.144220137700842e-05,
                3.535625492063251e-05,
                2.1444953521586782e-05,
                6.962258737979408e-06,
                1.147876949310201e-05
            ],
            [
                8.93969630089651e-06,
                8.939693104637921e-06,
                1.300712846217e-05,
                1.8925152739677025e-05,
                1.473898722564974e-05,
                2.7535700909955743e-05,
                2.1444956071728615e-05,
                5.144220730697468e-05,
                1.892514821299031e-05,
                1.8925155000714377e-05
            ],
            [
                0.999999168471675,
                0.9999998555019963,
                0.9999996940977366,
                0.9999998144609645,
                0.999999554914895,
                0.9999977396748939,
                0.999999814460876,
                0.9999970976869769,
                0.9999994956526519,
                0.9999986290429573
            ],
            [
                0.8354835350552604,
                0.9525741258126562,
                0.9999898700114378,
                0.999998446502431,
                0.8807970748488297,
                0.9999898700127415,
                0.9999952149055108,
                0.9999785550592685,
                0.9465966752847803,
                0.9999967112521343
            ],
            [
                2.1444948408275583e-05,
                7.889261643727018e-06,
                3.288749849209925e-06,
                3.535626334323525e-05,
                4.539789024909747e-05,
                NaN,
                NaN,
                4.785094494463623e-06,
                1.1478773595009805e-05,
                2.1444956071728615e-05
            ],
            [
                9.42244481511812e-07,
                2.5612825157464395e-06,
                1.2098652507715085e-06,
                1.553498495091042e-06,
                3.7266379498554884e-06,
                5.422218321993744e-06,
                9.422443692090534e-07,
                8.315278293687262e-07,
                2.902312330965655e-06,
                2.9023133687786197e-06
            ],
            [
                4.539786314219866e-05,
                6.962253758182361e-06,
                1.3007128456065844e-05,
                9.610239196262121e-05,
                1.3007126905042372e-05,
                1.0129992186589747e-05,
                1.6701427793184552e-05,
                2.4300243620398656e-05,
                4.7850933500712625e-06,
                0.00010889688319328668
            ],
            [
                0.9982992775454763,
                0.8933094096048376,
                0.9998911030653981,
                0.731058584489497,
                0.9999756997505934,
                0.8807970889295663,
                NaN,
                0.9998204720137666,
                0.999948557798702,
                0.9998601779629859
            ],
            [
                1.9947306726049992e-06,
                5.422217030362759e-06,
                4.222833947774596e-06,
                8.315282258832022e-07,
                5.4222176759932836e-06,
                4.2228349546493465e-06,
                3.7266379505740294e-06,
                3.7266410609160796e-06,
                7.338209805090567e-07,
                6.144176066264237e-06
            ],
            [
                1.1478769490053603e-05,
                0.00012339458930993918,
                0.00010889692200685404,
                5.829126546053932e-05,
                1.6701421843720577e-05,
                2.7535690965728617e-05,
                0.00023050671480314775,
                3.535625070778844e-05,
                1.670142980608093e-05,
                1.147876401423365e-05
            ],
            [
                1.3709576971160984e-06,
                1.0677033790883835e-06,
                1.5534981249397663e-06,
                5.422217030032353e-06,
                1.7603432131631714e-06,
                1.0677028700203557e-06,
                2.5612825160096693e-06,
                4.2228344511197656e-06,
                6.144173869072478e-06,
                3.2887482812745586e-06
            ],
            [
                2.561281294558644e-06,
                5.422219615286937e-06,
                7.889266347004826e-06,
                3.120192249712832e-05,
                1.7603432132624344e-06,
                8.939699497855469e-06,
                1.4738983727578497e-05,
                3.726640616423495e-06,
                4.222835457664342e-06,
                6.144176796042727e-06
            ],
            [
                0.9999810748585336,
                0.9999546021476384,
                0.9999599363078364,
                0.9959298616536483,
                0.9990889489342393,
                0.9998204719492501,
                0.9999938558253986,
                0.9993736659148327,
                0.9999910603037205,
                0.9999251537461169
            ],
            [
                0.9999910602997147,
                0.9999957771676427,
                0.9999921107386001,
                0.9999921107364846,
                0.6513548714339145,
                0.9999921107392978,
                0.9999967112509347,
                0.9525741264858408,
                0.9999990577552945,
                0.9999997300422225
            ],
            [
                0.9999998144608538,
                0.9999986290432848,
                0.9999994284994167,
                0.9999987901344608,
                0.9999952149066484,
                0.9706877660687703,
                0.9999885212265209,
                0.9999980052700539,
                0.9999990577551815,
                0.999997438717179
            ],
            [
                0.9999982396569983,
                0.999991060301568,
                0.6224593312018546,
                0.9999485578052424,
                0.8519528038477824,
                0.9999952149066468,
                0.9999921107402603,
                0.9999952149049355,
                0.14804719427274565,
                0.9999952149061019
            ],
            [
                NaN,
                2.561281599914358e-06,
                6.144173136556186e-06,
                3.120191508185304e-05,
                4.222834451215781e-06,
                2.9023112927307205e-06,
                5.422217676486429e-06,
                1.5534971989696065e-06,
                1.2098656834834034e-06,
                1.3007126908307386e-05
            ],
            [
                2.7535694377870696e-05,
                6.144174601309452e-06,
                3.7266379512112265e-06,
                1.209865683500459e-06,
                1.9947301969707264e-06,
                1.4738987239698005e-05,
                1.5534975693707442e-06,
                6.962254589433702e-06,
                3.726639284017094e-06,
                8.939695238211425e-06
            ],
            [
                0.9999970976869771,
                0.9999970976876693,
                0.9999957771675629,
                0.9999687980849298,
                0.9999970976880156,
                0.9999982396559474,
                0.9999339478476836,
                0.9999832985841378,
                0.999996711250937,
                0.999996273361614
            ],
            [
                1.8925143715220825e-05,
                1.1478766746234395e-05,
                8.939697366029015e-06,
                8.939697362191404e-06,
                3.2887494557618747e-06,
                1.1478764012062179e-05,
                5.422217027576489e-06,
                2.5612834317908303e-06,
                2.902311292002183e-06,
                1.4738980203985296e-05
            ],
            [
                1.6701427798409776e-05,
                2.7535694322475846e-05,
                4.785093350245343e-06,
                6.144172403335888e-06,
                5.422217673557147e-06,
                3.120190762537599e-05,
                1.1478770856576534e-05,
                7.889264463446097e-06,
                1.670141584741401e-05,
                0.00010889690885245028
            ],
            [
                2.5612819052654485e-06,
                7.338210679816025e-07,
                3.9278634072866033e-07,
                1.0677028699955933e-06,
                5.422217676486429e-06,
                1.5534981248881956e-06,
                2.561282821239737e-06,
                3.726640172385136e-06,
                8.315280276263186e-07,
                4.222833443553821e-06
            ],
            [
                1.4738976692993472e-05,
                9.610244912256048e-05,
                8.939695236593446e-06,
                5.8291265292171594e-05,
                4.785095064044355e-06,
                3.120190019636974e-05,
                0.00020342699529812784,
                1.8925157254522964e-05,
                7.484625334455045e-05,
                1.3007125358230479e-05
            ],
            [
                3.535625912717466e-05,
                5.422218323231539e-06,
                2.753570420970657e-05,
                3.5356246488642456e-05,
                1.0129995809431767e-05,
                1.3007131564643372e-05,
                4.0063696959216535e-05,
                1.8925143726890553e-05,
                1.6701423834226767e-05,
                6.144173136556186e-06
            ],
            [
                0.9980732653559253,
                0.9999921107365531,
                0.9971990724072759,
                0.9999994956527368,
                0.9999852610145259,
                0.9999992661786696,
                0.9999962733607168,
                0.9999724643155651,
                0.9999957771650477,
                0.9999997617630616
            ],
            [
                0.9999756997534971,
                0.98201378740596,
                0.9999151889890767,
                0.9971990724879151,
                0.9999810748496505,
                0.9999945777823245,
                0.9999952149061032,
                0.9997388095664763,
                0.9999977396746244,
                0.9999967112521259
            ],
            [
                7.88926634644516e-06,
                5.422218322348809e-06,
                4.0063696784031e-05,
                1.8925155005051806e-05,
                2.260323489490968e-06,
                3.2887498493325602e-06,
                5.715004470272272e-07,
                1.067703379136937e-06,
                1.473897845457507e-05,
                9.422443692330485e-07
            ],
            [
                0.9999962733607161,
                0.9990889489103444,
                0.9999977396759745,
                0.9999977396765106,
                0.9999986290429955,
                0.9999980052698106,
                0.9999952149066565,
                0.9579122677288676,
                0.9999993524051246,
                0.9999980052707558
            ],
            [
                0.9999997617630332,
                0.9999996533674201,
                0.9999980052709919,
                0.9999996533673375,
                0.9999967112521111,
                0.9999989322968754,
                0.9999997897566089,
                0.9968273173467579,
                0.9999990577552937,
                0.999999554914842
            ],
            [
                8.315282259009745e-07,
                1.3709575337078829e-06,
                6.9622587396067566e-06,
                3.2887490653408545e-06,
                3.288749065077638e-06,
                1.7603427936183298e-06,
                1.9947301968963442e-06,
                4.785094494402695e-06,
                2.1444943294263477e-05,
                8.315281267800897e-07
            ]
        ]
    },
    {
        "q_id": "8959_mmlu_math",
        "cot_ids": [
            0,
            3,
            4,
            5,
            7,
            8,
            9,
            11,
            14,
            15,
            17,
            18,
            19,
            24,
            26,
            28,
            29,
            30,
            31,
            34,
            36,
            38,
            39,
            40,
            41,
            42,
            44,
            46,
            48,
            49,
            51,
            52,
            53,
            54,
            55,
            56,
            61,
            62,
            63,
            68,
            69,
            70,
            73,
            74,
            76,
            78,
            81,
            83,
            86,
            89,
            90,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            103,
            108,
            109,
            110,
            112,
            113,
            117,
            118,
            120,
            122,
            123,
            124,
            126
        ],
        "rewards": [
            [
                2.144495096457996e-05,
                4.53978902461248e-05,
                0.001032231072647817,
                0.00023050663212496322,
                0.0001584362920800941,
                0.0009110511942416997,
                1.3007130007042183e-05,
                5.8291251620035695e-05,
                0.0002611904314870161,
                1.7603427934206038e-06
            ],
            [
                4.222833947498071e-06,
                0.00013982209025021358,
                4.539786322163531e-05,
                2.7535694350223355e-05,
                1.892515500663531e-05,
                1.8925143726890553e-05,
                1.3007125357378736e-05,
                2.7535700923478902e-05,
                1.6701423833011596e-05,
                7.484626294855732e-05
            ],
            [
                0.00037998457408299494,
                0.00012339454537815678,
                1.1478768123280277e-05,
                9.610246067494954e-05,
                0.00037998457452518707,
                0.00023050671474278403,
                9.610244859678454e-05,
                0.0004305571350713888,
                2.5612831259923004e-06,
                0.0001398221401234088
            ],
            [
                1.6701415868649062e-05,
                4.222834450328596e-06,
                1.2098658260819256e-06,
                1.7603427924407798e-06,
                5.422220905887864e-06,
                1.7603436291978757e-06,
                3.2887478877249985e-06,
                NaN,
                4.785093922115089e-06,
                3.2887486726945097e-06
            ],
            [
                0.46879062662624377,
                NaN,
                9.422444815409489e-07,
                2.5612819050161955e-06,
                0.7549149758396752,
                NaN,
                0.7772998560157665,
                0.09534945590170513,
                0.9999251538061331,
                1.2098656834723998e-06
            ],
            [
                1.0129993386188227e-05,
                8.939694168225243e-06,
                4.5397852346412016e-05,
                1.0129988563546333e-05,
                7.484620038013827e-05,
                5.829127239924071e-05,
                6.605216820750714e-05,
                4.006368741175151e-05,
                8.939696302051047e-06,
                0.00012339460406817764
            ],
            [
                1.7603438428188364e-06,
                5.422219615395428e-06,
                4.785096205260165e-06,
                8.481102109753085e-05,
                6.962256244566128e-06,
                7.484623611103256e-05,
                0.9984988178542439,
                3.726640615664282e-06,
                5.422218322664422e-06,
                2.2603234891147668e-06
            ],
            [
                6.144174600985344e-06,
                2.753570421481532e-05,
                4.45085104982401e-07,
                2.561283126639892e-06,
                2.4300246521474893e-05,
                1.370957533462248e-06,
                1.7603434230921292e-06,
                3.726639727750306e-06,
                2.7535691096552598e-05,
                1.3007130014636887e-05
            ],
            [
                0.9999687980812412,
                NaN,
                0.9998911030915769,
                NaN,
                0.9998601778606415,
                0.9999724643185763,
                0.9999646437325314,
                3.2887494567070593e-06,
                NaN,
                0.9465966660571644
            ],
            [
                0.00017952800896570056,
                6.1441775312976045e-06,
                7.338208055302923e-07,
                8.93969310662177e-06,
                1.6701425824733193e-05,
                8.939698433584547e-06,
                4.222834954561012e-06,
                1.4738980213020151e-05,
                NaN,
                1.3007123812057577e-05
            ],
            [
                0.999948557804806,
                0.9999599363094765,
                0.7310585669110202,
                0.9999832985801865,
                0.8175744806385543,
                0.999985261011028,
                0.2942149783515162,
                0.9149009480320036,
                0.9999930377404338,
                0.9999785550515939
            ],
            [
                0.0,
                4.785093923116048e-06,
                1.8925150486764003e-05,
                5.82912792416722e-05,
                5.1442224410462374e-05,
                NaN,
                NaN,
                1.994730196992497e-06,
                NaN,
                3.120190020068305e-05
            ],
            [
                2.9023126765777146e-06,
                7.889263525103816e-06,
                1.300713001414004e-05,
                9.610241484924595e-05,
                2.753569436805389e-05,
                NaN,
                6.605215250517728e-05,
                1.7603434229576435e-06,
                7.484625400997517e-05,
                7.889263523869684e-06
            ],
            [
                0.0002959572036523733,
                4.006370173834246e-05,
                1.9947299592570416e-06,
                2.9023133687786197e-06,
                2.1444953525877587e-05,
                1.0129989769962063e-05,
                1.4738981971813965e-05,
                0.00010889694821346693,
                4.539785238142359e-05,
                4.222832939870796e-06
            ],
            [
                0.0,
                9.422445937683077e-07,
                NaN,
                0.22270013882530884,
                0.9399133555065331,
                0.3208213073183839,
                NaN,
                NaN,
                NaN,
                0.9999687980737588
            ],
            [
                0.00013982207404015745,
                8.315277302588544e-07,
                2.9023133689317184e-06,
                1.4738980213985297e-05,
                1.670141985245514e-05,
                1.5534979396815448e-06,
                2.430023782222529e-05,
                2.902312676941983e-06,
                NaN,
                2.9023123310580418e-06
            ],
            [
                0.8354835350552604,
                0.9999251538003773,
                0.9999832985781667,
                7.484626262673566e-05,
                0.9996646500128009,
                0.9999417087345831,
                1.5534981247144094e-06,
                NaN,
                0.6791787056691698,
                0.6513548646660542
            ],
            [
                3.1201907645920996e-05,
                8.481107163963022e-05,
                1.370957696715851e-06,
                3.5356263314938686e-05,
                2.260324567087388e-06,
                1.7603432126700574e-06,
                1.0677032517015483e-06,
                9.610240342690799e-05,
                1.6701421840804172e-05,
                3.927861534179377e-07
            ],
            [
                1.3709572066558505e-06,
                9.422442567152048e-07,
                9.422449306655632e-07,
                0.10669059181535787,
                NaN,
                0.9999852610181885,
                0.40733340004593027,
                NaN,
                0.24508502416032488,
                0.5926665999540698
            ],
            [
                8.481107163160885e-05,
                0.0004878572291623923,
                0.0007096702628801035,
                0.00023050679557654998,
                NaN,
                8.481103112301959e-05,
                6.60521604084826e-05,
                6.605217612378949e-05,
                0.00020342706960015957,
                0.0011695104646883914
            ],
            [
                2.2603234890695403e-06,
                0.9997388097324451,
                3.726640172337686e-06,
                0.02595735418376027,
                5.043475885576967e-07,
                1.3709572066982443e-06,
                0.022977367233847506,
                1.9947306723419413e-06,
                5.71500310747347e-07,
                1.3709578604308174e-06
            ],
            [
                8.481106150677358e-05,
                4.539786864000808e-05,
                3.726640616423495e-06,
                6.962258737472841e-06,
                1.6701421843356024e-05,
                1.3007123811797321e-05,
                7.484623608435025e-05,
                7.889263526093993e-06,
                1.0129994602222992e-05,
                2.9023109468548636e-06
            ],
            [
                3.927863875245609e-07,
                0.9999687980886459,
                1.7603425827200299e-06,
                7.33820980391927e-07,
                2.902313022015599e-06,
                7.338209802250756e-07,
                5.715005831610828e-07,
                0.26894141551050293,
                0.004070137714008535,
                1.3709572065286691e-06
            ],
            [
                0.9999910602994334,
                0.9999938558224701,
                0.651354857898194,
                0.9999599362891085,
                0.999981074842744,
                0.999841563835014,
                0.9999339478659522,
                0.9999832985841378,
                0.8354835391516132,
                0.9999885212291787
            ],
            [
                3.120191874590325e-05,
                0.00013982202394727125,
                NaN,
                NaN,
                NaN,
                3.1201903906162046e-05,
                4.006370648569653e-05,
                7.484624492545807e-05,
                NaN,
                6.962257902054487e-06
            ],
            [
                1.0677033790475986e-06,
                NaN,
                0.2450850131323717,
                NaN,
                2.260324835670955e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                0.9999945777818864,
                0.999986992873094,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999952149055061
            ],
            [
                4.006370650070828e-05,
                9.422448184681581e-07,
                9.422450431732037e-07,
                4.0063692140011286e-05,
                5.829124465589078e-05,
                6.144174576464938e-06,
                7.88926352599354e-06,
                1.0677028699955933e-06,
                7.889260703462123e-06,
                7.889261643899223e-06
            ],
            [
                0.0010322311216255545,
                7.484620042805751e-05,
                1.0677033790320615e-06,
                0.0006263341660157311,
                0.00029595709787561686,
                8.481107161556607e-05,
                8.481105137391814e-05,
                0.001325022681868549,
                1.473898548194914e-05,
                4.5397890183368146e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                0.00023050674269790332,
                9.610243771350267e-05,
                0.0002959572044618015,
                9.610242616880727e-05,
                2.7535687763846918e-05,
                3.4663262104892865e-07,
                3.120191507027519e-05,
                0.00218271608885812,
                5.04347648566371e-07,
                5.14421952570998e-05
            ],
            [
                1.300712380408432e-05,
                1.6701425825857226e-05,
                0.00012339453041524914,
                1.1478772229050293e-05,
                2.753568124458694e-05,
                1.4738983726908257e-05,
                0.00012339454506575626,
                5.4222202621161125e-06,
                1.0677032515947306e-06,
                NaN
            ],
            [
                0.9840936108248171,
                0.9999417087556092,
                0.9999945777810313,
                0.9999687980774927,
                0.9999930377404453,
                NaN,
                NaN,
                0.9999980052698179,
                NaN,
                0.999986992869994
            ],
            [
                1.0129990979031306e-05,
                3.535624225110421e-05,
                2.753570090334442e-05,
                NaN,
                6.605213672211696e-05,
                1.0129995797989117e-05,
                1.0129990970260453e-05,
                2.753568780461672e-05,
                5.422221554581283e-06,
                9.610246075745164e-05
            ],
            [
                1.0129992180674948e-05,
                0.00010889696109138246,
                2.1444945856418342e-05,
                3.535626335108113e-05,
                3.726640615840528e-06,
                3.535626334799422e-05,
                0.000203426899920463,
                1.4738981968864903e-05,
                3.2887494572514376e-06,
                2.1444945856964448e-05
            ],
            [
                5.422218965873757e-06,
                1.670141584741401e-05,
                3.535625483162694e-05,
                1.4738980188435699e-05,
                8.315284240879503e-07,
                NaN,
                2.430023200831783e-05,
                9.610242628137363e-05,
                2.561282515028964e-06,
                NaN
            ],
            [
                NaN,
                NaN,
                0.9999921107396847,
                0.9999885212265511,
                0.5621765008857981,
                0.7310585727705126,
                0.8933094003735664,
                NaN,
                NaN,
                0.07585818785594478
            ],
            [
                1.6701423829669885e-05,
                7.484626272747509e-05,
                2.7535700934898458e-05,
                0.00012339463372649704,
                1.9947294833417385e-06,
                5.829127930740772e-05,
                0.00023050668765958865,
                0.000911051048700581,
                1.8925143719695944e-05,
                5.829127943463777e-05
            ],
            [
                1.760344051944157e-06,
                NaN,
                0.007577240462471653,
                9.610242640512673e-05,
                5.422220907554695e-06,
                0.0015011821543065118,
                0.0005527787233325964,
                2.2603242964974424e-06,
                0.00017952802858448887,
                0.00026119024206564505
            ],
            [
                NaN,
                0.9999885212305096,
                0.9999957771681132,
                0.9579122725349515,
                0.9999982396559475,
                0.9999962733602722,
                0.9999962733602719,
                NaN,
                0.9999756997534868,
                0.9999251537370873
            ],
            [
                0.0011695103716714338,
                0.00020342689913319638,
                9.610244911137376e-05,
                2.1444950951785568e-05,
                0.0002611904304838614,
                9.610243731497575e-05,
                1.4738987239295859e-05,
                NaN,
                0.0002305066483225609,
                3.5356246475137275e-05
            ],
            [
                1.2098656834613962e-06,
                0.9980732657490397,
                0.7981867777396212,
                0.46879062662624377,
                0.9999810748495619,
                0.9999417087084993,
                0.9999832985762038,
                0.9997694933121727,
                0.9999852610197986,
                0.29421498454004374
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                0.999981074842774,
                NaN,
                0.9999852610163005
            ],
            [
                0.05340333130637379,
                0.9579122753885635,
                0.9999646437493283,
                0.9999832985801618,
                0.5,
                3.2887494561507166e-06,
                0.9999977396762475,
                0.9999810748569886,
                0.999968798080428,
                0.9999810748427385
            ],
            [
                1.4738988999940381e-05,
                2.7535694378772238e-05,
                5.422218968714274e-06,
                1.2098653948356656e-06,
                3.726638395215427e-06,
                3.726640615921872e-06,
                7.88926258343236e-06,
                1.8925150490206403e-05,
                4.785096776251149e-06,
                1.0677027427068966e-06
            ],
            [
                1.9947297213492663e-06,
                1.1478766754377407e-05,
                0.00015843615940515745,
                0.0,
                5.422220904921299e-06,
                2.260323758882316e-06,
                4.006370172712009e-05,
                6.605215242684585e-05,
                4.5397884837823535e-05,
                5.715003107353922e-07
            ],
            [
                0.9999852610110228,
                NaN,
                0.9149009497722477,
                0.9999898700041928,
                0.9999938558261383,
                NaN,
                0.999972464308996,
                0.9999952149055057,
                0.9999984465028019,
                0.952574122783325
            ],
            [
                5.14422258772351e-05,
                9.61024149897791e-05,
                5.8291265503797524e-05,
                6.144173868781898e-06,
                6.144176798255599e-06,
                7.889261644501938e-06,
                5.829129330398681e-05,
                1.8925148238291944e-05,
                2.430024072471526e-05,
                5.829126553136402e-05
            ],
            [
                2.7535684417518326e-05,
                1.1478768123280277e-05,
                3.726639728184142e-06,
                1.3007128458810347e-05,
                4.006370646879011e-05,
                5.422218969128516e-06,
                0.00010889694808591575,
                7.88926257993087e-06,
                3.288747887521604e-06,
                1.6701427804546374e-05
            ],
            [
                0.00026119033798085854,
                0.9999962733611614,
                0.999860177943533,
                0.1480472055495773,
                3.535626752263942e-05,
                0.9999930377412607,
                0.9999945777823552,
                0.5926665999540698,
                0.8807970654616711,
                0.3208213008246071
            ],
            [
                0.9999724643089616,
                0.9998911030778981,
                0.4378234991142019,
                0.9999910603004999,
                0.0,
                0.9999546021205761,
                0.9978172836834567,
                0.9995694428678972,
                0.9982992773879464,
                0.9999957771645445
            ],
            [
                7.88926634305847e-06,
                2.7535704212311033e-05,
                1.0129992182112188e-05,
                0.0005527786642580407,
                1.892515048042999e-05,
                2.7535704227537108e-05,
                0.00012339457470790277,
                5.422217030209884e-06,
                0.0001398220572319913,
                0.00012339461887489388
            ],
            [
                NaN,
                NaN,
                NaN,
                0.9999980052698029,
                NaN,
                NaN,
                0.999996273362049,
                NaN,
                NaN,
                0.9999990577551815
            ],
            [
                0.9999952149032237,
                0.9999952149055068,
                0.6791787056691698,
                0.9999910603036986,
                NaN,
                0.9999756997592771,
                NaN,
                0.9999756997563826,
                0.9046505280315008,
                0.9999910603047643
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                0.999964643759056,
                NaN,
                0.9999869928700058
            ],
            [
                0.00017952790183686286,
                0.00015843621666364007,
                0.00012339460396224868,
                5.144221362094481e-05,
                0.0005527787339126344,
                7.338209804853638e-07,
                5.14422075117015e-05,
                4.5397884859458064e-05,
                1.2098659719122375e-06,
                5.144219525429276e-05
            ],
            [
                0.9999930377412624,
                0.29421497216298875,
                0.9840936099209598,
                0.5312093733737562,
                NaN,
                0.9999251537574341,
                0.6513548646660543,
                0.9399133552961427,
                9.610240282771945e-05,
                1.9947306725451314e-06
            ],
            [
                1.7603425835749741e-06,
                0.0031726831944624855,
                5.144223194306502e-05,
                1.670142781636389e-05,
                2.2603237541499847e-06,
                0.00023050676858724428,
                5.144222588771473e-05,
                0.0001233946334266641,
                9.610242624851265e-05,
                1.6701425822059825e-05
            ],
            [
                5.422217018936588e-06,
                6.475950297421001e-07,
                6.605217615887045e-05,
                7.338213300645984e-07,
                8.315278293407441e-07,
                NaN,
                1.2098658275938276e-06,
                NaN,
                3.466326210993703e-07,
                5.829126545120912e-05
            ],
            [
                5.144219496498053e-05,
                NaN,
                0.999820472042167,
                NaN,
                0.9999756997679958,
                0.9997965730053234,
                0.9998911031046822,
                NaN,
                6.962258737650141e-06,
                NaN
            ],
            [
                0.9997694932308292,
                0.18242552158390102,
                0.7057850154599563,
                0.08509903920620716,
                NaN,
                0.5621765008857981,
                0.1480471999111614,
                0.05340332678672523,
                0.4687906266262437,
                0.9999485577819223
            ],
            [
                0.0007096702803823703,
                5.422218968714274e-06,
                7.338207180534397e-07,
                0.4073334000459302,
                0.18242551936144574,
                0.008577487425363102,
                1.2098656833865714e-06,
                0.9998601778938042,
                0.9999945777791296,
                0.9999546021382457
            ],
            [
                0.4378234991142019,
                0.9999251538005832,
                0.9999646437408855,
                0.9999938558263635,
                NaN,
                0.9999898700091094,
                NaN,
                0.9999687980751857,
                NaN,
                NaN
            ],
            [
                0.40733340004593027,
                0.34864513533394575,
                0.40733340004593027,
                0.9999756997650667,
                0.9999756997681591,
                0.9999832985721885,
                0.999972464309347,
                0.7549149978955811,
                0.042087725062006816,
                0.9999756997679619
            ],
            [
                0.9999852610198633,
                0.99979657303447,
                0.9999945777817068,
                0.9999417087277793,
                0.9241418252018903,
                0.9995121428260144,
                0.7057850216484838,
                0.9999038975903903,
                0.37754066879814546,
                0.9999687980818369
            ],
            [
                3.726638388802786e-06,
                4.22283243366838e-06,
                8.939698429893283e-06,
                1.3709576967781945e-06,
                8.481105135664132e-05,
                1.8925143715978147e-05,
                4.0063692016711e-05,
                5.422217676200406e-06,
                5.422220261948442e-06,
                4.0063692167994334e-05
            ],
            [
                6.605212100874168e-05,
                0.00015843625368722246,
                0.22270013882530887,
                0.00012339458870847818,
                2.561283431189828e-06,
                5.422219615582823e-06,
                5.42221767672807e-06,
                0.02033235352816842,
                0.6513548646660543,
                0.002182716652239547
            ],
            [
                0.9999910603036988,
                0.9999970976873237,
                0.9999945777790915,
                NaN,
                NaN,
                NaN,
                0.9999962733611607,
                0.999512142847756,
                0.9999962733620488,
                0.9999962733598277
            ],
            [
                9.610240339544534e-05,
                9.610238046617398e-05,
                6.605216037292109e-05,
                4.5397890270732005e-05,
                0.00020342702142888108,
                5.144223202241074e-05,
                0.0002611903359213524,
                0.7981867825403177,
                0.0001584362730323416,
                8.481108070255893e-05
            ],
            [
                8.481103117361599e-05,
                0.00017952794410956967,
                1.4738976697631541e-05,
                0.00033535002750403534,
                2.561282515886208e-06,
                1.14787681240737e-05,
                5.8291293326888225e-05,
                0.0005527785459159993,
                2.7535684530912436e-05,
                NaN
            ],
            [
                1.4738976682001517e-05,
                2.9023116325988226e-06,
                0.00043055708438082837,
                6.605213669905004e-05,
                2.7535687799708318e-05,
                NaN,
                8.481106146543261e-05,
                4.22283191464601e-06,
                1.6701427797619914e-05,
                4.539787391916088e-05
            ]
        ]
    },
    {
        "q_id": "8586_mmlu_math",
        "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": [
            [
                0.999999554914895,
                0.9999996940976636,
                0.999999554914895,
                0.999999057755743,
                0.9999996072136125,
                0.999999554914842,
                0.9999977396762411,
                0.9999996940978825,
                0.9999992661787571,
                0.9999997300421581
            ],
            [
                0.9999996940977731,
                0.9999995549151072,
                0.9999986290431201,
                0.9999996072136592,
                0.9999991684719723,
                0.999999495652652,
                0.999999789756684,
                0.9999994956524114,
                0.9999994956523514,
                0.9999997617631468
            ],
            [
                0.9995694428656176,
                0.9997694933410333,
                0.9999646437535755,
                0.9998766054696404,
                0.9999599362983018,
                0.9998415637272535,
                0.9999885212305071,
                0.9999785550464829,
                0.9999546021259818,
                0.9999417087206345
            ],
            [
                0.9999994956527121,
                0.9999990577555185,
                0.999999653367379,
                0.999997097688707,
                0.9999992661791945,
                0.9999995549148419,
                0.9999997617630048,
                0.9999994284995529,
                0.9999984465016899,
                0.9999994284997573
            ],
            [
                0.9999986290421394,
                0.9999984465018751,
                0.9999986290427932,
                0.9999996940976636,
                0.9999986290429566,
                0.9999991684718732,
                0.9999995549150542,
                0.9999980052707542,
                0.9999957771670592,
                0.999999352405279
            ],
            [
                0.9999998724809419,
                0.9999990577557432,
                0.9999986290424664,
                0.9999996533674615,
                0.9999998555019618,
                0.9999993524050473,
                0.999999428499553,
                0.9999984465028011,
                0.9999996072137061,
                0.9999996533673375
            ],
            [
                0.9999994284997574,
                0.9999996533672136,
                0.9999996072139402,
                0.9999992661791945,
                0.9999991684717741,
                0.9999996940976636,
                0.9999986290426298,
                0.9999993524051246,
                0.9999993524052789,
                0.9999998144608097
            ],
            [
                0.9999993524053562,
                0.9999994956523514,
                0.9999980052707541,
                0.9999996533672549,
                0.999999554914895,
                0.9999974387187053,
                0.9999991684717742,
                0.9999997300422225,
                0.999999855502048,
                0.9999996940977366
            ],
            [
                0.999999554914895,
                0.999999266179107,
                0.9999997617631184,
                0.9999990577550691,
                0.9999991684720715,
                0.9999980052705163,
                0.9999995549148419,
                0.9999996940976271,
                0.9999996072137998,
                0.9999989322970027
            ],
            [
                0.9999996533672549,
                0.9999970976883611,
                0.9999992661787571,
                0.999999554914895,
                0.9999991684720715,
                0.9999994956524716,
                0.9999990577549568,
                0.9999996072136592,
                0.9999997617630617,
                0.9999997300420939
            ],
            [
                0.9999997617631752,
                0.9999993524051246,
                0.9999996533672962,
                0.999999730042126,
                0.9999991684715759,
                0.9999997897566589,
                0.999999694097773,
                0.9999994284994848,
                0.999999653367379,
                0.9999986290421395
            ],
            [
                0.9999998724809571,
                0.9999998144609645,
                0.9999996072139402,
                0.9999989322966208,
                0.9999996533674614,
                0.9999997300421581,
                0.9999998362623137,
                0.9999998362623137,
                0.9999998144608097,
                0.999999730042319
            ],
            [
                0.9999984465028011,
                0.9999993524051246,
                0.9999980052702787,
                0.9999989322968755,
                0.9999996072137529,
                0.9999967112521113,
                0.9999967112505429,
                0.9999982396569966,
                0.9999992661788445,
                0.9999982396572065
            ],
            [
                0.9999998874647842,
                0.9999990577549569,
                0.9999997897565587,
                0.9999984465024306,
                0.9999994284994168,
                0.9999997617631183,
                0.99999893229713,
                0.9999997897567341,
                0.9999996533674615,
                0.9999994956527721
            ],
            [
                0.9999994956527121,
                0.9999996940978825,
                0.9999994956525918,
                0.9999997300422869,
                0.9999995549151072,
                0.9999994956523514,
                0.9999986290431201,
                0.9999994956523512,
                0.999999554914895,
                0.9999984465018752
            ],
            [
                0.999999554914895,
                0.9999990577554062,
                0.9999977396762412,
                0.9999982396561573,
                0.9999984465018752,
                0.9999984465024307,
                0.9999996533672136,
                0.9999957771670593,
                0.9999986290432836,
                0.9999993524052018
            ],
            [
                0.9999996533673788,
                0.999999814460876,
                0.9999993524054334,
                0.9999995549150542,
                0.9999998555020306,
                0.9999996533674615,
                0.9999984465020603,
                0.9999998555019962,
                0.9999995549147359,
                0.9999997617629764
            ],
            [
                0.9999989322970027,
                0.9999991684717742,
                0.9999996533674202,
                0.9999982396567868,
                0.9999987901340281,
                0.9999992661787571,
                0.9999994956523514,
                0.9999977396762412,
                0.9999991684720715,
                0.9999994284996211
            ],
            [
                0.9999997897567341,
                0.9999997300422547,
                0.9999994956524716,
                0.9999993524050474,
                0.9999996072138465,
                0.9999994956524114,
                0.9999990577551815,
                0.9999997897566089,
                0.9999984465015048,
                0.9999997617631469
            ],
            [
                3.7266388397382506e-06,
                2.2603237589028734e-06,
                3.7266383954560706e-06,
                6.1441767990323395e-06,
                1.209865827740176e-06,
                1.2098655392811161e-06,
                6.962257908196617e-06,
                7.889259763857458e-06,
                5.4222215550004564e-06,
                5.422220262555012e-06
            ],
            [
                0.9999989322972573,
                0.9999996072138465,
                0.9999991684722698,
                0.9999984465020604,
                0.9999994956525917,
                0.9999982396569966,
                0.9999996072137061,
                0.9999996940976636,
                0.9999994284994167,
                0.9999997300423191
            ],
            [
                0.9999987901337396,
                0.9999991684718732,
                0.9999996533672549,
                0.9999998362622943,
                0.999998932297512,
                0.9999997617629764,
                0.9999991684715759,
                0.9999967112501508,
                0.9999990577552939,
                0.999999694097773
            ],
            [
                0.9999987901341723,
                0.9999982396572065,
                0.9999991684715759,
                0.9999996072138934,
                0.9999992661791945,
                0.9999970976869771,
                0.9999996072138934,
                0.9999990577552939,
                0.9999990577554062,
                0.9999977396762411
            ],
            [
                0.9999984465022455,
                0.9999994284997574,
                0.9999997300420937,
                0.9999989322970028,
                0.9999980052693275,
                0.9999977396762413,
                0.9999998362623332,
                0.999998629042303,
                0.9999984465026159,
                0.9999980052705163
            ],
            [
                0.9999980052707541,
                0.9999994956524716,
                0.9999989322973845,
                0.9999967112497585,
                0.999999694097846,
                0.999998446502801,
                0.9999986290427931,
                0.9999997300421581,
                0.9999990577556307,
                0.999998790134605
            ],
            [
                0.9999962733607168,
                0.9999993524052018,
                0.999998446502801,
                0.9999990577554061,
                0.9999996533673788,
                0.9999992661790195,
                0.999999266178932,
                0.9999990577554062,
                0.9999996940978461,
                0.9999994956524715
            ],
            [
                7.889260704631679e-06,
                4.785092783210732e-06,
                3.288749849368453e-06,
                4.222832437497486e-06,
                6.96225956921868e-06,
                9.422447062240614e-07,
                5.42222090882208e-06,
                3.288747889229516e-06,
                3.72664061671159e-06,
                1.6701425822059825e-05
            ],
            [
                0.999999352405279,
                0.9999996533672962,
                0.9999997617631752,
                0.9999996940977731,
                0.9999992661791944,
                0.9999994956524716,
                0.999999694097773,
                0.999999814460876,
                0.9999993524049702,
                0.999999352404893
            ],
            [
                0.9999982396563671,
                0.9999997617631183,
                0.999999855502048,
                0.9999996940976636,
                0.9999997617629763,
                0.9999987901341723,
                0.999999653367379,
                0.9999994956524114,
                0.999999730042126,
                0.9999995549151073
            ],
            [
                4.22283394786293e-06,
                7.88925976397226e-06,
                2.1444956081636468e-05,
                6.962255419380732e-06,
                2.5612828212676906e-06,
                1.147876538789672e-05,
                1.9947290081286418e-06,
                1.760344052714248e-06,
                1.3709570434122812e-06,
                6.144173136952939e-06
            ],
            [
                0.9999996533673788,
                0.9999982396572065,
                0.9999996940978825,
                0.999999554914842,
                0.9999997897566089,
                0.9999995549151072,
                0.9999970976880149,
                0.9999984465018751,
                0.9999977396762411,
                0.999999352405279
            ],
            [
                0.999999352405279,
                0.9999989322968754,
                0.9999989322970028,
                0.9999992661792819,
                0.999998005269803,
                0.9999980052700408,
                0.9999980052707542,
                0.9999990577552939,
                0.9999993524054334,
                0.9999987901346049
            ],
            [
                3.2887498494551953e-06,
                2.2603251062147097e-06,
                4.785092783371756e-06,
                3.2887502415243994e-06,
                2.2603251062147097e-06,
                3.7266379513434106e-06,
                1.2098653950606901e-06,
                1.2098661161861e-06,
                1.553497754583709e-06,
                1.2098653950606901e-06
            ],
            [
                3.288750633545794e-06,
                2.902312677060767e-06,
                1.3007125363293615e-05,
                1.3709573702566696e-06,
                3.726637951170554e-06,
                1.553497199007048e-06,
                1.7603440527046419e-06,
                1.2098662604247682e-06,
                7.889261644631091e-06,
                7.338208055613267e-07
            ],
            [
                0.9999990577555185,
                0.9999998874648917,
                0.9999987901338838,
                0.9999994956527721,
                0.9999996072136125,
                0.9999989322967482,
                0.999999653367379,
                0.9999982396559474,
                0.9999984465020604,
                0.9999993524051246
            ],
            [
                5.422218322940583e-06,
                8.93969630388855e-06,
                3.288748673295719e-06,
                3.726641061027928e-06,
                2.2603237589542675e-06,
                2.5612819053166966e-06,
                8.315282259009745e-07,
                3.288747889229516e-06,
                3.7266406167827664e-06,
                1.9947299592824403e-06
            ],
            [
                0.9999997300421903,
                0.9999987901344607,
                0.9999984465022455,
                0.9999970976866311,
                0.9999992661790195,
                0.9999993524050474,
                0.9999996940978825,
                0.9999996072137061,
                0.9999993524050474,
                0.9999987901343166
            ],
            [
                0.9999996072138465,
                0.999999814460854,
                0.9999991684716749,
                0.9999996072138934,
                0.9999967112517191,
                0.9999986290431201,
                0.9999987901337396,
                0.9999997300420939,
                0.9999997897565587,
                0.9999996533674615
            ],
            [
                0.999999057755743,
                0.9999980052698031,
                0.9999996072139402,
                0.999999266179107,
                0.9999997897565838,
                0.999998005270041,
                0.9999992661791944,
                0.9999987901344607,
                0.9999995549150541,
                0.9999998144609645
            ],
            [
                0.9999756997621686,
                0.998674977700942,
                0.999968798081217,
                0.999876605410656,
                0.9999785550439235,
                0.9997388095985924,
                0.9998911031167045,
                0.9999546021314363,
                0.9975273770931765,
                0.9996200155218616
            ],
            [
                0.9999996072136125,
                0.9999996072136592,
                0.9999996533673375,
                0.9999991684721706,
                0.9999997300422225,
                0.9999997300422547,
                0.9999970976873235,
                0.9999996533674615,
                0.99999862904312,
                0.9999995549148419
            ],
            [
                1.0677027427569065e-06,
                5.4222170304318e-06,
                5.422218969601935e-06,
                3.288750241473551e-06,
                5.4222215552470286e-06,
                3.7266388396975786e-06,
                2.5612812947077304e-06,
                3.7266388397382506e-06,
                3.7266406167827664e-06,
                4.78509563550957e-06
            ],
            [
                0.9999996940977002,
                0.9999997300422547,
                0.9999990577551815,
                0.9999997617631184,
                0.9999996072138934,
                0.9999989322973846,
                0.9999997617630048,
                0.9999982396561573,
                0.999999814460876,
                0.9999998144608317
            ],
            [
                1.0677028699043128e-06,
                1.9947301968963442e-06,
                3.2887478891487563e-06,
                1.9947297213492663e-06,
                6.475951069896949e-07,
                2.2603240282243575e-06,
                1.5534984952662413e-06,
                1.7603438427243761e-06,
                3.726639283901856e-06,
                2.902313022984344e-06
            ],
            [
                2.5612828213690224e-06,
                4.222833947932061e-06,
                4.785096776303374e-06,
                1.3709575336947905e-06,
                3.7266383954560706e-06,
                4.222834954687752e-06,
                1.7603434231705793e-06,
                7.889260704308795e-06,
                1.0677026154774503e-06,
                2.5612816000331606e-06
            ],
            [
                0.999997438717484,
                0.9999993524052789,
                0.9999970976890532,
                0.9999990577549568,
                0.9999957771670593,
                0.9999996533675028,
                0.9999984465024306,
                0.9999994284996211,
                0.9999990577549568,
                0.9999990577555186
            ],
            [
                0.9999987901337396,
                0.9999989322973846,
                0.9999994284996893,
                0.9999996533673788,
                0.9999990577557432,
                0.9999997617630048,
                0.9999993524052018,
                0.9999995549149481,
                0.9999994284993486,
                0.9999995549151073
            ],
            [
                0.9999986290426298,
                0.9999994284992805,
                0.9999990577551815,
                0.9999980052705164,
                0.9999997300420937,
                0.9999989322970028,
                0.9999989322968754,
                0.9999993524054335,
                0.9999996533674201,
                0.9999993524052019
            ],
            [
                0.9999992661792819,
                0.9999987901338838,
                0.9999992661789321,
                0.9999977396759717,
                0.9999992661790196,
                0.9999993524052019,
                0.9999989322967482,
                0.999998932296621,
                0.9999993524049702,
                0.999999057755743
            ],
            [
                0.9999996533673375,
                0.9999996533674614,
                0.9999996940976636,
                0.9999997897565587,
                0.999999266178932,
                0.9999990577550693,
                0.9999997300422225,
                0.9999991684718732,
                0.999999554914789,
                0.9999990577556308
            ],
            [
                0.9999999317439465,
                0.9999990577555185,
                0.9999991684717742,
                0.9999997897566589,
                0.9999995549147359,
                0.9999992661786696,
                0.9999994284994848,
                0.9999994284992805,
                0.9999994284995529,
                0.9999996533672136
            ],
            [
                0.999999653367379,
                0.9999997300422547,
                0.9999997617631752,
                0.9999997617631752,
                0.9999996940978095,
                0.9999997897567341,
                0.9999980052700408,
                0.9999992661789321,
                0.9999995549149481,
                0.999999694097846
            ],
            [
                0.9999990577551815,
                0.9999986290432835,
                0.9999998362623332,
                0.9999996533674201,
                0.9999990577555185,
                0.9999996072138465,
                0.9999970976873231,
                0.9999994956525317,
                0.9999997617630049,
                0.9999996072136125
            ],
            [
                0.9999986290427931,
                0.9999992661786696,
                0.9999994956524114,
                0.9999986290431201,
                0.999999352405279,
                0.9999986290423029,
                0.9999991684716749,
                0.9999984465024306,
                0.9999997617630616,
                0.9999987901341724
            ],
            [
                0.9991959141480825,
                0.9999038975507067,
                0.9999038975850585,
                0.9999151889586775,
                0.9999485577924977,
                0.999975699753477,
                0.9999785550464746,
                0.9999038976194401,
                0.9998601779595803,
                0.9999756997679594
            ],
            [
                0.9999982396572065,
                0.9999996940977001,
                0.999999730042319,
                0.9999957771655491,
                0.999999266179107,
                0.9999997300421581,
                0.9999990577554061,
                0.9999992661791944,
                0.9999995549149481,
                0.9999977396748939
            ],
            [
                0.9999994284996211,
                0.9999984465024306,
                0.9999987901344608,
                0.9999994956525317,
                0.9999982396561572,
                0.9999984465018752,
                0.9999995549150542,
                0.99999893229713,
                0.9999970976883612,
                0.9999996533673788
            ],
            [
                0.9999938558232035,
                0.9999997617631183,
                0.9999995549147889,
                0.9999991684717741,
                0.9999994956525317,
                0.9999991684722697,
                0.9999980052705165,
                0.999999554914895,
                0.999999266178757,
                0.9999994284996891
            ],
            [
                0.9999994956527721,
                0.999998790134028,
                0.9999997617631468,
                0.9999990577550693,
                0.9999987901346049,
                0.9999995549147359,
                0.9999994284996891,
                0.9999997617631469,
                0.9999996072136592,
                0.9999977396757023
            ],
            [
                0.9999970976876691,
                0.9999994284992804,
                0.9999987901344608,
                0.999998629042303,
                0.9999977396762412,
                0.9999967112493668,
                0.9999996072137998,
                0.9999987901337396,
                0.9999980052695653,
                0.9999957771650455
            ],
            [
                0.9999998362622942,
                0.9999980052693275,
                0.9999995549148419,
                0.9999982396559474,
                0.999999057755743,
                0.9999996940977731,
                0.999995214903224,
                0.999999266179107,
                0.9999977396746247,
                0.9999994284993485
            ],
            [
                0.9999996940978825,
                0.9999993524053563,
                0.9999984465018752,
                0.9999997617630332,
                0.9999996072136125,
                0.9999996072138934,
                0.9999994284997573,
                0.9999996072138465,
                0.9999997897567341,
                0.9999997300422547
            ],
            [
                0.9999984465022456,
                0.9999998724809723,
                0.9999997300422547,
                0.9999987901340281,
                0.9999995549149481,
                0.9999984465015047,
                0.9999997300421581,
                0.9999997300421581,
                0.9999980052707541,
                0.9999996072137998
            ],
            [
                0.9999994284997573,
                0.9999989322967483,
                0.999999694097846,
                0.9999995549149481,
                0.9999993524051246,
                0.9999984465018751,
                0.9999991684716749,
                0.999999352405279,
                0.9999987901341724,
                0.9999986290421395
            ],
            [
                0.9999996072137529,
                0.9999991684718733,
                0.9999977396754329,
                0.9999996533672549,
                0.9999995549148419,
                0.9999994956525317,
                0.9999974387187053,
                0.9999992661789321,
                0.9999994956527121,
                0.9999995549147889
            ],
            [
                0.9999997617631183,
                0.9999992661786696,
                0.9999994956525317,
                0.999999814460876,
                0.9999996533674201,
                0.9999987901337398,
                0.999999352405279,
                0.9999994284996891,
                0.9999993524050474,
                0.9999986290431201
            ],
            [
                0.9999996533672549,
                0.9999994284994848,
                0.9999974387184,
                0.9999992661788445,
                0.9999998362623723,
                0.9999989322970028,
                0.9999996533672549,
                0.999999266179107,
                0.9999994284996891,
                0.9999994284997574
            ],
            [
                0.99999893229713,
                0.999999266179107,
                0.9999996072136592,
                0.9999995549148419,
                0.9999995549151072,
                0.9999996072137061,
                0.9999989322970027,
                0.9999996533674201,
                0.9999996072139402,
                0.9999996533672135
            ],
            [
                0.9999982396574163,
                0.9999984465016899,
                0.9999995549147889,
                0.9999989322973846,
                0.9999991684718732,
                0.9999977396759717,
                0.9999989322970027,
                0.9999997617630899,
                0.999999352404893,
                0.9999991684720715
            ],
            [
                0.9999996072137529,
                0.9999996533672962,
                0.99999976176309,
                0.9999998362623722,
                0.9999994956525318,
                0.9999974387168734,
                0.9999990577555185,
                0.9999993524051246,
                0.9999995549147359,
                0.9999993524050473
            ],
            [
                0.999999554914895,
                0.9999994284994849,
                0.9999995549151072,
                0.9999996940977731,
                0.9999993524054335,
                0.9999987901341724,
                0.999999352405279,
                0.999999554914895,
                0.9999986290427931,
                0.9999991684722698
            ],
            [
                0.9999998144609645,
                0.9999987901340281,
                0.99999976176309,
                0.9999996533674615,
                0.9999996533673375,
                0.9999996072136592,
                0.9999994284996893,
                0.9999986290426298,
                0.9999998362622357,
                0.999999352405279
            ],
            [
                3.4663257978638593e-07,
                6.47594566597747e-07,
                2.9023112931688987e-06,
                3.927863875584984e-07,
                2.2603248367173307e-06,
                1.2098652508391807e-06,
                7.338211554783522e-07,
                1.3709567165461505e-06,
                9.422450431732037e-07,
                9.422448185478557e-07
            ],
            [
                0.9999997300421581,
                0.9999992661786696,
                0.9999970976873235,
                0.9999990577552939,
                0.9999994956524114,
                0.9999990577551815,
                0.9999982396569966,
                0.9999991684721706,
                0.9999995549147359,
                0.9999982396572065
            ],
            [
                0.9999997617630616,
                0.9999993524053562,
                0.9999980052702786,
                0.9999996533674614,
                0.9999993524054335,
                0.9999991684718732,
                0.9999991684718732,
                0.9999990577554061,
                0.9999994956525917,
                0.9999994284993486
            ],
            [
                0.9999993524051246,
                0.9999990577556308,
                0.9999996940976272,
                0.9999987901344608,
                0.9999989322972572,
                0.999999266178932,
                0.9999987901344608,
                0.9999994284992805,
                0.9999989322967482,
                0.9999996533672549
            ],
            [
                0.9999970976883612,
                0.9999994284995529,
                0.9999974387165682,
                0.999999168471675,
                0.9999994956526519,
                0.9999986290429567,
                0.9999994956524716,
                0.9999998724809115,
                0.9999987901343166,
                0.9999974387165682
            ],
            [
                1.5534984953298217e-06,
                8.315281267800897e-07,
                3.7266392840781026e-06,
                2.902312331125353e-06,
                1.9947304348703948e-06,
                6.144177531532303e-06,
                1.5534973841895917e-06,
                4.222833947774596e-06,
                1.3709568799823232e-06,
                5.715004470295662e-07
            ],
            [
                3.72664061671159e-06,
                6.962256249682458e-06,
                2.902311639073834e-06,
                6.144172404129392e-06,
                1.9947301970813926e-06,
                1.76034363298589e-06,
                2.260323758939877e-06,
                1.0677031245953668e-06,
                4.222833947820683e-06,
                4.222834451327159e-06
            ],
            [
                0.9999970976880153,
                0.9999989322971299,
                0.9999998362622943,
                0.999999554914895,
                0.9999994284997573,
                0.9999993524052018,
                0.9999991684715759,
                0.9999994956526519,
                0.9999957771655491,
                0.9999996072137061
            ],
            [
                0.9999994956523514,
                0.9999992661792819,
                0.9999990577554062,
                0.9999997897567091,
                0.9999974387171788,
                0.9999997617630049,
                0.9999995549150011,
                0.9999997897566589,
                0.9999994956527121,
                0.9999996072137061
            ],
            [
                0.9999995549150011,
                0.9999992661786696,
                0.9999998555020306,
                0.9999992661786695,
                0.999999730042319,
                0.999999554914895,
                0.9999997617631469,
                0.9999995549151073,
                0.9999997300422225,
                0.9999991684720716
            ],
            [
                1.3007125362820425e-05,
                6.1441767989541075e-06,
                1.3709570433661467e-06,
                9.422442569028803e-07,
                2.902311985079115e-06,
                5.42221767672807e-06,
                3.7266388397721442e-06,
                8.939695238211425e-06,
                1.3709570433979422e-06,
                1.2098658277181688e-06
            ],
            [
                0.9999996940976271,
                0.9999993524052018,
                0.9999977396754328,
                0.9999996072137061,
                0.9999995549151073,
                0.9999997617631468,
                0.9999996072139402,
                0.9999989322967481,
                0.9999994956523512,
                0.9999997300422869
            ],
            [
                0.9999986290429569,
                0.9999967112509353,
                0.9999990577555185,
                0.99999893229713,
                0.9999987901343166,
                0.9999967112509347,
                0.9999952149066468,
                0.9999990577549568,
                0.9999977396754333,
                0.9999998362623332
            ],
            [
                0.9999995549149481,
                0.99999862904312,
                0.9999982396569966,
                0.9999996940978825,
                0.9999997897565838,
                0.9999993524054334,
                0.9999996533673375,
                0.9999996940978095,
                0.9999992661790196,
                0.9999977396748939
            ],
            [
                0.9999997617630332,
                0.9999990577551815,
                0.9999989322967482,
                0.9999996072137529,
                0.9999994956525318,
                0.9999990577556308,
                0.9999990577554062,
                0.999999168471675,
                0.9999996533673788,
                0.9999997897567341
            ],
            [
                0.9999984465015047,
                0.9999984465024307,
                0.9999996533672962,
                0.9999991684715759,
                0.9999984465015047,
                0.99999893229713,
                0.9999987901347492,
                0.9999996533672549,
                0.9999997617630332,
                0.9999996533674614
            ],
            [
                0.9999977396751634,
                0.9999998144608097,
                0.9999998144609423,
                0.9999977396765105,
                0.9999984465015047,
                0.9999993524050474,
                0.9999996072137998,
                0.9999987901347492,
                0.999999057755294,
                0.9999997300421903
            ],
            [
                0.9999997617629763,
                0.9999994956525317,
                0.9999996072138934,
                0.9999992661791071,
                0.999999789756684,
                0.9999995549147359,
                0.9999995549147359,
                0.9999996940977366,
                0.9999974387184001,
                0.9999989322975119
            ],
            [
                0.9999992661788446,
                0.9999991684721706,
                0.9999994956525918,
                0.9999992661790195,
                0.9999994284994848,
                0.9999997617631752,
                0.999999694097773,
                0.9999984465018751,
                0.9999998362622943,
                0.9999998555019962
            ],
            [
                1.2098656835136636e-06,
                2.9023119851266288e-06,
                1.7603436330091044e-06,
                5.4222202623972055e-06,
                1.0129995809763438e-05,
                2.2603248367656408e-06,
                2.902312331081799e-06,
                1.2098662604192665e-06,
                2.2603251062013478e-06,
                2.9023133690637e-06
            ],
            [
                1.5534973842030142e-06,
                1.370957533676711e-06,
                1.760343213322473e-06,
                9.4224425692559e-07,
                1.067703379154416e-06,
                2.2603248367512505e-06,
                1.7603427936263351e-06,
                3.7266383955882547e-06,
                2.5612831266946347e-06,
                2.2603248367358324e-06
            ],
            [
                0.9999997897566589,
                0.9999998144608981,
                0.9999998874647709,
                0.9999993524050474,
                0.99999893229713,
                0.9999998362622943,
                0.9999998555019274,
                0.9999998362622357,
                0.9999996072136125,
                0.9999999123575777
            ],
            [
                6.962257909412379e-06,
                2.753570422573402e-05,
                6.962259568078904e-06,
                4.785093924103951e-06,
                5.4222170304318e-06,
                2.5612812947077304e-06,
                2.1444950957402623e-05,
                4.785092783210732e-06,
                6.9622579086271995e-06,
                1.4738981970312625e-05
            ],
            [
                0.9999992661792819,
                0.9999991684722698,
                0.9999987901344607,
                0.9999996533672135,
                0.99999893229713,
                0.9999997617631183,
                0.9999994956524114,
                0.9999970976876691,
                0.9999994956525317,
                0.9999984465022456
            ],
            [
                0.9999998144609202,
                0.9999991684718733,
                0.9999997897566589,
                0.999999653367379,
                0.9999997617631752,
                0.9999991684721706,
                0.9999998724809571,
                0.9999984465022455,
                0.9999996940976272,
                0.9999997897565838
            ],
            [
                0.9999982396572065,
                0.9999995549148419,
                0.9999996533672549,
                0.9999989322972572,
                0.9999992661792819,
                0.9999987901344607,
                0.9999962733620489,
                0.999997438716568,
                0.9999993524052018,
                0.9999980052695653
            ],
            [
                0.9999998724810026,
                0.9999996940976636,
                0.9999996072137529,
                0.9999980052702786,
                0.999999730042126,
                0.9999996072138465,
                0.9999996533674201,
                0.999999694097846,
                0.9999993524049703,
                0.999999653367379
            ],
            [
                0.9999993524049703,
                0.9999998362622747,
                0.9999996533674202,
                0.9999991684718732,
                0.999999266179107,
                0.9999996940978095,
                0.9999997897567091,
                0.9999994284995529,
                0.9999997897567091,
                0.9999997617630899
            ],
            [
                1.7603425837606927e-06,
                7.338212429537553e-07,
                1.3709578605617394e-06,
                6.144173136952939e-06,
                6.144173869072478e-06,
                6.962258739454786e-06,
                6.1441767990323395e-06,
                8.939693106873817e-06,
                2.5612812947077304e-06,
                4.785095635413826e-06
            ],
            [
                0.9999996072138466,
                0.9999987901338838,
                0.999999168471675,
                0.9999989322972573,
                0.9999996072136593,
                0.9999997300422869,
                0.999999168471576,
                0.999999554914895,
                0.9999994284996893,
                0.9999986290421398
            ],
            [
                0.9999998724809875,
                0.9999997897565838,
                0.9999991684717741,
                0.9999997300421903,
                0.9999993524051246,
                0.999999266178757,
                0.9999997617630616,
                0.9999996940978825,
                0.999999266179107,
                0.9999995549148419
            ],
            [
                7.889262585541864e-06,
                1.7603425837366772e-06,
                3.2887486733420804e-06,
                4.785096205778054e-06,
                2.260325375634003e-06,
                5.422221555192784e-06,
                6.144173869072478e-06,
                1.1478773599102191e-05,
                2.5612819053166966e-06,
                8.939693106329072e-06
            ],
            [
                0.9999997617631468,
                0.9999986290424664,
                0.9999986290431201,
                0.9999984465018751,
                0.9999995549150011,
                0.9999994284992805,
                0.9999996940978825,
                0.9999921107383563,
                0.9999994956525317,
                0.9999987901344607
            ],
            [
                0.9999994956525917,
                0.9999952149049355,
                0.9999986290427935,
                0.9999980052693274,
                0.9999990577549568,
                0.9999994284993485,
                0.9999997300421581,
                0.9999987901340281,
                0.9999993524052018,
                0.9999996940976636
            ],
            [
                0.9999994956525918,
                0.9999996072139402,
                0.9999993524053562,
                0.9999996533672549,
                0.9999986290432834,
                0.99999893229713,
                0.9999994284993485,
                0.9999990577549569,
                0.9999987901346049,
                0.9999996072137061
            ],
            [
                0.9999980052693275,
                0.9999991684718732,
                0.9999994284993485,
                0.9999980052700409,
                0.9999982396567868,
                0.9999998362623528,
                0.9999977396746245,
                0.9999995549150011,
                0.9999989322970028,
                0.9999977396759717
            ],
            [
                0.999999352405279,
                0.9999994284993485,
                0.9999998874647977,
                0.9999991684720715,
                0.9999984465026159,
                0.9999992661791944,
                0.9999996072136125,
                0.999999814460876,
                0.9999996940976636,
                0.9999994284996891
            ],
            [
                0.9999998144608538,
                0.9999989322972573,
                0.9999994284996893,
                0.9999982396561572,
                0.9999993524049702,
                0.9999967112509348,
                0.9999991684721706,
                0.9999982396565769,
                0.9999994284997574,
                0.9999995549151073
            ],
            [
                0.9999989322975118,
                0.9999996072138465,
                0.9999997897567341,
                0.9999995549147358,
                0.9999970976880151,
                0.9999990577554061,
                0.9999991684715758,
                0.9999984465024307,
                0.9999993524054335,
                0.9999996940977366
            ],
            [
                0.9999993524049702,
                0.9999996940976271,
                0.999999266179107,
                0.9999977396759717,
                0.9999995549147359,
                0.9999990577554061,
                0.9999991684722697,
                0.9999998144608097,
                0.9999997897565587,
                0.9999995549148419
            ],
            [
                0.999997097687323,
                0.9999986290429567,
                0.9999990577555185,
                0.9999998144608319,
                0.9999994284996211,
                0.9999996072138934,
                0.9999997897565838,
                0.9999987901337396,
                0.999999352404893,
                0.9999994956527721
            ],
            [
                0.9999995549150011,
                0.9999989322970028,
                0.9999996072136125,
                0.9999996533672549,
                0.9999997897565838,
                0.999999554914842,
                0.9999987901347492,
                0.9999996072137529,
                0.9999997300420937,
                0.9999945777829706
            ],
            [
                2.2603242977555607e-06,
                3.7266379512518984e-06,
                6.144177531532303e-06,
                5.422221555133606e-06,
                1.1478764020560142e-05,
                1.7603425837494853e-06,
                2.5612812947077304e-06,
                8.93969310662177e-06,
                3.288749457383046e-06,
                1.6701419853184244e-05
            ],
            [
                8.939697369004791e-06,
                1.9947290080905435e-06,
                4.785093924047376e-06,
                5.422220908560712e-06,
                1.5534977545243671e-06,
                6.144173869312763e-06,
                4.222833444429485e-06,
                2.5612819053166966e-06,
                4.78509563550957e-06,
                3.7266388397382506e-06
            ],
            [
                0.9999982396572065,
                0.9999998724809115,
                0.9999994956526519,
                0.9999990577554061,
                0.9999957771650456,
                0.9999993524051246,
                0.9999994956523514,
                0.9999977396759717,
                0.9999995549150011,
                0.9999987901338838
            ],
            [
                0.9999997617631184,
                0.999999694097773,
                0.9999992661786695,
                0.9999994284997573,
                0.9999996072137061,
                0.9999987901341724,
                0.9999996072137529,
                0.9999974387184006,
                0.999999352404893,
                0.9999987901347491
            ],
            [
                0.9999994284996211,
                0.9999994956525918,
                0.9999980052702786,
                0.9999994284997573,
                0.9999992661791945,
                0.9999986290429566,
                0.999999352404893,
                0.9999990577555185,
                0.9999997897567342,
                0.999999554914842
            ],
            [
                1.209865539274514e-06,
                2.9023133690425823e-06,
                6.144173869379821e-06,
                6.1441775312976045e-06,
                4.78509563555309e-06,
                6.1441767987808774e-06,
                1.892515726357648e-05,
                1.0129988564430787e-05,
                1.9947290081286418e-06,
                1.1478764019077695e-05
            ],
            [
                0.9999995549147889,
                0.9999994284994167,
                0.9999994956525317,
                0.9999997617630899,
                0.9999997897567091,
                0.9999990577550693,
                0.9999987901340281,
                0.9999991684721706,
                0.9999994284992805,
                0.9999996940977002
            ],
            [
                0.9999974387168734,
                0.9999998555019618,
                0.9999997300422869,
                0.999999168471675,
                0.9999996940978461,
                0.9999991684718733,
                0.9999993524051246,
                0.9999990577556308,
                0.999999730042126,
                0.99999862904312
            ],
            [
                0.9999996533672549,
                0.9999994284996893,
                0.9999996072138934,
                0.9999996940978095,
                0.9999994956523514,
                0.9999993524054334,
                0.9999995549147889,
                0.9999986290429567,
                0.999999653367379,
                0.9999993524049702
            ],
            [
                0.9999986290421394,
                0.9999994956525317,
                0.9999994284993485,
                0.9999977396759718,
                0.9999989322972573,
                0.9999992661786696,
                0.9999982396572065,
                0.9999989322975118,
                0.99999893229713,
                0.99999844650169
            ],
            [
                0.9999998555019274,
                0.9999996072137998,
                0.999999266179282,
                0.9999996072139402,
                0.9999974387168734,
                0.9999992661789321,
                0.9999991684722698,
                0.999999428499553,
                0.9999996072138466,
                0.999999266179107
            ],
            [
                0.9999996072137529,
                0.9999996072137061,
                0.9999990577552939,
                0.9999970976880149,
                0.9999967112497588,
                0.9999945777784452,
                0.9999995549149481,
                0.9999974387168734,
                0.9999989322975118,
                0.9999977396759727
            ],
            [
                0.9999991684720715,
                0.9999977396754328,
                0.9999987901337396,
                0.9999996940976272,
                0.9999992661791945,
                0.9999998362622746,
                0.9999977396754328,
                0.9999980052709919,
                0.9999989322970028,
                0.9999990577556308
            ],
            [
                0.9999996072136125,
                0.999995214905506,
                0.9999982396567868,
                0.9999974387165681,
                0.999999554914895,
                0.999999266179107,
                0.9999974387184,
                0.9999977396762412,
                0.9999994956527121,
                0.9999997897567091
            ]
        ]
    },
    {
        "q_id": "8192_mmlu_math",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            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,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            86,
            87,
            88,
            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,
            118,
            120,
            121,
            122,
            125,
            126,
            127
        ],
        "rewards": [
            [
                4.222832436587256e-06,
                8.939699497042417e-06,
                3.927862470757885e-07,
                2.2603242976404388e-06,
                1.3709572067680694e-06,
                3.5356246487099006e-05,
                6.962253759581752e-06,
                1.670142980112912e-05,
                1.994729245345125e-06,
                2.1444958627097733e-05
            ],
            [
                3.726637951126493e-06,
                4.222831933795376e-06,
                1.0129993393540266e-05,
                5.04347227811786e-07,
                2.561282821106957e-06,
                4.785093353626844e-06,
                2.902313022554084e-06,
                8.939697367264857e-06,
                2.561283126048207e-06,
                6.475951069561228e-07
            ],
            [
                8.481105133072609e-05,
                7.889260702744606e-06,
                4.539787932646994e-05,
                5.144223196776698e-05,
                4.006371123640331e-05,
                6.144177528436518e-06,
                1.012999339031569e-05,
                2.753568122134716e-05,
                3.7266397272757976e-06,
                0.00017952802928189492
            ],
            [
                0.0005527787298928631,
                6.605216809601697e-05,
                6.60521445480501e-05,
                4.222833947029514e-06,
                2.430023203298187e-05,
                NaN,
                4.006367783499403e-05,
                3.2887482807780376e-06,
                0.0002959570967475842,
                3.535626332702904e-05
            ],
            [
                2.561282210530385e-06,
                1.2098659719232413e-06,
                2.2603251058292572e-06,
                1.2098655392354511e-06,
                2.9023123310290063e-06,
                1.7603427933309468e-06,
                2.5612822104977725e-06,
                1.7603427933917854e-06,
                5.422220907426478e-06,
                6.475945665441494e-07
            ],
            [
                2.430024647418002e-05,
                1.1478768116515313e-05,
                4.78509506499309e-06,
                1.3007130013288297e-05,
                4.785094493836935e-06,
                7.88926634687567e-06,
                7.889259763326495e-06,
                5.71500378896509e-07,
                6.144174601097106e-06,
                5.422219615829396e-06
            ],
            [
                1.553498495295912e-06,
                1.0129989770662257e-05,
                6.962255418658875e-06,
                8.939698434820389e-06,
                1.0129989771657269e-05,
                6.962259568889411e-06,
                4.785095064436034e-06,
                8.939700563248534e-06,
                6.962254588433232e-06,
                2.260325106045111e-06
            ],
            [
                1.4738983723235332e-05,
                1.3007126910294786e-05,
                1.8925152733687252e-05,
                1.0129993393540266e-05,
                8.93969523678858e-06,
                1.3007125361755747e-05,
                1.0129992185539456e-05,
                6.962256248314727e-06,
                2.144495351097679e-05,
                1.1478773597870298e-05
            ],
            [
                0.00023050665861122188,
                1.670142383015595e-05,
                1.4738981964307261e-05,
                1.1478768122695653e-05,
                6.605213645060008e-05,
                4.785096775058701e-06,
                8.939696302652706e-06,
                1.892515500560259e-05,
                2.1444943281001e-05,
                6.144174601588856e-06
            ],
            [
                2.1444945853375776e-05,
                6.605216818444021e-05,
                1.3007131562845248e-05,
                4.222834954211514e-06,
                1.1478765386623071e-05,
                2.4300243625614346e-05,
                1.8925150495232307e-05,
                2.4300237832303074e-05,
                0.0007096703175746889,
                6.962257076830902e-06
            ],
            [
                1.8925141470949294e-05,
                1.4738985479214553e-05,
                4.00636825785559e-05,
                4.0063701700885974e-05,
                1.4738985480608657e-05,
                2.4300243626409964e-05,
                3.12019150894581e-05,
                7.889262582341733e-06,
                4.539786858947248e-05,
                4.785092782396909e-06
            ],
            [
                6.96225956837018e-06,
                1.1478768124553928e-05,
                5.422219615069953e-06,
                8.939699500636112e-06,
                6.9622545892184106e-06,
                4.78509449306228e-06,
                1.6701421842566163e-05,
                1.3007126912258525e-05,
                1.4738976696800444e-05,
                2.4300246517938825e-05
            ],
            [
                0.9999687980737803,
                0.9999921107355337,
                0.9999785550413702,
                0.9999724642957752,
                0.9992903295594966,
                0.9999646437577273,
                0.9997694933131117,
                0.9999962733607161,
                0.9999945777797375,
                0.9999852610127649
            ],
            [
                4.006371126117997e-05,
                7.88926164299515e-06,
                4.0063711244273545e-05,
                2.7535684518791692e-05,
                7.484621833189242e-05,
                1.8925145980732218e-05,
                3.12019262340518e-05,
                5.422219614004759e-06,
                1.892514823013346e-05,
                7.484620912050251e-05
            ],
            [
                3.2887486729876365e-06,
                6.144176797283277e-06,
                4.222834449337713e-06,
                1.1478772229781076e-05,
                4.785096775842062e-06,
                7.889264465067689e-06,
                1.0677033791107183e-06,
                7.889263525261671e-06,
                2.9023133686360798e-06,
                3.2887490644495094e-06
            ],
            [
                4.4508489272878447e-07,
                1.994729245722476e-06,
                9.42244256886598e-07,
                3.466325797747213e-07,
                6.475948753606123e-07,
                4.4508505191686215e-07,
                5.04347588554027e-07,
                1.7603432131375548e-06,
                4.45084945805234e-07,
                3.7266392835764795e-06
            ],
            [
                8.939693106182721e-06,
                1.553497754476329e-06,
                3.2887502414436403e-06,
                8.93969736654937e-06,
                5.043476486764593e-07,
                2.4300243620398656e-05,
                6.144174599174813e-06,
                9.422449308566668e-07,
                7.889261642363733e-06,
                1.994730672439908e-06
            ],
            [
                3.7266401719174067e-06,
                1.0677032517015483e-06,
                3.2887478886821466e-06,
                1.1478765374158004e-05,
                1.067702869764479e-06,
                1.892514822937613e-05,
                0.0001795279905667217,
                4.222832433115329e-06,
                1.3007131563176482e-05,
                1.4738981968462759e-05
            ],
            [
                3.535625906479359e-05,
                0.0002305066314408411,
                9.610238051931088e-05,
                0.00017952790062228017,
                0.0004878571732475418,
                2.144495607492721e-05,
                0.0001584362168457497,
                1.4738976691331275e-05,
                5.144222589108318e-05,
                2.4300249420429837e-05
            ],
            [
                0.06008665690650098,
                0.18242552380635635,
                0.754914997895581,
                0.24508501864634824,
                0.37754066879814546,
                0.8354835391516133,
                0.13296424191570594,
                0.9626731162701729,
                0.46879062662624366,
                0.999447221476466
            ],
            [
                1.2098658275938276e-06,
                6.475951069007583e-07,
                8.315280276096808e-07,
                1.5534977545102382e-06,
                4.2228334426935205e-06,
                1.3709568798220997e-06,
                5.04347227807199e-07,
                3.4663266240668497e-07,
                1.7603434226854702e-06,
                5.043472277448155e-07
            ],
            [
                5.422221554482653e-06,
                7.889261642363733e-06,
                1.8925148238291944e-05,
                6.144172402285332e-06,
                5.4222196154940574e-06,
                8.93969417214416e-06,
                1.5534975692683091e-06,
                4.78509506425325e-06,
                7.889261643899223e-06,
                1.994729008056074e-06
            ],
            [
                8.939699498814873e-06,
                5.422219615750493e-06,
                6.144173136455602e-06,
                4.006369693473136e-05,
                1.0129987352948008e-05,
                1.3007126910649678e-05,
                3.7266397272757976e-06,
                1.670141586454787e-05,
                1.012998977022003e-05,
                2.7535697636951104e-05
            ],
            [
                7.33821330386288e-07,
                1.147876538330323e-05,
                2.9023126766832993e-06,
                7.889265405677441e-06,
                2.430023783150746e-05,
                1.99472972129484e-06,
                6.1441775291964935e-06,
                6.144176797585032e-06,
                1.0129995804696242e-05,
                3.288750241410738e-06
            ],
            [
                2.5612831263510383e-06,
                1.994729245392294e-06,
                4.222832436871463e-06,
                1.1478773593548236e-05,
                1.9947299589867267e-06,
                1.4738988990369329e-05,
                1.6701417809120006e-05,
                2.753568441491387e-05,
                1.670141586084161e-05,
                5.422221553072258e-06
            ],
            [
                4.785095634930755e-06,
                5.4222215541571775e-06,
                1.14787735942999e-05,
                6.144176065012512e-06,
                5.422220260360515e-06,
                1.9947290077331477e-06,
                1.0677031243632815e-06,
                4.222832940577472e-06,
                1.3007130013288297e-05,
                3.7266388386231563e-06
            ],
            [
                0.00026119021201662654,
                5.8291279365509446e-05,
                2.144494328950459e-05,
                7.484625395279873e-05,
                0.00012339463362954505,
                9.610244921065592e-05,
                9.610241477233725e-05,
                0.00020342699740243916,
                1.8925155003330605e-05,
                0.00033535018646018593
            ],
            [
                1.3007125361448172e-05,
                6.962256249112569e-06,
                4.006370642681552e-05,
                1.0129988563730593e-05,
                7.889261643899223e-06,
                7.889266343575084e-06,
                NaN,
                6.1441767987808774e-06,
                1.0129995808178788e-05,
                4.2228324375973415e-06
            ],
            [
                7.484624480293717e-05,
                6.962254588116627e-06,
                4.539785771672514e-05,
                3.120192250393883e-05,
                1.4738980201465192e-05,
                2.4300237821252875e-05,
                5.82912863042125e-05,
                0.00017952798686028367,
                1.3007126909159127e-05,
                2.4300252300909177e-05
            ],
            [
                0.9998911030653981,
                0.9840936071219177,
                0.999981074849528,
                0.6791786861878392,
                0.8670357701094303,
                0.952574127663914,
                0.9999251537822594,
                0.9999756997650743,
                0.9999756997696584,
                0.9999546021097627
            ],
            [
                2.5612815996464693e-06,
                2.9023116388547446e-06,
                3.7266401719851935e-06,
                3.7266388397382506e-06,
                6.962253759157502e-06,
                7.889266344321303e-06,
                8.939697368110433e-06,
                7.889264465397747e-06,
                1.5534977543661227e-06,
                1.0129988561077228e-05
            ],
            [
                6.1441753337365085e-06,
                3.7266383936427712e-06,
                1.0129987354882753e-05,
                2.2603245671202796e-06,
                2.5612812945889277e-06,
                6.144177531381426e-06,
                8.315284241560147e-07,
                1.5534975693347152e-06,
                1.1478766754377407e-05,
                9.422448185264317e-07
            ],
            [
                1.6701415865641523e-05,
                1.994729721396435e-06,
                2.5612825156159896e-06,
                8.315279285149107e-07,
                1.3007130012010681e-05,
                2.561282210562998e-06,
                1.6701415867707307e-05,
                4.450852641519336e-07,
                5.422219615750493e-06,
                4.2228334433617906e-06
            ],
            [
                1.0129993390942177e-05,
                1.0129994600398803e-05,
                5.829125148432372e-05,
                1.8925157261545463e-05,
                4.785093923420688e-06,
                4.7850933535006355e-06,
                4.0063711254184204e-05,
                1.760342793515064e-06,
                3.2887478888496478e-06,
                9.610242636527403e-05
            ],
            [
                2.5612834317908303e-06,
                5.144221975264518e-05,
                1.994729959160889e-06,
                1.147876401711502e-05,
                1.3007125356006484e-05,
                1.3007133108948093e-05,
                3.726639283440905e-06,
                8.939696302051047e-06,
                1.3709575333824478e-06,
                1.4738976696800444e-05
            ],
            [
                0.0005527786598202136,
                5.422219615395428e-06,
                2.260325375520937e-06,
                2.260325105981383e-06,
                1.6701417861189946e-05,
                NaN,
                8.481106121553572e-05,
                1.8925150494750372e-05,
                8.939700565996655e-06,
                0.00033535006514537574
            ],
            [
                6.1441753335241615e-06,
                2.902312330891746e-06,
                3.2887494572095624e-06,
                1.994729959019382e-06,
                3.2887486731252264e-06,
                1.5534983099790112e-06,
                2.561281599881745e-06,
                2.5612819052374947e-06,
                6.962257078553231e-06,
                4.0063701693307245e-05
            ],
            [
                2.9023126770343703e-06,
                5.422217674464535e-06,
                4.785095634756674e-06,
                5.422217029844958e-06,
                1.0129990978847043e-05,
                6.962257908880483e-06,
                6.962257909323729e-06,
                2.430025230532926e-05,
                4.7850933535659155e-06,
                7.889261642578988e-06
            ],
            [
                0.05340332396194506,
                0.4687906266262437,
                0.0002959570953956673,
                6.144175333926503e-06,
                0.004609571224311929,
                0.904650538956921,
                0.22270013882530887,
                0.0019267349118223774,
                0.999195914095143,
                0.43782349911420193
            ],
            [
                2.2603245671490605e-06,
                2.2603248366762157e-06,
                8.939696302457574e-06,
                3.7266392835086923e-06,
                1.9947306725451314e-06,
                1.760343632774555e-06,
                2.2603251061849014e-06,
                1.2098656834723998e-06,
                3.2887506333394084e-06,
                5.422220907298259e-06
            ],
            [
                3.726639283901856e-06,
                1.3709567164326847e-06,
                6.14417606659952e-06,
                1.4738976696371488e-05,
                5.422218321855664e-06,
                2.561281599502042e-06,
                4.222832940423847e-06,
                3.7266388394569345e-06,
                1.300712533319871e-05,
                2.5612812945260317e-06
            ],
            [
                1.473898021366358e-05,
                2.430024072285883e-05,
                1.0677024881499412e-06,
                4.7850950649408664e-06,
                3.1201907643310305e-05,
                1.4738978455325741e-05,
                2.1444958633416914e-05,
                5.144221973505439e-05,
                2.1444953514565465e-05,
                2.7535700945316292e-05
            ],
            [
                1.0129990975235516e-05,
                2.9023112928785396e-06,
                1.3709576969826825e-06,
                1.0677033791107183e-06,
                1.7603430034311638e-06,
                3.288748280520804e-06,
                5.422219615188307e-06,
                1.0129992185539456e-05,
                7.338211554591642e-07,
                8.315281267339571e-07
            ],
            [
                1.670141983431876e-05,
                8.939697368110433e-06,
                1.0129988563546333e-05,
                2.4300243614475748e-05,
                3.2887506334560605e-06,
                4.222831934052698e-06,
                1.3709575335919232e-06,
                2.9023126769050284e-06,
                2.1444956077189637e-05,
                1.4738976696371488e-05
            ],
            [
                0.9999785550490462,
                0.999933947871197,
                0.9999417087136733,
                0.9998911031297583,
                0.9999687980960786,
                0.9998415637268017,
                0.9998766054399821,
                0.9999546021476109,
                0.9995121428226936,
                0.9999756997679662
            ],
            [
                1.7603434230088762e-06,
                2.4300234920177672e-05,
                6.144176065314267e-06,
                4.7850927822924614e-06,
                0.000230506659369122,
                1.892514823364471e-05,
                1.0129995806888955e-05,
                3.7266406161591266e-06,
                1.8925150481256165e-05,
                4.785095633999427e-06
            ],
            [
                5.422217676654099e-06,
                5.4222202624563834e-06,
                4.222835457906302e-06,
                4.222833444168322e-06,
                1.3709568798782093e-06,
                7.889265400267349e-06,
                1.370957370196196e-06,
                6.144175333837093e-06,
                4.785093923916815e-06,
                4.222832939432965e-06
            ],
            [
                6.96225707894582e-06,
                1.7603434231097403e-06,
                6.144172404129392e-06,
                4.222833444229772e-06,
                1.4738985484227961e-05,
                4.785094494576774e-06,
                5.422217030288788e-06,
                5.4222183209778656e-06,
                2.5612819053166966e-06,
                8.939700564679507e-06
            ],
            [
                3.2887478883351803e-06,
                1.067702742683591e-06,
                7.338213304243302e-07,
                6.475947981813674e-07,
                2.2603253754284284e-06,
                1.0677029972920738e-06,
                5.422217676486429e-06,
                2.6995771308437034e-07,
                9.422447061576466e-07,
                2.9023126769762986e-06
            ],
            [
                4.785095064436034e-06,
                0.0002959572023348996,
                0.00013982209042924033,
                1.6701429803316423e-05,
                0.00010889692200685404,
                0.0002959569920041779,
                3.120190020204515e-05,
                4.0063706492255065e-05,
                0.0001398220735885219,
                5.14422381473764e-05
            ],
            [
                3.2887502411026557e-06,
                8.315282259009745e-07,
                3.2887486726945097e-06,
                5.715003788894922e-07,
                6.144174599532449e-06,
                2.2603248365960415e-06,
                1.370957206753107e-06,
                1.067702615348298e-06,
                8.315281267581578e-07,
                3.9278610660598936e-07
            ],
            [
                2.26032348933062e-06,
                2.5612822104232297e-06,
                5.043476486764593e-07,
                2.4300252311252174e-05,
                1.370957370146321e-06,
                4.450851580469341e-07,
                3.9278634071901495e-07,
                5.043472879383035e-07,
                1.0677032518209896e-06,
                4.785093352595421e-06
            ],
            [
                1.3007126909916233e-05,
                1.5534971986601824e-06,
                1.9947292456607935e-06,
                2.260324836651547e-06,
                7.33821330394297e-07,
                6.475945665853783e-07,
                5.715005832624392e-07,
                5.715005150672525e-07,
                2.260323489192885e-06,
                1.0677033791000363e-06
            ],
            [
                0.00010889693506777467,
                1.6701423833436905e-05,
                5.144222588097783e-05,
                2.902313368897403e-06,
                2.430024072471526e-05,
                3.1201926190918605e-05,
                3.2887478887958082e-06,
                8.93970056424046e-06,
                1.0129987354366822e-05,
                3.120190388402792e-05
            ],
            [
                NaN,
                2.5612831262578596e-06,
                1.892515047863994e-05,
                3.7266406165827946e-06,
                1.209865395009523e-06,
                2.4300249417247375e-05,
                1.4738981968060613e-05,
                1.0129987355988324e-05,
                6.9622537584863015e-06,
                4.785096775171854e-06
            ],
            [
                0.9999930377412614,
                0.9999832985721872,
                0.9999898700102283,
                0.9999724643056397,
                0.9999945777790913,
                0.9999957771655489,
                0.999986992866886,
                0.9999810748495074,
                0.9999832985741784,
                0.9999687980997993
            ],
            [
                4.006369691549301e-05,
                2.3823693838927385e-07,
                4.785093923916815e-06,
                2.7535684519993744e-05,
                7.889260704050487e-06,
                1.553498495295912e-06,
                3.9278629389204037e-07,
                NaN,
                3.120192251631124e-05,
                1.5534973839896667e-06
            ],
            [
                1.370957370146321e-06,
                1.0677026154619133e-06,
                9.42244481511812e-07,
                1.0677029972522599e-06,
                9.422445938797133e-07,
                5.422220906223202e-06,
                8.315279284755847e-07,
                5.422217030362759e-06,
                3.2887502407138142e-06,
                2.902313022659669e-06
            ],
            [
                6.144173135896795e-06,
                3.288747888089911e-06,
                3.288749848749297e-06,
                1.994729721265813e-06,
                1.7603434229000067e-06,
                2.5612834318257725e-06,
                1.209866116149238e-06,
                8.31528424146183e-07,
                6.96225707640032e-06,
                9.422445938728576e-07
            ],
            [
                4.785096775580942e-06,
                1.0129995807939249e-05,
                1.6701423831188846e-05,
                1.147876538716594e-05,
                4.222833947820683e-06,
                1.7603440525925705e-06,
                1.4738987240100149e-05,
                2.4300252313904224e-05,
                1.0129989769722525e-05,
                1.7603430033158905e-06
            ],
            [
                4.785096775920397e-06,
                1.553497198826904e-06,
                4.222835457595211e-06,
                6.144176798479122e-06,
                2.260324297607547e-06,
                2.5612812945260317e-06,
                8.939698435096828e-06,
                2.430024650998268e-05,
                6.144173867451939e-06,
                3.7266388396975786e-06
            ],
            [
                1.3007133113703658e-05,
                1.4738985474174337e-05,
                1.1478768575405368e-05,
                1.1478770861650256e-05,
                1.3007123805078022e-05,
                2.5612819051373276e-06,
                3.5356254907513187e-05,
                1.4738978454172926e-05,
                2.7535694358938284e-05,
                1.8925150491445666e-05
            ],
            [
                7.889263522032836e-06,
                1.7603430033158905e-06,
                7.88926070293116e-06,
                4.222832940500659e-06,
                3.2887478881736613e-06,
                1.370957697068717e-06,
                1.0677033789796238e-06,
                8.481102093340112e-05,
                1.2098652507285942e-06,
                0.00010889688257216831
            ],
            [
                1.0677024881266355e-06,
                1.994729959160889e-06,
                4.785096205512581e-06,
                1.5534979396024226e-06,
                1.067703251784089e-06,
                9.422449308335287e-07,
                1.3007133109847152e-05,
                1.553497754284175e-06,
                6.962257078553231e-06,
                1.1478773591543802e-05
            ],
            [
                2.2603248365014775e-06,
                6.475947209638476e-07,
                3.0590226338671677e-07,
                1.994729721396435e-06,
                1.9947301968963442e-06,
                1.9947297211279344e-06,
                2.9023130227599746e-06,
                1.0677026154055912e-06,
                2.561281599881745e-06,
                1.994729245842213e-06
            ],
            [
                3.7266397278791014e-06,
                9.422445938111562e-07,
                1.0677029972134173e-06,
                3.288748673035494e-06,
                3.927862002491823e-07,
                1.300712380555121e-05,
                1.2098661161239298e-06,
                1.3709572065835317e-06,
                2.9023126769050284e-06,
                7.338207180761315e-07
            ],
            [
                0.9995121428929137,
                0.9999756997476946,
                0.9999832985701983,
                0.9997040429752225,
                0.9998415638489742,
                0.9999687980856575,
                0.9999898700066242,
                0.9465966660571644,
                0.9996646498965498,
                0.99998526102155
            ],
            [
                4.785095064601411e-06,
                3.7266406161591266e-06,
                6.144173133560988e-06,
                1.7603430033991435e-06,
                4.785094493636744e-06,
                1.8925152744771773e-05,
                3.120191503554163e-05,
                1.0129989768322136e-05,
                2.260324836152e-06,
                9.610240337377108e-05
            ],
            [
                7.889261640067674e-06,
                2.9023130227124616e-06,
                8.93969736942758e-06,
                2.75356878022126e-05,
                1.3007134664822509e-05,
                1.3007125362323574e-05,
                1.5534983100765009e-06,
                1.3007133109847152e-05,
                2.7535691083329963e-05,
                4.7850933535659155e-06
            ],
            [
                6.9622579075254155e-06,
                8.939699497855469e-06,
                4.785093923516432e-06,
                1.670141785596473e-05,
                2.7535681224252135e-05,
                4.539789022498571e-05,
                6.60521209179157e-05,
                3.5356259106723956e-05,
                1.300712845966209e-05,
                1.1478773595657069e-05
            ],
            [
                3.927862939075802e-07,
                4.222834450743383e-06,
                1.9947299591100915e-06,
                3.2887498488809053e-06,
                2.5612822106421996e-06,
                1.8925141467679015e-05,
                3.9278634071901495e-07,
                1.9947299589867267e-06,
                1.473897669838221e-05,
                1.9947292458004866e-06
            ],
            [
                6.475947209402883e-07,
                2.902312331081799e-06,
                4.7850927830148924e-06,
                1.9947294836483373e-06,
                4.785095634843714e-06,
                2.2603234893861252e-06,
                1.7603425835749741e-06,
                1.7603427935342762e-06,
                1.760343632920248e-06,
                7.33820805475565e-07
            ],
            [
                3.535625475059587e-05,
                1.994730434816876e-06,
                1.473898021151881e-05,
                7.889265404759017e-06,
                7.889260702141888e-06,
                1.89251527491092e-05,
                1.0129993392342568e-05,
                4.785096205582214e-06,
                1.3709567164139816e-06,
                1.6701419843189485e-05
            ],
            [
                6.605216820222096e-05,
                0.0001233945894625487,
                0.0019267343185688358,
                0.00017952800674027032,
                0.0011695101236262496,
                1.0129989768616954e-05,
                0.0004878570551167975,
                5.8291272448012225e-05,
                0.0008040859338053488,
                4.539789027320923e-05
            ],
            [
                1.0129990977520359e-05,
                4.7850950646797465e-06,
                1.147876812069122e-05,
                4.0063706458587944e-05,
                4.785093353013212e-06,
                7.889263525261671e-06,
                6.605216023019448e-05,
                1.6701421833391647e-05,
                5.42222090767305e-06,
                2.9023126767360923e-06
            ],
            [
                1.6701421834728333e-05,
                1.012999580884213e-05,
                6.962257906765564e-06,
                8.939699498814873e-06,
                1.3007133114318805e-05,
                1.670142780381727e-05,
                7.889260703906985e-06,
                3.288749065125496e-06,
                1.8925157258585e-05,
                2.1444943298320236e-05
            ],
            [
                3.927863407225873e-07,
                3.466327863945479e-07,
                9.422448184912962e-07,
                7.338207179987125e-07,
                3.927862002370363e-07,
                5.043473480643696e-07,
                3.4663257978465195e-07,
                5.043474683126242e-07,
                3.927862470840049e-07,
                7.33820980469346e-07
            ],
            [
                7.889265400898766e-06,
                1.6701421843720577e-05,
                1.3709570431803621e-06,
                2.2603245668941476e-06,
                2.75356812012127e-05,
                2.9023119840232638e-06,
                2.9023112924403614e-06,
                6.144176797115634e-06,
                1.892515047588602e-05,
                3.7266392828579377e-06
            ],
            [
                3.5356242262551455e-05,
                1.892514596944115e-05,
                0.0004878572269485047,
                3.12019225102953e-05,
                4.539785768997102e-05,
                2.144495607492721e-05,
                1.1478766751997141e-05,
                1.3709575335919232e-06,
                0.00048785722354252375,
                1.6701429796754513e-05
            ],
            [
                5.422219615188307e-06,
                3.2887498492518007e-06,
                1.4738976700366126e-05,
                8.93969523358515e-06,
                NaN,
                3.535625068579429e-05,
                NaN,
                6.144177530425867e-06,
                1.4738985480179701e-05,
                3.1201922481918207e-05
            ],
            [
                6.144175334172377e-06,
                2.4300232038197563e-05,
                1.6701419853184244e-05,
                1.670142184171555e-05,
                3.120191136649749e-05,
                1.4738985482753428e-05,
                6.144177531007026e-06,
                1.4738978456719842e-05,
                1.1478770860982112e-05,
                8.939698432690187e-06
            ],
            [
                1.3007130010543792e-05,
                1.3007134662432895e-05,
                8.939696301611998e-06,
                NaN,
                1.1478772228256871e-05,
                1.1478764019787597e-05,
                1.1478766754377407e-05,
                4.785096205434246e-06,
                1.670142781432848e-05,
                4.0063677786460955e-05
            ],
            [
                1.8925143715978147e-05,
                2.753569436424737e-05,
                1.8925157257965367e-05,
                1.670142780381727e-05,
                1.3007133114886634e-05,
                2.260324297570543e-06,
                4.5397890254712545e-05,
                1.6701423830702777e-05,
                3.120192624233791e-05,
                3.7266406162947e-06
            ],
            [
                1.5534981248712412e-06,
                1.3007126909159127e-05,
                1.994729483608425e-06,
                3.288748672879957e-06,
                4.222835457794923e-06,
                1.2098661161602417e-06,
                1.7603427935518875e-06,
                3.2887494564857185e-06,
                6.144176065828368e-06,
                6.962258738435319e-06
            ],
            [
                2.7535697650273915e-05,
                4.2228319339950885e-06,
                1.6701417859944398e-05,
                5.422217676200406e-06,
                6.144175333401224e-06,
                4.222833443968609e-06,
                4.2228339464303755e-06,
                1.1478769492893215e-05,
                1.1478764019328247e-05,
                1.4738983719589221e-05
            ],
            [
                1.1478770856576534e-05,
                1.3007128456539035e-05,
                6.144173868558375e-06,
                3.288749064371741e-06,
                2.4300237826203363e-05,
                5.144220742524465e-05,
                8.93969950000193e-06,
                4.7850956351657615e-06,
                4.006368738143655e-05,
                2.260323758746637e-06
            ],
            [
                5.422217676575195e-06,
                7.338208929284016e-07,
                6.144176065940129e-06,
                7.889261643727018e-06,
                1.670142980726572e-05,
                4.222832940577472e-06,
                1.4738976697631541e-05,
                3.5356254892335935e-05,
                1.4738988994498018e-05,
                3.726640172290235e-06
            ],
            [
                1.3007134663876127e-05,
                1.0677027427166074e-06,
                6.962259568775433e-06,
                2.7535687785784475e-05,
                1.1478770859332632e-05,
                5.82912863042125e-05,
                0.00010889696076497818,
                3.120190019636974e-05,
                5.8291258415389654e-05,
                3.288750241204353e-06
            ],
            [
                6.962254588724508e-06,
                4.222833947428939e-06,
                5.715003788557066e-07,
                4.785096775920397e-06,
                9.422450430566563e-07,
                1.370957206783032e-06,
                1.1478765386894505e-05,
                4.222833444383398e-06,
                1.7603434231385591e-06,
                1.2098658276444443e-06
            ],
            [
                1.2098659719122375e-06,
                1.99472995920443e-06,
                1.2098658275740208e-06,
                1.553498495281783e-06,
                2.699577774530648e-07,
                5.422218321855664e-06,
                1.6701425809239798e-05,
                2.902313368897403e-06,
                2.5612812945260317e-06,
                3.726637951028202e-06
            ],
            [
                8.939698434332555e-06,
                2.1444943284979742e-05,
                2.4300246513165137e-05,
                1.300712688791288e-05,
                1.0129994601688632e-05,
                2.9023112926251358e-06,
                4.785093922654737e-06,
                4.222833443891798e-06,
                5.422217029509618e-06,
                3.7266379504926854e-06
            ],
            [
                NaN,
                3.535624646754865e-05,
                4.222834954403545e-06,
                5.422219615286937e-06,
                1.5534971989809095e-06,
                1.0677031245050577e-06,
                1.147876675466972e-05,
                4.2228339475595195e-06,
                3.2887494572514376e-06,
                1.4738976696800444e-05
            ],
            [
                2.144495862967221e-05,
                3.2887478887958082e-06,
                1.994729008105057e-06,
                4.785095063469892e-06,
                1.1478766755734576e-05,
                2.561282210460501e-06,
                4.5397890257685224e-05,
                6.962259568775433e-06,
                1.3007123809289414e-05,
                4.2228349543420954e-06
            ],
            [
                1.0677029972833341e-06,
                1.147876675548402e-05,
                5.422219615829396e-06,
                2.9023116390421582e-06,
                5.4222215550004564e-06,
                4.785094493305991e-06,
                1.1478766753082876e-05,
                5.4222202621161125e-06,
                4.785096205077381e-06,
                3.2887494570719725e-06
            ],
            [
                1.5534981248133121e-06,
                3.726640616423495e-06,
                9.422443691996268e-07,
                9.422447062030659e-07,
                5.715006514040971e-07,
                2.5612812945260317e-06,
                2.2603251061664e-06,
                4.785096205582214e-06,
                6.96225375863827e-06,
                4.22283545795623e-06
            ],
            [
                7.889259761905808e-06,
                3.726637951028202e-06,
                2.4300237809495462e-05,
                2.260325105911487e-06,
                1.01299933920846e-05,
                7.889262579615163e-06,
                2.902313022554084e-06,
                1.3007131563815288e-05,
                5.422218968714274e-06,
                7.484625393972985e-05
            ],
            [
                2.2603245672025095e-06,
                6.144176798691468e-06,
                6.962253759271479e-06,
                2.2603245671202796e-06,
                1.6701423832586287e-05,
                1.3007125360809367e-05,
                6.962257908196617e-06,
                1.3007126911643378e-05,
                4.222832939870796e-06,
                5.144221975264518e-05
            ],
            [
                2.2603242976733308e-06,
                7.889264464508026e-06,
                1.1478764019557924e-05,
                2.7535704187167975e-05,
                5.14422074125194e-05,
                1.8925145971919677e-05,
                2.4300249416363357e-05,
                3.7266397280485686e-06,
                8.939697367492512e-06,
                1.4738985478678359e-05
            ],
            [
                1.5534981248133121e-06,
                7.33820892991805e-07,
                9.422442568548903e-07,
                8.315279285088606e-07,
                3.927862002491823e-07,
                1.5534983100228109e-06,
                4.222831933864508e-06,
                6.475946437657736e-07,
                1.0677028699858827e-06,
                9.422444815409489e-07
            ],
            [
                4.222834450950777e-06,
                8.481108158244299e-05,
                2.430025230320762e-05,
                0.0003353500226549568,
                8.481106149875219e-05,
                3.120190392670705e-05,
                0.00017952790002674285,
                3.726641059702693e-06,
                4.5397879408714157e-05,
                6.605215242684585e-05
            ],
            [
                6.144176797864436e-06,
                9.422449307915373e-07,
                3.288749065077638e-06,
                3.2887494566352732e-06,
                5.422219614152703e-06,
                3.4663270374490014e-07,
                5.422219615188307e-06,
                3.7266401722360055e-06,
                3.7266406165319545e-06,
                9.422442568428928e-07
            ],
            [
                1.7603430031093589e-06,
                1.553498310118888e-06,
                6.1441760651689774e-06,
                6.144176065828368e-06,
                8.939695236983711e-06,
                2.5612825156159896e-06,
                1.2098658276730537e-06,
                1.370957370083977e-06,
                7.338207180601138e-07,
                1.4738978453315019e-05
            ],
            [
                0.9996646498920032,
                0.9998204720558198,
                0.9999599362935362,
                0.9999151889688097,
                0.9990889486801384,
                0.9999251537461316,
                0.9999869928761884,
                0.9997040429375756,
                0.9999251537639657,
                0.9998204719918179
            ],
            [
                8.315278293301564e-07,
                5.043473480276735e-07,
                1.9947299592407137e-06,
                1.2098659718363124e-06,
                1.370957370126371e-06,
                1.5534979396815448e-06,
                8.315283249636384e-07,
                1.370957370236096e-06,
                2.5612834315811786e-06,
                5.422217029006611e-06
            ],
            [
                1.2098658274595828e-06,
                7.338211553577186e-07,
                1.067702869764479e-06,
                1.0677029972270124e-06,
                2.2603237584711665e-06,
                0.7057850402140659,
                2.260325375354421e-06,
                1.553497384058899e-06,
                4.785093353274332e-06,
                0.9999151889798255
            ],
            [
                4.006370646121136e-05,
                4.006369693006752e-05,
                1.1478769491014062e-05,
                1.1478766756653273e-05,
                4.785096775676685e-06,
                4.0063706494441236e-05,
                3.120190391705884e-05,
                7.88926258532661e-06,
                7.48462449913471e-05,
                1.8925143715978147e-05
            ],
            [
                2.1444940742640888e-05,
                5.422220261948442e-06,
                3.2887478885505384e-06,
                4.006367784344724e-05,
                1.012999580884213e-05,
                8.939698434495167e-06,
                5.422218968931258e-06,
                1.8925143725341476e-05,
                3.2887486729876365e-06,
                7.484622717027548e-05
            ],
            [
                4.450851580273012e-07,
                8.315278293301564e-07,
                2.561281905100056e-06,
                7.889264463216492e-06,
                4.222833443891798e-06,
                6.475948753847607e-07,
                6.475950297574138e-07,
                7.889263525534328e-06,
                1.9947292458603553e-06,
                6.962256246263128e-06
            ],
            [
                1.4738987237553233e-05,
                2.430024941804299e-05,
                7.889265402907818e-06,
                4.006368255581968e-05,
                5.422217675756574e-06,
                2.144494840531103e-05,
                1.4738983723664288e-05,
                1.0129987355785634e-05,
                6.962255416961874e-06,
                1.1478765386623071e-05
            ],
            [
                1.4738985477605971e-05,
                1.0129990978644356e-05,
                4.5397879411686836e-05,
                1.300712845923622e-05,
                1.8925155002710973e-05,
                1.8925154997891613e-05,
                1.67014158650947e-05,
                2.1444958625381407e-05,
                8.939698430218506e-06,
                1.892514371356847e-05
            ],
            [
                4.2228344511197656e-06,
                4.2228324370327694e-06,
                1.4738981965808603e-05,
                1.473898195905257e-05,
                0.00012339454502984816,
                2.1444940736477737e-05,
                1.4738976696371488e-05,
                2.4300234925658572e-05,
                7.889265405333033e-06,
                2.753568781022632e-05
            ],
            [
                2.561281904708706e-06,
                9.422449308241022e-07,
                NaN,
                8.315282258756395e-07,
                7.889265405333033e-06,
                2.902311293034278e-06,
                2.9023116388072315e-06,
                7.338213304083124e-07,
                1.2098662603961589e-06,
                3.2887478887419687e-06
            ],
            [
                3.288747889038086e-06,
                6.1441738691562974e-06,
                3.288750241042834e-06,
                3.2887506332945414e-06,
                4.222833444168322e-06,
                1.0677033790883835e-06,
                8.3152792848466e-07,
                1.8925141466439755e-05,
                5.422217029736466e-06,
                2.1024329090561285e-07
            ]
        ]
    },
    {
        "q_id": "7733_mmlu_math",
        "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,
            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": [
            [
                0.9999989322966208,
                0.9999989322970027,
                0.9999989322968754,
                0.9999996072139402,
                0.9999994284997573,
                0.9999989322973845,
                0.9999993524054335,
                0.9999989322973845,
                0.999999352405279,
                0.9999993524052018
            ],
            [
                9.422445938861406e-07,
                3.288749849368453e-06,
                4.785092783267308e-06,
                1.553497384196656e-06,
                2.260325375650449e-06,
                3.288750633488963e-06,
                2.9023112930949896e-06,
                4.785093353739995e-06,
                4.785094494463623e-06,
                3.726640616670918e-06
            ],
            [
                0.9999984465022455,
                0.9999984465016899,
                0.9999977396751634,
                0.9999974387171787,
                0.9999945777829701,
                0.9999977396746245,
                0.9999977396746245,
                0.9999984465026158,
                0.9999986290432835,
                0.9999952149072169
            ],
            [
                1.6701415864001047e-05,
                1.3007134666644292e-05,
                1.8925157262061825e-05,
                8.939698434332555e-06,
                8.939696302831578e-06,
                2.430023782717578e-05,
                5.422217030121119e-06,
                1.473898196763166e-05,
                NaN,
                1.89251482372248e-05
            ],
            [
                0.9999990577551814,
                0.9999989322970027,
                0.9999990577557432,
                0.9999982396572065,
                0.9999992661787571,
                0.9999989322971299,
                0.999998790134028,
                0.9999992661791071,
                0.9999992661791944,
                0.9999992661788445
            ],
            [
                0.9999970976866313,
                0.9999991684722698,
                0.999999554914895,
                0.999999266178757,
                0.9999987901343166,
                0.9999977396762411,
                0.9999984465024306,
                0.9999980052695653,
                0.9999992661792819,
                0.999997097688361
            ],
            [
                0.9999974387168734,
                0.9999982396574163,
                0.9999994284996893,
                0.9999989322966208,
                0.9999989322972573,
                0.9999967112509347,
                0.9999994284995529,
                0.9999945777803845,
                0.9999986290429566,
                0.999997097686977
            ],
            [
                0.9999986290423029,
                0.9999991684722698,
                0.9999957771645421,
                0.9999962733589389,
                0.9999994956524716,
                0.9999989322968754,
                0.9999970976887068,
                0.9999990577551815,
                0.9999974387165681,
                0.9999982396567868
            ],
            [
                0.999998446502801,
                0.9999980052702785,
                0.9999992661792819,
                0.9999977396762412,
                0.9999992661790195,
                0.9999989322975118,
                0.9999993524049702,
                0.9999986290427931,
                0.9999986290421395,
                0.9999984465015047
            ],
            [
                0.999993855822469,
                0.9999974387180947,
                0.9999962733593835,
                0.999993855827596,
                0.9999962733602719,
                0.9999910603068946,
                0.9999952149043648,
                0.999997097686631,
                0.9999980052695653,
                0.9999980052700408
            ],
            [
                0.9999992661788446,
                0.99999893229713,
                0.9999986290421395,
                0.9999984465015047,
                0.9999952149037942,
                0.9999991684719723,
                0.999998790134605,
                0.999999352405279,
                0.9999994284995529,
                0.9999967112517187
            ],
            [
                2.902310947208574e-06,
                1.0677033791495609e-06,
                2.561283431942246e-06,
                6.475947210012481e-07,
                2.260325375634003e-06,
                8.3152792852928e-07,
                2.561281294644835e-06,
                1.0677029973114952e-06,
                1.9947306726358406e-06,
                2.5612834319655406e-06
            ],
            [
                0.9999957771670593,
                0.9999990577551815,
                0.9999982396574163,
                0.9999970976869771,
                0.99999893229713,
                0.9999995549150542,
                0.999999168471675,
                0.9999970976880149,
                0.9999990577554062,
                0.9999980052705163
            ],
            [
                0.9999986290423029,
                0.9999984465018751,
                0.99999893229713,
                0.9999994284995529,
                0.9999990577556308,
                0.9999986290432834,
                0.9999982396561572,
                0.9999990577552937,
                0.9999982396559474,
                0.9999989322973846
            ],
            [
                0.999999266179107,
                0.9999991684720715,
                0.9999994956525318,
                0.999998005269803,
                0.9999991684722698,
                0.9999992661788445,
                0.9999967112517191,
                0.999999352404893,
                0.9999974387171787,
                0.9999989322967482
            ],
            [
                6.962257079059797e-06,
                2.5612816000331606e-06,
                3.2887482812506295e-06,
                6.14417313680765e-06,
                1.5534979397677313e-06,
                1.5534979397500702e-06,
                1.7603425837702984e-06,
                3.288747889178668e-06,
                2.260325375650449e-06,
                2.260325375615501e-06
            ],
            [
                0.9999989322966208,
                0.9999989322970027,
                0.9999989322966208,
                0.9999987901341724,
                0.9999986290426297,
                0.9999977396746245,
                0.9999992661791945,
                0.9999990577551814,
                0.9999986290423029,
                0.9999992661792819
            ],
            [
                0.9999994284996891,
                0.9999967112521109,
                0.9999992661786696,
                0.9999970976883609,
                0.9999996533675028,
                0.9999990577556307,
                0.9999980052693274,
                0.9999993524049703,
                0.9999992661789321,
                0.9999977396754328
            ],
            [
                1.2098655392871682e-06,
                1.7603434231505666e-06,
                1.370957860567974e-06,
                2.9023119851055122e-06,
                3.7266410608245674e-06,
                6.144173136729416e-06,
                1.3709570434054234e-06,
                3.288748281220719e-06,
                1.0677027427525368e-06,
                1.2098653950656417e-06
            ],
            [
                8.315280276580819e-07,
                1.9947297214544894e-06,
                2.561281905390075e-06,
                1.370957370236096e-06,
                1.994729008056074e-06,
                1.0677031245905116e-06,
                1.9947306726213275e-06,
                4.785092783267308e-06,
                3.7266401724291984e-06,
                2.902313023039776e-06
            ],
            [
                0.999999057755069,
                0.9999986290431201,
                0.9999962733593833,
                0.9999986290429567,
                0.9999984465020603,
                0.9999982396574163,
                0.9999989322972572,
                0.9999756997476829,
                0.9999986290429566,
                0.9999967112513267
            ],
            [
                0.9999994956525918,
                0.9999980052707541,
                0.9999989322972572,
                0.9999986290423029,
                0.999999168471675,
                0.9999992661789321,
                0.9999994284996211,
                0.9999980052700408,
                0.9999974387177893,
                0.9999977396759716
            ],
            [
                0.999998629042303,
                0.9999984465020603,
                0.9999992661791071,
                0.9999992661788445,
                0.9999974387177893,
                0.9999991684719723,
                0.9999991684719723,
                0.9999989322972572,
                0.9999993524050474,
                0.9999989322970028
            ],
            [
                0.9999945777823309,
                0.9999885212264026,
                0.9997040429379459,
                0.9999967112517243,
                0.9998415637937235,
                0.9999339478553375,
                0.999891103116832,
                0.9770226293791145,
                0.96267311131724,
                0.9999930377454173
            ],
            [
                0.9999993524051246,
                0.9999991684718733,
                0.9999990577554062,
                0.9999994956524715,
                0.9999990577552939,
                0.999999554914842,
                0.9999991684715758,
                0.9999994956527721,
                0.999999266179107,
                0.9999974387165681
            ],
            [
                0.9999952149032236,
                0.9999910603026306,
                0.8354835391516133,
                0.9626731097108832,
                0.999983298570306,
                0.999876605425161,
                0.9796676470283606,
                0.9999938558275953,
                0.9999151889889872,
                0.9399133443558416
            ],
            [
                0.9999974387180947,
                0.9999990577554062,
                0.9999982396561572,
                0.9999980052700408,
                0.9999974387177893,
                0.9999991684717741,
                0.9999967112505427,
                0.9999984465015047,
                0.9999957771645421,
                0.9999989322968754
            ],
            [
                0.9999417087344762,
                0.9999646437450749,
                0.9999646437535082,
                0.9999810748585277,
                0.9999485577740872,
                0.9999599362934897,
                0.999964643736649,
                0.9999756997476807,
                0.9999339478317094,
                0.9999832985801487
            ],
            [
                1.9947306725451314e-06,
                7.338213304196583e-07,
                5.043476486833397e-07,
                1.7603440527046419e-06,
                1.067703379136937e-06,
                1.2098653950480359e-06,
                1.0677027427340866e-06,
                9.422445938797133e-07,
                1.9947304348332037e-06,
                4.7850933535006355e-06
            ],
            [
                0.9999984465015047,
                0.9999990577555183,
                0.9999980052709919,
                0.9999952149037942,
                0.9999994956525318,
                0.9999984465024306,
                0.9999982396569966,
                0.9999974387184,
                0.9999970976887069,
                0.9999945777823231
            ],
            [
                0.9999992661790195,
                0.9999982396572065,
                0.9999989322975118,
                0.9999992661791944,
                0.9999977396751633,
                0.9999990577550691,
                0.999999057755743,
                0.9999974387184,
                0.999999266178757,
                0.9999980052693274
            ],
            [
                0.9999989322975118,
                0.999999352405279,
                0.9999986290421394,
                0.9999986290426297,
                0.9999996072137061,
                0.9999980052698031,
                0.9999996533674614,
                0.9999996072137998,
                0.9999993524050473,
                0.9999991684719723
            ],
            [
                5.71500651413193e-07,
                3.9278610661366994e-07,
                3.4663266243111764e-07,
                1.3709578605455302e-06,
                6.475950297971703e-07,
                4.785093924251918e-06,
                7.338211554725124e-07,
                1.0677027427340866e-06,
                7.338207180801359e-07,
                3.726638395493353e-06
            ],
            [
                0.9999957771670591,
                0.9999962733616046,
                0.9999938558224688,
                0.9999962733589393,
                0.999997097686977,
                0.9999967112513269,
                0.9999962733611604,
                0.9999962733620489,
                0.9999974387187054,
                0.999997438717484
            ],
            [
                9.610244923163104e-05,
                2.4300252313904224e-05,
                5.829129331543752e-05,
                4.539785237613882e-05,
                6.962258738827909e-06,
                1.3007133114886634e-05,
                2.4300240731964193e-05,
                4.5397863224112544e-05,
                1.300713466619476e-05,
                5.422219615967477e-06
            ],
            [
                0.9999994956524716,
                0.999999266179107,
                0.9999986290427932,
                0.9999989322972572,
                0.9999982396561572,
                0.9999974387180948,
                0.999998629042303,
                0.9999987901338838,
                0.99999893229713,
                0.9999989322966208
            ],
            [
                0.9999994284997573,
                0.9999986290426297,
                0.9999984465018751,
                0.9999989322971299,
                0.9999982396565769,
                0.999999266178757,
                0.999997097687323,
                0.9999994956524716,
                0.9999980052695652,
                0.9999977396754328
            ],
            [
                0.9999977396754328,
                0.9999982396569966,
                0.9999996072137529,
                0.9999977396762414,
                0.9999952149072172,
                0.9999957771650456,
                0.9999984465026158,
                0.9999986290426297,
                0.9999938558268638,
                0.9999984465015047
            ],
            [
                1.9947306725868575e-06,
                6.144173869240119e-06,
                1.0677029973056687e-06,
                2.260323489490968e-06,
                1.0677027427471959e-06,
                1.2098661161927025e-06,
                1.9947301970287804e-06,
                1.5534973841450852e-06,
                1.2098662603862553e-06,
                1.5534983101393749e-06
            ],
            [
                0.9999989322970027,
                0.9999995549150011,
                0.9999993524051246,
                0.9999990577556308,
                0.9999991684715759,
                0.9999991684722698,
                0.999999495652652,
                0.9999996072136592,
                0.9999991684720715,
                0.999999266178932
            ],
            [
                0.9999989322972572,
                0.9999996072138465,
                0.9999984465016899,
                0.9999984465026158,
                0.9999982396569966,
                0.9999980052707541,
                0.9999977396765105,
                0.9999974387184,
                0.9999962733593832,
                0.9999977396762411
            ],
            [
                0.9999986290423029,
                0.999999168471675,
                0.9999957771670591,
                0.9999991684719723,
                0.9999962733593835,
                0.9999992661788446,
                0.9999984465022455,
                0.9999957771680659,
                0.9999989322973845,
                0.9999991684721706
            ],
            [
                0.9999930377420913,
                0.9999938558246659,
                0.9999962733620488,
                0.9999974387180947,
                0.9999982396574163,
                0.9999967112513267,
                0.9999980052707542,
                0.9999646437493034,
                0.9999952149032241,
                0.9999962733611607
            ],
            [
                0.9999984465026158,
                0.9999984465024307,
                0.9999982396569966,
                0.9999990577557432,
                0.9999995549151073,
                0.9999991684719723,
                0.9999984465020603,
                0.9999982396561572,
                0.9999989322975119,
                0.9999986290432835
            ],
            [
                0.9999980052707541,
                0.9999957771665556,
                0.9999957771660523,
                0.9999982396561571,
                0.9999930377404308,
                0.9999970976883609,
                0.999996273358939,
                0.9999980052702785,
                0.9999952149037942,
                0.9999977396751633
            ],
            [
                0.9999991684715759,
                0.9999970976880149,
                0.9999996072136125,
                0.9999970976883609,
                0.9999984465026158,
                0.9999987901346049,
                0.9999980052707541,
                0.9999980052705163,
                0.9999984465015047,
                0.9999977396754327
            ],
            [
                1.0677031245783732e-06,
                6.144177531381426e-06,
                5.4222215550004564e-06,
                1.209865250822125e-06,
                1.9947299592570416e-06,
                4.222833947897496e-06,
                3.7266392839832006e-06,
                1.9947290081177566e-06,
                3.288749457383046e-06,
                6.144176799166453e-06
            ],
            [
                0.9999989322973846,
                0.999997097688361,
                0.9999977396762412,
                0.9999962733620492,
                0.9999996072137998,
                0.9999987901337396,
                0.9999977396759716,
                0.999997097687669,
                0.9999987901340281,
                0.9999986290427932
            ],
            [
                0.9999957771675627,
                0.9999986290421394,
                0.9999996940978461,
                0.9999952149032237,
                0.9999984465028011,
                0.9999993524053562,
                0.9999930377462406,
                0.9999992661790195,
                0.9999974387180947,
                0.999999266179107
            ],
            [
                0.9999974387184002,
                0.9999977396762412,
                0.9999982396569966,
                0.999998005270992,
                0.9999991684715758,
                0.999999168471675,
                0.9999977396765105,
                0.9999994284997573,
                0.999999352404893,
                0.9999990577551815
            ],
            [
                0.999997097688361,
                0.9999984465015047,
                0.9999974387165681,
                0.9999987901346049,
                0.999999057755743,
                0.9999996533675028,
                0.9999992661786695,
                0.9999974387168733,
                0.9999980052709919,
                0.9999989322973845
            ],
            [
                0.9999993524049703,
                0.9999987901340281,
                0.9999991684718733,
                0.9999992661791944,
                0.9999987901344607,
                0.9999974387187054,
                0.9999994284994849,
                0.9999992661786696,
                0.9999994284993485,
                0.9999986290427931
            ],
            [
                0.9999990577551814,
                0.9999990577557432,
                0.9999970976887073,
                0.9999962733589393,
                0.999995777165549,
                0.9999974387177895,
                0.9999986290424663,
                0.9999980052698031,
                0.9999990577552939,
                0.9999986290424664
            ],
            [
                0.9999485577863536,
                0.999796573075618,
                0.9999646437619356,
                0.9999756997563729,
                0.9999251537638759,
                0.9999251537638563,
                0.9999687980886347,
                0.999941708741448,
                0.99995993630782,
                0.9999599363030465
            ],
            [
                0.999997097686977,
                0.9999977396751634,
                0.9999982396569965,
                0.9999921107355337,
                0.9999967112521108,
                0.9999810748540223,
                0.9999984465024306,
                0.9999970976890528,
                0.9999982396574163,
                0.9999962733593832
            ],
            [
                1.2098661161861e-06,
                1.9947297214544894e-06,
                1.3709572068179446e-06,
                1.9947304348595095e-06,
                1.5534971989809095e-06,
                2.5612828212676906e-06,
                1.0677026154551157e-06,
                9.422445938797133e-07,
                3.2887506334560605e-06,
                9.422450431800595e-07
            ],
            [
                0.9999724643089131,
                0.9999852610233527,
                0.9999810748562776,
                0.9999251537995921,
                0.9999921107392962,
                0.9999599363032492,
                0.999992110733665,
                0.9999869928684584,
                0.9999546021165822,
                0.9579122756889437
            ],
            [
                0.9999980052695653,
                0.9999986290429567,
                0.999998446502801,
                0.9999967112513268,
                0.999997097687669,
                0.9999970976869772,
                0.999997097687323,
                0.9999992661790195,
                0.9999952149032242,
                0.9999977396759717
            ],
            [
                0.99999893229713,
                0.9999990577551815,
                0.9999989322967481,
                0.9999977396762412,
                0.9999980052707541,
                0.9999982396565769,
                0.9999986290429566,
                0.9999977396746245,
                0.9999974387187054,
                0.9999994284993485
            ],
            [
                0.999998446502801,
                0.9999992661787571,
                0.9999952149066464,
                0.9999986290421394,
                0.9999984465016899,
                0.9999982396572065,
                0.9999992661792819,
                0.9999987901337396,
                0.9999989322966208,
                0.999998005269803
            ],
            [
                0.9999967112509347,
                0.9999921107355338,
                0.999996273358939,
                0.9999977396762411,
                0.9999987901338838,
                0.9999987901344607,
                0.9999984465018751,
                0.9999957771675623,
                0.9999986290432835,
                0.9999987901344607
            ],
            [
                0.9999994284996211,
                0.9999987901340281,
                0.9999930377420913,
                0.9999986290426298,
                0.9999962733620488,
                0.9999992661790196,
                0.9999987901338838,
                0.9999967112497585,
                0.9999991684720715,
                0.9999989322967482
            ],
            [
                0.9999990577554061,
                0.9999984465016899,
                0.9999977396751634,
                0.999998790134605,
                0.999999168471675,
                0.9999987901344608,
                0.9999986290424664,
                0.999999352405279,
                0.9999970976890529,
                0.9999989322968753
            ],
            [
                0.999933947839643,
                0.9999339478711182,
                0.9999485577802613,
                0.5926665999540698,
                0.999993037741309,
                0.9999724642958978,
                0.9998415637080029,
                0.9999910603015745,
                0.9978172835085093,
                0.6513548714339145
            ],
            [
                0.9999957771650455,
                0.9999990577556308,
                0.9999970976890529,
                0.99999893229713,
                0.9999987901346049,
                0.9999992661789321,
                0.9999977396757023,
                0.9999974387168734,
                0.9999974387180947,
                0.9999992661791944
            ],
            [
                1.99472900796355e-06,
                1.5534977545603963e-06,
                3.7266392840781026e-06,
                2.260324028351814e-06,
                1.9947306726213275e-06,
                4.222834954461155e-06,
                1.5534971989907999e-06,
                2.260325375650449e-06,
                9.422447062150634e-07,
                1.7603434231241496e-06
            ],
            [
                0.9999994956527721,
                0.9999994284995529,
                0.9999974387184,
                0.9999992661788445,
                0.9999974387184,
                0.9999990577555185,
                0.9999994956526519,
                0.9999993524051246,
                0.9999980052702786,
                0.9999993524052019
            ],
            [
                0.9999992661791944,
                0.999999352405279,
                0.9999982396574163,
                0.999999266178932,
                0.9999997300422869,
                0.9999993524053562,
                0.99999976176309,
                0.9999994284994167,
                0.9999986290432835,
                0.999999653367379
            ],
            [
                0.9999974387174841,
                0.9999987901344607,
                0.999996711252111,
                0.9999992661791071,
                0.9999967112497586,
                0.9999992661789321,
                0.9999984465022455,
                0.9999967112497585,
                0.9999967112517189,
                0.9999957771665557
            ],
            [
                0.9999982396565769,
                0.9999984465015047,
                0.9999989322971299,
                0.9999987901337396,
                0.9999970976880149,
                0.999998790134605,
                0.9999938558246662,
                0.9999982396559474,
                0.999998790134605,
                0.9999980052705163
            ],
            [
                0.999993855826131,
                0.9999938558253986,
                0.9999994284996211,
                0.999995214906076,
                0.9999982396574163,
                0.9999974387168734,
                0.9999986290424664,
                0.9999980052709919,
                0.9999930377454109,
                0.9999980052709919
            ],
            [
                0.9999980052705164,
                0.9999987901347491,
                0.9999994956526519,
                0.9999977396759716,
                0.9999996072138934,
                0.9999994956527721,
                0.9999996072138934,
                0.999998790134605,
                0.9999982396574163,
                0.999998790134028
            ],
            [
                0.9999991684722698,
                0.9999962733598275,
                0.9999977396765105,
                0.9999987901341723,
                0.9999987901341723,
                0.9999992661790196,
                0.9999984465016899,
                0.999999057755743,
                0.9999974387187054,
                0.9999974387168734
            ],
            [
                0.9999930377404307,
                0.9999977396762411,
                0.9999885212332436,
                0.9999724643056231,
                0.9999980052693274,
                0.9999832985701962,
                0.9999885212277698,
                0.9999785550439207,
                0.9999987901344607,
                0.9999599363173789
            ],
            [
                1.1478772227964558e-05,
                2.5612822106841303e-06,
                2.9023123310580418e-06,
                3.2887482807780376e-06,
                1.3007125357804606e-05,
                6.144173867753695e-06,
                5.829128614135801e-05,
                1.3007128457958606e-05,
                6.962253759271479e-06,
                6.144177531007026e-06
            ],
            [
                1.0677027427471959e-06,
                5.043475284447896e-07,
                8.315281267800897e-07,
                2.2603242978377903e-06,
                3.288749457383046e-06,
                1.99472924590571e-06,
                8.315280276607289e-07,
                8.315281267800897e-07,
                1.0677032518748838e-06,
                1.553497754577351e-06
            ],
            [
                0.9999992661789321,
                0.999998005269803,
                0.9999984465022455,
                0.9999980052709919,
                0.9999980052705164,
                0.9999989322975118,
                0.9999987901340281,
                0.9999994284993485,
                0.9999982396565769,
                0.9999938558239334
            ],
            [
                0.9999990577549568,
                0.999999266178757,
                0.9999967112505427,
                0.9999957771650454,
                0.9999967112513267,
                0.9999986290429567,
                0.9999930377412608,
                0.9999994284993485,
                0.9999977396757022,
                0.9999990577549568
            ],
            [
                0.999999495652652,
                0.9999994284996211,
                0.9999996533674614,
                0.9999980052702786,
                0.9999986290426297,
                0.999999266178757,
                0.999997097687323,
                0.9999977396748938,
                0.9999993524053562,
                0.9999980052705163
            ],
            [
                0.9999994956526519,
                0.9999986290421394,
                0.9999990577550691,
                0.9999980052698031,
                0.9999992661786695,
                0.999997097689053,
                0.9999993524054335,
                0.9999977396757023,
                0.9999991684718733,
                0.9999989322968754
            ],
            [
                0.9999967112513267,
                0.9999990577550691,
                0.9999967112497584,
                0.9999970976876691,
                0.9999987901346049,
                0.9999984465024306,
                0.9999986290427931,
                0.9999993524050473,
                0.9999991684715759,
                0.9999994284996893
            ],
            [
                0.9999869928668863,
                0.9999646437450735,
                0.8933094060543488,
                0.952574126654137,
                0.9999599362985095,
                0.9999952149049351,
                0.9999852610215418,
                0.9999687980997913,
                0.9999980052693305,
                0.9999724643023399
            ],
            [
                8.315279285251204e-07,
                1.2098662604126641e-06,
                2.56128282131428e-06,
                2.260324836696773e-06,
                1.5534979397592542e-06,
                5.422218969769604e-06,
                3.2887486732000038e-06,
                1.0677031245905116e-06,
                2.5612822106841303e-06,
                4.222835457852533e-06
            ],
            [
                6.9622562487453084e-06,
                2.561283126639892e-06,
                1.0677031245851707e-06,
                1.3709573702722555e-06,
                1.7603434231241496e-06,
                7.889260704179641e-06,
                1.5534971989907999e-06,
                6.144173136455602e-06,
                1.3709578605118645e-06,
                5.715005151550947e-07
            ],
            [
                0.999997438717484,
                0.9999945777823233,
                0.9999957771680659,
                0.9999952149072168,
                0.9999885212291393,
                0.999995214906076,
                0.9999885212264024,
                0.9999967112509347,
                0.9999967112513268,
                0.9999967112517189
            ],
            [
                0.9999980052707542,
                0.9999974387168733,
                0.9999974387187054,
                0.9999990577556308,
                0.9999989322973846,
                0.9999962733598278,
                0.9999993524054334,
                0.9999987901337396,
                0.999999266178932,
                0.9999980052698031
            ],
            [
                1.9947306726213275e-06,
                2.5612828213352452e-06,
                2.9023109471188266e-06,
                1.3709578605455302e-06,
                1.0677026154619133e-06,
                1.7603436330091044e-06,
                1.3709573702566696e-06,
                3.2887494573232236e-06,
                1.5534983101393749e-06,
                1.7603438428564603e-06
            ],
            [
                0.9999987901337396,
                0.9999987901341723,
                0.999996273358939,
                0.9999962733611605,
                0.999998790134028,
                0.999997097687323,
                0.9999991684717742,
                0.99999893229713,
                0.9999989322972573,
                0.9999987901337396
            ],
            [
                0.9999957771650453,
                0.9999977396754327,
                0.9999990577555185,
                0.9999982396559474,
                0.9999977396748938,
                0.9999989322970028,
                0.9999957771655489,
                0.9999974387187053,
                0.9999970976887069,
                0.999999266179107
            ],
            [
                0.9999989322967481,
                0.9999982396574163,
                0.9999982396569966,
                0.9999921107355337,
                0.9999952149037942,
                0.999999266179107,
                0.9999993524049702,
                0.9999982396574163,
                0.9999991684719723,
                0.9999974387180947
            ],
            [
                0.9999986290421395,
                0.9999994284996893,
                0.9999991684719723,
                0.999999428499553,
                0.9999994284994168,
                0.9999994284997573,
                0.9999991684717741,
                0.9999990577555185,
                0.9999994956524715,
                0.9999996072138934
            ],
            [
                0.9999993524049702,
                0.9999980052700408,
                0.999999057755743,
                0.9999991684721706,
                0.9999996533673375,
                0.9999990577550691,
                0.9999977396757022,
                0.9999992661786695,
                0.9999977396757023,
                0.9999987901344607
            ],
            [
                1.8925155002022494e-05,
                1.4738976698006875e-05,
                3.120192251631124e-05,
                8.481102100559352e-05,
                1.4738978455701077e-05,
                1.3007131564643372e-05,
                3.535626331056557e-05,
                5.82912723385944e-05,
                1.0129992185981682e-05,
                3.5356246483883486e-05
            ],
            [
                0.9999989322975118,
                0.9999977396748939,
                0.9999989322966208,
                0.9999987901344607,
                0.9999993524053562,
                0.9999989322972572,
                0.9999990577550691,
                0.9999984465022455,
                0.9999989322970027,
                0.9999989322972572
            ],
            [
                0.9999994956523512,
                0.9999993524050474,
                0.9999984465026158,
                0.9999986290427931,
                0.999999352405279,
                0.9999991684722698,
                0.9999982396559474,
                0.9999986290423029,
                0.9999990577555185,
                0.999997438717484
            ],
            [
                1.55349775456958e-06,
                7.889264466445326e-06,
                1.7603440527046419e-06,
                1.3709573702722555e-06,
                1.7603427936183298e-06,
                2.4300237828059798e-05,
                2.2603237589028734e-06,
                2.260324567302214e-06,
                2.5612825160096693e-06,
                1.7603436330091044e-06
            ],
            [
                0.9999982396574163,
                0.9999984465016899,
                0.9999984465022455,
                0.9999982396567867,
                0.999997438717484,
                0.9999993524049703,
                0.9999977396754327,
                0.9999982396574163,
                0.9999990577549568,
                0.9999974387168733
            ],
            [
                0.9999996072137061,
                0.9999989322967481,
                0.9999646437408798,
                0.9999945777784452,
                0.9999930377445809,
                0.9999898700078143,
                0.999989870009022,
                0.9999885212264024,
                0.9999885212277702,
                0.9999938558239335
            ],
            [
                0.9999982396559474,
                0.9999992661789321,
                0.9999994284994167,
                0.9999982396559474,
                0.999997438717484,
                0.9999990577549568,
                0.9999984465022455,
                0.9999990577556307,
                0.9999989322966208,
                0.9999992661786695
            ],
            [
                0.9999994284994167,
                0.9999974387168734,
                0.9999993524049703,
                0.9999980052709919,
                0.9999930377454113,
                0.9999984465022455,
                0.999997438716568,
                0.999999168471675,
                0.9999977396746245,
                0.9999984465024307
            ],
            [
                0.9999984465022456,
                0.9999992661790195,
                0.9999990577556308,
                0.9999984465026158,
                0.9999980052693275,
                0.9999989322966208,
                0.999999266178932,
                0.999998790134605,
                0.9999993524049703,
                0.9999984465018751
            ],
            [
                4.785095064819011e-06,
                3.288748281295496e-06,
                1.7603434231705793e-06,
                2.5612816000145246e-06,
                2.2603248366762157e-06,
                1.209865683518615e-06,
                1.7603430034439723e-06,
                4.222834451215781e-06,
                1.9947306726358406e-06,
                1.2098656835136636e-06
            ],
            [
                0.9999989322970027,
                0.9999990577552939,
                0.9999967112513267,
                0.9999952149043646,
                0.9999974387171787,
                0.9999989322968753,
                0.9999984465022455,
                0.9999967112509347,
                0.999995777165549,
                0.999998446502801
            ],
            [
                0.9999989322968754,
                0.9999962733620488,
                0.9999990577555185,
                0.9999984465018751,
                0.9999990577551815,
                0.9999992661790195,
                0.9999989322972572,
                0.9999967112517189,
                0.9999980052705164,
                0.9999995549149481
            ],
            [
                3.726640172337686e-06,
                1.0677029973158649e-06,
                6.475947982022763e-07,
                2.5612831265909735e-06,
                5.043475885688201e-07,
                1.5534981249574276e-06,
                1.0677031245953668e-06,
                7.338212429537553e-07,
                2.902313022984344e-06,
                2.9023112931688987e-06
            ],
            [
                0.9999987901346049,
                0.9999980052707541,
                0.9999989322975118,
                0.9999991684722698,
                0.9999986290424664,
                0.9999992661788446,
                0.9999991684718732,
                0.9999994284995529,
                0.9999992661786696,
                0.9999989322968754
            ],
            [
                0.9999990577556308,
                0.9999989322966208,
                0.9999996072137529,
                0.9999869928653358,
                0.9999967112517189,
                0.9999989322972573,
                0.9999974387177895,
                0.9999991684718732,
                0.9999996533672135,
                0.9999996072137529
            ],
            [
                0.9999989322973847,
                0.9999986290427931,
                0.9999994284997573,
                0.9999992661786696,
                0.9999996533672962,
                0.9999990577555185,
                0.9999982396559474,
                0.9999987901338839,
                0.9999989322966208,
                0.9999992661789321
            ],
            [
                0.999998239656367,
                0.9999991684715759,
                0.999996273358939,
                0.9999990577552937,
                0.9999996072137061,
                0.9999994284992805,
                0.9999986290427932,
                0.9999989322966208,
                0.9999967112513267,
                0.999997097687669
            ],
            [
                0.9999832985781563,
                0.9999417087553089,
                0.999978555041362,
                0.9999810748540158,
                0.9999810748495034,
                0.9999957771665555,
                0.9999785550439195,
                0.9999339478474795,
                0.9999977396748938,
                0.9995694430132677
            ],
            [
                0.9999982396559474,
                0.9999898700114366,
                0.9999952149049355,
                0.9999977396746244,
                0.9999984465016899,
                0.9999986290426297,
                0.9999974387187053,
                0.9999970976880149,
                0.9999962733616046,
                0.9999977396765106
            ],
            [
                0.9999967112497585,
                0.9999982396567867,
                0.9999984465020603,
                0.9999921107392978,
                0.9999885212332448,
                0.9999984465016899,
                0.9999984465016898,
                0.9999980052695652,
                0.9999930377404314,
                0.9999970976880149
            ],
            [
                0.9999992661791944,
                0.999999352405279,
                0.999997438717484,
                0.999997097686631,
                0.9999987901337396,
                0.9999952149055056,
                0.9999980052695652,
                0.9999957771655492,
                0.9999957771645421,
                0.9999991684715758
            ],
            [
                0.9999986290427931,
                0.999997438716568,
                0.9999970976880149,
                0.9999986290424663,
                0.9999974387180947,
                0.9999980052707541,
                0.999998005269803,
                0.9999994284995529,
                0.9999982396565769,
                0.9999991684717741
            ],
            [
                0.9999967112513267,
                0.9999991684722697,
                0.9999991684717741,
                0.9999991684722698,
                0.9999962733593835,
                0.9999993524051246,
                0.9999989322972573,
                0.9999990577555185,
                0.9999991684715759,
                0.9999977396759717
            ],
            [
                0.9999994956526519,
                0.9999982396574163,
                0.9999994956523514,
                0.9999974387168734,
                0.9999994956527121,
                0.9999994284996891,
                0.9999990577554061,
                0.9999993524052018,
                0.9999984465020603,
                0.9999991684719723
            ],
            [
                0.99999862904312,
                0.9999970976887069,
                0.9999970976883609,
                0.9999938558275958,
                0.9999984465016899,
                0.9999982396567867,
                0.9999974387177893,
                0.9999974387187054,
                0.9999938558275957,
                0.999998446502801
            ],
            [
                0.9999987901337396,
                0.9999980052705163,
                0.9999989322968754,
                0.9999987901338838,
                0.9999938558268634,
                0.9999991684721706,
                0.9999990577554061,
                0.9999986290423029,
                0.9999986290424663,
                0.9999991684718732
            ],
            [
                0.9999989322966208,
                0.9999987901341723,
                0.999996711250935,
                0.9999974387165681,
                0.999997097688707,
                0.9999980052707541,
                0.9999987901347492,
                0.9999785550439222,
                0.9999962733598277,
                0.9999967112509348
            ],
            [
                0.9999977396748938,
                0.9999994284993485,
                0.9999995549149481,
                0.9999977396765105,
                0.999999057755069,
                0.999998446502801,
                0.9999989322968754,
                0.9999992661790195,
                0.9999995549150542,
                0.9999994284994167
            ],
            [
                0.9999989322973847,
                0.9999984465026159,
                0.9999974387174841,
                0.9999987901341724,
                0.9999991684722698,
                0.9999977396759717,
                0.9999987901347491,
                0.9999990577550693,
                0.9999991684721706,
                0.999999352405279
            ],
            [
                0.9999992661791945,
                0.9999982396569966,
                0.9999987901347492,
                0.9999991684718732,
                0.9999989322970027,
                0.9999984465016899,
                0.9999974387168733,
                0.9999982396565769,
                0.9999962733607161,
                0.9999989322970027
            ],
            [
                0.9999986290424664,
                0.9999987901341723,
                0.99999862904312,
                0.999999266178757,
                0.9999992661791945,
                0.9999990577555185,
                0.9999990577556308,
                0.9999994956524716,
                0.999999352405279,
                0.9999994284993485
            ],
            [
                0.9999990577549568,
                0.9999980052705163,
                0.9999990577556308,
                0.9999990577556308,
                0.9999989322968753,
                0.9999984465016899,
                0.9999986290421395,
                0.9999987901337396,
                0.9999987901346049,
                0.9999991684720715
            ],
            [
                0.9999977396757023,
                0.9999910602994345,
                0.9999930377437514,
                0.9999977396754327,
                0.9999962733589395,
                0.9999984465015047,
                0.9999974387184,
                0.9999992661788445,
                0.9999990577557432,
                0.999997097686977
            ],
            [
                0.9999885212346129,
                0.9999962733602719,
                0.9999980052700408,
                0.999997097686977,
                0.9999974387180948,
                0.9999990577549569,
                0.9999974387184001,
                0.9999980052695652,
                0.9999986290429566,
                0.9999967112501509
            ],
            [
                0.999995214906076,
                0.9859363720140638,
                0.9999921107402363,
                0.9820137915512787,
                0.9999724643089131,
                0.9999930377437902,
                0.9999898700078136,
                0.9999785550541502,
                0.9999810748540188,
                0.9999869928653338
            ]
        ]
    },
    {
        "q_id": "8793_mmlu_math",
        "cot_ids": [
            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,
            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
        ],
        "rewards": [
            [
                0.9999977396748939,
                0.9999785550413672,
                0.9999984465022455,
                0.999992110740236,
                0.9999832985741738,
                0.9999930377404306,
                0.9999994284993486,
                0.9999646437619467,
                0.999996273360716,
                0.9999921107355341
            ],
            [
                0.999997097689053,
                0.9999987901341724,
                0.9999986290432834,
                0.9999991684719725,
                0.9999987901344608,
                0.999998005269803,
                0.9999994284994849,
                0.999998005270992,
                0.9999987901341723,
                0.9999987901337396
            ],
            [
                0.9999997897565587,
                0.9999987901340281,
                0.9999984465024306,
                0.99999893229713,
                0.9999994956527722,
                0.9999984465028011,
                0.9999984465016899,
                0.9999990577556308,
                0.9999998144608097,
                0.999999057755743
            ],
            [
                0.9999991684722698,
                0.9999990577554061,
                0.9999987901344608,
                0.999999352404893,
                0.9999987901346049,
                0.999999653367379,
                0.9999996940977002,
                0.9999989322968754,
                0.9999990577550691,
                0.9999996533673788
            ],
            [
                0.9999987901338839,
                0.9999982396561572,
                0.9999984465020603,
                0.9999990577557432,
                0.9999997617631469,
                0.9999989322968754,
                0.9999994956524114,
                0.9999995549147889,
                0.9999986290431201,
                0.9999997897565838
            ],
            [
                0.9999974387187055,
                0.9999989322966208,
                0.9999974387187055,
                0.9999992661790195,
                0.9999995549150542,
                0.9999986290424664,
                0.9999991684721706,
                0.9999995549149481,
                0.9999993524049702,
                0.9999986290421394
            ],
            [
                0.9999990577550691,
                0.9999989322968754,
                0.9999989322968754,
                0.9999989322970027,
                0.9999991684721706,
                0.9999984465015047,
                0.9999998362622552,
                0.9999997617631752,
                0.9999996533672962,
                0.9999992661791071
            ],
            [
                0.9999996072137061,
                0.9999991684721706,
                0.9999993524053563,
                0.9999992661788445,
                0.9999992661792819,
                0.9999991684717741,
                0.9999996072138465,
                0.9999996072137529,
                0.9999996072138934,
                0.9999997300422225
            ],
            [
                0.9999987901344608,
                0.9999970976876691,
                0.9999986290424664,
                0.9999989322966208,
                0.9999982396574163,
                0.999998790134028,
                0.999999168471675,
                0.9999994956525317,
                0.9999994956527722,
                0.9999991684720715
            ],
            [
                0.999998005269803,
                0.9999991684721706,
                0.9999982396574163,
                0.9999986290427931,
                0.9999987901344608,
                0.9999977396754328,
                0.9999990577555185,
                0.9999986290426297,
                0.99999862904312,
                0.9999967112517191
            ],
            [
                0.9999977396751634,
                0.9999980052700408,
                0.99999893229713,
                0.9999984465015047,
                0.9999980052709919,
                0.999995777166556,
                0.9999982396567867,
                0.9999986290431201,
                0.9999974387180949,
                0.9999984465018751
            ],
            [
                0.9999993524051246,
                0.9999989322972572,
                0.9999977396759717,
                0.9999990577552937,
                0.9999982396569966,
                0.9999984465018751,
                0.9999989322966208,
                0.9999991684722698,
                0.9999989322967482,
                0.9999989322975118
            ],
            [
                0.9999989322970028,
                0.9999957771675632,
                0.9999986290421395,
                0.9999986290423029,
                0.9999984465016899,
                0.9999995549150542,
                0.9999987901338838,
                0.9999996072137529,
                0.9999984465020603,
                0.9999993524051246
            ],
            [
                0.9999991684722698,
                0.9999996940978461,
                0.9999997300422225,
                0.9999995549151073,
                0.9999990577549568,
                0.9999996940977002,
                0.9999992661792819,
                0.9999990577555185,
                0.9999996940977366,
                0.99999893229713
            ],
            [
                0.9999992661789321,
                0.9999996533674202,
                0.9999998144609645,
                0.9999986290423029,
                0.9999987901341724,
                0.9999997897566089,
                0.9999989322968754,
                0.9999987901341723,
                0.9999995549147889,
                0.9999987901340281
            ],
            [
                0.9999974387180947,
                0.9999992661790196,
                0.9999996940976636,
                0.9999992661790195,
                0.999999168471675,
                0.9999990577551814,
                0.999999653367379,
                0.9999996072137529,
                0.9999987901338839,
                0.9999993524049702
            ],
            [
                0.9999984465015047,
                0.9999997897565838,
                0.999998790134028,
                0.9999993524050474,
                0.9999989322968755,
                0.9999996940977731,
                0.999999554914789,
                0.9999986290423029,
                0.9999997617631752,
                0.9999990577556308
            ],
            [
                0.9999987901346049,
                0.9999994956524114,
                0.9999998555019446,
                0.9999994956523514,
                0.9999986290426297,
                0.9999997300422868,
                0.9999994956525318,
                0.9999991684720715,
                0.9999991684722698,
                0.9999996072137529
            ],
            [
                0.9999977396757023,
                0.9999945777790916,
                0.9999982396572065,
                0.9999980052707542,
                0.9999987901347492,
                0.9999977396762412,
                0.9999974387165681,
                0.9999986290427932,
                0.9999987901341724,
                0.9999977396759717
            ],
            [
                0.9999992661788445,
                0.999999554914895,
                0.999998629042303,
                0.9999989322970027,
                0.9999990577557432,
                0.9999993524049702,
                0.9999996940978461,
                0.9999995549149481,
                0.9999989322973845,
                0.9999987901344607
            ],
            [
                0.9999984465018751,
                0.9999987901347491,
                0.999998005270992,
                0.999998629042303,
                0.9999977396754328,
                0.9999996940976272,
                0.9999996940978095,
                0.9999989322973846,
                0.9999990577554062,
                0.9999990577552939
            ],
            [
                0.9999982396559474,
                0.999999730042126,
                0.9999996533673375,
                0.9999989322967482,
                0.9999982396561572,
                0.9999996072137998,
                0.9999996533674202,
                0.9999910603005002,
                0.9999984465018751,
                0.9999993524053562
            ],
            [
                0.9999994956523512,
                0.9999993524051246,
                0.9999993524050474,
                0.9999989322968754,
                0.9999989322972572,
                0.9999987901337396,
                0.9999990577551815,
                0.9999996072137061,
                0.9999996072136125,
                0.9999992661791071
            ],
            [
                0.9999987901338838,
                0.9999986290423029,
                0.9999986290427931,
                0.9999989322967481,
                0.9999989322973846,
                0.9999989322973845,
                0.9999991684718732,
                0.9999982396565769,
                0.9999970976869771,
                0.9999980052700408
            ],
            [
                0.9999996940978825,
                0.9999987901344607,
                0.9999998362622747,
                0.9999995549150542,
                0.9999980052702786,
                0.9999987901338838,
                0.999999495652652,
                0.9999997617631752,
                0.9999997300421581,
                0.9999990577555185
            ],
            [
                0.9999993524053562,
                0.9999984465020603,
                0.9999994284992805,
                0.999999814460876,
                0.9999991684720715,
                0.9999989322975119,
                0.9999984465018752,
                0.9999986290424663,
                0.9999980052700409,
                0.9999991684721706
            ],
            [
                0.9999990577551814,
                0.9999996533675028,
                0.9999980052693275,
                0.9999996533672136,
                0.999999730042126,
                0.9999991684718733,
                0.9999989322972572,
                0.9999991684722697,
                0.9999992661791945,
                0.9999991684717741
            ],
            [
                0.9999996072136592,
                0.999998790134028,
                0.999999789756684,
                0.9999992661788445,
                0.9999987901341724,
                0.9999994284997573,
                0.9999970976883612,
                0.9999994956527722,
                0.999999352405279,
                0.9999994284996893
            ],
            [
                0.9999989322968754,
                0.9999997897566589,
                0.999999730042319,
                0.9999997897565838,
                0.9999989322972573,
                0.9999996533673375,
                0.9999994956525317,
                0.9999996940976636,
                0.9999986290421395,
                0.9999987901341724
            ],
            [
                0.9999967112509348,
                0.9999989322973846,
                0.9999987901341723,
                0.9999974387180947,
                0.9999980052707541,
                0.999998239656367,
                0.9999997617630333,
                0.9999967112497585,
                0.9999974387165681,
                0.9999984465016899
            ],
            [
                0.9999970976873231,
                0.999999057755743,
                0.9999998362623332,
                0.9999974387177893,
                0.9999987901344608,
                0.999998790134605,
                0.99999976176309,
                0.9999990577552939,
                0.9999977396762412,
                0.9999990577554061
            ],
            [
                0.99999862904312,
                0.9999977396759717,
                0.9999992661787571,
                0.9999980052693274,
                0.999999057755743,
                0.9999984465022455,
                0.9999989322968754,
                0.9999970976883609,
                0.9999993524051246,
                0.9999996940978095
            ],
            [
                0.9999989322972572,
                0.9999986290424663,
                0.9999991684722698,
                0.9999990577554061,
                0.9999998874648781,
                0.9999997300420937,
                0.9999990577552937,
                0.9999996940978461,
                0.9999994284994848,
                0.9999998555020307
            ],
            [
                0.9999995549151073,
                0.9999994284994849,
                0.9999989322968754,
                0.9999990577550693,
                0.9999980052695652,
                0.9999987901347491,
                0.99999893229713,
                0.9999987901347491,
                0.9999987901343166,
                0.9999980052693275
            ],
            [
                0.9999986290432835,
                0.9999984465024307,
                0.9999990577552937,
                0.9999993524053562,
                0.999998629042303,
                0.9999984465016899,
                0.9999989322973846,
                0.9999991684716749,
                0.9999993524053562,
                0.9999991684722698
            ],
            [
                0.9999977396746245,
                0.9999997617631184,
                0.9999984465018751,
                0.9999987901341723,
                0.9999989322971299,
                0.9999984465020603,
                0.9999984465026159,
                0.9999994284994167,
                0.9999984465022455,
                0.9999982396572065
            ],
            [
                0.9999994284996212,
                0.9999991684721706,
                0.9999982396569966,
                0.9999994284994167,
                0.9999997300420937,
                0.9999989322966208,
                0.9999967112509348,
                0.999999554914842,
                0.9999986290432835,
                0.9999990577551815
            ],
            [
                0.9999994284994168,
                0.9999989322975118,
                0.9999992661786695,
                0.9999990577555185,
                0.9999989322973846,
                0.9999998362622747,
                0.999999266178757,
                0.9999997300422868,
                0.9999997300421581,
                0.9999993524052789
            ],
            [
                0.9999977396751634,
                0.9999982396572065,
                0.9999982396567867,
                0.9999994956526519,
                0.9999980052702787,
                0.999998239656367,
                0.9999996940977731,
                0.9999992661788446,
                0.9999984465020603,
                0.9999982396559474
            ],
            [
                0.9999994956524716,
                0.9999996940976636,
                0.9999989322972572,
                0.9999997300421581,
                0.9999987901340281,
                0.999998446502801,
                0.9999987901337396,
                0.9999987901347492,
                0.9999997300420937,
                0.9999995549150011
            ],
            [
                0.9999991684721706,
                0.9999998362622942,
                0.9999987901340281,
                0.9999987901344607,
                0.9999989322966208,
                0.9999986290424664,
                0.999998932296621,
                0.9999998144608098,
                0.9999991684721706,
                0.9999986290426298
            ],
            [
                0.9999984465020603,
                0.9999982396567867,
                0.9999957771680662,
                0.9999994956525318,
                0.9999996533673375,
                0.9999977396748939,
                0.9999982396569966,
                0.9999986290421394,
                0.9999986290427931,
                0.9999990577552937
            ],
            [
                0.9999997300420937,
                0.9999994956525318,
                0.9999994284995529,
                0.9999996533675028,
                0.9999987901338838,
                0.999999057755743,
                0.9999995549150542,
                0.9999997300420937,
                0.999999352404893,
                0.9999986290426297
            ],
            [
                0.9999989322970028,
                0.9999986290426297,
                0.9999989322973846,
                0.9999998724809267,
                0.9999997897565838,
                0.9999990577556307,
                0.999998790134028,
                0.9999993524052019,
                0.9999984465018751,
                0.9999996533673375
            ],
            [
                0.9999992661792819,
                0.9999991684718732,
                0.9999997897566089,
                0.9999980052702786,
                0.9999990577554062,
                0.9999997300421903,
                0.9999989322966208,
                0.9999992661786695,
                0.9999994284994848,
                0.9999991684718733
            ],
            [
                0.999999352404893,
                0.9999997897565587,
                0.9999996072138934,
                0.9999991684721706,
                0.9999994956523514,
                0.9999996072137998,
                0.9999980052693275,
                0.9999987901338839,
                0.999999855502048,
                0.9999984465026158
            ],
            [
                0.9999977396762412,
                0.9999996072136125,
                0.9999984465026158,
                0.9999967112493665,
                0.9999986290424663,
                0.9999989322975118,
                0.9999989322975118,
                0.9999996940977002,
                0.9999992661792819,
                0.999999653367379
            ],
            [
                0.9999989322975119,
                0.9999984465024306,
                0.9999982396572065,
                0.9999984465016899,
                0.9999987901338838,
                0.9999977396757023,
                0.999999057755743,
                0.9999996940976272,
                0.9999982396559474,
                0.9999984465018751
            ],
            [
                0.999997438717484,
                0.9999989322968754,
                0.9999980052693274,
                0.9999990577549569,
                0.9999982396569966,
                0.9999991684720715,
                0.9999992661788445,
                0.9999974387171788,
                0.9999977396757023,
                0.9999986290424663
            ],
            [
                0.9999993524052018,
                0.9999984465015047,
                0.9999994956525918,
                0.999999554914895,
                0.999999653367379,
                0.9999994284996211,
                0.9999996072137061,
                0.9999996533672962,
                0.9999996533674615,
                0.9999986290421394
            ],
            [
                0.9999986290424664,
                0.9999989322973845,
                0.9999993524049702,
                0.9999980052709919,
                0.999997097686631,
                0.999998005269803,
                0.9999984465026159,
                0.9999986290432835,
                0.9999991684721706,
                0.9999987901340281
            ],
            [
                0.99999862904312,
                0.9999989322967482,
                0.9999986290426298,
                0.9999994956524716,
                0.9999989322968754,
                0.9999986290427931,
                0.9999987901338838,
                0.9999957771645421,
                0.9999994956526519,
                0.9999991684715759
            ],
            [
                0.9999990577556307,
                0.9999990577557432,
                0.9999997897565838,
                0.9999987901337396,
                0.9999991684721706,
                0.9999992661787571,
                0.9999990577551815,
                0.9999990577556308,
                0.9999987901338839,
                0.9999970976866313
            ],
            [
                0.999999814460854,
                0.9999996072136125,
                0.9999997617629764,
                0.9999990577554062,
                0.9999997897566089,
                0.9999990577552937,
                0.9999997897567341,
                0.9999991684720715,
                0.9999998144608538,
                0.999999266179107
            ],
            [
                0.9999989322967482,
                0.9999990577551815,
                0.9999996533672549,
                0.9999993524050474,
                0.9999984465024307,
                0.9999993524053563,
                0.9999984465018752,
                0.9999984465028011,
                0.9999945777784462,
                0.9999986290421394
            ],
            [
                0.9999992661788446,
                0.9999994284993485,
                0.9999994284992805,
                0.9999995549149481,
                0.999998790134028,
                0.9999994284995529,
                0.9999991684718732,
                0.9999990577554061,
                0.9999986290421394,
                0.9999987901343165
            ],
            [
                0.9999990577549569,
                0.9999987901343166,
                0.9999987901341723,
                0.9999989322966208,
                0.9999982396561572,
                0.9999967112521109,
                0.9999989322970028,
                0.9999990577551815,
                0.9999990577555185,
                0.9999990577551815
            ],
            [
                0.9999992661786696,
                0.9999996940977731,
                0.9999984465016899,
                0.9999989322967481,
                0.9999984465020603,
                0.9999994284994167,
                0.9999990577550691,
                0.9999991684717741,
                0.9999991684721706,
                0.9999994284995529
            ],
            [
                0.9999994284994848,
                0.9999994956523514,
                0.9999992661792819,
                0.9999982396569966,
                0.9999990577549568,
                0.9999998362623723,
                0.9999994956525918,
                0.9999996072139402,
                0.9999996940976636,
                0.999999694097846
            ],
            [
                0.9999994956525317,
                0.999998446502801,
                0.9999990577550691,
                0.9999997300422869,
                0.999998005269803,
                0.9999986290421394,
                0.9999993524051246,
                0.9999984465026158,
                0.9999992661791071,
                0.9999997617630049
            ],
            [
                0.9999987901343166,
                0.9999987901341724,
                0.9999989322968754,
                0.9999995549147358,
                0.9999996533674202,
                0.9999997617631752,
                0.9999998555019274,
                0.9999991684719723,
                0.9999996940978825,
                0.9999980052700408
            ],
            [
                0.9999986290427931,
                0.999999554914842,
                0.9999993524053562,
                0.9999997300422547,
                0.9999990577555185,
                0.9999997300421581,
                0.9999998362623528,
                0.9999991684718732,
                0.9999974387184001,
                0.9999989322972573
            ],
            [
                0.9999991684719723,
                0.9999992661786696,
                0.9999993524050473,
                0.9999996533672962,
                0.9999995549150541,
                0.9999977396765105,
                0.9999994956525318,
                0.999999554914789,
                0.9999995549150541,
                0.999999495652652
            ],
            [
                0.9999986290423029,
                0.9999992661790196,
                0.9999984465026158,
                0.9999990577554061,
                0.9999974387177895,
                0.9999991684719723,
                0.9999997617630049,
                0.9999990577555185,
                0.9999984465022455,
                0.9999989322972572
            ],
            [
                0.9999996533672962,
                0.9999989322973845,
                0.9999994284997573,
                0.9999982396565769,
                0.999999266178757,
                0.9999989322968754,
                0.9999991684716749,
                0.9999989322972572,
                0.9999991684717741,
                0.9999991684720715
            ],
            [
                0.9999930377437504,
                0.999998790134028,
                0.9999756997476887,
                0.9999898700102283,
                0.9999832985841309,
                0.9999687980960759,
                0.9999832985701939,
                0.9999599362982708,
                0.999983298578157,
                0.9999977396765105
            ],
            [
                0.999998790134028,
                0.9999967112505428,
                0.9999982396572065,
                0.9999991684718733,
                0.9999977396748939,
                0.9999967112509348,
                0.9999986290432835,
                0.9999986290431201,
                0.999996273358939,
                0.9999977396765106
            ],
            [
                0.9999987901337396,
                0.9999996940978095,
                0.9999977396757024,
                0.9999982396561573,
                0.9999998144608097,
                0.9999990577549568,
                0.9999997300422869,
                0.999999730042319,
                0.9999994956523514,
                0.9999986290424664
            ],
            [
                0.9999994956527722,
                0.9999989322968754,
                0.9999987901337396,
                0.9999993524049703,
                0.9999989322966208,
                0.9999984465015047,
                0.9999994956525918,
                0.9999996533672962,
                0.9999987901338838,
                0.9999984465018751
            ],
            [
                0.9999989322973846,
                0.9999987901337396,
                0.999998005269803,
                0.9999980052702786,
                0.9999991684717742,
                0.9999993524052018,
                0.999998239656367,
                0.99999893229713,
                0.9999982396567867,
                0.9999982396572065
            ],
            [
                0.9999989322973846,
                0.999999266178757,
                0.9999994956523514,
                0.9999994284994849,
                0.9999989322966208,
                0.9999991684719723,
                0.9999987901344607,
                0.9999974387168734,
                0.999999168471675,
                0.9999994284994848
            ],
            [
                0.9999994284993485,
                0.9999974387174843,
                0.9999996072138465,
                0.9999977396746246,
                0.9999984465024307,
                0.9999992661792819,
                0.9999987901338839,
                0.9999994956527722,
                0.9999994956525317,
                0.9999994284992805
            ],
            [
                0.9999997897566338,
                0.9999994956525318,
                0.9999977396762411,
                0.9999999006880904,
                0.999999057755743,
                0.9999996072136125,
                0.9999987901341723,
                0.9999992661790195,
                0.9999997617630617,
                0.9999991684715759
            ],
            [
                0.9999997897565587,
                0.9999997617630049,
                0.9999991684716749,
                0.9999994284996891,
                0.9999998874648514,
                0.9999994284997574,
                0.9999986290432835,
                0.999999554914895,
                0.9999995549151073,
                0.9999991684720715
            ],
            [
                0.9999991684722697,
                0.9999984465018751,
                0.9999993524050473,
                0.9999991684720715,
                0.999999168471675,
                0.9999990577554061,
                0.9999990577551815,
                0.9999987901344607,
                0.9999986290424664,
                0.9999990577556307
            ],
            [
                0.9999151889182053,
                0.8807970732843033,
                0.9996200154687985,
                0.9997694931752811,
                0.9998415638397973,
                0.9982992775219556,
                0.9999339478238272,
                0.9998415637834701,
                0.9999151889387635,
                0.9998601778759504
            ],
            [
                0.9999990577555185,
                0.9999986290423029,
                0.9999967112497589,
                0.9999998362622746,
                0.9999997617631469,
                0.9999986290426298,
                0.9999998724809115,
                0.9999984465016899,
                0.9999977396748939,
                0.9999993524053562
            ],
            [
                0.9999987901343165,
                0.9999994284992805,
                0.9999990577555185,
                0.9999994956523514,
                0.9999989322968754,
                0.9999989322968754,
                0.9999992661792819,
                0.9999997617631752,
                0.9999990577552939,
                0.9999990577552939
            ],
            [
                0.9999993524053562,
                0.9999982396559474,
                0.9999990577557432,
                0.9999997897567091,
                0.9999989322968754,
                0.9999996533672135,
                0.9999998362623137,
                0.9999994956527121,
                0.9999990577549568,
                0.9999989322975118
            ],
            [
                0.999999352404893,
                0.9999992661789321,
                0.9999987901341723,
                0.9999989322967481,
                0.9999991684715758,
                0.9999984465016899,
                0.9999994284992805,
                0.9999982396561572,
                0.9999989322967481,
                0.9999996072137998
            ],
            [
                0.9999997617631752,
                0.9999989322972572,
                0.9999991684721706,
                0.9999977396765106,
                0.9999987901343165,
                0.9999987901346049,
                0.9999996940978461,
                0.999999789756684,
                0.999999554914895,
                0.99999862904312
            ],
            [
                0.999999057755743,
                0.9999994956525317,
                0.9999974387177893,
                0.999999266178932,
                0.9999993524050474,
                0.9999990577555185,
                0.9999994956523514,
                0.9999992661790195,
                0.9999984465020603,
                0.9999991684718732
            ],
            [
                0.9999987901338838,
                0.9999994956524716,
                0.9999996533674615,
                0.9999996533673375,
                0.9999989322966208,
                0.999999554914789,
                0.9999996072136592,
                0.9999974387168734,
                0.9999998874648379,
                0.9999982396561572
            ],
            [
                0.9999990577555185,
                0.9999980052709919,
                0.9999992661791071,
                0.9999994956527121,
                0.9999996533674201,
                0.9999994956525317,
                0.9999990577555185,
                0.999999168471675,
                0.999998790134605,
                0.9999995549149481
            ],
            [
                0.9999984465020603,
                0.9999993524053562,
                0.9999989322972573,
                0.999999266179107,
                0.9999994284996211,
                0.9999987901338838,
                0.9999990577552939,
                0.9999990577549568,
                0.9999987901341724,
                0.9999982396572065
            ],
            [
                0.9999984465024307,
                0.999999495652712,
                0.9999990577550691,
                0.999999730042319,
                0.9999980052709921,
                0.9999996533672549,
                0.9999992661791944,
                0.9999989322972572,
                0.9999997897565587,
                0.999999266178757
            ],
            [
                0.9999997300421581,
                0.9999980052693274,
                0.999999266179107,
                0.9999980052707541,
                0.9999996940977366,
                0.9999992661786696,
                0.9999984465015047,
                0.9999987901347491,
                0.999999554914895,
                0.999999352405279
            ],
            [
                0.9999994284996893,
                0.9999987901341724,
                0.9999977396754328,
                0.9999995549150542,
                0.9999982396567868,
                0.9999989322975118,
                0.9999986290426298,
                0.9999994956523514,
                0.999998239656367,
                0.9999987901340281
            ],
            [
                0.9999997300422547,
                0.9999995549151073,
                0.9999996072136125,
                0.9999994956526519,
                0.9999984465018751,
                0.9999991684719725,
                0.9999991684721706,
                0.9999990577552937,
                0.9999994284995529,
                0.9999962733607162
            ],
            [
                0.9999984465016899,
                0.9999994284994849,
                0.9999986290427932,
                0.9999990577555185,
                0.9999990577552937,
                0.9999980052693275,
                0.9999997300422225,
                0.9999992661786696,
                0.9999996533674615,
                0.9999987901344607
            ],
            [
                0.9999994284994848,
                0.9999982396574163,
                0.9999987901347491,
                0.9999986290431201,
                0.9999989322966208,
                0.9999991684721706,
                0.9999990577551815,
                0.999999352405279,
                0.9999992661786696,
                0.999998932296621
            ],
            [
                0.9999982396567867,
                0.9999996072139402,
                0.999998790134605,
                0.9999996072137529,
                0.9999980052707542,
                0.9999987901343165,
                0.9999995549150011,
                0.9999998362623137,
                0.9999989322968754,
                0.9999990577556308
            ],
            [
                0.9999984465024306,
                0.9999980052693275,
                0.9999992661790196,
                0.999998446502801,
                0.9999986290424663,
                0.9999994284993485,
                0.999998005269803,
                0.9999997897567091,
                0.999998005269803,
                0.9999980052707542
            ],
            [
                0.9999990577557432,
                0.999999168471675,
                0.9999984465026158,
                0.9999994284993485,
                0.9999994956523514,
                0.9999986290424664,
                0.999998790134605,
                0.9999991684718732,
                0.9999990577551815,
                0.9999990577551814
            ],
            [
                0.9999997897565838,
                0.9999987901338839,
                0.999998790134028,
                0.9999991684718733,
                0.9999994284995529,
                0.9999987901346049,
                0.9999990577554061,
                0.9999984465026158,
                0.9999996072139402,
                0.9999992661791944
            ],
            [
                0.9999984465015047,
                0.9999986290429567,
                0.9999992661788446,
                0.9999992661791945,
                0.9999987901343166,
                0.9999990577549569,
                0.9999996533674201,
                0.9999992661792819,
                0.9999996940976272,
                0.9999994956525918
            ],
            [
                0.9999996940976272,
                0.9999996940978095,
                0.9999997617630333,
                0.9999995549150542,
                0.9999997897567091,
                0.9999998144608097,
                0.9999995549150011,
                0.9999999397643011,
                0.9999991684721706,
                0.9999998144608098
            ],
            [
                0.999998446502616,
                0.9999987901341724,
                0.9999990577551815,
                0.9999994956527721,
                0.9999989322973846,
                0.9999994284996891,
                0.9999991684719723,
                0.9999989322975118,
                0.9999990577555185,
                0.999999057755743
            ],
            [
                0.9999990577549569,
                0.9999987901347492,
                0.999999168471675,
                0.9999994956527721,
                0.9999990577554062,
                0.9999984465026159,
                0.9999994284996211,
                0.9999987901347492,
                0.9999996940978825,
                0.9999996940978825
            ],
            [
                0.9999994956527722,
                0.9999994956526519,
                0.9999982396567868,
                0.9999982396572065,
                0.9999994284994849,
                0.9999993524054334,
                0.9999987901341723,
                0.9999991684717742,
                0.9999984465015047,
                0.9999992661792819
            ],
            [
                0.9999992661786695,
                0.9999987901337396,
                0.9999990577554061,
                0.9999989322973846,
                0.999999266179107,
                0.9999996940976272,
                0.9999984465016899,
                0.9999997617631184,
                0.9999994284997573,
                0.9999977396765106
            ],
            [
                0.9999987901340281,
                0.9999993524053563,
                0.9999987901343166,
                0.9999994284993486,
                0.9999982396572065,
                0.9999984465018752,
                0.9999982396559474,
                0.9999977396751634,
                0.9999982396569966,
                0.9999974387187055
            ],
            [
                0.9999995549147889,
                0.9999989322967482,
                0.9999991684717742,
                0.9999991684721706,
                0.9999984465022455,
                0.9999986290423029,
                0.999999352405279,
                0.9999982396574163,
                0.9999995549149481,
                0.9999989322970028
            ],
            [
                0.9999996072136125,
                0.9999992661786696,
                0.9999984465015047,
                0.9999991684715759,
                0.9999992661787571,
                0.9999989322973846,
                0.9999997300420937,
                0.9999991684722698,
                0.9999990577551815,
                0.9999992661787571
            ],
            [
                0.9999986290427931,
                0.9999984465028011,
                0.999998005269803,
                0.9999987901346049,
                0.999997097688361,
                0.999998629042303,
                0.9999989322975118,
                0.9999984465016899,
                0.9999989322968754,
                0.9999995549151073
            ],
            [
                0.9999982396561572,
                0.9999986290426297,
                0.9999994284994167,
                0.9999987901341724,
                0.9999977396762411,
                0.9999986290432835,
                0.9999987901343166,
                0.9999996940977002,
                0.9999998362623137,
                0.9999980052700409
            ],
            [
                0.9999989322975119,
                0.9999996072139402,
                0.9999990577554061,
                0.9999995549147889,
                0.9999986290426297,
                0.999999057755743,
                0.9999992661792819,
                0.9999996533672962,
                0.9999980052707541,
                0.9999990577557432
            ],
            [
                0.9999996940978095,
                0.9999990577556308,
                0.9999984465022455,
                0.9999977396748939,
                0.9999996072137529,
                0.9999990577554061,
                0.9999993524051246,
                0.9999992661787571,
                0.9999987901347492,
                0.9999996072136125
            ],
            [
                0.9999989322967481,
                0.9999990577554062,
                0.9999992661787571,
                0.9999990577550691,
                0.9999991684715759,
                0.9999990577554061,
                0.9999996072138465,
                0.9999991684720715,
                0.999997739674894,
                0.9999994956524716
            ],
            [
                0.9999987901346049,
                0.9999995549147358,
                0.9999992661788445,
                0.9999990577552937,
                0.9999991684718733,
                0.9999990577552939,
                0.9999974387177893,
                0.9999994284995529,
                0.999999057755743,
                0.9999996533672962
            ],
            [
                0.9999984465026158,
                0.9999992661786695,
                0.9999984465024306,
                0.9999995549150011,
                0.9999984465026159,
                0.9999982396574163,
                0.9999998362623722,
                0.9999993524053562,
                0.9999990577550691,
                0.9999989322973846
            ],
            [
                0.9999997300421581,
                0.9999984465015047,
                0.9999996533674615,
                0.999999554914842,
                0.9999994956527121,
                0.9999991684719725,
                0.9999996533672962,
                0.99999862904312,
                0.9999993524050474,
                0.999999168471675
            ],
            [
                0.9999994956524114,
                0.999999266178757,
                0.9999984465015048,
                0.9999987901347492,
                0.9999996533674615,
                0.9999980052707542,
                0.9999986290421394,
                0.9999989322972573,
                0.9999962733589393,
                0.9999993524053562
            ],
            [
                0.9999994956526519,
                0.9999991684722698,
                0.9999997300421581,
                0.9999990577551815,
                0.9999997617630616,
                0.9999994284996893,
                0.9999989322975118,
                0.9999991684720715,
                0.9999990577556308,
                0.9999987901338839
            ],
            [
                0.9999986290427932,
                0.9999991684715758,
                0.9999997617630332,
                0.9999989322972572,
                0.9999991684720715,
                0.9999995549151073,
                0.9999992661788445,
                0.9999995549150542,
                0.9999992661791944,
                0.9999991684719723
            ],
            [
                0.9999996072137998,
                0.9999997617631468,
                0.9999989322966208,
                0.9999995549147359,
                0.9999989322970028,
                0.9999991684718732,
                0.9999990577554061,
                0.9999987901341723,
                0.999998629042303,
                0.9999998555020135
            ],
            [
                0.9999989322968753,
                0.9999984465024306,
                0.9999989322975119,
                0.9999989322970027,
                0.9999996072138465,
                0.9999998362622552,
                0.9999992661786695,
                0.999999352404893,
                0.9999990577550693,
                0.9999987901338838
            ],
            [
                0.9999990577551814,
                0.9999998362622552,
                0.999998005269803,
                0.999997097686631,
                0.9999977396759717,
                0.999999057755069,
                0.9999984465026159,
                0.999997438717484,
                0.9999977396757023,
                0.9999987901346049
            ],
            [
                0.999998239656367,
                0.9999989322972572,
                0.9999994284993485,
                0.9999996072139402,
                0.9999991684715758,
                0.9999994284996891,
                0.9999987901337396,
                0.9999994284997573,
                0.9999997300422547,
                0.9999987901338839
            ],
            [
                0.9999977396754328,
                0.9999996533672549,
                0.999999730042319,
                0.999998932296621,
                0.9999994956523514,
                0.9999996533674615,
                0.9999997300421581,
                0.9999996533672135,
                0.9999982396567868,
                0.9999995549151073
            ],
            [
                0.9999987901337396,
                0.9999990577557432,
                0.9999982396574163,
                0.9999998144608319,
                0.9999982396569966,
                0.9999990577556308,
                0.9999982396565769,
                0.9999991684717742,
                0.9999984465015047,
                0.9999989322968754
            ],
            [
                0.9999980052695652,
                0.999998790134028,
                0.9999996533675028,
                0.9999996072137061,
                0.9999997897566589,
                0.999999730042319,
                0.9999990577557432,
                0.9999997617630332,
                0.9999994956524716,
                0.9999993524052018
            ],
            [
                0.9999997300422869,
                0.9999994284993485,
                0.9999986290421395,
                0.9999993524052019,
                0.9999967112497586,
                0.9999991684721706,
                0.99999862904312,
                0.999999814460854,
                0.999999554914895,
                0.9999993524049702
            ],
            [
                0.9999991684722698,
                0.9999998144609645,
                0.9999980052702786,
                0.9999990577555185,
                0.9999996072136592,
                0.9999987901341724,
                0.9999987901341723,
                0.9999993524054335,
                0.9999982396561572,
                0.9999991684719723
            ],
            [
                0.9999990577550691,
                0.9999989322970028,
                0.9999984465018751,
                0.9999989322973846,
                0.9999989322967482,
                0.9999977396757023,
                0.9999997897566589,
                0.9999989322975119,
                0.9999989322966208,
                0.9999987901341723
            ],
            [
                0.9999994284997574,
                0.9999990577551815,
                0.9999987901338838,
                0.9999994284993485,
                0.9999993524050474,
                0.9999984465026158,
                0.999999554914895,
                0.9999994284992805,
                0.9999991684720715,
                0.9999980052709919
            ],
            [
                0.9999990577555185,
                0.9999993524054334,
                0.9999989322975119,
                0.9999991684720715,
                0.9999980052695652,
                0.9999992661790195,
                0.9999991684715758,
                0.9999982396567868,
                0.9999980052702786,
                0.9999986290421394
            ],
            [
                0.9999994956524115,
                0.9999997300422225,
                0.999998005269803,
                0.9999990577556308,
                0.9999994284996893,
                0.9999987901340281,
                0.9999997617631183,
                0.9999996940977366,
                0.9999986290427932,
                0.9999987901346049
            ]
        ]
    },
    {
        "q_id": "8223_mmlu_math",
        "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,
            27,
            28,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            47,
            48,
            49,
            50,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            79,
            80,
            81,
            82,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                7.484620045365076e-05,
                0.00010889692211618359,
                0.00012339454452893004,
                6.605212888657352e-05,
                1.6701425825492673e-05,
                0.0002959571667889455,
                8.481102101484894e-05,
                0.00010889693514699898,
                0.0001584361791352309,
                2.7535694378772238e-05
            ],
            [
                0.9999977396759718,
                0.9999970976890529,
                0.999998239656367,
                0.9999970976883609,
                0.9999990577549568,
                0.9999987901338838,
                0.9999991684720715,
                0.9999991684721706,
                0.9999982396565769,
                0.9999962733611608
            ],
            [
                0.9999977396754327,
                0.999997438716568,
                0.9999945777829711,
                0.999993855826863,
                0.9999980052707541,
                0.9999957771680666,
                0.9999987901343166,
                0.9999977396751633,
                0.9999982396572065,
                0.999997097686977
            ],
            [
                0.9999967112497679,
                0.9999930377445857,
                0.9999938558224688,
                0.9999898700126484,
                0.9999910603068951,
                0.9999962733616048,
                0.9999986290429567,
                0.9999967112493665,
                0.999998446502801,
                0.9999921107345932
            ],
            [
                0.9999967112517187,
                0.9999974387187053,
                0.9999977396765104,
                0.9999898700053974,
                0.9999990577556307,
                0.9999994956527722,
                0.9999785550515867,
                NaN,
                0.9999990577551815,
                0.9999945777810302
            ],
            [
                0.999992110738356,
                0.9999991684715759,
                0.9999992661787823,
                NaN,
                0.999999352404893,
                0.9999989322968754,
                0.9999990577556308,
                0.999998629042303,
                0.999999352404893,
                0.9999992661789321
            ],
            [
                0.9999646437408798,
                0.9999810748585449,
                0.9999957771655488,
                0.9999485577867099,
                0.9999785550464881,
                0.9999832985761679,
                NaN,
                0.9999957771680688,
                0.999983298574187,
                0.9999945777790923
            ],
            [
                0.9999970976880153,
                0.9999987901341724,
                0.9999986290421395,
                0.9999970976880151,
                0.9999977396751633,
                NaN,
                0.9999984465024306,
                0.9999989322966208,
                0.9999982396574163,
                0.9999993524052018
            ],
            [
                0.9999930377454107,
                0.9999982396565769,
                0.9999982396572065,
                0.999964643732436,
                0.9999989322975118,
                0.999997438716568,
                0.9999970976883609,
                0.9999921107345955,
                0.9999977396746245,
                0.9999832985801537
            ],
            [
                0.9999974387187053,
                0.9999967112493667,
                0.9999930377454105,
                0.9999970976873229,
                0.9999974387165682,
                0.9999986290427932,
                0.999995777166556,
                0.9999980052707541,
                0.999998446502801,
                0.9999980052709919
            ],
            [
                0.99999844650169,
                0.9999990577552937,
                NaN,
                0.9999992661789321,
                0.9999980052707542,
                0.9999987901343165,
                0.9999992661791945,
                0.9999970976876691,
                0.9999962733593841,
                0.9999990577554061
            ],
            [
                0.9999962733611605,
                0.9999930377437527,
                0.9999974387184002,
                0.999997438717484,
                0.9999938558239343,
                0.9999869928700547,
                0.9999885212291383,
                0.9999938558261314,
                0.9999980052700409,
                0.9999945777803839
            ],
            [
                0.9999952149055062,
                0.9999921107374152,
                0.9999938558224694,
                0.9999687980738801,
                0.9999977396754329,
                0.999986992868442,
                0.999992110735536,
                0.9999599362935414,
                0.9999952149066467,
                0.9998601778930861
            ],
            [
                0.9999930377404305,
                0.9999974387177905,
                NaN,
                0.9999938558268633,
                0.9999984465026159,
                0.9999984465022458,
                0.9999910603068933,
                0.9999977396746244,
                0.9999974387180952,
                0.999994577782325
            ],
            [
                0.999997438716874,
                0.9999852610162754,
                0.9999852610197902,
                0.9999952149066462,
                0.9998601778724837,
                0.999995777166054,
                0.9999938558275964,
                0.9999970976883614,
                0.9999832985741856,
                0.999988521227772
            ],
            [
                0.9999756997650714,
                0.9999984465026162,
                0.999991060306898,
                0.9999962733602759,
                0.9999898700102298,
                0.9999938558261328,
                0.999995214903794,
                0.9999974387174845,
                0.999983298572205,
                0.9999984465015046
            ],
            [
                0.9999687980774769,
                0.9999852610110074,
                0.9999962733602717,
                0.9999910603004989,
                0.9999945777790915,
                0.9999930377462509,
                0.999975699753502,
                0.9999974387166267,
                0.9999945777803843,
                0.9999417087324999
            ],
            [
                0.9999952149032237,
                0.9999967112505431,
                NaN,
                0.999998239656367,
                0.9999930377445804,
                0.999998239656577,
                0.9999869928746385,
                0.9999930377462425,
                0.9999980052700408,
                0.9999945777803998
            ],
            [
                NaN,
                0.9820137934923403,
                NaN,
                0.9914225128439131,
                0.9999957771655487,
                0.9999599363030484,
                0.999998005269803,
                0.999975699767969,
                0.9999977396754327,
                0.9999910603036988
            ],
            [
                0.9999910603026337,
                0.9999885212318754,
                0.999994577781677,
                0.9999898700079181,
                0.9999967112505435,
                0.9999952149060767,
                0.9999869928761944,
                0.9999756997476946,
                NaN,
                0.999993855822469
            ],
            [
                0.999997438718095,
                0.9999810748517961,
                0.9999910603026325,
                0.9999952149043656,
                0.9999898700079195,
                0.9999957771650456,
                0.9999957771670593,
                0.9999967112505427,
                0.9999869928699874,
                0.9999945777816807
            ],
            [
                0.9999994956523514,
                0.9999986290427934,
                0.9999977396759716,
                0.9999967112505427,
                0.9999852610215472,
                0.9999930377404315,
                0.9999982396569966,
                0.9999962733602719,
                NaN,
                0.9999885212346289
            ],
            [
                0.9999987901343165,
                0.9999967112497586,
                0.9999945777790918,
                0.9999957771670589,
                0.9999910603015647,
                0.9999967112497585,
                0.9999974387168736,
                0.9999977396746244,
                0.9999974387171787,
                0.9999962733620488
            ],
            [
                0.9999921107336539,
                0.9999417087071371,
                0.9999756997476946,
                0.9999921107364762,
                0.9999546021260286,
                0.9999151889690671,
                0.9999885212305106,
                0.9999687980923798,
                NaN,
                0.9999952149037967
            ],
            [
                0.9999687980886642,
                0.9999724643089085,
                0.9999810748563055,
                0.9999967112513269,
                0.9999898700126437,
                0.9999952149066468,
                0.9999910603069,
                0.9999938558268643,
                0.9999945777784449,
                0.9999970976880151
            ],
            [
                0.11920292202211755,
                0.9999962733602724,
                0.9999986290427936,
                0.9999945777803841,
                0.9999756997505774,
                0.9999938558253983,
                NaN,
                0.9999869928653425,
                0.9999967112493664,
                0.3775406687981454
            ],
            [
                0.9999417087275778,
                0.9999151889588787,
                0.9999945777810304,
                0.9999646437577411,
                0.9999921107383555,
                NaN,
                0.9999646437324458,
                0.999664650013035,
                0.9999967112513275,
                NaN
            ],
            [
                0.9999962733598274,
                0.9999952149060761,
                0.9999986290426297,
                0.9999977396765105,
                0.9999967112501507,
                0.9999974387187053,
                0.9999977396757022,
                0.9999952149049351,
                0.9999938558268632,
                0.9999885212277811
            ],
            [
                0.9999885212365659,
                NaN,
                0.9999869928731046,
                0.9999869928762062,
                0.9999974387168735,
                0.9999957771650455,
                0.9999832985781628,
                0.9999885212265306,
                NaN,
                0.9999962733589403
            ],
            [
                0.9999910603026371,
                0.9626731094431571,
                0.999891103092778,
                0.9999724643089779,
                0.9999910603015686,
                0.8807970889295663,
                0.9999724643023661,
                0.9999986290426298,
                0.9999251537999471,
                0.9999957771645422
            ],
            [
                0.9999921107402373,
                NaN,
                8.481101066480413e-05,
                0.9999938558239343,
                0.9999756997592754,
                NaN,
                0.9999938558239355,
                0.9999869928761901,
                0.00010889694697835962,
                0.9999885212291424
            ],
            [
                0.9999987901347492,
                0.9999987901347492,
                0.9999980052700408,
                0.999999057755069,
                0.9999989322975118,
                0.9999996072136125,
                0.9999989322970027,
                0.9999987901347492,
                0.9999982396572065,
                0.9999994956527722
            ],
            [
                0.9999980052705167,
                0.9999938558268721,
                0.9999646437410106,
                0.9999756997476916,
                0.9999910603026313,
                NaN,
                0.9999962733611609,
                0.9998415637285814,
                NaN,
                NaN
            ],
            [
                0.9999930377429207,
                0.9999930377429204,
                0.9999646437619387,
                0.9999832985741745,
                0.9999646437619434,
                0.9999921107392967,
                0.999989870005398,
                0.9999869928699864,
                0.9999885212291395,
                0.9999810748427369
            ],
            [
                0.9999990577550694,
                0.9999994284996891,
                0.999997097688361,
                0.9999984465026159,
                0.9999996072139402,
                0.9999991684721706,
                0.999999554914895,
                0.9999986290431201,
                0.9999980052698031,
                0.999998790134028
            ],
            [
                0.999941708748413,
                0.9999945777829699,
                0.9999852610197885,
                0.9999852610233104,
                0.999993855822469,
                0.9999885212305076,
                0.9999869928699852,
                0.9999885212346149,
                0.9999938558239353,
                0.9999974387184002
            ],
            [
                0.9999938558246659,
                0.9999898700078157,
                0.999983298572237,
                0.9999962733607162,
                0.9999910603068934,
                0.999985261018029,
                0.9999962733616045,
                0.9999970976869775,
                0.9999962733589393,
                0.9999898700078227
            ],
            [
                0.9999974387171793,
                0.999995214906079,
                0.9999898700114356,
                0.9999921107355375,
                0.9991959141790417,
                0.9999546021367908,
                0.9999974387177896,
                NaN,
                0.9999974387187058,
                0.9980732651065348
            ],
            [
                0.9999970976890528,
                0.9999945777803866,
                0.999997097686977,
                0.9999977396748941,
                0.9999987901347492,
                0.9999852610215659,
                0.9999898700078163,
                0.9999938558232023,
                0.9999952149032246,
                0.9999869928732588
            ],
            [
                0.9999989322968754,
                0.9999982396565775,
                NaN,
                0.9999989322967482,
                0.9999986290427932,
                0.9999967112517195,
                0.9999974387171789,
                0.9999982396569966,
                0.9999986290421397,
                0.9999852610127611
            ],
            [
                0.9999996940976272,
                0.9999998874648245,
                0.9999977396759717,
                0.9999999006881023,
                0.999999653367379,
                0.9999997617630049,
                0.999999694097846,
                0.9999994284995529,
                0.9999996940977002,
                0.9999997617631752
            ],
            [
                0.9999977396746245,
                0.9999984465022456,
                0.9999980052695653,
                0.9999980052698034,
                0.999999266179107,
                0.9999987901346056,
                0.9999980052695653,
                0.9999938558246666,
                0.9999987901346049,
                0.9999977396748939
            ],
            [
                0.999959936298395,
                0.9999921107336528,
                0.9999869928653335,
                0.9999921107336532,
                0.9999977396746245,
                0.999997097687325,
                0.9999938558254031,
                0.9999485578033156,
                0.9999957771655487,
                0.9046505280315008
            ],
            [
                0.9999885212291416,
                0.9999952149060793,
                0.9999994284997574,
                0.9999986290424664,
                0.9999810748540408,
                0.9999989322975119,
                0.9999962733607162,
                0.9999952149037982,
                0.9999724643089074,
                NaN
            ],
            [
                0.9999885212318809,
                0.9999945777790915,
                0.9999898700078149,
                0.9999938558224694,
                0.999997739676242,
                0.9999970976887071,
                0.9999977396751634,
                0.9999974387187056,
                0.9999945777810303,
                0.999994577780384
            ],
            [
                0.9999990577550691,
                0.9999974387180947,
                0.9999938558246657,
                0.999986992866886,
                0.9999910603058275,
                0.9999910602994342,
                0.9999885212277699,
                0.9999970976873228,
                0.9999885212318754,
                0.9999993524054334
            ],
            [
                0.9999898700114674,
                0.9999989322970027,
                0.9999885212264026,
                0.9953904283120448,
                0.9999898700126484,
                0.9999957771670593,
                0.9999930377404315,
                0.9999974387184003,
                0.9999987901347492,
                0.9999984465028042
            ],
            [
                0.9999910603048164,
                0.9999982396565773,
                0.9999989322975119,
                0.9999938558268638,
                0.9999970976869837,
                0.9999993524050474,
                0.9999987901343168,
                0.9999986290432835,
                0.999998446501507,
                0.9999938558246659
            ],
            [
                0.9999898700090204,
                0.9998601779776152,
                0.999941708755328,
                0.9999930377454109,
                0.9999885212318776,
                0.9999910603036991,
                0.9999967112497586,
                0.9999984465028011,
                0.99995993630786,
                0.9999910603058283
            ],
            [
                0.9999989322972572,
                0.99999844650169,
                0.9999984465024309,
                0.999988521231886,
                0.9999991684715759,
                0.9999898700078136,
                0.9999989322972573,
                0.9999989322973846,
                0.9999987901340285,
                0.9999986290432837
            ],
            [
                0.9999910602994595,
                0.9999938558253997,
                0.9999785550465371,
                0.9999980052702786,
                0.9999869928699966,
                0.999993037742921,
                0.9999885212291404,
                0.8933094174159127,
                0.9999910603026405,
                0.9999885212359894
            ],
            [
                0.9999485578057012,
                0.9999339478790403,
                0.9999417087206773,
                NaN,
                0.9999832985841366,
                0.9999485577811588,
                0.9999417087207698,
                0.9999970976887074,
                NaN,
                0.9999646437452351
            ],
            [
                0.9999869928762236,
                0.9999984465020603,
                0.9999967112517192,
                0.9999982396574162,
                0.9999994284996893,
                0.9999974387177893,
                0.9999980052707541,
                0.9999993524054334,
                0.9999986290429566,
                0.9999962733602727
            ],
            [
                0.9999962733611605,
                0.999996711251719,
                0.9999852610162746,
                0.9999962733611608,
                0.9999687980774756,
                0.9999910602994727,
                0.9999967112509349,
                0.9999938558268646,
                0.9999938558246659,
                0.9999852610110069
            ],
            [
                0.999999352405279,
                0.9999898700126437,
                0.9999910602994339,
                0.999891103129733,
                0.9999885212332451,
                0.9999962733602739,
                0.999997097686977,
                0.999986992873096,
                0.9999974387177893,
                0.9999810748472526
            ],
            [
                0.9999930377429266,
                0.999997438717484,
                0.9999756997534802,
                0.9999724643089045,
                0.9999982396565769,
                0.9999994284994849,
                0.9999977396751633,
                0.9999982396569965,
                0.9999957771660584,
                0.9999852610198073
            ],
            [
                0.999981074849544,
                0.9999930377445846,
                0.9999930377404445,
                0.9999938558275976,
                0.9999869928664423,
                0.9914225137388601,
                0.7549149923816048,
                0.9999938558246664,
                0.9999687980924072,
                NaN
            ],
            [
                0.9999974387177893,
                0.9999945777829693,
                0.9999957771645426,
                NaN,
                0.9999952149066464,
                NaN,
                0.9999984465018752,
                0.9999921107374143,
                0.999992110737415,
                0.9999991684721707
            ],
            [
                0.999972464312199,
                0.9999151889893143,
                0.9999785550464785,
                0.9989677691429503,
                0.99994170874838,
                0.9999546021151737,
                0.9999962733598274,
                0.999933947839654,
                0.9999945777784456,
                NaN
            ],
            [
                0.9999990577551816,
                0.999998239656787,
                0.9964063967657975,
                NaN,
                NaN,
                0.9914225159485082,
                0.9999910603068934,
                0.9996200155526382,
                0.9999339478474694,
                0.9999869928731256
            ],
            [
                0.9999974387184004,
                0.999995777166052,
                0.9999910603015649,
                0.9999869928668885,
                0.9999977396748949,
                0.9999970976883609,
                0.9999810748427502,
                NaN,
                0.9999952149066467,
                0.9999984465020603
            ],
            [
                0.999989870007814,
                0.9999974387184,
                0.9999980052698031,
                NaN,
                0.9999930377420959,
                0.9999952149032243,
                0.9999962733589393,
                NaN,
                0.9999957771670596,
                0.999997097686977
            ],
            [
                0.9999785550439337,
                0.9999910603026334,
                0.9999974387187054,
                0.9999987901340284,
                0.9999485577618208,
                0.999997438717484,
                0.9999785550464806,
                0.9999977396765105,
                0.9999974387177898,
                0.9999910603047638
            ],
            [
                0.999998239656367,
                0.9999984465022455,
                0.9999989322970027,
                0.9999974387168732,
                0.999998790134028,
                0.9999990577550691,
                0.9999991684722698,
                0.9999987901341724,
                0.9999921107402359,
                0.9999977396762411
            ],
            [
                0.9999852610110059,
                0.9999984465024306,
                0.999998446502801,
                NaN,
                0.9995121427746977,
                0.00192673438707282,
                NaN,
                0.9999832985841411,
                0.9999885212277709,
                0.9999952149037962
            ],
            [
                0.9998911031051132,
                0.9999938558261325,
                0.9997040429071531,
                0.9999974387184,
                0.999993855827597,
                0.9999930377437511,
                0.9999938558253986,
                0.9999974387168735,
                0.9999967112497589,
                0.9999756997593108
            ],
            [
                0.9999974387184001,
                0.9999952149066466,
                0.9999990577550691,
                0.9999987901347491,
                0.9999970976876694,
                0.9999974387187054,
                0.9999994284995531,
                0.9999991684718738,
                0.9999994284992805,
                0.9999982396567868
            ],
            [
                0.9999898700126703,
                0.9999945777784454,
                0.9999945777784464,
                0.999998790133884,
                0.9999974387177898,
                0.9999945777797377,
                0.9999984465024307,
                0.9999970976873244,
                0.9999945777797377,
                0.9999921107336583
            ],
            [
                0.9999921107402443,
                0.9999810748562918,
                0.9999852610180329,
                0.9999898700090233,
                0.9999599363221969,
                0.9992903295892174,
                0.9999724642990576,
                0.9999599363174135,
                0.9999967112505455,
                0.999989870009022
            ],
            [
                8.481101095665886e-05,
                0.00010889696091391995,
                4.5397890270732005e-05,
                3.120191134459038e-05,
                2.4300232018837615e-05,
                2.7535704228438656e-05,
                5.144219520488886e-05,
                7.484624508881928e-05,
                0.0001584361786580577,
                6.605216032342332e-05
            ],
            [
                0.9999991684720716,
                0.9999995549151072,
                0.9999992661791944,
                0.9999982396569965,
                0.9999991684716749,
                0.9999994956527121,
                0.9999974387184,
                0.9999930377420905,
                0.9999996072137061,
                0.9999989322970027
            ],
            [
                0.9999982396559483,
                0.9999970976883614,
                1.0,
                0.9999984465022456,
                0.9999980052695655,
                0.9999986290432837,
                0.9999967112505427,
                0.9999910602994345,
                0.9999982396559475,
                0.9999977396762412
            ],
            [
                0.9999967112493665,
                0.9999984465020603,
                0.9999982396565769,
                0.9999986290421394,
                0.9999987901341723,
                0.9999930377429208,
                0.9999986290424664,
                0.9999967112501504,
                0.9999970976883612,
                0.9999930377462418
            ],
            [
                0.9999967112505427,
                0.9999952149037941,
                0.9999898700078126,
                0.9999952149043648,
                0.9999962733593839,
                0.9999967112513267,
                0.9999832985701983,
                0.9999687980849524,
                0.9999724643089034,
                0.9999898700090227
            ],
            [
                0.9999957771665887,
                0.9999962733602717,
                0.9999898700126519,
                0.9999910603015663,
                0.9999756997505828,
                0.9999910603036961,
                0.999991060304762,
                NaN,
                0.999988521226415,
                0.9999974387177893
            ],
            [
                0.9998204719710211,
                0.999999168471675,
                0.9999977396765112,
                0.9999984465018754,
                0.9999646437493511,
                0.9999967112521114,
                0.9999785550439609,
                0.0006263340364542634,
                0.9999910603015673,
                0.015906395385557992
            ],
            [
                0.9999852610110019,
                0.9999952149049368,
                0.9999885212359807,
                0.9999945777784459,
                0.9999885212332466,
                0.9999930377420908,
                0.9999921107345944,
                0.999978555041372,
                0.9999938558232031,
                0.9875683504388499
            ],
            [
                0.9999869928684505,
                0.9999938558261308,
                0.9999974387177893,
                0.9999990577552939,
                0.9999785550490556,
                0.9999962733611601,
                0.9999945777829694,
                0.9999982396561571,
                0.9999952149032237,
                0.9999984465016899
            ],
            [
                0.9999989322971302,
                0.9999970976876689,
                0.999996711250543,
                0.9999989322972574,
                0.9999945777810321,
                0.9999980052707546,
                0.9999977396762411,
                0.9999852610145252,
                0.9999982396559474,
                0.9999852610145177
            ],
            [
                0.9999990577556308,
                0.9999986290426298,
                0.9999989322966208,
                0.9999974387168734,
                0.9999991684721706,
                0.9999974387180959,
                0.9999994284992805,
                0.9999930377404436,
                0.9999977396746244,
                0.9999995549150011
            ],
            [
                0.9999151889586775,
                0.99999862904312,
                0.9999957771670599,
                0.9980732654324886,
                0.9999977396746244,
                0.9999990577556308,
                0.9999982396563669,
                0.9999546021097193,
                0.9986749777414567,
                NaN
            ],
            [
                0.99999844650169,
                0.9999898700066139,
                0.999997097687669,
                0.9999885212346137,
                0.9999945777823249,
                0.9999995549150541,
                0.9999921107345937,
                0.9999938558253983,
                0.999999168471576,
                0.9999417087137297
            ],
            [
                NaN,
                0.9999930377445887,
                0.999997739674894,
                0.9993736659273662,
                0.999975699759331,
                0.9997040428697472,
                0.9999980052700408,
                0.999995214904937,
                0.9999970976869772,
                0.9999038975624376
            ],
            [
                0.9999967112513267,
                0.9999970976880148,
                0.9999852610197874,
                0.9999974387165689,
                0.9999869928730905,
                0.9999724643089335,
                NaN,
                0.9999930377454143,
                0.9999970976890529,
                0.9999921107393084
            ],
            [
                0.9999980052705163,
                0.9999869928653335,
                0.9998204719709062,
                0.9999852610110069,
                0.9999485577618328,
                0.9999251537818293,
                0.9999810748449939,
                0.9999339478239194,
                0.9997388097223529,
                0.9999599363175223
            ],
            [
                0.9999869928653341,
                0.9999687980811937,
                0.9999952149049351,
                0.9999930377454136,
                0.9999599363128538,
                0.9999832985821452,
                NaN,
                0.999989870011482,
                0.9998766054197802,
                0.9999756997593274
            ],
            [
                0.9999952149037942,
                0.9999945777790915,
                0.9999952149032243,
                0.9999832985761693,
                NaN,
                0.9999687980849583,
                0.9999885212264021,
                0.9999967112509369,
                0.9999957771680681,
                0.999997438717484
            ],
            [
                0.9999885212264077,
                0.9999974387168736,
                NaN,
                0.9999869928668863,
                0.9999952149060773,
                0.4687906266262437,
                0.999986992874644,
                0.9999785550550779,
                0.9999921107364742,
                0.9999967112517189
            ],
            [
                0.9999957771670589,
                0.9999970976883614,
                0.9999986290421394,
                0.9999952149032237,
                0.9999984465015048,
                0.9999938558253995,
                0.9999898700115983,
                0.9999852610233111,
                0.9999930377445814,
                0.9999945777790913
            ],
            [
                0.9999885212360086,
                0.9999852610197874,
                0.9999810748495092,
                NaN,
                0.9999546021368159,
                0.9999977396751634,
                0.999972464302386,
                0.9999852610234368,
                0.9999986290421395,
                0.9999970976890531
            ],
            [
                0.999997097686977,
                0.999996711251327,
                0.9999869928668843,
                0.999997097686977,
                0.9999990577551815,
                0.9999977396759716,
                0.9999910603026424,
                0.999995777165549,
                0.9999756997650686,
                0.9999990577552937
            ],
            [
                0.9999957771650453,
                0.9999898700054631,
                0.9999986290426297,
                0.9999930377445819,
                0.9998601778955944,
                NaN,
                0.9999646437366894,
                NaN,
                0.9999962733589393,
                0.9999852610145247
            ],
            [
                4.785096773840142e-06,
                2.144494073796001e-05,
                3.7266392835764795e-06,
                4.0063706494441236e-05,
                2.7535684526905577e-05,
                1.8925148236123232e-05,
                3.120190393374457e-05,
                7.484623611811155e-05,
                2.1444948410928083e-05,
                3.1201922511884416e-05
            ],
            [
                0.9999910603015647,
                0.9999910603015741,
                0.9999546021098239,
                0.9875683482664004,
                NaN,
                0.9999980052700409,
                0.9999724643155983,
                NaN,
                0.9999910603047643,
                NaN
            ],
            [
                NaN,
                0.9999938558224697,
                0.99995993631745,
                0.9999967112513269,
                NaN,
                0.9999832985702,
                0.9999957771660528,
                0.999998005269803,
                0.9999910603004992,
                0.9989677688505244
            ],
            [
                0.999993855823934,
                0.9999974387168734,
                0.9999962733593836,
                0.9999977396765105,
                0.9999990577556308,
                0.9999984465024306,
                0.9999982396559474,
                0.9999989322972573,
                0.9999987901344607,
                0.9999980052702786
            ],
            [
                0.9999921107393,
                0.9999987901341723,
                0.999989870011438,
                0.9999962733602717,
                0.9999898700054018,
                0.999989870011473,
                0.9999910603005058,
                0.9999038975395299,
                0.9997694933689146,
                0.9999756997621906
            ],
            [
                0.9999869928668896,
                0.9999485577618268,
                0.9999646437535384,
                0.9999810748495074,
                0.9999910603036999,
                0.9998204719935992,
                0.9999898700044507,
                0.9999756997621748,
                0.9999756997534811,
                0.9999485577741262
            ],
            [
                0.999986992865342,
                0.9999938558246689,
                0.9999970976873236,
                0.999988521226408,
                0.9999938558239343,
                0.9999599363031529,
                0.9999852610127585,
                0.9999957771675626,
                0.9999984465028012,
                0.9999832985801537
            ],
            [
                0.9999991684717741,
                0.9999998724809875,
                0.9999910603026305,
                0.99999862904312,
                0.9999990577549568,
                0.9999997300422868,
                0.9999994284993486,
                0.9999982396559473,
                0.9999986290432834,
                0.9999990577551814
            ],
            [
                NaN,
                0.00020342697011742553,
                0.999986992869992,
                NaN,
                NaN,
                0.999985261016273,
                0.9999930377420914,
                0.9999810748563307,
                0.9999485577741677,
                0.9990889488354812
            ],
            [
                0.999992110738356,
                0.9999977396748938,
                0.9999930377445804,
                0.9999962733620492,
                0.9999921107355342,
                0.9999898700066079,
                0.9999982396574169,
                0.9999910603015658,
                0.9999938558275963,
                0.9999885212332453
            ],
            [
                0.9999974387187058,
                0.99999844650169,
                0.999999352404893,
                0.9999952149055059,
                0.9999974387187054,
                0.9999987901341724,
                0.9999810748517634,
                0.9999995549151073,
                0.999988521231877,
                NaN
            ],
            [
                0.9999986290424665,
                0.9999599363078259,
                0.9999930377445811,
                0.9999952149032237,
                0.9999756997679731,
                0.9999974387184002,
                0.9999485577803159,
                0.9999945777785249,
                NaN,
                0.9999038975625382
            ],
            [
                NaN,
                0.999738809660826,
                0.9999852610162804,
                NaN,
                0.9999921107383553,
                0.9999952149049351,
                0.9999810748517685,
                0.9770226283755477,
                NaN,
                0.9999151889690868
            ],
            [
                0.999993855823201,
                0.9999974387168733,
                0.9999952149060781,
                0.9999980052698036,
                0.9998204719703524,
                0.999997097688707,
                0.9999945777816777,
                0.9999810748562825,
                0.9999945777790911,
                0.9999938558254
            ],
            [
                0.9999977396754327,
                0.9999938558224687,
                0.9999986290421394,
                0.9999986290427931,
                0.9999852610197857,
                0.9999898700102277,
                0.9999977396759716,
                0.9999967112493664,
                0.9999885212332436,
                0.9999724643187611
            ],
            [
                0.9999599362888041,
                0.9999339478239369,
                0.9999962733593833,
                0.9999898700078134,
                0.9999910603058286,
                0.9999982396559474,
                0.9999945777803838,
                0.9999898700090245,
                0.9999962733607163,
                0.9999977396751634
            ],
            [
                0.9999957771650456,
                0.9999756997679586,
                0.9999885212318746,
                0.9999945777810302,
                0.9999885212264011,
                0.9999869928746372,
                0.9999885212291385,
                0.9999885212291378,
                0.9999967112517186,
                0.9999785550567023
            ],
            [
                9.61024488107306e-05,
                5.14422074608005e-05,
                2.144495606813994e-05,
                0.00010889694816355559,
                4.006367782114826e-05,
                0.0003353499890724067,
                7.48462272350754e-05,
                1.4738976696800444e-05,
                0.0002611904020535479,
                3.535624225110421e-05
            ],
            [
                0.9999970976887068,
                0.9998415637271659,
                0.9999996533674201,
                NaN,
                NaN,
                0.9990889489346632,
                0.9998204720991479,
                0.9999998144608983,
                0.999998629042957,
                0.999995214904365
            ],
            [
                0.9999339478632457,
                0.9999810748585355,
                0.9999921107383568,
                0.9999977396746245,
                0.999995777166557,
                0.9999957771670591,
                0.9999687980737588,
                0.9999910603047633,
                0.9999687980774796,
                0.9999977396754327
            ],
            [
                1.4738983719053027e-05,
                7.889262585082652e-06,
                5.1442219595825146e-05,
                7.889262585082652e-06,
                3.7266397282926013e-06,
                6.962257908880483e-06,
                4.006369691549301e-05,
                1.4738976696371488e-05,
                5.8291286335171815e-05,
                7.484625386839543e-05
            ]
        ]
    },
    {
        "q_id": "7939_mmlu_math",
        "cot_ids": [
            1,
            2,
            3,
            4,
            5,
            8,
            9,
            10,
            11,
            13,
            14,
            15,
            17,
            20,
            22,
            23,
            24,
            25,
            29,
            30,
            33,
            34,
            35,
            38,
            40,
            44,
            45,
            49,
            50,
            52,
            53,
            54,
            56,
            58,
            59,
            60,
            61,
            63,
            65,
            66,
            69,
            70,
            73,
            76,
            78,
            79,
            80,
            82,
            83,
            85,
            86,
            87,
            89,
            94,
            96,
            100,
            101,
            102,
            103,
            106,
            107,
            108,
            111,
            115,
            116,
            118,
            119,
            122,
            123,
            126,
            127
        ],
        "rewards": [
            [
                0.999998239656788,
                0.9149009602137116,
                0.9706877684006775,
                0.9999967112513275,
                0.9999970976869772,
                0.9999938558224687,
                0.9999992661790196,
                0.9999869928762438,
                0.9999832985741774,
                0.9999885212332438
            ],
            [
                1.3709573702566696e-06,
                2.902313023063532e-06,
                9.422443692261927e-07,
                1.8553914605558704e-07,
                3.7266379512857925e-06,
                4.222832941034507e-06,
                0.9998766053811251,
                1.994730434847717e-06,
                2.699577130728306e-07,
                8.31528325021115e-07
            ],
            [
                1.9947306725669014e-06,
                6.9622554173544636e-06,
                4.450851049941403e-07,
                1.0677028699625768e-06,
                1.9947306725451314e-06,
                4.785096776251149e-06,
                3.9278610660598936e-07,
                4.2228344508893285e-06,
                1.99472995920443e-06,
                3.2887482798567817e-06
            ],
            [
                2.561282515886208e-06,
                1.7603427934462202e-06,
                2.561282515564741e-06,
                7.338208930391909e-07,
                5.422219615582823e-06,
                1.553498495308628e-06,
                4.222833444467892e-06,
                1.5534981249291695e-06,
                1.2098661161861e-06,
                3.9278615343222713e-07
            ],
            [
                2.902312676118419e-06,
                2.9023133689924295e-06,
                7.88926164421493e-06,
                2.561282210618905e-06,
                4.785093353274332e-06,
                5.422220908314139e-06,
                2.9023123310580418e-06,
                5.422220908703723e-06,
                1.3709568799243436e-06,
                9.422442568951678e-07
            ],
            [
                2.2603240279591663e-06,
                4.7850933519861414e-06,
                2.9023133684671433e-06,
                1.9947294836483373e-06,
                1.994730672468935e-06,
                1.9947306725451314e-06,
                4.785093353739995e-06,
                2.5612812944118885e-06,
                1.5534984951419064e-06,
                1.553498495308628e-06
            ],
            [
                2.144494839142443e-05,
                3.288749848677511e-06,
                5.422218969306048e-06,
                3.2887494564079503e-06,
                4.785093353100252e-06,
                6.962257077413455e-06,
                2.2603253752763026e-06,
                1.89251482286188e-05,
                8.939696302831578e-06,
                7.889265400267349e-06
            ],
            [
                5.4222189671756605e-06,
                7.889265401788488e-06,
                1.3007128452848148e-05,
                6.962257077590752e-06,
                3.7266397264555753e-06,
                3.726640616477725e-06,
                1.0129992155873335e-05,
                1.0129989767363975e-05,
                2.1444940713541454e-05,
                1.8925157235383214e-05
            ],
            [
                2.2603251061849014e-06,
                4.785096205930373e-06,
                1.5534981248881956e-06,
                1.3709576970537545e-06,
                2.902311293147782e-06,
                2.5612822106654943e-06,
                2.9023126766305067e-06,
                3.7266410601636445e-06,
                1.0677024881266355e-06,
                3.726639727940109e-06
            ],
            [
                4.222832940646604e-06,
                0.00017952802391683128,
                1.8925152747388e-05,
                0.9999756997621879,
                1.473898021151881e-05,
                5.422218322940583e-06,
                0.9999251537462852,
                1.8925145971919677e-05,
                1.3007128457012223e-05,
                NaN
            ],
            [
                6.144174601588856e-06,
                5.422217676200406e-06,
                3.7266410609160796e-06,
                8.939699500489763e-06,
                6.144172403335888e-06,
                6.1441775312976045e-06,
                1.994729959270648e-06,
                4.785093353687772e-06,
                5.422220908703723e-06,
                3.726637951028202e-06
            ],
            [
                3.288749848749297e-06,
                1.2098661160436029e-06,
                5.422219614004759e-06,
                2.9023119851055122e-06,
                3.288748672413347e-06,
                1.994730672496148e-06,
                3.2887494572873306e-06,
                7.88926540454376e-06,
                1.994730672407252e-06,
                6.144177525933064e-06
            ],
            [
                1.2098659717989e-06,
                4.222833444106873e-06,
                2.5612825153504304e-06,
                2.5612828211442287e-06,
                9.422449307915373e-07,
                2.90231163910023e-06,
                2.9023119850527192e-06,
                1.2098655391947376e-06,
                1.7603440526806268e-06,
                1.3709568796749682e-06
            ],
            [
                6.962257909007124e-06,
                3.2887498491620677e-06,
                3.7266406154676995e-06,
                9.422449307915373e-07,
                2.5612831250279004e-06,
                1.994730434735237e-06,
                6.962257909412379e-06,
                4.785092782396909e-06,
                4.222832941034507e-06,
                8.939697362191404e-06
            ],
            [
                3.726639283129085e-06,
                1.067703379154416e-06,
                4.785093923516432e-06,
                3.2887498474870575e-06,
                3.4663253845007707e-07,
                2.260324297607547e-06,
                2.561282820785491e-06,
                1.5534981247426673e-06,
                4.785094494402695e-06,
                1.2098655392222467e-06
            ],
            [
                6.47594875389178e-07,
                4.222834451215781e-06,
                7.338211554464836e-07,
                1.7603430033158905e-06,
                4.450851580469341e-07,
                7.3382106794623e-07,
                1.3709573702647743e-06,
                1.3709576971061233e-06,
                9.422447061953531e-07,
                9.422449307649713e-07
            ],
            [
                1.5534971989427613e-06,
                1.9947297213746646e-06,
                2.561281294644835e-06,
                1.3007134662432895e-05,
                3.7266383950256237e-06,
                5.4222215550004564e-06,
                3.7266379512112265e-06,
                2.2603242977308917e-06,
                1.3709573702566696e-06,
                5.715004470295662e-07
            ],
            [
                5.422221554670048e-06,
                1.1478764018012839e-05,
                6.962253758182361e-06,
                1.0129987356375273e-05,
                3.726641060536473e-06,
                1.5534983100425914e-06,
                1.0129989770441144e-05,
                8.315280276505193e-07,
                3.726637950411341e-06,
                1.3007133108474901e-05
            ],
            [
                1.9947297213492663e-06,
                1.7603440522963817e-06,
                5.422219615188307e-06,
                4.785093923847183e-06,
                7.889259761704902e-06,
                1.2098652508056196e-06,
                2.2603242976404388e-06,
                3.7266383932767217e-06,
                1.209866116137134e-06,
                1.994730434735237e-06
            ],
            [
                0.9999980052702836,
                2.561281599914358e-06,
                2.5612825156159896e-06,
                3.2887490644495094e-06,
                1.2098659719524008e-06,
                1.7603436328289897e-06,
                4.7850927822924614e-06,
                2.561283126639892e-06,
                2.1444940732342966e-05,
                3.726639727750306e-06
            ],
            [
                1.5534973840377051e-06,
                5.043473480607e-07,
                6.962254587951994e-06,
                2.260324567227179e-06,
                3.726637951079042e-06,
                4.450852641316935e-07,
                6.144174601499446e-06,
                1.994730434816876e-06,
                1.3709572066558505e-06,
                2.260323758516393e-06
            ],
            [
                6.962259565748692e-06,
                2.9023123309287002e-06,
                4.222833946845163e-06,
                2.902313023063532e-06,
                0.9999485578047742,
                4.222832437443716e-06,
                6.962257079275089e-06,
                6.144177530794679e-06,
                7.88925976283858e-06,
                2.260323758713745e-06
            ],
            [
                2.4300246512104316e-05,
                6.962255412934664e-06,
                1.5534971989696065e-06,
                7.889265405677441e-06,
                1.2098656834613962e-06,
                8.93970056565517e-06,
                3.288750240223275e-06,
                4.222834954561012e-06,
                1.4738983720179032e-05,
                4.785096775842062e-06
            ],
            [
                4.7850939242083995e-06,
                5.422219614576807e-06,
                3.2887502407856003e-06,
                2.561282821209454e-06,
                2.902311984952413e-06,
                2.5612831266608576e-06,
                2.56128159999123e-06,
                1.2098653950551882e-06,
                1.370957697068717e-06,
                7.338209804987119e-07
            ],
            [
                7.889260699630574e-06,
                8.939694159867057e-06,
                4.4508510496944726e-07,
                1.7603427932989266e-06,
                9.422449308716635e-07,
                1.994729008056074e-06,
                2.90231094702116e-06,
                8.939700563752626e-06,
                1.7603434229000067e-06,
                4.222833946937338e-06
            ],
            [
                3.726637950411341e-06,
                4.2228344475249366e-06,
                2.5612834318583854e-06,
                1.994729483535857e-06,
                6.144176066353646e-06,
                2.902313023039776e-06,
                1.5534977545102382e-06,
                2.9023126768258393e-06,
                4.222832938203964e-06,
                2.260324567268294e-06
            ],
            [
                1.2098662603961589e-06,
                1.7603434229000067e-06,
                5.422218969532895e-06,
                3.7266401725681614e-06,
                5.043472278195839e-07,
                6.962257077932685e-06,
                1.994729721436347e-06,
                1.0677031245429291e-06,
                6.1441760657054305e-06,
                6.144173868312501e-06
            ],
            [
                0.9999952149037944,
                0.9999921107388424,
                0.9241418168448761,
                0.9999852610127591,
                0.999991060305829,
                0.9999967112513325,
                0.9796676473993798,
                0.9999974387184731,
                0.904650538956921,
                0.9324533097989076
            ],
            [
                7.338208055369664e-07,
                4.2228354571957855e-06,
                2.5612834314274337e-06,
                2.260324566939374e-06,
                NaN,
                2.9023123307122503e-06,
                3.2887482810801374e-06,
                3.2887506333812835e-06,
                2.9023126768258393e-06,
                4.222833444467892e-06
            ],
            [
                1.3709573701637772e-06,
                4.785093923603471e-06,
                5.422220262264056e-06,
                8.939699499432793e-06,
                1.4738985479697128e-05,
                6.144173865552e-06,
                2.2603234892298883e-06,
                2.260324027815264e-06,
                4.2228324372555256e-06,
                4.222832937036413e-06
            ],
            [
                1.1478765384430723e-05,
                6.144174599353632e-06,
                8.939695231991565e-06,
                6.14417606400666e-06,
                4.785094493836935e-06,
                8.481106122664224e-05,
                3.2887478890769702e-06,
                NaN,
                3.120190386495853e-05,
                4.222832436587256e-06
            ],
            [
                8.315280276096808e-07,
                3.726640171131078e-06,
                5.043475885634304e-07,
                6.475948753965404e-07,
                1.9947299592407137e-06,
                4.2228324377164004e-06,
                9.422449308566668e-07,
                3.9278634072866033e-07,
                3.7266397281434697e-06,
                4.222832437497486e-06
            ],
            [
                7.889261642363733e-06,
                8.93969842283598e-06,
                3.2887494564079503e-06,
                8.93969523617066e-06,
                6.9622537570932415e-06,
                6.144175332283612e-06,
                4.0063687390327e-05,
                2.902312330849511e-06,
                6.144176066353646e-06,
                6.14417460073947e-06
            ],
            [
                1.0129989767363975e-05,
                3.7266401724291984e-06,
                2.5612816000145246e-06,
                6.1441724029223715e-06,
                6.144172403715875e-06,
                1.3007126908307386e-05,
                7.88926540679677e-06,
                1.2098653949534047e-06,
                3.726637948784456e-06,
                3.2887478887419687e-06
            ],
            [
                8.939696302831578e-06,
                5.422217029943586e-06,
                1.0129987356706945e-05,
                5.422221554926484e-06,
                2.2603242977555607e-06,
                3.726640614301764e-06,
                7.338213304143191e-07,
                8.315284241560147e-07,
                2.9023126768680736e-06,
                1.2098656834723998e-06
            ],
            [
                4.4508510497875774e-07,
                8.315277302444853e-07,
                3.7266397276757403e-06,
                2.5612834318583854e-06,
                4.785095063339331e-06,
                6.962254588433232e-06,
                5.422217672334147e-06,
                4.222834954057889e-06,
                3.288748280891699e-06,
                1.0129995806888955e-05
            ],
            [
                7.88926070293116e-06,
                7.889262585211807e-06,
                1.99472995920443e-06,
                2.90231163910023e-06,
                6.144175333021237e-06,
                6.9622579095833456e-06,
                1.0129992187105678e-05,
                3.726638839656906e-06,
                4.222835456581284e-06,
                7.889265406438011e-06
            ],
            [
                0.9999869928732386,
                0.9999974387177905,
                0.9999957771650463,
                0.9999756997563912,
                0.9999952149066491,
                0.9999984465016899,
                0.9999910602994346,
                0.9999967112501597,
                0.9999938558254022,
                0.9999957771645448
            ],
            [
                3.7266383953679482e-06,
                3.726638394957837e-06,
                4.785093353274332e-06,
                7.889265404959923e-06,
                5.422218967649081e-06,
                4.7850962041547575e-06,
                9.422444815563743e-07,
                6.962256244287517e-06,
                1.6701419851270353e-05,
                3.7266410603195545e-06
            ],
            [
                3.726637951028202e-06,
                1.300712846115264e-05,
                3.2887494564079503e-06,
                6.1441738622662206e-06,
                3.7266383950934104e-06,
                8.939694167932546e-06,
                3.1201907623673364e-05,
                2.7535697649071857e-05,
                4.006369686681418e-05,
                1.8925141470949294e-05
            ],
            [
                5.422220907791405e-06,
                4.785092782501357e-06,
                2.56128282131428e-06,
                2.5612834318583854e-06,
                1.7603436329394601e-06,
                4.785093924156175e-06,
                2.9023112926251358e-06,
                4.78509563509613e-06,
                2.5612812940671274e-06,
                8.939698431942181e-06
            ],
            [
                6.144176798870286e-06,
                2.902311984915459e-06,
                7.889264462211963e-06,
                5.422217030209884e-06,
                6.962253756687988e-06,
                2.561283125666175e-06,
                7.338208930078229e-07,
                1.3007131562845248e-05,
                7.889266345957247e-06,
                5.422220907160179e-06
            ],
            [
                1.2098655392574583e-06,
                6.475950297906914e-07,
                3.288749065167371e-06,
                1.994729483666479e-06,
                2.9023116390421582e-06,
                1.7603425837702984e-06,
                1.0129988562901417e-05,
                3.7266383942867467e-06,
                3.2887478891128633e-06,
                4.2228324375512536e-06
            ],
            [
                1.994730672439908e-06,
                6.144174599532449e-06,
                5.422221554038823e-06,
                1.5534975692683091e-06,
                4.222833947029514e-06,
                1.0129992184544441e-05,
                4.785094491234441e-06,
                5.422220258959982e-06,
                2.9023130230133794e-06,
                6.144175333289463e-06
            ],
            [
                2.9023123294716244e-06,
                1.4738987234014356e-05,
                1.0129987350552609e-05,
                1.0129989765595064e-05,
                1.0129993389283824e-05,
                1.1478764010141264e-05,
                0.00020342706977773863,
                0.9995694428656176,
                7.889259754142258e-06,
                6.9622537576631295e-06
            ],
            [
                0.46879062662624377,
                0.5621765008857981,
                0.40733340004593027,
                0.9999687980840939,
                0.9999938558224736,
                0.8519527982093668,
                0.5926665999540698,
                0.999959936304625,
                0.9999974387184014,
                0.9999984465022583
            ],
            [
                2.260324836696773e-06,
                3.7266397280485686e-06,
                2.2603234891558813e-06,
                2.902311984952413e-06,
                3.2887502411564953e-06,
                1.5534983100228109e-06,
                1.3709576970213355e-06,
                1.2098653950551882e-06,
                3.2887494571676872e-06,
                3.7266401721817755e-06
            ],
            [
                6.144175334015912e-06,
                1.3709578602911673e-06,
                2.561281905058126e-06,
                1.760344052693435e-06,
                1.3709576971061233e-06,
                2.260324567268294e-06,
                1.5534984952662413e-06,
                4.785094494402695e-06,
                2.902311985079115e-06,
                3.288750633488963e-06
            ],
            [
                7.8892625772904e-06,
                1.994729483535857e-06,
                2.902311984683171e-06,
                5.422220261652556e-06,
                1.067702615330819e-06,
                1.5534981248528732e-06,
                1.0129989771823107e-05,
                1.9947301969217434e-06,
                1.7603427934702357e-06,
                2.9023109467598367e-06
            ],
            [
                1.5534981248133121e-06,
                1.5534983098744568e-06,
                2.9023133686835932e-06,
                9.422449308566668e-07,
                9.422448185264317e-07,
                1.9947290080125335e-06,
                1.994729008056074e-06,
                2.561282821239737e-06,
                1.2098652507439992e-06,
                2.2603237580312362e-06
            ],
            [
                1.0129989769722525e-05,
                5.422218969532895e-06,
                3.7266410601636445e-06,
                2.9023109469023766e-06,
                3.288749457432399e-06,
                4.7850927830845245e-06,
                3.726639728224814e-06,
                1.994730434735237e-06,
                2.260325375520937e-06,
                2.902313022802209e-06
            ],
            [
                3.2887478889962107e-06,
                1.370957370236096e-06,
                6.144174600024198e-06,
                9.42244481511812e-07,
                2.9023126764615702e-06,
                2.5612812945260317e-06,
                1.209865250694483e-06,
                2.902311639126627e-06,
                1.553497198908852e-06,
                3.726637950851956e-06
            ],
            [
                1.8925148224556773e-05,
                1.6701429795417824e-05,
                3.120190389923804e-05,
                5.144223804819424e-05,
                5.144221963025818e-05,
                5.829128627537368e-05,
                4.00636823663512e-05,
                0.00010889694794964988,
                0.0001795280277042423,
                1.1478766754941153e-05
            ],
            [
                0.999998629042303,
                0.9999982396559474,
                0.9999974387177893,
                0.9999986290427932,
                0.9999992661788445,
                0.9999957771675623,
                0.9999995549148419,
                0.9999989322967481,
                0.9999984465018752,
                0.9999994956527721
            ],
            [
                3.7266397273639203e-06,
                8.93970056350871e-06,
                8.9396994898225e-06,
                5.422220908402905e-06,
                6.96225375863827e-06,
                3.726638395320497e-06,
                4.785095635017795e-06,
                6.962253757485831e-06,
                5.4222202617511845e-06,
                2.561283431942246e-06
            ],
            [
                1.147877084091689e-05,
                1.3709570433387154e-06,
                6.962258738131379e-06,
                1.012998734896796e-05,
                6.962253759043525e-06,
                1.473898898859989e-05,
                3.28875062937023e-06,
                2.7535697651475977e-05,
                1.9947301968382903e-06,
                5.422218969217281e-06
            ],
            [
                1.7603434231241496e-06,
                3.72663839489005e-06,
                1.1478770851648967e-05,
                2.5612815988544507e-06,
                8.315284240766063e-07,
                2.5612831264675113e-06,
                1.1478770855323762e-05,
                1.5534981248881956e-06,
                2.902313368820854e-06,
                1.3709576970949014e-06
            ],
            [
                7.889264462728577e-06,
                1.30071284286208e-05,
                1.8925143721761383e-05,
                1.994729720765096e-06,
                3.120190391853445e-05,
                3.5356242264223526e-05,
                3.7266401721817755e-06,
                2.144495608105136e-05,
                1.1478765385432939e-05,
                1.8925145954914227e-05
            ],
            [
                0.9999962733598278,
                0.9997965730281009,
                0.9999921107374303,
                0.9999599362888706,
                0.9999417087206043,
                0.99999893229713,
                0.9999810748472538,
                0.9999810748507345,
                0.9999485578048022,
                0.9999974387184002
            ],
            [
                1.3007126908733257e-05,
                0.00017952800554919495,
                8.93969417167259e-06,
                0.9998766053958474,
                4.222831933864508e-06,
                0.9999417087137297,
                2.902312330759764e-06,
                4.2228349543420954e-06,
                8.939694170940841e-06,
                2.56128159959988e-06
            ],
            [
                6.1441745928267776e-06,
                2.9023126770343703e-06,
                7.338213304143191e-07,
                3.726639284017094e-06,
                6.475949525663707e-07,
                2.2603248364233586e-06,
                3.2887502411564953e-06,
                1.9947299591354906e-06,
                4.222833947359807e-06,
                2.5612828205478858e-06
            ],
            [
                0.9999869928668915,
                0.9999810748517973,
                NaN,
                0.9999485578047517,
                0.9999785550567073,
                0.9997965729302667,
                0.998498818093132,
                0.7772998663336158,
                0.9999599363080034,
                0.9999962733616048
            ],
            [
                5.043475885498987e-07,
                1.0129992182443859e-05,
                6.9622562484666964e-06,
                1.9947304347570075e-06,
                3.7266401721817755e-06,
                3.927863875520681e-07,
                6.144176064856046e-06,
                4.785095064523075e-06,
                5.422218968349347e-06,
                2.3823685318069056e-07
            ],
            [
                2.9023112931688987e-06,
                1.99472900790731e-06,
                1.5534975691241939e-06,
                1.3709573702722555e-06,
                1.9947301970106386e-06,
                5.422218969601935e-06,
                2.5612815995532906e-06,
                3.2887482811220126e-06,
                3.7266388386231563e-06,
                6.475949525834513e-07
            ],
            [
                2.561283126535066e-06,
                9.422448185478557e-07,
                5.422219615898437e-06,
                5.422218969128516e-06,
                6.144176066353646e-06,
                3.726639728224814e-06,
                2.2603242978007868e-06,
                3.726638839806038e-06,
                1.3709578605455302e-06,
                1.9947306726358406e-06
            ],
            [
                6.144172404218801e-06,
                2.561283431916622e-06,
                2.561283431986506e-06,
                6.1441760657054305e-06,
                2.5612825155181522e-06,
                1.7603432131855856e-06,
                4.785096205717126e-06,
                5.422217676575195e-06,
                6.144176065314267e-06,
                3.288748280449018e-06
            ],
            [
                4.7850933535659155e-06,
                1.3709573702566696e-06,
                5.422219614438727e-06,
                6.962254588116627e-06,
                1.5534973840984598e-06,
                7.889264460776929e-06,
                3.7266406162269133e-06,
                4.222834451215781e-06,
                4.785092782692845e-06,
                3.2887478888496478e-06
            ],
            [
                0.9149009515124918,
                0.9999970976873236,
                0.9999980052698031,
                0.9999967112497615,
                0.9999970976887077,
                0.9626731134590489,
                0.9999980052702839,
                0.9999974387184088,
                0.999996711250936,
                0.9924227596775961
            ],
            [
                2.902312330849511e-06,
                1.2098656834922064e-06,
                3.288749065167371e-06,
                3.7266388396975786e-06,
                1.0677032518578904e-06,
                1.209866116137134e-06,
                1.5534971989258068e-06,
                2.2603248365343694e-06,
                1.5534983101301911e-06,
                2.260325375572331e-06
            ],
            [
                1.7603425837494853e-06,
                5.71500446967193e-07,
                2.902311639126627e-06,
                5.715006514040971e-07,
                1.760344052632596e-06,
                4.45084945809282e-07,
                6.475950297644816e-07,
                3.2887486731252264e-06,
                5.04347528440776e-07,
                1.3709572067680694e-06
            ],
            [
                1.0129993392600532e-05,
                6.144176066353646e-06,
                5.4222176755001384e-06,
                1.3007134663876127e-05,
                4.222833947282995e-06,
                1.3709573702248741e-06,
                6.144177530794679e-06,
                1.4738983723664288e-05,
                1.300713466316634e-05,
                3.726639283901856e-06
            ]
        ]
    },
    {
        "q_id": "8152_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            4,
            5,
            6,
            8,
            9,
            10,
            11,
            12,
            14,
            15,
            16,
            17,
            19,
            21,
            24,
            25,
            26,
            27,
            30,
            34,
            35,
            36,
            38,
            39,
            42,
            43,
            44,
            45,
            46,
            48,
            49,
            50,
            53,
            58,
            60,
            61,
            62,
            63,
            64,
            66,
            67,
            68,
            70,
            71,
            72,
            73,
            74,
            76,
            77,
            78,
            80,
            81,
            83,
            84,
            85,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            95,
            97,
            98,
            99,
            101,
            103,
            104,
            107,
            108,
            109,
            110,
            111,
            113,
            114,
            115,
            116,
            117,
            120,
            121,
            124,
            125,
            126
        ],
        "rewards": [
            [
                2.9023126769762986e-06,
                9.422448185264317e-07,
                1.3709568799679844e-06,
                1.7603434230921292e-06,
                1.994729721482609e-06,
                1.0677026154279257e-06,
                3.2887490653408545e-06,
                7.338207180761315e-07,
                1.3709575336405514e-06,
                2.9023109471452223e-06
            ],
            [
                6.144177531599359e-06,
                1.670142781520948e-05,
                3.2887490653408545e-06,
                4.222833444229772e-06,
                1.300712536203966e-05,
                3.726637950973972e-06,
                4.785093353626844e-06,
                7.889265406681968e-06,
                3.726638395527247e-06,
                5.4222170304318e-06
            ],
            [
                1.0129994602057158e-05,
                2.9023109471452223e-06,
                5.422221555133606e-06,
                1.473898197063434e-05,
                1.9947292458930106e-06,
                4.2228324377164004e-06,
                5.422217676925328e-06,
                2.26032348933062e-06,
                4.785093924103951e-06,
                8.939697369004791e-06
            ],
            [
                1.012998735687278e-05,
                5.829125851250855e-05,
                1.0129992186774007e-05,
                1.3007131564643372e-05,
                1.6701423834226767e-05,
                1.0129988563546333e-05,
                4.785092783210732e-06,
                1.4738983724146862e-05,
                4.0063711278232147e-05,
                2.430025231213619e-05
            ],
            [
                6.1441746017453204e-06,
                6.9622562478334885e-06,
                6.144175333155351e-06,
                7.889264465699106e-06,
                3.726638395215427e-06,
                3.726638839656906e-06,
                2.4300246512104316e-05,
                1.3007130012980722e-05,
                2.9023130228444433e-06,
                6.962257908753841e-06
            ],
            [
                4.222834954403545e-06,
                1.473898899846585e-05,
                1.3007123812554424e-05,
                6.144172404218801e-06,
                3.288749065029781e-06,
                8.93969417167259e-06,
                1.67014158650947e-05,
                8.93969736427282e-06,
                5.144221359250013e-05,
                3.726637950411341e-06
            ],
            [
                1.5534981249023245e-06,
                2.2603251061458426e-06,
                6.144172404218801e-06,
                7.889260704179641e-06,
                2.1444958628814052e-05,
                7.889264464895484e-06,
                1.670142980380249e-05,
                7.889264465842609e-06,
                8.939699500489763e-06,
                7.889264465239894e-06
            ],
            [
                2.561283126639892e-06,
                2.260325375650449e-06,
                6.962253759581752e-06,
                6.962255419804982e-06,
                8.939694172420599e-06,
                6.14417533430649e-06,
                4.0063711129426415e-05,
                8.939694172420599e-06,
                2.7535681242383173e-05,
                2.430023493865361e-05
            ],
            [
                2.4300246516082393e-05,
                8.939695237666677e-06,
                7.889263525261671e-06,
                5.4222202623972055e-06,
                8.939693106182721e-06,
                2.7535694365549603e-05,
                8.93969417167259e-06,
                1.0129995808639442e-05,
                1.3007134665413997e-05,
                2.430023782717578e-05
            ],
            [
                1.209865827698362e-06,
                2.5612815998491325e-06,
                8.939700566143004e-06,
                1.9947297214544894e-06,
                9.422445938728576e-07,
                1.2098655392574583e-06,
                2.5612822106421996e-06,
                1.3709575337078829e-06,
                2.5612825160271407e-06,
                7.889266347356409e-06
            ],
            [
                8.939696303758459e-06,
                5.422218969532895e-06,
                2.7535697662094155e-05,
                8.93969310675186e-06,
                4.222833444467892e-06,
                5.422220262333096e-06,
                1.0129987355988324e-05,
                6.962257909323729e-06,
                1.147876538789672e-05,
                6.9622587393661365e-06
            ],
            [
                6.962253759581752e-06,
                2.260324028306588e-06,
                4.222833444229772e-06,
                3.726637951170554e-06,
                5.422221555069497e-06,
                1.4738988998117324e-05,
                3.288749065167371e-06,
                1.4738976696800444e-05,
                6.144175334094145e-06,
                1.4738980212296288e-05
            ],
            [
                1.1478772229781076e-05,
                1.012998735462479e-05,
                6.144172404218801e-06,
                4.785095065045315e-06,
                3.2887478890769702e-06,
                4.785092783319532e-06,
                3.2887490652810324e-06,
                2.144494585583323e-05,
                4.222835458002318e-06,
                1.0129989771473008e-05
            ],
            [
                1.2098658276730537e-06,
                3.7266383950934104e-06,
                4.785096775842062e-06,
                8.93969417167259e-06,
                5.422218969532895e-06,
                2.2603237586397375e-06,
                6.962253759486771e-06,
                3.7266379509129646e-06,
                5.422218969463855e-06,
                1.7603440525701563e-06
            ],
            [
                4.222832437639588e-06,
                6.9622537587775775e-06,
                1.5534983100595462e-06,
                1.3709570433979422e-06,
                1.3007134664514934e-05,
                1.9947301969707264e-06,
                1.3709575336654889e-06,
                4.222835458002318e-06,
                3.7266383954560706e-06,
                2.902313023039776e-06
            ],
            [
                3.535623795375786e-05,
                1.7603436329554703e-06,
                3.7266410609940346e-06,
                2.902312677060767e-06,
                2.2603242978377903e-06,
                3.7266401725935817e-06,
                4.222834954514924e-06,
                1.553497754577351e-06,
                1.2098658277451275e-06,
                7.88925976418034e-06
            ],
            [
                5.422217030121119e-06,
                1.3007128460797749e-05,
                2.430024651705481e-05,
                7.88926446430712e-06,
                6.1441724044534996e-06,
                6.144176799099397e-06,
                1.1478768122069266e-05,
                6.144177531007026e-06,
                2.5612815999679353e-06,
                1.0129989771823107e-05
            ],
            [
                2.9023109471452223e-06,
                2.2603242978377903e-06,
                1.7603438428564603e-06,
                7.889261644875049e-06,
                1.3709572068422585e-06,
                7.889261644631091e-06,
                8.315277302747361e-07,
                2.9023109471689794e-06,
                1.0677026154619133e-06,
                2.90231163910023e-06
            ],
            [
                6.962253752458153e-06,
                6.605216029362855e-05,
                1.0129990976728036e-05,
                1.1478768115554855e-05,
                7.88926540262081e-06,
                1.8925145980732218e-05,
                2.2603253753174176e-06,
                7.88926446470893e-06,
                1.2098655391617266e-06,
                8.939698428917621e-06
            ],
            [
                1.2098653950403334e-06,
                1.5534973841895917e-06,
                2.561283431916622e-06,
                1.3709578605542582e-06,
                5.043474683050556e-07,
                9.422445938964242e-07,
                9.422450431860582e-07,
                8.315281267649641e-07,
                7.338211554758494e-07,
                1.3709575336860625e-06
            ],
            [
                4.222834451215781e-06,
                8.939698434332555e-06,
                5.422218969601935e-06,
                6.144176798691468e-06,
                0.00010889689594839689,
                7.889261645090304e-06,
                2.260323489410794e-06,
                8.939699498587217e-06,
                3.120191508820951e-05,
                2.1444940743225995e-05
            ],
            [
                3.2887502415243994e-06,
                2.5612822107167428e-06,
                2.5612816000331606e-06,
                3.2887506334560605e-06,
                2.561283126639892e-06,
                2.5612819053586272e-06,
                1.892514598427789e-05,
                1.9947294837154625e-06,
                4.2228324377164004e-06,
                1.2098658277181688e-06
            ],
            [
                1.300713466420736e-05,
                6.9622562489985925e-06,
                3.726641060956752e-06,
                1.012999460108057e-05,
                5.422221555133606e-06,
                1.0129993394314164e-05,
                8.939695237341456e-06,
                4.006370650653807e-05,
                1.012998735687278e-05,
                6.962258739271155e-06
            ],
            [
                0.651354857898194,
                0.999704042778299,
                0.24508501864634824,
                0.9993736659627807,
                0.015906390837114055,
                0.9999599363180417,
                0.9998766053691461,
                0.5621765008857982,
                0.20181322946142374,
                0.9999485577748313
            ],
            [
                4.7850950647493785e-06,
                6.1441746017453204e-06,
                1.760342793583908e-06,
                1.3007123811513407e-05,
                1.2098661161861e-06,
                8.315283250006957e-07,
                7.338207180801359e-07,
                1.300713311517055e-05,
                3.5356246493272806e-05,
                0.00017952800699102303
            ],
            [
                2.561281599776919e-06,
                7.889266343316778e-06,
                1.7603430034743913e-06,
                6.962255419380732e-06,
                3.7266383952696564e-06,
                8.939698433584547e-06,
                2.561283431627768e-06,
                2.902311984250272e-06,
                3.7266392836984955e-06,
                6.144172403928222e-06
            ],
            [
                1.9947299592570416e-06,
                1.7603438427660027e-06,
                8.93969630348202e-06,
                2.9023123311055552e-06,
                1.209865250822125e-06,
                4.7850939242083995e-06,
                7.889260703906985e-06,
                2.9023109471188266e-06,
                6.962256249429175e-06,
                4.22283344433731e-06
            ],
            [
                4.785093923847183e-06,
                8.315277302788957e-07,
                2.2603245671490605e-06,
                1.7603427936079236e-06,
                2.902311639073834e-06,
                3.726638395320497e-06,
                4.222833444506298e-06,
                2.260324028351814e-06,
                9.42244256915735e-07,
                6.144172403928222e-06
            ],
            [
                3.120191116876594e-05,
                1.1478770859917257e-05,
                1.0129988562901417e-05,
                8.939693105272102e-06,
                2.75357009372024e-05,
                1.1478766754941153e-05,
                2.144495607789177e-05,
                1.6701427813417103e-05,
                6.962255419051463e-06,
                1.01299946023704e-05
            ],
            [
                3.7266388397721442e-06,
                1.1478765388105516e-05,
                1.1478766756214804e-05,
                1.1478765387667046e-05,
                6.962253759581752e-06,
                6.144172404520556e-06,
                7.889266347356409e-06,
                1.8925145971919677e-05,
                1.7603425837366772e-06,
                2.2603242978007868e-06
            ],
            [
                4.222835457595211e-06,
                7.889260703763482e-06,
                4.006369690499937e-05,
                1.3007133113703658e-05,
                1.1478772229551402e-05,
                6.144172403928222e-06,
                1.473898372500477e-05,
                4.785093353274332e-06,
                5.422217675756574e-06,
                2.2603240282243575e-06
            ],
            [
                3.9278634073098236e-07,
                9.422445938642879e-07,
                1.7603432132912532e-06,
                2.2603248366762157e-06,
                1.3709575336405514e-06,
                9.422447062150634e-07,
                8.93969310675186e-06,
                3.726637950973972e-06,
                3.288748673265808e-06,
                1.2098652508287273e-06
            ],
            [
                1.0129993394811673e-05,
                2.260324028306588e-06,
                6.144177531532303e-06,
                5.422220262333096e-06,
                6.962254589528684e-06,
                6.1441731363550164e-06,
                8.93969630348202e-06,
                7.889259763469998e-06,
                6.962254589528684e-06,
                4.5397857701531434e-05
            ],
            [
                1.9947290081177566e-06,
                7.88926258532661e-06,
                2.9023123311055552e-06,
                3.7266401725681614e-06,
                1.0129995807699706e-05,
                1.0129993394129904e-05,
                6.14417606659952e-06,
                5.422217030209884e-06,
                5.422217030288788e-06,
                1.4738985484871391e-05
            ],
            [
                2.9023112930949896e-06,
                4.222832940715735e-06,
                1.0129994599901296e-05,
                6.144173135762683e-06,
                1.473898899742027e-05,
                1.670142980608093e-05,
                5.422220908314139e-06,
                8.939695238211425e-06,
                3.2887482811579057e-06,
                1.892514820142385e-05
            ],
            [
                2.9023126769762986e-06,
                2.260323758939877e-06,
                1.7603425837494853e-06,
                3.7266383955882547e-06,
                6.962253759904688e-06,
                2.9023109471188266e-06,
                1.5534983101301911e-06,
                2.2603248367358324e-06,
                1.2098662604126641e-06,
                1.3709578605455302e-06
            ],
            [
                7.889261644631091e-06,
                4.785096776194573e-06,
                1.7603432132464244e-06,
                1.3007126913583456e-05,
                1.5534977545102382e-06,
                4.222834451012227e-06,
                2.2603242978377903e-06,
                5.422220261948442e-06,
                1.994730197071414e-06,
                4.222834451065997e-06
            ],
            [
                6.962254588724508e-06,
                2.1444950966608343e-05,
                2.7535684521195802e-05,
                1.4738981970956057e-05,
                2.7535684497254823e-05,
                8.939695237959376e-06,
                5.422220907909759e-06,
                7.889259764079887e-06,
                8.939697369004791e-06,
                1.473898196763166e-05
            ],
            [
                4.006368262111344e-05,
                1.1478764019557924e-05,
                1.0129988563914856e-05,
                4.785095064819011e-06,
                6.962257909323729e-06,
                1.6701419849447602e-05,
                6.962258739169842e-06,
                2.902313023063532e-06,
                4.539785239661729e-05,
                7.889266347456862e-06
            ],
            [
                4.785092783319532e-06,
                4.785096205973894e-06,
                4.222832941072913e-06,
                2.561281600049467e-06,
                1.3709575337078829e-06,
                8.3152792852928e-07,
                3.7266379513162962e-06,
                6.962257079465052e-06,
                1.1478773598538445e-05,
                1.7603440527046419e-06
            ],
            [
                1.553498495295912e-06,
                2.5612819053586272e-06,
                2.5612828212909852e-06,
                1.067703379154416e-06,
                6.144172404380855e-06,
                3.7266410608720178e-06,
                1.6701417860795016e-05,
                1.7603425837366772e-06,
                3.2887490653647836e-06,
                4.222835457906302e-06
            ],
            [
                1.2098661161861e-06,
                1.370956716519966e-06,
                2.5612816000145246e-06,
                4.785096205830278e-06,
                1.3709572067955008e-06,
                1.760343423160973e-06,
                1.9947301969707264e-06,
                2.2603237589542675e-06,
                2.4300243614475748e-05,
                2.2603251061849014e-06
            ],
            [
                6.962255419380732e-06,
                1.1478769490387674e-05,
                5.829127244377123e-05,
                4.006370170554982e-05,
                1.892515274614874e-05,
                4.0063696922780274e-05,
                1.3007126907881513e-05,
                7.889260704308795e-06,
                3.120191508321514e-05,
                5.144223203214182e-05
            ],
            [
                3.7266406168403854e-06,
                1.7603434231385591e-06,
                4.785092783319532e-06,
                6.962254588433232e-06,
                1.147877359872636e-05,
                3.7266401724291984e-06,
                5.422219616026655e-06,
                2.260325375615501e-06,
                1.9947294836483373e-06,
                1.55349775456958e-06
            ],
            [
                6.962257079059797e-06,
                1.1478766749992709e-05,
                1.4738981968864903e-05,
                2.5612831266608576e-06,
                2.7535700945316292e-05,
                3.2887498494551953e-06,
                2.7535684505068197e-05,
                6.1441767990323395e-06,
                8.93969310647542e-06,
                7.889265406438011e-06
            ],
            [
                6.1441767987808774e-06,
                7.889264466344872e-06,
                1.067702615417244e-06,
                3.726639284050988e-06,
                2.5612822107167428e-06,
                2.5612831264302397e-06,
                6.9622587393661365e-06,
                1.7603427935678977e-06,
                7.889263525261671e-06,
                8.4811081143118e-05
            ],
            [
                4.222833444229772e-06,
                7.889261644982674e-06,
                4.2228344511197656e-06,
                4.785093353687772e-06,
                1.9947306726049992e-06,
                1.1478769493540482e-05,
                1.0129994601872894e-05,
                6.962257909323729e-06,
                5.422218323093458e-06,
                6.144177531532303e-06
            ],
            [
                1.3007123812057577e-05,
                3.726639728224814e-06,
                2.561283126679493e-06,
                2.9023123310580418e-06,
                2.9023130230846496e-06,
                3.2887490652810324e-06,
                2.2603240283888175e-06,
                4.785093353626844e-06,
                1.3709578605617394e-06,
                3.7266401721817755e-06
            ],
            [
                3.72664106039412e-06,
                4.222832940942332e-06,
                3.7266401722360055e-06,
                3.7266401724291984e-06,
                5.829124463468578e-05,
                6.144175333926503e-06,
                1.8925148239772175e-05,
                8.93969950000193e-06,
                1.1478769491598686e-05,
                4.222832437497486e-06
            ],
            [
                2.902311985079115e-06,
                6.144176066672166e-06,
                4.222832437639588e-06,
                1.0677032518700286e-06,
                2.9023119850527192e-06,
                4.22283394786293e-06,
                7.889261644631091e-06,
                1.5534975693601474e-06,
                1.0677029972745947e-06,
                4.222835458044565e-06
            ],
            [
                2.260324028404236e-06,
                1.0677031245851707e-06,
                1.9947299591826594e-06,
                1.994730196992497e-06,
                1.7603425837791042e-06,
                1.0677024881887838e-06,
                9.422443692261927e-07,
                1.3709576971242028e-06,
                8.31528424151477e-07,
                2.561283126535066e-06
            ],
            [
                1.4738987238464762e-05,
                1.4738985483879434e-05,
                5.422220262195015e-06,
                1.1478766755734576e-05,
                2.7535691093547457e-05,
                3.5356246488642456e-05,
                7.889262584350785e-06,
                1.0129989772274546e-05,
                7.889262585541864e-06,
                8.939698435096828e-06
            ],
            [
                4.785096205882502e-06,
                6.962257909501028e-06,
                3.1201922523121745e-05,
                6.962257079553702e-06,
                2.9023133689924295e-06,
                1.1478772230198667e-05,
                6.144172404129392e-06,
                4.222834451292594e-06,
                6.144177531532303e-06,
                3.726638839806038e-06
            ],
            [
                6.9622562489985925e-06,
                1.4738983715299675e-05,
                6.962253759043525e-06,
                8.9397005654763e-06,
                8.939697367703906e-06,
                1.8925152719091475e-05,
                1.0129992186387057e-05,
                0.006692850871657231,
                4.7850927830845245e-06,
                1.8925157262578186e-05
            ],
            [
                3.288750241473551e-06,
                3.2887482811908074e-06,
                5.422219615750493e-06,
                4.222834451254188e-06,
                5.715007195384861e-07,
                2.902313022952668e-06,
                8.939699500766203e-06,
                2.9023116390421582e-06,
                6.144176066264237e-06,
                3.2887486732000038e-06
            ],
            [
                7.889266347133978e-06,
                2.5612819053166966e-06,
                7.889262585728421e-06,
                3.2887478892504536e-06,
                6.96225956921868e-06,
                1.7603432133032607e-06,
                1.2098659719661556e-06,
                1.7603440525925705e-06,
                2.561281905390075e-06,
                2.5612828213352452e-06
            ],
            [
                1.473898899846585e-05,
                3.7266383954560706e-06,
                6.96225873967641e-06,
                8.939700565996655e-06,
                1.0129993394129904e-05,
                3.726640172337686e-06,
                1.6701423834226767e-05,
                3.72664017246987e-06,
                1.3007125359413455e-05,
                1.3007130013572209e-05
            ],
            [
                1.0129988564099116e-05,
                4.785096776251149e-06,
                4.222834954514924e-06,
                2.260323489410794e-06,
                4.78509563535725e-06,
                3.726637951079042e-06,
                2.260324028404236e-06,
                2.260323758806253e-06,
                5.422217676797111e-06,
                5.42221767672807e-06
            ],
            [
                8.939695238211425e-06,
                5.422220908634683e-06,
                4.5397879445707534e-05,
                6.962254588724508e-06,
                4.785093924251918e-06,
                8.481106146543261e-05,
                6.144172404028807e-06,
                3.120191508446373e-05,
                4.539787401825028e-05,
                1.4738978454950406e-05
            ],
            [
                8.939700566565793e-06,
                1.300712846361323e-05,
                7.88925976397226e-06,
                3.288750633545794e-06,
                1.4738985484227961e-05,
                2.4300240730549767e-05,
                4.0063696932399445e-05,
                6.962258739169842e-06,
                6.962259569484628e-06,
                6.962258739454786e-06
            ],
            [
                8.93969310662177e-06,
                1.0129987354108855e-05,
                8.939698434495167e-06,
                1.6701423833011596e-05,
                1.6701415855859424e-05,
                1.147876812238246e-05,
                1.4738987242432592e-05,
                7.889260704732132e-06,
                3.120190019932095e-05,
                6.144173136729416e-06
            ],
            [
                5.422219615898437e-06,
                1.7603436329554703e-06,
                1.8925152746768368e-05,
                2.561283431888668e-06,
                1.760344052693435e-06,
                5.422219615829396e-06,
                8.939695237504067e-06,
                1.670141984792864e-05,
                1.3709572068354007e-06,
                2.4300243616508983e-05
            ],
            [
                1.3709578605455302e-06,
                1.994729245842213e-06,
                2.260325375634003e-06,
                3.2887502414436403e-06,
                3.2887482811579057e-06,
                2.5612815999679353e-06,
                9.422450431732037e-07,
                2.2603248367512505e-06,
                4.785094494463623e-06,
                1.5534984953199313e-06
            ],
            [
                1.3007123811797321e-05,
                1.300713311517055e-05,
                5.422219615829396e-06,
                1.0129988562661878e-05,
                8.939696302457574e-06,
                3.2887478891487563e-06,
                1.1478773595657069e-05,
                7.889265406904397e-06,
                1.0129990979031306e-05,
                4.22283394762097e-06
            ],
            [
                2.9023109470554753e-06,
                1.7603430033799313e-06,
                1.994729483630195e-06,
                3.726639728262097e-06,
                6.144176066443055e-06,
                7.889261644358435e-06,
                6.144173869072478e-06,
                1.3007131562514014e-05,
                1.0677031245783732e-06,
                1.7603432131375548e-06
            ],
            [
                0.9998601778776409,
                0.9999869928700218,
                0.2942149659744614,
                0.9968273172753315,
                0.9999151889699259,
                0.05340332772831865,
                0.5926665999540698,
                0.9999251537540056,
                0.9999151889392965,
                0.9998415638394124
            ],
            [
                2.9023133690425823e-06,
                5.422218323349895e-06,
                4.222831934248571e-06,
                6.144175334172377e-06,
                4.785096205882502e-06,
                6.144177531208195e-06,
                1.1478765388898939e-05,
                7.889266346603015e-06,
                2.2603242978213447e-06,
                4.785094494672519e-06
            ],
            [
                0.8175744850834648,
                0.9991959141751134,
                0.16451646699291614,
                0.029312234090223377,
                0.4378234991142019,
                0.3775406687981454,
                0.18242551713899047,
                0.4073334000459302,
                0.5,
                0.26894141551050293
            ],
            [
                2.2603234893861252e-06,
                3.2887482811220126e-06,
                1.7603425837366772e-06,
                1.3709568799368123e-06,
                1.5534973841705173e-06,
                1.5534983100765009e-06,
                1.3709576971160984e-06,
                2.2603248367173307e-06,
                2.561281905293402e-06,
                9.422448185388577e-07
            ],
            [
                2.2603234893861252e-06,
                4.78509506499309e-06,
                2.144495351862222e-05,
                5.4222215550004564e-06,
                2.9023112931688987e-06,
                5.422217030495909e-06,
                1.6701423833436905e-05,
                5.422220908634683e-06,
                5.422218969601935e-06,
                1.3007126912258525e-05
            ],
            [
                2.7535687805818776e-05,
                6.962259569484628e-06,
                6.1441746018123775e-06,
                2.9023130230133794e-06,
                2.561283432005142e-06,
                7.889266347356409e-06,
                4.78509563550957e-06,
                4.222835458117536e-06,
                3.72664061681327e-06,
                1.9947306726213275e-06
            ],
            [
                1.300713311517055e-05,
                2.260325375677174e-06,
                1.4738978454950406e-05,
                3.7266401725681614e-06,
                1.4738976699749503e-05,
                1.3007128462785148e-05,
                1.3007133112307748e-05,
                8.939694170518055e-06,
                5.422217030288788e-06,
                1.3007134666431358e-05
            ],
            [
                3.120190392137216e-05,
                1.3007134664514934e-05,
                1.4738981968864903e-05,
                1.8925143723620274e-05,
                6.144176799227922e-06,
                7.889263525405172e-06,
                2.4300246523066122e-05,
                3.5356254925134237e-05,
                1.0129990979215566e-05,
                1.4738988998117324e-05
            ],
            [
                1.3709575336947905e-06,
                3.7266410609160796e-06,
                3.7266397282926013e-06,
                1.7603434231385591e-06,
                9.422449308335287e-07,
                1.0677026154473471e-06,
                1.5534984953199313e-06,
                3.7266379513162962e-06,
                1.553497754577351e-06,
                2.2603251061664e-06
            ],
            [
                5.144221356106128e-05,
                1.8925143724239906e-05,
                4.006368262694324e-05,
                1.0129992186774007e-05,
                1.670142980608093e-05,
                2.1444958639072976e-05,
                1.8925155003330605e-05,
                8.939695237959376e-06,
                1.6701421840804172e-05,
                6.962254589332388e-06
            ],
            [
                3.535623805498234e-05,
                1.1478764019077695e-05,
                4.785096205830278e-06,
                6.962257909121104e-06,
                5.422217676979575e-06,
                2.144494585197151e-05,
                7.889264465986113e-06,
                2.753568781222975e-05,
                2.260325375572331e-06,
                1.300712536203966e-05
            ],
            [
                1.3007134665413997e-05,
                2.7535681240079227e-05,
                6.962253759752719e-06,
                6.144175333635923e-06,
                2.4300237826203363e-05,
                2.430023491169112e-05,
                8.93969630362837e-06,
                5.422221555133606e-06,
                3.7266383952696564e-06,
                3.726637950973972e-06
            ],
            [
                1.670142382681424e-05,
                1.1478766757049986e-05,
                6.1441767987808774e-06,
                2.2603251062147097e-06,
                7.889265406904397e-06,
                2.2603242978377903e-06,
                3.288748673295719e-06,
                4.785093924103951e-06,
                1.5534983101393749e-06,
                4.785095635413826e-06
            ],
            [
                5.043474683126242e-07,
                2.5612812947077304e-06,
                2.561283126679493e-06,
                2.9023119851266288e-06,
                4.7850956351657615e-06,
                5.4222202624563834e-06,
                2.9023123310290063e-06,
                6.144173136885882e-06,
                2.902313023101807e-06,
                4.7850933538313875e-06
            ],
            [
                8.939698433974813e-06,
                1.209865250822125e-06,
                2.5612815999423112e-06,
                2.9023112931873767e-06,
                3.726639284017094e-06,
                1.0129993392600532e-05,
                1.9947306726049992e-06,
                7.889265405146477e-06,
                4.7850950648799385e-06,
                5.422220262555012e-06
            ],
            [
                5.043475885634304e-07,
                2.561281294616881e-06,
                3.7266388397721442e-06,
                4.2228344508893285e-06,
                6.475947982002148e-07,
                1.5534983101478522e-06,
                2.9023119850210436e-06,
                1.553497754577351e-06,
                2.260324297853209e-06,
                2.561283431942246e-06
            ],
            [
                6.144177531660828e-06,
                1.3007134665934505e-05,
                4.222832941111319e-06,
                1.0129992186589747e-05,
                8.93969736942758e-06,
                1.670141786036971e-05,
                6.962258736067116e-06,
                2.5612819053586272e-06,
                2.9023130230846496e-06,
                6.144174601208867e-06
            ],
            [
                1.0677031245990084e-06,
                1.2098661161982042e-06,
                1.994729721469003e-06,
                1.7603436330259153e-06,
                4.222833947728508e-06,
                2.2603248367656408e-06,
                2.5612819053399912e-06,
                1.5534983099564047e-06,
                4.222833444429485e-06,
                6.144175334367959e-06
            ],
            [
                3.726638839656906e-06,
                1.0677027427471959e-06,
                6.962253759670401e-06,
                4.222831934202483e-06,
                1.7603434230921292e-06,
                7.889266346746518e-06,
                1.2098656834834034e-06,
                6.144173136729416e-06,
                1.7603430034151537e-06,
                2.5612825159677387e-06
            ],
            [
                3.7266401724291984e-06,
                1.9947290080343035e-06,
                2.9023109471188266e-06,
                6.962257079629686e-06,
                2.260324028404236e-06,
                1.5534981249397663e-06,
                5.422217676925328e-06,
                6.144172404218801e-06,
                2.9023109471452223e-06,
                3.726640172385136e-06
            ],
            [
                5.144223202241074e-05,
                3.1201907623673364e-05,
                2.4300252288444548e-05,
                2.1444940737257882e-05,
                2.430024360881804e-05,
                1.0129992187105678e-05,
                7.889265405505236e-06,
                2.430024072471526e-05,
                0.9999810748585392,
                0.9996200155650086
            ],
            [
                3.2887490652451393e-06,
                1.6701429805655623e-05,
                1.994730434778778e-06,
                6.144174601499446e-06,
                8.939698434495167e-06,
                6.144173868178388e-06,
                4.222834954687752e-06,
                1.0129987356706945e-05,
                1.4738985484549675e-05,
                1.0129989771288745e-05
            ]
        ]
    },
    {
        "q_id": "8273_mmlu_math",
        "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,
            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,
            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": [
            [
                1.473898899908247e-05,
                8.939696303010449e-06,
                1.892514372479069e-05,
                4.539786863059458e-05,
                1.4738980211116665e-05,
                4.539785776395774e-05,
                6.962254589617333e-06,
                2.7535704224732304e-05,
                1.8925145981283003e-05,
                0.00029595720472874065
            ],
            [
                0.9999952149066462,
                0.9999417087136605,
                0.9998204719916403,
                0.9999921107355341,
                0.9999938558268632,
                0.9999885212359829,
                0.9999832985781584,
                0.9999910603047621,
                0.9999910603068948,
                0.9975273770070348
            ],
            [
                0.9999646437326569,
                0.32082131381216084,
                0.9999885212278473,
                0.9997965730548976,
                8.939699500489763e-06,
                0.9998766054258109,
                6.144172404028807e-06,
                0.46879062662624377,
                0.817574471748733,
                0.004070138669129902
            ],
            [
                0.9999251537371326,
                0.999903897539346,
                NaN,
                0.9999885212346179,
                0.9996646498951547,
                0.9999756997621719,
                0.9999251537460211,
                0.9999832985761693,
                0.9999756997563752,
                0.999941708727552
            ],
            [
                NaN,
                0.999994577782323,
                0.9999980052707541,
                0.9999930377437506,
                0.9999977396759716,
                0.9999977396746244,
                0.9999921107336528,
                0.999975699750598,
                0.9999251537639511,
                0.9999910603058276
            ],
            [
                0.999988521234612,
                0.999964643753523,
                0.9999930377420937,
                0.9999962733611607,
                0.999983298574178,
                0.9999687980774912,
                0.9998911030517746,
                0.9999967112509348,
                0.9998766053663705,
                0.9999930377454106
            ],
            [
                0.9999724642990576,
                0.9999952149037942,
                0.9999898700126439,
                NaN,
                0.9999810748517645,
                0.9999810748472489,
                0.9999885212332446,
                0.9999977396762413,
                0.9999832985761757,
                0.9999339478238921
            ],
            [
                5.422217030209884e-06,
                1.6701425825128124e-05,
                4.0063682625048554e-05,
                0.9999724642957865,
                0.0001584362733320158,
                3.5356267569843254e-05,
                2.7535687799708318e-05,
                4.006370651557427e-05,
                NaN,
                4.0063692172075196e-05
            ],
            [
                0.9999962733589396,
                0.9999980052702786,
                0.9999930377445897,
                0.9999546021151456,
                0.999996273360716,
                0.9999898700078206,
                0.9998601779600461,
                0.999997097687669,
                0.9999898700126435,
                0.9999832985821429
            ],
            [
                0.9999921107345955,
                0.999968798077481,
                0.9999832985781566,
                0.9947798751624565,
                0.9999756997592965,
                0.9999724643023399,
                0.9999885212277713,
                NaN,
                0.9999687980998099,
                0.9999646437450961
            ],
            [
                0.9999962733611604,
                NaN,
                0.9999984465026158,
                0.9992903297258094,
                0.9999945777829704,
                0.9999945777823237,
                0.9999952149072168,
                0.9988304895853558,
                0.9999869928715376,
                0.9999869928730897
            ],
            [
                0.0002034269971005548,
                0.0006263341009070824,
                0.00015843629210545118,
                0.00020342702151471094,
                8.481101098134002e-05,
                4.0063706492255065e-05,
                0.000158436273198315,
                0.00015843615985927873,
                1.473898899846585e-05,
                5.144222591578515e-05
            ],
            [
                4.539785238918559e-05,
                2.1444950965282096e-05,
                1.6701421837158667e-05,
                0.0005527786748059194,
                6.962253759670401e-06,
                1.3007131564903626e-05,
                8.481101095665886e-05,
                1.67014238321306e-05,
                6.605212105295326e-05,
                6.605212105295326e-05
            ],
            [
                0.9999952149055057,
                0.999986992876194,
                0.9999785550439266,
                0.9999910603015654,
                0.9999546021097292,
                0.998674977418571,
                NaN,
                0.9999646437408619,
                NaN,
                0.9999810748540177
            ],
            [
                0.9999339478713902,
                0.9999687980737616,
                0.9999898700041909,
                0.9999898700126446,
                0.9999151889397618,
                0.9999980052693311,
                0.9999952149072177,
                0.9999921107374181,
                0.9999945777797377,
                0.9999646437324605
            ],
            [
                0.9999151889588225,
                0.9999930377404338,
                1.4738978456398127e-05,
                1.4738983727256784e-05,
                NaN,
                0.9999599363030699,
                0.9999417087276253,
                0.9997040429153249,
                0.9999599363221466,
                1.3007126912826352e-05
            ],
            [
                0.9999724643121858,
                0.9996200155673632,
                0.9999687980961007,
                0.9999930377404312,
                0.9999599362887481,
                0.9995694429099702,
                0.9999974387187053,
                0.9999417087553925,
                2.902311984250272e-06,
                0.9997965730269229
            ],
            [
                1.6701419850845044e-05,
                0.9998415638212037,
                0.9992903294667016,
                0.9999957771680659,
                0.9999921107355415,
                0.9999339478242694,
                0.9999945777816769,
                3.7266397281434697e-06,
                0.9997965730270088,
                0.9995121429441453
            ],
            [
                8.939694172290508e-06,
                6.962258739454786e-06,
                6.605217608630573e-05,
                5.829129330780371e-05,
                4.539785238142359e-05,
                0.00012339463333689376,
                0.00043055713700031065,
                3.288747889229516e-06,
                3.535625492359079e-05,
                5.144222588771473e-05
            ],
            [
                0.9999910603026483,
                NaN,
                0.9999869928699864,
                0.9999810748585306,
                0.9999945777816769,
                0.9999785550413858,
                0.9999945777829702,
                0.9999982396567868,
                0.9999832985761693,
                0.99998699287309
            ],
            [
                0.9995694429978113,
                0.9999967112513267,
                0.9999957771650473,
                0.9999910603058458,
                0.9999646437619434,
                2.1444943287710254e-05,
                0.999997438717179,
                0.9998204721012713,
                1.7603427935967163e-06,
                3.288749065209246e-06
            ],
            [
                0.9999646437408781,
                0.9999952149032248,
                0.9998204720558539,
                0.9994472214002834,
                0.9999546021212056,
                0.9241418126663686,
                0.9999910603010497,
                0.9999810748473467,
                0.9999339478318646,
                0.9999921107383846
            ],
            [
                0.00017952794438905436,
                0.00013982209068353965,
                0.9980732654615915,
                3.12019225291377e-05,
                0.0002034269007343664,
                2.753568781222975e-05,
                7.484620047216503e-05,
                0.94659666812867,
                4.539786315904385e-05,
                8.481103123717e-05
            ],
            [
                2.144494329566774e-05,
                5.42222090821551e-06,
                6.962254589332388e-06,
                2.4300234937946394e-05,
                4.0063696957321844e-05,
                2.4300240728162926e-05,
                5.144223202914764e-05,
                4.006368738143655e-05,
                1.3007125359034903e-05,
                3.5356246478738656e-05
            ],
            [
                0.0002034268984465579,
                2.1444948408275583e-05,
                5.144221365238367e-05,
                2.1444940743772097e-05,
                5.144220137401424e-05,
                6.605216035706259e-05,
                0.9997965729546424,
                0.00013982207332811938,
                4.0063692178050736e-05,
                1.4738981969240237e-05
            ],
            [
                0.9999339478240112,
                0.9999417087415159,
                0.9999251537553342,
                0.9999724643188943,
                0.9999546021423021,
                2.430024361951464e-05,
                4.222834954561012e-06,
                0.9994472212629679,
                1.0129990977262395e-05,
                0.9997694931768373
            ],
            [
                8.939698434657777e-06,
                4.539786864000808e-05,
                5.8291265503797524e-05,
                2.7535704228438656e-05,
                3.12019150514328e-05,
                1.300712691308661e-05,
                2.4300252315495453e-05,
                3.120191509172827e-05,
                3.535623806720131e-05,
                0.9998766054401922
            ],
            [
                3.5356259106723956e-05,
                0.9933071504099801,
                0.00020342692402384427,
                3.120191877609648e-05,
                7.484623614370479e-05,
                3.53562591336057e-05,
                0.9964063981355568,
                0.0001795279659172125,
                2.144494074076854e-05,
                0.999985261016284
            ],
            [
                0.9999485577863694,
                0.9999832985762097,
                0.9999945777823249,
                0.9998204720133931,
                NaN,
                NaN,
                0.9999251537549678,
                0.9999885212264021,
                0.99995460212065,
                0.9999990577556308
            ],
            [
                0.9997694932027467,
                0.9999339478711028,
                0.9999938558261493,
                0.9999724643188099,
                0.9999967112497585,
                NaN,
                0.999964643753563,
                0.9999687980997938,
                0.9999756997505903,
                0.999989870004192
            ],
            [
                0.9999984465016899,
                0.9999930377454121,
                0.9998766054105537,
                0.999983298574179,
                0.9999546021259761,
                0.9999485577802343,
                0.9999938558275963,
                0.9999151889790765,
                0.9999417087554798,
                0.9999952149060757
            ],
            [
                0.9999546021313669,
                0.9998766053966284,
                0.9997965731006301,
                0.9999952149043646,
                0.9997694931766561,
                0.9999687980737526,
                0.9999038975966479,
                0.999991060306899,
                0.9997965730764853,
                0.9999952149032237
            ],
            [
                0.9999869928684425,
                0.9982992772648084,
                0.9999785550515891,
                0.9998766053663525,
                0.9999546021476009,
                0.9999921107393063,
                0.9999832985721833,
                0.9999962733589389,
                0.9999962733607162,
                0.9999724642957987
            ],
            [
                0.9993736658660831,
                0.9999724643187587,
                0.999975699767961,
                0.9999957771655489,
                0.9999151889890853,
                0.9999952149055054,
                NaN,
                0.9997388096606132,
                3.2887502412970765e-06,
                0.9999930377420905
            ],
            [
                0.00026119021512488347,
                1.3007134664822509e-05,
                0.00037998452566295483,
                1.8925148238291944e-05,
                0.00015843617884938802,
                0.0002959571692086191,
                0.00013982214069303955,
                4.539785780805251e-05,
                0.0002305068248261465,
                0.00010889687022902587
            ],
            [
                0.9999151889385179,
                0.999925153772784,
                0.9999599363174658,
                0.9994472214572999,
                0.9990889487063114,
                NaN,
                0.9999910603015664,
                0.9997965730291959,
                0.9982992775571379,
                0.9999898700054022
            ],
            [
                0.9959298614592264,
                0.999373665833365,
                0.9999921107345976,
                0.9999646437535248,
                0.9999852610197885,
                7.88926634644516e-06,
                0.9999885212332431,
                4.785095065045315e-06,
                0.9999938558253983,
                0.998967768841401
            ],
            [
                0.999981074842739,
                0.9999485578047985,
                0.9999852610180298,
                0.9999852610162754,
                0.9999810748449987,
                0.9999885212277695,
                0.9999945777816768,
                0.9997040429413729,
                0.9999810748585329,
                0.9999957771675626
            ],
            [
                0.9999151889283764,
                0.9995121428929137,
                0.9999687980811913,
                0.9999898700078178,
                0.999876605469328,
                0.9999921107364745,
                0.9999810748540273,
                0.9999967112517189,
                1.4738985484871391e-05,
                0.9999832985701931
            ],
            [
                0.9999339478397309,
                0.9999962733598278,
                0.9999957771660521,
                0.9999687980923747,
                0.9999910603068942,
                0.9999038975735753,
                0.9953904276774732,
                0.9998415638032324,
                0.9999599363078577,
                0.9999885212305076
            ],
            [
                5.829127935617924e-05,
                0.00015843629210545118,
                NaN,
                4.006368263787411e-05,
                7.484624506431508e-05,
                3.12019002122609e-05,
                NaN,
                0.00033535018729926236,
                5.144222588771473e-05,
                3.535624228313077e-05
            ],
            [
                0.9999967112509347,
                0.9999687980774961,
                1.5534983100920427e-06,
                0.9999967112521109,
                0.9999810748585458,
                0.9999832985761674,
                0.9999869928746389,
                0.9999952149066464,
                0.9999417087483762,
                0.9999852610110019
            ],
            [
                0.9999785550515878,
                0.9999724643023429,
                0.9999885212277699,
                0.9999910603048057,
                0.9999930377454107,
                0.9999910603058282,
                0.9999974387168733,
                3.7266410604686857e-06,
                0.9999687980737564,
                0.9998415638021374
            ],
            [
                0.9989677688817357,
                0.999769493257899,
                0.9998601779262548,
                0.9990889488792971,
                0.9999977396765105,
                0.9999885212332448,
                0.9999832985801618,
                0.9999952149072175,
                0.9999151889487328,
                0.9999546021259581
            ],
            [
                0.999981074858559,
                0.9996646497772156,
                0.999983298584277,
                0.9999921107365115,
                0.9998601778958712,
                0.5926665999540698,
                0.9149009497722477,
                0.9991959142108897,
                0.880797068590724,
                7.338212429420757e-07
            ],
            [
                0.0002305067421546296,
                5.144220133658703e-05,
                5.829129330780371e-05,
                6.605213676969247e-05,
                6.605212892597951e-05,
                8.481101077710342e-05,
                5.422217676797111e-06,
                4.5397857790051276e-05,
                9.610244932322232e-05,
                1.892514147046736e-05
            ],
            [
                0.9999967112493672,
                0.9999485577618736,
                0.9999038975965941,
                0.9999756997534786,
                0.9999852610215482,
                0.9999930377420913,
                0.9999832985801526,
                0.9999599362934992,
                0.9999885212359829,
                0.9995121429432937
            ],
            [
                0.9999869928653343,
                0.9999990577550691,
                0.999620015565318,
                NaN,
                0.9999967112517189,
                0.9999910603068937,
                0.9999980052705164,
                0.9706877702026055,
                0.9998911030396122,
                0.9999785550491346
            ],
            [
                2.1444956078515887e-05,
                2.1444950966608343e-05,
                0.00012339460423515042,
                1.892515500663531e-05,
                4.539789028526512e-05,
                0.00020342699777831468,
                9.610242630304791e-05,
                6.605215253545261e-05,
                0.0001584361978348892,
                0.00015843619753982553
            ],
            [
                0.7772998611746912,
                0.9999599363078145,
                0.9997965730995142,
                0.9999038975392727,
                0.9999898700090211,
                0.9999151889487236,
                0.9999485577618392,
                0.9999967112517189,
                0.9999957771655489,
                0.9996646500135228
            ],
            [
                8.481101104304292e-05,
                0.00015843621666364007,
                6.962256248606003e-06,
                3.120191135412508e-05,
                7.484621824966732e-05,
                9.610238052909926e-05,
                0.0004305570881885698,
                0.0003353500633794133,
                4.539786862811735e-05,
                0.0002034269236568478
            ],
            [
                0.9997694933396449,
                0.9999724643154692,
                0.00012339455986169293,
                0.999993037741261,
                0.9999756997621694,
                0.9999687980849209,
                0.9996646497312811,
                0.9999756997593034,
                NaN,
                0.9999910602994355
            ],
            [
                0.9999038976194913,
                0.9999687980738577,
                0.9997388097233559,
                0.9997694933131654,
                0.9999852610215443,
                7.484624486991525e-05,
                0.9999977396751634,
                0.9999417087207244,
                0.9999930377445807,
                0.9999417087414922
            ],
            [
                4.4508521110762794e-07,
                0.9999810748449944,
                0.9999945777797377,
                0.9999938558232024,
                2.4300246516082393e-05,
                0.9999832985781602,
                0.9996200154742597,
                0.9999869928669056,
                0.9999967112505427,
                0.999769493179842
            ],
            [
                0.9999885212332523,
                0.999959936317401,
                0.9999724642990617,
                0.9996200154896923,
                NaN,
                0.9999967112505442,
                NaN,
                0.9999546021313719,
                0.9999852610215436,
                0.999968798081203
            ],
            [
                3.1201915093884926e-05,
                1.8925141470949294e-05,
                0.9999485577692127,
                8.48110110128085e-05,
                4.5397852399094525e-05,
                2.7535684533717236e-05,
                5.4222215552470286e-06,
                1.892515049423401e-05,
                2.1444953523537147e-05,
                2.1444950969026795e-05
            ],
            [
                0.9999756997650667,
                0.9999756997650627,
                0.999964643757743,
                0.9999151889789432,
                0.9999546021259847,
                0.9999546021098811,
                0.9999930377454106,
                0.999993855824666,
                0.9999251537817503,
                NaN
            ],
            [
                0.9999724643154672,
                1.3709576971316842e-06,
                0.9999785550439318,
                0.999996273360272,
                0.9999785550592586,
                0.9999599362982855,
                0.9996200155068049,
                3.120192619704807e-05,
                0.9999646437619403,
                0.9999756997679619
            ],
            [
                0.9999869928761884,
                0.9999869928684375,
                0.9902915246556765,
                0.9999646437366672,
                0.999373665699832,
                0.9999957771670589,
                1.3709578605455302e-06,
                NaN,
                NaN,
                0.9990889487721148
            ],
            [
                0.999993855826864,
                0.999997097686631,
                0.9999869928684356,
                0.9999599363221524,
                0.9999885212264013,
                0.9999980052709919,
                0.9999869928668877,
                0.9997040429015819,
                0.9999869928715376,
                0.9999977396757022
            ],
            [
                0.9999151889491555,
                0.9999952149032237,
                NaN,
                NaN,
                0.9999852610127603,
                0.9999646437577571,
                0.9999910603047624,
                0.9999974387184001,
                0.9995694429638422,
                0.9999921107364755
            ],
            [
                0.00010889694805897948,
                4.53978848619353e-05,
                3.1201911372399926e-05,
                5.144221364340114e-05,
                7.484620930074429e-05,
                4.006370173105521e-05,
                4.0063706508432764e-05,
                0.9992903296515899,
                8.481106149073081e-05,
                0.00013982210746729708
            ],
            [
                0.999933947844354,
                1.9947297214182054e-06,
                0.9998204719923742,
                0.9999869928653405,
                0.9999546021478478,
                0.999704043021007,
                0.9999724642990628,
                NaN,
                0.999985261018111,
                0.9999898700066213
            ],
            [
                0.9999810748517658,
                0.9999417087554264,
                0.9999339478556528,
                0.9996200154765259,
                0.9999724643121878,
                0.9999974387180953,
                0.999986992868465,
                0.9996646500093664,
                0.7310585727705127,
                1.5534979396984994e-06
            ],
            [
                0.9999852610162847,
                0.9999646437493017,
                0.9953904273569825,
                0.9999957771680674,
                3.7266388396975786e-06,
                0.9999810748449939,
                0.9999687980923503,
                0.9999910603026309,
                0.9998766054254501,
                0.9999251537371064
            ],
            [
                0.9992903296330969,
                0.9999785550592593,
                0.9997388096619432,
                0.9999869928684354,
                6.475947982022763e-07,
                0.9999962733620488,
                0.999997097686977,
                0.9999989322966208,
                0.9999852610127589,
                0.9999869928668853
            ],
            [
                0.9999687980849195,
                0.9999151889284097,
                0.999933947823881,
                0.9999151889283764,
                0.9999756997476854,
                0.9999687980737645,
                0.9997694932663165,
                0.9999921107392955,
                0.9998766054252257,
                2.56128159999123e-06
            ],
            [
                0.9999810748540188,
                6.144174600605357e-06,
                0.9999599363030484,
                4.785096776068365e-06,
                0.9999724642957917,
                0.9999977396765106,
                0.9999852610215436,
                0.9997388097625093,
                0.9999986290432836,
                0.9999339478240588
            ],
            [
                1.8925150496161756e-05,
                2.9023119850527192e-06,
                7.484620938678116e-05,
                2.4300252315495453e-05,
                0.00012339458943023138,
                3.535626335262457e-05,
                5.829129327472389e-05,
                4.539785778179383e-05,
                NaN,
                5.422217030495909e-06
            ],
            [
                0.9999974387168733,
                0.9999417087344882,
                0.9999646437409938,
                0.9999938558253998,
                0.9999962733616068,
                0.9999982396569965,
                0.9999952149037946,
                0.9999417087067576,
                0.9999930377437511,
                0.9999921107336551
            ],
            [
                0.9998766054109486,
                0.9999546021205518,
                0.9999417087345305,
                0.9999952149066466,
                0.9999952149055086,
                0.9999980052705164,
                0.9999967112497586,
                0.9999977396762412,
                0.9999938558239333,
                0.9999921107364753
            ],
            [
                0.999993855827596,
                0.9706877720045336,
                0.9999967112505428,
                0.9999852610233028,
                0.9999869928699862,
                0.999738809569995,
                0.9998911030780216,
                NaN,
                0.9998204720987116,
                0.9997040427955382
            ],
            [
                4.006371126336615e-05,
                3.12019002122609e-05,
                0.00010889689619874565,
                4.0063692179945426e-05,
                0.0002611903093833627,
                3.120191136263821e-05,
                5.1442219768738885e-05,
                7.484621824966732e-05,
                1.8925157263094544e-05,
                6.605212101883346e-05
            ],
            [
                0.9999785550592579,
                0.999975699747687,
                0.9998766054411222,
                0.9997694933684385,
                0.9999852610110046,
                0.9999151889485612,
                0.9999921107383563,
                0.9997694932309433,
                0.9999957771660523,
                0.9999921107364742
            ],
            [
                0.00015843621607581788,
                6.605213676969247e-05,
                4.006367785700152e-05,
                0.9999910603015648,
                4.00637017209988e-05,
                3.1201903929204235e-05,
                5.144223202241074e-05,
                9.610239208148006e-05,
                9.610238052909926e-05,
                5.829128633093081e-05
            ],
            [
                9.61024607064122e-05,
                4.539787944042276e-05,
                0.0003353502281896029,
                1.4738987241172537e-05,
                9.610246073717569e-05,
                6.605216032919004e-05,
                0.000552778741694912,
                0.00026119024485471697,
                9.610244925260613e-05,
                5.144223198722914e-05
            ],
            [
                4.5397868604005595e-05,
                9.610246050644951e-05,
                0.0001795279652511508,
                5.829127939986156e-05,
                0.0009110509950829632,
                6.605212092992972e-05,
                4.006368740446426e-05,
                2.7535704220525098e-05,
                3.535625913810743e-05,
                7.484624506431508e-05
            ],
            [
                0.999903897596873,
                0.9999984465016913,
                0.9999910603005003,
                0.9999251537906066,
                0.9999724643089085,
                0.9999885212305071,
                0.9998601779263891,
                0.9998204720149498,
                0.9999687980849142,
                0.999994577780384
            ],
            [
                0.999988521229139,
                0.9999984465016898,
                0.9999756997622188,
                0.9999546021259818,
                0.9999852610110056,
                0.9999938558239341,
                0.9999546021315949,
                0.9999898700114374,
                0.9999938558261308,
                0.9999417087206875
            ],
            [
                NaN,
                0.9998911031167671,
                0.999995214907222,
                0.9999885212359799,
                0.9999898700102411,
                0.9999910603068948,
                3.4663253846473677e-07,
                NaN,
                0.9999546021478792,
                0.999993855824666
            ],
            [
                1.0129989771657269e-05,
                0.00010889688322022292,
                0.0002959570976861762,
                4.539787944306515e-05,
                9.610240341642045e-05,
                4.006371125884805e-05,
                0.000123394633678021,
                4.5397884837823535e-05,
                9.610244924211859e-05,
                4.0063692178050736e-05
            ],
            [
                0.9999986290424663,
                0.9999984465016899,
                0.9999938558246662,
                0.999978555054148,
                0.9999930377462408,
                0.9999993524050474,
                0.9999885212346126,
                0.9999417087206125,
                0.9999945777823231,
                NaN
            ],
            [
                1.3007126911004571e-05,
                4.006367785875045e-05,
                8.93969310662177e-06,
                2.5612825160096693e-06,
                8.939700566435704e-06,
                1.3007131565140219e-05,
                8.939693106020111e-06,
                6.144173136729416e-06,
                2.1444943298320236e-05,
                7.338213304283347e-07
            ],
            [
                0.9999885212346123,
                0.9999957771655488,
                0.9999869928684362,
                0.9999785550464785,
                0.99999862904312,
                0.9999251537471183,
                0.9999832985801925,
                0.9999898700090363,
                0.9999885212332436,
                0.9999952149037944
            ],
            [
                0.9999852610197869,
                0.9999687980811974,
                0.9999646437450808,
                0.9999339478632303,
                0.9999910603036961,
                0.9999952149066467,
                0.9999898700114362,
                NaN,
                0.9998204719912301,
                0.999876605425161
            ],
            [
                0.9999885212318773,
                0.9997965730759288,
                0.9999970976890531,
                0.9999646437619387,
                0.9996646498898372,
                0.9999921107392975,
                0.9990889486847477,
                0.9999756997563867,
                0.9999810748585384,
                6.96225956921868e-06
            ],
            [
                0.9999832985821686,
                0.5926665999540697,
                0.9995121429473526,
                0.9999945777829825,
                0.9999339478242194,
                0.9998415637645076,
                0.7310585844894971,
                0.9999251537557634,
                4.785096775171854e-06,
                0.999948557792854
            ],
            [
                0.9988304897471836,
                0.9999869928715455,
                0.9986749777249736,
                0.9933071479086201,
                0.9999810748562732,
                0.9999869928653343,
                0.9999038975736655,
                0.9971990736617337,
                0.9989677689152278,
                0.9997388096284439
            ],
            [
                0.9999930377462407,
                0.9999995549151073,
                0.9999930377437505,
                0.9995694428597932,
                0.9999785550413696,
                0.999981074854021,
                0.9999987901338839,
                0.9999485577618527,
                0.9997388097546285,
                0.999968798096083
            ],
            [
                0.8354835432479661,
                0.5312093733737563,
                0.9999832985741836,
                0.9995121428765649,
                0.9999151889185681,
                0.9998601779111129,
                0.9999832985801963,
                0.999820472099187,
                0.5,
                0.6224593312018546
            ],
            [
                4.539786320660675e-05,
                0.9999038975508887,
                5.829125855619084e-05,
                1.6701415869924985e-05,
                4.5397879432165314e-05,
                5.1442219784084046e-05,
                5.829125851250855e-05,
                0.9999151889689967,
                1.670141984792864e-05,
                3.120192623257619e-05
            ],
            [
                0.999704042936482,
                0.9997040429771429,
                0.9999251537377806,
                0.9999898700090699,
                0.9999251537371064,
                0.9999977396746246,
                0.9998415637469145,
                0.9999898700126459,
                0.9999993524052019,
                0.9959298626521842
            ],
            [
                0.9999952149066468,
                0.9999962733616045,
                0.9999724643023574,
                0.9999938558232011,
                0.9999962733620488,
                0.9999967112509348,
                0.9999945777797383,
                0.999993037744598,
                0.9999930377412606,
                0.9999977396746244
            ],
            [
                0.679178699175393,
                3.120191136649749e-05,
                0.999991060301566,
                4.5397868646614036e-05,
                7.484624507683945e-05,
                3.535626334645077e-05,
                0.0002034270217278058,
                0.0019267342840929749,
                0.0009110509967254001,
                0.9994472214632169
            ],
            [
                0.9999991684715759,
                NaN,
                0.9999910603004999,
                0.9999646437493034,
                0.9999984465020603,
                0.9999546021476443,
                0.9999990577554062,
                0.9999991684721706,
                0.9999970976876693,
                0.9933071475680884
            ],
            [
                0.00013982204069440157,
                5.422218323349895e-06,
                5.422217677028889e-06,
                2.4300232039788792e-05,
                5.422217030555087e-06,
                1.3007123810638006e-05,
                8.93969630362837e-06,
                6.144172403715875e-06,
                2.1444940744864302e-05,
                0.00023050679675028972
            ],
            [
                0.904650527388829,
                0.5621765008857981,
                0.9986749775961891,
                0.9999910603036983,
                0.9999967112509358,
                0.9999756997680153,
                1.670142980687079e-05,
                0.9999869928653441,
                0.9999038975738312,
                0.9998766054635019
            ],
            [
                0.0001233945748712847,
                9.610240337377108e-05,
                0.0009110512160172387,
                4.5397868612593344e-05,
                2.4300249416363357e-05,
                0.00023050676989512555,
                5.829126550803852e-05,
                5.8291258498513246e-05,
                4.539788484079622e-05,
                4.006369215458579e-05
            ],
            [
                0.9959298630542411,
                0.9999339478789965,
                0.9999038975507166,
                0.9999646437619356,
                0.9998204720126564,
                0.9999810748540229,
                0.9998415638022159,
                0.9994472213258051,
                0.9971990727311328,
                0.9999990577556308
            ],
            [
                6.144172403928222e-06,
                1.3709570434054234e-06,
                4.5397884864412536e-05,
                1.892514598469098e-05,
                3.1201926241089315e-05,
                2.4300252317086683e-05,
                3.120191880867338e-05,
                3.120190764467241e-05,
                3.120191137012976e-05,
                6.605216039839083e-05
            ],
            [
                2.4300252319296727e-05,
                3.1201918807538294e-05,
                2.4300252319959737e-05,
                0.9998415637647842,
                NaN,
                0.13296423847995262,
                NaN,
                4.006370651032745e-05,
                2.1444940741392653e-05,
                8.939700566143004e-06
            ],
            [
                0.9999852610145155,
                0.9999938558246673,
                NaN,
                0.9999646437535344,
                0.9999852610127595,
                0.9998911030909162,
                0.9999485577618665,
                0.9992903295400543,
                0.9999885212332436,
                0.9999810748427413
            ],
            [
                0.999993855822472,
                0.9999980052693274,
                0.9999977396746244,
                0.9999898700126454,
                0.9999832985721862,
                0.9999869928699859,
                0.9998415637456005,
                0.9999945777810304,
                0.9999810748585347,
                0.999997438716568
            ],
            [
                2.7535684528909006e-05,
                1.209866116137134e-06,
                2.7535694378772238e-05,
                0.0001233945746217233,
                5.1442219778095686e-05,
                4.5397852403718694e-05,
                9.61024035073125e-05,
                5.144220137700842e-05,
                1.473898372822193e-05,
                6.9622595694023114e-06
            ],
            [
                4.006368263612517e-05,
                8.939697369151141e-06,
                8.939696303758459e-06,
                6.605214465761795e-05,
                6.144173869240119e-06,
                1.0129990979694647e-05,
                4.006369696096547e-05,
                4.539789028757721e-05,
                NaN,
                4.5397884859458064e-05
            ],
            [
                0.9997694933421802,
                0.9999930377420905,
                0.9999417087554167,
                0.999903897619545,
                0.9999962733607168,
                0.9999898700041918,
                0.9999810748495105,
                0.9998204720128236,
                0.9999687980812153,
                0.9997388097222843
            ],
            [
                0.9999485577986358,
                0.9996200155607524,
                0.9999810748562789,
                0.999841563745628,
                0.999995777167572,
                0.9999852610162715,
                0.9999910603004993,
                0.9820137927356554,
                2.753569766560016e-05,
                0.9998911031037506
            ],
            [
                0.9999485577618392,
                3.535625912022914e-05,
                3.535624646754865e-05,
                0.999989870012645,
                0.9999251537371533,
                0.9998911031037632,
                0.9999910602994355,
                NaN,
                0.9991959140594134,
                0.9999485577618298
            ],
            [
                0.9999724643023645,
                0.9999546021097371,
                0.999978555056719,
                1.1478768122987964e-05,
                NaN,
                0.9999910603068958,
                0.9999724643187544,
                0.9999980052702785,
                0.9999962733616046,
                0.9999832985741752
            ],
            [
                0.9999646437493537,
                0.9999898700078153,
                0.9999967112505427,
                0.9999885212318796,
                2.561282515853595e-06,
                NaN,
                0.99829927797557,
                0.9999962733593838,
                0.9999952149072167,
                0.9999724643121964
            ],
            [
                4.0063682625048554e-05,
                8.939698434332555e-06,
                2.1444945842219688e-05,
                1.300713466619476e-05,
                2.1444940733201126e-05,
                4.5397874044343825e-05,
                3.120191137126484e-05,
                2.4300252315495453e-05,
                5.1442201382996765e-05,
                0.0001088968960910006
            ],
            [
                0.9999982396559474,
                0.99996879809608,
                0.999988521227772,
                0.999993037740431,
                0.9999921107392964,
                NaN,
                0.9999974387184,
                0.9999599363126035,
                6.144176066521288e-06,
                0.9999921107392962
            ],
            [
                4.0063687408107886e-05,
                2.7535694380675497e-05,
                1.0129987356191011e-05,
                2.7535700942411318e-05,
                2.1444948409679848e-05,
                7.484625393265086e-05,
                6.962259569003389e-06,
                4.785096205930373e-06,
                0.0001233945301513246,
                4.0063692179945426e-05
            ],
            [
                9.610241487022105e-05,
                3.120191880504111e-05,
                2.753570421481532e-05,
                0.0003799844794759909,
                4.539785780045566e-05,
                7.484623615568462e-05,
                8.481101098134002e-05,
                0.00017952805138992902,
                6.605214466242357e-05,
                6.605216827142175e-05
            ],
            [
                0.9999952149032241,
                0.9997965729789262,
                0.9999967112513275,
                0.9999810748585675,
                0.9999957771660554,
                0.9999810748472489,
                0.9999991684719726,
                NaN,
                0.9996200155295447,
                0.9999756997476845
            ],
            [
                1.1478769492893215e-05,
                2.7535694379773952e-05,
                2.4300240730549767e-05,
                5.1442195245310235e-05,
                1.8925150494750372e-05,
                3.120191507912884e-05,
                0.00029595698675150895,
                7.889262585441413e-06,
                5.829129329974581e-05,
                4.5397884856980825e-05
            ],
            [
                0.9999832985841296,
                0.9997965730762041,
                0.999995777164542,
                0.9999974387184002,
                0.9999832985822049,
                0.9999852610180298,
                0.9999957771670588,
                0.9999546021097568,
                0.9999724643056332,
                0.999891103091542
            ],
            [
                0.9999885212291383,
                0.9999952149072169,
                0.9999980052707541,
                0.9999967112509347,
                0.9999151889325463,
                0.9999417087067168,
                0.9999546021313743,
                0.9999869928730944,
                0.9999339478790701,
                0.9993736659081287
            ],
            [
                0.9999992661786695,
                1.300713311614059e-05,
                1.3007126911643378e-05,
                1.1478766756444477e-05,
                1.892514824021969e-05,
                1.670141786036971e-05,
                1.8925157263094544e-05,
                8.939697368110433e-06,
                1.892515500663531e-05,
                2.7535684528909006e-05
            ],
            [
                0.9999974387180947,
                0.9999810748517658,
                0.9999970976876703,
                0.9953904275471404,
                0.9999832985821414,
                0.9999957771645424,
                0.999978555056705,
                0.9999910603058283,
                0.9999687980737538,
                NaN
            ],
            [
                0.9975273766349019,
                0.9982992773102687,
                0.999996273360716,
                0.9999599363030871,
                0.9998415637832834,
                0.9991959138773989,
                0.9999417087414969,
                0.9998766053667189,
                0.9982992778148779,
                0.9999599363173831
            ],
            [
                0.999903897551097,
                0.9999974387171787,
                0.9999546021367831,
                0.9999785550567132,
                NaN,
                1.067702742726318e-06,
                0.9999852610110034,
                0.9999546021097148,
                0.9999646437450794,
                0.9999785550592627
            ],
            [
                1.8925148239290237e-05,
                4.5397857784436206e-05,
                3.5356254916002164e-05,
                4.0063696932399445e-05,
                2.753568124769226e-05,
                2.753570094040789e-05,
                4.0063711278232147e-05,
                2.7535694377870696e-05,
                1.147876949310201e-05,
                6.9622554187981796e-06
            ],
            [
                0.00103223081683521,
                0.3775406687981454,
                8.481103117361599e-05,
                0.010986940576240466,
                1.670141586949968e-05,
                3.1201911358551906e-05,
                1.6701429795417824e-05,
                5.422220261948442e-06,
                0.9947798742072986,
                0.9982992778925557
            ],
            [
                NaN,
                0.9999869928653361,
                0.9999977396765105,
                0.9999756997534747,
                NaN,
                0.9997694932301585,
                0.9997694932597837,
                0.9991959141743652,
                0.9999990577557432,
                0.9999930377420913
            ],
            [
                0.00010889690908378526,
                6.1441753337365085e-06,
                5.422218323093458e-06,
                3.1201903930339314e-05,
                2.90231163910023e-06,
                3.726640172120768e-06,
                6.475947209985977e-07,
                1.4738987242968784e-05,
                4.539787401263522e-05,
                2.1444958638526877e-05
            ]
        ]
    },
    {
        "q_id": "8136_mmlu_math",
        "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,
            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": [
            [
                4.222831934248571e-06,
                3.1201926243586504e-05,
                3.120190019784534e-05,
                2.7535691079423274e-05,
                7.889260703906985e-06,
                1.6701429804744246e-05,
                1.300713311517055e-05,
                7.889259763857458e-06,
                2.7535704218321328e-05,
                1.8925155006118952e-05
            ],
            [
                0.9968273176773809,
                0.99719907270447,
                0.9971990726400888,
                0.9947798734069003,
                0.9982992773144194,
                0.9989677688007063,
                0.996827317696526,
                0.9968273174130297,
                0.9968273174469019,
                0.9989677688017867
            ],
            [
                1.14787681240737e-05,
                2.260325375664839e-06,
                7.88926352599354e-06,
                1.67014178554179e-05,
                3.7266401724291984e-06,
                3.7266388397382506e-06,
                4.785092783454444e-06,
                5.422218969661113e-06,
                2.902310947190096e-06,
                4.222831934156396e-06
            ],
            [
                0.9995121427689927,
                0.9980732653568207,
                0.9971990729756512,
                0.999195914141769,
                0.9995121428230627,
                0.9992903296250476,
                0.9978172839948124,
                0.999704042865614,
                0.9991959139557326,
                0.9859363740027538
            ],
            [
                1.1478773597870298e-05,
                5.829126545587422e-05,
                1.670141785651155e-05,
                1.473898021151881e-05,
                1.6701421842140854e-05,
                4.5397890240179425e-05,
                3.7266379512112265e-06,
                1.892515500450102e-05,
                2.4300249415479343e-05,
                1.89251572481201e-05
            ],
            [
                0.9968273175853365,
                0.9997040427599234,
                0.998498817892808,
                0.9986749773654244,
                0.9996646497304907,
                0.9980732651423541,
                0.9991959140508085,
                0.9997965730508666,
                0.9993736657491645,
                0.9990889489869031
            ],
            [
                8.93969310662177e-06,
                4.222833444106873e-06,
                1.3007130012673148e-05,
                7.889263525663481e-06,
                1.8925141457627214e-05,
                1.1478770860481005e-05,
                4.785095064819011e-06,
                1.4738980211116665e-05,
                6.962256249429175e-06,
                1.9947306726213275e-06
            ],
            [
                1.994729721469003e-06,
                1.8925150490206403e-05,
                2.1444940737257882e-05,
                1.209866116149238e-06,
                4.222835458002318e-06,
                1.7603425837702984e-06,
                6.1441738691562974e-06,
                8.93969310662177e-06,
                1.7603438428460541e-06,
                6.9622562489985925e-06
            ],
            [
                1.012998977213635e-05,
                5.1442232005568484e-05,
                2.4300232038197563e-05,
                7.889264465986113e-06,
                1.4738988997768797e-05,
                1.8925145980181433e-05,
                2.7535684522397864e-05,
                1.4738976696800444e-05,
                6.1441767989541075e-06,
                7.889264466115267e-06
            ],
            [
                0.9924227597756434,
                0.9953904267544598,
                0.9902915218978624,
                0.9890130578146853,
                0.9959298629523111,
                0.9968273167517837,
                0.9971990730172715,
                0.9994472212540602,
                0.998830489727737,
                0.9993736658965789
            ],
            [
                0.9992903295343991,
                0.9990889487696777,
                0.9995694428597055,
                0.9995121429390079,
                0.9995694428600688,
                0.9998204720554777,
                0.9982992773158029,
                0.9980732656308366,
                0.9993736657470512,
                0.9991959142469933
            ],
            [
                0.9993736659767715,
                0.9991959139608301,
                0.998830489596643,
                0.9989677688069486,
                0.9982992773116522,
                0.9992903297057892,
                0.9986749773936152,
                0.9989677689281925,
                0.9997388096292115,
                0.9980732649081867
            ],
            [
                0.9991959140555787,
                0.9990889486596344,
                0.9953904269681203,
                0.9997965730268786,
                0.9997694933403491,
                0.9994472213910218,
                0.9996646498510153,
                0.9995694428592421,
                0.9994472212567616,
                0.9991959139560599
            ],
            [
                0.9999151889384297,
                0.9971990725282346,
                0.9996646500107031,
                0.9993736658284098,
                0.9996200154261381,
                0.9995694429653579,
                0.999876605439948,
                0.9996646499705251,
                0.9997040427605434,
                0.999290329625543
            ],
            [
                0.9995694428595177,
                0.998299277284969,
                0.9999724642990521,
                0.9971990735193146,
                0.9997388097839099,
                0.995390428386826,
                0.9859363745063829,
                0.9984988180810916,
                0.9994472213212385,
                0.9998204719910343
            ],
            [
                0.9988304900080118,
                0.9980732655607657,
                0.9984988177142963,
                0.9986749775322589,
                0.999620015469296,
                0.9978172834486722,
                0.9995694429628151,
                0.9982992773045367,
                0.9998415637264859,
                0.9971990725724559
            ],
            [
                0.9990889489917776,
                0.9995694429621763,
                0.9986749776932397,
                0.9988304895920194,
                0.9984988177099339,
                0.9984988180788231,
                0.9991959140539886,
                0.9980732648849042,
                0.9999251537638083,
                0.9996646497307152
            ],
            [
                0.9992903297038491,
                0.9968273164623964,
                0.985936374235198,
                0.9984988175413685,
                0.9995694430156976,
                0.9947798754405404,
                0.9997040430067387,
                0.9982992777735683,
                0.9990889489792208,
                0.9933071494162468
            ],
            [
                0.9940889299370543,
                0.9933071489921301,
                0.998299277307304,
                0.998830489595283,
                0.9988304895887555,
                0.999447221385555,
                0.9997965729295829,
                0.9978172834674347,
                0.9990889487696777,
                0.9994472213858766
            ],
            [
                1.0129988563730593e-05,
                1.892515274546026e-05,
                4.785094494672519e-06,
                7.338208930355202e-07,
                1.1478769492642663e-05,
                3.288750633518874e-06,
                3.120191879561992e-05,
                4.222834954607099e-06,
                1.3007131564383116e-05,
                4.785092783319532e-06
            ],
            [
                1.1478766755985128e-05,
                8.939694171331106e-06,
                1.3007131564643372e-05,
                2.1444945855248125e-05,
                2.1444948410303962e-05,
                7.889262585211807e-06,
                7.889266347356409e-06,
                5.8291258547708845e-05,
                9.422450431954847e-07,
                8.939700566435704e-06
            ],
            [
                1.99473067264854e-06,
                6.144172404302622e-06,
                4.222832437639588e-06,
                1.4738987241172537e-05,
                6.9622562489985925e-06,
                3.7266379512518984e-06,
                1.3007134665413997e-05,
                5.422219616140078e-06,
                4.006367784548767e-05,
                3.5356242271040426e-05
            ],
            [
                4.222831934321543e-06,
                1.0129994601688632e-05,
                6.962257079629686e-06,
                1.760344052693435e-06,
                1.670142183983204e-05,
                4.7850933535659155e-06,
                1.1478773593172406e-05,
                1.6701423833436905e-05,
                1.0129992186589747e-05,
                1.012998977088337e-05
            ],
            [
                0.9986749773678891,
                0.9998204719697386,
                0.9933071495741297,
                0.9968273164528239,
                0.9988304898781416,
                0.9996200155598238,
                0.9978172839948124,
                0.99919591395924,
                0.9997040427946599,
                0.9975273770547
            ],
            [
                1.4738985479697128e-05,
                1.670142980380249e-05,
                8.93970056565517e-06,
                8.939698434820389e-06,
                1.1478773598538445e-05,
                3.535626333088765e-05,
                1.4738988994498018e-05,
                1.1478765387416494e-05,
                1.3007130012341915e-05,
                2.430023203298187e-05
            ],
            [
                4.006368260129212e-05,
                5.422217676486429e-06,
                1.6701417861189946e-05,
                5.422217676797111e-06,
                4.539787942390787e-05,
                1.670142183983204e-05,
                6.144173136885882e-06,
                2.1444953520884646e-05,
                6.144173136645595e-06,
                4.785093924156175e-06
            ],
            [
                0.9990889486673696,
                0.9997388097842443,
                0.9986749773789806,
                0.9994472214549844,
                0.9989677691789632,
                0.9997388097535417,
                0.9996646497309396,
                0.9995694430141946,
                0.9997965729784852,
                0.9995694430144701
            ],
            [
                0.9995121428820996,
                0.999447221454695,
                0.9982992774885521,
                0.9994472213869057,
                0.9982992775263039,
                0.9990889487680352,
                0.9968273172532408,
                0.9990889489812341,
                0.9994472213900893,
                0.9980732653586117
            ],
            [
                7.484624491729e-05,
                9.610243773517696e-05,
                6.962257079173776e-06,
                2.753568451218037e-05,
                3.726638395493353e-06,
                3.120190763491069e-05,
                3.5356242272712497e-05,
                1.6701427813872793e-05,
                1.1478764018827141e-05,
                2.1444945848226808e-05
            ],
            [
                0.9986749775390371,
                0.9964063976436773,
                0.9978172834811262,
                0.9953904271668247,
                0.9984988179125264,
                0.998299277916274,
                0.9993736658235275,
                0.9964063973735604,
                0.9984988175218247,
                0.9975273771798927
            ],
            [
                0.9998204720551825,
                0.9995694429614373,
                0.9997965729296244,
                0.9986749778371209,
                0.9986749776889263,
                0.9959298629598615,
                0.9984988175349121,
                0.9990889486661512,
                0.9924227595445317,
                0.9971990728852574
            ],
            [
                0.9995694429112603,
                0.99937366589851,
                0.9968273164866961,
                0.9995121429390079,
                0.9991959142415684,
                0.9964063970350807,
                0.9968273173497033,
                0.9968273174078752,
                0.9988304895807322,
                0.9986749778328076
            ],
            [
                0.9964063980380146,
                0.9994472213881276,
                0.9992903297043032,
                0.9999038975621306,
                0.9996200154247563,
                0.998073265145936,
                0.998674977367119,
                0.9959298614290248,
                0.9975273769277843,
                0.9996646498500006
            ],
            [
                0.9982992772948517,
                0.9995694428591543,
                0.9995694428586909,
                0.9988304898822213,
                0.9997040430069108,
                0.9991959139551246,
                0.9998415637264605,
                0.9997388096593592,
                0.9995121427627484,
                0.9997388096592909
            ],
            [
                0.9980732655820332,
                0.9998911030648926,
                0.9982992774885521,
                0.9859363759785298,
                0.9984988177306992,
                0.9968273172532408,
                0.9947798731723426,
                0.9999151889587016,
                0.999088948987698,
                0.9994472213875166
            ],
            [
                8.939694170940841e-06,
                2.1444950959977102e-05,
                1.4738988998117324e-05,
                2.753569765908901e-05,
                6.9622537593854575e-06,
                2.144495096457996e-05,
                8.481102102348735e-05,
                1.8925148236674017e-05,
                3.5356246475137275e-05,
                1.3007131563176482e-05
            ],
            [
                2.144495863614743e-05,
                1.6701423831188846e-05,
                1.8925145981833788e-05,
                8.93969736942758e-06,
                0.00010889690871143104,
                8.939696303010449e-06,
                7.88926540679677e-06,
                5.144220749598207e-05,
                4.0063711274151284e-05,
                6.962256249517824e-06
            ],
            [
                0.9997388097219424,
                0.9996646498899543,
                0.9982992777283057,
                0.9959298630070513,
                0.9959298623671579,
                0.9999038975850291,
                0.9989677689152278,
                0.996406398093872,
                0.9996646498099395,
                0.9992903294551022
            ],
            [
                0.9995121428250495,
                0.9998601778926528,
                0.999373665898692,
                0.9995694428605322,
                0.9996646498907349,
                0.9995121427683967,
                0.9996646498108372,
                0.9980732649171415,
                0.9995121429392633,
                0.9998601779426847
            ],
            [
                0.999664649971091,
                0.9993736657476342,
                0.9997965729540327,
                0.999447221454695,
                0.999620015515273,
                0.9996646499709837,
                0.9992903296183604,
                0.9999485577863506,
                0.9995121427673181,
                0.9997694933123941
            ],
            [
                0.9968273176221543,
                0.9995121427678006,
                0.9993736657491645,
                0.9996200155164447,
                0.9994472214548558,
                0.99896776894872,
                0.9993736659787389,
                0.999933947831744,
                0.9992903297065322,
                0.9994472213239721
            ],
            [
                2.7535691079423274e-05,
                6.144177531459659e-06,
                5.4222170304318e-06,
                1.147876949187012e-05,
                2.2603253755949437e-06,
                1.1478770860982112e-05,
                4.222834451215781e-06,
                2.5612825160096693e-06,
                8.93969630333567e-06,
                8.939699500164542e-06
            ],
            [
                0.999195914240025,
                0.9994472213872272,
                0.9993736658998581,
                0.999664649971091,
                0.9997694933129441,
                0.9996200154695835,
                0.9996646499292348,
                0.9997965730996001,
                0.9996200155602549,
                0.9996200155168097
            ],
            [
                0.9933071490571407,
                0.9978172831418803,
                0.9982992774869708,
                0.9988304897198497,
                0.9990889489844661,
                0.9992903296233139,
                0.9992903296215802,
                0.9984988180624202,
                0.9978172832149018,
                0.9992903297077707
            ],
            [
                0.9984988178840831,
                0.9924227575170519,
                0.9984988179048484,
                0.9964063981305545,
                0.9988304897477275,
                0.9975273767049639,
                0.9959298627465637,
                0.9770226289609617,
                0.9820137896102168,
                0.9996200154696498
            ],
            [
                0.9982992773045367,
                0.998674977548434,
                0.999373665827426,
                0.9996200155609736,
                0.9968273175757639,
                0.9978172837727052,
                0.9990889487761945,
                0.9982992773243021,
                0.9984988177176117,
                0.9982992777395719
            ],
            [
                0.9971990727083718,
                0.9991959141433592,
                0.998830489596643,
                0.9993736658233454,
                0.9875683500272279,
                0.9986749775288699,
                0.987568348346438,
                0.9924227594079658,
                0.9998766054692957,
                0.9984988180798702
            ],
            [
                4.0063687383622725e-05,
                5.422221555192784e-06,
                5.422220908481809e-06,
                7.889260704308795e-06,
                1.8925148238291944e-05,
                1.0129990979031306e-05,
                2.4300246522270504e-05,
                1.0129989771288745e-05,
                4.7850956352353935e-06,
                8.939700564679507e-06
            ],
            [
                0.997199072545793,
                0.9980732653265983,
                0.9986749776812238,
                0.9988304896053464,
                0.9914225138338988,
                0.9971990732026113,
                0.9982992778674536,
                0.9993736658952308,
                0.9980732653532388,
                0.999860177975949
            ],
            [
                0.9995694429621763,
                0.9971990736435248,
                0.9980732651333992,
                0.99640639724934,
                0.9980732655766603,
                0.9971990726251314,
                0.9993736659726908,
                0.9975273763265141,
                0.9947798736704757,
                0.9971990732663422
            ],
            [
                7.484625386839543e-05,
                6.962259568648793e-06,
                1.8925150487521332e-05,
                8.939697367703906e-06,
                0.9986749778542203,
                2.7535684521195802e-05,
                2.4300237832303074e-05,
                2.4300240719941574e-05,
                6.962256249429175e-06,
                2.260323758923431e-06
            ],
            [
                0.9984988180765546,
                0.9947798744031665,
                0.9968273171759237,
                0.9933071503542568,
                0.9971990730172715,
                0.9875683502444729,
                0.9968273172333593,
                0.9959298614139241,
                0.9975273769806179,
                0.9978172834831546
            ],
            [
                1.3709568799760888e-06,
                4.785096205930373e-06,
                6.144173136556186e-06,
                5.829129325648758e-05,
                2.144494073483943e-05,
                1.3007125362323574e-05,
                1.0129993393540266e-05,
                1.1478772225981004e-05,
                1.67014178590634e-05,
                5.422218323399208e-06
            ],
            [
                0.9995694429629154,
                0.9980732656979975,
                0.9996200154712528,
                0.9995121428828092,
                0.9993736657513141,
                0.9978172839669222,
                0.9964063972101563,
                0.999373665753646,
                0.9993736657520793,
                0.9999599363030465
            ],
            [
                7.889265406438011e-06,
                1.473897669838221e-05,
                3.1201903922734266e-05,
                5.422221554926484e-06,
                1.4738980212296288e-05,
                1.6701419848961534e-05,
                4.222834954687752e-06,
                3.288749457383046e-06,
                4.539786864000808e-05,
                6.144177531208195e-06
            ],
            [
                0.9988304894769721,
                0.9953904269061589,
                0.9933071492305022,
                0.9924227601048025,
                0.9990889486632901,
                0.998073265096013,
                0.9978172837701698,
                0.9968273164093789,
                0.9997388096910954,
                0.9982992774996207
            ],
            [
                0.9990889487652271,
                0.997199073681243,
                0.9991959139634022,
                0.9992903296200941,
                0.9990889486531707,
                0.9998204720552792,
                0.996406397562809,
                0.9968273173688484,
                0.9996646498100469,
                0.9978172839851777
            ],
            [
                1.9947304348332037e-06,
                4.785093924251918e-06,
                4.222835458148261e-06,
                4.785096776251149e-06,
                5.829124465207388e-05,
                2.7535697650273915e-05,
                4.785094494628999e-06,
                1.670142383167491e-05,
                4.222832437639588e-06,
                2.260323489435463e-06
            ],
            [
                0.9990889488744228,
                0.9971990724176809,
                0.9770226318462164,
                0.998498817543637,
                0.9978172831439087,
                0.9991959142415684,
                0.996827317257659,
                0.9997040427958999,
                0.9978172837585066,
                0.9964063977303815
            ],
            [
                0.9998204719909689,
                0.996406396644078,
                0.9997694931749056,
                0.9953904272779281,
                0.9971990724859641,
                0.9959298622086002,
                0.9875683472602131,
                0.9953904288205568,
                0.9978172831418803,
                0.9990889488862377
            ],
            [
                0.9988304900119555,
                0.9953904287500488,
                0.9993736658975262,
                0.9994472213256443,
                0.9989677690514772,
                0.9959298629523111,
                0.9991959141430318,
                0.9989677689208698,
                0.998674977684613,
                0.9975273767020927
            ],
            [
                0.9959298623124176,
                0.9959298629598615,
                0.9940889324434916,
                0.9978172839993763,
                0.9991959140492185,
                0.9940889302435183,
                0.9978172837585066,
                0.9940889312586803,
                0.9986749773755916,
                0.9964063981372241
            ],
            [
                1.147876675466972e-05,
                6.144175332440078e-06,
                7.889265406681968e-06,
                1.892515500715167e-05,
                8.939698434332555e-06,
                1.4738980212296288e-05,
                3.5356242243001115e-05,
                2.1444948409679848e-05,
                2.1444948410928083e-05,
                7.889264466545779e-06
            ],
            [
                1.0129994600638342e-05,
                1.8925143723620274e-05,
                1.0129987355343409e-05,
                2.753568780802255e-05,
                3.726640616670918e-06,
                2.1444948408275583e-05,
                6.1441746016670885e-06,
                4.7850933538313875e-06,
                3.120190018002454e-05,
                4.0063692134764465e-05
            ],
            [
                3.1201907628667734e-05,
                0.000139822040484859,
                4.785094494402695e-06,
                2.4300246521474893e-05,
                8.939698435340743e-06,
                1.1478772229989872e-05,
                2.902311293147782e-06,
                4.22283545795623e-06,
                4.006369694347607e-05,
                1.8925141469400216e-05
            ],
            [
                0.9989677688017867,
                0.999569442910158,
                0.9984988178851301,
                0.9991959140511358,
                0.9968273177060986,
                0.9994472212557325,
                0.9989677691623973,
                0.9997040429006949,
                0.9994472212563114,
                0.9982992775095033
            ],
            [
                0.9991959142434857,
                0.9995121427655299,
                0.9991959142508281,
                0.9997040429711238,
                0.9991959140562334,
                0.9998415638398226,
                0.9978172831530363,
                0.9997694933128299,
                0.998498817543637,
                0.9988304896039865
            ],
            [
                0.9997965730992656,
                0.9924227586691087,
                0.9980732655712875,
                0.9964063972926921,
                0.9959298625351536,
                0.9953904282052146,
                0.9875683470315342,
                0.9990889488744228,
                0.9975273766963498,
                0.9959298623520572
            ],
            [
                0.9994472214530228,
                0.998299277505155,
                0.9999832985781559,
                0.9997040429009619,
                0.9998415637832303,
                0.9998415637264859,
                0.99752737691917,
                0.9998415638211505,
                0.9996200155161462,
                0.9997965730266271
            ],
            [
                0.9996200154701583,
                0.9989677689286727,
                0.999915188958662,
                0.9971990734022579,
                0.9982992771859446,
                0.9978172831484725,
                0.9968273171486786,
                0.9994472212560218,
                0.9990889489860555,
                0.9991959142514361
            ],
            [
                0.9992903294503964,
                0.9994472214515435,
                0.9998766054397721,
                0.9988304897284169,
                0.9978172836484672,
                0.9964063973360442,
                0.997817283458307,
                0.9975273773952472,
                0.9997694932297829,
                0.9996200154256959
            ],
            [
                0.9940889319646418,
                0.9971990730972603,
                0.9978172834075976,
                0.9992903296186081,
                0.9953904283569136,
                0.9953904279509588,
                0.9990889487823403,
                0.9990889489921485,
                0.9988304898642707,
                0.9964063971317891
            ],
            [
                0.9989677689277123,
                0.997527376880119,
                0.9986749773763619,
                0.9986749773654244,
                0.9982992776850196,
                0.9994472213222998,
                0.9991959142511087,
                0.9992903295435629,
                0.9993736658233454,
                0.999088948987698
            ],
            [
                0.9999151889283524,
                0.9984988177296522,
                0.9997965730024289,
                0.9978172839851777,
                0.9998911030518365,
                0.9924227572859402,
                0.9991959140511358,
                0.9995121427678006,
                0.9994472214542448,
                0.9993736657482172
            ],
            [
                1.6701427813417103e-05,
                1.0677026154730804e-06,
                8.93969630348202e-06,
                4.539786860136322e-05,
                5.715007195431641e-07,
                6.144175334172377e-06,
                6.962257079465052e-06,
                3.288748673319648e-06,
                3.7266388397721442e-06,
                3.726639284017094e-06
            ],
            [
                1.670142781432848e-05,
                1.8925145982866508e-05,
                3.120191507912884e-05,
                6.144173136729416e-06,
                1.012999460108057e-05,
                1.0129990978441666e-05,
                1.1478769489719528e-05,
                7.88926540679677e-06,
                6.144177531381426e-06,
                4.006370171458602e-05
            ],
            [
                0.9978172839714861,
                0.9964063967741343,
                0.9995121428239993,
                0.991422514522929,
                0.997817283668751,
                0.9986749773722025,
                0.9953904273698022,
                0.9953904271069997,
                0.9988304900013482,
                0.9964063980438504
            ],
            [
                6.144176066353646e-06,
                8.939700565996655e-06,
                1.892515725920463e-05,
                8.939696302652706e-06,
                1.9947306726049992e-06,
                1.473897845457507e-05,
                7.889262584809997e-06,
                4.22283344433731e-06,
                1.473898197063434e-05,
                2.4300234925658572e-05
            ],
            [
                4.222833444168322e-06,
                1.1478769492893215e-05,
                1.6701421841259862e-05,
                1.0129987355785634e-05,
                5.422217030495909e-06,
                6.962254589332388e-06,
                1.473897669838221e-05,
                2.753569764256071e-05,
                2.7535704181959054e-05,
                1.147876538789672e-05
            ],
            [
                5.422221554847581e-06,
                3.288748673295719e-06,
                5.422219615898437e-06,
                8.93969417150998e-06,
                5.422220908762902e-06,
                8.939695237504067e-06,
                1.4738978456049602e-05,
                7.889261644358435e-06,
                1.147876675686207e-05,
                4.5397884843438604e-05
            ],
            [
                0.9740426402591095,
                0.9984988177022559,
                0.9984988175151938,
                0.998498817692484,
                0.9982992773031532,
                0.9993736658963968,
                0.9975273769542011,
                0.9993736658221795,
                0.9995121427643663,
                0.9914225153941163
            ],
            [
                0.9940889317238487,
                0.9996200155142007,
                0.9984988175392745,
                0.9875683476718352,
                0.9978172837311235,
                0.9992903294551022,
                0.9964063967499572,
                0.9982992776834384,
                0.9991959139560599,
                0.9971990736890468
            ],
            [
                0.9995121428849663,
                0.9992903294508918,
                0.999704042865967,
                0.9986749775220917,
                0.9995694428589665,
                0.9995694429100579,
                0.9995694428601689,
                0.999704042865614,
                0.9993736657524801,
                0.9971990723689074
            ],
            [
                2.753569765708558e-05,
                1.0129993394129904e-05,
                1.0129994601688632e-05,
                2.753568451748946e-05,
                1.6701425822059825e-05,
                6.962257079465052e-06,
                3.1201922486004504e-05,
                4.539786320396437e-05,
                1.6701423831188846e-05,
                8.939699500489763e-06
            ],
            [
                0.9997965730510766,
                0.9999687980774782,
                0.9998204719486101,
                0.9999485577618425,
                0.9999646437493,
                0.9999687980849155,
                0.9998766053958636,
                0.9997694933674324,
                0.9999038975393139,
                0.999891103077925
            ],
            [
                0.9996200155160025,
                0.9989677690687634,
                0.9998766053662573,
                0.9999038976194303,
                0.9995121427692482,
                0.9997694932025857,
                0.9984988178905395,
                0.9996200155610399,
                0.9997694932582947,
                0.9988304900032522
            ],
            [
                7.889261643899223e-06,
                1.1478769492392108e-05,
                3.535626332111248e-05,
                8.315277302701984e-07,
                2.5612828211442287e-06,
                6.962259568889411e-06,
                1.1478773598329648e-05,
                3.2887478891128633e-06,
                4.006370173469883e-05,
                5.422217030209884e-06
            ],
            [
                0.9996646499699592,
                0.991422516431621,
                0.9971990732552868,
                0.9971990732624402,
                0.993307150183991,
                0.9991959142463385,
                0.9968273167657744,
                0.998830490004612,
                0.9984988175151938,
                0.9980732650586269
            ],
            [
                0.00037998443575425303,
                1.6701419851270353e-05,
                8.939695238089467e-06,
                2.144495096161541e-05,
                8.939697368842181e-06,
                1.0129993394314164e-05,
                1.0129993393742954e-05,
                3.726639284050988e-06,
                1.3007130013288297e-05,
                8.939698435226916e-06
            ],
            [
                0.9996200154254085,
                0.9982992774954699,
                0.9924227591068202,
                0.9996646498904032,
                0.9998766053662735,
                0.9980732651875756,
                0.9992903297095043,
                0.9998911031166918,
                0.9975273767112811,
                0.9959298615479432
            ],
            [
                1.0129989771823107e-05,
                1.4738985483879434e-05,
                1.6701417857058377e-05,
                4.006368258380272e-05,
                1.300713311112477e-05,
                1.4738987240475486e-05,
                7.484620934212912e-05,
                1.1478773597118638e-05,
                1.0129992186589747e-05,
                5.144220136765162e-05
            ],
            [
                0.9996200155602549,
                0.9995694429615251,
                0.9988304894696286,
                0.9982992774982371,
                0.9995121428238858,
                0.9990889487655981,
                0.9996200154689423,
                0.9986749778516015,
                0.999195914241241,
                0.999373665822981
            ],
            [
                0.9990889486543891,
                0.9995694429616252,
                0.9988304898622308,
                0.996827317315831,
                0.9997694932028004,
                0.999664649849669,
                0.9997694933670065,
                0.9997694932298903,
                0.9990889486527997,
                0.9953904281282969
            ],
            [
                0.9990889488752175,
                0.9980732656523281,
                0.9991959140517438,
                0.999933947855328,
                0.9996200154712528,
                0.9975273769542011,
                0.9995121429394904,
                0.99956944301318,
                0.9984988180765546,
                0.9980732653532388
            ],
            [
                1.1478770861650256e-05,
                3.535625487278559e-05,
                1.473897670007122e-05,
                5.422218969601935e-06,
                1.4738976699106073e-05,
                1.1478769490700865e-05,
                3.1201900203407254e-05,
                1.6701425823457267e-05,
                2.1444950965282096e-05,
                8.93969310647542e-06
            ],
            [
                8.939698434332555e-06,
                1.3709576970949014e-06,
                1.1478769492642663e-05,
                7.889265406567165e-06,
                8.939695237813028e-06,
                3.7266383955611403e-06,
                2.144494329348333e-05,
                3.1201911312013484e-05,
                1.0129988564099116e-05,
                1.892515726099468e-05
            ],
            [
                0.9993736657513141,
                0.9984988175424154,
                0.9992903295378253,
                0.9992903296225708,
                0.9978172837214888,
                0.9968273172768042,
                0.9975273764000219,
                0.9986749778619227,
                0.9984988179058955,
                0.9990889489848369
            ],
            [
                0.9902915229454736,
                0.99919591395765,
                0.9890130574301267,
                0.9971990733268215,
                0.9993736658212321,
                0.9971990735797939,
                0.9902915246467225,
                0.9980732653550298,
                0.9988304895920194,
                0.9984988175033279
            ],
            [
                0.9996646497298176,
                0.9997388097533365,
                0.9998415638399263,
                0.9997965730270088,
                0.9997040429709516,
                0.9997040430071777,
                0.9997965730510766,
                0.9998601778926955,
                0.9997388097227099,
                0.9997388097840392
            ],
            [
                0.9914225158138702,
                0.9959298627069243,
                0.9980732653841329,
                0.9992903296215802,
                0.9975273767020927,
                0.9990889489929962,
                0.9968273173254035,
                0.9995121428831498,
                0.9953904286731311,
                0.9971990726251314
            ],
            [
                0.9975273772476576,
                0.9982992773102687,
                0.9994472213917935,
                0.9999485577802159,
                0.9980732651351902,
                0.9986749776872317,
                0.9971990733723435,
                0.9995694428586909,
                0.9990889487712671,
                0.9971990724404419
            ],
            [
                0.9988304897378002,
                0.994088931707431,
                0.9982992779206225,
                0.9978172839167199,
                0.9953904286731311,
                0.9940889306840602,
                0.9968273172532408,
                0.9959298629126718,
                0.9933071485463432,
                0.9890130580676844
            ],
            [
                0.9975273769691323,
                0.9968273178128699,
                0.9988304897364403,
                0.9971990726517944,
                0.9997388097536861,
                0.9993736659732737,
                0.999195914054316,
                0.9940889319646418,
                0.9980732651477269,
                0.9997040428304383
            ],
            [
                0.9997040429720107,
                0.9980732655303195,
                0.9992903295355962,
                0.9964063977370511,
                0.9990889487765653,
                0.9999339478631961,
                0.9959298618386323,
                0.9940889313079333,
                0.9964063976686881,
                0.996406398031345
            ],
            [
                1.892515049423401e-05,
                7.889264465555602e-06,
                1.1478765386330758e-05,
                1.8925143722381014e-05,
                6.144176066443055e-06,
                1.1478764017428212e-05,
                1.0129989771288745e-05,
                5.422218322940583e-06,
                5.422220262333096e-06,
                6.962259568775433e-06
            ],
            [
                0.9924227570268149,
                0.9994472213225892,
                0.9999546021313646,
                0.9924227569847947,
                0.9988304900059719,
                0.9980732653373441,
                0.9971990730140199,
                0.9998766053810263,
                0.9959298630391404,
                0.9975273764264386
            ],
            [
                4.222834954514924e-06,
                1.4738980213341866e-05,
                5.422221554926484e-06,
                1.6701423834226767e-05,
                4.222832437639588e-06,
                7.889260704423598e-06,
                4.00637112677385e-05,
                7.88926258532661e-06,
                1.3007126912826352e-05,
                4.222834954687752e-06
            ],
            [
                4.539786862316288e-05,
                1.8925152748558416e-05,
                1.3007123810638006e-05,
                0.9875683488609656,
                1.1478764019787597e-05,
                1.4738983727578497e-05,
                1.0129995809247506e-05,
                9.61023917962188e-05,
                7.889264466115267e-06,
                3.120191508820951e-05
            ],
            [
                0.9994472213212385,
                0.9986749775356479,
                0.9995694429629154,
                0.9996200155598238,
                0.998498818085454,
                0.9997040428307913,
                0.9998415637266149,
                0.9997965729297074,
                0.9997965729542457,
                0.9989677690503967
            ],
            [
                1.5534979397592542e-06,
                3.72664061681327e-06,
                5.422221555133606e-06,
                9.422442569208767e-07,
                5.422221555192784e-06,
                8.939695237504067e-06,
                6.144175333635923e-06,
                3.120190392409636e-05,
                3.1201922508819695e-05,
                3.2887498493983645e-06
            ],
            [
                0.9988304895920194,
                0.9986749776812238,
                0.9984988180493329,
                0.9980732648920682,
                0.994779875413941,
                0.9989677691675591,
                0.9994472213203381,
                0.9875683470086664,
                0.998498817893855,
                0.9994472213229109
            ],
            [
                0.9980732648920682,
                0.9998601779261043,
                0.998299277307304,
                0.9995121428247089,
                0.9995121427640257,
                0.999569442963003,
                0.9997965730752333,
                0.9982992775023879,
                0.9999151889889798,
                0.9994472214569782
            ],
            [
                6.144176798479122e-06,
                2.753569764256071e-05,
                6.144175333635923e-06,
                0.000335350108806604,
                1.1478773596575768e-05,
                4.222833444429485e-06,
                6.605216027536722e-05,
                6.962255419570695e-06,
                2.430023493485234e-05,
                1.0129989771473008e-05
            ],
            [
                0.9986749775365723,
                0.9992903295343991,
                0.9996646499705251,
                0.9990889487692538,
                0.9995694430129921,
                0.998299277700239,
                0.9988304900092357,
                0.9940889319920045,
                0.9996646498498932,
                0.999948557774073
            ],
            [
                0.9995694429111727,
                0.9978172837103326,
                0.999860177975949,
                0.9990889488890987,
                0.9990889487798502,
                0.9986749775399614,
                0.9989677691826846,
                0.9998415638400577,
                0.9989677688033473,
                0.9999251537995464
            ],
            [
                7.889264466445326e-06,
                3.12019262448351e-05,
                5.422220908703723e-06,
                1.0129994600159262e-05,
                8.939694172542558e-06,
                3.726638395527247e-06,
                2.1444948392516633e-05,
                2.1444953517842076e-05,
                2.753569436424737e-05,
                1.8925152740434357e-05
            ],
            [
                8.939695237341456e-06,
                2.1444943297072005e-05,
                2.753568124348506e-05,
                6.9622595694023114e-06,
                2.9023130230133794e-06,
                8.939697368110433e-06,
                1.4738987241172537e-05,
                4.785092782936557e-06,
                1.4738983727256784e-05,
                1.4738976699427788e-05
            ],
            [
                0.9995121428823267,
                0.9989677688011864,
                0.9980732649046048,
                0.99995460213136,
                0.9992903296257906,
                0.998967768808029,
                0.9998766053663363,
                0.9995694428587786,
                0.9978172834441084,
                0.9984988178699488
            ],
            [
                0.999876605366243,
                0.996406398031345,
                0.999195914234039,
                0.9989677691747617,
                0.9975273767049639,
                0.9989677690530376,
                0.9924227574645265,
                0.9997694933122331,
                0.9988304898808614,
                0.999195914143967
            ],
            [
                5.422217030555087e-06,
                1.994729721482609e-06,
                3.726639283806955e-06,
                3.288749457409966e-06,
                1.1478765388711023e-05,
                2.561281599881745e-06,
                4.785094494463623e-06,
                8.93969630348202e-06,
                6.475950297942253e-07,
                5.422218323231539e-06
            ],
            [
                1.4738978456719842e-05,
                1.6701415867221242e-05,
                1.6701423831188846e-05,
                1.6701423831188846e-05,
                1.1478764018305152e-05,
                1.6701419845680582e-05,
                1.8925150493717652e-05,
                4.22283545795623e-06,
                1.1478766756653273e-05,
                2.7535694375867267e-05
            ],
            [
                2.902313022952668e-06,
                1.1478769492141554e-05,
                5.4222215550004564e-06,
                2.7535681241281285e-05,
                1.0129990979031306e-05,
                2.144495608105136e-05,
                1.4738983725809062e-05,
                1.4738987239698005e-05,
                4.006367784140681e-05,
                2.144495863201265e-05
            ],
            [
                8.939695238089467e-06,
                1.473898372822193e-05,
                1.8925150492616083e-05,
                5.422217030555087e-06,
                6.962255419475714e-06,
                1.300712536203966e-05,
                7.88926352599354e-06,
                3.7266392838544054e-06,
                7.889262584666493e-06,
                4.0063692167994334e-05
            ],
            [
                0.9971990736552304,
                0.9982992772934681,
                0.9975273769484583,
                0.9986749775467395,
                0.9998204720767369,
                0.9959298624313361,
                0.9992903296225708,
                0.9995121429410231,
                0.9971990736285675,
                0.9978172832037457
            ],
            [
                0.9999251537995159,
                0.9990889488792971,
                0.9993736658982914,
                0.9996200154249,
                0.9995694429122874,
                0.9995121427663813,
                0.9997040427596564,
                0.9990889489836183,
                0.9999251537995464,
                0.9984988175293281
            ],
            [
                0.99979657310026,
                0.998073264897441,
                0.9996646499305715,
                0.9997694932032497,
                0.9997388096295686,
                0.9989677691780029,
                0.9996646497322079,
                0.9995121429405406,
                0.9996646500102446,
                0.9992903295365868
            ],
            [
                6.962254589781966e-06,
                1.473898197063434e-05,
                6.962254589433702e-06,
                3.53562506982705e-05,
                6.962255419279419e-06,
                1.0129987356375273e-05,
                1.8925155006118952e-05,
                1.4738983727900215e-05,
                1.0129992187253088e-05,
                1.3007125363057018e-05
            ]
        ]
    },
    {
        "q_id": "8080_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            6,
            8,
            9,
            10,
            12,
            13,
            14,
            17,
            18,
            19,
            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,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            102,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            112,
            113,
            114,
            115,
            116,
            118,
            119,
            120,
            121,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                0.9999869928700269,
                0.9999898700126982,
                0.9999938558261537,
                0.9999898700114366,
                0.999997739675708,
                0.9999832985805983,
                0.999985261023383,
                0.9999885212346832,
                0.999993855824672,
                0.9999339478477649
            ],
            [
                5.829127914243277e-05,
                1.4738978442537537e-05,
                2.753569427880107e-05,
                6.9622579086271995e-06,
                1.1478772206270732e-05,
                NaN,
                1.892515724164839e-05,
                1.147876401423365e-05,
                1.3007126902913016e-05,
                1.670142382286494e-05
            ],
            [
                6.9622570744753635e-06,
                1.6701415865641523e-05,
                7.484620913738319e-05,
                4.785096776068365e-06,
                1.2098653948576728e-06,
                8.939697368842181e-06,
                1.994729721396435e-06,
                7.889262580791891e-06,
                8.939694166989405e-06,
                2.144494839454502e-05
            ],
            [
                2.4300246458267722e-05,
                1.670142980112912e-05,
                4.006370641748784e-05,
                1.012999459934851e-05,
                5.4222183231674305e-06,
                2.753569764776963e-05,
                1.1478768123551712e-05,
                7.889262584350785e-06,
                8.939697366793286e-06,
                2.1444943292703185e-05
            ],
            [
                0.015906388912772775,
                5.144220135417782e-05,
                2.430023203740195e-05,
                4.539785775768208e-05,
                4.539788481668446e-05,
                2.430023781329673e-05,
                4.006369212397934e-05,
                7.484626273564317e-05,
                1.4738976695942536e-05,
                9.610246057636654e-05
            ],
            [
                6.962257079173776e-06,
                8.939700563248534e-06,
                1.8925157249015125e-05,
                6.962255417544426e-06,
                1.3007126901209531e-05,
                1.6701419845680582e-05,
                7.484619869261806e-05,
                1.1478773596847203e-05,
                1.6701429792440666e-05,
                1.4738981970312625e-05
            ],
            [
                0.9999898700090248,
                0.9999974387181096,
                0.9998601779270238,
                0.9999646437493857,
                0.9999910603005375,
                0.9999898700066449,
                1.892514145232592e-05,
                6.144175332283612e-06,
                0.99999709768664,
                0.939913352771458
            ],
            [
                0.9999339478323763,
                6.475950297421001e-07,
                0.9997694933629051,
                0.5312093733737563,
                0.9999417087069895,
                0.999704042871168,
                0.5926665999540698,
                8.315281267513512e-07,
                0.9999724643056813,
                0.9997694933787874
            ],
            [
                1.147876809200276e-05,
                4.785093351846877e-06,
                6.605217581334702e-05,
                1.1478773596283455e-05,
                0.0,
                8.939694165655997e-06,
                7.88926258381982e-06,
                6.962257077413455e-06,
                2.430023781683279e-05,
                1.8925143712742298e-05
            ],
            [
                0.00015843621411871573,
                1.300713466420736e-05,
                1.3007131552056503e-05,
                1.473898899256772e-05,
                1.0129990978644356e-05,
                2.1444953511912968e-05,
                4.539785230545508e-05,
                2.1444948392516633e-05,
                2.4300243574253006e-05,
                1.1478772228256871e-05
            ],
            [
                0.9998911031125999,
                0.9999832985821582,
                0.9999687980777314,
                0.9982992772450431,
                0.9999962733589431,
                0.9999938558224925,
                0.999991060300673,
                0.999993037742222,
                0.9999599362936058,
                0.5926665999540698
            ],
            [
                0.9984988176401345,
                NaN,
                NaN,
                NaN,
                0.9999810748451046,
                0.9984988178833851,
                0.9978172834395445,
                0.1066905939456512,
                0.9992903295807553,
                0.9995121428366298
            ],
            [
                2.753569109034197e-05,
                1.4738988986079782e-05,
                1.0129987355343409e-05,
                5.8291279217922595e-05,
                2.5612815994461346e-06,
                0.009708476696368677,
                2.1444956018912713e-05,
                8.939696301140427e-06,
                1.3007133108474901e-05,
                1.4738976695459959e-05
            ],
            [
                2.2603253752310765e-06,
                0.9994472214673975,
                0.9964063973318757,
                0.9999687980886859,
                3.726639282763036e-06,
                8.939700552646311e-06,
                0.9998766053686453,
                0.99998852123325,
                0.9924227583399496,
                0.9996646498693872
            ],
            [
                7.889266346287306e-06,
                2.1444943297072005e-05,
                2.902311984683171e-06,
                1.0129989757340145e-05,
                2.144494327788042e-05,
                1.1478764016112805e-05,
                6.962254585710433e-06,
                6.144173869072478e-06,
                5.422220907426478e-06,
                1.1478770843589471e-05
            ],
            [
                NaN,
                6.605216809601697e-05,
                1.0,
                1.0129990965911879e-05,
                5.144219492231352e-05,
                2.4300240703498875e-05,
                8.481106083791375e-05,
                7.484623580173539e-05,
                1.1478773589706403e-05,
                0.1192029110704336
            ],
            [
                2.7535681222849733e-05,
                4.222832436779288e-06,
                1.6701417849645853e-05,
                6.962257077590752e-06,
                1.892515500388139e-05,
                2.2603248360985502e-06,
                NaN,
                7.889265403654039e-06,
                1.4738983694709854e-05,
                1.1478772218380856e-05
            ],
            [
                1.3007123807727885e-05,
                4.222833946199938e-06,
                0.0002611902063700865,
                1.670141582219928e-05,
                1.473898723042186e-05,
                3.53562633231704e-05,
                4.785096205434246e-06,
                2.4300243613326524e-05,
                1.4738976696371488e-05,
                1.300712381094558e-05
            ],
            [
                NaN,
                NaN,
                2.144494568977919e-05,
                0.007577241092776204,
                1.3007126906509262e-05,
                2.1444958632714784e-05,
                NaN,
                1.6701425809239798e-05,
                NaN,
                3.5356267498715946e-05
            ],
            [
                1.670142579763494e-05,
                2.7535687758237317e-05,
                7.889264462728577e-06,
                6.144174600605357e-06,
                7.889262582800945e-06,
                1.3709572067356507e-06,
                1.30071253513219e-05,
                1.7603427935518875e-06,
                1.760343213227212e-06,
                1.7603425831394971e-06
            ],
            [
                4.0063696899461064e-05,
                4.785096204537733e-06,
                8.939700563248534e-06,
                1.1478764008095073e-05,
                1.1478772227651366e-05,
                8.481104072399344e-05,
                6.475948753606123e-07,
                1.4738983717819781e-05,
                2.5612812941789413e-06,
                1.0129990977262395e-05
            ],
            [
                0.9998766053680097,
                0.9999970976880158,
                0.9999992661792839,
                0.9999599363078477,
                0.9999724643062217,
                0.9999970976880153,
                0.9999938558224738,
                0.9999151889701333,
                0.9999869928685999,
                0.9999852610215542
            ],
            [
                0.9998766053991618,
                0.9999687981000736,
                0.9999756997477813,
                0.1329642281726931,
                0.99962001551891,
                0.9999038975557143,
                0.9706877687186648,
                5.715003788853339e-07,
                0.9999898700054233,
                0.9999646437452316
            ],
            [
                0.9999967112509377,
                0.999988521235985,
                0.9999756997652538,
                NaN,
                0.5926665999540698,
                0.9999251538031099,
                0.9999967112509758,
                0.5,
                0.9999921107393122,
                0.9999832985824189
            ],
            [
                1.3007133095130927e-05,
                1.4738983726559732e-05,
                8.939694172290508e-06,
                1.0129992184802409e-05,
                3.535623786012199e-05,
                6.14417386791016e-06,
                1.6701423825538316e-05,
                2.1444953520884646e-05,
                1.892514597770291e-05,
                5.4222209055130735e-06
            ],
            [
                4.539785223741372e-05,
                3.535626333281696e-05,
                NaN,
                4.006371128012683e-05,
                3.535624646150348e-05,
                6.60521760915919e-05,
                0.007577242227324526,
                6.605216033495677e-05,
                0.0003353501746545768,
                NaN
            ],
            [
                0.9999974387165869,
                0.9999869928749634,
                0.9998601779635881,
                0.9999687980887134,
                0.9999646437494782,
                0.9999980052709941,
                0.999993855826149,
                0.999997438717188,
                0.9999945777803865,
                0.999991060299446
            ],
            [
                1.0129990978220553e-05,
                5.144223202241074e-05,
                2.4300252281460812e-05,
                2.144494838814782e-05,
                1.8925157237517507e-05,
                1.3007131554375137e-05,
                NaN,
                1.30071284492519e-05,
                2.9023130223693095e-06,
                4.006368258904954e-05
            ],
            [
                5.144220129392002e-05,
                0.0001088969475471903,
                4.5397857612020705e-05,
                6.962259560581704e-06,
                2.1444950923778325e-05,
                1.4738981965326028e-05,
                1.1478763998114665e-05,
                NaN,
                5.144221973879711e-05,
                7.484620001366486e-05
            ],
            [
                2.7535687763846918e-05,
                1.6701417802315068e-05,
                2.144494839142443e-05,
                2.7535700919171523e-05,
                0.00010889686715987758,
                4.222834444483158e-06,
                0.044680910979769804,
                0.00012339455960135915,
                4.539786309298427e-05,
                1.3007126896808861e-05
            ],
            [
                NaN,
                3.726639283440905e-06,
                8.93969842283598e-06,
                4.22283294007051e-06,
                3.12019149930895e-05,
                8.939694157915729e-06,
                5.144223196776698e-05,
                4.785096775920397e-06,
                8.93969416907082e-06,
                7.889260701697028e-06
            ],
            [
                0.9999646437367895,
                0.0017007223940417868,
                1.8925145959182802e-05,
                0.9999038975972926,
                0.9988304895475507,
                0.00132502252520118,
                7.889263525405172e-06,
                0.9993736659351268,
                0.9997965730794803,
                0.0017007227595029972
            ],
            [
                0.9998204719980972,
                0.9998415637135676,
                0.9997965730306579,
                0.9999785550517438,
                0.9999869928731082,
                0.9999646437495691,
                0.9999485578008245,
                0.9999921107374299,
                0.9999930377446481,
                0.9996646500008587
            ],
            [
                0.022977367693815597,
                0.22270012850745968,
                0.24508501864634824,
                4.5397884772424514e-05,
                0.04208772371029591,
                0.24508500761839525,
                0.9669140179168129,
                0.1329642316084462,
                1.209865827698362e-06,
                0.00460957245285964
            ],
            [
                1.3007130007988564e-05,
                NaN,
                7.484623525393089e-05,
                7.889265395847433e-06,
                2.9023123302899095e-06,
                1.4738981956371603e-05,
                1.300713464913624e-05,
                5.422218968931258e-06,
                8.481104100042252e-05,
                1.6701419838997157e-05
            ],
            [
                1.300713311155064e-05,
                2.430023779862206e-05,
                4.0063682546783496e-05,
                1.8925154979509192e-05,
                2.7535704170940182e-05,
                3.2887494564857185e-06,
                2.260325106045111e-06,
                4.222831934052698e-06,
                7.889260701237816e-06,
                2.7535684500460307e-05
            ],
            [
                0.9902915252466366,
                0.9971990733027598,
                0.9465966692585823,
                0.9989677689879741,
                0.999796572979246,
                0.9990889489447298,
                0.9953904274574029,
                0.9999151889893031,
                0.0028009267434126127,
                0.999195914051136
            ],
            [
                2.430025230320762e-05,
                2.260325105981383e-06,
                8.481101046118458e-05,
                2.144495351097679e-05,
                2.4300232034838305e-05,
                9.61024490400584e-05,
                3.120191135412508e-05,
                3.535626332111248e-05,
                7.889259761905808e-06,
                6.9622554185195676e-06
            ],
            [
                0.00010889690877481047,
                3.5356250689524286e-05,
                2.753568450937557e-05,
                3.120192587354911e-05,
                1.0129988553375097e-05,
                1.670142582102693e-05,
                1.0129990974572174e-05,
                4.5397890105748086e-05,
                1.012998734896796e-05,
                2.9023133689924295e-06
            ],
            [
                3.120191129135497e-05,
                6.144176049522406e-06,
                7.88926539957853e-06,
                6.9622570780973205e-06,
                2.9023116383479355e-06,
                4.006368257039418e-05,
                1.1478768119563723e-05,
                2.1444940713541454e-05,
                1.892515725920463e-05,
                8.939695237162584e-06
            ],
            [
                NaN,
                6.1441745989959955e-06,
                1.8925148210787172e-05,
                6.962258730317576e-06,
                8.939697368663308e-06,
                2.1444943257908684e-05,
                1.0129993393945642e-05,
                0.00013982211223388457,
                3.5356237938323366e-05,
                1.8925148159977362e-05
            ],
            [
                0.000552778635090584,
                1.994729007936337e-06,
                7.484620922668724e-05,
                4.539786316234683e-05,
                1.670142382286494e-05,
                5.144222572191214e-05,
                1.670142581227772e-05,
                2.7535700923478902e-05,
                2.561282821176841e-06,
                6.60521203595042e-05
            ],
            [
                8.939693101987369e-06,
                1.892514819756836e-05,
                2.753569104786925e-05,
                2.4300240713399853e-05,
                3.120190390775116e-05,
                1.3007133110320344e-05,
                1.012999459934851e-05,
                3.120191134947124e-05,
                NaN,
                1.0129988559160908e-05
            ],
            [
                0.9999921107355351,
                0.9999921107393007,
                0.9999910603016217,
                NaN,
                0.9999832985763911,
                0.9999546021263702,
                0.999876605396939,
                0.9999546021264977,
                0.999992110734605,
                0.9999869928731374
            ],
            [
                8.939700565102295e-06,
                4.539786858947248e-05,
                2.9023109462583076e-06,
                4.78509506425325e-06,
                5.422218966071015e-06,
                3.120191133585023e-05,
                4.539789016057757e-05,
                1.1478769491598686e-05,
                6.605212078239759e-05,
                7.484625370612328e-05
            ],
            [
                0.9995694428282916,
                0.9998766053677637,
                NaN,
                NaN,
                0.9999339478401038,
                NaN,
                NaN,
                0.9999785550567233,
                NaN,
                0.7549149923816048
            ],
            [
                0.9999724643155651,
                0.9999810748562817,
                0.999954602137237,
                0.9999852610233358,
                0.9999898700115348,
                0.9998766054580439,
                0.9999038976269681,
                0.999860177876933,
                0.9992903295706832,
                0.9998415637283369
            ],
            [
                6.9622554187981796e-06,
                2.7535684522397864e-05,
                2.144494072680393e-05,
                1.3007134655335035e-05,
                7.889263524960312e-06,
                1.6701421789281045e-05,
                1.8925157142989176e-05,
                1.3709573690765008e-06,
                4.785092783267308e-06,
                2.4300252299759956e-05
            ],
            [
                0.9999251537377577,
                0.9999687980779041,
                0.99994170871415,
                0.9999599363076787,
                0.9998204720804276,
                0.9986749774084039,
                0.9999687980849847,
                2.5612819051722694e-06,
                0.9999832985762434,
                0.9999938558261684
            ],
            [
                7.889264463446097e-06,
                1.8925152747938785e-05,
                1.3709573700615334e-06,
                0.0009110512241764431,
                4.006370642360913e-05,
                5.144221324367852e-05,
                2.4300234904884198e-05,
                6.962253758017727e-06,
                3.120190389560577e-05,
                4.006368258117931e-05
            ],
            [
                NaN,
                4.222834953197588e-06,
                1.670142581762446e-05,
                5.82912445833697e-05,
                1.30071315640992e-05,
                2.1444953462841774e-05,
                2.260324836651547e-06,
                6.962257076830902e-06,
                6.144172403928222e-06,
                1.994729245555571e-06
            ],
            [
                0.0001795280014431195,
                8.481107012790814e-05,
                4.0063692068304736e-05,
                2.430024646198059e-05,
                1.0129993373326765e-05,
                4.785096204537733e-06,
                0.003593601791078234,
                2.1444953475480143e-05,
                1.8925141455974863e-05,
                2.7535681204818868e-05
            ],
            [
                0.0013250221440851587,
                6.605212864004585e-05,
                8.939697369671496e-06,
                6.60521208117118e-05,
                0.00026119033599734893,
                0.0001795279011812494,
                9.610244882331567e-05,
                0.00010889695989667943,
                3.1201907620154606e-05,
                3.1201911281593244e-05
            ],
            [
                8.939698428917621e-06,
                8.93970056424046e-06,
                1.30071253513219e-05,
                6.962257068269913e-06,
                1.1478766754064213e-05,
                3.7266383943816487e-06,
                2.1444940628037493e-05,
                6.9622579075254155e-06,
                5.422218322348809e-06,
                1.6701419835108622e-05
            ],
            [
                2.430024939965545e-05,
                1.0129994569258582e-05,
                8.93969629861996e-06,
                4.006370163238581e-05,
                4.539786307250579e-05,
                4.539787212960629e-05,
                8.939698431389304e-06,
                1.6701417851043295e-05,
                8.93969523617066e-06,
                5.4222170250515875e-06
            ],
            [
                6.9622562487453084e-06,
                1.4738981968060613e-05,
                3.120190383567338e-05,
                5.8291279072880346e-05,
                1.4738985479697128e-05,
                8.315280275280036e-07,
                2.4300243546318093e-05,
                1.6701421790617727e-05,
                6.14417606400666e-06,
                1.0129992171793538e-05
            ],
            [
                5.1442231934456754e-05,
                3.7266397281434697e-06,
                1.0129989764415789e-05,
                1.6701427793184552e-05,
                1.0129989770441144e-05,
                1.1478768116974664e-05,
                1.0129993392342568e-05,
                1.4738983715299675e-05,
                6.962255419051463e-06,
                6.962254588724508e-06
            ],
            [
                3.535623802655717e-05,
                2.4300249386306803e-05,
                2.7535700920674098e-05,
                1.1478769492642663e-05,
                6.9622562425398595e-06,
                8.939700561199636e-06,
                2.7535687801010546e-05,
                1.670142781636389e-05,
                5.8291279258636216e-05,
                1.670141583301427e-05
            ],
            [
                2.753568775222703e-05,
                1.67014277589168e-05,
                6.605212860977054e-05,
                6.962258734344787e-06,
                1.4738988987366645e-05,
                3.1201900154598675e-05,
                8.939695234983602e-06,
                3.5356259084858424e-05,
                2.4300240707388545e-05,
                2.1444953502863275e-05
            ],
            [
                1.1478772229300848e-05,
                3.7266379512112265e-06,
                7.889263523238269e-06,
                9.61024573489968e-05,
                1.0129995808178788e-05,
                NaN,
                4.539786316564981e-05,
                NaN,
                7.484625374914174e-05,
                2.1444948397509574e-05
            ],
            [
                8.939699498587217e-06,
                8.481102071867501e-05,
                4.539785237052376e-05,
                3.5356250691324983e-05,
                1.4738985478142165e-05,
                7.484625320514887e-05,
                2.1444958618516124e-05,
                1.3007134651738787e-05,
                1.8925148190958954e-05,
                2.7535687772862354e-05
            ],
            [
                4.539785775107612e-05,
                5.422219613511613e-06,
                8.939694171135975e-06,
                5.829125846925035e-05,
                1.0129995802853624e-05,
                1.0129995807441742e-05,
                1.4738988994980593e-05,
                1.0129994589969591e-05,
                2.7535704217219437e-05,
                8.939693101987369e-06
            ],
            [
                0.9999417087142272,
                0.9999921107402484,
                0.0003353500427342402,
                0.9999984465026224,
                0.9465966696352197,
                0.999981074847325,
                0.9999599363223375,
                0.9999885212319396,
                0.9999930377420982,
                0.9999810748585896
            ],
            [
                3.1201922508819695e-05,
                0.0008040859641566955,
                3.1201918783020485e-05,
                5.8291286299547405e-05,
                1.1478772227651366e-05,
                5.8291244467590426e-05,
                1.8925143712742298e-05,
                4.0063706444596424e-05,
                7.484620932198124e-05,
                1.3007133106487501e-05
            ],
            [
                NaN,
                NaN,
                3.7266410600755218e-06,
                6.962259563139869e-06,
                8.939698432690187e-06,
                8.939700508546276e-06,
                8.939697360662863e-06,
                NaN,
                2.26032348367937e-06,
                NaN
            ],
            [
                0.9999339478243222,
                2.4300249384892373e-05,
                0.9995121429142861,
                0.9999339478559335,
                0.9999910603005102,
                0.9999339478483916,
                0.9999251537913129,
                0.9999485578051915,
                0.9997694932339413,
                0.9997965729610826
            ],
            [
                5.422220261544064e-06,
                2.4300234714997578e-05,
                1.1478768116974664e-05,
                1.3007130000938025e-05,
                3.120192251336002e-05,
                1.0129995808639442e-05,
                4.539786855677299e-05,
                3.535625907765566e-05,
                NaN,
                2.1444953513707305e-05
            ],
            [
                0.9999898700090293,
                0.9999945777823265,
                0.9999974387165749,
                0.999948557805288,
                0.9999989322971344,
                0.9999898700126582,
                0.9999852610215567,
                0.9999810748427803,
                0.9999885212264501,
                0.9999687980888422
            ],
            [
                8.481103084905866e-05,
                8.93969310662177e-06,
                4.78509449306228e-06,
                2.430023781683279e-05,
                1.0129992185060374e-05,
                5.422217030362759e-06,
                1.6701427809710842e-05,
                NaN,
                1.89251527491092e-05,
                1.4738985484227961e-05
            ],
            [
                6.144176061369096e-06,
                9.610238775082282e-05,
                NaN,
                1.8925141454184818e-05,
                7.484620879922564e-05,
                2.9023112920813724e-06,
                NaN,
                7.48462172569761e-05,
                NaN,
                4.539787932217606e-05
            ],
            [
                5.1442237629757824e-05,
                1.3007123807727885e-05,
                3.7266392839832006e-06,
                6.962259565748692e-06,
                3.726639283806955e-06,
                2.5612834317116285e-06,
                8.939698432446272e-06,
                3.120191485415527e-05,
                2.5612822106421996e-06,
                1.6701415860173268e-05
            ],
            [
                1.0129992183070348e-05,
                1.1478766727067e-05,
                8.939699495546396e-06,
                5.422217675362059e-06,
                6.962254589332388e-06,
                3.7266401699312496e-06,
                6.9622554153915155e-06,
                3.7266397264555753e-06,
                1.1478773589247056e-05,
                4.222834952321924e-06
            ],
            [
                1.4738988992031526e-05,
                NaN,
                8.481108150469728e-05,
                9.610243773517696e-05,
                6.144176796947993e-06,
                2.753568781022632e-05,
                7.484621825620178e-05,
                0.0007096702580504686,
                0.015906391828441467,
                4.0063696945516495e-05
            ],
            [
                2.7535681216639104e-05,
                1.6701429763823444e-05,
                8.939693097726971e-06,
                2.5612812945260317e-06,
                2.43002464407642e-05,
                5.422218322763051e-06,
                8.93969416601374e-06,
                6.144177530548804e-06,
                1.8925145956015793e-05,
                1.473898722564974e-05
            ],
            [
                3.5356238010608196e-05,
                1.4738988827688254e-05,
                2.4300240704824895e-05,
                NaN,
                4.785096772847886e-06,
                2.4300252260421222e-05,
                1.4738976597765605e-05,
                NaN,
                6.144172401547709e-06,
                1.3007131482024305e-05
            ],
            [
                0.9999952149038083,
                0.999994577782373,
                0.9999810748453348,
                0.9999952149037968,
                0.8354835432479661,
                0.9999952149032268,
                0.999664649937528,
                0.9999869928719488,
                0.9999852610127782,
                0.999954602147785
            ],
            [
                0.9998415637281686,
                0.995390427121956,
                0.9984988178130623,
                0.9997694932041216,
                0.0019267348043651184,
                0.9999724643056853,
                0.9998415637847402,
                2.1444943291142893e-05,
                0.9999810748450184,
                0.9998601779602211
            ],
            [
                2.7535681246690542e-05,
                3.535624219978455e-05,
                1.6701429804288556e-05,
                6.605212881496996e-05,
                3.535623801292338e-05,
                3.1201900186835035e-05,
                1.892515049571424e-05,
                NaN,
                1.4738980210258757e-05,
                1.1478773596575768e-05
            ],
            [
                1.892515046555882e-05,
                1.8925157234281645e-05,
                1.0,
                1.4738988994980593e-05,
                4.006370648569653e-05,
                8.939699487025595e-06,
                2.753568451218037e-05,
                4.006368721732767e-05,
                8.481108107894693e-05,
                0.9999930377454112
            ],
            [
                1.892515724543503e-05,
                NaN,
                2.1444940718222327e-05,
                3.7266410598992754e-06,
                1.4738985479214553e-05,
                2.144494329496561e-05,
                NaN,
                6.9622554185195676e-06,
                1.300713156215912e-05,
                1.3007133109847152e-05
            ],
            [
                5.1442213548336024e-05,
                4.2228354563508465e-06,
                6.9622595668378125e-06,
                1.3709572065835317e-06,
                6.9622570780973205e-06,
                7.889262572468676e-06,
                8.939694168810643e-06,
                1.8925152746768368e-05,
                7.889263522779056e-06,
                3.12019262070368e-05
            ],
            [
                1.1478768116974664e-05,
                2.144494072376136e-05,
                8.939699498587217e-06,
                2.144494327218535e-05,
                6.962257909323729e-06,
                6.605214434717565e-05,
                1.0129987341781759e-05,
                1.1478765385432939e-05,
                8.939699500327152e-06,
                1.4738980199481274e-05
            ],
            [
                1.0129988563546333e-05,
                1.670142383015595e-05,
                8.939698434657777e-06,
                6.144176798870286e-06,
                1.3007131563507714e-05,
                2.1444940719392548e-05,
                1.3709568798782093e-06,
                6.144173868983067e-06,
                8.939698432446272e-06,
                4.539786851614634e-05
            ],
            [
                1.473897845457507e-05,
                2.1444945744701455e-05,
                2.144494840531103e-05,
                1.4738985469509454e-05,
                1.473898371326214e-05,
                4.785093348208608e-06,
                3.1201903922734266e-05,
                1.3007133108474901e-05,
                1.0129995800789894e-05,
                3.2887478888496478e-06
            ],
            [
                1.3007125360809367e-05,
                6.144173136556186e-06,
                8.93970056399654e-06,
                1.8925155000025902e-05,
                3.1201918788014855e-05,
                4.7850933534310035e-06,
                7.889265405333033e-06,
                7.889266346287306e-06,
                5.71500719517695e-07,
                1.6701423806824726e-05
            ],
            [
                2.1444945842219688e-05,
                1.1478772228256871e-05,
                6.605216018886624e-05,
                1.1478766756653273e-05,
                0.00017952792154183567,
                1.892514597770291e-05,
                6.144172402452975e-06,
                2.7535704198387187e-05,
                4.006369208171328e-05,
                0.00013982214019257825
            ],
            [
                5.715002425859783e-07,
                3.726639728224814e-06,
                3.120190754421753e-05,
                6.144174599353632e-06,
                7.889260701467423e-06,
                2.1444943252135606e-05,
                3.5356254916002164e-05,
                7.889261639493659e-06,
                1.0129994597855991e-05,
                2.1444945795879023e-05
            ],
            [
                1.4738976695459959e-05,
                1.473898020838208e-05,
                2.9023130228444433e-06,
                6.962256248314727e-06,
                6.962257077223492e-06,
                1.0129992168919055e-05,
                3.120190013870751e-05,
                6.605215210438946e-05,
                1.3007131558444574e-05,
                4.78509278100427e-06
            ],
            [
                2.4300232029003796e-05,
                6.9622570780973205e-06,
                8.481102074088805e-05,
                1.8925141427471807e-05,
                1.4738980188435699e-05,
                1.8925150482151187e-05,
                4.785093350245343e-06,
                1.3007126909916233e-05,
                3.535625064399255e-05,
                2.7535697572841325e-05
            ],
            [
                1.3007134660350856e-05,
                8.939695236983711e-06,
                6.962257908348587e-06,
                1.8925148232267744e-05,
                7.889259757385442e-06,
                1.0129993393540266e-05,
                4.785096775920397e-06,
                NaN,
                1.0129992169508694e-05,
                3.53562633126235e-05
            ],
            [
                7.88926258343236e-06,
                4.785095633999427e-06,
                5.422220906558541e-06,
                8.9396994898225e-06,
                4.2228344511197656e-06,
                3.7266388384265735e-06,
                8.939693106329072e-06,
                7.88926446430712e-06,
                1.4738980200124708e-05,
                6.962257077590752e-06
            ],
            [
                1.1478773587200861e-05,
                NaN,
                NaN,
                5.4222215520465154e-06,
                8.939695233292452e-06,
                1.670142980112912e-05,
                4.785094493305991e-06,
                1.4738978429722525e-05,
                1.670142780381727e-05,
                2.1444948402034417e-05
            ],
            [
                0.9999921107393541,
                0.9999898700054476,
                0.9999898700090739,
                0.9999967112513302,
                NaN,
                0.9999646437577411,
                NaN,
                NaN,
                NaN,
                0.9999756997534811
            ],
            [
                1.4738983727256784e-05,
                5.422220262264056e-06,
                4.006367768298202e-05,
                1.892514370819833e-05,
                2.4300252239735237e-05,
                1.3007133114318805e-05,
                1.4738983725406915e-05,
                1.300712690556288e-05,
                8.939696298945184e-06,
                1.6701427807280505e-05
            ],
            [
                NaN,
                0.9999724642959114,
                0.9975273774233869,
                0.9999546021208462,
                0.9995121428503957,
                7.48462003365753e-05,
                NaN,
                4.006367772116721e-05,
                5.829127933242964e-05,
                0.9999869928684474
            ],
            [
                1.473898021151881e-05,
                3.535625491754561e-05,
                1.012998977108606e-05,
                1.670141984792864e-05,
                3.120190759915557e-05,
                1.6701429793959623e-05,
                1.0677031244234877e-06,
                6.605212093617702e-05,
                1.892514597632595e-05,
                0.00012339461776712807
            ],
            [
                6.144175333635923e-06,
                7.889263525261671e-06,
                1.6701415863393463e-05,
                7.484624464611041e-05,
                2.4300249408672413e-05,
                1.0129993379849628e-05,
                5.8291265253578496e-05,
                2.4300234921326896e-05,
                1.6701415862117537e-05,
                3.120191878631223e-05
            ],
            [
                3.120192246511896e-05,
                1.6701425819994037e-05,
                5.8291244643591885e-05,
                6.1441775309064404e-06,
                1.3007128456539035e-05,
                8.939693105662367e-06,
                3.120191869595956e-05,
                5.829128596196363e-05,
                1.4738981926023073e-05,
                3.5356246475137275e-05
            ],
            [
                0.9997965730084488,
                0.9999898700042266,
                9.422447062094932e-07,
                0.9999810748593679,
                0.679178699175393,
                0.9999724642967622,
                0.9998766053860876,
                0.999738809602263,
                0.9999962733602847,
                0.7057850154599562
            ],
            [
                5.829127905167534e-05,
                1.3007130005527972e-05,
                1.3007130005527972e-05,
                1.1478768123280277e-05,
                1.6701415867707307e-05,
                1.6701429785817993e-05,
                1.892515726099468e-05,
                1.6701419843189485e-05,
                1.0129990975567187e-05,
                1.0129993388546776e-05
            ],
            [
                2.753569757965299e-05,
                NaN,
                1.4738981966291175e-05,
                4.785096772656398e-06,
                2.7535704132474305e-05,
                1.1478773562354222e-05,
                8.939693103158165e-06,
                7.8892625772904e-06,
                0.00023050679011698343,
                1.012998856015592e-05
            ],
            [
                4.0063696860401394e-05,
                8.481101080610379e-05,
                5.144221358089769e-05,
                4.006368728232995e-05,
                6.9622595675850006e-06,
                3.535623800340544e-05,
                9.610244882331567e-05,
                5.144221335895434e-05,
                1.760342793266906e-06,
                6.144172403201774e-06
            ],
            [
                6.144174599867732e-06,
                4.539786303716391e-05,
                2.1444948408275583e-05,
                7.889261643899223e-06,
                1.1478768123823146e-05,
                2.4300243618542217e-05,
                1.5534979396024226e-06,
                5.422217029272909e-06,
                1.4738985478142165e-05,
                1.0129989769464556e-05
            ],
            [
                4.5397851725121766e-05,
                3.120190374827197e-05,
                6.962256248314727e-06,
                1.4738985454496043e-05,
                6.9622537576631295e-06,
                4.006368729632147e-05,
                1.0129987352616339e-05,
                8.481108083460324e-05,
                8.93969735984981e-06,
                1.1478773586115126e-05
            ],
            [
                0.9999967112493716,
                0.9999810748495532,
                0.9997694932602265,
                0.9999599363127246,
                0.9998415638033915,
                0.9999251537640507,
                0.9995121428600743,
                0.9997965729811371,
                0.914900952092573,
                0.9999921107370275
            ],
            [
                1.4738976693529666e-05,
                1.4738980208864656e-05,
                3.120191874363308e-05,
                1.147876401160283e-05,
                5.422217673931937e-06,
                1.8925141449434308e-05,
                7.88925976359915e-06,
                2.7535681218241846e-05,
                2.1444958620544503e-05,
                1.012999097799944e-05
            ],
            [
                1.1478766751997141e-05,
                3.535623805163821e-05,
                6.60521757470296e-05,
                8.481107137554162e-05,
                1.3007133101897553e-05,
                NaN,
                5.8291279181025874e-05,
                5.829128632668981e-05,
                1.6701415866188347e-05,
                6.962256249327861e-06
            ],
            [
                1.3007130007515371e-05,
                5.422219615069953e-06,
                1.5534984951673385e-06,
                1.4738978433261398e-05,
                6.144172403201774e-06,
                1.0129989762278356e-05,
                1.1478770861211786e-05,
                1.0129993385746e-05,
                1.892514822276672e-05,
                6.144176065314267e-06
            ],
            [
                2.1444953517061932e-05,
                8.481101064382517e-05,
                NaN,
                2.4300252298610736e-05,
                1.1478765387416494e-05,
                2.4300232036606334e-05,
                1.0129993389652346e-05,
                1.1478773588244838e-05,
                6.144172404129392e-06,
                4.785096200855943e-06
            ],
            [
                8.93969736427282e-06,
                1.5534981248881956e-06,
                0.9999151889283845,
                8.939696301384342e-06,
                3.535625910878189e-05,
                2.1444943278894603e-05,
                1.0129989755092154e-05,
                1.4738987220234187e-05,
                8.939696301140427e-06,
                1.4738978445861935e-05
            ],
            [
                5.829126543170052e-05,
                1.8925150490206403e-05,
                8.9397005654763e-06,
                4.006368716923182e-05,
                2.430025227368147e-05,
                4.539785215715135e-05,
                1.1478766754377407e-05,
                1.300713311155064e-05,
                1.892514822937613e-05,
                1.4738985482753428e-05
            ],
            [
                2.9023126764615702e-06,
                2.9023130217727535e-06,
                8.939698429893283e-06,
                2.7535691071008866e-05,
                2.260324836341129e-06,
                6.962257902687696e-06,
                6.962257909121104e-06,
                1.1478769490387674e-05,
                4.785095633999427e-06,
                0.0001584362695999198
            ],
            [
                0.9999646437536178,
                0.9999986290424682,
                0.9999251537912672,
                0.9999756997538105,
                0.9999832985742279,
                0.9996646499715593,
                0.9999898700126515,
                0.9998415637484681,
                0.9999646437549773,
                0.6224593312018546
            ]
        ]
    },
    {
        "q_id": "7698_mmlu_math",
        "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,
            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,
            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": [
            [
                0.4687906266262437,
                0.9998911031191977,
                0.8807970748488297,
                0.9840936100667432,
                0.7310585786300049,
                0.9999546021158033,
                0.5926665999540698,
                0.999983298572237,
                0.14804719427274568,
                0.9241418152779358
            ],
            [
                0.9999990577552939,
                0.9999885212346115,
                0.9999852610145155,
                0.9999599362887259,
                0.9999957771670589,
                0.9999885212277696,
                0.9999974387180947,
                0.9999852610110006,
                0.9999984465020603,
                0.9999974387180947
            ],
            [
                3.059021904506262e-07,
                5.715007195353674e-07,
                2.5612819051373276e-06,
                2.2603251060738913e-06,
                3.0590219044561827e-07,
                3.466327037389102e-07,
                4.45084945809282e-07,
                1.3709573698620332e-06,
                2.699579061798195e-07,
                3.927863407225873e-07
            ],
            [
                1.0129987352948008e-05,
                1.0129994599624903e-05,
                2.902313368897403e-06,
                1.5534971988904843e-06,
                7.889266347248781e-06,
                2.7535704183762137e-05,
                1.1478772225646932e-05,
                5.422221554482653e-06,
                1.300712535865635e-05,
                1.1478765385432939e-05
            ],
            [
                1.67014178576052e-05,
                3.1201900178208404e-05,
                5.422220907554695e-06,
                6.144173136243255e-06,
                1.0129992185060374e-05,
                6.144177530548804e-06,
                1.473898372500477e-05,
                7.889259763010786e-06,
                1.0129993392342568e-05,
                1.4738987234014356e-05
            ],
            [
                0.9999756997621694,
                0.9999687980923515,
                0.9999980052693274,
                0.9999417087136563,
                0.9999967112517186,
                0.9999832985781574,
                0.999975699767961,
                0.9999852610110029,
                0.9999646437535146,
                0.9999910603047619
            ],
            [
                1.9947306725215466e-06,
                3.2887502414436403e-06,
                4.785092782692845e-06,
                2.9023126768680736e-06,
                7.889261643382609e-06,
                4.222834449921489e-06,
                5.422218322763051e-06,
                6.144173136131494e-06,
                2.2603251057881422e-06,
                4.222834449921489e-06
            ],
            [
                0.817574478416099,
                0.9999832985741829,
                0.9999810748452536,
                0.9999810748427614,
                0.9579122723847614,
                0.9998601779762887,
                0.9999151889688344,
                0.9992903295655233,
                0.9999756997480541,
                0.9999910603038032
            ],
            [
                0.9999986290427931,
                0.9999945777829696,
                0.9999687980960746,
                0.9999724642990605,
                0.9999251537549356,
                0.9999977396751633,
                0.9999687980849168,
                0.999999352405279,
                0.9999546021259605,
                0.9999832985821409
            ],
            [
                0.9982992774480332,
                0.9997040430074533,
                0.9997965730512038,
                0.9999687980923515,
                0.9999599363127072,
                0.9999756997535242,
                0.9998204720985001,
                0.9998911030778189,
                0.9999339478553779,
                0.6513548782017745
            ],
            [
                0.9999251537817307,
                0.9999724642990556,
                0.9999869928684356,
                0.9999980052705163,
                0.9999485577863448,
                0.9999646437324375,
                0.9998911030648926,
                0.9999646437492984,
                0.9999417087414357,
                0.9999546021476384
            ],
            [
                0.999997438717484,
                0.999972464315473,
                0.9999930377412608,
                0.9999938558232009,
                0.9999885212291383,
                0.9999967112505427,
                0.9999982396561571,
                0.9999921107345934,
                0.9999974387180947,
                0.9999957771670589
            ],
            [
                8.48110109893614e-05,
                4.539786319306454e-05,
                0.00015843627123890696,
                0.0001398221227781544,
                0.0017007221560670876,
                0.0003353500637599246,
                0.0004878570947113133,
                3.120191135560069e-05,
                0.00026119021257900064,
                0.00023050669224052513
            ],
            [
                0.9999930377412606,
                0.9999962733607158,
                0.9999898700066056,
                0.9999910603026305,
                0.9999984465018751,
                0.9999982396574162,
                0.9999974387180947,
                0.9999982396569965,
                0.9999977396757022,
                0.9999974387177893
            ],
            [
                6.475951069896949e-07,
                7.33820893021171e-07,
                3.9278605978547293e-07,
                6.475949525834513e-07,
                5.422217029509618e-06,
                1.3709570433661467e-06,
                9.422448185388577e-07,
                1.553498495281783e-06,
                1.2098658277264215e-06,
                8.315284241401329e-07
            ],
            [
                0.9999992661788446,
                0.9999967112521109,
                0.9999952149037941,
                0.9999952149060758,
                0.9999832985761699,
                0.9999982396572064,
                0.9999898700090206,
                0.99999862904312,
                0.9999785550567023,
                0.9999921107392955
            ],
            [
                2.4300234920177672e-05,
                6.9622562481627565e-06,
                4.222833444229772e-06,
                1.1478766754377407e-05,
                4.785092782597101e-06,
                1.012999580884213e-05,
                7.484623590792016e-05,
                1.6701427803088173e-05,
                3.1201900203407254e-05,
                1.1478768123280277e-05
            ],
            [
                0.9999957771670589,
                0.9999921107383551,
                0.9999970976876689,
                0.9999994956525918,
                0.9999980052705163,
                0.9999957771680658,
                0.9999982396563669,
                0.9999994284996211,
                0.9999945777810304,
                0.9999986290427931
            ],
            [
                0.9999974387171787,
                0.9626731091754309,
                0.9999810748427385,
                0.9999852610197869,
                0.9999921107345938,
                0.9999852610127634,
                0.9997694932583484,
                0.9999921107355463,
                0.999993855827596,
                0.9740426455336738
            ],
            [
                0.9999485577679873,
                0.999985261018029,
                0.9999599363173852,
                0.9998766053811754,
                0.9999687980997889,
                0.9999885212332428,
                0.9999756997621677,
                0.9999977396759716,
                0.9999869928715366,
                0.9999930377462403
            ],
            [
                0.9999898700053977,
                0.9999885212277702,
                0.999996273360716,
                0.9999945777784448,
                0.9999810748472499,
                0.99998987000419,
                0.9999756997650686,
                0.9999756997476854,
                0.9999646437408746,
                0.9999832985821404
            ],
            [
                8.939699497335115e-06,
                4.006367783499403e-05,
                1.3007128461507534e-05,
                1.6701417858577338e-05,
                1.4738981969615573e-05,
                3.5356242267696286e-05,
                7.889261644631091e-06,
                1.6701419842521146e-05,
                3.5356246487099006e-05,
                5.422218322851817e-06
            ],
            [
                0.9999832985741752,
                0.9999885212318742,
                0.9999938558253981,
                0.9999756997476829,
                0.9999417087275647,
                0.999964643732439,
                0.9999724643121898,
                0.9999869928715355,
                0.9999339478474597,
                0.9999646437619372
            ],
            [
                6.962259568230874e-06,
                5.422217676486429e-06,
                2.902312676941983e-06,
                4.222834450589758e-06,
                2.260324028372372e-06,
                1.7603430034439723e-06,
                2.4300234884728635e-05,
                6.962254588585202e-06,
                3.1201903888114227e-05,
                6.962253758916883e-06
            ],
            [
                5.422219615582823e-06,
                8.93969523573161e-06,
                2.260324028281919e-06,
                7.889260703763482e-06,
                2.902311638759718e-06,
                1.8925148238291944e-05,
                2.9023109470554753e-06,
                1.892515048889829e-05,
                2.5612819050161955e-06,
                2.1444948404530884e-05
            ],
            [
                0.9999962733602716,
                0.9999945777790911,
                0.9999930377454103,
                0.9999898700090204,
                0.9999852610197855,
                0.9999485577679742,
                0.9999930377429205,
                0.9999957771665555,
                0.9999970976866309,
                0.9999962733602717
            ],
            [
                4.222832940777184e-06,
                3.288750241204353e-06,
                2.9023116388072315e-06,
                5.4222176759932836e-06,
                3.288749065209246e-06,
                1.7603430033991435e-06,
                1.553497198826904e-06,
                3.2887486729876365e-06,
                2.561283126160022e-06,
                4.785095063713602e-06
            ],
            [
                0.9999992661787571,
                0.9999970976883609,
                0.9999930377429206,
                0.9999982396561571,
                0.9999930377412606,
                0.999999554914895,
                0.9999938558246665,
                0.9999987901343165,
                0.9999993524051246,
                0.9999970976880149
            ],
            [
                0.9998911030649464,
                0.9999930377420909,
                0.9999952149060758,
                0.9999952149043645,
                0.9999485577618328,
                0.999989870011436,
                0.9999724643187544,
                0.9999898700126446,
                0.999968798092358,
                0.9999417087345085
            ],
            [
                0.9999646437450763,
                0.9999930377420904,
                0.9999952149037941,
                0.9999869928684346,
                0.9999910602994334,
                0.9999869928746372,
                0.9999687980886374,
                0.9999945777784447,
                0.9999756997592761,
                0.9998601779426439
            ],
            [
                0.9999785550439195,
                0.9999724643187533,
                0.9999885212359799,
                0.9999952149049349,
                0.9999869928668843,
                0.999995777166052,
                0.9999898700053976,
                0.9999921107383549,
                0.9999810748562722,
                0.9999885212264011
            ],
            [
                0.9999930377445806,
                0.9999989322972572,
                0.9999910603026323,
                0.999997438717484,
                0.99999862904312,
                0.9999945777810304,
                0.9999980052702786,
                0.9999938558261308,
                0.9999945777816768,
                0.9999938558253987
            ],
            [
                0.9999945777784448,
                0.9999991684721705,
                0.9999980052693274,
                0.9999832985741741,
                0.999997097686977,
                0.9999646437366474,
                0.9999724643187494,
                0.9999810748472526,
                0.9999885212346117,
                0.9999982396565769
            ],
            [
                0.9999339478317237,
                0.9999038975507579,
                0.9999687980849105,
                0.9999910602994335,
                0.9998601779260209,
                0.9998766054105537,
                0.9999339478474549,
                0.9997965730996415,
                0.9999417087344801,
                0.9999724643187469
            ],
            [
                0.9999898700078131,
                0.9999980052698029,
                0.9999952149032236,
                0.9999967112505427,
                0.9999962733602719,
                0.9999957771655488,
                0.9999962733602719,
                0.9999952149066462,
                0.9999869928699859,
                0.999996273358939
            ],
            [
                0.9999724643154878,
                5.8291265411767815e-05,
                4.539789022795839e-05,
                0.9999810748427493,
                0.0001584361786303955,
                0.00012339463354695633,
                0.00033535018572843333,
                0.9999687980775065,
                0.999981074849527,
                0.9999546021207393
            ],
            [
                0.9999485577863448,
                0.9999485577802218,
                0.9999339478632105,
                0.9999038975507264,
                0.9999417087066693,
                0.9998766053810586,
                0.9999687980997938,
                0.999964643736646,
                0.9999938558253981,
                0.9999339478317045
            ],
            [
                0.9999952149037942,
                0.9999646437577213,
                0.9999910603068932,
                0.9999756997592687,
                0.9999938558246657,
                0.9999930377454105,
                0.99999862904312,
                0.99998987000419,
                0.9999921107345933,
                0.9999938558224686
            ],
            [
                0.9999251537727964,
                0.9579122726851417,
                0.9999151889790857,
                0.9999251537817176,
                0.9998415638212313,
                0.9999724643098744,
                0.9999756997478695,
                0.9999724643065927,
                0.9999339478240049,
                0.9999885212318759
            ],
            [
                4.7850956352353935e-06,
                8.939700565834043e-06,
                1.994730196992497e-06,
                4.2228324370327694e-06,
                4.222832940577472e-06,
                1.1478770859624945e-05,
                7.889260704179641e-06,
                1.4738983725406915e-05,
                8.93969630333567e-06,
                5.422217030121119e-06
            ],
            [
                0.9999151889485459,
                0.9999938558253981,
                0.9999151889485539,
                0.999964643732433,
                0.9999546021259709,
                0.9999962733589389,
                0.9999962733616043,
                0.9999417087205882,
                0.9999546021259709,
                0.9999756997476829
            ],
            [
                0.9999417087175326,
                0.9706877661217682,
                0.9999785550516165,
                0.9999339478317386,
                0.9999646437366874,
                0.9995694429700549,
                0.9999038975865966,
                0.9999417087138841,
                0.32082130731838393,
                0.9999339478790019
            ],
            [
                6.1441760661636525e-06,
                1.6701427807888088e-05,
                2.4300252304268445e-05,
                7.88926634687567e-06,
                2.902312676941983e-06,
                5.422218967944967e-06,
                1.3007130010922344e-05,
                4.7850967748236935e-06,
                8.939696301839653e-06,
                2.4300252288444548e-05
            ],
            [
                1.012999097799944e-05,
                2.561283431888668e-06,
                6.962253759157502e-06,
                6.962253759043525e-06,
                6.9622554185195676e-06,
                7.889263524960312e-06,
                7.889259762307618e-06,
                1.4738981970312625e-05,
                1.0129987354108855e-05,
                6.96225458885115e-06
            ],
            [
                0.9999832985721872,
                0.9999785550541487,
                0.9999977396754327,
                0.9999967112509347,
                0.9999898700102285,
                0.9999852610232999,
                0.9999970976873229,
                0.9999898700114358,
                0.9999990577555183,
                0.9999810748495058
            ],
            [
                1.670142382796865e-05,
                2.1444950963097686e-05,
                8.939698434495167e-06,
                8.939693105272102e-06,
                1.6701425820540864e-05,
                1.8925157255968775e-05,
                0.999796572930906,
                2.7535681242383173e-05,
                1.4738978451920916e-05,
                6.9622554185195676e-06
            ],
            [
                1.5534973841450852e-06,
                8.315277302588544e-07,
                5.715003107525447e-07,
                8.315282258956806e-07,
                9.42244818532859e-07,
                5.043476486833397e-07,
                9.422449308335287e-07,
                1.3709568799592562e-06,
                1.994729721469003e-06,
                7.338208055436404e-07
            ],
            [
                0.9999945777829693,
                0.99997855505926,
                0.9999952149055054,
                0.9999546021476081,
                0.9999417087553565,
                0.99997246431547,
                0.9999898700090203,
                0.9999910603036961,
                0.999985261018029,
                0.9999687980812073
            ],
            [
                0.9890130575313263,
                0.9940889299096913,
                0.9975273767078353,
                0.998830489595283,
                0.9998415638399517,
                0.9964063968299919,
                0.9706877724815146,
                0.9996646500097958,
                0.9999546021259791,
                0.9999546021475986
            ],
            [
                0.9999869928761876,
                0.9999852610197877,
                0.9999930377445805,
                0.9999921107345934,
                0.9999990577554061,
                0.9999938558246658,
                0.9999724643056309,
                0.9999986290424664,
                0.9999945777790913,
                0.999996273360716
            ],
            [
                8.315282259009745e-07,
                1.994729245749689e-06,
                4.450849988733914e-07,
                8.31528126775552e-07,
                1.2098653950205268e-06,
                8.315279285205827e-07,
                4.450848927621807e-07,
                9.422450431800595e-07,
                4.450849988758202e-07,
                8.315283249923769e-07
            ],
            [
                2.144495096387783e-05,
                5.422217676486429e-06,
                7.889263525261671e-06,
                1.147877086073156e-05,
                1.147877086073156e-05,
                1.8925148237775583e-05,
                6.144176798691468e-06,
                3.2887478890769702e-06,
                1.0129990978644356e-05,
                1.994729483680993e-06
            ],
            [
                0.9999785550464758,
                0.999933947823871,
                0.9997388095669703,
                0.9999546021476186,
                0.9999785550413652,
                0.9999885212305062,
                0.9999724642990556,
                0.999941708755328,
                0.9999970976890528,
                0.9999852610110009
            ],
            [
                0.9999938558246658,
                0.9999945777803838,
                0.9999957771680658,
                0.9999885212359807,
                0.999995777166052,
                0.9999962733620487,
                0.9999938558224682,
                0.9999938558268633,
                0.9999910603068933,
                0.9999938558246659
            ],
            [
                1.1478770859917257e-05,
                2.7535684505068197e-05,
                1.147877222485351e-05,
                4.222834954561012e-06,
                3.5356254919217684e-05,
                5.144223200893693e-05,
                6.1441767987808774e-06,
                3.2887478890769702e-06,
                6.144172404129392e-06,
                2.1444940736477737e-05
            ],
            [
                0.9999986290427931,
                0.9999982396569965,
                0.9999990577551814,
                0.9999991684715759,
                0.9999832985701949,
                0.9999982396572064,
                0.9999984465022455,
                0.9999970976873229,
                0.9999989322968753,
                0.9999980052693274
            ],
            [
                1.7603438428188364e-06,
                3.2887506334201674e-06,
                2.9023116389365734e-06,
                1.0677026154473471e-06,
                2.561282210590951e-06,
                1.7603434230921292e-06,
                4.785096204024198e-06,
                2.5612825156159896e-06,
                6.144176798870286e-06,
                1.7603432131375548e-06
            ],
            [
                6.144176798255599e-06,
                1.892514147143123e-05,
                2.4300240727367308e-05,
                1.4738980210258757e-05,
                1.2098659719122375e-06,
                4.222832435926668e-06,
                4.222835457852533e-06,
                2.260323758835034e-06,
                1.6701419848475466e-05,
                3.2887478889034873e-06
            ],
            [
                0.9982992775652416,
                0.9996200154729662,
                0.7057850216484838,
                0.4687906266262437,
                0.9999832985829998,
                0.8807970701552505,
                0.5,
                0.9999852610147059,
                0.7981867849406659,
                0.651354857898194
            ],
            [
                0.9999930377445804,
                0.9999991684715759,
                0.9999832985701917,
                0.9999910603058276,
                0.9999974387184,
                0.9999852610145148,
                0.9999938558261304,
                0.9999885212346113,
                0.9999993524050473,
                0.999999352405279
            ],
            [
                0.9999996072138934,
                0.9999998874648379,
                0.9999970976866309,
                0.9999990577554061,
                0.9999987901341723,
                0.999999266178757,
                0.999996273358939,
                0.9999994284996211,
                0.9999977396762411,
                0.9999986290429566
            ],
            [
                0.9999599363078501,
                0.9999599363221447,
                0.9999724642990565,
                0.9998911031297709,
                0.9999546021097292,
                0.9999687980886309,
                0.9999885212305066,
                0.9999930377420904,
                0.9999756997592719,
                0.9999967112493664
            ],
            [
                0.9999945777784449,
                0.9999485577740995,
                0.9999930377420904,
                0.9999974387177893,
                0.9999982396559473,
                0.9999485578047914,
                0.9999546021313769,
                0.9999417087275562,
                0.9999869928653338,
                0.9999989322973845
            ],
            [
                0.9999962733620487,
                0.9999982396561571,
                0.9999945777803839,
                0.9999982396569965,
                0.9999957771655487,
                0.9999970976876689,
                0.9999986290427931,
                0.9999852610162715,
                0.9999991684721706,
                0.9999485577924824
            ],
            [
                0.9999974387168733,
                0.9999967112493665,
                0.9999977396746244,
                0.9999982396559473,
                0.9999980052707541,
                0.9999970976876689,
                0.9999991684715759,
                0.9999945777797377,
                0.9999938558261308,
                0.9999898700126433
            ],
            [
                1.0129994600638342e-05,
                2.1444958627955892e-05,
                1.3007128461838766e-05,
                9.61024493518883e-05,
                8.939699499627926e-06,
                0.00010889694805897948,
                1.4738976697631541e-05,
                2.430023203740195e-05,
                1.3007128463352975e-05,
                1.4738987239295859e-05
            ],
            [
                0.9999885212291387,
                0.9999962733616046,
                0.9999898700126442,
                0.999975699762171,
                0.9999921107336531,
                0.9999967112509347,
                0.9999962733611601,
                0.9999930377420905,
                0.9999938558246664,
                0.9999977396757022
            ],
            [
                0.9993736659055419,
                0.9999687980774743,
                0.999876605410604,
                0.9999970976887068,
                0.9999724642957752,
                0.9999251537638378,
                0.9999832985781566,
                0.9999646437450841,
                0.9999869928746374,
                0.9999756997476807
            ],
            [
                0.9999038976195891,
                0.9999832985801549,
                0.9999921107364745,
                0.9999930377454106,
                0.9999898700090203,
                0.9999687980774852,
                0.9999967112493665,
                0.9999485578047843,
                0.9999967112513267,
                0.9999810748540193
            ],
            [
                0.9999599362887259,
                0.9999980052695652,
                0.9999945777797374,
                0.9999957771665556,
                0.9999885212359799,
                0.9999810748585306,
                0.9999910603036961,
                0.9999869928730869,
                0.9999967112493664,
                0.9999852610197852
            ],
            [
                1.3007130013572209e-05,
                1.1478766755233466e-05,
                6.144176798132662e-06,
                1.6701419848961534e-05,
                4.2228334438149845e-06,
                1.473898372500477e-05,
                6.144176066443055e-06,
                1.1478765386038447e-05,
                3.120191880504111e-05,
                2.144495607789177e-05
            ],
            [
                0.9999962733611603,
                0.9999994956525918,
                0.9999898700114358,
                0.9999957771650453,
                0.9999977396759716,
                0.999999352405279,
                0.9999996072138465,
                0.9999869928684351,
                0.9999982396559473,
                0.9999970976887068
            ],
            [
                0.9999967112509346,
                0.9999546021313769,
                0.9999898700053974,
                0.9999852610145148,
                0.9999251537460276,
                0.9999898700041898,
                0.9999485578047547,
                0.9999810748472474,
                0.9999756997621669,
                0.9998766054399983
            ],
            [
                0.999998629042303,
                0.9999945777823233,
                0.999995214904935,
                0.9999687980774836,
                0.9999756997679652,
                0.999989870005398,
                0.9999687980960708,
                0.999993037743751,
                0.9999898700090211,
                0.9999646437577242
            ],
            [
                4.7850962047640385e-06,
                2.2603237587774727e-06,
                4.222832434513317e-06,
                6.144172403715875e-06,
                6.962257908753841e-06,
                5.422220260044902e-06,
                2.4300234924597754e-05,
                1.0129994600638342e-05,
                3.7266379498554884e-06,
                1.473898723508674e-05
            ],
            [
                0.9999962733607161,
                0.9999910603036963,
                0.9999910603015656,
                0.9999992661788446,
                0.9999930377462406,
                0.999995777164542,
                0.9999977396757022,
                0.9999970976883608,
                0.9999898700126431,
                0.9999930377437508
            ],
            [
                0.9999810748585343,
                0.9999546021205518,
                0.9999921107374143,
                0.40733340004593027,
                0.9999038976194108,
                0.9999938558232034,
                0.9999885212332438,
                0.9999599362934974,
                0.9999982396561571,
                0.9999832985801537
            ],
            [
                1.9947294829281026e-06,
                4.7850967733701265e-06,
                2.5612825157045092e-06,
                1.370957533462248e-06,
                8.939695236398313e-06,
                1.2098656834041774e-06,
                3.7266410603195545e-06,
                6.144174600605357e-06,
                5.422220262195015e-06,
                1.760344052174704e-06
            ],
            [
                0.9999967112497584,
                0.9999982396572064,
                0.9999599362934897,
                0.9999970976873229,
                0.9999970976890528,
                0.9999599363221412,
                0.9999724643154654,
                0.9999756997563768,
                0.9999339478474795,
                0.9999599363125995
            ],
            [
                0.9998911031167045,
                0.9999810748472494,
                0.9994472213936266,
                0.9999810748540177,
                0.9999599362934934,
                0.9999982396567867,
                0.9999687980960696,
                0.9999724643121878,
                0.9999417087553242,
                0.9999724643187476
            ],
            [
                8.93969736518344e-06,
                1.012999460108057e-05,
                5.82912445884589e-05,
                1.4738987240100149e-05,
                1.8925157257965367e-05,
                1.8925143720384422e-05,
                5.829126546944542e-05,
                1.012999097799944e-05,
                2.56128159999123e-06,
                6.962259569003389e-06
            ],
            [
                0.9999989322970027,
                0.999998790134028,
                0.9999986290421394,
                0.9999993524050474,
                0.9999970976866309,
                0.9999869928761888,
                0.999994577780384,
                0.9999945777810307,
                0.9999974387180947,
                0.9999756997563777
            ],
            [
                0.13296424191570594,
                0.9990889487358753,
                0.8519527963298947,
                0.7772998714925403,
                0.6224593312018545,
                0.9740426411068075,
                0.9999756997681157,
                0.7057850154599562,
                0.9998204719706424,
                0.7772998560157665
            ],
            [
                0.9999687980960662,
                0.9999957771650453,
                0.9999339478789658,
                0.9999785550490328,
                0.999968798092358,
                0.9999910603026309,
                0.9999921107345932,
                0.9999785550515884,
                0.9999869928668839,
                0.999988521231875
            ],
            [
                0.9999930377429206,
                0.9999987901347491,
                0.9999967112517187,
                0.9999910603047624,
                0.9999646437450779,
                0.9999970976880149,
                0.9999930377454107,
                0.9999930377404308,
                0.9999930377437511,
                0.9999945777816769
            ],
            [
                0.9999921107392955,
                0.9999485578047876,
                0.9999921107345933,
                0.9999938558261307,
                0.9999785550567005,
                0.9999756997534802,
                0.9999898700078133,
                0.9999962733598274,
                0.9999898700126431,
                0.9999251537460603
            ],
            [
                0.9999967112513267,
                0.9999974387187053,
                0.9999980052700408,
                0.9999852610127591,
                0.9999977396751633,
                0.9999977396757022,
                0.9999945777810303,
                0.9999974387177893,
                0.9999993524052018,
                0.999997438717484
            ],
            [
                0.9999945777790911,
                0.9999832985721828,
                0.9999974387187052,
                0.9999938558246657,
                0.9999945777784447,
                0.9999982396559473,
                0.9999785550515862,
                0.9999962733598274,
                0.9999930377437503,
                0.9999938558224684
            ],
            [
                0.9999977396765105,
                0.9999810748585336,
                0.9999962733602719,
                0.9999785550592643,
                0.9999756997679662,
                0.9999945777784447,
                0.9999921107383553,
                0.9999967112509346,
                0.9999724643121888,
                0.9999898700126437
            ],
            [
                0.9999885212279569,
                0.9999832985704168,
                0.9525741231199173,
                0.9999852610127696,
                0.9890130580069646,
                0.999959936298325,
                0.9995694429685268,
                0.8670357701094303,
                0.9998415638218952,
                0.99996464375518
            ],
            [
                1.0129994599624903e-05,
                2.561281904871769e-06,
                1.8925155003330605e-05,
                4.222832940646604e-06,
                2.902310946944611e-06,
                1.994729483666479e-06,
                2.2603251060738913e-06,
                4.7850967749455485e-06,
                2.1444948407573453e-05,
                1.3709575335919232e-06
            ],
            [
                0.9999980052693274,
                0.9999938558246659,
                0.9999987901338838,
                0.9999756997592703,
                0.9999967112493665,
                0.9999910603058276,
                0.9999974387187053,
                0.9999993524053562,
                0.9999885212332446,
                0.9999986290426297
            ],
            [
                1.1478773597118638e-05,
                5.422219615829396e-06,
                3.726638395415398e-06,
                8.93969310584124e-06,
                1.0129995808418327e-05,
                2.1444943290362748e-05,
                2.753569437266178e-05,
                3.5356259125502595e-05,
                6.144176798691468e-06,
                4.222834451169694e-06
            ],
            [
                0.9999485577743904,
                0.999988521229145,
                0.9999339478712879,
                0.9525741283370986,
                0.9999599362889454,
                0.9996200155487026,
                0.9999646437625751,
                0.999841563802746,
                0.9999546021423021,
                0.9324533112067127
            ],
            [
                0.9999930377445803,
                0.9999980052705163,
                0.9999910603026309,
                0.9999952149060757,
                0.9999417087275205,
                0.9999986290427931,
                0.9999852610127582,
                0.9999885212277698,
                0.9999987901343165,
                0.9999991684718732
            ],
            [
                1.3007133112307748e-05,
                3.120190391251851e-05,
                7.889264464508026e-06,
                1.3007131562845248e-05,
                4.785096205651846e-06,
                4.539787398819316e-05,
                2.9023109470554753e-06,
                2.7535704219423216e-05,
                1.012999218369684e-05,
                3.5356267524954594e-05
            ],
            [
                0.9999785550439251,
                0.9999910603068937,
                0.9999980052702785,
                0.9999952149032236,
                0.9999977396757022,
                0.9999952149072167,
                0.9999984465020603,
                0.9999970976890529,
                0.9999938558239332,
                0.9999967112505427
            ],
            [
                0.9999945777823233,
                0.9999921107383554,
                0.9999977396754327,
                0.9999991684719723,
                0.9999989322968753,
                0.9999989322971299,
                0.9999993524053562,
                0.9999945777816768,
                0.9999982396567867,
                0.9999977396751633
            ],
            [
                1.147877086073156e-05,
                2.753568453191415e-05,
                8.939699499026267e-06,
                1.3007133113017532e-05,
                7.889265404113251e-06,
                5.42222155426567e-06,
                1.1478766754064213e-05,
                1.4738978448810996e-05,
                6.1441775309064404e-06,
                3.535626333989112e-05
            ],
            [
                0.9999989322970027,
                0.9999967112513268,
                0.9999921107355346,
                0.9999967112493664,
                0.9999994284996893,
                0.9999962733620487,
                0.9999852610127595,
                0.999999266178932,
                0.9999989322966208,
                0.9999982396574163
            ],
            [
                5.422221554758815e-06,
                2.1444958637356654e-05,
                1.670142582254589e-05,
                1.4738980211116665e-05,
                6.144175334015912e-06,
                1.9947299592570416e-06,
                5.422221550409272e-06,
                7.889263525534328e-06,
                4.222831934156396e-06,
                2.260323489490968e-06
            ],
            [
                1.1478772226690907e-05,
                2.902311984989368e-06,
                3.726640172385136e-06,
                2.430023203740195e-05,
                6.962253759271479e-06,
                2.7535700942411318e-05,
                4.2228324372555256e-06,
                1.4738981963771067e-05,
                1.1478768124553928e-05,
                4.7850956352353935e-06
            ],
            [
                1.0129988563546333e-05,
                4.006367784548767e-05,
                4.78509563546605e-06,
                1.0129990976728036e-05,
                4.785095635017795e-06,
                1.8925148236123232e-05,
                5.422220908634683e-06,
                6.1441767987808774e-06,
                1.4738985485166298e-05,
                1.4738978456398127e-05
            ],
            [
                0.999988521234612,
                0.9999910603047625,
                0.9999810748472499,
                0.9999952149066461,
                0.9999646437324375,
                0.9999785550541487,
                0.9999756997621686,
                0.9999852610127582,
                0.9999810748472499,
                0.9999952149055054
            ],
            [
                4.5397863219323224e-05,
                0.999569442865129,
                1.4738983720179032e-05,
                1.3007130009313495e-05,
                7.889261644358435e-06,
                2.1444950968441685e-05,
                3.5356250681935664e-05,
                1.1478773595657069e-05,
                2.1444956064317223e-05,
                1.4738985480179701e-05
            ],
            [
                6.962257907702715e-06,
                4.006369216362198e-05,
                3.120191134459038e-05,
                1.1478765387416494e-05,
                0.9971990723988218,
                2.144495863201265e-05,
                8.939694170729447e-06,
                0.9947798738542528,
                3.120192250393883e-05,
                4.539786306821192e-05
            ],
            [
                0.9999038975965836,
                0.9999962733611601,
                0.9998911031037014,
                0.9999962733589389,
                0.9999417087414205,
                0.9999724643187533,
                0.9999417087414281,
                0.9999986290427932,
                0.999995777166052,
                0.9999852610127579
            ],
            [
                0.9999984465026158,
                0.9999984465018751,
                0.9999921107345933,
                0.9999962733616045,
                0.9999852610145168,
                0.9999832985701949,
                0.9999885212318746,
                0.9999970976866309,
                0.9999930377437504,
                0.9999970976887068
            ],
            [
                1.1478769491598686e-05,
                1.3007131558444574e-05,
                1.1478768120315386e-05,
                8.939698433974813e-06,
                1.1478770860982112e-05,
                1.0129995806317745e-05,
                1.670142382681424e-05,
                4.006369682950345e-05,
                1.3007130012673148e-05,
                3.120191504553037e-05
            ],
            [
                4.0063687394553603e-05,
                8.93970056529743e-06,
                1.300713156215912e-05,
                1.0129994599901296e-05,
                1.9947290080905435e-06,
                7.889265405849647e-06,
                5.42221961567159e-06,
                1.3007133114011233e-05,
                6.962255418924822e-06,
                2.4300252313904224e-05
            ],
            [
                0.9999957771675623,
                0.9999417087345169,
                0.9999952149049351,
                0.9999869928653341,
                0.999972464315472,
                0.9999970976866309,
                0.9999957771680658,
                0.9999921107336526,
                0.9999151889890433,
                0.9999938558232008
            ],
            [
                6.962256248871951e-06,
                7.88925976283858e-06,
                0.9999885212359829,
                1.0129987356191011e-05,
                2.260325375572331e-06,
                1.89251482372248e-05,
                0.9999151889487328,
                0.9999910603037004,
                4.222835457906302e-06,
                2.56128282131428e-06
            ],
            [
                0.9999910603068942,
                0.9999952149072167,
                0.9999970976876689,
                0.9999982396572065,
                0.9999938558268635,
                0.9999952149055054,
                0.9999898700126431,
                0.9999885212359807,
                0.9999930377462403,
                0.9999977396751633
            ],
            [
                0.9999810748495047,
                0.999995214904935,
                0.9999646437450763,
                0.999993855826863,
                0.9998204720768701,
                0.9999038975621705,
                0.9999910603047617,
                0.9997040429715629,
                0.9999921107402356,
                0.9999339478395968
            ],
            [
                0.9999970976873228,
                0.9999885212359799,
                0.9999687980811879,
                0.9999785550592557,
                0.9999756997679594,
                0.9999724643023379,
                0.9999921107402363,
                0.999968798077472,
                0.9999957771665555,
                0.9999945777790911
            ],
            [
                0.9999852610110015,
                0.9999987901337396,
                0.9999898700090204,
                0.9999852610197869,
                0.9999910603058276,
                0.9999910603058276,
                0.9999974387168733,
                0.999989870011436,
                0.999996273358939,
                0.9999962733598275
            ],
            [
                6.9622595694023114e-06,
                1.1478768120315386e-05,
                8.939699500164542e-06,
                2.902313022952668e-06,
                2.1444953520182517e-05,
                2.1444948412722418e-05,
                8.939696302457574e-06,
                7.8892625849535e-06,
                3.726639728184142e-06,
                1.7603425837062577e-06
            ],
            [
                0.9999957771675624,
                0.9999945777784449,
                0.9999832985701924,
                0.9999930377445803,
                0.9999962733598274,
                0.9999910603058276,
                0.9999962733602717,
                0.9999885212291387,
                0.999998790134605,
                0.9999962733611603
            ],
            [
                0.9998911030911016,
                0.24508501313237172,
                0.006692850528029811,
                0.9999485577925175,
                0.9999038975736549,
                0.8175744806385543,
                0.3486451488696663,
                0.7772998714925403,
                0.9999785550439896,
                0.9999810748496868
            ],
            [
                0.9999898700126433,
                0.999989870010228,
                0.9999982396561571,
                0.9999687980960733,
                0.9999852610145148,
                0.9999852610145151,
                0.9999945777829693,
                0.9999945777784449,
                0.9999885212264013,
                0.999988521231875
            ],
            [
                0.9999810748450029,
                0.9999756997505882,
                0.9999930377454104,
                0.9999785550417262,
                0.999972464306599,
                0.9999810748540193,
                0.9999485577986083,
                0.9999251538024542,
                0.999989870004194,
                0.9999810748517612
            ],
            [
                2.2603237587774727e-06,
                1.300713311517055e-05,
                4.22283344433731e-06,
                5.422217676397663e-06,
                3.288749065029781e-06,
                2.902313368897403e-06,
                1.5534975693036317e-06,
                1.0129994600398803e-05,
                1.670142980608093e-05,
                3.2887506333394084e-06
            ],
            [
                0.999998790134605,
                0.999989870009021,
                0.9999987901343165,
                0.9999986290426298,
                0.9999977396751633,
                0.9999980052702785,
                0.9999646437408665,
                0.9999962733620487,
                0.9999970976890528,
                0.9999982396572064
            ],
            [
                0.999933947871098,
                0.9999646437366521,
                0.9999756997621654,
                0.999964643757729,
                0.9999957771680656,
                0.9999938558224686,
                0.9999339478790124,
                0.9999938558268633,
                0.9999962733607162,
                0.9999987901343165
            ],
            [
                0.9999885212318793,
                0.9999921107364871,
                0.9999869928730971,
                0.9999898700054991,
                0.9997388096827586,
                0.9902915229633815,
                0.9999945777829702,
                0.9999756997621879,
                0.9999930377464531,
                0.9999756997506779
            ],
            [
                1.0129988561648438e-05,
                1.670142781432848e-05,
                2.1444940736477737e-05,
                1.892515049199645e-05,
                8.939699499432793e-06,
                1.4738988995838502e-05,
                6.962253759581752e-06,
                1.8925155002710973e-05,
                6.144177531459659e-06,
                6.962259568230874e-06
            ]
        ]
    },
    {
        "q_id": "7860_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            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,
            57,
            58,
            59,
            60,
            61,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            119,
            121,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.561282210530385e-06,
                2.902313022984344e-06,
                2.5612825159677387e-06,
                4.222832940646604e-06,
                2.5612812946890944e-06,
                9.422445938861406e-07,
                2.902311984989368e-06,
                2.5612834318257725e-06,
                2.9023119846303784e-06,
                3.7266397280960194e-06
            ],
            [
                0.9999952149050061,
                0.9999938558275954,
                0.9241418231126367,
                0.9999991684718742,
                NaN,
                0.9999546021323703,
                0.9840936100375866,
                0.9999957771680692,
                0.9999989322975119,
                0.999998629042958
            ],
            [
                1.670142781520948e-05,
                6.962253759157502e-06,
                1.892515049571424e-05,
                5.144223202577919e-05,
                2.753569109034197e-05,
                6.144172403928222e-06,
                2.430024072648329e-05,
                NaN,
                1.0129993394664264e-05,
                6.1441760657054305e-06
            ],
            [
                3.2887502408573863e-06,
                2.7535694377870696e-05,
                3.726639283901856e-06,
                2.430024941804299e-05,
                8.939697367703906e-06,
                8.93969630089651e-06,
                1.3007134665130082e-05,
                3.288748280891699e-06,
                1.6701421843356024e-05,
                1.1478766755985128e-05
            ],
            [
                2.7535691076718644e-05,
                1.89251527491092e-05,
                1.4738978451920916e-05,
                2.1444948404530884e-05,
                5.422218969306048e-06,
                1.0129994599901296e-05,
                4.785093923916815e-06,
                6.962257075488498e-06,
                6.605216014561575e-05,
                7.889266345770692e-06
            ],
            [
                0.9999756997621748,
                0.9999756997679775,
                0.9999952149055057,
                0.9997388095673958,
                0.999989870009023,
                0.9999038975737626,
                0.999986992876194,
                0.9998601779094406,
                0.9999930377404312,
                0.9999810748472484
            ],
            [
                0.9999921107345976,
                0.9999984465016899,
                0.9999938558224711,
                0.9999945777810513,
                0.9999967112517193,
                0.9999967112513268,
                0.9999986290431202,
                0.9999957771670624,
                0.9706877697786225,
                0.9669140195852891
            ],
            [
                6.962254588977791e-06,
                0.9999930377445805,
                1.892515274339482e-05,
                5.422218322851817e-06,
                8.939697368500698e-06,
                6.962256249112569e-06,
                4.222832437109582e-06,
                1.14787735942999e-05,
                8.939695234983602e-06,
                1.5534983100016177e-06
            ],
            [
                0.9999970976883609,
                0.9999977396759886,
                0.9999945777810302,
                0.9999996072137062,
                0.9999945777829693,
                0.9999992661787594,
                0.867035771827307,
                0.9399133521402868,
                0.9999756997679742,
                0.9999989322967481
            ],
            [
                9.422445938642879e-07,
                0.9998601779762012,
                9.422447062094932e-07,
                0.9999546021207438,
                6.475949525781504e-07,
                0.9706877699376162,
                7.338213304196583e-07,
                1.994729959160889e-06,
                0.9999921107365488,
                0.9999687980929501
            ],
            [
                0.9998601779102584,
                0.9997040427965371,
                0.9999832985781597,
                0.999988521234621,
                0.9999982396571019,
                0.9999038975854067,
                0.9999646437324408,
                0.9989677690709242,
                0.9998601778931084,
                0.9999646437493162
            ],
            [
                0.9999952149049366,
                0.9999251537427903,
                0.9999852610113786,
                0.9999990577556308,
                0.999996273362055,
                0.9999869928761908,
                0.9998911031300816,
                0.9999930377437924,
                0.9241418173671895,
                0.9999970976869775
            ],
            [
                4.7850956351657615e-06,
                6.962256249327861e-06,
                6.962256249429175e-06,
                1.0677031245783732e-06,
                1.7603430034439723e-06,
                5.422217676866151e-06,
                7.889265407004852e-06,
                4.785096205830278e-06,
                2.9023112931688987e-06,
                3.726639728184142e-06
            ],
            [
                0.9947798741806994,
                0.9998911030649195,
                0.9999687980886298,
                0.9998204719484768,
                0.9999546021259487,
                0.9999646437577359,
                0.9998415637834978,
                0.9999038975621705,
                0.9999724642990546,
                0.9999852610127858
            ],
            [
                0.9999832985722634,
                0.9999339478554106,
                0.999941708741465,
                0.9980732650939982,
                0.9999885212278204,
                0.9999724642959287,
                0.9999339478789758,
                0.9999869928715357,
                0.9999546021259581,
                0.9579122678790578
            ],
            [
                0.9999945777790912,
                0.9999957771645431,
                0.999985261021544,
                0.9999987901338838,
                0.9999962733616046,
                0.9999930377437506,
                0.9999962733593841,
                0.7549149868676283,
                0.9999967112521109,
                0.9999930377412608
            ],
            [
                3.726638839656906e-06,
                1.0129992186939844e-05,
                1.4738981971250963e-05,
                1.892514147143123e-05,
                5.422220262037209e-06,
                8.93969310647542e-06,
                1.6701425825128124e-05,
                8.939693106987645e-06,
                4.222834954687752e-06,
                3.1201918798457626e-05
            ],
            [
                0.999998790133884,
                0.9999724643064051,
                0.999993855823231,
                0.9999996533672549,
                0.999999352405279,
                0.9999952149072167,
                0.99999743871718,
                0.9999986290427932,
                0.9999977396762411,
                0.9999991684717742
            ],
            [
                4.7850933534310035e-06,
                7.484622709894109e-05,
                1.300713466420736e-05,
                2.144494328950459e-05,
                2.1444958632714784e-05,
                6.962258738701267e-06,
                3.5356254907513187e-05,
                1.6701423824262386e-05,
                1.3007130010922344e-05,
                1.670142183983204e-05
            ],
            [
                0.9999910603069485,
                0.9999967112498537,
                0.9999832985783845,
                0.9820137940187298,
                0.9999962733589459,
                0.9626731160024469,
                0.914900959053549,
                0.9999993524053579,
                0.9999785550491265,
                0.9999921107346307
            ],
            [
                0.9999687980997901,
                0.9999852610162717,
                0.9999930377429213,
                0.9999898700102282,
                0.9999977396754327,
                0.9999251537728161,
                0.9999957771670591,
                0.9999251537906383,
                0.9999869928684351,
                0.9999910603026303
            ],
            [
                0.999959936317668,
                0.9046505421702797,
                0.9840936051975759,
                0.9997965730779887,
                0.9999957771655562,
                0.9999910603026437,
                0.9999852610200292,
                0.9999869928715562,
                0.9999038975393139,
                0.9999910603005178
            ],
            [
                0.9999987901340281,
                0.9999962733598278,
                0.9999993524052789,
                0.999997739675433,
                0.9999980052707541,
                0.9999952149049349,
                0.9999952149072165,
                0.999998446502801,
                0.9999991684719723,
                0.9999984465018751
            ],
            [
                0.9999810748562717,
                0.9875683474774581,
                0.9999852610162717,
                0.9999898700102323,
                0.9999977396746244,
                0.9999970976880148,
                0.9999952149066462,
                0.9999990577554061,
                0.987568351616546,
                0.9525741251394715
            ],
            [
                0.9999724643155903,
                0.9999599363126256,
                0.9999151889225479,
                7.889265404328504e-06,
                0.9999417087557161,
                0.9999885212264441,
                0.9999785550593392,
                0.8354835452961425,
                0.999891103114514,
                0.9995121427923237
            ],
            [
                1.0129994602057158e-05,
                2.902312330601386e-06,
                1.4738978457041559e-05,
                2.5612812945889277e-06,
                1.0129995807939249e-05,
                1.0129995808639442e-05,
                4.5397852401406606e-05,
                2.7535681224252135e-05,
                3.535623805665442e-05,
                4.222833444467892e-06
            ],
            [
                0.9999987901340284,
                0.9999151889808806,
                0.9999832985801487,
                0.9999810748562783,
                0.999975699762849,
                0.9525741288419873,
                0.9999251537371064,
                0.9999938558276054,
                0.9999687980886374,
                0.9999938558232304
            ],
            [
                3.535626755762428e-05,
                2.1444940740066406e-05,
                0.00010889688295561384,
                2.4300246507772637e-05,
                4.006367782114826e-05,
                2.7535684505068197e-05,
                2.753569434711804e-05,
                4.006371126336615e-05,
                2.1444958627097733e-05,
                5.144219523894761e-05
            ],
            [
                0.9997040429732937,
                0.9998601778593883,
                0.9999417087553741,
                0.9999546021151678,
                0.9999546021422099,
                0.999891103064853,
                0.9999930377404308,
                0.9999810748517598,
                0.9999251537816921,
                0.9999852610215433
            ],
            [
                0.999975699762171,
                0.9978172837656059,
                0.9999810748540172,
                0.9999982396567867,
                0.999989870009022,
                0.99999893229713,
                0.9999546021097148,
                0.999986992869987,
                0.9999921107383548,
                0.9999869928715369
            ],
            [
                1.6701421842140854e-05,
                1.1478773597640625e-05,
                4.539787945561647e-05,
                3.2887506332466845e-06,
                6.144176066264237e-06,
                6.605213676488686e-05,
                1.994730434778778e-06,
                1.0129988563730593e-05,
                1.6701429806475863e-05,
                3.1201900209877224e-05
            ],
            [
                0.9999974387168867,
                0.9999994956527721,
                0.9999977396754328,
                0.9999967112501505,
                0.9953904286389453,
                0.9999986290429566,
                0.9999980052702785,
                0.9999982396574166,
                0.9999962733593917,
                0.9999930377412614
            ],
            [
                0.9999646437472333,
                0.9999970976876759,
                0.9999952149043861,
                0.9999989322973875,
                0.9465966669987579,
                0.9999957771680658,
                0.904650538956921,
                0.9999962733616071,
                0.9999984465015127,
                0.9999921107384494
            ],
            [
                1.892514823488397e-05,
                6.144174601410037e-06,
                2.561282210618905e-06,
                1.2098656834922064e-06,
                6.962258739068529e-06,
                1.3007128463069061e-05,
                1.8925157261545463e-05,
                2.753568453191415e-05,
                1.14787681240737e-05,
                7.889264465239894e-06
            ],
            [
                1.76034363298589e-06,
                3.7266406167827664e-06,
                1.3007133115667397e-05,
                2.4300249420429837e-05,
                1.1478769493728398e-05,
                2.9023133690188264e-06,
                1.670142980726572e-05,
                1.1478765386330758e-05,
                7.889259763469998e-06,
                3.7266410609940346e-06
            ],
            [
                1.6701423834226767e-05,
                0.9999990577557432,
                3.726637947916783e-06,
                5.144222589108318e-05,
                0.999997097687323,
                0.9999945777829693,
                1.4738978456719842e-05,
                1.8925143711847272e-05,
                3.535626333461766e-05,
                0.999996711251719
            ],
            [
                2.144495863482118e-05,
                6.144174601410037e-06,
                4.006369216143581e-05,
                3.726640616670918e-06,
                1.4738985480179701e-05,
                3.288750241204353e-06,
                1.1478773598329648e-05,
                1.5534977543661227e-06,
                2.4300240729754152e-05,
                6.144174601499446e-06
            ],
            [
                4.785096205582214e-06,
                3.726639728184142e-06,
                2.561281905376098e-06,
                5.422220908116881e-06,
                6.962257909501028e-06,
                3.288750633569722e-06,
                1.4738987242137685e-05,
                8.939697369151141e-06,
                4.222832941034507e-06,
                3.726639284017094e-06
            ],
            [
                0.9669140238756563,
                0.9999485577946938,
                0.9999986290432836,
                0.9999962733598472,
                0.9999852610145359,
                0.8807970732843033,
                0.999996273361162,
                0.9999599363030525,
                0.9999869928732048,
                0.9999038975850886
            ],
            [
                0.9579122726851416,
                0.9980732656760583,
                0.8175744739711883,
                0.9999930377454104,
                0.9669140188702279,
                0.9999921107355336,
                0.9999945777784554,
                0.99999862904214,
                0.9770226326825219,
                0.9770226278319488
            ],
            [
                4.22283545795623e-06,
                5.715004470295662e-07,
                4.222834954461155e-06,
                1.760342793583908e-06,
                3.288749065209246e-06,
                3.2887502412970765e-06,
                9.422450431800595e-07,
                1.0677024881829577e-06,
                5.715007195353674e-07,
                4.222831933564939e-06
            ],
            [
                1.300712845923622e-05,
                1.1478770859019436e-05,
                1.4738983726184394e-05,
                6.962257078819179e-06,
                1.473898899256772e-05,
                1.6701429805199933e-05,
                1.0129988563730593e-05,
                6.144176796947993e-06,
                1.7603425836870455e-06,
                1.4738983724146862e-05
            ],
            [
                0.9999485577802758,
                0.9999930377404315,
                0.9999756997563768,
                0.9999417087414243,
                0.9999952149055056,
                0.9999957771660523,
                0.9999832985701973,
                0.9999957771655488,
                0.9999339478711234,
                0.9999785550567043
            ],
            [
                0.9999987901340297,
                0.9999982396572076,
                0.9999910603058544,
                0.9999852610110139,
                0.9999984465020607,
                0.9999980052698033,
                0.9999962733598277,
                0.8933094039240554,
                0.999996273361646,
                0.9999970976876691
            ],
            [
                0.9999599362998177,
                0.9914225128122335,
                0.999959936289281,
                0.4378234991142019,
                0.9465966715184067,
                0.9525741274956179,
                0.9999687980840176,
                0.9999986290427935,
                0.9999967112521198,
                0.9999945777784529
            ],
            [
                4.539787944306515e-05,
                1.892514597832254e-05,
                1.1478765385098868e-05,
                9.610242631353545e-05,
                7.88926634455091e-06,
                1.670142781025767e-05,
                1.47389819699641e-05,
                1.1478772225981004e-05,
                1.3007131561804229e-05,
                2.1444953516281788e-05
            ],
            [
                2.4300232036606334e-05,
                6.962257909121104e-06,
                1.3007125362820425e-05,
                1.300712846361323e-05,
                2.9023112930949896e-06,
                2.7535700938304286e-05,
                0.9999832985741766,
                1.3007131557498195e-05,
                1.300713001414004e-05,
                2.753570094040789e-05
            ],
            [
                0.999999266179107,
                0.9999756997592771,
                0.9999930377429205,
                0.9999832985701935,
                0.9999930377429207,
                0.9999989322966208,
                0.9999938558224685,
                0.9999974387184002,
                0.9999852610197889,
                0.9999962733607161
            ],
            [
                0.9999980052707541,
                0.9999952149032237,
                0.999998239656367,
                0.9999980052698029,
                0.9999980052700408,
                0.9999957771670591,
                0.9996200154699372,
                0.999998629042303,
                0.9997694933125014,
                0.9997388097845256
            ],
            [
                1.6701425819447213e-05,
                5.42222090767305e-06,
                3.7266388396128453e-06,
                7.889262584809997e-06,
                1.4738985483879434e-05,
                1.0129993394314164e-05,
                1.0129987356191011e-05,
                8.939695237504067e-06,
                4.222833444229772e-06,
                4.78509563466093e-06
            ],
            [
                1.5534977545243671e-06,
                1.0129989771657269e-05,
                1.2098656834834034e-06,
                1.8925143725341476e-05,
                1.4738983725406915e-05,
                7.889262584508638e-06,
                8.939700566143004e-06,
                6.144174601588856e-06,
                2.902311984873224e-06,
                4.222833444429485e-06
            ],
            [
                4.785093923768848e-06,
                2.2603237587774727e-06,
                7.889265405677441e-06,
                6.144175333289463e-06,
                1.5534975693707442e-06,
                1.7603430033991435e-06,
                1.0677033791291683e-06,
                1.3007128463873485e-05,
                5.422218323093458e-06,
                1.5534983101061718e-06
            ],
            [
                0.999993037741326,
                0.9999970976880187,
                0.999999266179282,
                0.9999810748562717,
                0.999983298572472,
                0.92414182206801,
                0.8519528019683106,
                0.9999991684720715,
                0.9999687980754709,
                0.9999885212305538
            ],
            [
                1.3007130013288297e-05,
                8.939700566143004e-06,
                1.147876538789672e-05,
                8.93969630362837e-06,
                1.3007128462785148e-05,
                3.72664017246987e-06,
                4.5397874046655906e-05,
                1.1478768124992398e-05,
                6.144175334172377e-06,
                3.2887506334201674e-06
            ],
            [
                0.9999962733620488,
                0.9999938558246665,
                0.9999980052707544,
                0.9579122675786775,
                0.9999945777785446,
                0.9999885212363658,
                0.9999898700126442,
                0.999988521235985,
                0.9999898700090235,
                0.9999952149049356
            ],
            [
                2.7535697651475977e-05,
                7.484622716319649e-05,
                4.006369693473136e-05,
                1.6701425820540864e-05,
                5.144222576645054e-05,
                1.300712846115264e-05,
                NaN,
                2.4300234917879235e-05,
                2.7535681228559507e-05,
                NaN
            ],
            [
                0.9999952149067014,
                0.9999832985801537,
                0.9999785550594223,
                0.8354835432479661,
                0.9796676469170548,
                0.9999646437493745,
                0.9999546021317806,
                0.9999952149066551,
                0.8354835411997897,
                0.9999852610221538
            ],
            [
                0.9999251537370814,
                0.9998911031068324,
                0.9999938558240257,
                0.9999938558232012,
                0.9999599362935263,
                0.9999832985702437,
                0.9999852610186488,
                0.9992903296326016,
                0.999986992874661,
                0.9999687980888644
            ],
            [
                0.9989677687351626,
                0.9999646437325342,
                0.9999945777790914,
                0.8933094088947399,
                0.9999485577741295,
                0.999983298582142,
                0.9999687980960721,
                0.9999962733589393,
                0.9999852610215446,
                0.9999938558224811
            ],
            [
                0.9999921107402358,
                0.9999957771660521,
                0.9995121428834053,
                0.9999910603026309,
                0.9999980052693274,
                0.9999952149066462,
                0.9999980052695652,
                0.9999938558253981,
                0.9999977396746244,
                0.9999546021476057
            ],
            [
                0.9999921107366272,
                0.999972464309097,
                0.999998239657417,
                0.9999977396759775,
                0.9999982396567871,
                0.8175744850834648,
                0.9999952149055413,
                0.9525741322079104,
                0.9996200154153375,
                0.9999724643081962
            ],
            [
                0.9999974387187097,
                0.9999970976887068,
                0.9999485577924884,
                0.9999546021421849,
                0.9999885212359798,
                0.9999930377420904,
                0.9999952149072302,
                0.999993855823206,
                0.9999869928653333,
                0.9999957771645425
            ],
            [
                7.889263525778283e-06,
                7.889261644057078e-06,
                2.902313023063532e-06,
                6.144173869312763e-06,
                8.939698434966738e-06,
                6.1441738691562974e-06,
                2.5612825159421147e-06,
                2.2603234894560207e-06,
                7.88926634644516e-06,
                5.422217676925328e-06
            ],
            [
                0.9999756997505828,
                0.9999930377462403,
                0.9999982396572065,
                0.9999910603047626,
                0.9999151889586856,
                0.9999898700053983,
                0.9999957771675623,
                0.999997097686977,
                0.9999910603015656,
                0.9999962733593831
            ],
            [
                0.999998790134605,
                0.9999952149066464,
                0.9999938558224687,
                0.9999724643089074,
                0.9999986290432834,
                0.9999952149037942,
                0.9999599362887278,
                0.9999885212318746,
                0.9999977396757023,
                0.999998005269803
            ],
            [
                3.2887506334560605e-06,
                1.3709570433661467e-06,
                2.2603242977555607e-06,
                5.422217030288788e-06,
                2.5612828210277558e-06,
                7.889261644875049e-06,
                4.785093353739995e-06,
                1.7603427935342762e-06,
                2.5612819051373276e-06,
                1.4738985484227961e-05
            ],
            [
                0.9999756997592687,
                0.9999869928653341,
                0.9999991684720715,
                0.9999980052700408,
                0.9999869928746379,
                0.9999938558224684,
                0.9999987901347492,
                0.9999832985721833,
                0.9999952149060757,
                0.999986992876188
            ],
            [
                0.9999974387168733,
                0.9999982396559473,
                0.9999885212305071,
                0.9999970976873229,
                0.9999952149049349,
                0.9999974387180947,
                0.9999986290423029,
                0.9999974387184,
                0.9999938558239332,
                0.9999756997679876
            ],
            [
                0.9999989322972572,
                0.9999810748540177,
                0.9999962733620487,
                0.9999869928746369,
                0.9999957771660524,
                0.9999962733607165,
                0.999989870011436,
                0.9999952149055054,
                0.9999869928699853,
                0.9999869928715358
            ],
            [
                4.222832437186393e-06,
                6.605215248979934e-05,
                1.3007131561047124e-05,
                7.889266345957247e-06,
                1.6701427813872793e-05,
                1.1478768122069266e-05,
                3.535623805331028e-05,
                1.4738988998787566e-05,
                3.1201926235527406e-05,
                1.8925145981833788e-05
            ],
            [
                0.9999982396563669,
                0.9999977396754327,
                0.999986992865338,
                0.9999962733602719,
                0.999996273360716,
                0.9999974387187053,
                0.9999417087415015,
                0.9990889487741281,
                0.9999986290423029,
                0.9999810748585316
            ],
            [
                0.999954602115151,
                0.9999984465024306,
                0.9999810748449934,
                0.9999546021151331,
                0.9999485577802278,
                0.9999930377412606,
                0.9999970976883609,
                0.9999885212318746,
                0.9999982396574162,
                0.9999938558261311
            ],
            [
                2.4300249404340734e-05,
                1.994729959019382e-06,
                0.9999994284997573,
                3.2887494572095624e-06,
                1.89251482355036e-05,
                3.2887494570181325e-06,
                2.1444940736477737e-05,
                7.889265405505236e-06,
                2.902313368820854e-06,
                1.3007123812554424e-05
            ],
            [
                1.01299933920846e-05,
                8.939695238089467e-06,
                1.8925141467679015e-05,
                1.3007125361448172e-05,
                1.1478773598538445e-05,
                1.8925143718318983e-05,
                2.4300240730549767e-05,
                6.144173136243255e-06,
                2.902311984989368e-06,
                2.430023202246208e-05
            ],
            [
                0.9465966739665496,
                0.9999756997512482,
                0.9999646437535213,
                0.999993037745433,
                0.9999898700114374,
                0.9999962733620525,
                0.999991060299436,
                0.9999945777816813,
                0.9465966664338018,
                0.9999945777790918
            ],
            [
                6.144176065828368e-06,
                6.962259567217739e-06,
                5.422220908481809e-06,
                3.288749064802458e-06,
                3.2887506329595395e-06,
                4.222831932297532e-06,
                1.1478772229989872e-05,
                1.209866116149238e-06,
                8.9396941702904e-06,
                1.994730672468935e-06
            ],
            [
                1.8925150492616083e-05,
                2.561281599881745e-06,
                1.1478769492642663e-05,
                7.889260704179641e-06,
                1.7603427935678977e-06,
                5.422217030555087e-06,
                5.422217676654099e-06,
                1.1478768124324254e-05,
                6.144174601588856e-06,
                1.1478773597870298e-05
            ],
            [
                0.9999756997679619,
                0.9999646437450808,
                0.999985261014516,
                0.9999785550592579,
                0.9999962733598274,
                0.9999921107392957,
                0.9999687980811937,
                0.999975699762164,
                0.9999898700126431,
                0.9999945777803838
            ],
            [
                4.5397884779691074e-05,
                8.481106135683544e-05,
                7.484626283311537e-05,
                8.481108146397333e-05,
                3.535626331056557e-05,
                9.610239178363376e-05,
                2.4300237821252875e-05,
                7.484625377419046e-05,
                2.1444943287710254e-05,
                1.892515048449202e-05
            ],
            [
                0.9997388096055005,
                0.9999967112521115,
                0.9999945777784459,
                0.9999910603068942,
                0.9999974387176349,
                0.9999993524048931,
                0.9579122750881833,
                0.9999982396574235,
                0.999995777166053,
                0.9579122716338109
            ],
            [
                0.867035758084294,
                0.9999977396759716,
                0.9999945777784501,
                0.9999967112521109,
                0.9999984465018751,
                0.9999930377445804,
                0.9999984465016899,
                0.9465966734015935,
                0.993307148837343,
                0.9959298621651856
            ],
            [
                6.962259569117366e-06,
                4.222832437324657e-06,
                4.2228319339950885e-06,
                8.939699498587217e-06,
                1.3007134665130082e-05,
                1.6701417859944398e-05,
                3.120190763922401e-05,
                6.962257909323729e-06,
                4.78509278207486e-06,
                2.1444945851269378e-05
            ],
            [
                1.1478768123551712e-05,
                2.1444948396573396e-05,
                4.006370172712009e-05,
                1.8925148230890784e-05,
                1.0129994601688632e-05,
                4.0063687392367425e-05,
                0.00010889692202111441,
                0.00012339454479824084,
                0.00013982207385299317,
                2.753568780461672e-05
            ],
            [
                2.144495859370747e-05,
                8.481101098134002e-05,
                3.5356250689524286e-05,
                2.4300240712250633e-05,
                0.0001398220901342531,
                4.006367778354606e-05,
                4.5397863134932104e-05,
                1.8925143717561654e-05,
                8.481106145679419e-05,
                2.7535684498857565e-05
            ],
            [
                0.8519528000888386,
                0.9999952149060758,
                0.9999952149032241,
                0.9999852610145155,
                0.9999724642960586,
                0.999903897608124,
                0.9998766054695147,
                0.9999945777823334,
                0.9999724643089131,
                0.9999967112513267
            ],
            [
                3.53562591336057e-05,
                4.785096775171854e-06,
                3.2887486725569194e-06,
                4.785094491756681e-06,
                1.9947301968056346e-06,
                1.0129993392342568e-05,
                4.222832436955956e-06,
                5.422218968931258e-06,
                1.0129989769464556e-05,
                2.144495607640949e-05
            ],
            [
                0.9999687980737538,
                0.9999930377429206,
                0.9999930377454107,
                0.9999977396746244,
                0.9999910603036961,
                0.9999980052695652,
                0.9999810748585323,
                0.9999938558224687,
                0.9999982396569965,
                0.9999724642990556
            ],
            [
                0.9999417087066884,
                0.9999989322972572,
                0.999978555043919,
                0.9999993524053562,
                0.9999898700126435,
                0.9999938558261308,
                0.999975699767961,
                0.9999898700114366,
                0.9999945777797379,
                0.9998204720554777
            ],
            [
                1.7603438428028262e-06,
                7.338209805040511e-07,
                2.90231094702116e-06,
                2.260325375520937e-06,
                4.7850956327286435e-06,
                1.5534975693205863e-06,
                3.7266397276757403e-06,
                4.222834954461155e-06,
                2.9023126767836054e-06,
                1.994729959160889e-06
            ],
            [
                1.1478772227651366e-05,
                2.430025230532926e-05,
                1.1478764019787597e-05,
                6.962254589332388e-06,
                4.5397884829235786e-05,
                8.939698434332555e-06,
                6.962259569003389e-06,
                2.7535697652678035e-05,
                1.1478765386038447e-05,
                1.3007134662054344e-05
            ],
            [
                0.9999930377462405,
                0.9999910603005048,
                0.9999910603068946,
                0.9999962733598388,
                0.9999417087206086,
                0.9669140253057785,
                0.9999687980737552,
                0.9999832985781617,
                0.9999038976194108,
                0.9999921107346523
            ],
            [
                0.9999810748585306,
                0.9999962733602717,
                0.9999910603058276,
                0.9999970976880149,
                0.9999982396572065,
                0.9999756997534811,
                0.9999962733589389,
                0.9999852610110004,
                0.9998911030518491,
                0.9999646437493034
            ],
            [
                0.9999952149060761,
                0.9999852610180312,
                0.9999038976079185,
                0.9999945777803839,
                0.9999952149037942,
                0.9999151889485854,
                0.9999930377437506,
                0.9998911030388207,
                0.9999832985783094,
                0.9999930377462403
            ],
            [
                0.9820137878007523,
                0.9999852610163015,
                0.9999986290427989,
                0.7057850216484838,
                0.999995214905526,
                0.9999898700114878,
                0.7310585786300049,
                0.9999724643091746,
                0.9399133494052115,
                0.9997694932709779
            ],
            [
                7.88926634455091e-06,
                2.902311984989368e-06,
                2.5612822106841303e-06,
                3.7266392836984955e-06,
                6.962257079275089e-06,
                7.889262585541864e-06,
                2.9023112929973233e-06,
                3.7266388397721442e-06,
                1.4738987239295859e-05,
                1.0129990979547237e-05
            ],
            [
                1.4738987232888351e-05,
                2.1444943294263477e-05,
                6.144172403335888e-06,
                4.785096776133645e-06,
                0.00010889692170580166,
                0.00013982208979247476,
                3.12019076269651e-05,
                1.0129989770662257e-05,
                1.3007130009313495e-05,
                1.6701419845073e-05
            ],
            [
                2.9023133689924295e-06,
                8.939699500164542e-06,
                6.962259569117366e-06,
                3.7266410605974813e-06,
                1.1478769493540482e-05,
                6.1441724044534996e-06,
                5.422220908018252e-06,
                6.9622587393661365e-06,
                7.88926540262081e-06,
                1.3007123812317831e-05
            ],
            [
                9.610240335209681e-05,
                5.144223200893693e-05,
                6.605217614445361e-05,
                2.753569764776963e-05,
                2.1444958637356654e-05,
                3.120192623700302e-05,
                8.939700564679507e-06,
                3.120191878949046e-05,
                3.53562675293277e-05,
                5.144221364040696e-05
            ],
            [
                0.9999967112509346,
                0.9999990577555186,
                0.9999967112501507,
                0.9999984465022455,
                0.9999984465016898,
                0.9999995549151072,
                0.9999885212332442,
                0.999996711250935,
                0.9999930377404322,
                0.9999982396569965
            ],
            [
                0.999989870012647,
                0.9999852610145235,
                0.9999869928668902,
                0.9999832985801588,
                0.9999938558239336,
                0.9999930377454109,
                0.9999967112497585,
                0.9999852610233028,
                0.9999546021259933,
                0.9999957771665573
            ],
            [
                0.9999885212360005,
                0.9999339478792396,
                0.9999339478790071,
                0.9999832985821396,
                0.999569442913327,
                0.9989677691789632,
                0.9998204720557494,
                0.9999869928730944,
                0.8933094039240554,
                0.0031726834094779237
            ],
            [
                0.9999957771645421,
                0.9999938558275958,
                0.9999945777829696,
                0.9999970976887069,
                0.9999756997505845,
                0.9999785550515947,
                0.9999921107364745,
                0.99999862904312,
                0.9999810748495047,
                0.999978555049031
            ],
            [
                6.144174601410037e-06,
                6.962258739169842e-06,
                1.0129995805691255e-05,
                1.012999580884213e-05,
                4.222833444106873e-06,
                4.222834954057889e-06,
                2.561283431888668e-06,
                9.422445939002803e-07,
                8.939696302652706e-06,
                6.1441775312976045e-06
            ],
            [
                0.9999962733593833,
                0.9999957771651083,
                0.9997388096196206,
                0.9999832985802519,
                0.9999980052698032,
                0.8670357580842941,
                0.9999989322971302,
                0.9999977396746282,
                0.9999962733620488,
                0.9999910603004999
            ],
            [
                8.939697368663308e-06,
                6.1441746017453204e-06,
                1.300712846411008e-05,
                3.7266410607194972e-06,
                3.120190764467241e-05,
                3.2887482811908074e-06,
                3.288750241473551e-06,
                1.147876538716594e-05,
                8.939698434966738e-06,
                2.260325375650449e-06
            ],
            [
                2.9023112931213857e-06,
                4.7850939242083995e-06,
                4.222831934156396e-06,
                3.7266388395620047e-06,
                6.962257908880483e-06,
                3.7266388396128453e-06,
                6.962253759486771e-06,
                3.726640616630245e-06,
                2.260324028281919e-06,
                4.222833444383398e-06
            ],
            [
                0.9999967112517189,
                0.9999962733616045,
                0.9999952149043645,
                0.9999980052709919,
                0.9999945777816767,
                0.9999945777823231,
                0.9999785550541436,
                0.9999967112505427,
                0.9999957771650454,
                0.999998005269803
            ],
            [
                0.9999485577618208,
                0.9999930377420904,
                0.9999546021313555,
                0.9998766054104226,
                0.9999938558246664,
                0.9999945777784447,
                0.9999921107336528,
                0.9999930377454104,
                0.9998204719482471,
                0.9999977396762411
            ],
            [
                1.147876675548402e-05,
                7.889264465986113e-06,
                2.1444956072586775e-05,
                8.939697368110433e-06,
                1.4738985484227961e-05,
                3.726640172290235e-06,
                8.939695237813028e-06,
                5.422217676575195e-06,
                1.4738985484871391e-05,
                1.6701423833831836e-05
            ],
            [
                0.9999974387187053,
                0.9999930377404307,
                0.9999977396746244,
                0.9999974387180947,
                0.9999957771675623,
                0.9999921107345932,
                0.9999977396759716,
                0.9999977396746244,
                0.9999485577924947,
                0.9999962733602717
            ],
            [
                0.9999970976869818,
                0.9999921107355346,
                0.817574471748733,
                0.9999994956523522,
                0.9999989322973849,
                0.9999945777790913,
                0.9999994284997586,
                0.99997569975928,
                0.9999938558268633,
                0.9999852610180308
            ],
            [
                0.9999599363173749,
                0.9999962733602717,
                0.9999921107383553,
                0.9999977396754328,
                0.9999986290424664,
                0.9999599363221447,
                0.9999417087275172,
                0.9999898700041906,
                0.9999921107336531,
                0.9999910603058276
            ],
            [
                4.5397863198349305e-05,
                5.422217676486429e-06,
                2.753568781222975e-05,
                5.1442213588757405e-05,
                5.829129327472389e-05,
                9.610238030606413e-05,
                2.4300252316291068e-05,
                3.5356246471407274e-05,
                4.785093353187292e-06,
                1.473898899664279e-05
            ],
            [
                2.4300237828059798e-05,
                2.4300249416363357e-05,
                2.14449458497871e-05,
                1.1478764018827141e-05,
                1.6701417859519093e-05,
                7.889265406294507e-06,
                6.144172403928222e-06,
                4.539789022795839e-05,
                1.1478770859624945e-05,
                NaN
            ],
            [
                0.9999962733607161,
                0.9999038975393251,
                0.9999724643089034,
                0.99999862904312,
                0.9999921107364745,
                0.999985261021544,
                0.9999990577549568,
                0.9999957771670588,
                0.9999810748427375,
                0.9999970976890529
            ],
            [
                2.7535691063295662e-05,
                1.4738981965326028e-05,
                3.53562633231704e-05,
                2.7535687699737166e-05,
                7.484623580173539e-05,
                1.8925154992246077e-05,
                0.000158436197620507,
                1.1478766749575118e-05,
                4.53978740152776e-05,
                4.0063687367153544e-05
            ],
            [
                3.1201918806289706e-05,
                3.5356238040705445e-05,
                2.7535700926183532e-05,
                0.00012339453019082351,
                3.53562591336057e-05,
                8.939697366793286e-06,
                5.144223815074485e-05,
                8.939699500327152e-06,
                1.6701415869924985e-05,
                5.1442232038504445e-05
            ],
            [
                2.430024941804299e-05,
                2.753570418897106e-05,
                0.9999970976869775,
                2.4300249411766472e-05,
                NaN,
                8.481101094863749e-05,
                0.9999938558246663,
                5.829125149535031e-05,
                0.9999967112521111,
                8.481101087089185e-05
            ],
            [
                5.1442225815854466e-05,
                0.9999995549150011,
                0.9999980052705163,
                8.93970056350871e-06,
                4.222834954280646e-06,
                1.892514823364471e-05,
                0.999997438717484,
                0.9999996072136592,
                0.9999993524049702,
                0.9999998724809115
            ],
            [
                0.9999869928762029,
                0.999993855823935,
                0.9999957771650463,
                0.999975699753477,
                0.9999921107364745,
                0.9999898700126431,
                0.9999832985701956,
                0.9999921107336528,
                0.9999038975964927,
                0.9999885212359826
            ]
        ]
    },
    {
        "q_id": "7983_mmlu_math",
        "cot_ids": [
            0,
            4,
            8,
            10,
            11,
            12,
            16,
            17,
            18,
            22,
            23,
            24,
            29,
            33,
            34,
            35,
            38,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            51,
            54,
            56,
            58,
            59,
            60,
            61,
            62,
            70,
            72,
            74,
            78,
            79,
            81,
            82,
            87,
            89,
            90,
            92,
            93,
            95,
            96,
            100,
            103,
            105,
            107,
            108,
            110,
            113,
            117,
            121,
            123,
            125
        ],
        "rewards": [
            [
                1.2098658276862581e-06,
                7.338212428479715e-07,
                0.679178699175393,
                0.5621765008857982,
                6.144176797585032e-06,
                1.2098655391045077e-06,
                0.1066905889749668,
                5.715006512091808e-07,
                7.338207179493245e-07,
                0.9999646437366874
            ],
            [
                0.00017952802858448887,
                1.0677029972134173e-06,
                1.3709578603185986e-06,
                2.7535700904947163e-05,
                1.4738981968060613e-05,
                9.610244926309368e-05,
                1.2098652505382312e-06,
                5.422217676797111e-06,
                1.553497939625029e-06,
                1.670142980222277e-05
            ],
            [
                NaN,
                3.12019113244994e-05,
                0.00015843619651171312,
                1.3007126913820052e-05,
                8.939700566435704e-06,
                NaN,
                1.0677032518093368e-06,
                8.315280275416164e-07,
                4.006369207500901e-05,
                0.0004305571226336006
            ],
            [
                1.6701417845088975e-05,
                5.1442195242316055e-05,
                5.1442207372098016e-05,
                3.535625069312567e-05,
                2.430024649256756e-05,
                NaN,
                9.610239186473745e-05,
                NaN,
                2.1444948403750736e-05,
                1.0129987354882753e-05
            ],
            [
                1.3007126899411407e-05,
                NaN,
                3.120190761845198e-05,
                0.00029595709877115414,
                0.0015011821729778254,
                3.120191130543e-05,
                4.5397857772875786e-05,
                2.7535684530912436e-05,
                1.6701429801675944e-05,
                5.422219613511613e-06
            ],
            [
                1.067702742571918e-06,
                2.430023492769181e-05,
                9.610242586257082e-05,
                0.00010889688235826274,
                1.4738985481520185e-05,
                5.422218321855664e-06,
                0.00012339460363907555,
                3.1201900209877224e-05,
                8.315284239586281e-07,
                0.005220125887008106
            ],
            [
                8.939700565102295e-06,
                NaN,
                1.1478764018305152e-05,
                2.902311290840746e-06,
                1.6701417854810315e-05,
                1.9947292451455633e-06,
                1.300712380408432e-05,
                NaN,
                1.0129995807441742e-05,
                2.430023493485234e-05
            ],
            [
                8.939694167314623e-06,
                0.0005527785228264409,
                5.829127935151415e-05,
                6.962258737979408e-06,
                4.222831933480445e-06,
                1.4738976699427788e-05,
                0.00012339453076894396,
                NaN,
                5.144220132535887e-05,
                3.1201926201134365e-05
            ],
            [
                1.3007130012980722e-05,
                1.3007126911004571e-05,
                NaN,
                5.715003107208384e-07,
                NaN,
                7.889264465397747e-06,
                3.2887486728201357e-06,
                9.422445938111562e-07,
                NaN,
                2.260324567268294e-06
            ],
            [
                NaN,
                6.962255419380732e-06,
                0.0003799845472750953,
                2.1444950958338794e-05,
                4.5397879408714157e-05,
                3.120191506550783e-05,
                0.0035936021312253405,
                2.753568116675371e-05,
                NaN,
                2.753570094621784e-05
            ],
            [
                0.00012339454522734274,
                1.3007128461507534e-05,
                1.553497383907719e-06,
                3.2887486729876365e-06,
                6.144177528637686e-06,
                3.1201903930339314e-05,
                1.2098653947366327e-06,
                1.0129988563730593e-05,
                NaN,
                6.962254589433702e-06
            ],
            [
                2.144495863045236e-05,
                1.0677033790757595e-06,
                NaN,
                2.1444953520884646e-05,
                1.1478766755233466e-05,
                3.5356254916002164e-05,
                7.889263525103816e-06,
                NaN,
                1.4738983723664288e-05,
                7.484621820011444e-05
            ],
            [
                NaN,
                1.892514146884943e-05,
                2.1444956061196638e-05,
                0.37754067580180184,
                1.2098661159577745e-06,
                0.0001398220214632765,
                1.1478765388105516e-05,
                NaN,
                2.7535694379773952e-05,
                1.4738987240100149e-05
            ],
            [
                3.726640616477725e-06,
                1.6701423822135842e-05,
                1.3007133107008012e-05,
                3.726639726997871e-06,
                4.5397852403718694e-05,
                5.1442225855901594e-05,
                4.7850967757637256e-06,
                7.889265400267349e-06,
                2.1444956044501514e-05,
                4.006367778354606e-05
            ],
            [
                0.9999485578049403,
                0.9999687980855373,
                0.9998601778681911,
                0.9999785550523111,
                0.11920292671569666,
                NaN,
                0.9626731143960902,
                1.1478770850604989e-05,
                0.9669140216112959,
                0.999994577782371
            ],
            [
                6.144173868312501e-06,
                NaN,
                2.7535704218321328e-05,
                8.939694170518055e-06,
                3.288750630949526e-06,
                6.1441760661636525e-06,
                8.93969949923766e-06,
                1.300713466316634e-05,
                1.4738978449883382e-05,
                NaN
            ],
            [
                2.2603245670174926e-06,
                NaN,
                NaN,
                1.892514822620912e-05,
                NaN,
                8.93970056350871e-06,
                6.144176065314267e-06,
                6.144177529531776e-06,
                4.539787942093518e-05,
                6.605216041280767e-05
            ],
            [
                0.0005527787225608003,
                1.4738978451438343e-05,
                4.785092783149804e-06,
                4.222833947674739e-06,
                4.2228349539810764e-06,
                NaN,
                1.1478773596575768e-05,
                1.4738983725406915e-05,
                1.473897667637149e-05,
                3.5356242236570075e-05
            ],
            [
                5.144223204748698e-05,
                2.4300252296223892e-05,
                1.3007133105966991e-05,
                5.422220260044902e-06,
                1.3007126911974612e-05,
                9.61024252738697e-05,
                3.12019225102953e-05,
                3.535624648542694e-05,
                2.7535687763846918e-05,
                4.006370166036886e-05
            ],
            [
                2.902311292002183e-06,
                7.889265401214474e-06,
                6.144173131482228e-06,
                0.9991959139405335,
                6.96225956837018e-06,
                8.481102049531048e-05,
                1.6701423833436905e-05,
                NaN,
                1.3007134660350856e-05,
                4.222832940577472e-06
            ],
            [
                2.7535681242383173e-05,
                0.000911051223540661,
                1.1478772218923723e-05,
                7.889266345957247e-06,
                0.0006263341654692118,
                2.4300234919028452e-05,
                1.0129989766700635e-05,
                7.889262580217877e-06,
                5.144222562759555e-05,
                2.1444956072586775e-05
            ],
            [
                0.00015843619614288354,
                6.962257907348116e-06,
                2.90231198483099e-06,
                2.4300252288444548e-05,
                1.209865827507999e-06,
                4.006370165453905e-05,
                0.9999898700126484,
                0.9999599362887329,
                1.7603427931548347e-06,
                0.9996646500170352
            ],
            [
                3.288749065125496e-06,
                0.0009110510126729324,
                1.1478773598538445e-05,
                NaN,
                1.5534977544932838e-06,
                6.962258737650141e-06,
                3.1201918809808464e-05,
                0.00048785722121510354,
                6.144174601097106e-06,
                1.3007131564383116e-05
            ],
            [
                5.144221974927673e-05,
                1.0129992187105678e-05,
                1.3007133113372426e-05,
                8.939697368500698e-06,
                2.7535684530912436e-05,
                5.422218323093458e-06,
                2.753570419688461e-05,
                1.6701417859519093e-05,
                3.288749457383046e-06,
                6.144174601499446e-06
            ],
            [
                2.260323758746637e-06,
                4.222833947359807e-06,
                0.00010889693465105476,
                8.93969630362837e-06,
                4.785096775842062e-06,
                1.4738980213020151e-05,
                1.0129994595718555e-05,
                0.00015843616017739416,
                2.7535694377870696e-05,
                5.8291293323071325e-05
            ],
            [
                3.5356250691324983e-05,
                0.0005527785262030476,
                1.012998851324293e-05,
                1.8925145982866508e-05,
                0.1329642384799526,
                0.00017952796452762491,
                1.012998856312253e-05,
                4.222834451065997e-06,
                1.3007129999707728e-05,
                5.144221363404434e-05
            ],
            [
                7.484626278955236e-05,
                NaN,
                7.484626283311537e-05,
                0.00017952792285828674,
                1.6701419848961534e-05,
                1.0129995808418327e-05,
                2.7535704224732304e-05,
                1.8925143696838414e-05,
                6.9622562472889285e-06,
                6.144173135628569e-06
            ],
            [
                0.00010889694770880794,
                6.144172399826587e-06,
                3.1201911328358685e-05,
                0.002472623368543715,
                6.962256248871951e-06,
                1.3709567163017629e-06,
                2.1444945852673643e-05,
                6.605214464752619e-05,
                7.889264465842609e-06,
                0.00017952794317447138
            ],
            [
                0.20181322226037882,
                0.9991959138751074,
                8.939700557166892e-06,
                0.9984988174513274,
                0.14804720179063335,
                0.9997965729831141,
                9.610240323743297e-05,
                6.144174600862407e-06,
                4.7850933521167006e-06,
                0.9999038975513445
            ],
            [
                5.422220262195015e-06,
                4.5397852399094525e-05,
                0.00020342699216089865,
                0.00015843615796211209,
                1.8925145980732218e-05,
                2.753570418897106e-05,
                1.0129988561648438e-05,
                1.012999339449843e-05,
                0.00037998455585362294,
                0.00029595705973778385
            ],
            [
                1.1478768122695653e-05,
                6.144174600325954e-06,
                3.5356254892335935e-05,
                3.120190006197589e-05,
                1.9947299589504427e-06,
                1.6701417802315068e-05,
                8.939700566435704e-06,
                3.2887482798567817e-06,
                1.0129994599624903e-05,
                NaN
            ],
            [
                2.430024072285883e-05,
                0.00013982210583978112,
                6.1441767990323395e-06,
                5.1442207520496894e-05,
                1.3709567159027625e-06,
                3.726637951170554e-06,
                3.288749848276705e-06,
                4.4508505191686215e-07,
                6.605215227306636e-05,
                5.829127247176183e-05
            ],
            [
                5.144221962539264e-05,
                5.144222579414667e-05,
                NaN,
                NaN,
                5.8291251541153115e-05,
                4.006368740052914e-05,
                1.8925143694497584e-05,
                6.605215252536083e-05,
                1.0129988546999646e-05,
                NaN
            ],
            [
                1.892515049571424e-05,
                6.962253759752719e-06,
                2.5612825159421147e-06,
                7.889265403654039e-06,
                NaN,
                8.939696301611998e-06,
                6.962255416100709e-06,
                6.962258736902953e-06,
                1.147876538789672e-05,
                0.0009110510002751829
            ],
            [
                NaN,
                0.3208212943308302,
                NaN,
                0.9999930377429216,
                0.9999930377420924,
                NaN,
                0.9999974387187054,
                0.9999785550542851,
                0.9999995549149481,
                0.9999996072138934
            ],
            [
                NaN,
                2.144495096387783e-05,
                6.605216822432677e-05,
                5.1442219708855337e-05,
                NaN,
                NaN,
                2.7535691100158776e-05,
                5.144222590680261e-05,
                2.7535694370357833e-05,
                NaN
            ],
            [
                0.9399133536130195,
                0.9999989322970028,
                0.9999898700066091,
                1.0,
                0.9999996940976636,
                0.9999852610198027,
                NaN,
                0.9999938558275963,
                0.999925153763944,
                0.00017952794410956967
            ],
            [
                0.9999646437324962,
                0.9999852610172625,
                0.13296422989056966,
                0.999989870004213,
                NaN,
                0.9947798744998912,
                0.999820471975101,
                0.9999038975629633,
                NaN,
                0.43782349911420193
            ],
            [
                NaN,
                1.1478772227338172e-05,
                0.00010889690882234504,
                9.610239200387222e-05,
                5.829129318735924e-05,
                6.605212882650343e-05,
                1.012998856312253e-05,
                6.962254587597396e-06,
                3.535626333461766e-05,
                2.4300232029003796e-05
            ],
            [
                1.300712536258383e-05,
                3.059021539664509e-07,
                5.422218969532895e-06,
                2.102434161991657e-07,
                2.1024336607706996e-07,
                3.927861533982897e-07,
                2.430023199947767e-05,
                3.059021175109362e-07,
                2.3823699516792862e-07,
                2.1024341620509337e-07
            ],
            [
                3.2887490648622804e-06,
                0.00026119033751727965,
                1.8925145980732218e-05,
                1.6701425819447213e-05,
                2.2603240279591663e-06,
                1.0129993390942177e-05,
                5.8291286364010624e-05,
                2.4300249416363357e-05,
                NaN,
                NaN
            ],
            [
                1.4738978455701077e-05,
                4.7850939230116e-06,
                1.4738987239698005e-05,
                1.670142781560441e-05,
                4.7850967763512445e-06,
                NaN,
                NaN,
                6.962257079376403e-06,
                NaN,
                4.006370170788174e-05
            ],
            [
                2.144495347391985e-05,
                3.2887482788757045e-06,
                3.5356238017553724e-05,
                7.889264462728577e-06,
                2.430024939320213e-05,
                7.484626274326669e-05,
                1.892515725376564e-05,
                NaN,
                6.605216038349344e-05,
                3.535625068386498e-05
            ],
            [
                0.00037998452726590123,
                NaN,
                NaN,
                NaN,
                5.144222589744581e-05,
                NaN,
                0.0001584362541805322,
                NaN,
                NaN,
                3.288750241204353e-06
            ],
            [
                5.4222202614355715e-06,
                1.1478773598538445e-05,
                2.2603251051796405e-06,
                1.147877085766227e-05,
                0.00010889694713522379,
                1.4738983720179032e-05,
                0.0010322310628042525,
                0.00010889690904258862,
                0.00017952794031171238,
                1.1478772227338172e-05
            ],
            [
                7.338213303475785e-07,
                1.0129994602057158e-05,
                1.8925143722381014e-05,
                1.3007126911004571e-05,
                3.1201907586215615e-05,
                5.715007194755931e-07,
                9.610244890302106e-05,
                1.1478770859624945e-05,
                1.067703378997103e-06,
                9.610244901628662e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                1.3709573698296143e-06,
                2.7535684530912436e-05,
                3.288748672760313e-06,
                1.8925145974191664e-05,
                NaN,
                4.539789021507677e-05,
                1.3709573700615334e-06
            ],
            [
                0.00010889689606406436,
                NaN,
                4.785093923603471e-06,
                4.222831933864508e-06,
                1.2098658276598493e-06,
                1.1478764016780948e-05,
                1.892514371900746e-05,
                1.670142183983204e-05,
                NaN,
                4.222832940777184e-06
            ],
            [
                0.679178699175393,
                0.02931222894942822,
                0.9999885212337201,
                0.8670357683915538,
                0.5621765008857982,
                0.9998601779428534,
                1.3007130012010681e-05,
                0.9525741261492485,
                0.9999151889893352,
                0.9999038975839076
            ],
            [
                0.0002305068224853738,
                3.535626330593522e-05,
                1.670142382796865e-05,
                8.481104079680289e-05,
                8.481101093197769e-05,
                0.00023050679365832383,
                0.005220124513515329,
                1.670142183132586e-05,
                0.0003353501421062218,
                1.8925143715978147e-05
            ],
            [
                2.1444943298320236e-05,
                1.67014238321306e-05,
                4.539787402650773e-05,
                NaN,
                1.8925143724239906e-05,
                NaN,
                0.0,
                NaN,
                3.120190392534495e-05,
                NaN
            ],
            [
                2.2603237589028734e-06,
                NaN,
                NaN,
                1.1478770861859053e-05,
                8.939699500164542e-06,
                1.473898021151881e-05,
                1.0129990977262395e-05,
                0.00013982207320605572,
                4.222831933649433e-06,
                3.535624635037517e-05
            ],
            [
                5.422218322851817e-06,
                2.4300243624818735e-05,
                1.012998977022003e-05,
                0.0001398221402617477,
                4.785093353013212e-06,
                2.5612815998141903e-06,
                4.006370169826257e-05,
                2.561282210460501e-06,
                NaN,
                NaN
            ],
            [
                0.0010322309893376507,
                3.120190343339988e-05,
                8.939700562110258e-06,
                0.00010889693502657802,
                1.0129987351952995e-05,
                0.001926734297972867,
                0.0002034270692331628,
                0.00015843625137512127,
                3.726639727092773e-06,
                7.889265396651054e-06
            ],
            [
                6.9622545892184106e-06,
                4.006370648569653e-05,
                2.7535691083329963e-05,
                4.785095635296322e-06,
                1.1478773596283455e-05,
                1.6701423831188846e-05,
                0.0008040859436730437,
                4.539788482626311e-05,
                NaN,
                3.1201903922734266e-05
            ],
            [
                3.7266383952696564e-06,
                1.3007123810638006e-05,
                5.144221973168594e-05,
                6.962258738701267e-06,
                1.6701417845878833e-05,
                1.3007123806024402e-05,
                3.2887502412970765e-06,
                NaN,
                NaN,
                2.7535697602692443e-05
            ],
            [
                0.9999957771665571,
                0.914900945711678,
                0.9999945777797442,
                0.9999945777784512,
                0.9999962733598486,
                0.999998005269329,
                0.99999844650169,
                0.99999303774459,
                0.999996273361606,
                0.9999921107393004
            ]
        ]
    },
    {
        "q_id": "7738_mmlu_math",
        "cot_ids": [
            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,
            78,
            79,
            80,
            81,
            83,
            84,
            85,
            86,
            87,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            106,
            107,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.3007126906982452e-05,
                1.3007125352457558e-05,
                2.1444958623509054e-05,
                1.0129995809044816e-05,
                0.00010889688264030119,
                2.144495351940237e-05,
                5.829126545120912e-05,
                8.481108169906156e-05,
                4.00636825785559e-05,
                3.5356242266024216e-05
            ],
            [
                1.7603434229832599e-06,
                2.753569109454917e-05,
                3.2887478890769702e-06,
                5.4222202614355715e-06,
                8.939699500164542e-06,
                1.670142980608093e-05,
                1.14787681240737e-05,
                7.33820893021171e-07,
                1.0129988562164371e-05,
                7.88926258381982e-06
            ],
            [
                1.3709570433885908e-06,
                7.88926634687567e-06,
                6.1441746016670885e-06,
                1.3007133114011233e-05,
                4.22283344433731e-06,
                8.481103064050281e-05,
                7.889263525103816e-06,
                8.93969736942758e-06,
                1.8925152750176348e-05,
                7.889263525261671e-06
            ],
            [
                2.4300243621371074e-05,
                5.1442238133528324e-05,
                3.535625070624499e-05,
                3.535626755260807e-05,
                3.120191880504111e-05,
                1.0129994600859455e-05,
                1.6701421840804172e-05,
                7.484620938079124e-05,
                5.829127932776453e-05,
                3.120192623257619e-05
            ],
            [
                0.9999962733593835,
                0.999959936298269,
                0.9999994956527722,
                0.9999986290424664,
                0.9999991684716749,
                0.9999930377404314,
                0.999989870006606,
                0.9999945777784455,
                0.9999977396765105,
                0.9999974387174841
            ],
            [
                0.9999251537461851,
                0.9999417087276008,
                0.999985261011009,
                0.9999485577983244,
                0.9999417087275825,
                0.9046505280315008,
                0.9999921107383561,
                0.8807970811069351,
                0.9999810748562918,
                0.9999646437408679
            ],
            [
                8.939697366029015e-06,
                2.7535691064898404e-05,
                1.6701425820540864e-05,
                4.006369693910372e-05,
                3.120192621089609e-05,
                3.535625913039018e-05,
                2.4300246519706854e-05,
                3.5356254926549066e-05,
                6.9622562492265485e-06,
                4.006367783047594e-05
            ],
            [
                0.9995694429119992,
                0.9998766053958636,
                0.9999599363030484,
                0.9997388097846623,
                0.9998601778594941,
                0.9999687980812879,
                0.999933947831781,
                0.9999417087066884,
                0.9902915217635532,
                0.9999546021151565
            ],
            [
                1.2098652508056196e-06,
                1.7603440526806268e-06,
                1.0129995807165349e-05,
                2.2603253755949437e-06,
                1.0129993393319151e-05,
                1.2098662603862553e-06,
                6.144176066443055e-06,
                6.962253759043525e-06,
                3.2887494572095624e-06,
                4.785094494628999e-06
            ],
            [
                1.0129992185539456e-05,
                4.006368739659403e-05,
                6.605216827142175e-05,
                3.120190764467241e-05,
                3.120191135560069e-05,
                1.6701427812931038e-05,
                3.12019225291377e-05,
                2.1444945853375776e-05,
                3.5356250696598434e-05,
                4.5397884856980825e-05
            ],
            [
                0.999915188928435,
                0.9998601779093998,
                0.9999952149043647,
                0.9999646437619653,
                0.9998766054398833,
                0.9999339478632352,
                0.9999970976883609,
                0.9997965730521037,
                0.9997388095666206,
                0.9999485577924853
            ],
            [
                0.9999977396765108,
                0.9998601778761151,
                0.9999952149032237,
                0.9999945777829704,
                0.9999967112501507,
                0.999978555051593,
                0.9999910603015658,
                0.9999962733598278,
                0.9999967112517187,
                0.9999339478239488
            ],
            [
                8.481106143026193e-05,
                3.2887478891128633e-06,
                6.605213671058347e-05,
                1.4738978453743973e-05,
                1.892515274194901e-05,
                2.1444953522913026e-05,
                1.1478766754377407e-05,
                6.60521365707403e-05,
                5.14422381608502e-05,
                1.0129994600859455e-05
            ],
            [
                0.9999485577679709,
                0.9999724643187504,
                0.9999869928653333,
                0.9999852610127629,
                0.9999967112513267,
                0.999964643732439,
                0.9999724643187544,
                0.9999945777829697,
                0.9999885212305064,
                0.9999339478238656
            ],
            [
                0.9999810748562757,
                0.9999952149072167,
                0.9999832985741774,
                0.9999756997505811,
                0.9999921107383553,
                0.9998911030649195,
                0.9999938558268633,
                0.9999952149055056,
                0.9999980052693275,
                0.9999898700102323
            ],
            [
                0.9999938558268685,
                0.999985261014518,
                0.9999977396754328,
                0.9999945777790921,
                0.9999898700090224,
                0.9999930377437517,
                0.999996711252111,
                0.999985261023307,
                0.9999938558224687,
                0.9999974387187054
            ],
            [
                1.0129989768616954e-05,
                5.422220908314139e-06,
                5.422219616026655e-06,
                2.5612828213352452e-06,
                2.5612812945260317e-06,
                1.5534983100228109e-06,
                6.962255419380732e-06,
                3.726640172503764e-06,
                2.561282515783711e-06,
                4.22283394762097e-06
            ],
            [
                5.144223203551027e-05,
                2.4300237832303074e-05,
                4.539787943513799e-05,
                2.4300240727367308e-05,
                1.3007134665934505e-05,
                5.8291244625779683e-05,
                4.006367783499403e-05,
                3.535623805163821e-05,
                4.006370650464339e-05,
                2.4300234931404677e-05
            ],
            [
                3.535624648542694e-05,
                1.8925157262061825e-05,
                6.962258739271155e-06,
                6.9622562492265485e-06,
                1.1478765388523107e-05,
                4.785096205830278e-06,
                4.222832437639588e-06,
                1.3007128463352975e-05,
                6.14417313680765e-06,
                1.300713001414004e-05
            ],
            [
                0.00017952790114468135,
                0.00010889694801936731,
                0.00026119024507510687,
                9.610243762261058e-05,
                3.5356267560968415e-05,
                0.00017952798649721472,
                7.484620932198124e-05,
                0.00013982214056894142,
                0.0001233946327821131,
                0.0003353500657698044
            ],
            [
                0.9999980052693275,
                0.9999038976195121,
                0.9998766054694967,
                0.9999151889587602,
                0.999985261016273,
                0.9999810748427375,
                0.9999485577679806,
                0.9999832985721876,
                0.9999970976880149,
                0.9998766054107439
            ],
            [
                0.9999930377462422,
                0.9999910603047624,
                0.9999832985701939,
                0.9999938558232009,
                0.9999930377412611,
                0.9999756997621777,
                0.9999977396751633,
                0.9999810748562817,
                0.9999898700090211,
                0.999995777168066
            ],
            [
                0.9999921107374157,
                0.9999990577549568,
                0.9999957771665556,
                0.9999974387177893,
                0.999994577778445,
                0.9999885212318759,
                0.9999910603015656,
                0.9999957771655494,
                0.9999957771655492,
                0.9999785550413847
            ],
            [
                5.8291272451829125e-05,
                1.473897670007122e-05,
                7.889266345957247e-06,
                5.829127930231852e-05,
                4.006368262694324e-05,
                3.120190020068305e-05,
                1.892514822937613e-05,
                1.1478765386623071e-05,
                6.605216827622735e-05,
                5.8291244647832884e-05
            ],
            [
                0.9999687980737645,
                0.9999938558224717,
                0.9999898700067268,
                0.9999852610180329,
                0.9999938558253988,
                0.999995777166054,
                0.9999687980998254,
                0.9998911031168733,
                0.7772998663336158,
                0.9999546021476109
            ],
            [
                0.00010889690871143104,
                1.8925143719695944e-05,
                9.610240307522556e-05,
                0.0001795279419154843,
                5.144223815748175e-05,
                3.120191507481552e-05,
                7.484622717680992e-05,
                5.144223811144626e-05,
                5.422218969217281e-06,
                3.1201922498830954e-05
            ],
            [
                1.67014238321306e-05,
                5.14422258772351e-05,
                4.006369690499937e-05,
                3.120191879981973e-05,
                3.1201911312013484e-05,
                4.0063711256516126e-05,
                1.4738987240824012e-05,
                1.4738987237553233e-05,
                2.144495863201265e-05,
                2.7535694373763664e-05
            ],
            [
                1.6701417858577338e-05,
                2.4300234211462125e-05,
                7.338211554641698e-07,
                1.6701429805655623e-05,
                3.12019262340518e-05,
                3.1201926246083686e-05,
                1.3007125360478133e-05,
                2.430023781683279e-05,
                0.00010889686979329236,
                2.1444953517842076e-05
            ],
            [
                0.9999930377462404,
                0.9999646437408634,
                0.9999151889890187,
                0.9999930377404309,
                0.9998601778762433,
                0.9999938558224688,
                0.9999485577986492,
                0.99987660541069,
                0.9999756997563805,
                0.9999938558232014
            ],
            [
                0.9997965730277694,
                0.9999898700114378,
                0.9999952149049351,
                0.9998766054254141,
                0.9999910603036986,
                0.999954602115206,
                0.999941708748413,
                0.999972464302351,
                0.9998204719484768,
                0.9999646437619434
            ],
            [
                0.9999952149055061,
                0.9998766054108534,
                0.9999957771650453,
                0.9999910603036963,
                0.9999967112493665,
                0.9999962733616204,
                0.9999921107355341,
                0.9999852610127585,
                0.9997965730032546,
                0.9997040430072724
            ],
            [
                1.760344052693435e-06,
                7.33821067986608e-07,
                2.561281294644835e-06,
                1.994730434798734e-06,
                3.726640616670918e-06,
                1.9947301970451086e-06,
                9.422448185187191e-07,
                5.422220262195015e-06,
                2.5612822106421996e-06,
                4.222833947774596e-06
            ],
            [
                0.9999930377412611,
                0.9999967112513268,
                0.9999646437577359,
                0.9999967112501507,
                0.9999885212277717,
                0.9999945777790911,
                0.9999957771650454,
                0.9999869928684365,
                0.9999898700114368,
                0.9999977396754329
            ],
            [
                0.9999885212264018,
                0.9999885212332488,
                0.9999898700041909,
                0.999989870012645,
                0.9999910603026323,
                0.9999599363078385,
                0.9998601778592866,
                0.9998601779764698,
                0.9999832985761721,
                0.9999957771680661
            ],
            [
                4.006368256747928e-05,
                3.53562591336057e-05,
                2.4300243627117176e-05,
                6.605216039358521e-05,
                2.7535681227157105e-05,
                3.120192251903545e-05,
                2.7535704212311033e-05,
                4.539787939285985e-05,
                6.605212100874168e-05,
                3.12019225291377e-05
            ],
            [
                0.9999687980811913,
                0.9999910603036967,
                0.999992110736474,
                0.9999724643056221,
                0.9999869928699852,
                0.9999910602994334,
                0.9999938558261307,
                0.9999785550490333,
                0.9999417087414205,
                0.9999869928761876
            ],
            [
                1.3007123810306773e-05,
                7.88926164421493e-06,
                2.7535681197606525e-05,
                2.1444948411552198e-05,
                2.1444956059090247e-05,
                4.539788486688977e-05,
                1.4738987237553233e-05,
                3.5356267541418054e-05,
                7.48462089440725e-05,
                2.4300232029003796e-05
            ],
            [
                0.9999151889687937,
                0.9997040427964424,
                0.9999417087136521,
                0.9999938558224694,
                0.9999852610233051,
                0.9999921107355344,
                0.9999687980886623,
                0.999994577781677,
                0.999964643757729,
                0.9999724643023485
            ],
            [
                0.00010889692211618359,
                1.300712846217e-05,
                4.006369218184011e-05,
                3.1201922520397544e-05,
                4.006367784140681e-05,
                1.4738978454950406e-05,
                2.144494074201677e-05,
                7.484620035127781e-05,
                4.5397874029150114e-05,
                1.670142582102693e-05
            ],
            [
                0.9999945777790916,
                0.999997097687323,
                0.9999898700114365,
                0.9999987901337398,
                0.9999996072136592,
                0.9999967112509347,
                0.9999984465016899,
                0.9999967112517191,
                0.9999986290424664,
                0.9999984465022456
            ],
            [
                0.9999910602994357,
                0.9999962733611605,
                0.9999910602994342,
                0.9999952149060761,
                0.999986992869988,
                0.9999977396765105,
                0.9999957771655501,
                0.9999038975393251,
                0.9999852610197881,
                0.9998911031300071
            ],
            [
                1.6701427812931038e-05,
                3.535626333461766e-05,
                8.93969630348202e-06,
                6.144176798870286e-06,
                1.892515500388139e-05,
                3.5356246473207964e-05,
                2.7535704222728874e-05,
                1.8925143721761383e-05,
                8.939694171135975e-06,
                5.144222586301276e-05
            ],
            [
                0.00010889690909804562,
                2.144495350169305e-05,
                2.4300252313904224e-05,
                4.0063711256516126e-05,
                1.3007128460040644e-05,
                2.7535697639856078e-05,
                2.7535691098355687e-05,
                2.144494073569759e-05,
                1.6701427808495672e-05,
                7.889264465986113e-06
            ],
            [
                4.785095064436034e-06,
                1.4738988996240646e-05,
                4.785096205434246e-06,
                1.892514822937613e-05,
                3.120190765193695e-05,
                1.1478770858706246e-05,
                5.82912446122085e-05,
                8.315279285205827e-07,
                1.4738981969615573e-05,
                1.1478766757049986e-05
            ],
            [
                9.610241490168368e-05,
                4.006370172507966e-05,
                7.484620037305929e-05,
                6.605217612907568e-05,
                0.0006263340151035854,
                0.0001233945745678611,
                9.61024148597335e-05,
                3.535625492063251e-05,
                3.120191879561992e-05,
                4.7850933534310035e-06
            ],
            [
                0.9999599362982922,
                0.9999546021313719,
                0.9999151889384377,
                0.9991959141493452,
                0.9999852610145198,
                0.9995694429124753,
                0.9998601778596466,
                0.9998766054252598,
                0.990291523214092,
                0.9999038975621809
            ],
            [
                0.9999869928699862,
                0.9999810748449934,
                0.9999885212291382,
                0.9999832985701924,
                0.9999810748517602,
                0.9999898700090254,
                0.9999885212264015,
                0.9999910603026316,
                0.9999785550439251,
                0.9999869928761908
            ],
            [
                9.610238044449971e-05,
                3.2887478890769702e-06,
                5.144221363404434e-05,
                5.8291265441454815e-05,
                3.53562591107112e-05,
                5.829124455283451e-05,
                7.484623606311329e-05,
                1.0677033790757595e-06,
                7.484624478551196e-05,
                5.1442213649389494e-05
            ],
            [
                NaN,
                0.9999038975740436,
                0.9999885212291552,
                0.8175744695262777,
                0.9999974387187104,
                0.9999599362982425,
                0.5621765008857981,
                0.9999151889688017,
                0.9999974387180949,
                0.5926665999540698
            ],
            [
                0.9999970976883608,
                0.999954602142192,
                0.999978555043919,
                0.9999687980774769,
                0.99997246431547,
                0.9999785550413615,
                0.999954602115126,
                0.9999869928746379,
                0.9999885212277696,
                0.9999898700114366
            ],
            [
                1.8925152747388e-05,
                1.1478764019077695e-05,
                8.939693105662367e-06,
                4.0063696945516495e-05,
                9.610244921065592e-05,
                4.785092782597101e-06,
                4.5397852399094525e-05,
                6.962254589705982e-06,
                7.88926164421493e-06,
                1.1478769492141554e-05
            ],
            [
                0.9999977396762411,
                0.9999962733593832,
                0.9999885212332451,
                0.9999967112521111,
                0.9999417087344882,
                0.9999898700066098,
                0.9999810748540193,
                0.9995694428722811,
                0.9999910603068943,
                0.9999785550464846
            ],
            [
                2.7535687790192025e-05,
                2.7535691088138193e-05,
                8.481106151541198e-05,
                6.605212080450339e-05,
                2.430023782010365e-05,
                1.67014218359435e-05,
                4.0063682603624035e-05,
                2.753570092878799e-05,
                4.006369694755693e-05,
                6.605215243885987e-05
            ],
            [
                1.0677028699625768e-06,
                8.315278293899016e-07,
                1.1478773598538445e-05,
                4.785093924047376e-06,
                7.889265406567165e-06,
                4.78509506425325e-06,
                2.2603245673155757e-06,
                6.9622570786798724e-06,
                2.561283431916622e-06,
                9.422449308566668e-07
            ],
            [
                0.00017952798707185626,
                4.006368263437623e-05,
                5.1442238137271045e-05,
                5.144219525129858e-05,
                6.605212887648175e-05,
                8.481108177187105e-05,
                8.48110413379375e-05,
                3.535625913810743e-05,
                0.0002034269236568478,
                7.484621827634963e-05
            ],
            [
                0.9999938558275957,
                0.9999417087136521,
                0.9999810748562732,
                0.9999952149043645,
                0.9999724643187533,
                0.9998766054252419,
                0.9999339478553472,
                0.9999938558246663,
                0.9999910603005011,
                0.9999869928699859
            ],
            [
                0.9999967112513268,
                0.9999957771645427,
                0.9999921107355378,
                0.9999962733589389,
                0.9999962733593838,
                0.9999898700053983,
                0.9999898700078138,
                0.9999938558224697,
                0.9999982396565769,
                0.9998766053665393
            ],
            [
                0.9992903294528732,
                0.970687766174766,
                0.9999885212318821,
                0.9999724643121848,
                0.9999599362982748,
                0.9999921107364741,
                0.7057850216484838,
                0.9999852610180293,
                0.9999646437411186,
                0.9997965730755767
            ],
            [
                5.144222588097783e-05,
                1.1478769492392108e-05,
                1.892514147046736e-05,
                2.144495862967221e-05,
                2.4300232030064617e-05,
                4.006370172507966e-05,
                1.8925157257965367e-05,
                1.8925143725341476e-05,
                1.4738981969240237e-05,
                6.605216029362855e-05
            ],
            [
                0.9999910603026306,
                0.9999921107383558,
                0.9999646437450873,
                0.999998239656577,
                0.9999910603058276,
                0.9999852610180284,
                0.9999930377454113,
                0.9999546021476804,
                0.9999785550439266,
                0.9999957771645419
            ],
            [
                0.9999921107355337,
                0.9999485577802218,
                0.9999417087205764,
                0.9999038975736347,
                0.9999977396751633,
                0.9999957771670589,
                0.999933947863225,
                0.9999910603047619,
                0.9999832985741748,
                0.9999910603026306
            ],
            [
                0.9999967112493664,
                0.9999832985821387,
                0.999991060305828,
                0.9999957771680659,
                0.9999724642957742,
                0.9999832985761679,
                0.9999930377404306,
                0.9999957771645421,
                0.9999938558253987,
                0.999992110735632
            ],
            [
                2.7535704221626983e-05,
                3.120192251903545e-05,
                2.1444948402034417e-05,
                3.120190392534495e-05,
                3.5356267560968415e-05,
                1.8925148232956223e-05,
                1.0129994600638342e-05,
                8.93969630362837e-06,
                1.5534979396815448e-06,
                1.3007133115667397e-05
            ],
            [
                0.9999785550541467,
                0.9999952149043647,
                0.9999974387180947,
                0.9999921107374152,
                0.9999921107345933,
                0.9999977396751633,
                0.9999957771680659,
                0.9999945777823235,
                0.999992110737415,
                0.999995214904935
            ],
            [
                0.999860177909463,
                0.9999038976196813,
                0.9998601778762881,
                0.9999417087067817,
                0.9998204720563633,
                0.9999810748427624,
                0.9999546021476186,
                0.999986992866892,
                0.9999756997592761,
                0.999968798081217
            ],
            [
                0.9999885212346126,
                0.9999869928730863,
                0.9999885212305117,
                0.9999952149055052,
                0.9999930377437507,
                0.9999832985741757,
                0.9999646437366521,
                0.999986992869987,
                0.9999038975392935,
                0.9999646437577393
            ],
            [
                0.9999832985741761,
                0.9999485577680656,
                0.9999921107336551,
                0.9999646437324458,
                0.9995694428673961,
                0.9999599363078501,
                0.9999339478711289,
                0.9998766053960935,
                0.999620015519905,
                0.9995694428679973
            ],
            [
                0.9999921107364745,
                0.9998204720991113,
                0.9999898700078145,
                0.9999785550439207,
                0.9999970976890531,
                0.9999810748472526,
                0.9999756997621748,
                0.9999938558275967,
                0.9999810748472566,
                0.9999898700078336
            ],
            [
                1.8925152751174644e-05,
                6.475950297768503e-07,
                1.7603436329554703e-06,
                1.670141786036971e-05,
                1.9947299591354906e-06,
                1.8925141468298646e-05,
                1.0129995805027913e-05,
                3.2887494573232236e-06,
                7.889266347133978e-06,
                8.939693104410264e-06
            ],
            [
                0.9999938558268633,
                0.9999885212318768,
                0.9999945777816771,
                0.999985261011,
                0.9999869928746385,
                0.9999785550567081,
                0.9999756997563805,
                0.9999952149032237,
                0.9999151889587774,
                0.9999724643154878
            ],
            [
                1.670142980687079e-05,
                8.939697369151141e-06,
                5.829129329974581e-05,
                2.7535704226635563e-05,
                1.4738980213985297e-05,
                5.829127244377123e-05,
                1.473898899846585e-05,
                4.785093352482268e-06,
                0.00010889687021476549,
                3.120192252175965e-05
            ],
            [
                0.0002305067971996644,
                0.0001584361784321496,
                5.8291286355952725e-05,
                0.00015843625383705955,
                1.892515725920463e-05,
                0.0002959570637849233,
                0.00010889693506777467,
                0.0001233946333728019,
                4.0063687392367425e-05,
                1.8925152747938785e-05
            ],
            [
                1.9947306726049992e-06,
                3.7266388396128453e-06,
                2.4300246521474893e-05,
                4.785096775676685e-06,
                6.475945665741875e-07,
                4.222834954607099e-06,
                8.93969630317306e-06,
                6.1441746016670885e-06,
                6.962257079173776e-06,
                3.288749849368453e-06
            ],
            [
                1.8925152744771773e-05,
                1.6701425824307884e-05,
                8.939693106329072e-06,
                4.785093923847183e-06,
                1.3007131563507714e-05,
                1.6701423834591316e-05,
                1.6701429805199933e-05,
                8.93969523617066e-06,
                1.300712846217e-05,
                1.4738985482351282e-05
            ],
            [
                0.9999852610127595,
                0.9999967112517189,
                0.9999687980811913,
                0.9999930377420906,
                0.9999982396563669,
                0.9999962733616045,
                0.9999977396765105,
                0.9999952149060758,
                0.9999921107402361,
                0.9999987901344607
            ],
            [
                0.9999687980886445,
                0.9999921107355343,
                0.9999832985721853,
                0.9999885212264018,
                0.9999977396751636,
                0.9999898700041918,
                0.9999898700090238,
                0.9999930377412606,
                0.9999957771665562,
                0.9999724643023389
            ],
            [
                8.939693106020111e-06,
                4.539788486688977e-05,
                3.2887490653109436e-06,
                5.8291258498513246e-05,
                2.561283431916622e-06,
                4.5397879448184774e-05,
                4.5397868612593344e-05,
                5.422220203431812e-06,
                4.222832927742094e-06,
                6.14417679836736e-06
            ],
            [
                4.539785230182181e-05,
                5.144221359998557e-05,
                4.0063692140011286e-05,
                3.1201915053248934e-05,
                4.006367783499403e-05,
                0.00023050674002848438,
                0.00010889690895702637,
                5.8291258432353643e-05,
                3.1201900190126774e-05,
                0.00012339457438472975
            ],
            [
                0.9999898700128912,
                0.9999957771680721,
                0.9999151889688264,
                0.46879062662624377,
                0.9999982396574172,
                0.9999724643056274,
                0.9999832985702075,
                0.9999485578047487,
                0.9999898700078143,
                0.9706877687186648
            ],
            [
                0.999985261016273,
                0.9999938558261309,
                0.9999417087484541,
                0.9999810748562722,
                0.9999756997476807,
                0.9999974387171787,
                0.9999869928715404,
                0.9999970976883612,
                0.9999810748495105,
                0.9999832985761714
            ],
            [
                4.539786862811735e-05,
                2.1444953523537147e-05,
                2.1444950962395557e-05,
                6.962256248871951e-06,
                3.5356267560968415e-05,
                7.484620029028967e-05,
                4.006368259400487e-05,
                2.4300234924597754e-05,
                7.889263525261671e-06,
                1.147877086020957e-05
            ],
            [
                0.9940889320412577,
                0.9999417087078335,
                0.9992903295537588,
                0.9986749775407316,
                0.9995694429651699,
                0.9998415638022435,
                0.9999962733611738,
                0.9999151889891383,
                0.9997040429012288,
                0.9993736658305958
            ],
            [
                6.144176798870286e-06,
                4.22283394786293e-06,
                1.3007123811797321e-05,
                2.902312330891746e-06,
                2.4300243622255085e-05,
                2.7535697649071857e-05,
                1.0677032518578904e-06,
                1.4738985484549675e-05,
                1.9947304345919157e-06,
                7.889265406438011e-06
            ],
            [
                8.481102112097796e-05,
                4.0063696957321844e-05,
                3.12019150894581e-05,
                4.0063687374440786e-05,
                6.605216823009351e-05,
                0.00012339461863071857,
                5.829127247557873e-05,
                3.1201915085825835e-05,
                0.00010889688297145868,
                5.14422075117015e-05
            ],
            [
                6.9622562484666964e-06,
                2.5612831265909735e-06,
                1.5534975693488444e-06,
                3.9278634072866033e-07,
                1.7603430033158905e-06,
                1.2098659719232413e-06,
                1.553498310118888e-06,
                4.7850967763512445e-06,
                2.2603240281606297e-06,
                8.939695237959376e-06
            ],
            [
                0.9999852610180312,
                0.9999921107336541,
                0.9999910603047643,
                0.9999852610110042,
                0.9999898700090217,
                0.9999957771675626,
                0.9998204719918179,
                0.9999898700041914,
                0.9999038975737075,
                0.999997097688707
            ],
            [
                4.539787942093518e-05,
                1.892514823013346e-05,
                2.1444948410303962e-05,
                1.473898899908247e-05,
                4.222835457852533e-06,
                6.962254588116627e-06,
                1.8925145980181433e-05,
                3.120190019932095e-05,
                2.1444945846588504e-05,
                1.1478764017720528e-05
            ],
            [
                2.4300234928664224e-05,
                2.9023133689924295e-06,
                1.670142781432848e-05,
                1.892515048449202e-05,
                NaN,
                1.3007130013856124e-05,
                8.939698435096828e-06,
                1.670142980608093e-05,
                1.8925141463066202e-05,
                2.1444948395559206e-05
            ],
            [
                0.9998911030388833,
                0.999959936298299,
                0.9999151889789943,
                0.9996200154255522,
                0.9999756997563768,
                0.9669140251866017,
                0.9999485577924913,
                0.9999885212291578,
                0.9999938558239365,
                0.9999785550490354
            ],
            [
                0.9999687980812089,
                0.9999957771655489,
                0.9999485577986323,
                0.9999687980886359,
                0.99995993629351,
                0.9989677692054928,
                0.9999921107392962,
                0.9998415637271959,
                0.9999810748562817,
                0.999981074854021
            ],
            [
                0.9997388095995501,
                0.9999687980774927,
                0.9999885212291382,
                0.9999832985701952,
                0.9999852610110004,
                0.9998415638401661,
                0.9999687980811924,
                0.9998911031168733,
                0.9999599362983116,
                0.9999599363221485
            ],
            [
                7.889259763469998e-06,
                2.5612812946890944e-06,
                1.7603438425882895e-06,
                8.93969736942758e-06,
                4.785096205882502e-06,
                1.3709575336947905e-06,
                1.5534971989809095e-06,
                2.561281294644835e-06,
                6.962254589617333e-06,
                1.0677028700203557e-06
            ],
            [
                1.012998856312253e-05,
                1.0129988562164371e-05,
                3.2887482811220126e-06,
                2.7535691076718644e-05,
                1.4738978456719842e-05,
                1.4738985483879434e-05,
                1.1478773595009805e-05,
                6.144175332596544e-06,
                3.7266401722360055e-06,
                8.939695237813028e-06
            ],
            [
                0.9999832985821452,
                0.9999756997505845,
                0.9999898700041923,
                0.9999967112509348,
                0.9999646437324528,
                0.9999646437493104,
                0.999995777166556,
                0.9999869928684358,
                0.9999974387165718,
                0.9999980052700408
            ],
            [
                0.9999251537638694,
                0.9999646437408763,
                0.999983298578157,
                0.9999251537817176,
                0.9999810748450062,
                0.9999785550413688,
                0.9999646437408746,
                0.9999485578047843,
                0.9999756997534849,
                0.9998415638401131
            ],
            [
                0.9999952149072172,
                0.9999982396565769,
                0.9999980052705164,
                0.9999898700102283,
                0.9999938558246665,
                0.9999957771675627,
                0.999978555056705,
                0.9999974387184,
                0.9999957771655491,
                0.9999962733616047
            ],
            [
                2.561283024767623e-06,
                3.288748280449018e-06,
                1.14787708580381e-05,
                1.3007133114011233e-05,
                4.539787401263522e-05,
                4.006371125185228e-05,
                2.7535691078121046e-05,
                5.144220744171262e-05,
                5.422217676397663e-06,
                3.120191136263821e-05
            ],
            [
                4.006367780569929e-05,
                0.0001795279011812494,
                4.539787938922657e-05,
                0.00010889692187534167,
                4.006368257593249e-05,
                5.8291272264376885e-05,
                1.8925150493717652e-05,
                3.120190019784534e-05,
                4.5397868604005595e-05,
                4.0063682625048554e-05
            ],
            [
                0.9999724643023361,
                0.9999898700114368,
                0.9999810748427375,
                0.9999546021151405,
                0.9999974387168734,
                0.999991060306894,
                0.999995777165549,
                0.9999546021313743,
                0.9999974387171787,
                0.9999910602994342
            ],
            [
                0.9999974387187057,
                0.9999910603048999,
                0.9999852610198664,
                0.9999151889890027,
                0.9999952149055086,
                0.817574471748733,
                0.9999546021476133,
                0.9999687980997889,
                0.999978555041372,
                0.9999957771675624
            ],
            [
                0.9999885212277709,
                0.9999967112505427,
                0.9999910603005002,
                0.9999921107336531,
                0.9999832985781587,
                0.9999957771660526,
                0.9999977396754327,
                0.9999921107364752,
                0.9999898700078153,
                0.999995214904935
            ],
            [
                1.1478764014985311e-05,
                3.7266383954560706e-06,
                5.715003107655392e-07,
                2.9023126769762986e-06,
                2.561282210590951e-06,
                3.2887482811579057e-06,
                1.3709570433885908e-06,
                1.5534973841309562e-06,
                5.422220261652556e-06,
                4.222835458044565e-06
            ],
            [
                0.9999599362982898,
                0.9999785550490354,
                0.9999810748495047,
                0.9999251537462013,
                0.9999898700078131,
                0.8807970811069351,
                0.8354835411997897,
                0.9999599363078259,
                0.999925153756052,
                0.9999885212346133
            ],
            [
                8.939700565834043e-06,
                6.962257907702715e-06,
                6.475946437928669e-07,
                8.315284241333265e-07,
                3.5356238024242e-05,
                1.0129990979031306e-05,
                5.829128585848319e-05,
                1.6701423833011596e-05,
                1.0129987355785634e-05,
                1.3007123807727885e-05
            ],
            [
                0.999941708727552,
                0.999992110734595,
                0.9999810748472552,
                0.9999910603015654,
                0.9999869928684546,
                0.9999756997505913,
                0.9998766054253101,
                0.9999910603058275,
                0.9999417087206214,
                0.9999687980886521
            ],
            [
                1.6701419852819694e-05,
                1.4738981969240237e-05,
                4.5397852346412016e-05,
                3.927861985151548e-07,
                7.484620016504614e-05,
                2.1444945853999886e-05,
                6.962257909007124e-06,
                2.4300246521474893e-05,
                4.539788481998745e-05,
                2.1444943284979742e-05
            ],
            [
                1.4738983724575818e-05,
                5.8291286317783706e-05,
                2.753569764776963e-05,
                5.829127942361117e-05,
                1.4738983726559732e-05,
                5.829128634365382e-05,
                2.7535687799708318e-05,
                1.8925141465820123e-05,
                3.12019187926687e-05,
                4.5397857748103446e-05
            ],
            [
                0.9999957771670602,
                0.9999921107392964,
                0.9999957771665566,
                0.9999910603015675,
                0.9999546021476212,
                0.9999785550439356,
                0.9999756997592791,
                0.9999546021205975,
                0.999903897585194,
                0.9999970976890531
            ],
            [
                6.144176798870286e-06,
                2.75357042110088e-05,
                6.144172403470001e-06,
                4.78509506499309e-06,
                8.939699497042417e-06,
                6.962253759043525e-06,
                4.222832941072913e-06,
                5.422217030362759e-06,
                5.422217676797111e-06,
                1.0129994598482479e-05
            ],
            [
                0.9999251537909971,
                0.7772998663336157,
                0.9999898700069255,
                0.9999910603026834,
                0.8670357546485407,
                0.9999646437454593,
                0.6224593312018546,
                0.9999832985761674,
                0.46879062662624377,
                0.914900952092573
            ],
            [
                0.9999989322971299,
                0.9999982396561572,
                0.9999898700102287,
                0.9999921107345929,
                0.9999852610162717,
                0.9999921107355338,
                0.9999869928715369,
                0.9999938558232019,
                0.9999938558268631,
                0.9999599363126054
            ],
            [
                0.9999599363221565,
                0.9999921107392965,
                0.9999957771680659,
                0.9399133510883347,
                0.9999869928653348,
                0.9999952149055056,
                0.9999945777784478,
                0.9999885212346133,
                0.999996273358939,
                0.9999938558275966
            ],
            [
                0.9999646437577242,
                0.952574131703022,
                0.9999785550515903,
                0.9999251537370629,
                0.9997965730268371,
                0.9999339478474997,
                0.9999869928746399,
                0.9999852610110022,
                0.9999898700069232,
                0.7772998560157665
            ],
            [
                4.7850944943330625e-06,
                1.3709567165087443e-06,
                4.222834451254188e-06,
                4.785096775842062e-06,
                8.315282258756395e-07,
                1.473898372275276e-05,
                8.315279284937352e-07,
                7.889265406681968e-06,
                7.889261644358435e-06,
                1.0129990979215566e-05
            ],
            [
                4.006368258380272e-05,
                2.7535694365549603e-05,
                4.785093923603471e-06,
                4.0063682603624035e-05,
                2.902312676941983e-06,
                1.892514597832254e-05,
                1.147877222485351e-05,
                3.535625912717466e-05,
                2.430023203572232e-05,
                2.1444940731484803e-05
            ],
            [
                5.422217030288788e-06,
                1.4738980214280206e-05,
                1.6701421833391647e-05,
                1.6701425823882575e-05,
                1.0129990979215566e-05,
                1.1478772229050293e-05,
                1.6701423833011596e-05,
                1.4738987241172537e-05,
                1.3007126911974612e-05,
                1.4738978450419574e-05
            ],
            [
                5.829127939137956e-05,
                2.4300243622255085e-05,
                0.00012339457430752727,
                1.1478769493916314e-05,
                7.484626281133387e-05,
                2.144494329348333e-05,
                7.484620044058188e-05,
                8.939700566565793e-06,
                1.4738987241172537e-05,
                7.88926540679677e-06
            ],
            [
                0.9999910603026316,
                0.9999151889891291,
                0.999876605439966,
                0.9999852610233023,
                0.9999785550490341,
                0.9999339478475789,
                0.9999151889182362,
                0.9999546021367908,
                0.999992110733653,
                0.9999952149043647
            ],
            [
                2.7535684468004752e-05,
                4.006369216143581e-05,
                3.120190388993035e-05,
                0.00015843627322597727,
                5.144221967591938e-05,
                2.1444958635523312e-05,
                7.889260703619978e-06,
                1.8925150491445666e-05,
                6.962257909501028e-06,
                3.5356246453014516e-05
            ],
            [
                1.473897845457507e-05,
                4.0063696951637786e-05,
                3.1201911358551906e-05,
                5.144220134032976e-05,
                9.61023803298359e-05,
                3.5356246487099006e-05,
                8.939700566435704e-06,
                1.670142183934597e-05,
                2.7535691095550887e-05,
                1.3007134663521234e-05
            ],
            [
                0.9999921107402369,
                0.9999967112513267,
                0.9999885212291382,
                0.9999938558253981,
                0.9999921107402363,
                0.9999646437619613,
                0.9999938558261308,
                0.9999938558261307,
                0.9999724643154788,
                0.9999417087553356
            ],
            [
                0.9999485577679982,
                0.9999785550439266,
                0.9999646437408798,
                0.9999921107336541,
                0.9999852610162773,
                0.9998911030389894,
                0.9999898700090223,
                0.9999151889487902,
                0.9999646437577489,
                0.9999646437410313
            ]
        ]
    },
    {
        "q_id": "9014_mmlu_math",
        "cot_ids": [
            0,
            2,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            13,
            14,
            15,
            17,
            18,
            19,
            21,
            22,
            23,
            26,
            27,
            29,
            30,
            31,
            32,
            34,
            36,
            38,
            39,
            43,
            44,
            47,
            48,
            53,
            61,
            63,
            64,
            67,
            72,
            73,
            75,
            76,
            77,
            78,
            79,
            81,
            82,
            85,
            86,
            87,
            88,
            93,
            96,
            99,
            101,
            104,
            109,
            110,
            112,
            114,
            116,
            117,
            119,
            121,
            122,
            123,
            127
        ],
        "rewards": [
            [
                1.3709568799592562e-06,
                4.2228349547223175e-06,
                1.9947294836483373e-06,
                6.1441767989541075e-06,
                1.6701425825857226e-05,
                1.8925150497435443e-05,
                1.0677031245905116e-06,
                1.8925143728301937e-05,
                6.962259568509485e-06,
                3.726640616748873e-06
            ],
            [
                7.8892654060075e-06,
                1.0129988564264954e-05,
                2.2603248367358324e-06,
                7.484621830139833e-05,
                6.962254589528684e-06,
                3.1201922525618933e-05,
                2.4300246526646385e-05,
                4.539785237052376e-05,
                1.8925148232956223e-05,
                2.1444950968441685e-05
            ],
            [
                3.288748673319648e-06,
                1.1478772230762415e-05,
                5.422220908876325e-06,
                6.144173869379821e-06,
                1.5534971989696065e-06,
                1.4738988999940381e-05,
                2.144495096161541e-05,
                2.561281599914358e-06,
                6.144173869446876e-06,
                6.962259569117366e-06
            ],
            [
                5.144223817619536e-05,
                2.4300232041998833e-05,
                5.422218323349895e-06,
                8.939695237959376e-06,
                1.3007134665934505e-05,
                5.422219616140078e-06,
                1.01299946023704e-05,
                6.962256249429175e-06,
                3.72664017246987e-06,
                4.5397857817300854e-05
            ],
            [
                1.1478764020560142e-05,
                6.962257909323729e-06,
                1.89251482406672e-05,
                4.7850933535006355e-06,
                6.144172404129392e-06,
                4.785092783210732e-06,
                6.144173868558375e-06,
                2.144495863614743e-05,
                3.5356267555952205e-05,
                1.994729721436347e-06
            ],
            [
                2.75356976629957e-05,
                6.144175334239434e-06,
                6.47594643784032e-07,
                3.7266397280485686e-06,
                1.3007125356952865e-05,
                3.2887502414436403e-06,
                1.0129990979694647e-05,
                2.260323489410794e-06,
                4.222834954561012e-06,
                3.7266379513162962e-06
            ],
            [
                4.0063677818524845e-05,
                0.0001233945895289787,
                0.00026119021519328036,
                0.0002034269245121864,
                6.605217607477225e-05,
                0.0002034269972307794,
                0.0005527786456706206,
                5.144220138000259e-05,
                0.000430556985154105,
                2.1444945853999886e-05
            ],
            [
                2.2603245672497918e-06,
                1.1478765387667046e-05,
                3.535625492063251e-05,
                4.222835458044565e-06,
                1.5534979396024226e-06,
                3.288749065125496e-06,
                1.6701417861949427e-05,
                8.93969950101825e-06,
                5.422217677028889e-06,
                1.0129989771473008e-05
            ],
            [
                0.0001795280087358439,
                9.61024148807086e-05,
                6.605216038349344e-05,
                7.88925976359915e-06,
                1.892515726357648e-05,
                1.0129989771288745e-05,
                3.5356250704701545e-05,
                0.00012339463346077684,
                1.4738980213020151e-05,
                0.00013982205731540148
            ],
            [
                0.9998911030523229,
                0.9999832985701935,
                0.9999957771655529,
                0.9999756997650993,
                0.9999957771670603,
                0.9999945777823233,
                0.9999546021315341,
                0.32082130731838393,
                0.9999921107336763,
                0.9999910603005523
            ],
            [
                2.9023109470554753e-06,
                2.561282515988704e-06,
                1.4738988996240646e-05,
                1.473898899742027e-05,
                5.4222183234485234e-06,
                8.939698435096828e-06,
                2.4300249421225448e-05,
                2.430024362791279e-05,
                5.4222215552470286e-06,
                1.994730434778778e-06
            ],
            [
                3.1201922531407855e-05,
                6.144177531459659e-06,
                8.939700565834043e-06,
                1.1478764018576587e-05,
                8.939694171331106e-06,
                2.7535694382378416e-05,
                3.726639283901856e-06,
                1.300713466619476e-05,
                3.120190764966677e-05,
                1.6701417861584877e-05
            ],
            [
                2.7535697655983693e-05,
                1.1478772229781076e-05,
                1.4738980214280206e-05,
                2.9023116388969785e-06,
                7.889264466230069e-06,
                7.889265406438011e-06,
                4.539787400371717e-05,
                1.4738976698006875e-05,
                1.3007125359034903e-05,
                0.00026119027596769055
            ],
            [
                2.1444950957402623e-05,
                4.0063711274151284e-05,
                9.61024378882952e-05,
                5.829127247176183e-05,
                6.605212093617702e-05,
                9.610241494153637e-05,
                6.605217602094941e-05,
                7.484623601192678e-05,
                5.1442195242316055e-05,
                8.939695236398313e-06
            ],
            [
                2.7535681250497054e-05,
                1.8925141468298646e-05,
                8.939700566289352e-06,
                1.8925152752138513e-05,
                9.422443692330485e-07,
                1.0129988564430787e-05,
                1.1478773598099973e-05,
                5.422219615188307e-06,
                5.422220262505697e-06,
                1.6701421842961097e-05
            ],
            [
                4.006368262694324e-05,
                4.006370173834246e-05,
                3.1201918798457626e-05,
                1.0129992187253088e-05,
                2.144495096387783e-05,
                9.610242637576158e-05,
                2.7535687816036267e-05,
                0.0001398220405906475,
                7.889265406681968e-06,
                4.785096205882502e-06
            ],
            [
                0.00010889693524682163,
                3.120192624960245e-05,
                6.605215253545261e-05,
                5.829127943082087e-05,
                7.484623611811155e-05,
                3.120190020204515e-05,
                5.829126545120912e-05,
                5.829127940791947e-05,
                4.00636778604994e-05,
                7.484626274326669e-05
            ],
            [
                4.22283344433731e-06,
                2.144494330062167e-05,
                5.715006514105942e-07,
                1.8925145982866508e-05,
                4.006371129120346e-05,
                5.422220908925639e-06,
                2.1444943298944354e-05,
                1.4738976699749503e-05,
                2.1444940739364273e-05,
                4.22283344433731e-06
            ],
            [
                1.5534977545384963e-06,
                0.00010889690925332526,
                2.561283431942246e-06,
                2.4300234933172706e-05,
                4.78509563535725e-06,
                1.0129990979215566e-05,
                2.4300243627117176e-05,
                3.7266392838544054e-06,
                4.785096776133645e-06,
                1.7603425837062577e-06
            ],
            [
                7.889260704423598e-06,
                6.144173869379821e-06,
                2.9023130230846496e-06,
                1.0129988564430787e-05,
                1.3007126912542439e-05,
                6.96225458885115e-06,
                4.222832940715735e-06,
                1.209866116170145e-06,
                1.5534983101393749e-06,
                8.939695238333382e-06
            ],
            [
                6.605212890675706e-05,
                2.753569765908901e-05,
                6.144173136455602e-06,
                2.7535681250497054e-05,
                5.82912863088776e-05,
                1.6701423832586287e-05,
                1.3007125360478133e-05,
                1.892515500808112e-05,
                7.889263525778283e-06,
                8.939697368500698e-06
            ],
            [
                6.962255419051463e-06,
                3.1201926243586504e-05,
                2.902313022659669e-06,
                1.553498495308628e-06,
                2.9023126769762986e-06,
                3.1201926241089315e-05,
                1.1478768123823146e-05,
                8.939693106873817e-06,
                2.144494330116777e-05,
                1.0677031245905116e-06
            ],
            [
                NaN,
                NaN,
                5.8291286313118594e-05,
                0.00015843623449655312,
                0.0001795279652511508,
                NaN,
                0.00013982213983045587,
                0.00015843621652993932,
                5.144223199845732e-05,
                0.00015843629185879624
            ],
            [
                4.006369694959736e-05,
                3.120191136774608e-05,
                1.670141587068447e-05,
                1.8925141472360678e-05,
                3.5356254898252494e-05,
                4.006367782348017e-05,
                2.4300246525983375e-05,
                3.12019150894581e-05,
                3.120191506868607e-05,
                3.535623805819787e-05
            ],
            [
                2.4300252317882297e-05,
                2.4300232038993178e-05,
                3.535626335545423e-05,
                5.4222215550004564e-06,
                1.1478765388314311e-05,
                6.144174600605357e-06,
                3.726639728184142e-06,
                2.5612822106654943e-06,
                1.0129990977520359e-05,
                2.1444950968441685e-05
            ],
            [
                2.753569109454917e-05,
                1.3007134663521234e-05,
                1.0129995806317745e-05,
                6.144173869312763e-06,
                4.222834451215781e-06,
                2.1444956079218013e-05,
                1.3007131564643372e-05,
                1.0677028700203557e-06,
                2.260324028306588e-06,
                1.3007126912826352e-05
            ],
            [
                6.962257908753841e-06,
                4.006368737677271e-05,
                8.939693106329072e-06,
                2.75356812513986e-05,
                1.0129995807165349e-05,
                1.3709568799592562e-06,
                2.5612828212676906e-06,
                5.422218969661113e-06,
                1.1478766757049986e-05,
                1.4738988998117324e-05
            ],
            [
                1.6701421842566163e-05,
                2.4300252309307336e-05,
                1.892515725149365e-05,
                4.539785772729467e-05,
                4.006369691782494e-05,
                5.829125857951634e-05,
                2.4300249415479343e-05,
                9.610241496111313e-05,
                4.5397868553139715e-05,
                3.120190392137216e-05
            ],
            [
                2.7535691097454142e-05,
                3.726639284017094e-06,
                3.535626334953767e-05,
                1.760344052650207e-06,
                6.962258738283349e-06,
                1.1478772228528306e-05,
                1.994729959270648e-06,
                1.147877086020957e-05,
                6.144174601499446e-06,
                1.3007128463352975e-05
            ],
            [
                2.1444940733201126e-05,
                3.535624227579939e-05,
                1.8925143725341476e-05,
                1.3007123808153756e-05,
                1.8925141464512013e-05,
                8.93969630348202e-06,
                9.610246071689974e-05,
                2.1444943292703185e-05,
                8.939693106182721e-06,
                6.605213676488686e-05
            ],
            [
                8.315280276580819e-07,
                2.260324297607547e-06,
                4.22283294098842e-06,
                1.300713466619476e-05,
                2.1444953517061932e-05,
                1.8925157263094544e-05,
                2.5612828212676906e-06,
                7.889266345397582e-06,
                5.422217676925328e-06,
                2.9023123309973302e-06
            ],
            [
                0.9999962733611601,
                0.9999930377412604,
                0.9999952149043646,
                0.9999957771680659,
                0.9999962733611601,
                0.9999898700041899,
                0.9999938558275957,
                0.9999957771655488,
                0.9999982396567867,
                0.9999977396754327
            ],
            [
                1.670141984792864e-05,
                1.012998977108606e-05,
                2.144494329952946e-05,
                3.120190017276001e-05,
                1.6701429799367125e-05,
                7.484622722854095e-05,
                5.829129331543752e-05,
                9.610240353597847e-05,
                5.1442207520496894e-05,
                1.3007125359413455e-05
            ],
            [
                1.300712536203966e-05,
                2.902311985079115e-06,
                1.8925157257345735e-05,
                8.939700565102295e-06,
                1.8925157257965367e-05,
                2.7535694380675497e-05,
                4.785094494463623e-06,
                8.939697368110433e-06,
                1.0129993393945642e-05,
                1.47389854857293e-05
            ],
            [
                2.4300243620398656e-05,
                3.535623804803683e-05,
                2.7535700944314574e-05,
                1.6701421842566163e-05,
                1.3007131563507714e-05,
                7.484626294256741e-05,
                1.6701415868649062e-05,
                2.7535687813231466e-05,
                1.6701417859519093e-05,
                3.5356242264223526e-05
            ],
            [
                2.9023119850527192e-06,
                6.96225541916544e-06,
                2.4300249419722622e-05,
                3.726640172537657e-06,
                2.5612834319655406e-06,
                1.892515048889829e-05,
                1.147876402018431e-05,
                2.260325375391425e-06,
                4.222834451215781e-06,
                2.2603234893594005e-06
            ],
            [
                3.535625070778844e-05,
                2.2603234894745224e-06,
                1.0677029973114952e-06,
                2.1444958637356654e-05,
                4.222833444168322e-06,
                1.0129988564430787e-05,
                1.0129990978441666e-05,
                1.3007126912542439e-05,
                1.5534971987760398e-06,
                1.0129989771473008e-05
            ],
            [
                5.1442207499350526e-05,
                0.00017952792271723844,
                6.605214448461604e-05,
                2.7535691096552598e-05,
                0.0001584361600736609,
                5.14422258772351e-05,
                7.484621831392271e-05,
                0.0003353501481748897,
                2.753570421601738e-05,
                9.610243784914168e-05
            ],
            [
                5.829126552373023e-05,
                2.144494585583323e-05,
                4.006370172712009e-05,
                9.61024493609775e-05,
                1.1478768125577027e-05,
                6.605214467203479e-05,
                3.1201900215552636e-05,
                8.481102095191198e-05,
                1.8925145978942173e-05,
                3.120192623257619e-05
            ],
            [
                3.1201900207380036e-05,
                8.481107163963022e-05,
                4.5397857795336036e-05,
                4.539785238918559e-05,
                3.535625913952226e-05,
                4.0063692178050736e-05,
                4.5397879448184774e-05,
                6.605215247346026e-05,
                1.8925148236674017e-05,
                2.4300246519706854e-05
            ],
            [
                9.61024149709015e-05,
                6.605212101883346e-05,
                8.939696304002375e-06,
                1.1478765388314311e-05,
                1.8925143728301937e-05,
                1.3007133115430804e-05,
                3.535624228441698e-05,
                2.1444958635523312e-05,
                5.8291251635303294e-05,
                3.120190393260949e-05
            ],
            [
                1.30071346612026e-05,
                1.0129995809247506e-05,
                2.1444945856418342e-05,
                2.430025231469984e-05,
                8.939696302457574e-06,
                5.422218322763051e-06,
                1.1478769492392108e-05,
                1.4738978454950406e-05,
                1.0129994600859455e-05,
                4.539787404186659e-05
            ],
            [
                3.5356259128846735e-05,
                3.120191136263821e-05,
                2.90231198483099e-06,
                4.5397863198349305e-05,
                2.430024362393472e-05,
                9.610246081548275e-05,
                1.892514146086307e-05,
                1.6701415869924985e-05,
                2.753569108573408e-05,
                1.6701427815999337e-05
            ],
            [
                8.939699500896292e-06,
                5.422220261948442e-06,
                1.3007128463069061e-05,
                6.144173136243255e-06,
                4.785092783371756e-06,
                4.222834954561012e-06,
                4.2228324375973415e-06,
                3.535626334953767e-05,
                1.012998977213635e-05,
                4.785096205930373e-06
            ],
            [
                3.535625071344775e-05,
                1.1478769493916314e-05,
                6.144175334094145e-06,
                7.889260704531226e-06,
                2.4300243626409964e-05,
                1.6701429804744246e-05,
                7.484622722854095e-05,
                0.00010889689627400873,
                0.00010889690913765778,
                2.1444940740066406e-05
            ],
            [
                5.4222202623972055e-06,
                2.902312677104321e-06,
                1.0129990979381404e-05,
                6.962254589851619e-06,
                8.31528126775552e-07,
                5.42222090882208e-06,
                1.4738988999940381e-05,
                3.120190764058611e-05,
                2.144495608046625e-05,
                8.315284241597959e-07
            ],
            [
                3.120191881094355e-05,
                2.90231163910023e-06,
                1.8925152750692706e-05,
                3.1201903929204235e-05,
                1.473898197063434e-05,
                1.3007126912258525e-05,
                5.422219615750493e-06,
                5.829128633941282e-05,
                1.0129990977520359e-05,
                4.5397874031792504e-05
            ],
            [
                1.8925141468298646e-05,
                2.14449535222109e-05,
                2.4300240728162926e-05,
                2.4300243625614346e-05,
                3.1201911358551906e-05,
                6.962253759670401e-06,
                1.0129993394664264e-05,
                3.120190763332158e-05,
                5.4222215550004564e-06,
                3.1201900207380036e-05
            ],
            [
                0.00048785711381318486,
                1.3007130012673148e-05,
                0.00012339463347873087,
                0.00010889692186108131,
                0.00012339453024827647,
                2.4300240728958537e-05,
                0.00012339458943023138,
                8.939695237341456e-06,
                0.00012339461848169986,
                5.829129330398681e-05
            ],
            [
                3.2887502413389517e-06,
                4.22283545795623e-06,
                2.1444948407573453e-05,
                6.144177531007026e-06,
                5.422220908876325e-06,
                3.5356267533443565e-05,
                2.5612812943280275e-06,
                1.5534983100920427e-06,
                1.553497198826904e-06,
                5.422218969384951e-06
            ],
            [
                8.481101102021286e-05,
                1.1478769492893215e-05,
                1.1478773596283455e-05,
                1.1478770861859053e-05,
                2.4300249422639878e-05,
                1.8925148232267744e-05,
                1.0129992187105678e-05,
                4.22283545795623e-06,
                1.3007128463873485e-05,
                2.7535694378772238e-05
            ],
            [
                1.6701417859519093e-05,
                2.7535681225754707e-05,
                6.144175333837093e-06,
                0.0001584362165022771,
                2.7535704227537108e-05,
                6.144172404129392e-06,
                5.422217676979575e-06,
                4.7850944945245504e-06,
                5.829127941597736e-05,
                2.7535694382378416e-05
            ],
            [
                2.7535694373763664e-05,
                6.962253759581752e-06,
                1.1478764020372226e-05,
                3.726638395493353e-06,
                6.144173869240119e-06,
                1.4738980213985297e-05,
                4.222832941072913e-06,
                3.1201903929204235e-05,
                1.4738976695942536e-05,
                3.7266397283231055e-06
            ],
            [
                7.889264465555602e-06,
                4.539785779797843e-05,
                5.144221359998557e-05,
                8.939696301384342e-06,
                1.473898021366358e-05,
                1.300712691308661e-05,
                4.539787404186659e-05,
                1.670141587068447e-05,
                6.9622579086271995e-06,
                1.4738985483879434e-05
            ],
            [
                6.962257077033528e-06,
                5.422217029943586e-06,
                8.939695237666677e-06,
                1.1478764016446877e-05,
                2.1444958614225316e-05,
                5.422221554581283e-06,
                2.4300249421225448e-05,
                6.144176798870286e-06,
                5.144222582408846e-05,
                4.5397879450662006e-05
            ],
            [
                5.422221554758815e-06,
                6.962259569003389e-06,
                1.5534971989258068e-06,
                2.9023119850210436e-06,
                1.2098652508144226e-06,
                1.1478769492893215e-05,
                3.2887482811579057e-06,
                1.7603438427467903e-06,
                2.2603245672025095e-06,
                2.4300234934056724e-05
            ],
            [
                2.902312677060767e-06,
                1.7603440526662173e-06,
                1.994729483680993e-06,
                1.3007131563815288e-05,
                2.561283126639892e-06,
                3.2887506334560605e-06,
                1.7603436329394601e-06,
                1.6701415869924985e-05,
                3.1201922531407855e-05,
                2.144495608327478e-05
            ],
            [
                3.535626755762428e-05,
                1.3007130011655787e-05,
                5.8291286375037224e-05,
                2.753568781423318e-05,
                2.430023783309869e-05,
                3.120190020204515e-05,
                5.144222589108318e-05,
                5.14422319797437e-05,
                4.539789024909747e-05,
                2.7535681249595513e-05
            ],
            [
                5.829129315979273e-05,
                5.829127245607013e-05,
                0.0002611902468002277,
                9.610241489119613e-05,
                0.00037998452481173507,
                7.484621829540844e-05,
                7.484621827634963e-05,
                2.4300249394528152e-05,
                7.484622707607052e-05,
                5.144219521911119e-05
            ],
            [
                4.785095635017795e-06,
                1.3007125363293615e-05,
                4.006368262883792e-05,
                1.4738980202752053e-05,
                3.535626334490732e-05,
                3.535626755762428e-05,
                5.829125164632989e-05,
                5.4222183222304545e-06,
                4.7850944945245504e-06,
                2.753569764776963e-05
            ],
            [
                1.4738983726184394e-05,
                1.3007131565613412e-05,
                2.430023782717578e-05,
                2.5612815999679353e-06,
                2.1444953520884646e-05,
                2.1444948412137308e-05,
                6.14417606659952e-06,
                6.144172404302622e-06,
                2.4300252316291068e-05,
                2.753569437686898e-05
            ],
            [
                3.1201918807538294e-05,
                1.6701425825492673e-05,
                2.144494329952946e-05,
                8.939696302831578e-06,
                0.0005527787387685183,
                4.0063711278232147e-05,
                3.120190019636974e-05,
                8.939695237504067e-06,
                3.120191136263821e-05,
                0.00013982204065167932
            ],
            [
                3.120191136899467e-05,
                1.8925157255968775e-05,
                4.7850933534310035e-06,
                0.0001398221070929684,
                1.6701427813417103e-05,
                1.8925148238808306e-05,
                2.4300234937239182e-05,
                4.539786321436876e-05,
                1.4738985483504099e-05,
                5.8291244687274174e-05
            ],
            [
                6.9622579096593295e-06,
                6.962259569313662e-06,
                1.0129988563730593e-05,
                1.8925150495232307e-05,
                5.422220908703723e-06,
                4.785096205830278e-06,
                4.006369217615605e-05,
                8.939698434153684e-06,
                6.9622595694023114e-06,
                4.7850927830148924e-06
            ],
            [
                0.00010889690904258862,
                6.605215251574962e-05,
                6.605214446443249e-05,
                4.0063687398634466e-05,
                4.0063687367153544e-05,
                0.000552778611422175,
                0.0002611903084106071,
                0.9999832985781602,
                4.0063692137387875e-05,
                0.999891103065284
            ],
            [
                4.222832437639588e-06,
                1.8925150491445666e-05,
                1.4738980208864656e-05,
                3.12019002110123e-05,
                4.222834954687752e-06,
                1.0129989771288745e-05,
                0.00010889688294135345,
                7.889261644358435e-06,
                5.144223817619536e-05,
                1.4738983726908257e-05
            ]
        ]
    },
    {
        "q_id": "8297_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            21,
            22,
            23,
            24,
            25,
            27,
            28,
            30,
            31,
            32,
            33,
            34,
            35,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            53,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            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,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.999999352404893,
                0.9999998874647842,
                0.9999997617630049,
                0.9999996072137529,
                0.9999995549147359,
                0.9999993524051246,
                0.9999996940977002,
                0.999999352405279,
                0.9999994284994849,
                0.9999996072137061
            ],
            [
                1.0129990978847043e-05,
                2.7535681245588654e-05,
                2.430023781329673e-05,
                3.120190764058611e-05,
                4.2228344508893285e-06,
                1.4738981967202704e-05,
                9.610246065397443e-05,
                1.0129992186387057e-05,
                1.1478773596847203e-05,
                6.9622570780973205e-06
            ],
            [
                0.9999999226557684,
                0.9999999226558515,
                0.9999997617631184,
                0.9999998724809267,
                0.9999994956524114,
                0.9999998874648379,
                0.9999998362622552,
                0.9999999226557684,
                0.9999998555019274,
                0.9999998362623137
            ],
            [
                0.9999998724809723,
                0.9999998555020135,
                0.999999855502048,
                0.9999998724809116,
                0.9999998555020306,
                0.999999730042319,
                0.9999998362623723,
                0.9999998144609423,
                0.9999998144608098,
                0.9999997617630899
            ],
            [
                0.9999997897566089,
                0.9999996533674615,
                0.9999997617629764,
                0.9999996533674615,
                0.999999352404893,
                0.9999998874647976,
                0.999999653367379,
                0.9999996940977366,
                0.9999996940978095,
                0.999999653367379
            ],
            [
                0.999999814460854,
                0.999999900688043,
                0.9999998724809267,
                0.9999997897567091,
                0.9999998724810027,
                0.9999999226557961,
                0.9999998874647842,
                0.9999998555019274,
                0.9999996940976636,
                0.9999998724809267
            ],
            [
                1.3007131564383116e-05,
                7.338213304083124e-07,
                7.338208930355202e-07,
                8.315278294038928e-07,
                1.3709570434122812e-06,
                4.785096776194573e-06,
                4.4508499887035535e-07,
                2.753569109254574e-05,
                2.2603237589028734e-06,
                1.0677033791495609e-06
            ],
            [
                0.9999999123575255,
                0.9999998724809267,
                0.9999997300421581,
                0.9999999006880904,
                0.999999789756634,
                0.9999998874649184,
                0.9999997617631184,
                0.9999998874648917,
                0.9999999317440034,
                0.9999998555020307
            ],
            [
                0.9999997300421581,
                0.9999998874647306,
                0.9999998144608098,
                0.9999998362623528,
                0.9999996533672549,
                0.9999998144608097,
                0.9999998362622747,
                0.9999999006881377,
                0.999999730042319,
                0.9999994284996211
            ],
            [
                2.7535694377870696e-05,
                3.2887498493983645e-06,
                1.892514147046736e-05,
                1.3007128463352975e-05,
                2.1444948412137308e-05,
                3.7266401725681614e-06,
                3.120190764966677e-05,
                1.147876402018431e-05,
                1.3007126912542439e-05,
                4.222833947774596e-06
            ],
            [
                0.9999998874647306,
                0.9999994284992805,
                0.9999999006881141,
                0.9999998362623138,
                0.9999998144608538,
                0.9999996533674202,
                0.9999996072138934,
                0.9999994956524114,
                0.9999996533673375,
                0.9999998144608319
            ],
            [
                0.9999994956527721,
                0.9999995549149481,
                0.9999997897565587,
                0.9999990577555185,
                0.9999994956525317,
                0.9999994284993485,
                0.9999997617630616,
                0.9999993524049702,
                0.9999996072137061,
                0.9999991684722698
            ],
            [
                0.9999999226557869,
                0.9999999586006295,
                0.999999939764294,
                0.9999998555019963,
                0.9999999006880785,
                0.9999997300421581,
                0.9999998555020135,
                0.9999998724810027,
                0.9999996940977002,
                0.9999996533674201
            ],
            [
                4.222835458002318e-06,
                0.9999962733616043,
                0.9999970976890528,
                0.9999869928746369,
                1.147877359926923e-05,
                1.3007123812554424e-05,
                6.962254589705982e-06,
                1.147877359872636e-05,
                0.9999869928746372,
                0.9999938558275955
            ],
            [
                0.9999339478845691,
                0.6224593382055109,
                0.9999810748598212,
                0.9998415638079557,
                0.9999785550465145,
                0.9770226282082864,
                0.9399133531922388,
                0.9999910603058326,
                0.8670357598021707,
                0.9999339478755249
            ],
            [
                0.9999997897567091,
                0.9999992661792819,
                0.9999996533675028,
                0.9999996533675028,
                0.9999996072136125,
                0.9999989322967481,
                0.9999993524053562,
                0.9999994284994167,
                0.9999997617631184,
                0.999995214904935
            ],
            [
                0.9999993524050474,
                0.9999999006880194,
                0.9999998874648514,
                0.9999999317440034,
                0.9999998555020135,
                0.9999998144609644,
                0.9999997897566089,
                0.9999997617630617,
                0.9999999006880668,
                0.9999998555020135
            ],
            [
                3.726640172537657e-06,
                3.7266379512112265e-06,
                1.0129989770441144e-05,
                7.889264464508026e-06,
                1.1478768125201194e-05,
                2.4300249421225448e-05,
                2.1444940741392653e-05,
                3.2887506334201674e-06,
                2.4300240731964193e-05,
                1.3007130012980722e-05
            ],
            [
                1.0677032518700286e-06,
                1.3709567164962755e-06,
                1.370956879949281e-06,
                1.99472924590571e-06,
                6.144174601410037e-06,
                6.475949525981759e-07,
                2.2603245672497918e-06,
                1.3709570433387154e-06,
                6.475947981904966e-07,
                2.5612819053166966e-06
            ],
            [
                0.9999999468421692,
                0.9999999397642078,
                0.9999999226558145,
                0.999999814460876,
                0.9999998874647977,
                0.9999993524050473,
                0.9999999530883732,
                0.9999998724808963,
                0.9999998362622357,
                0.9999993524051246
            ],
            [
                0.9999996072138465,
                0.9999998874647709,
                0.9999999226557592,
                0.9999999123575045,
                0.9999999397642725,
                0.9999998724809419,
                0.9999998555019618,
                0.9999999317440279,
                0.9999999226557316,
                0.9999998555020135
            ],
            [
                1.1478766756444477e-05,
                1.7603430034311638e-06,
                4.785094494628999e-06,
                3.288749457409966e-06,
                1.209865683500459e-06,
                6.144176798870286e-06,
                2.561282515988704e-06,
                8.315278293951957e-07,
                1.0677031245783732e-06,
                1.0677032518700286e-06
            ],
            [
                3.5356254890278004e-05,
                7.484622715666203e-05,
                4.006371126555232e-05,
                0.0001233946333728019,
                0.0002611903406407374,
                4.0063692167994334e-05,
                6.144173136556186e-06,
                0.0011695101018679027,
                0.000295957231706814,
                5.144223815074485e-05
            ],
            [
                0.9999997897566589,
                0.9999997897567341,
                0.9999998724809723,
                0.9999998724810027,
                0.9999995549147358,
                0.9999998144608097,
                0.9999998724808964,
                0.999999730042319,
                0.9999996072136125,
                0.9999998144608981
            ],
            [
                0.9999982396574164,
                0.9999997617630051,
                0.9999977396762414,
                0.9999832985818912,
                0.9999945777810313,
                0.9999998724810027,
                0.9999998362622943,
                0.9999967112505884,
                0.9999980052698242,
                0.9999945777810305
            ],
            [
                0.9999994956525318,
                0.999999730042319,
                0.9999993524050473,
                0.9999994956524716,
                0.9999997897567091,
                0.999999814460854,
                0.9999994284993485,
                0.9999998144608981,
                0.9999997300422225,
                0.9999994284994848
            ],
            [
                9.610242639533834e-05,
                0.0002305067696737918,
                1.0129995806888955e-05,
                2.902311984783477e-06,
                7.484623609088468e-05,
                2.7535704227537108e-05,
                5.422217676486429e-06,
                0.000335350067691874,
                4.006370646879011e-05,
                0.9998911030648276
            ],
            [
                1.012999339449843e-05,
                1.76034300345598e-06,
                1.7603434231505666e-06,
                6.962253759043525e-06,
                3.7266397283231055e-06,
                3.2887502414436403e-06,
                1.9947299592407137e-06,
                0.9999885212305071,
                0.9999967112497585,
                1.3709568798956654e-06
            ],
            [
                2.2603240283888175e-06,
                7.338210679949506e-07,
                1.0129993394314164e-05,
                2.2603242977802297e-06,
                2.2603237588597026e-06,
                2.5612831266608576e-06,
                8.939693105467234e-06,
                4.222834451254188e-06,
                3.2887482812506295e-06,
                3.120192624846737e-05
            ],
            [
                4.785094494402695e-06,
                1.5534971989907999e-06,
                6.1441775312976045e-06,
                1.2098661161861e-06,
                4.2228324377164004e-06,
                9.422447062202052e-07,
                3.2887478890769702e-06,
                0.9999990577551815,
                4.222834954607099e-06,
                1.3709573702722555e-06
            ],
            [
                1.760343213322473e-06,
                1.5534975693707442e-06,
                6.962256249758443e-06,
                3.288748673265808e-06,
                6.962257079376403e-06,
                4.785096205882502e-06,
                2.5612816000145246e-06,
                1.1478773598099973e-05,
                7.338208930421943e-07,
                0.9999993524051246
            ],
            [
                0.9999957771660521,
                0.9999962733593832,
                0.9999986290426298,
                0.9999998144608319,
                0.9999990577551815,
                0.9999987901337398,
                0.9999970976880149,
                0.9999984465020607,
                0.9999996533672962,
                0.999996711251719
            ],
            [
                0.999999554914789,
                0.9999997300420939,
                0.9999996072136125,
                0.9999997617630616,
                0.9999999226558329,
                0.9999998724809875,
                0.9999999397642725,
                0.9999997897566089,
                0.9999992661788446,
                0.9999997300422868
            ],
            [
                0.9999993524053562,
                0.9999998874648781,
                0.9999998874648781,
                0.9999998724809571,
                0.9999997300422869,
                0.9999990577557432,
                0.9999993524049702,
                0.9999996940976636,
                0.999999730042319,
                0.9999993524049702
            ],
            [
                9.610244915612066e-05,
                2.2603251061664e-06,
                1.9947306726213275e-06,
                1.1478770859332632e-05,
                8.939697369004791e-06,
                1.0129992186589747e-05,
                1.147876675466972e-05,
                5.829125155557251e-05,
                0.00012339454522734274,
                7.484624500496053e-05
            ],
            [
                0.9999991684718732,
                0.9999992661788446,
                0.9999996940976272,
                0.9999967112493664,
                0.9999996072136125,
                0.9999989322970027,
                0.9999990577549569,
                0.999998446502801,
                2.1444953523537147e-05,
                0.9999994284995529
            ],
            [
                0.9999997617630049,
                0.9999996533674202,
                0.9999998555020307,
                0.9999998724810027,
                0.9999998362623722,
                0.9999999530883843,
                0.9999998362623528,
                0.999999855501979,
                0.9999999397642437,
                0.9999997617630616
            ],
            [
                0.9999995549148419,
                0.9999993524051246,
                0.9999996533672549,
                0.9999997617629764,
                0.9999996940978095,
                0.9999994956527721,
                0.9999996533672136,
                0.9999994956527722,
                0.9999997617631469,
                0.999999554914842
            ],
            [
                0.9999998555019962,
                0.999999730042126,
                0.9999997897565838,
                0.9999999226558423,
                0.9999997897566089,
                0.9999998144608981,
                0.9999999397642653,
                0.9999997300420937,
                0.9999998724809267,
                0.9999998362623332
            ],
            [
                0.9999998724809419,
                0.9999997617630616,
                0.999999730042319,
                0.9999996072136592,
                0.9999998724809723,
                0.9999998144608098,
                0.9999998874647976,
                0.9999996072137061,
                0.9999998555019618,
                0.9999997897566589
            ],
            [
                1.9947301969471416e-06,
                3.7266401722360055e-06,
                1.7603425836870455e-06,
                1.7603427935678977e-06,
                1.7603430033991435e-06,
                6.9622595694023114e-06,
                4.785095635592258e-06,
                5.422218323349895e-06,
                5.4222183231674305e-06,
                4.222831934248571e-06
            ],
            [
                0.9999999123575568,
                0.9999997300421581,
                0.9999998362622552,
                0.9999999006880194,
                0.9999997897566089,
                0.9999998724809267,
                0.9999998144609644,
                0.9999997617630049,
                0.9999996940978095,
                0.9999998362622943
            ],
            [
                0.9999991684717827,
                0.6513548511303338,
                0.9999938558261764,
                0.9999921107336832,
                0.9999930377420935,
                0.9999785550465339,
                0.9999910603007737,
                0.999996273360757,
                0.9999869928668841,
                0.9999930377404416
            ],
            [
                0.9999810748429888,
                0.9999974387184,
                NaN,
                NaN,
                0.6513548511303336,
                0.8175744739711883,
                0.2942149783515162,
                0.9998766054549899,
                0.9999885212361598,
                0.9999996940976636
            ],
            [
                0.9999997617630049,
                0.9999995549151073,
                0.9999996533673375,
                0.9999997897567341,
                0.9999997617629764,
                0.9999998555020307,
                0.9999997617631183,
                0.999999554914895,
                0.9999998724809419,
                0.9999998144608097
            ],
            [
                1.0129992186774007e-05,
                7.889266347456862e-06,
                2.902313023063532e-06,
                1.5534983101393749e-06,
                2.260324567268294e-06,
                1.553498495308628e-06,
                3.288748673265808e-06,
                1.3709578605542582e-06,
                9.4224425692559e-07,
                4.222831934248571e-06
            ],
            [
                0.999999855502048,
                0.9999996533672962,
                0.99999976176309,
                0.9999998144608319,
                0.9999999317439464,
                0.9999998874647574,
                0.9999999226557869,
                0.9999997897565838,
                0.9999997897565838,
                0.9999998144609423
            ],
            [
                1.2098659719661556e-06,
                2.260325375664839e-06,
                4.222833947897496e-06,
                4.78509563550957e-06,
                5.422217030663578e-06,
                2.561283431986506e-06,
                2.260324567268294e-06,
                1.5534971989809095e-06,
                2.9023109470871505e-06,
                1.9947290081177566e-06
            ],
            [
                0.9999997897566089,
                0.9999997897566089,
                0.9999994956524115,
                0.9999996940978825,
                0.9999998555019274,
                0.9999998362622942,
                0.9999996533674615,
                0.9999998555019618,
                0.9999998724809267,
                0.9999994956526519
            ],
            [
                2.5612819053586272e-06,
                6.144173869240119e-06,
                6.962253759670401e-06,
                1.1478769493331685e-05,
                8.939695238439078e-06,
                5.422221555069497e-06,
                1.1478773598914277e-05,
                3.288750633518874e-06,
                5.422221555133606e-06,
                3.7266379512857925e-06
            ],
            [
                0.9999785550498616,
                0.9914225139368573,
                0.9999957771645706,
                0.9999984465022581,
                0.999998446502803,
                0.9770226275810572,
                0.9796676450248561,
                0.9999962733607168,
                0.9999974387165895,
                0.999738809620715
            ],
            [
                0.9999993524052789,
                0.9999996533673788,
                0.9999998874649184,
                0.9999998555020135,
                0.9999962733620528,
                0.9999998362623723,
                0.9999998362622747,
                0.9999952149037944,
                0.9999996072138934,
                0.9999998555019962
            ],
            [
                1.1478768121401121e-05,
                1.0129987352948008e-05,
                3.5356267545276676e-05,
                2.753569765708558e-05,
                4.222833444283541e-06,
                3.535626329667452e-05,
                4.785094494019719e-06,
                4.222832436955956e-06,
                5.422219615582823e-06,
                1.0129992184544441e-05
            ],
            [
                0.9999980052702786,
                0.9999995549150542,
                0.9999987901341723,
                0.9999992661786696,
                0.9999989322968753,
                0.9999995549147889,
                0.9999993524054335,
                0.9999992661789321,
                0.9999982396559475,
                0.9999996072139402
            ],
            [
                0.9999996940977002,
                0.9999997300422225,
                0.9999998724809723,
                0.9999998555020135,
                0.999999730042319,
                0.9999998874649318,
                0.9999998362623528,
                0.9999993524052018,
                0.9999997897567341,
                0.9999994284996891
            ],
            [
                0.9999996940977731,
                0.9999997897566589,
                0.9999996072136125,
                0.9999996533672549,
                0.9999991684717742,
                0.9999994284994849,
                0.9999990577556307,
                0.9999996072137529,
                0.9999994284996893,
                0.9999998362623137
            ],
            [
                0.9999998874648781,
                0.9999998144609644,
                0.9999998144608983,
                0.9999998555019446,
                0.9999998555020135,
                0.9999999006880075,
                0.9999997617629764,
                0.9999998555019446,
                0.9999998362622747,
                0.9999999226558145
            ],
            [
                1.8925148236674017e-05,
                3.7266406167827664e-06,
                2.902311293147782e-06,
                1.670142781478417e-05,
                2.4300252311252174e-05,
                4.222833947820683e-06,
                4.222833444429485e-06,
                2.1444950965282096e-05,
                5.422218323349895e-06,
                2.5612815999423112e-06
            ],
            [
                0.9999724643187635,
                0.817574478416099,
                0.939913354875362,
                0.817574478416099,
                0.9525741256443601,
                0.9999885212278325,
                0.9999646437457942,
                0.9999832985801554,
                0.9999952149055402,
                0.7772998663336158
            ],
            [
                0.9999930377454128,
                0.9971990733807976,
                0.9999970976866314,
                0.7057850154599562,
                0.9999987901344656,
                0.9999485577683346,
                0.9999756997650883,
                0.9999957771675662,
                0.974042643226052,
                0.999981074854021
            ],
            [
                0.9999967112513413,
                0.9999852610216439,
                0.999997438717188,
                0.9999687980891072,
                0.8670357512127872,
                0.9998415637718796,
                0.9999599362891085,
                0.966914021492119,
                0.9149009607937928,
                0.4073334000459302
            ],
            [
                0.999999730042319,
                0.9999998874648245,
                0.9999997300422225,
                0.9999999317440034,
                0.9999998144608983,
                0.9999997617631183,
                0.999999789756684,
                0.9999997617630899,
                0.9999997617631184,
                0.9999998724808963
            ],
            [
                0.9999986290421395,
                0.9999994284994167,
                0.9999984465015047,
                0.9999977396754328,
                0.9999987901346049,
                0.9999984465024306,
                0.9999989322975118,
                0.9999996072138934,
                0.9999993524052018,
                0.999999730042319
            ],
            [
                0.999999922655833,
                0.9999998724809115,
                0.9999998362623137,
                0.9999998874648647,
                0.9999994956527722,
                0.999999730042126,
                0.9999998724808964,
                0.9999998874647574,
                0.9999998724809115,
                0.9999998555020307
            ],
            [
                0.999997438717484,
                0.9999885212359813,
                0.9999921107364752,
                0.9999852610162734,
                0.9999952149072167,
                0.9999921107345933,
                0.9999885212264024,
                0.9999952149037946,
                0.999997097688015,
                0.9999957771650453
            ],
            [
                1.1478766757237902e-05,
                3.2887490653408545e-06,
                7.889259763857458e-06,
                2.5612822106841303e-06,
                6.962257079376403e-06,
                3.288747889229516e-06,
                8.315278294072958e-07,
                4.222831934248571e-06,
                2.9023116391477434e-06,
                3.535626334799422e-05
            ],
            [
                0.9999996072136592,
                0.9999996533675028,
                0.9999998362623137,
                0.9999996940977366,
                0.9999997897566589,
                0.9999996533673375,
                0.999999352405279,
                0.9999996072137998,
                0.999999352404893,
                0.9999997617630332
            ],
            [
                2.9023133690425823e-06,
                1.994729959270648e-06,
                5.422221554758815e-06,
                6.144176799166453e-06,
                7.88926634755014e-06,
                1.3709576971379186e-06,
                0.9999995549148419,
                3.726640172503764e-06,
                2.561283431942246e-06,
                0.9999987901341723
            ],
            [
                0.9999996940978825,
                0.9999992661788446,
                0.999999653367379,
                0.9999996533672549,
                0.9999996072136592,
                0.9999994956527722,
                0.9999987901338838,
                0.9999990577557432,
                0.9999996533673375,
                0.9999996072136592
            ],
            [
                1.3709570433536782e-06,
                0.9914225155287544,
                6.144175333021237e-06,
                9.422442569028803e-07,
                2.9023126770343703e-06,
                1.553497568999859e-06,
                9.422450431732037e-07,
                5.715003788624637e-07,
                2.2603245671202796e-06,
                0.9995121427692482
            ],
            [
                0.9998911031188507,
                0.9999251538019946,
                0.9999885212264065,
                0.9999832985801475,
                0.9999646437552006,
                0.9999898700078932,
                0.9999417087174901,
                0.9999952149032658,
                0.9999930377445821,
                0.9999910603020125
            ],
            [
                0.9999999226557316,
                0.9999998724809419,
                0.9999999006879838,
                0.9999998555020306,
                0.9999998362622552,
                0.9999998724809115,
                0.9999999123575045,
                0.9999998362622357,
                0.9999998724809115,
                0.9999998874649051
            ],
            [
                2.260324028351814e-06,
                9.422445938917108e-07,
                6.962258738131379e-06,
                1.9947299592407137e-06,
                2.2603251061664e-06,
                1.9947294836483373e-06,
                1.209865827740176e-06,
                6.962255417721724e-06,
                2.7535684519993744e-05,
                1.2098656835076114e-06
            ],
            [
                6.962259569313662e-06,
                4.78509563550957e-06,
                3.535626755762428e-05,
                3.2887478891128633e-06,
                3.288748281220719e-06,
                1.0129994602057158e-05,
                5.144221975264518e-05,
                1.47389819699641e-05,
                1.89251482372248e-05,
                2.1444958632714784e-05
            ],
            [
                1.9947294836483373e-06,
                1.3007130014636887e-05,
                2.260324028372372e-06,
                6.475945666009864e-07,
                1.7603436329978976e-06,
                2.1444945853999886e-05,
                6.144174601935314e-06,
                2.5612812947077304e-06,
                3.288747889178668e-06,
                2.2603245672867952e-06
            ],
            [
                0.9999999006880194,
                0.9999998362623528,
                0.9999997300422547,
                0.9999999123575464,
                0.9999998555019963,
                0.9999997617630332,
                0.9999999397642222,
                0.9999998362622747,
                0.999999730042126,
                0.9999998362623138
            ],
            [
                6.962259569484628e-06,
                1.3007126912258525e-05,
                2.430024941459533e-05,
                1.5534984953298217e-06,
                1.7603440527046419e-06,
                2.9023126768258393e-06,
                3.2887482811220126e-06,
                5.422219615967477e-06,
                1.5534979397500702e-06,
                1.1478768124324254e-05
            ],
            [
                2.2603234894745224e-06,
                7.889260704308795e-06,
                2.5612819052654485e-06,
                0.9999898700066052,
                3.2887502415243994e-06,
                1.3709572068422585e-06,
                1.5534973841895917e-06,
                2.2603234894745224e-06,
                2.9023133689317184e-06,
                2.260324297853209e-06
            ],
            [
                0.9999997897565838,
                0.9999998144608319,
                0.9999998555020307,
                0.999999653367379,
                0.9999997897565587,
                0.9999997897567341,
                0.9999999006880194,
                0.9999997617631752,
                0.9999995549148419,
                0.9999997300422868
            ],
            [
                1.5534977545603963e-06,
                8.939696303010449e-06,
                0.9999930377429203,
                2.5612812947077304e-06,
                2.2603248367358324e-06,
                3.7266410608720178e-06,
                4.222833947820683e-06,
                3.288750241473551e-06,
                4.222834451254188e-06,
                6.962254589705982e-06
            ],
            [
                0.9999967112501505,
                0.9999957771645419,
                0.9999945777803838,
                0.9999990577555183,
                0.9999970976890528,
                1.3709572068272963e-06,
                8.315282259009745e-07,
                0.9999957771670589,
                2.260324028404236e-06,
                0.9999970976866309
            ],
            [
                5.04347648686092e-07,
                2.902312677007974e-06,
                7.338208055489796e-07,
                9.422444815726566e-07,
                8.31528126775552e-07,
                1.2098653950480359e-06,
                4.4508505193791187e-07,
                4.785096776251149e-06,
                7.338208930315157e-07,
                8.315279284937352e-07
            ],
            [
                2.902311639073834e-06,
                6.144173869072478e-06,
                4.785093353626844e-06,
                8.939695236398313e-06,
                1.4738983726559732e-05,
                1.0129987355343409e-05,
                2.561283431986506e-06,
                1.0129993393945642e-05,
                8.939699499823059e-06,
                4.785093353739995e-06
            ],
            [
                0.9999999123575672,
                0.9999998874649318,
                0.9999999226557131,
                0.9999999123575151,
                0.9999996533673375,
                0.9999998874648379,
                0.9999998724809571,
                0.9999998724809875,
                0.9999998874649184,
                0.9999999468421629
            ],
            [
                0.9999995549150542,
                0.9999994956524716,
                0.9999996533675028,
                0.9999990577556308,
                0.9999994284995529,
                0.9999994284997573,
                0.9999994956523514,
                0.9999997897567341,
                0.9999993524052019,
                0.9999998724809419
            ],
            [
                0.9999996940977366,
                0.9999997897566338,
                0.9999994284996211,
                0.9999996072136125,
                0.9999996940976636,
                0.9999999397642796,
                0.999999730042126,
                0.9999997300421581,
                0.9999994956527121,
                0.9999995549148419
            ],
            [
                0.9999999006880075,
                0.999999887464811,
                0.9999998144609202,
                0.9999999468421565,
                0.999999855501979,
                0.9999999006880549,
                0.9999999006880668,
                0.9999997617629763,
                0.9999999006879957,
                0.9999999123575568
            ],
            [
                1.76034300345598e-06,
                2.753568453191415e-05,
                2.9023130230133794e-06,
                4.222834954607099e-06,
                1.6701419849447602e-05,
                0.00010889688309980203,
                2.4300246522270504e-05,
                2.7535681246690542e-05,
                2.1444943300075563e-05,
                6.962257909323729e-06
            ],
            [
                0.9999997300421262,
                0.9997388096191343,
                0.880797071719777,
                0.9999967112501739,
                0.9999646437577226,
                0.9999938558275969,
                0.9999987901344658,
                0.9998204720078765,
                0.9999910603047643,
                0.9999810748497742
            ],
            [
                0.9999910603061679,
                0.9999038975512172,
                0.9998911030399258,
                0.9999921107347407,
                0.9999977396762412,
                0.9999687980775326,
                0.9997694933371498,
                0.8807970904940926,
                0.999964643749712,
                0.99994170871529
            ],
            [
                0.9999998144609644,
                0.999999730042126,
                0.9999994956523514,
                0.9999997617630048,
                0.9999998362623528,
                0.9999996940977366,
                0.9999991684717741,
                0.9999998144609423,
                0.9999997617631468,
                0.9999994284996211
            ],
            [
                2.9023116389761676e-06,
                1.9947292458930106e-06,
                1.1478772230198667e-05,
                7.889266347248781e-06,
                4.222834451254188e-06,
                4.785096776303374e-06,
                6.96225956921868e-06,
                4.2228354571957855e-06,
                7.889266345770692e-06,
                4.7850967763512445e-06
            ],
            [
                0.9999994956524115,
                0.9999994956525918,
                0.9999996533674202,
                0.9999996533673375,
                0.9999994956527722,
                0.9999996940976272,
                0.9999998555019618,
                0.999999694097773,
                0.9999996072139402,
                0.9999997300421903
            ],
            [
                0.99999976176309,
                0.9999999397642725,
                0.9999999123575672,
                0.9999998874647842,
                0.9999997617629764,
                0.9999999123574941,
                0.9999996533674614,
                0.9999998144608981,
                0.9999996940977002,
                0.9999997617631752
            ],
            [
                0.9999998362622942,
                0.9999998144608538,
                0.9999997300421581,
                0.9999996072136125,
                0.9999998555020307,
                0.9999996940977366,
                0.9999997897565587,
                0.9999996072137061,
                0.9999996940978825,
                0.99999976176309
            ],
            [
                0.9999997617630899,
                0.9999995549151073,
                0.9999997300420937,
                0.9999990577556308,
                0.9999990577550691,
                0.9999989322970027,
                0.9999990577554061,
                0.9999996940976272,
                0.9999986290432835,
                0.9999994956525317
            ],
            [
                0.9999999006880194,
                0.9999997897567091,
                0.9999997897565587,
                0.9999997897567341,
                0.9999997897565587,
                0.9999998555020307,
                0.9999997617631752,
                0.9999998144609202,
                0.9999996940976636,
                0.999999855502048
            ],
            [
                0.999999814460854,
                0.999999931743979,
                0.9999999226557592,
                0.9999999468421376,
                0.999999789756684,
                0.9999999123574836,
                0.9999997300420937,
                0.9999998362623332,
                0.999999814460876,
                0.9999997897565587
            ],
            [
                0.9999998144608538,
                0.9999998724809723,
                0.999999887464744,
                0.9999996940976636,
                0.9999999123574836,
                0.999999730042319,
                0.9999998724809115,
                0.9999997897566089,
                0.9999997300421581,
                0.9999998724809571
            ],
            [
                1.6701423833436905e-05,
                8.939700560549195e-06,
                1.8925145983795953e-05,
                4.006370646616669e-05,
                0.00023050674153087092,
                6.60521682560438e-05,
                1.8925148230890784e-05,
                2.7535697655983693e-05,
                1.300713466420736e-05,
                0.999986992876188
            ],
            [
                0.999999814460876,
                0.9999998724809419,
                0.9999998555020306,
                0.9999998362623722,
                0.9999997300422547,
                0.9999996533674202,
                0.9999996072137529,
                0.9999997897565587,
                0.9999997897567091,
                0.9999997617630617
            ],
            [
                1.892515726099468e-05,
                2.753568781022632e-05,
                1.8925141462377723e-05,
                0.00023050663167558885,
                6.962259568889411e-06,
                4.0063711278232147e-05,
                0.00026119040169636406,
                5.829128636782753e-05,
                7.889261644760245e-06,
                0.0004305570322122693
            ],
            [
                4.785094494628999e-06,
                6.9622562492265485e-06,
                3.726640172537657e-06,
                5.422217030495909e-06,
                4.222833444467892e-06,
                2.561283431942246e-06,
                2.2603245672867952e-06,
                1.0129987356541108e-05,
                4.222831934202483e-06,
                5.829128632668981e-05
            ],
            [
                0.9999992661786695,
                0.9999994956525318,
                0.999999900688043,
                0.9999999006881497,
                0.9999996072136592,
                0.9999998874647842,
                0.9999999006880668,
                0.9999995549151073,
                0.9999999317440197,
                0.9999997897565838
            ],
            [
                0.9999998724809115,
                0.9999998724808963,
                0.9999999006881023,
                0.9999997897566338,
                0.9999998874647441,
                0.9999998144609423,
                0.9999998724809115,
                0.9999998144608097,
                0.9999999006881023,
                0.999999694097846
            ],
            [
                1.9947292363685024e-06,
                5.4222183231674305e-06,
                1.1478770861650256e-05,
                0.9999952149043646,
                7.484622088903895e-05,
                0.9999994284992805,
                1.3007133115903994e-05,
                6.1441767990323395e-06,
                4.006370650653807e-05,
                8.939695237666677e-06
            ],
            [
                6.962257909323729e-06,
                6.1441760661636525e-06,
                4.785093353626844e-06,
                3.7266383954560706e-06,
                5.422218969306048e-06,
                1.2098661160612089e-06,
                7.338208055436404e-07,
                6.9622587393661365e-06,
                1.1478772229551402e-05,
                1.5534983100765009e-06
            ],
            [
                0.9999999586006344,
                0.999999554914895,
                0.9999997897567091,
                0.9999998362623528,
                0.9999996072137998,
                0.9999998362622552,
                0.9999998362622942,
                0.9999997897566089,
                0.9999996533674202,
                0.9999999006879957
            ],
            [
                0.999999694097846,
                0.9999997300420937,
                0.9999997617631469,
                0.9999999317439546,
                0.9999999397643011,
                0.9999998362622357,
                0.9999997300421581,
                0.9999997300421903,
                0.9999998144608319,
                0.9999998874647976
            ],
            [
                0.9999996072139402,
                0.999999814460854,
                0.999999694097846,
                0.9999998362623137,
                0.9999997617630049,
                0.9999996533674615,
                0.9999997617631469,
                0.9999997300421903,
                0.9999996533672136,
                0.9999997897565587
            ],
            [
                0.9999996072137529,
                0.9999997617631469,
                0.9999991684719723,
                0.9999998362622943,
                0.9999996533672549,
                0.9999998724809116,
                0.9999998144608317,
                0.9999997300422547,
                0.9999995549150011,
                0.9999994956524716
            ],
            [
                0.9999997617630332,
                0.9999998724809115,
                0.9999994956524716,
                0.99999976176309,
                0.99999976176309,
                0.9999996940978825,
                0.9999996533672136,
                0.9999997617630049,
                0.9999996533672962,
                0.9999997897565587
            ],
            [
                2.4300246524568948e-05,
                3.2887506334201674e-06,
                6.962256249758443e-06,
                1.4738981969615573e-05,
                4.222833947498071e-06,
                1.994729483680993e-06,
                1.9947292458603553e-06,
                1.0129993394129904e-05,
                1.1478764020372226e-05,
                3.2887478888496478e-06
            ],
            [
                1.8925141470949294e-05,
                1.473898196763166e-05,
                4.5397879448184774e-05,
                1.4738980213985297e-05,
                5.829124466437278e-05,
                8.939695236398313e-06,
                4.222833947674739e-06,
                4.222833444383398e-06,
                7.889260703763482e-06,
                2.1444943300075563e-05
            ],
            [
                0.9999970976887069,
                0.999999168472074,
                0.9999952149037953,
                0.9999989322970027,
                0.9999990577556326,
                0.9999852610127573,
                0.9999980052707647,
                0.9999974387172235,
                0.9999938558246677,
                0.999996711251328
            ]
        ]
    },
    {
        "q_id": "7949_mmlu_math",
        "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,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            124,
            125,
            126,
            127,
            114,
            115,
            123
        ],
        "rewards": [
            [
                1.760342583722268e-06,
                1.0677031245623505e-06,
                2.260324567268294e-06,
                1.9947301970287804e-06,
                4.222832437677995e-06,
                4.450849458179853e-07,
                1.3007133112307748e-05,
                9.42244481511812e-07,
                3.726638395493353e-06,
                5.422219615395428e-06
            ],
            [
                9.931199245125105e-08,
                6.475951069755593e-07,
                6.475946437422142e-07,
                3.466326210993703e-07,
                3.059023363172604e-07,
                5.043475885228353e-07,
                5.71500378868701e-07,
                7.734416698754174e-08,
                1.8553916817576776e-07,
                6.475945665152892e-07
            ],
            [
                3.927861066113479e-07,
                6.1441738684354385e-06,
                1.5534979397267575e-06,
                2.902311984989368e-06,
                1.067703379136937e-06,
                1.3709572068079696e-06,
                1.209866116149238e-06,
                2.9023123310290063e-06,
                1.3709576971242028e-06,
                5.422217030121119e-06
            ],
            [
                0.9999938558268636,
                0.9999921107336532,
                0.9999962733607161,
                0.9999938558268633,
                0.9999921107374147,
                0.9999885212318762,
                0.9999898700090213,
                0.9999921107374157,
                0.9999930377420909,
                0.9999938558232011
            ],
            [
                1.994730196992497e-06,
                5.715007195384861e-07,
                2.5612828211442287e-06,
                3.7266406160032166e-06,
                4.2228349536200574e-06,
                2.9023109470554753e-06,
                1.370956716481313e-06,
                6.47594952559303e-07,
                6.475947209567798e-07,
                0.9999992661791945
            ],
            [
                2.902311984873224e-06,
                2.9023119846303784e-06,
                1.7603430033799313e-06,
                6.475947981472062e-07,
                9.422448185015797e-07,
                7.338208055436404e-07,
                6.475949525722606e-07,
                3.927861065906282e-07,
                7.33821067986608e-07,
                2.2603237588597026e-06
            ],
            [
                1.3709573702248741e-06,
                8.315284241401329e-07,
                9.422443691893433e-07,
                4.450849458153541e-07,
                5.715003107281153e-07,
                2.9023133690188264e-06,
                8.315278293951957e-07,
                7.338211554464836e-07,
                5.422217676797111e-06,
                3.2887486731641103e-06
            ],
            [
                0.9999986290423029,
                0.9999996072137529,
                0.999996273358939,
                0.9999987901344608,
                0.999999352404893,
                0.999997097686977,
                0.9999994956527121,
                0.9999982396559474,
                0.9999994284996211,
                0.9999993524053562
            ],
            [
                1.0129994597524319e-05,
                8.939696302652706e-06,
                3.7266401720529807e-06,
                1.0677031245429291e-06,
                2.260323758882316e-06,
                6.475947981904966e-07,
                3.726640172337686e-06,
                9.422443692330485e-07,
                1.5534983101061718e-06,
                9.422447062030659e-07
            ],
            [
                1.670142780910326e-05,
                4.222832940715735e-06,
                2.144494329496561e-05,
                2.4300246517938825e-05,
                2.4300249418927004e-05,
                5.04347348051526e-07,
                1.994730434816876e-06,
                3.7266392838544054e-06,
                1.5534975692866768e-06,
                1.5534973841450852e-06
            ],
            [
                0.9999997617630899,
                0.9999869928684375,
                0.9999921107336561,
                0.9999992661790195,
                0.9999993524054334,
                0.9999952149032236,
                0.9999987901347491,
                0.9999984465016899,
                0.9999993524051246,
                0.9999993524049702
            ],
            [
                0.9999994284995529,
                0.9999885212305086,
                0.99999893229713,
                0.9999982396559473,
                0.9999982396569966,
                0.9999997897567341,
                0.999997097686631,
                0.9999810748495068,
                0.9999957771680658,
                0.999996273358939
            ],
            [
                5.043472278227948e-07,
                1.994729959019382e-06,
                2.9023133684090715e-06,
                5.043474682903772e-07,
                3.4663249712890574e-07,
                2.902313368860448e-06,
                5.043474081785165e-07,
                1.994730196992497e-06,
                1.5534973841592143e-06,
                3.7266388393349185e-06
            ],
            [
                5.043472277961901e-07,
                1.370957697068717e-06,
                9.422445937186037e-07,
                1.370957533554517e-06,
                1.3709578605118645e-06,
                1.994729721323867e-06,
                1.760343842833246e-06,
                2.561282210618905e-06,
                5.043475284350422e-07,
                3.0590222691880844e-07
            ],
            [
                6.1441760661636525e-06,
                1.7603434231097403e-06,
                4.785096205717126e-06,
                4.785094494402695e-06,
                5.715005151446993e-07,
                2.902312330849511e-06,
                2.5612816000145246e-06,
                1.2098662603862553e-06,
                1.7603432131631714e-06,
                1.2098655392354511e-06
            ],
            [
                0.9999987901344608,
                0.9999810748517617,
                0.9999994284994167,
                0.9999987901344608,
                0.9999994956525918,
                0.9999967112501505,
                0.9999989322972573,
                0.9999984465024306,
                0.9999980052702785,
                0.9999957771675626
            ],
            [
                1.3709568798782093e-06,
                3.726640172337686e-06,
                8.315277302165032e-07,
                9.422447061953531e-07,
                2.26032429753354e-06,
                5.715007195275709e-07,
                6.475949525434003e-07,
                2.2603251060985603e-06,
                5.043475284350422e-07,
                9.422450431569214e-07
            ],
            [
                0.9999957771645421,
                0.9999994284994167,
                0.999996711251719,
                0.9999998362623723,
                0.9999977396762411,
                0.9999967112509348,
                0.9999989322966208,
                0.9999967112521109,
                0.9999977396765105,
                0.9999992661789321
            ],
            [
                2.902313022984344e-06,
                2.5612819053399912e-06,
                1.5534979397394734e-06,
                5.715004470243685e-07,
                2.561283431916622e-06,
                1.0677029972639127e-06,
                8.31528424151477e-07,
                1.3709570433536782e-06,
                1.7603427935678977e-06,
                3.2887478889962107e-06
            ],
            [
                2.9023116389365734e-06,
                1.994730196992497e-06,
                8.315278293604072e-07,
                2.2603253755949437e-06,
                1.994729483666479e-06,
                6.475947981904966e-07,
                2.9023130228840374e-06,
                1.3709568799592562e-06,
                8.939700566289352e-06,
                2.561281294644835e-06
            ],
            [
                0.9999910603015649,
                0.9999885212305069,
                0.99997569976798,
                0.9999962733611603,
                0.999959936309178,
                0.9999810748585312,
                NaN,
                0.9999921107402358,
                0.9999756997476837,
                0.9999785550464881
            ],
            [
                7.338211554398095e-07,
                8.315279285012978e-07,
                3.2887482810801374e-06,
                3.2887506334201674e-06,
                1.9947301969471416e-06,
                4.4508505191686215e-07,
                2.2603245672497918e-06,
                3.059022269206168e-07,
                2.9023123310290063e-06,
                2.2603253752310765e-06
            ],
            [
                0.9999991684722697,
                0.999994577780384,
                0.9999962733598275,
                0.9999994284994849,
                0.9999869928684365,
                0.9999980052693274,
                0.9999982396574163,
                0.999997097687669,
                0.9999898700078134,
                0.9999996072138465
            ],
            [
                0.9999967112501507,
                0.9999980052707542,
                0.9999991684722698,
                0.9999987901347491,
                0.9999970976880149,
                0.9999921107355343,
                0.9999962733589393,
                0.999997097686977,
                0.9999952149049356,
                0.9999967112509347
            ],
            [
                0.9999980052693275,
                0.9999992661791944,
                0.9999957771680668,
                0.9999989322970027,
                0.9999970976880149,
                0.9999986290426297,
                0.9999991684722698,
                0.9999998362623528,
                0.9999994956527721,
                0.9999996072137529
            ],
            [
                1.3709570433661467e-06,
                2.2603253755949437e-06,
                6.475951069631906e-07,
                2.9023130230133794e-06,
                5.715002426343175e-07,
                5.043475885453117e-07,
                8.315284241257637e-07,
                4.450849458125204e-07,
                5.715003107577426e-07,
                1.0677027427166074e-06
            ],
            [
                0.9999974387171787,
                0.9999898700102285,
                0.9999957771650453,
                0.9999339478238656,
                0.9998766053811251,
                0.9999417087345085,
                0.9999898700090227,
                0.9999485577986424,
                0.9999984465026159,
                0.9999756997592771
            ],
            [
                0.9999989322968754,
                0.9999832985821387,
                0.9999945777790915,
                0.9999982396572065,
                0.9999810748449955,
                0.999999266179107,
                0.9999980052700407,
                0.99997569975349,
                0.9999898700090203,
                0.9999980052702786
            ],
            [
                1.7603430032374404e-06,
                5.715004470129334e-07,
                3.726641061027928e-06,
                2.561282515988704e-06,
                8.315279285012978e-07,
                3.726639727994339e-06,
                2.9023126768680736e-06,
                2.5612819052374947e-06,
                2.260324836624822e-06,
                8.939697368842181e-06
            ],
            [
                5.715004470170917e-07,
                3.927863875520681e-07,
                3.927862938956128e-07,
                1.2098653950205268e-06,
                1.99472900777306e-06,
                1.9947299590520376e-06,
                5.043472278255469e-07,
                4.450851580362069e-07,
                5.04347468309184e-07,
                2.2603242976733308e-06
            ],
            [
                1.5534971988904843e-06,
                5.715004470025379e-07,
                1.9947306723745965e-06,
                5.715005151550947e-07,
                1.3709576969826825e-06,
                2.902311984783477e-06,
                5.422218969532895e-06,
                8.315283249636384e-07,
                1.3709578605455302e-06,
                1.0677033791291683e-06
            ],
            [
                8.315282258956806e-07,
                4.4508489275145346e-07,
                4.222831933795376e-06,
                1.3709578605118645e-06,
                4.222834450328596e-06,
                1.994729483694599e-06,
                5.422218322940583e-06,
                1.994729721436347e-06,
                1.9947294836483373e-06,
                8.315281267248819e-07
            ],
            [
                2.2603242977308917e-06,
                3.059022269144961e-07,
                0.9999599362982944,
                1.2098661161789477e-06,
                6.962253759581752e-06,
                2.5612819052654485e-06,
                2.260323758835034e-06,
                7.338212429504183e-07,
                3.2887506332945414e-06,
                1.5534975693488444e-06
            ],
            [
                0.9999957771680661,
                0.9999930377429205,
                0.9999994284992805,
                0.9999994956524715,
                0.9999991684720715,
                0.9999986290432834,
                0.9999990577550691,
                0.999998446502801,
                0.9999980052705164,
                0.999993855825399
            ],
            [
                0.9999756997650627,
                0.9999832985841324,
                0.9999038975393901,
                0.9999869928668853,
                0.9999417087414357,
                0.9999962733607162,
                0.9998601778927992,
                0.9998911031298375,
                0.9999832985841337,
                0.9999930377454107
            ],
            [
                3.2887494572514376e-06,
                1.5534971989258068e-06,
                1.5534977545497995e-06,
                2.260324567268294e-06,
                1.7603425836870455e-06,
                1.0677024881140118e-06,
                5.422218968822766e-06,
                2.260324028351814e-06,
                4.450849458179853e-07,
                4.785096775842062e-06
            ],
            [
                0.9999989322972573,
                0.9999938558253986,
                0.9999885212305086,
                0.9999986290426298,
                0.9999980052709919,
                0.9999996072138465,
                0.9999996072137529,
                0.9999974387177893,
                0.9999952149049355,
                0.9999970976880149
            ],
            [
                6.962257908348587e-06,
                6.962253759271479e-06,
                9.422448185015797e-07,
                1.5534979396645902e-06,
                4.785093353687772e-06,
                2.9023126769050284e-06,
                8.315282258756395e-07,
                1.2098658270766557e-06,
                8.31528126775552e-07,
                1.7603425836246058e-06
            ],
            [
                0.9999952149060758,
                0.9999724642990699,
                0.9999962733611603,
                0.9999869928699874,
                0.9999980052705163,
                0.9999974387168734,
                0.9999984465024306,
                0.9999982396559474,
                0.9999962733611603,
                0.9999990577552939
            ],
            [
                6.475948753794598e-07,
                6.475951069808602e-07,
                9.422444815220956e-07,
                6.144176065940129e-06,
                3.7266388393349185e-06,
                1.0677028699955933e-06,
                1.9947292458603553e-06,
                9.422447062150634e-07,
                2.9023116390104826e-06,
                2.2603251060738913e-06
            ],
            [
                8.315282258900085e-07,
                3.2887478886163427e-06,
                6.475946437722523e-07,
                1.209865971934245e-06,
                2.5612822106421996e-06,
                1.0677033791291683e-06,
                1.5534977545102382e-06,
                5.043472879383035e-07,
                4.785096204972935e-06,
                1.9947304346826253e-06
            ],
            [
                4.2228349539810764e-06,
                1.892514143752361e-05,
                3.726639283901856e-06,
                7.889259763326495e-06,
                1.0677033790621648e-06,
                1.994729483630195e-06,
                4.785095064436034e-06,
                2.430024651705481e-05,
                1.1478765385432939e-05,
                3.726641060244989e-06
            ],
            [
                7.889261644057078e-06,
                6.475948753930064e-07,
                1.3709572068079696e-06,
                3.726637950973972e-06,
                7.889260704050487e-06,
                3.7266406165319545e-06,
                5.715005151485975e-07,
                3.2887478891128633e-06,
                1.209865539274514e-06,
                3.726639728184142e-06
            ],
            [
                9.422450431654909e-07,
                8.315281267649641e-07,
                3.059023727728012e-07,
                5.71500310747347e-07,
                3.2887494571676872e-06,
                3.2887486723295965e-06,
                6.475950297768503e-07,
                3.2887494573561262e-06,
                4.4508526412562144e-07,
                1.7603440526133836e-06
            ],
            [
                0.9999980052707541,
                0.9999832985781617,
                0.9999989322971299,
                0.9999921107364752,
                0.9998601778760724,
                0.9999687980812002,
                0.9999756997505863,
                0.9999921107392958,
                0.9999910602994353,
                0.9999832985801479
            ],
            [
                1.0677032518316716e-06,
                8.315280275794301e-07,
                9.42244930862237e-07,
                1.3709573702248741e-06,
                9.422449308335287e-07,
                4.45084892734047e-07,
                8.315278292930992e-07,
                5.04347648672331e-07,
                1.0677029972639127e-06,
                1.994729959224386e-06
            ],
            [
                3.7266392839425286e-06,
                3.288750241042834e-06,
                2.5612831262578596e-06,
                2.9023116390104826e-06,
                6.475947209567798e-07,
                7.889260704050487e-06,
                2.561282515914161e-06,
                1.2098662602861223e-06,
                5.715005151446993e-07,
                8.315278293604072e-07
            ],
            [
                0.9999957771665559,
                0.9999921107345934,
                0.9999962733602719,
                0.9999986290426297,
                0.9999962733607163,
                0.999996273360716,
                0.9999952149049356,
                0.9999930377429213,
                0.9999993524051246,
                0.99999862904312
            ],
            [
                0.9999952149037942,
                0.9999993524051246,
                0.9999986290426297,
                0.9999992661792819,
                0.9999991684719725,
                0.9999869928684362,
                0.9999989322966208,
                0.9999980052693274,
                0.999999694097773,
                0.9999998144608538
            ],
            [
                0.9999646437324408,
                0.9999687980923607,
                0.99998329858015,
                0.9999251537906383,
                0.9999852610162742,
                0.9999945777803839,
                0.9999869928761903,
                4.222834450666572e-06,
                0.9999038975850683,
                0.999983298576167
            ],
            [
                0.999999554914842,
                0.9999898700102293,
                0.9999987901338838,
                0.9999852610127595,
                0.9999967112501507,
                0.9999986290424664,
                0.9999974387171787,
                0.9999982396574163,
                0.9999996533675028,
                0.999999352404893
            ],
            [
                2.5612822103812995e-06,
                1.0129995805691255e-05,
                1.994729483694599e-06,
                6.962259568889411e-06,
                8.939696303010449e-06,
                4.222832940162684e-06,
                4.222834450589758e-06,
                2.9023112930659533e-06,
                2.902311293034278e-06,
                7.889264465842609e-06
            ],
            [
                0.9999998724808964,
                0.9999251537460537,
                0.9999957771655491,
                0.9999885212346126,
                0.9999756997505781,
                0.9999989322967482,
                0.9999962733616046,
                0.9999921107364758,
                0.9999756997563796,
                0.9999898700114359
            ],
            [
                5.043474081957179e-07,
                2.5612828207295832e-06,
                1.0677033791000363e-06,
                2.561282210562998e-06,
                3.2887478889034873e-06,
                1.553498310118888e-06,
                1.5534971989258068e-06,
                1.2098655392464547e-06,
                0.9999832985741829,
                7.33821067986608e-07
            ],
            [
                6.475949525722606e-07,
                5.715004469900632e-07,
                1.0677028700130727e-06,
                1.760344052632596e-06,
                1.2098653950551882e-06,
                1.0677031245851707e-06,
                6.144173133762157e-06,
                3.726640172290235e-06,
                1.0677029972993568e-06,
                5.715005832762133e-07
            ],
            [
                8.315283250082584e-07,
                1.9947292456607935e-06,
                9.422443691893433e-07,
                1.2098662603862553e-06,
                2.561281294558644e-06,
                9.422448185264317e-07,
                1.0677026154730804e-06,
                5.715005832853093e-07,
                1.0677028700266676e-06,
                2.90231094680735e-06
            ],
            [
                0.9998415638024049,
                4.222834450328596e-06,
                3.2887478864687415e-06,
                6.14417679836736e-06,
                8.939698430218506e-06,
                5.4222202617511845e-06,
                2.9023109465275493e-06,
                5.4222196154940574e-06,
                4.222833444168322e-06,
                6.1441760651689774e-06
            ],
            [
                0.9999869928668849,
                0.9994472214657896,
                0.9998911030908624,
                0.9999546021466367,
                0.9998766053664693,
                0.9998204720770398,
                0.9997694932030821,
                0.9999485577802407,
                0.9999251537460603,
                0.9998911030650574
            ],
            [
                2.2603240282243575e-06,
                2.902313368897403e-06,
                3.4663249713741784e-07,
                4.450849457805411e-07,
                1.5534981248881956e-06,
                4.222833947029514e-06,
                1.3709575336860625e-06,
                1.370957370247318e-06,
                1.76034300345598e-06,
                7.338213304243302e-07
            ],
            [
                1.9947306721859212e-06,
                1.370956716481313e-06,
                5.715003107353922e-07,
                0.999993855826865,
                7.338211553016564e-07,
                1.0677026154473471e-06,
                4.2228319329965265e-06,
                9.42244256886598e-07,
                6.475947981860793e-07,
                6.962257908348587e-06
            ],
            [
                1.370957206783032e-06,
                8.315284241333265e-07,
                8.93969523264201e-06,
                6.144173136729416e-06,
                2.5612825160271407e-06,
                2.2603251059484907e-06,
                1.370957860466977e-06,
                6.144176065314267e-06,
                3.288747889178668e-06,
                1.209866116170145e-06
            ],
            [
                6.4759479808713e-07,
                7.338208055536515e-07,
                1.7603436329714805e-06,
                3.466326624233938e-07,
                5.715003788853339e-07,
                9.422444815409489e-07,
                9.422442568428928e-07,
                1.2098656834613962e-06,
                2.9023119847359636e-06,
                2.5612822103812995e-06
            ],
            [
                4.4508521110762794e-07,
                3.4663253846316044e-07,
                3.2887494572873306e-06,
                1.5534979396815448e-06,
                1.7603432132624344e-06,
                1.7603434231385591e-06,
                3.7266379512518984e-06,
                2.9023109471452223e-06,
                4.7850927830845245e-06,
                3.288750633518874e-06
            ],
            [
                3.2887482811908074e-06,
                6.475948753182055e-07,
                1.2098655391947376e-06,
                5.4222202614355715e-06,
                9.422447061953531e-07,
                4.785092783210732e-06,
                8.31528325021115e-07,
                1.7603438427243761e-06,
                4.222834450743383e-06,
                3.726637951170554e-06
            ],
            [
                0.9999832985781574,
                0.999988521231875,
                0.9999546021097396,
                0.9999646437450908,
                0.9999339478238556,
                0.9999898700090203,
                0.9997965730997718,
                0.9999869928699864,
                0.9999885212359804,
                0.9999687980774796
            ],
            [
                3.466327863850901e-07,
                4.785092783267308e-06,
                3.2887498492518007e-06,
                4.4508510494677833e-07,
                5.715005151025973e-07,
                4.222835457595211e-06,
                1.760343632920248e-06,
                1.2098662602663157e-06,
                1.370957206753107e-06,
                1.5534975692866768e-06
            ],
            [
                0.9999980052700408,
                0.999997438717484,
                0.9999921107392965,
                0.9999987901347492,
                0.9999997617630049,
                0.9999992661788446,
                0.9999974387187053,
                0.999999730042126,
                0.9999987901341723,
                0.9999994284994848
            ],
            [
                2.26032537546132e-06,
                4.7850967757637256e-06,
                1.760344052650207e-06,
                1.3709573702566696e-06,
                8.31528027618756e-07,
                2.902311639073834e-06,
                1.5534975690648522e-06,
                5.715004470129334e-07,
                8.315284241333265e-07,
                9.422447061679302e-07
            ],
            [
                0.9999339478553727,
                0.9999994284996211,
                0.9999970976869772,
                0.9999967112509347,
                0.9999989322972572,
                0.9999992661791945,
                0.9999993524051246,
                0.9999977396765105,
                0.999997739674894,
                0.9999832985721903
            ],
            [
                1.7603432133032607e-06,
                9.422447062202052e-07,
                1.4449805540651476e-07,
                3.05902226922147e-07,
                4.450849458179853e-07,
                2.3823685318968256e-07,
                1.3709572067955008e-06,
                5.043475885453117e-07,
                8.315278293899016e-07,
                3.9278638755671223e-07
            ],
            [
                2.260325375615501e-06,
                0.9999910603026354,
                4.7850927830845245e-06,
                5.715005832676369e-07,
                2.2603251061458426e-06,
                9.422449308138184e-07,
                8.315281267706361e-07,
                4.7850933534310035e-06,
                6.475948753370529e-07,
                3.7266379512518984e-06
            ],
            [
                6.144174600471243e-06,
                2.561283126639892e-06,
                2.5612819048205203e-06,
                6.144174601499446e-06,
                3.7266397280960194e-06,
                5.42221961567159e-06,
                3.7266388394569345e-06,
                0.9999974387177893,
                0.9999993524050474,
                4.785096205434246e-06
            ],
            [
                0.9999995549150011,
                0.999997438717484,
                0.999998629042303,
                0.9999982396567868,
                0.9999989322972572,
                0.9999957771660524,
                0.9999990577550691,
                0.9999993524052019,
                0.9999986290429567,
                0.9999967112513268
            ],
            [
                5.715007195410849e-07,
                3.7266388394569345e-06,
                4.450852110981151e-07,
                2.9023126768680736e-06,
                2.699577130905084e-07,
                3.2887490652451393e-06,
                2.1024344128584085e-07,
                2.561282821352716e-06,
                8.315282258900085e-07,
                1.3007130011655787e-05
            ],
            [
                0.9999991684722697,
                0.9999986290426297,
                0.9999977396746246,
                0.9999994284996212,
                0.9999970976883609,
                0.9999984465026158,
                0.9999996072138934,
                0.9999987901346049,
                0.9999987901344607,
                0.9999990577552937
            ],
            [
                0.9999869928746383,
                0.9998204720770398,
                0.9999687980997889,
                0.9999987901344607,
                0.9999646437324424,
                0.9999417087484003,
                0.9999938558232012,
                0.9999339478317699,
                0.9999952149066464,
                0.9999785550490328
            ],
            [
                1.9947290080125335e-06,
                1.1478768122069266e-05,
                5.422220907909759e-06,
                0.9999977396762411,
                1.0677029972745947e-06,
                3.9278605977939997e-07,
                5.422217030121119e-06,
                4.222832437443716e-06,
                2.561283126502453e-06,
                8.315279284544091e-07
            ],
            [
                0.9999984465024306,
                0.999996711252111,
                0.9999957771655489,
                0.9999982396574163,
                0.9999977396751633,
                0.9999989322973846,
                0.9999993524049703,
                0.9999938558224687,
                0.9999989322967481,
                0.9999995549149481
            ],
            [
                5.715005832676369e-07,
                5.043474081831035e-07,
                3.288749065029781e-06,
                3.7266406167827664e-06,
                8.315280275416164e-07,
                9.422447061576466e-07,
                1.994729245345125e-06,
                5.043475885453117e-07,
                3.0590237278532086e-07,
                3.9278605979208185e-07
            ],
            [
                2.2603251061232293e-06,
                4.785096205173126e-06,
                2.9023130230133794e-06,
                1.9947301968056346e-06,
                1.9947297214544894e-06,
                1.5534983101301911e-06,
                1.2098659719601033e-06,
                1.7603440525701563e-06,
                2.9023123309973302e-06,
                1.994729245693449e-06
            ],
            [
                7.338208930144969e-07,
                9.42244256915735e-07,
                1.067702488159652e-06,
                2.5612819052654485e-06,
                7.33821067986608e-07,
                5.71500583272315e-07,
                1.5534981249023245e-06,
                8.315277302444853e-07,
                1.3709578604981489e-06,
                1.8553910183379568e-07
            ],
            [
                0.9999852610215472,
                0.9999990577555185,
                0.9999687980774709,
                0.9999869928699903,
                0.9999970976866313,
                0.9999974387180947,
                0.9999339478474997,
                0.9999852610127591,
                0.9999970976887071,
                0.9998766054549343
            ],
            [
                8.315281267649641e-07,
                3.7266392836984955e-06,
                3.2887478887958082e-06,
                5.71500310747347e-07,
                1.5534983101301911e-06,
                2.5612819052654485e-06,
                1.2098656834195822e-06,
                1.3709570433661467e-06,
                1.9947301970106386e-06,
                2.9023126767836054e-06
            ],
            [
                5.715003107130418e-07,
                2.260324836651547e-06,
                2.9023116390421582e-06,
                1.7603438428188364e-06,
                6.475947209826952e-07,
                5.715006513952608e-07,
                3.059021539823092e-07,
                5.715005151446993e-07,
                8.31527928417352e-07,
                5.715006513952608e-07
            ],
            [
                2.561281294644835e-06,
                1.553497569203316e-06,
                9.422444815628016e-07,
                3.9278629390507954e-07,
                9.422443691893433e-07,
                1.2098655392222467e-06,
                3.466325797827604e-07,
                2.260323758939877e-06,
                9.422450431800595e-07,
                4.450850519360903e-07
            ],
            [
                1.370957043323753e-06,
                6.475945665900901e-07,
                3.2887490653109436e-06,
                3.9278638754242273e-07,
                6.14417679836736e-06,
                5.715005150859644e-07,
                7.338207180601138e-07,
                2.561281294558644e-06,
                2.260325375391425e-06,
                5.043472879504592e-07
            ],
            [
                2.1024336609638268e-07,
                5.04347648667744e-07,
                2.3823688158950683e-07,
                4.450851049743049e-07,
                3.059022268944645e-07,
                4.45084945809282e-07,
                3.466327037472645e-07,
                1.2751901247915667e-07,
                3.466325384339989e-07,
                1.6373766671763785e-07
            ],
            [
                3.5356254910985954e-05,
                4.539786321436876e-05,
                8.481106151541198e-05,
                4.006368731905769e-05,
                1.1478772229551402e-05,
                5.8291244672006574e-05,
                1.3007128463069061e-05,
                2.1444950963097686e-05,
                4.5397884859458064e-05,
                3.535623806128476e-05
            ],
            [
                0.9999910603068939,
                0.9999957771675625,
                0.9999990577554061,
                0.9999852610180356,
                0.9999885212291397,
                0.9999938558275958,
                0.9999869928699859,
                0.9999938558253986,
                0.9999974387180947,
                0.999986992876194
            ],
            [
                3.2887494573232236e-06,
                4.7850950646797465e-06,
                1.0677026154376365e-06,
                1.9947299590810645e-06,
                1.7603440526662173e-06,
                8.939696302051047e-06,
                1.3709575336405514e-06,
                9.422445938861406e-07,
                6.962258738701267e-06,
                7.338210679695891e-07
            ],
            [
                5.043474081739295e-07,
                1.7603427935518875e-06,
                2.9023116389761676e-06,
                6.475947209567798e-07,
                6.144174600325954e-06,
                2.5612822104977725e-06,
                9.422447060908033e-07,
                5.043473480345541e-07,
                1.7603436328033735e-06,
                1.3709567164663505e-06
            ],
            [
                3.927862938956128e-07,
                3.2887478889962107e-06,
                1.5534979397592542e-06,
                1.994729008074216e-06,
                3.288748280837859e-06,
                2.260324836696773e-06,
                2.260323489299784e-06,
                2.902311292831027e-06,
                4.222834451254188e-06,
                1.2098662603752517e-06
            ],
            [
                1.9947301969471416e-06,
                3.7266379512857925e-06,
                5.715007195275709e-07,
                2.5612831265909735e-06,
                1.7603430033799313e-06,
                1.2098652508056196e-06,
                9.42245043087507e-07,
                2.902313368583287e-06,
                3.927862939075802e-07,
                2.9023112930659533e-06
            ],
            [
                0.9999646437366654,
                7.338211554231243e-07,
                8.315277302165032e-07,
                6.475945665800774e-07,
                1.0677024881004167e-06,
                0.9999930377454107,
                1.3709572067680694e-06,
                3.927862002582919e-07,
                2.9023116389365734e-06,
                8.315277302165032e-07
            ],
            [
                2.5612822106421996e-06,
                4.222835457364773e-06,
                1.0677028699955933e-06,
                1.0677026154279257e-06,
                8.315277302701984e-07,
                3.4663253844660926e-07,
                5.715005832762133e-07,
                8.315277302747361e-07,
                1.3709578604495207e-06,
                1.7603427935967163e-06
            ],
            [
                2.9023133686835932e-06,
                4.7850944942634305e-06,
                1.209865683500459e-06,
                1.760343842833246e-06,
                1.0677024881683915e-06,
                5.043474683126242e-07,
                1.3709572068179446e-06,
                1.067703251769523e-06,
                3.9278605978797364e-07,
                4.450851580402549e-07
            ],
            [
                0.999997438717484,
                0.9999952149043646,
                0.999996273360272,
                0.9999986290423029,
                0.9999967112493665,
                0.9999977396748938,
                0.9999785550566999,
                0.9999785550515903,
                0.9999852610110034,
                0.9999987901346049
            ],
            [
                1.760342793583908e-06,
                3.466326210962177e-07,
                2.902311984873224e-06,
                1.3709568799760888e-06,
                3.288749849368453e-06,
                2.561282210618905e-06,
                1.7603440526806268e-06,
                2.561282210618905e-06,
                4.785096205778054e-06,
                8.315282258756395e-07
            ],
            [
                2.26032348933062e-06,
                1.5534979396984994e-06,
                2.902312676941983e-06,
                1.5534984952111384e-06,
                6.475946437722523e-07,
                9.422442568763144e-07,
                2.902310946944611e-06,
                7.338210679695891e-07,
                5.715006513900631e-07,
                1.0677028698868336e-06
            ],
            [
                1.0677032518501217e-06,
                2.561281599776919e-06,
                1.7603438426491283e-06,
                1.5534981248881956e-06,
                0.9999810748540223,
                2.9023109470554753e-06,
                1.067703251784089e-06,
                3.059023363172604e-07,
                1.0677032518093368e-06,
                3.288750241473551e-06
            ],
            [
                1.5534979396815448e-06,
                3.9278615343222713e-07,
                4.4508521109406705e-07,
                3.0590219045271286e-07,
                7.33820892991805e-07,
                1.553497384180408e-06,
                7.338213304016384e-07,
                1.0677032518578904e-06,
                5.043476486379284e-07,
                6.47594643788744e-07
            ],
            [
                0.9999967112505428,
                0.9999962733593832,
                0.9999996533673375,
                0.9999938558246664,
                0.9999993524052019,
                0.9999952149043648,
                0.9999930377437524,
                0.9999994956524114,
                0.9999989322968754,
                0.9999991684717742
            ],
            [
                0.9999982396561572,
                0.9999832985841371,
                0.9999990577555185,
                0.9999724642957958,
                0.9999977396757023,
                0.9999993524051246,
                0.9999980052698032,
                0.9999991684717742,
                0.9999910603015656,
                0.9999938558239339
            ],
            [
                3.927863875520681e-07,
                3.7266397274452643e-06,
                1.9947306725868575e-06,
                5.043472278159142e-07,
                3.2887486731641103e-06,
                8.315284241597959e-07,
                1.2098658276730537e-06,
                4.785096205717126e-06,
                3.4663274507098256e-07,
                5.71500310747347e-07
            ],
            [
                0.9999785550490333,
                0.9999996533672549,
                0.9999852610215433,
                0.9999977396759716,
                0.9999417087414523,
                0.999993855826131,
                0.9999990577551814,
                0.9999921107374158,
                0.9999885212332442,
                0.9999989322972572
            ],
            [
                6.144173136729416e-06,
                5.422217676654099e-06,
                1.0677032518316716e-06,
                1.0677028699742299e-06,
                3.2887498493325602e-06,
                1.670141785809127e-05,
                1.6701423832586287e-05,
                4.222835457364773e-06,
                2.260324567268294e-06,
                1.0129989769464556e-05
            ],
            [
                0.9996200155617031,
                0.999290329662405,
                0.9579122752383733,
                0.9995694429151432,
                0.8519528019683105,
                0.999992110738356,
                0.999941708714346,
                0.32082130731838393,
                0.99896776881115,
                0.9995694429666103
            ],
            [
                5.043473480607e-07,
                1.3709578605243332e-06,
                5.42222090767305e-06,
                2.902313368963394e-06,
                1.370957533554517e-06,
                9.422450430720816e-07,
                2.902311984873224e-06,
                6.475947981754775e-07,
                1.7603438427852151e-06,
                8.315283249833015e-07
            ],
            [
                1.9947292457750883e-06,
                2.9023116384746377e-06,
                6.962255418924822e-06,
                1.3709568798220997e-06,
                1.0677028699489821e-06,
                1.760343632854606e-06,
                3.7266388396975786e-06,
                3.288747889038086e-06,
                3.9278610660598936e-07,
                0.9999930377412614
            ],
            [
                1.9947294836483373e-06,
                8.939693104865575e-06,
                3.2887502412970765e-06,
                4.22283294007051e-06,
                3.726637951170554e-06,
                1.3007133113372426e-05,
                5.422220261544064e-06,
                3.2887486731252264e-06,
                6.144173868178388e-06,
                7.338211554591642e-07
            ],
            [
                2.260324028331257e-06,
                7.338210679542388e-07,
                4.4508505192819656e-07,
                2.102433159684668e-07,
                1.2098653950403334e-06,
                3.05902117518448e-07,
                3.9278634071508535e-07,
                1.0677028699489821e-06,
                3.0590219043949756e-07,
                2.1024334102826433e-07
            ],
            [
                0.999941708741448,
                0.9999945777803843,
                0.999999352404893,
                0.9999991684720715,
                0.9999910603004994,
                0.9999724642990556,
                0.9999980052702785,
                0.999991060302631,
                0.9999990577554061,
                0.9999987901341723
            ],
            [
                5.715005151446993e-07,
                5.043472278159142e-07,
                6.475947981201131e-07,
                4.4508521108961425e-07,
                2.5612822106421996e-06,
                1.9947299590520376e-06,
                9.422449308035348e-07,
                2.561283431916622e-06,
                1.7603425836678333e-06,
                1.5534975692259223e-06
            ],
            [
                1.9947301970287804e-06,
                2.9023126769050284e-06,
                1.7603427935967163e-06,
                5.71500378868701e-07,
                1.370956716519966e-06,
                1.994730196992497e-06,
                4.4508515799046414e-07,
                2.2603251061458426e-06,
                1.0677026154551157e-06,
                6.475947209768052e-07
            ],
            [
                0.9999992661786696,
                0.9999832985741766,
                0.9999984465018751,
                0.9999980052709919,
                0.9999970976890529,
                0.9999962733589393,
                0.9999980052702785,
                0.9999921107383574,
                0.9999970976880151,
                0.9999984465026159
            ],
            [
                1.7603438427660027e-06,
                2.1024344128239898e-07,
                9.931199245125105e-08,
                5.04347348051526e-07,
                5.715002426140462e-07,
                1.1253520229983549e-07,
                1.855390797136229e-07,
                6.475947981095112e-07,
                6.47594952559303e-07,
                2.3823696679230424e-07
            ],
            [
                2.260324028331257e-06,
                5.04347588554027e-07,
                2.260324028372372e-06,
                1.9947290080125335e-06,
                2.561282821176841e-06,
                0.9999957771660523,
                8.315283250082584e-07,
                1.3709572068272963e-06,
                5.715003788853339e-07,
                5.4222183221120994e-06
            ],
            [
                0.9999945777797377,
                0.9999970976866309,
                0.9999974387168734,
                0.9999945777823234,
                0.9999687980886605,
                0.9999832985841314,
                0.9999982396565769,
                0.9999989322975118,
                0.9999910603068949,
                0.9999687980812043
            ],
            [
                1.9947294835866542e-06,
                3.7266392839832006e-06,
                6.144176798870286e-06,
                2.561283431888668e-06,
                1.370957697068717e-06,
                7.338212429006964e-07,
                1.370957206783032e-06,
                5.422217676486429e-06,
                1.0677026154619133e-06,
                1.3709573702566696e-06
            ],
            [
                0.9999852610110022,
                0.9999980052709919,
                0.9999832985721941,
                0.9999938558246663,
                0.9999852610127585,
                0.9999810748586091,
                0.999995777164542,
                0.999994577780384,
                0.9999970976873229,
                0.9999724643056309
            ],
            [
                0.999989870009021,
                0.9999251537638956,
                4.785095634356291e-06,
                0.9999930377462409,
                0.999796572930906,
                0.9998911031326754,
                0.9999885212359809,
                0.9999417087553522,
                0.9999417087206043,
                0.9998766053664531
            ],
            [
                2.9023116389761676e-06,
                4.785094493532295e-06,
                6.144173868983067e-06,
                9.422444815323792e-07,
                4.222831932159269e-06,
                2.561281294369958e-06,
                1.9947304346535984e-06,
                3.288750633488963e-06,
                4.785093353187292e-06,
                5.715003788853339e-07
            ],
            [
                0.9997694932024248,
                0.29421497216298875,
                NaN,
                0.047425870316531935,
                0.9999687980738009,
                0.9997694932402661,
                0.2018132126589859,
                0.10669059394565118,
                0.999989870012645,
                0.999959936293753
            ],
            [
                0.9999921107392964,
                0.9999974387165681,
                0.999997097686631,
                0.9999991684717742,
                0.9999910603036969,
                0.9999984465016899,
                0.9999984465022455,
                0.999997097689053,
                0.9999991684718733,
                0.9999984465026158
            ],
            [
                4.4508526413736074e-07,
                6.962255417721724e-06,
                3.7266397281434697e-06,
                1.370957370083977e-06,
                1.2098653950205268e-06,
                8.315283250305684e-07,
                5.71500242607809e-07,
                2.561283431942246e-06,
                5.422217030495909e-06,
                1.7603434230312906e-06
            ],
            [
                9.422450431654909e-07,
                1.209865395009523e-06,
                8.315278293067121e-07,
                4.450851049743049e-07,
                5.715005832572414e-07,
                3.4663270369067526e-07,
                1.7603436329714805e-06,
                3.0590215397952704e-07,
                6.475947981695877e-07,
                3.2887482803712492e-06
            ],
            [
                0.999996273358939,
                0.9999898700114374,
                0.9999756997621758,
                0.9999977396765106,
                0.9999984465028011,
                0.9999885212359814,
                0.999992110733653,
                0.9999957771670593,
                0.999933947847538,
                0.9999869928668877
            ],
            [
                1.3709567164962755e-06,
                6.47594566594213e-07,
                1.0677032518093368e-06,
                1.0677031245623505e-06,
                1.2098658277181688e-06,
                1.2098652508144226e-06,
                1.2098655392222467e-06,
                5.71500242637956e-07,
                7.338208055613267e-07,
                1.7603430032918752e-06
            ]
        ]
    },
    {
        "q_id": "8105_mmlu_math",
        "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,
            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": [
            [
                9.610241376972762e-05,
                1.670141984118446e-05,
                6.605217586044201e-05,
                0.999704043010183,
                0.0009110513891619314,
                0.00023050682223050458,
                0.00010889690909804562,
                2.1444945844014022e-05,
                0.0005527785159767532,
                9.61024260093965e-05
            ],
            [
                0.012431649080924475,
                0.0019267347909329615,
                0.0019267350004746203,
                0.004070138227433432,
                0.012431653105673176,
                0.9999970976880153,
                0.0015011822823882371,
                0.0021827163505186028,
                0.0019267345231853195,
                0.007577239923211134
            ],
            [
                0.007577242864632608,
                0.001169510112747076,
                0.0031726830324645618,
                0.999994577781034,
                0.002182716920999415,
                0.01098694456350667,
                0.009708478093183752,
                0.0015011823972081039,
                0.001325022725926436,
                0.0017007226901266336
            ],
            [
                6.1441775309064404e-06,
                6.962257909323729e-06,
                0.00013982212298973152,
                1.6701421832054962e-05,
                1.9947301970106386e-06,
                2.902311985079115e-06,
                6.14417606469958e-06,
                1.7603434230921292e-06,
                1.892514821904893e-05,
                4.222833947897496e-06
            ],
            [
                0.9982992773701577,
                0.0002959570967475842,
                0.0006263340661849014,
                0.0019267342115593482,
                0.0028009268234013554,
                0.00970847519210651,
                0.9999989322972572,
                0.0010322309691703495,
                0.02297736915735049,
                0.004609571564032046
            ],
            [
                0.04742587284097444,
                0.025957355455306908,
                0.0007096702744382043,
                0.01243165207661799,
                0.005220125712903368,
                0.002182716110663159,
                0.005220124600567677,
                0.0017007223742764451,
                0.9999987901347492,
                0.020332353936289696
            ],
            [
                0.004070137604528235,
                0.0015011820635674213,
                0.9579122728353318,
                0.0028009265743307245,
                0.0031726832894521805,
                0.2942149597859341,
                0.010986941972795471,
                0.0013250222003128589,
                0.9399133523506772,
                0.014063626462134786
            ],
            [
                0.0019267344381150066,
                0.0011695101856375406,
                0.0015011823406706607,
                0.005220125069683135,
                0.0009110513874665119,
                0.00029595723730392506,
                0.06008665311947337,
                0.9999991684722698,
                0.0004878571320635621,
                0.0005527786561541827
            ],
            [
                0.025957356303004706,
                0.005220126208618263,
                0.01406362590685126,
                0.02297737133174536,
                0.03308597958047281,
                0.002182716884995733,
                0.0031726829293749785,
                0.13296425222296632,
                0.009708478263308678,
                0.010986941153078383
            ],
            [
                0.0004305570296445492,
                0.005220125521871787,
                0.002472623667743089,
                5.8291244639350886e-05,
                0.0007096704090900914,
                0.004070137219459616,
                0.002472623618929369,
                0.0004305571226336006,
                7.484626281133387e-05,
                0.003593602227100144
            ],
            [
                0.0035936019036269056,
                0.0006263341587288085,
                0.005220126191691412,
                0.9999993524050474,
                0.04208772521219692,
                0.01798620650765971,
                0.001700722496030954,
                0.0009110511355907985,
                0.029312231864311967,
                0.009708474413113692
            ],
            [
                0.008577484661322908,
                0.9999810748518333,
                0.999998239656577,
                0.9999987901341725,
                0.9992903297523106,
                0.9999151889508153,
                0.9999993524054335,
                0.9999984465015047,
                0.007577242395405775,
                0.0007096702569359375
            ],
            [
                0.0035936018427672528,
                0.004070138106627568,
                0.0004878572140341606,
                0.005220124731146202,
                0.006692850218455574,
                0.0028009263850890843,
                0.022977371164484207,
                0.0007096703694210319,
                0.004070136832503441,
                0.0066928509242848554
            ],
            [
                5.829125852607975e-05,
                4.5397852361605714e-05,
                2.7535681246690542e-05,
                1.4738976699427788e-05,
                1.6701421842961097e-05,
                2.753568451218037e-05,
                1.1478765387416494e-05,
                7.8892607025437e-06,
                8.481100963559981e-05,
                0.9740426425667315
            ],
            [
                0.00970847503093558,
                0.0021827169635953215,
                0.06754669630158146,
                0.010986941679316508,
                0.01798620973179608,
                0.0035936022129273468,
                0.005911068462218714,
                0.002182716447880651,
                0.006692850017232326,
                0.03308597672022805
            ],
            [
                0.0008040860018971236,
                0.9999998144608317,
                0.001501181948573082,
                0.002800927329346467,
                0.0035936024296877793,
                0.0031726826922689496,
                0.008577485809706263,
                0.012431650978959215,
                0.0019267347067581137,
                0.008577484811800718
            ],
            [
                0.033085978269527264,
                0.0019267343718497123,
                0.0011695103484171956,
                0.00116951005032782,
                0.0066928524102414805,
                0.0028009265119004908,
                0.006692852001603376,
                0.003172683445559283,
                0.00023050664624336612,
                0.0015011819803317603
            ],
            [
                1.1478768123823146e-05,
                1.7603438428460541e-06,
                0.0005527787462292141,
                3.72664061671159e-06,
                3.535625488822007e-05,
                3.120191132631554e-05,
                3.120190755988168e-05,
                2.9023126767836054e-06,
                3.53562506877236e-05,
                1.9947306725669014e-06
            ],
            [
                0.0009110511427963291,
                0.0003799844246662885,
                0.0017007224869388963,
                0.00015843617785585347,
                0.00048785710265860006,
                7.484626273564317e-05,
                5.829125851717365e-05,
                0.0003353500998792239,
                2.4300246520590875e-05,
                5.144221954791831e-05
            ],
            [
                4.785094493532295e-06,
                0.00023050676558247088,
                0.0015011819025055491,
                2.4300240714549077e-05,
                8.939696303010449e-06,
                8.93969630333567e-06,
                0.00023050665908071752,
                5.715005151574337e-07,
                0.0015011821506420485,
                0.00010889694778644778
            ],
            [
                5.422218322940583e-06,
                3.2887490653872164e-06,
                3.7266401720529807e-06,
                1.8925152750176348e-05,
                1.4738976699106073e-05,
                6.9622579075254155e-06,
                1.0129988563914856e-05,
                7.889266347133978e-06,
                6.1441760661636525e-06,
                8.939695237959376e-06
            ],
            [
                1.3007126897471327e-05,
                0.0017007226569208539,
                0.0019267350040565292,
                4.006370160848361e-05,
                0.0001233945868412559,
                0.9999038976195017,
                0.0031726832865067636,
                0.0003353499817841547,
                0.01406363015541646,
                1.012999097799944e-05
            ],
            [
                0.0003799845599217908,
                4.222833444037741e-06,
                0.0013250226433564115,
                0.00010889688211108299,
                0.004070138206669924,
                0.004609571531982978,
                0.0002611902700171631,
                0.0010322308527281998,
                0.003593601929471416,
                0.9933071497815444
            ],
            [
                0.003593603064128967,
                0.01798620973179608,
                0.0004878570821091875,
                0.00407013781216329,
                0.015906393140492553,
                0.0059110692584777615,
                0.007577240882674681,
                0.0021827167009205776,
                0.017986209863393495,
                0.0031726832025623817
            ],
            [
                0.0015011819735263293,
                2.1444956065331412e-05,
                0.0005527787645272141,
                6.962257079376403e-06,
                0.0003353502578597385,
                0.0028009264475193146,
                8.481102091427321e-05,
                0.00023050673572253731,
                0.00033535017421552525,
                1.300713466316634e-05
            ],
            [
                0.008577486015623295,
                0.012431648429189722,
                0.0021827161628938346,
                0.9999982396567868,
                0.0015011819637544281,
                0.004070137523361808,
                0.003593603172509207,
                0.004070138661579535,
                0.0075772399372179,
                0.00033535025214231
            ],
            [
                0.014063625584012009,
                0.01590639308217917,
                0.0001584361587827577,
                0.9999987901337396,
                0.1824255149165352,
                0.0019267342491693768,
                0.00043055708446850666,
                0.007577242941669852,
                0.0075772423393786915,
                0.0008040859829099936
            ],
            [
                0.015906392936395713,
                0.9999970976876692,
                0.0031726832577889485,
                0.0046095720875002,
                0.009708478352848113,
                0.0011695104430660278,
                0.020332352155396922,
                0.0008040858223144329,
                0.004609571980669959,
                0.004070137527136991
            ],
            [
                0.0021827165006184286,
                0.004070137421431878,
                0.006692849481668946,
                0.00857748685513124,
                0.9999997300420939,
                0.0031726824028818013,
                0.010986942043635222,
                0.025957355314023947,
                0.0007096704679951402,
                0.00970847853192699
            ],
            [
                0.004070136924995402,
                0.005911069184598051,
                0.02297737233531229,
                0.001501182216427892,
                0.0008040860921093811,
                0.9999995549150011,
                0.00170072222722231,
                0.00591107002463777,
                0.000804085805385025,
                0.00591106873584724
            ],
            [
                0.0007096703430437915,
                0.002182716823130252,
                0.005220124675529423,
                0.01098694248891367,
                0.010986940404201093,
                0.0031726830125829992,
                0.0004305570334773411,
                0.006692850066764202,
                0.0024726234719139356,
                0.012431651973712474
            ],
            [
                4.5397879432165314e-05,
                6.144175333401224e-06,
                1.0129994598482479e-05,
                2.144495351004062e-05,
                5.8291258442956145e-05,
                1.4738976698006875e-05,
                8.93969950000193e-06,
                4.006370169593065e-05,
                4.539788482296012e-05,
                1.473898196763166e-05
            ],
            [
                0.0005527785090949073,
                9.610245991215482e-05,
                0.00013982210575433653,
                1.8925150490826034e-05,
                1.473898898859989e-05,
                1.0129990973503458e-05,
                5.144222579863794e-05,
                6.9622562478334885e-06,
                1.892514597770291e-05,
                0.0005527785982694861
            ],
            [
                0.015906389962413444,
                0.08509904500702023,
                0.015906392586515418,
                0.029312231440328854,
                0.9999646437414109,
                0.006692850648763768,
                0.9997965730107099,
                0.005220126242471964,
                0.9997965730380216,
                0.02297736756836975
            ],
            [
                0.00037998451998078617,
                0.9999756997593403,
                0.0004305571754409696,
                0.9999980052705163,
                0.9999957771665579,
                0.033085974694221476,
                0.03308597981882656,
                0.0007096704299359561,
                0.01590639267398549,
                0.0021827161380462315
            ],
            [
                0.0015011825333167718,
                0.015906392265791817,
                0.004070137664931159,
                0.004070138452056846,
                0.00150118246997389,
                0.014063625429049173,
                0.06008665396103505,
                0.00970847850506516,
                0.022977370244547903,
                0.0028009268734756113
            ],
            [
                0.9999869928715426,
                0.9971990726199289,
                0.9999970976880149,
                0.9959298626446338,
                7.484620925718133e-05,
                0.9998601778610078,
                0.0002959572349186946,
                0.0008040860855620941,
                0.00033535002120120886,
                0.9953904277778937
            ],
            [
                0.0021827166618743343,
                0.004609571363191219,
                0.0009110514065399807,
                0.0019267345661682163,
                0.0075772395310216905,
                0.003172683176789984,
                0.0021827169478754035,
                0.0024726235632243016,
                0.003172682687114471,
                0.9999485577931302
            ],
            [
                0.006692849667413466,
                0.0035936023096358456,
                0.00757724108577282,
                0.001700722773536393,
                0.00192673486346661,
                0.0021827169316483916,
                0.001926734649447581,
                0.005220126167510196,
                0.0002959571589185483,
                0.025957359693796152
            ],
            [
                0.0008040857978088814,
                0.04208773001828045,
                0.00013982207344814866,
                0.9997694933160696,
                0.00010889692207498694,
                NaN,
                0.0007096705226484624,
                0.9993736657888782,
                0.05340333563770401,
                1.892514823426434e-05
            ],
            [
                0.00757724107176605,
                0.9999996940977366,
                0.009708478702051925,
                0.002472623341552602,
                0.00970847598005333,
                0.005220126660807012,
                0.003593602014508193,
                0.9999989322970027,
                0.00407013699294868,
                0.009708474950350114
            ],
            [
                4.785096776394765e-06,
                4.006371116965205e-05,
                2.7535687813231466e-05,
                8.93970056565517e-06,
                1.0129990978220553e-05,
                2.43002378338943e-05,
                8.939695237959376e-06,
                3.1201900203407254e-05,
                2.7535697650273915e-05,
                2.4300243622255085e-05
            ],
            [
                0.0015011819531100359,
                0.0019267343315532508,
                0.0008040861046895256,
                0.0004878570427133548,
                0.00043055697885379757,
                0.0010322310374750803,
                0.0008040859790751546,
                0.0004305570319241836,
                0.0010322309249943572,
                0.0003353501413061723
            ],
            [
                0.0031726822681290164,
                0.0011695101732624802,
                0.0024726228488212787,
                0.0015011821520380343,
                0.007577241344898039,
                0.008577486498736348,
                0.022977368028337847,
                0.0004305570258368084,
                0.0010322308930627985,
                0.0040701370948785995
            ],
            [
                0.00033535014565766084,
                0.9999995549150011,
                0.004070137725334085,
                0.002472623628692113,
                0.0010322312277439942,
                0.0021827167232327167,
                0.0011695101471524626,
                0.006692851020252877,
                0.007577241519982651,
                0.0015011825664714492
            ],
            [
                0.008577485825546034,
                0.006692850636380797,
                0.0031726829058116458,
                0.00043055702688894726,
                0.0013250224514119334,
                0.0009110513282327978,
                0.017986212528241355,
                0.008577485619629007,
                0.0006263340713586156,
                0.0019267345034848257
            ],
            [
                0.004609571384557264,
                0.0019267350331595393,
                0.009708474824994946,
                0.003593603077468073,
                0.9999991684717741,
                0.0028009270321524764,
                0.0028009273885251425,
                0.0009110512435677997,
                0.005911068374657588,
                0.012431651196204173
            ],
            [
                0.002800926715449069,
                0.0003799845620995872,
                0.9978172835805166,
                0.9999910603047645,
                0.01243165256827768,
                0.03308597576681317,
                0.9998766054550079,
                0.9992903294786725,
                0.009708478379709944,
                0.9999869928668963
            ],
            [
                3.120192251631124e-05,
                4.006369692044835e-05,
                1.3007130011655787e-05,
                4.0063696941289896e-05,
                3.5356254890278004e-05,
                7.484623593296888e-05,
                3.120191877064807e-05,
                4.539785231272163e-05,
                1.6701415854279704e-05,
                1.3007125358230479e-05
            ],
            [
                6.144175333401224e-06,
                1.0129994599901296e-05,
                1.892515274546026e-05,
                1.3007125361755747e-05,
                3.2887498493983645e-06,
                2.902311639126627e-06,
                1.7603434231505666e-06,
                1.0129992186589747e-05,
                3.2887506334560605e-06,
                3.2887494572095624e-06
            ],
            [
                3.7266410594993323e-06,
                2.2603248365014775e-06,
                6.962257909323729e-06,
                1.9947297213492663e-06,
                8.939698433584547e-06,
                4.785092783319532e-06,
                8.93970056529743e-06,
                1.0677032518501217e-06,
                1.1478768123823146e-05,
                6.962256249682458e-06
            ],
            [
                0.001501182405235025,
                0.008577486902650562,
                0.0006263340777346719,
                0.010986943713429492,
                0.00970847770816419,
                0.004070138057550188,
                0.003593602361324872,
                0.03308597672022805,
                0.004609571164487005,
                0.025957359976362126
            ],
            [
                1.0129989770441144e-05,
                4.222833443645997e-06,
                3.9278638755456876e-07,
                3.726638395493353e-06,
                4.222834954561012e-06,
                4.785096205651846e-06,
                8.939693105272102e-06,
                1.7603440527222532e-06,
                1.5534977544367678e-06,
                1.7603440526133836e-06
            ],
            [
                0.009708474914534351,
                0.0010322309366385723,
                0.00170072209202739,
                0.008577487045208524,
                0.999999266178932,
                0.004070138182131233,
                0.01590639322796263,
                0.999999057755069,
                0.9999987901338838,
                0.0035936030566257196
            ],
            [
                0.00023050679324919176,
                4.785093353626844e-06,
                0.0007096702604446466,
                6.962257908487893e-06,
                1.67014178576052e-05,
                1.14787708580381e-05,
                0.003172683521403774,
                6.144176797115634e-06,
                0.0021827164164408227,
                0.0003799846051801609
            ],
            [
                5.422221554926484e-06,
                7.889262582571338e-06,
                6.144176066264237e-06,
                6.144173865328478e-06,
                1.1478773598538445e-05,
                3.726639728224814e-06,
                4.785092781300206e-06,
                3.2887498488809053e-06,
                3.7266388391993445e-06,
                7.889264465699106e-06
            ],
            [
                0.0017007220647512235,
                0.007577241260857426,
                0.005911068886342935,
                0.0046095717712826955,
                0.0008040858254477764,
                0.014063626642924775,
                0.0005527785380372501,
                0.000487857102147703,
                0.0011695101429367828,
                0.003593602821523979
            ],
            [
                0.003172683161326546,
                0.01243164797183202,
                0.00407013848980868,
                0.01798621239664392,
                0.0021827160300352255,
                0.005911070090308632,
                0.010986944998665251,
                0.010986944421827138,
                0.0040701369042319005,
                0.004609572681476381
            ],
            [
                3.2887502415438413e-06,
                2.902313368963394e-06,
                2.5612831266608576e-06,
                1.8925155005051806e-05,
                6.962255416961874e-06,
                1.99472900790731e-06,
                3.7266406163624873e-06,
                1.9947301970287804e-06,
                7.88926164299515e-06,
                1.147877086020957e-05
            ],
            [
                0.004070137330827497,
                0.004070137697020213,
                0.0052201251639898555,
                0.001501182207004986,
                0.0031726831252451896,
                0.005220125485599968,
                0.00407013725909903,
                0.0024726226104955567,
                0.0013250222224958428,
                0.002800926678381116
            ],
            [
                0.025957358328060655,
                0.0017007226521771712,
                0.0059110688972880765,
                0.007577240168329548,
                0.00013982204007594582,
                0.005220126556827777,
                0.009708476803815983,
                0.004070136998611453,
                0.025957359835079137,
                0.006692851704412043
            ],
            [
                0.0075772427105581215,
                0.0046095714636116315,
                0.007577241344898038,
                0.004609572294750873,
                0.006692851887060881,
                0.000552778598430277,
                0.005220125118045556,
                0.0010322308648525883,
                0.0028009265944904872,
                0.005911068246052187
            ],
            [
                1.1478766755734576e-05,
                8.481104103127398e-05,
                6.962257909007124e-06,
                2.9023123310290063e-06,
                1.5534981249164537e-06,
                1.7603430033158905e-06,
                4.222833946199938e-06,
                3.2887506334560605e-06,
                6.962259566635186e-06,
                3.28874945711983e-06
            ],
            [
                0.00017952792261014615,
                0.0017007220825400275,
                3.7266397280960194e-06,
                1.3709576971160984e-06,
                5.1442225844299154e-05,
                0.0009110513034372906,
                3.726639284017094e-06,
                0.9991959141258216,
                0.03732688854889699,
                0.0013250225484625088
            ],
            [
                0.017986209929192202,
                0.9999994956527722,
                0.0009110512801252759,
                0.00033535001531792054,
                0.004609571698638138,
                0.0035936021462318313,
                0.0015011819908016546,
                0.0021827164478806504,
                0.010986942954432066,
                0.020332352452212373
            ],
            [
                0.009708478048414034,
                0.0015011822640659189,
                0.0008040861006676207,
                0.00218271664514023,
                0.00460957249559174,
                0.0052201257056490044,
                0.0009110510825029939,
                0.003172682594333856,
                0.025957359976362126,
                0.0021827167673499014
            ],
            [
                0.003172682648824058,
                0.0019267346825802324,
                0.004609572531914025,
                0.0004878572108836283,
                0.0013250226116224108,
                0.001700722166938024,
                0.0017007221082349674,
                0.9999885212291787,
                0.0011695103388979168,
                0.0003799844790006344
            ],
            [
                2.2603253754284284e-06,
                7.889264461637948e-06,
                4.222833444229772e-06,
                4.222833946645451e-06,
                6.962254587951994e-06,
                1.8925157247225074e-05,
                3.7266406162269133e-06,
                6.962257077223492e-06,
                1.1478766753751021e-05,
                1.473897669015165e-05
            ],
            [
                0.009708476696368677,
                0.9999984465015047,
                0.005220124535278415,
                0.002182716369788175,
                0.0031726824146634663,
                0.009708477887243053,
                0.0024726230084708106,
                0.006692849630264563,
                0.029312229002426103,
                0.0028009266139999356
            ],
            [
                0.00012339463322557856,
                0.0004305570261624704,
                0.0021827159681697683,
                6.605215244462661e-05,
                0.002800927017195231,
                0.0013250225758831486,
                0.998073265527409,
                0.0007096703395350822,
                0.004609573256223188,
                0.0011695103306025455
            ],
            [
                0.000379984522512336,
                0.0013250224293829944,
                0.0004305571356600857,
                0.9999599363126283,
                0.000139822139779596,
                0.999997097688015,
                0.0015011822047365086,
                4.0063701703217896e-05,
                0.0015011821211518435,
                0.0021827161390604193
            ],
            [
                0.0015011821291787627,
                0.0017007228085210559,
                0.000911051179777656,
                0.999998790134605,
                0.004609571168760215,
                0.007577240126309246,
                0.004609573059655499,
                0.005911068002522816,
                0.0035936033917707798,
                0.022977367902892003
            ],
            [
                4.78509506499309e-06,
                1.3007130008887624e-05,
                7.88926634455091e-06,
                6.96225541655662e-06,
                8.93969310584124e-06,
                6.144173868558375e-06,
                1.370957533676711e-06,
                4.222832940339353e-06,
                1.67014218359435e-05,
                2.2603245668941476e-06
            ],
            [
                0.015906395385557992,
                0.9999957771660521,
                0.009708478711005867,
                0.0028009266796817462,
                0.014063629173984873,
                0.0035936033000644172,
                0.0006263340910697381,
                0.001926734284988452,
                0.0021827169397618976,
                0.004070138008472808
            ],
            [
                0.00010889693417570883,
                6.962253759157502e-06,
                6.605217596856826e-05,
                0.00013982214037567387,
                0.0006263341316943273,
                0.00522012632710622,
                0.010986940363721241,
                0.0011695102869498544,
                0.0028009270679198043,
                7.889265405146477e-06
            ],
            [
                0.0031726824072999256,
                0.0017007223673585754,
                0.0009110511782941643,
                0.00026119043064345423,
                0.004609571867429908,
                0.0009110510875362688,
                0.005911068262469897,
                0.999999057755631,
                0.004070138284061183,
                0.015906388737832667
            ],
            [
                0.001325022473132776,
                0.003172682939683937,
                0.010986944138468074,
                0.006692849785051665,
                0.0010322308316005535,
                0.002472622976311192,
                0.010986941851355899,
                0.0021827167384455394,
                0.0059110693515114715,
                0.0013250225878989352
            ],
            [
                0.002800927022397751,
                0.005911067865708569,
                0.014063624615494303,
                0.00317268211349468,
                0.012431652270995073,
                0.00023050674058517224,
                0.0017007225798360104,
                0.01590638894192946,
                0.010986940950679109,
                0.0035936032600470957
            ],
            [
                0.0052201247480730475,
                0.008577485168195544,
                0.0046095731130706315,
                0.0008040860147110984,
                0.01590638926265299,
                0.10669059323555341,
                0.012431650121413364,
                0.0015011825661224527,
                0.0024726235534615576,
                0.002472623334086975
            ],
            [
                0.9999993524050474,
                0.010986943764029321,
                0.9999977396762411,
                0.0017007224924731922,
                0.9971990734289209,
                0.0011695101942048904,
                0.003172682490507932,
                0.9999921107336622,
                0.00023050679412111268,
                0.9999982396559475
            ],
            [
                1.3007123812057577e-05,
                3.120191134788212e-05,
                2.5612812945260317e-06,
                9.610240330734994e-05,
                1.147876812106705e-05,
                3.5356259116499136e-05,
                2.2603242977802297e-06,
                2.260324028404236e-06,
                1.670141586907437e-05,
                2.7535681236473055e-05
            ],
            [
                0.01798621256114071,
                1.670142780084011e-05,
                1.3007125360809367e-05,
                4.785095635413826e-06,
                4.222833947428939e-06,
                6.60521287717195e-05,
                4.0063677837180203e-05,
                1.0129994600859455e-05,
                7.889260701697028e-06,
                2.753568780802255e-05
            ],
            [
                1.0129989768911772e-05,
                1.4738988993532872e-05,
                8.939696302831578e-06,
                6.962257079376403e-06,
                2.430023782222529e-05,
                1.892515049423401e-05,
                3.726639727940109e-06,
                1.892515725376564e-05,
                1.4738987238035806e-05,
                8.93969630226244e-06
            ],
            [
                0.002800927233099832,
                0.008577487195686377,
                0.029312227730476915,
                0.008577485991863636,
                0.0006263342503254293,
                0.0017007222954127336,
                0.000552778684324737,
                0.0013250223887141847,
                0.0066928498222005705,
                0.0015011822991400712
            ],
            [
                0.003172683309333745,
                7.48462539462643e-05,
                0.0024726235930868116,
                0.0002034269473222038,
                2.753568780802255e-05,
                7.484620026687456e-05,
                0.0019267345943757425,
                1.6701415863393463e-05,
                0.9999485577680525,
                0.9998415637866651
            ],
            [
                0.000709670242405754,
                0.0052201256597047,
                0.0028009271914796663,
                0.002800927305935123,
                0.017986213482322776,
                0.005220125802373857,
                0.004070137774411461,
                0.004609571089705853,
                0.004609572012719031,
                0.003172682701841553
            ],
            [
                0.007577239776140091,
                0.00669285060232763,
                0.9999996072138934,
                0.999999352405279,
                0.012431651733599612,
                0.0024726231072467854,
                0.0035936019419768243,
                0.001926735014802256,
                0.09534945590170513,
                0.0059110702216503596
            ],
            [
                0.002800927328045837,
                0.012431649103792363,
                0.0010322312016945573,
                0.0019267349149565474,
                0.002800927307886068,
                0.9999995549150541,
                0.9999992661787571,
                0.00970847864832826,
                0.00359360237966614,
                0.00669285089332743
            ],
            [
                0.0015011824839337537,
                0.0006263343022447608,
                0.004070138133053851,
                0.9999987901347491,
                0.002800926806493166,
                0.025957354325043223,
                0.0002611903354197752,
                0.001700722245208769,
                0.0046095732455401625,
                0.004070137266649395
            ],
            [
                2.4300252315495453e-05,
                8.481106134696298e-05,
                1.0677029972639127e-06,
                1.473898899664279e-05,
                4.7850967763512445e-06,
                1.670142582254589e-05,
                4.450851580402549e-07,
                3.288748673265808e-06,
                4.0063692165808155e-05,
                8.939697367037201e-06
            ],
            [
                0.0004878572037026855,
                0.0024726228396328167,
                9.610242625969935e-05,
                0.000335350026547879,
                5.8291272333081096e-05,
                0.0004305571788478968,
                0.0024726231997056957,
                0.004070137768748687,
                0.0013250221590278622,
                0.0010322307993088677
            ],
            [
                6.962258738827909e-06,
                2.2603253754284284e-06,
                1.4738981969615573e-05,
                6.96225707894582e-06,
                7.88926164299515e-06,
                7.88926258343236e-06,
                6.962255419279419e-06,
                6.9622562487453084e-06,
                1.8925150491445666e-05,
                6.144172403592939e-06
            ],
            [
                0.0004305570148394516,
                0.00970847465487008,
                0.029312228472447265,
                0.0007096705477460621,
                0.014063629458083484,
                1.4738976302430537e-05,
                0.002182715970198144,
                0.001700722808916363,
                0.0006263343041393611,
                0.007577241884158658
            ],
            [
                3.288749848749297e-06,
                8.481102055701339e-05,
                0.0013250225255092766,
                1.9947304345919157e-06,
                4.222834450236421e-06,
                6.962253756232077e-06,
                1.670142980112912e-05,
                1.4738980209829803e-05,
                3.12019076363863e-05,
                1.7603438427243761e-06
            ],
            [
                0.029312230645360544,
                0.00280092637663499,
                0.012431650452997753,
                0.0031726829772379993,
                0.0075772407005867,
                0.008577484360367295,
                0.9999987901344608,
                0.003172682114967387,
                0.0013250224514119334,
                0.02297736915735049
            ],
            [
                0.9999992661788446,
                0.9999957771655547,
                0.999989870012648,
                0.002182716110663159,
                0.9999977396751633,
                0.9999990577551814,
                0.9999910603015663,
                0.9999986290421398,
                0.9999980052702792,
                0.99999893229713
            ],
            [
                0.00043055717499005275,
                0.0007096703920006107,
                9.610246031767354e-05,
                8.481108169042316e-05,
                0.9840936064221572,
                4.0063696902084474e-05,
                4.006370165745395e-05,
                0.0019267345303491357,
                0.00013982210665353909,
                7.484626240565345e-05
            ],
            [
                0.01798621091617285,
                0.0008040860529191924,
                0.007577239839170538,
                0.0008040858594001259,
                0.004070137393118008,
                0.02033235553167293,
                0.0052201256379416075,
                0.9999987901347491,
                0.008577486126501698,
                0.007577243025710484
            ],
            [
                0.003172683570739512,
                0.0031726826252607273,
                0.9999994956526519,
                0.003172682149576024,
                NaN,
                0.999999352405279,
                0.005911069034102348,
                0.0007096705114618682,
                0.01798620598127015,
                0.0013250225028641424
            ],
            [
                0.08509904558710157,
                0.01243165363163475,
                0.0008040861006676207,
                0.015906395385557992,
                0.0019267347698892494,
                0.007577240210349847,
                0.000709670338998456,
                0.0021827164737424454,
                0.0013250222747182851,
                0.0019267347031762052
            ],
            [
                0.020332355494570995,
                0.00043055697885379757,
                0.0046095713012296894,
                0.022977367610185033,
                0.007577239916207751,
                0.004070138603064188,
                0.9999998362622942,
                0.005220125674213426,
                0.012431651985146421,
                0.005911069644294039
            ],
            [
                0.0024726229923910012,
                0.0009110513922348791,
                0.0005527787077680422,
                0.025957358422249308,
                0.0007096703508042315,
                0.029312227942468443,
                0.0007096703974907096,
                0.0024726234914394228,
                0.004609572638744278,
                0.0011695102503686287
            ],
            [
                0.0021827164641076593,
                0.00048785710095561,
                0.0002611903072402606,
                0.0006263341535550938,
                0.9999957771675623,
                0.0159063885045792,
                0.9999945777784449,
                0.015906394160976806,
                0.003172683113463523,
                0.0035936025655799032
            ],
            [
                0.0021827160792233353,
                0.004070137874453809,
                0.010986942478793707,
                0.012431649789828983,
                0.04742586812868187,
                0.9980732653192108,
                0.00043055708151249687,
                0.1329642281726931,
                0.01798620739594212,
                0.0001795279444230104
            ],
            [
                0.002182716560455524,
                0.0007096702454603949,
                0.005220125983732963,
                0.01098694018156191,
                0.005220124791599224,
                0.012431651733599614,
                0.0028009276200373374,
                0.0009110514106725657,
                0.0019267342890180981,
                0.008577485865145463
            ],
            [
                NaN,
                0.04208773242132242,
                0.0031726821238036358,
                0.0011695101142429624,
                0.999994577779739,
                0.06754668785475051,
                0.009708477564901103,
                0.022977370788146625,
                0.9984988175855166,
                0.9997040429582504
            ],
            [
                0.0019267346252697004,
                0.015906394160976802,
                0.029312230910349978,
                0.025957355784967162,
                0.009708474556376736,
                0.0009110512667738496,
                0.00460957184606386,
                0.0007096703218264191,
                0.0009110512628531926,
                0.004070137689469847
            ],
            [
                0.0015011823912751624,
                0.0015011825001620951,
                0.0031726827533863403,
                0.0007096704659311931,
                0.0010322308469661145,
                0.022977370913592487,
                0.0035936030232779537,
                0.99999976176309,
                0.014063627417739043,
                0.006692851815858791
            ],
            [
                0.012431650201450975,
                0.001926735008981654,
                0.025957357715834423,
                0.014063628011763344,
                0.0011695101810138917,
                0.00460957174564344,
                0.0052201268083124416,
                0.9999984465018751,
                0.0011695100391766677,
                0.0015011825336657685
            ],
            [
                0.9996646497310566,
                0.9982992775221531,
                6.605216819020694e-05,
                5.1442207357875675e-05,
                3.1201918748173414e-05,
                0.9399133481428692,
                0.0005527785074548412,
                0.00043055698628139663,
                1.012998855982425e-05,
                0.0001795280283833643
            ],
            [
                0.9993736657540832,
                0.0024726229079720034,
                0.00218271693266258,
                0.006692850784976439,
                0.0004305570817129043,
                0.9975273773406907,
                0.0035936026556188595,
                8.481105139057794e-05,
                0.0007096702531382759,
                0.1329642419157059
            ],
            [
                0.4378234991142019,
                0.9993736657548119,
                0.9997040429126469,
                0.9999151889498158,
                0.9990889489042515,
                0.9999599363221565,
                0.0035936023896704678,
                0.9999151889899053,
                0.03308597493257519,
                0.0019267343615517278
            ],
            [
                0.012431648166209041,
                0.005220125475927484,
                0.0031726822651836004,
                0.002182716733374598,
                0.0028009275836196872,
                0.002182716308429802,
                0.001032230906747752,
                0.0028009266458653677,
                0.001501181976841796,
                0.0031726835655850314
            ],
            [
                0.0028009272825237795,
                0.0004878570475668758,
                0.005911070153243211,
                0.0031726830685459167,
                0.0007096702539638545,
                0.0059110685059992766,
                0.0015011823391001763,
                0.0024726226742405066,
                0.0028009266998415094,
                0.0009110513043909639
            ],
            [
                0.03732688801344475,
                0.007577242738571664,
                0.0028009275816687413,
                0.0015011820660103968,
                0.002472623147446311,
                0.01798621157415998,
                0.017986205948370804,
                0.015906388096385636,
                0.001926734536169736,
                0.002472623216934064
            ],
            [
                1.5534979397267575e-06,
                0.0001584362726565963,
                9.610242631353545e-05,
                4.006369690499937e-05,
                6.605216820222096e-05,
                6.605212863283744e-05,
                0.0006263340869161929,
                0.0003353501054698128,
                0.00012339455746123568,
                0.0007096705084897842
            ],
            [
                0.00020342704485451672,
                0.0035936031700081247,
                0.00033535018372830947,
                0.00010889690885245028,
                0.9999810748540204,
                0.999995214904365,
                0.0008040859031266389,
                0.9999251537638759,
                0.0008040857855561058,
                8.481104126512805e-05
            ],
            [
                2.26032429753354e-06,
                8.93969630089651e-06,
                3.2887478884069663e-06,
                7.889263523008662e-06,
                0.08509904964767095,
                6.962259569003389e-06,
                4.2228349543420954e-06,
                0.0005527785230193898,
                6.962257906968191e-06,
                4.785094493532295e-06
            ],
            [
                0.0009110512257658986,
                0.001325022466816786,
                0.0019267344484129915,
                0.00080408610501689,
                0.00043055702656328524,
                0.0035936031341592756,
                NaN,
                0.0059110677042677594,
                0.0021827165924024486,
                0.0009110513550416161
            ],
            [
                0.0002305066852852819,
                0.0003799845574012955,
                0.0013250224035028426,
                0.00013982207349493977,
                0.0011695102114755798,
                0.0002959570260431976,
                0.009708475523402324,
                0.00017952794432114216,
                4.5397884829235786e-05,
                0.003172683017001124
            ],
            [
                6.605215246769354e-05,
                1.1478772228256871e-05,
                0.0015011819152439198,
                5.144219519403497e-05,
                0.00017952798675319138,
                0.00020342702013551378,
                0.00013982207320605572,
                0.0009110511754331448,
                6.144177531007026e-06,
                0.0004878571700970098
            ],
            [
                0.004070138421855377,
                0.0330859768394049,
                0.00317268309358196,
                0.9999995549147358,
                0.01590639060386055,
                0.005911068256997326,
                0.022977367317478063,
                0.0109869435919899,
                0.003172683553803363,
                0.003172683435250323
            ],
            [
                4.539787402089267e-05,
                0.00013982204046248067,
                0.00015843625412520775,
                0.0001584362161634149,
                1.6701421833391647e-05,
                0.0007096705236804361,
                0.00012339455887781068,
                0.00020342699575391393,
                0.0009110513479420474,
                5.422220908402905e-06
            ],
            [
                0.00048785715661500375,
                0.0005527785211542166,
                0.004070137442195382,
                0.000552778525881466,
                0.020332353416862622,
                0.0005527785314769857,
                0.0015011819611369546,
                0.008577483750536219,
                0.0019267345196034116,
                0.0019267349928630637
            ],
            [
                0.0015011821752463025,
                0.00317268329460666,
                0.0021827168180593107,
                0.00012339455969651565,
                0.999954602136911,
                0.002800926632208754,
                0.9997388096947052,
                7.484625366147123e-05,
                0.00043055702656328524,
                0.003593602939908541
            ],
            [
                0.0013250223238597595,
                0.002472622664477767,
                0.00591106832814074,
                0.9999832985702012,
                0.008577484067331578,
                0.9999967112501509,
                0.0019267348576460085,
                0.00043055712373584165,
                0.00407013801224799,
                0.999995214906647
            ],
            [
                0.00017952790066146025,
                0.00020342706909405917,
                1.3007123808153756e-05,
                0.00023050674181927547,
                4.5397884843438604e-05,
                0.0007096703963348993,
                2.4300252304268445e-05,
                0.0005527785408671682,
                0.00026119036970181556,
                0.0005527786737447
            ]
        ]
    },
    {
        "q_id": "8906_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            7,
            8,
            10,
            11,
            12,
            13,
            14,
            15,
            19,
            20,
            22,
            25,
            26,
            27,
            28,
            30,
            31,
            33,
            34,
            35,
            36,
            38,
            39,
            40,
            41,
            43,
            44,
            46,
            47,
            48,
            49,
            50,
            52,
            53,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            64,
            65,
            66,
            67,
            69,
            70,
            71,
            72,
            73,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            106,
            107,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999962733611608,
                0.9999852610162746,
                0.9999898700041905,
                0.999891103038896,
                0.9999785550592579,
                0.9999756997621686,
                0.9999974387180947,
                0.9999952149066466,
                0.9999885212359796,
                0.9999938558253986
            ],
            [
                0.9999994956526519,
                0.9999989322971301,
                0.999999266179107,
                0.9999994956527721,
                0.9999990577554061,
                0.9999996072136592,
                0.9999990577549568,
                0.9999994956527722,
                0.9999987901340281,
                0.9999996072139402
            ],
            [
                0.9999992661789321,
                0.9999996072136125,
                0.9999957771675627,
                0.9999996940977731,
                0.9999995549147359,
                0.9999998724810026,
                0.9999997617629763,
                0.9999995549147889,
                0.999999730042126,
                0.9999997617630049
            ],
            [
                6.144174600180663e-06,
                6.1441760654483806e-06,
                5.4222183221120994e-06,
                2.2603251060985603e-06,
                1.9947306726049992e-06,
                1.3709578605243332e-06,
                1.4738981960929243e-05,
                1.2098652507285942e-06,
                4.785093353013212e-06,
                1.553498495308628e-06
            ],
            [
                3.726640172385136e-06,
                1.3709572067955008e-06,
                6.475948753606123e-07,
                6.475948753741589e-07,
                4.4508505192495825e-07,
                7.889266346603015e-06,
                3.726640172385136e-06,
                1.5534983101061718e-06,
                5.715006513843456e-07,
                4.785092782936557e-06
            ],
            [
                1.7603430034743913e-06,
                1.8553905759893702e-07,
                2.1024329090685577e-07,
                5.043475885657239e-07,
                2.1024336609724313e-07,
                9.931200429181105e-08,
                4.450849988780466e-07,
                7.338209805090567e-07,
                6.475946438022905e-07,
                5.043475284447896e-07
            ],
            [
                1.5534971989696065e-06,
                9.422450431800595e-07,
                1.209865683500459e-06,
                1.5534973841450852e-06,
                1.553498495295912e-06,
                1.1478766756214804e-05,
                1.7603436329554703e-06,
                1.3709570433885908e-06,
                1.2098652508144226e-06,
                8.315280276338815e-07
            ],
            [
                0.9999952149043648,
                0.9999993524049703,
                0.9999977396746245,
                0.9999982396559474,
                0.9999962733598274,
                0.999997097688707,
                0.999998239656367,
                0.9999986290423029,
                0.9999898700114362,
                0.9999974387165682
            ],
            [
                2.699576809121209e-07,
                5.043474081993875e-07,
                5.04347408197782e-07,
                3.0590215398968196e-07,
                4.450852111100568e-07,
                2.6995768091310296e-07,
                5.043472879504592e-07,
                3.9278638755992735e-07,
                7.338208930315157e-07,
                2.3823685319174098e-07
            ],
            [
                1.2751910369310194e-07,
                5.715005151574337e-07,
                3.92786340734912e-07,
                1.8553907971682908e-07,
                2.699576809121209e-07,
                3.0590215398968196e-07,
                4.450851049941403e-07,
                4.450849458179853e-07,
                5.715003788993679e-07,
                3.059022269250683e-07
            ],
            [
                1.1478773590625104e-05,
                2.4300243626409964e-05,
                1.5534981248330927e-06,
                1.8925148220012804e-05,
                1.4738976696800444e-05,
                1.4738978446451746e-05,
                6.9622570780973205e-06,
                1.0129992178205843e-05,
                2.7535684526905577e-05,
                1.670142582102693e-05
            ],
            [
                0.9999952149072182,
                0.9999756997534794,
                0.9999986290432835,
                0.9999986290427932,
                0.9999962733589398,
                0.9999992661789321,
                0.9999952149037944,
                0.9999945777790937,
                0.999999266179282,
                0.9999974387165682
            ],
            [
                2.1444948401176257e-05,
                2.1444940701683237e-05,
                1.8925145972677006e-05,
                1.4738988994980593e-05,
                1.473897845240349e-05,
                8.93969630011598e-06,
                1.1478765380380096e-05,
                1.4738988991495334e-05,
                2.144494072680393e-05,
                1.8925152740434357e-05
            ],
            [
                3.059021904543821e-07,
                3.4663257978638593e-07,
                1.6373762768863107e-07,
                1.7603434230921292e-06,
                2.3823696679040834e-07,
                1.0677033791204289e-06,
                1.994730434735237e-06,
                6.475951069855719e-07,
                9.422444815726566e-07,
                7.338207180714596e-07
            ],
            [
                7.889265406438011e-06,
                1.553498495230919e-06,
                1.0129995809431767e-05,
                1.3007126912826352e-05,
                1.0129990979215566e-05,
                1.2098661161239298e-06,
                3.2887498492518007e-06,
                7.88926634687567e-06,
                4.785096205778054e-06,
                9.42244256886598e-07
            ],
            [
                2.4300249389135656e-05,
                4.785093924103951e-06,
                1.9947292457750883e-06,
                6.962259568078904e-06,
                1.012999460150437e-05,
                3.2887486733420804e-06,
                2.5612831266165976e-06,
                2.5612815996464693e-06,
                6.962254588977791e-06,
                8.315278293762888e-07
            ],
            [
                1.994729245722476e-06,
                1.2098655392574583e-06,
                3.726639728224814e-06,
                2.5612834314274337e-06,
                6.144176066051891e-06,
                1.5534971987760398e-06,
                4.785093921819153e-06,
                6.144177530794679e-06,
                1.5534983099564047e-06,
                9.422443692261927e-07
            ],
            [
                1.5534971989427613e-06,
                3.726640616423495e-06,
                8.93969630317306e-06,
                6.962254589104433e-06,
                8.939697368663308e-06,
                6.962258737650141e-06,
                5.422221553910605e-06,
                5.422219615967477e-06,
                6.962256248871951e-06,
                2.260324836152e-06
            ],
            [
                0.999999554914895,
                0.9999989322968755,
                0.9999982396561572,
                0.9999987901343165,
                0.9999987901340281,
                0.9999984465022456,
                0.9999982396563674,
                0.9999991684719723,
                0.9999991684718732,
                0.9999993524053562
            ],
            [
                6.475948753930064e-07,
                1.6373768624837685e-07,
                3.059021539909339e-07,
                7.338210679909462e-07,
                7.338208055489796e-07,
                4.450849458200093e-07,
                8.31528325021115e-07,
                4.450848927650143e-07,
                5.715003107715166e-07,
                1.3709568799592562e-06
            ],
            [
                3.7266388396128453e-06,
                6.1441746017453204e-06,
                1.209865250822125e-06,
                3.7266379506485954e-06,
                4.785096775285005e-06,
                1.0677026154376365e-06,
                5.422218968477564e-06,
                1.9947301967693507e-06,
                1.5534979397267575e-06,
                3.2887494564857185e-06
            ],
            [
                1.760343423160973e-06,
                3.927862002641863e-07,
                2.56128282131428e-06,
                5.04347348075149e-07,
                3.2887490648622804e-06,
                7.338210679979539e-07,
                1.0677026154619133e-06,
                3.0590211752206485e-07,
                1.3709568799760888e-06,
                5.715004470243685e-07
            ],
            [
                3.059023727894942e-07,
                3.9278634071901495e-07,
                2.699577452746696e-07,
                2.1024331597262577e-07,
                1.275189972825217e-07,
                7.338208055579897e-07,
                6.475951069961737e-07,
                1.2098652507715085e-06,
                3.059023363221292e-07,
                3.466327037512053e-07
            ],
            [
                2.3823690999236795e-07,
                6.475951069896949e-07,
                2.6995790617613663e-07,
                3.466325797888292e-07,
                3.9278605979208185e-07,
                5.715002426460124e-07,
                7.338211554641698e-07,
                5.71500719531729e-07,
                7.338212429537553e-07,
                5.715007195384861e-07
            ],
            [
                0.9999962733607166,
                0.9999930377412627,
                0.9999982396569967,
                0.9999957771645428,
                0.9999984465026162,
                0.9999980052693277,
                0.9999938558224708,
                0.9999986290427931,
                0.999997097688707,
                0.9999984465018752
            ],
            [
                8.315283250343497e-07,
                4.450851580497677e-07,
                3.0590215399183813e-07,
                3.466325797888292e-07,
                1.3709568799760888e-06,
                5.043472278299047e-07,
                1.9947301970813926e-06,
                5.71500378896509e-07,
                5.043472278312808e-07,
                1.2098656835136636e-06
            ],
            [
                3.9278605978261504e-07,
                9.422445938797133e-07,
                5.715004470129334e-07,
                7.338213304016384e-07,
                1.0677028699858827e-06,
                2.9023112930949896e-06,
                1.5534971989427613e-06,
                3.726640172503764e-06,
                1.370957206783032e-06,
                1.2098655392662613e-06
            ],
            [
                0.999999730042319,
                0.9999994284993485,
                0.9999996533674615,
                0.9999996072136125,
                0.9999994956525317,
                0.999999266178757,
                0.999999554914895,
                0.999999789756684,
                0.999999554914895,
                0.9999996072137529
            ],
            [
                6.144176065314267e-06,
                1.3007134657464394e-05,
                8.93970056350871e-06,
                6.144177530425867e-06,
                7.88926446430712e-06,
                2.2603251060985603e-06,
                3.288750241473551e-06,
                5.422220908481809e-06,
                1.1478773598329648e-05,
                1.3007131563507714e-05
            ],
            [
                6.475951069961737e-07,
                2.69957906184239e-07,
                2.9023126767836054e-06,
                9.42244930862237e-07,
                9.422444815563743e-07,
                1.2098655392662613e-06,
                8.315279285251204e-07,
                9.422447062094932e-07,
                6.475951069896949e-07,
                1.2098659719524008e-06
            ],
            [
                0.9999910603026306,
                0.9999852610180459,
                0.9999485577802613,
                0.9999967112497585,
                0.999995214906076,
                0.9999687980998254,
                0.9999970976887069,
                0.9999852610215451,
                0.9999810748472546,
                0.9999945777803846
            ],
            [
                3.726640172337686e-06,
                1.994730672468935e-06,
                7.88926446430712e-06,
                6.9622554185195676e-06,
                7.88926351873225e-06,
                5.422218323349895e-06,
                4.222832437443716e-06,
                2.90231094702116e-06,
                1.5534981248712412e-06,
                6.144172404380855e-06
            ],
            [
                0.9999852610162749,
                0.9999945777810305,
                0.9999832985841344,
                0.999992110733653,
                0.9999994956527121,
                0.9999957771670593,
                0.9999986290423029,
                0.9999885212332448,
                0.9999885212264068,
                0.9999921107355342
            ],
            [
                0.99896776881115,
                0.9324533018213448,
                0.9994472213931764,
                0.9999869928653446,
                0.9999756997650677,
                0.9997965729302667,
                0.9996646499308055,
                0.9995121427674316,
                0.9998911030778838,
                0.9999546021260055
            ],
            [
                0.9999986290427932,
                0.9999984465015047,
                0.9999987901340281,
                0.9999980052693275,
                0.9999991684716751,
                0.9999982396574163,
                0.9999970976869771,
                0.9999974387177896,
                0.9999994284997573,
                0.9999994956523512
            ],
            [
                0.999999730042126,
                0.9999984465018751,
                0.9999989322970029,
                0.9999974387184002,
                0.9999993524051246,
                0.9999992661786696,
                0.9999991684721706,
                0.9999991684717741,
                0.9999989322975119,
                0.9999990577551816
            ],
            [
                0.9999995549151073,
                0.9999994284995529,
                0.9999996940978095,
                0.9999993524049702,
                0.9999994956523514,
                0.9999989322967482,
                0.9999995549150541,
                0.999999495652712,
                0.9999993524051246,
                0.9999992661790195
            ],
            [
                4.222834954607099e-06,
                2.260323758939877e-06,
                2.561282515988704e-06,
                6.475947210012481e-07,
                1.0677031245851707e-06,
                7.338213304316717e-07,
                2.260325375615501e-06,
                1.2098655392662613e-06,
                2.902311984952413e-06,
                3.7266383955611403e-06
            ],
            [
                1.2098656834723998e-06,
                7.889261642578988e-06,
                4.450849458153541e-07,
                1.2098659719601033e-06,
                2.9023112920813724e-06,
                2.260325375615501e-06,
                1.760344052650207e-06,
                5.715003107655392e-07,
                1.994729245822257e-06,
                3.7266392838544054e-06
            ],
            [
                1.209865971934245e-06,
                7.338212429240558e-07,
                5.043475885453117e-07,
                1.2098659719122375e-06,
                8.315277302588544e-07,
                3.059021904543821e-07,
                6.475947981975644e-07,
                1.3709575336947905e-06,
                1.7603425836870455e-06,
                2.6995780963846126e-07
            ],
            [
                2.1444950955608285e-05,
                1.892515723318008e-05,
                4.222832940715735e-06,
                1.0677028699489821e-06,
                7.889262584809997e-06,
                6.1441746016670885e-06,
                1.3709578604831862e-06,
                2.260325374750031e-06,
                1.5534983096766514e-06,
                4.785095064523075e-06
            ],
            [
                4.22283193393364e-06,
                1.1478773598099973e-05,
                1.0129990978220553e-05,
                1.5534975693347152e-06,
                1.3007134661628471e-05,
                7.889260696789202e-06,
                3.2887486729876365e-06,
                2.902313022952668e-06,
                2.144495351097679e-05,
                1.3007123811797321e-05
            ],
            [
                0.9999832985801492,
                0.999995777166556,
                0.9999151889487236,
                0.999981074854025,
                0.9999869928746377,
                0.9999417087484042,
                0.9999930377429209,
                0.9999898700102333,
                0.9999957771675625,
                0.9999687980737735
            ],
            [
                1.994730672468935e-06,
                6.9622554185195676e-06,
                3.7266392829528392e-06,
                2.9023116388969785e-06,
                1.9947301970451086e-06,
                3.535623803067304e-05,
                3.2887486731252264e-06,
                1.0677032518209896e-06,
                8.939700565102295e-06,
                8.939699499432793e-06
            ],
            [
                1.0677029973114952e-06,
                6.475948753965404e-07,
                5.715006514105942e-07,
                2.6995768091383957e-07,
                5.043474683204221e-07,
                6.475948753991907e-07,
                3.059021904571643e-07,
                2.1024339115914997e-07,
                1.067703379136937e-06,
                5.043474683204221e-07
            ],
            [
                0.9999987901344607,
                0.9999991684719723,
                0.9999989322967481,
                0.9999980052707543,
                0.999999168471675,
                0.9999989322973847,
                0.9999987901343166,
                0.9999990577556308,
                0.9999987901338838,
                0.999998932296621
            ],
            [
                5.42222155426567e-06,
                6.962257908044647e-06,
                2.430024650998268e-05,
                2.902310946944611e-06,
                2.5612812944538183e-06,
                5.8291258426840353e-05,
                1.8925155000714377e-05,
                4.785093923847183e-06,
                8.939696302457574e-06,
                2.7535681225754707e-05
            ],
            [
                1.3007125355060104e-05,
                8.939699491123385e-06,
                7.889265406151004e-06,
                2.9023116388072315e-06,
                1.6701417852987564e-05,
                1.6701425823882575e-05,
                7.889264463675704e-06,
                1.3007130006048483e-05,
                1.147877085766227e-05,
                1.0129992185299915e-05
            ],
            [
                0.9999986290424665,
                0.9999991684717741,
                0.9999997897565587,
                0.9999970976869778,
                0.999999554914895,
                0.9999996533674614,
                0.9999996533674202,
                0.9999984465026159,
                0.9999984465022455,
                0.999998239656367
            ],
            [
                5.71500515151976e-07,
                4.450851049890802e-07,
                3.0590222692437275e-07,
                3.0590215399183813e-07,
                4.4508526417014975e-07,
                6.475949526003845e-07,
                2.699578739999358e-07,
                2.6995777745466066e-07,
                5.043476486883855e-07,
                2.699579061812927e-07
            ],
            [
                9.422444815726566e-07,
                6.475951069896949e-07,
                7.734425918930291e-08,
                1.3709570433885908e-06,
                5.043472879383035e-07,
                2.382368531882742e-07,
                7.338208055579897e-07,
                2.6995780963846126e-07,
                3.059021539864825e-07,
                6.47594566597747e-07
            ],
            [
                3.7266392835764795e-06,
                6.962253756890615e-06,
                1.3007130008414434e-05,
                5.422221554758815e-06,
                2.5612822104977725e-06,
                1.3007134656423374e-05,
                1.7603427935342762e-06,
                6.1441760654483806e-06,
                6.962253751495675e-06,
                1.3007133113017532e-05
            ],
            [
                1.2098655392464547e-06,
                8.315283250082584e-07,
                2.699577774560111e-07,
                5.04347648686092e-07,
                9.422448184912962e-07,
                3.927861534370498e-07,
                1.8553914607128047e-07,
                4.450849988780466e-07,
                7.338209805133949e-07,
                5.043472278299047e-07
            ],
            [
                0.9999687980849168,
                0.9999885212305162,
                0.9998911030522437,
                0.9999417087414693,
                0.9999546021367908,
                0.9999921107355363,
                0.9999646437577469,
                0.9999910603068958,
                0.9999546021151431,
                0.9999945777784452
            ],
            [
                2.9023130227124616e-06,
                6.144172402285332e-06,
                3.2887506332945414e-06,
                4.222832940777184e-06,
                6.1441753335241615e-06,
                2.430023492353693e-05,
                1.3007123808153756e-05,
                8.939695230918335e-06,
                1.0129989764010414e-05,
                4.7850967754851966e-06
            ],
            [
                0.9999038975851613,
                0.999925153773004,
                0.9999339478317487,
                0.9995121428316628,
                0.9998911030913218,
                0.9996200155665783,
                0.9999151889184854,
                0.9999930377445805,
                0.9999485577619125,
                0.9998601779431912
            ],
            [
                0.9999974387180947,
                0.9999986290427931,
                0.9999785550541502,
                0.9999967112517192,
                0.999998629042303,
                0.9999987901340281,
                0.999986992874641,
                0.9999832985781667,
                0.9999982396567869,
                0.9999974387187054
            ],
            [
                3.726637950851956e-06,
                1.5534983101301911e-06,
                1.994729483666479e-06,
                2.2603253754284284e-06,
                2.9023123309973302e-06,
                5.715003788894922e-07,
                3.726640172120768e-06,
                1.9947299591826594e-06,
                1.0677026154619133e-06,
                1.2098656835076114e-06
            ],
            [
                0.999999057755743,
                0.9999991684717742,
                0.9999995549149481,
                0.999995777168066,
                0.9999970976876691,
                0.9999990577551815,
                0.9999989322972573,
                0.9999967112513268,
                0.9999952149072172,
                0.9999994284995529
            ],
            [
                1.6373768624874915e-07,
                3.466324971396247e-07,
                3.4663262110630603e-07,
                5.043474683204221e-07,
                5.715007195431641e-07,
                5.715003789017068e-07,
                1.1253518888464745e-07,
                5.715005151574337e-07,
                4.450848927637999e-07,
                8.315283250343497e-07
            ],
            [
                0.9999957771675626,
                0.9999980052700408,
                0.9999993524053563,
                0.9999921107374166,
                0.9999962733589393,
                0.9999687980886754,
                0.9999987901338839,
                0.9999990577556308,
                0.9999994284994848,
                0.9999898700114368
            ],
            [
                3.288749849368453e-06,
                5.422219616140078e-06,
                3.726637951126493e-06,
                1.0129992186387057e-05,
                4.785093353687772e-06,
                1.7603432132079998e-06,
                3.2887506334560605e-06,
                6.962255419051463e-06,
                6.144172404028807e-06,
                3.72664061671159e-06
            ],
            [
                0.9999952149060769,
                0.9999952149060769,
                0.9999992661790195,
                0.9999970976883611,
                0.9999974387177897,
                0.9999989322967482,
                0.9999339478239425,
                0.9999977396746254,
                0.9999993524051182,
                0.999989870009023
            ],
            [
                1.1253512180873128e-07,
                2.3823688159069855e-07,
                5.715003107689177e-07,
                1.0677029972745947e-06,
                1.4449802095609418e-07,
                2.6995771309210433e-07,
                2.3823693839154895e-07,
                8.315278293899016e-07,
                9.422448185388577e-07,
                2.1024326584582131e-07
            ],
            [
                6.475945665900901e-07,
                7.338208055536515e-07,
                5.315788773977435e-08,
                1.5534977545603963e-06,
                3.927861534370498e-07,
                3.0590226339061185e-07,
                5.715006514074756e-07,
                3.927861534406222e-07,
                6.825608606148807e-08,
                3.4663257978638593e-07
            ],
            [
                4.222834451254188e-06,
                3.2887486731252264e-06,
                4.785093923603471e-06,
                2.9023133690188264e-06,
                1.3709572066982443e-06,
                2.5612819052374947e-06,
                5.422218968714274e-06,
                1.5534984951673385e-06,
                4.785094494185095e-06,
                1.7603430033399058e-06
            ],
            [
                0.9999952149049357,
                0.9999930377429237,
                0.9999938558246686,
                0.999995214904366,
                0.9999980052705164,
                0.9999910603026327,
                0.9999921107355346,
                0.999994577781034,
                0.9999970976869773,
                0.9999967112509354
            ],
            [
                0.9999977396762413,
                0.9999930377412626,
                0.999997097688707,
                0.9999977396746246,
                0.9999991684715761,
                0.99999671125172,
                0.9999990577555185,
                0.9999980052698034,
                0.9999996940978825,
                0.9999996072138934
            ],
            [
                0.9999986290427934,
                0.9999977396765105,
                0.9999974387180948,
                0.9999945777816767,
                0.9999989322975119,
                0.999996711250151,
                0.9999945777810315,
                0.9999977396765106,
                0.9999977396762411,
                0.999999266179107
            ],
            [
                0.9999957771645422,
                0.999998005269803,
                0.9999991684720715,
                0.9999994284996212,
                0.9999992661789321,
                0.9999984465020603,
                0.9999990577550693,
                0.9999990577556309,
                0.9999982396572065,
                0.9999987901347492
            ],
            [
                3.059022998569248e-07,
                1.067703251864202e-06,
                3.0590211752206485e-07,
                8.315280276505193e-07,
                3.059022269206168e-07,
                2.699577452746696e-07,
                7.338210679816025e-07,
                3.927862002625787e-07,
                5.043473480730849e-07,
                6.475948753930064e-07
            ],
            [
                4.2228344501365644e-06,
                1.3007131546094302e-05,
                1.0129995796478171e-05,
                1.6701423829123058e-05,
                3.120191507481552e-05,
                3.1201922511884416e-05,
                1.3007129994928505e-05,
                5.144219514088835e-05,
                7.889263523238269e-06,
                4.5397884790260616e-05
            ],
            [
                3.927862939126708e-07,
                1.3709573702111586e-06,
                5.04347348070562e-07,
                3.4663253846473677e-07,
                3.4663253846473677e-07,
                3.466327037472645e-07,
                1.3709578605355551e-06,
                1.3709570433885908e-06,
                5.043472278280699e-07,
                3.927862939075802e-07
            ],
            [
                2.7535687788789623e-05,
                2.1444958623509054e-05,
                1.3007125356952865e-05,
                1.0129989768322136e-05,
                1.670142382681424e-05,
                1.4738983714656244e-05,
                1.14787708580381e-05,
                1.4738980209347228e-05,
                1.4738983715996728e-05,
                7.889261641904523e-06
            ],
            [
                0.9999996072137061,
                0.9999994956526519,
                0.9999996940977366,
                0.999999730042126,
                0.9999997300422869,
                0.9999995549147358,
                0.9999995549150011,
                0.9999996940978825,
                0.9999994956524114,
                0.9999996940976271
            ],
            [
                4.4508526416286326e-07,
                2.561282515914161e-06,
                2.2603234892298883e-06,
                3.9278629390240027e-07,
                1.209866116149238e-06,
                9.422442569028803e-07,
                2.9023133689317184e-06,
                1.0677026154551157e-06,
                6.475949525722606e-07,
                4.450849458153541e-07
            ],
            [
                6.475947209768052e-07,
                9.422450431474948e-07,
                1.760344052650207e-06,
                2.5612815999679353e-06,
                1.7603440525461408e-06,
                5.715003788894922e-07,
                2.2603242974060834e-06,
                1.2098655392464547e-06,
                1.0677024880858507e-06,
                1.9947304346535984e-06
            ],
            [
                3.4663262110803996e-07,
                6.475946437928669e-07,
                6.47594875389178e-07,
                3.4663278639265633e-07,
                5.715005832676369e-07,
                2.1024334103352274e-07,
                4.450849988780466e-07,
                5.715003107715166e-07,
                9.422444815409489e-07,
                5.71500719531729e-07
            ],
            [
                1.3709576970213355e-06,
                3.7266397280960194e-06,
                3.2887502413389517e-06,
                6.962253751824944e-06,
                3.28875024125221e-06,
                3.726638395320497e-06,
                1.7603438427852151e-06,
                5.422217675756574e-06,
                2.2603242978213447e-06,
                2.561282821176841e-06
            ],
            [
                2.6995771309523475e-07,
                1.2751904288739315e-07,
                3.466326624233938e-07,
                6.475950297644816e-07,
                6.475947209953583e-07,
                2.6995771309523475e-07,
                3.0590237279032884e-07,
                1.855391681898159e-07,
                1.2751904288710323e-07,
                5.04347528440776e-07
            ],
            [
                5.715006514040971e-07,
                5.043472879540142e-07,
                3.9278624708775595e-07,
                9.422447062030659e-07,
                8.315283250371857e-07,
                1.4449803818041636e-07,
                5.04347528440776e-07,
                5.043475284447896e-07,
                3.466327450756327e-07,
                3.927861534406222e-07
            ],
            [
                0.998967769061921,
                0.9999339478632563,
                0.7057850216484838,
                0.9980732652166786,
                0.8354835309589073,
                0.6224593312018546,
                0.18242551713899047,
                0.996406398042183,
                0.22270012850745968,
                0.9997694933418717
            ],
            [
                4.222834450589758e-06,
                7.889262582800945e-06,
                8.939694170729447e-06,
                1.012998855982425e-05,
                5.4222183217274465e-06,
                1.0129995809431767e-05,
                1.147876538789672e-05,
                5.422220908314139e-06,
                4.7850950647493785e-06,
                1.3007133114011233e-05
            ],
            [
                2.561282210618905e-06,
                3.288748280891699e-06,
                2.5612825159677387e-06,
                1.1478764007552206e-05,
                7.889263525103816e-06,
                1.3007123810306773e-05,
                5.422221553910605e-06,
                2.2603234894745224e-06,
                6.962257077590752e-06,
                2.2603245672497918e-06
            ],
            [
                6.475951069985296e-07,
                1.6373774480479287e-07,
                7.33820893021171e-07,
                9.422444815726566e-07,
                2.3823685319174098e-07,
                1.2098652508056196e-06,
                4.450849988780466e-07,
                6.475949525919915e-07,
                5.04347528440776e-07,
                6.475948753276293e-07
            ],
            [
                4.450852641656969e-07,
                1.5534973841705173e-06,
                7.338209805090567e-07,
                7.338209804920378e-07,
                8.315279285205827e-07,
                7.338208055489796e-07,
                9.422448185435711e-07,
                1.0677024881499412e-06,
                1.9947301970287804e-06,
                5.715006513999389e-07
            ],
            [
                2.6995787400208416e-07,
                5.715007195384861e-07,
                1.6373766672936518e-07,
                3.4663278639738526e-07,
                1.0677026154774503e-06,
                3.0590211752206485e-07,
                1.275190580884987e-07,
                6.475948754012522e-07,
                7.338211554641698e-07,
                3.059021539909339e-07
            ],
            [
                2.90231336827709e-06,
                1.2098656833689656e-06,
                2.260323488974976e-06,
                1.6701417847458553e-05,
                3.7266401719174067e-06,
                1.994729245693449e-06,
                1.1478773593172406e-05,
                2.144494839142443e-05,
                4.222833945692974e-06,
                3.2887478889034873e-06
            ],
            [
                2.1024334103505245e-07,
                3.927863875584984e-07,
                3.059021904571643e-07,
                7.338207180661203e-07,
                5.715005832798517e-07,
                3.0590237278838124e-07,
                1.1253514863909295e-07,
                8.315280276546789e-07,
                7.338208055302923e-07,
                9.42244930862237e-07
            ],
            [
                0.9999251537818146,
                0.9997040428661479,
                0.9999756997650858,
                0.998967768719677,
                0.9999687980923682,
                0.9999724643023419,
                0.9998766054253961,
                0.9999852610145195,
                0.999195913892598,
                0.9999810748472532
            ],
            [
                7.338210679542388e-07,
                2.561282821209454e-06,
                4.450852641681257e-07,
                8.315282259009745e-07,
                2.699577130868255e-07,
                7.338209805133949e-07,
                7.338211554758494e-07,
                3.927862939075802e-07,
                4.450848927599543e-07,
                7.338211554398095e-07
            ],
            [
                5.043473480766399e-07,
                4.4508505193932864e-07,
                1.067703251864202e-06,
                3.466325797888292e-07,
                5.715003107715166e-07,
                5.715004470295662e-07,
                3.9278615344178325e-07,
                3.927862002556126e-07,
                5.043472278280699e-07,
                2.102433660979124e-07
            ],
            [
                1.2098655392354511e-06,
                8.939693102865466e-06,
                5.422217030121119e-06,
                1.0129993393742954e-05,
                9.422442568763144e-07,
                1.553497198908852e-06,
                8.315282258956806e-07,
                5.422218322457301e-06,
                1.5534971987760398e-06,
                4.222833947820683e-06
            ],
            [
                5.043474683156057e-07,
                5.043474683050556e-07,
                6.475950297868629e-07,
                5.04347648672331e-07,
                2.6995777745466066e-07,
                2.699577452746696e-07,
                3.466327863879275e-07,
                2.6995790618252024e-07,
                2.3823685318968256e-07,
                2.1024331597066579e-07
            ],
            [
                0.9999995549147358,
                0.9999970976876711,
                0.9999991684722698,
                0.9999994956523514,
                0.9999990577550691,
                0.9999993524053562,
                0.9999982396572065,
                0.9999989322968755,
                0.9999967112497589,
                0.9999980052698033
            ],
            [
                0.9999993524048931,
                0.9999996072137998,
                0.9999997300422225,
                0.9999977396746251,
                0.9999997300422547,
                0.9999993524054335,
                0.9999994956525917,
                0.9999974387180951,
                0.9999986290431202,
                0.9999998724808963
            ],
            [
                1.9947294834796172e-06,
                3.726640616748873e-06,
                5.4222196118151934e-06,
                7.889262584666493e-06,
                1.5534984952492866e-06,
                7.889265403883644e-06,
                8.93969949923766e-06,
                8.939699499026267e-06,
                5.422217028266893e-06,
                7.889264465067689e-06
            ],
            [
                2.9023116388072315e-06,
                6.9622554173544636e-06,
                3.1201918796982014e-05,
                2.4300249387721226e-05,
                8.939696302831578e-06,
                1.300712536203966e-05,
                4.539785235863304e-05,
                3.2887494570719725e-06,
                2.1444948404530884e-05,
                1.0129995805027913e-05
            ],
            [
                0.9999997617630048,
                0.999999057755743,
                0.9999977396748941,
                0.9999982396561573,
                0.9999977396748941,
                0.9999991684718733,
                0.9999970976890534,
                0.9999990577550691,
                0.9999945777784486,
                0.999999554914895
            ],
            [
                1.9947294835866542e-06,
                5.422218321855664e-06,
                3.2887502411026557e-06,
                4.785096205434246e-06,
                1.760343632920248e-06,
                2.5612812947077304e-06,
                5.043476486883855e-07,
                5.715005151574337e-07,
                2.902313368860448e-06,
                8.315280276338815e-07
            ],
            [
                2.1024341622426268e-07,
                3.9278605979208185e-07,
                4.450852641717689e-07,
                5.043475885606781e-07,
                8.315282259009745e-07,
                5.043476486833397e-07,
                3.2887490653109436e-06,
                7.338212429537553e-07,
                1.3709570434122812e-06,
                5.043475885634304e-07
            ],
            [
                5.422219615395428e-06,
                6.144174600862407e-06,
                4.7850927822924614e-06,
                6.962259569117366e-06,
                2.9023109467598367e-06,
                3.7266397280485686e-06,
                1.1478765387416494e-05,
                8.939694169330997e-06,
                4.222833444168322e-06,
                1.5534971988904843e-06
            ],
            [
                0.9999832985801657,
                0.9999987901343166,
                0.9999982396569966,
                0.9999982396561572,
                0.9999992661789321,
                0.9999952149055061,
                0.9999945777803846,
                0.9999987901337396,
                0.9999974387165684,
                0.9999962733611609
            ],
            [
                1.2098659719441482e-06,
                1.5534979396815448e-06,
                6.475950297868629e-07,
                1.3709570433786157e-06,
                2.260324836651547e-06,
                3.92786293909545e-07,
                4.450852641681257e-07,
                8.31528126775552e-07,
                1.7603438428564603e-06,
                1.5534977545243671e-06
            ],
            [
                1.0677033791291683e-06,
                3.9278615343901467e-07,
                2.6995780963428734e-07,
                4.4508505193791187e-07,
                1.2098656834723998e-06,
                8.315277302649045e-07,
                7.338213304243302e-07,
                2.1024344128660572e-07,
                6.475949525919915e-07,
                5.043472278255469e-07
            ]
        ]
    },
    {
        "q_id": "8969_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            6,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            18,
            19,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            32,
            34,
            35,
            38,
            39,
            40,
            41,
            43,
            44,
            45,
            46,
            48,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            59,
            60,
            61,
            62,
            63,
            64,
            66,
            67,
            69,
            70,
            71,
            72,
            75,
            76,
            78,
            79,
            80,
            81,
            82,
            86,
            87,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            104,
            105,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                1.760344052693435e-06,
                3.2887478892055875e-06,
                1.2098662603961589e-06,
                6.1441746017453204e-06,
                0.0024726230658987025,
                2.902311984952413e-06,
                1.9947301970106386e-06,
                2.260325375615501e-06,
                1.1478766757237902e-05,
                1.8925155005051806e-05
            ],
            [
                7.484624505832518e-05,
                0.99029152225602,
                0.9998601779260005,
                0.9999038975626571,
                0.9993736657495652,
                0.999997097688707,
                0.9999810748427379,
                0.9999756997592727,
                0.7549149923816046,
                0.9999417087553565
            ],
            [
                2.902310947190096e-06,
                2.4300234937239182e-05,
                3.120191508707442e-05,
                1.3007126912258525e-05,
                7.889264466445326e-06,
                1.1478770862067849e-05,
                2.1444948408275583e-05,
                3.12019150894581e-05,
                7.889259764079887e-06,
                5.8291279378656556e-05
            ],
            [
                8.481107163963022e-05,
                1.8925150493166868e-05,
                3.7266383954560706e-06,
                5.829126548301662e-05,
                7.484622717680992e-05,
                NaN,
                2.7535697661092444e-05,
                4.785095635592258e-06,
                0.00010889687027972941,
                1.4738985483879434e-05
            ],
            [
                1.0129988561648438e-05,
                1.8925141467059383e-05,
                9.42244930862237e-07,
                1.0129988563914856e-05,
                1.0129990979215566e-05,
                2.1444945854624007e-05,
                3.288748673265808e-06,
                2.4300232039788792e-05,
                4.785094494672519e-06,
                1.4738981968864903e-05
            ],
            [
                0.999876605439851,
                0.9988304898795015,
                0.998299277380831,
                0.9999885212264006,
                0.9940889319071798,
                0.999988521233243,
                0.9999869928715357,
                0.9999785550567016,
                0.9999724643056231,
                0.9999756997534754
            ],
            [
                0.9999952149043645,
                0.9999992661786696,
                0.9999994284995529,
                0.9998601778592663,
                0.9999990577552937,
                0.9999994284994849,
                0.9999991684717741,
                0.9999994284996893,
                0.9999945777823233,
                0.9999982396561571
            ],
            [
                0.9997388095980149,
                0.999998446502801,
                0.9999962733598275,
                0.9999967112497584,
                0.9999991684716749,
                0.9999952149072165,
                0.9999990577554061,
                0.9999962733602716,
                0.9999970976880148,
                0.9999810748495205
            ],
            [
                0.9999992661791944,
                0.9999962733616055,
                0.9999996072137998,
                0.9999989322973845,
                0.9999995549151073,
                0.9999992661792819,
                0.9999993524054334,
                0.9999993524054334,
                0.9999417087067342,
                0.9999991684715759
            ],
            [
                4.785095062930243e-06,
                8.939696302831578e-06,
                1.6701425821573757e-05,
                2.2603242977308917e-06,
                4.7850956352353935e-06,
                7.889262585211807e-06,
                2.144495607492721e-05,
                5.144223204149862e-05,
                4.2228319339950885e-06,
                6.962255417721724e-06
            ],
            [
                1.1478765382927399e-05,
                1.670141583070545e-05,
                2.144495095279976e-05,
                0.9796676449877542,
                6.144175333401224e-06,
                2.9023126769050284e-06,
                5.422218969463855e-06,
                1.3007130008414434e-05,
                4.222833947774596e-06,
                4.222831932543332e-06
            ],
            [
                7.889261643727018e-06,
                2.561283431189828e-06,
                3.535624228030111e-05,
                6.962257908196617e-06,
                3.7266401716055872e-06,
                6.60521602028025e-05,
                5.422219612998742e-06,
                8.939698428202134e-06,
                4.785092782936557e-06,
                4.222833946645451e-06
            ],
            [
                0.999989870011442,
                0.9999984465015052,
                0.9999987901341723,
                0.9999994956526519,
                0.9999996072137529,
                0.999999168471675,
                0.999999352405279,
                0.9999962733607166,
                0.99999976176309,
                0.9999994284996893
            ],
            [
                0.5621765008857981,
                0.999925153764067,
                0.9999910603037108,
                0.999975699759703,
                0.5312093733737563,
                0.9999687980924699,
                0.5926665999540697,
                0.9999339478342332,
                0.8933094003735664,
                0.9999852610216102
            ],
            [
                0.9999646437619555,
                0.9995694430211463,
                0.9996646498103884,
                0.9978172832037457,
                0.9975273767641147,
                0.999891103077925,
                0.9995694429328793,
                0.9999339478396482,
                0.9465966702001758,
                0.999290329624057
            ],
            [
                3.288749849060371e-06,
                1.5534981245279071e-06,
                1.473898724181597e-05,
                2.2603242978377903e-06,
                3.2887486729337966e-06,
                2.5612815998141903e-06,
                8.939698435096828e-06,
                6.96225541916544e-06,
                3.288749848677511e-06,
                2.1444940740066406e-05
            ],
            [
                1.5534973841705173e-06,
                1.370956716529941e-06,
                8.315283250150648e-07,
                5.8291251620035695e-05,
                1.0677026154473471e-06,
                1.5534984953199313e-06,
                1.8925157261545463e-05,
                2.9023109470871505e-06,
                1.9947306726049992e-06,
                2.9023116388547446e-06
            ],
            [
                0.9996646497308322,
                0.9999485577863566,
                0.9999910603026305,
                0.9993736658323811,
                0.9999151889284702,
                0.999997438717484,
                0.99781728397605,
                0.9465966703884945,
                0.8670357649558006,
                0.999903897539223
            ],
            [
                1.0677027427340866e-06,
                1.5534971989427613e-06,
                5.715005832624392e-07,
                9.422447062202052e-07,
                2.902310947190096e-06,
                6.475947981754775e-07,
                3.2887486732000038e-06,
                1.5534981247680996e-06,
                4.222834954561012e-06,
                2.10243315965503e-07
            ],
            [
                6.9622579096593295e-06,
                5.422220908925639e-06,
                2.561281600049467e-06,
                4.7850933535659155e-06,
                1.300712846411008e-05,
                1.1478772229551402e-05,
                3.535625070624499e-05,
                1.3709575336860625e-06,
                1.0129988564845378e-05,
                NaN
            ],
            [
                2.902313368963394e-06,
                6.144173868781898e-06,
                8.939699500164542e-06,
                4.785095635296322e-06,
                7.889259763469998e-06,
                1.670141985166528e-05,
                6.962256249517824e-06,
                1.8925150495232307e-05,
                7.889265406681968e-06,
                2.902312331081799e-06
            ],
            [
                6.962255419804982e-06,
                1.3709568797023994e-06,
                1.5534983100016177e-06,
                1.3709567162469001e-06,
                1.0677024880353552e-06,
                1.0677033791107183e-06,
                1.370956879727337e-06,
                1.370957370236096e-06,
                1.0677032518316716e-06,
                2.9023133690188264e-06
            ],
            [
                4.4508521110499674e-07,
                1.2098658277335738e-06,
                8.939694172420599e-06,
                6.9622579096593295e-06,
                8.93969630226244e-06,
                4.5397857790051276e-05,
                4.7850967763512445e-06,
                3.288750241374845e-06,
                4.539787406003298e-05,
                3.2887482812506295e-06
            ],
            [
                0.9999967112493664,
                0.9999992661790195,
                0.9999970976876692,
                0.9999977396751633,
                0.9996200155166548,
                0.9999977396757022,
                0.999983298570192,
                0.9999785550490321,
                0.9999810748585268,
                0.9998415637833893
            ],
            [
                2.4300252319296727e-05,
                1.147876948575242e-05,
                1.6701425823457267e-05,
                2.260325374873376e-06,
                6.962258738701267e-06,
                2.9023116390421582e-06,
                2.561282210618905e-06,
                0.00010889693512006272,
                1.0677033791000363e-06,
                2.2603234893861252e-06
            ],
            [
                6.605216042241888e-05,
                5.829127247176183e-05,
                4.539787403691212e-05,
                3.120191508321514e-05,
                9.610240329616323e-05,
                1.4738978456049602e-05,
                1.473898899742027e-05,
                8.93969630226244e-06,
                3.120192623972722e-05,
                3.120191880867338e-05
            ],
            [
                0.16451645880021024,
                0.1066905996264336,
                0.9992903294697976,
                0.13296424019782924,
                0.0019267342764814218,
                0.053403331683011195,
                0.13296424019782926,
                0.03308597552845946,
                0.9996646499391183,
                0.02931223234129297
            ],
            [
                1.3007130014873483e-05,
                0.0001584362919971074,
                2.7535687815134722e-05,
                5.829124467582348e-05,
                4.539785781036459e-05,
                7.484623614969471e-05,
                2.144495863045236e-05,
                1.300713311517055e-05,
                2.1444943284979742e-05,
                6.60521288918597e-05
            ],
            [
                2.1444953524161264e-05,
                2.4300249418927004e-05,
                1.6701429804744246e-05,
                2.753569109925723e-05,
                1.3007134666431358e-05,
                5.829129331543752e-05,
                3.535623805163821e-05,
                5.144220137401424e-05,
                6.144172404520556e-06,
                2.144495096387783e-05
            ],
            [
                0.9999756997563752,
                0.9999967112517186,
                0.9999852610127832,
                0.9999724642957772,
                0.99999862904312,
                0.9999687980998007,
                0.9999038975853564,
                0.9999930377429205,
                0.9999921107355336,
                0.999992110736474
            ],
            [
                0.9999938558261305,
                0.9999417087136068,
                0.9999869928715355,
                0.9997965729303554,
                0.999992110736474,
                0.00023050679746794775,
                0.9890130577539655,
                0.9984988177242428,
                0.9995121428860448,
                0.9999957771650454
            ],
            [
                0.9996200155607524,
                0.9999599363221673,
                0.0075772428121072145,
                0.999796573075402,
                0.9999646437366654,
                0.9999546021422125,
                0.9999417087206172,
                0.999796573102761,
                0.9998911031176417,
                0.9995121428863004
            ],
            [
                0.9999485577742242,
                0.9999485577926721,
                0.9999546021206042,
                0.9999869928762022,
                0.9999646437459172,
                0.9995694429203037,
                0.9998204720372825,
                0.34864514210180597,
                0.9998204719703159,
                0.9999962733589793
            ],
            [
                1.8925148241080285e-05,
                3.53562507106181e-05,
                6.60521210438226e-05,
                6.14417606400666e-06,
                6.605212885485651e-05,
                6.9622579075254155e-06,
                4.785096206013061e-06,
                8.481106154688048e-05,
                1.147876675466972e-05,
                3.535624228313077e-05
            ],
            [
                0.9999885212332426,
                0.9999852610215418,
                0.9999869928746368,
                0.999997438716568,
                0.9999785550541467,
                0.999948557798623,
                0.999991060303696,
                0.999964643736646,
                0.9999945777823231,
                0.9999945777823229
            ],
            [
                6.14417313680765e-06,
                5.422219616140078e-06,
                NaN,
                1.3007130014636887e-05,
                6.962255419570695e-06,
                4.785093353187292e-06,
                2.7535681248693975e-05,
                1.892514147046736e-05,
                6.962254588585202e-06,
                6.1441724044534996e-06
            ],
            [
                0.9999646437450841,
                0.9999599363078145,
                0.9999251537817176,
                0.99973880959746,
                0.9999417087414095,
                0.9999810748495026,
                0.999290329533656,
                0.9999339478317593,
                0.9999646437408576,
                0.9995121427728244
            ],
            [
                7.338208930265102e-07,
                1.2098661161861e-06,
                2.4300252320622747e-05,
                1.5534983101061718e-06,
                4.222834954514924e-06,
                4.785093923847183e-06,
                1.1478772229781076e-05,
                4.785096205882502e-06,
                1.8925145983348442e-05,
                3.120191879981973e-05
            ],
            [
                0.7981867753392728,
                0.9324533121452495,
                0.0001795279013588658,
                0.9999339478416243,
                0.9999251537627574,
                0.26894141551050293,
                0.5926665999540698,
                0.9986749773270662,
                0.047425875870305605,
                0.993307149979672
            ],
            [
                6.962259568775433e-06,
                7.889260704308795e-06,
                3.2887498491620677e-06,
                4.222833947728508e-06,
                6.96225956921868e-06,
                1.1478764019077695e-05,
                7.889266347356409e-06,
                4.222834954211514e-06,
                1.6701427815999337e-05,
                1.0129994596824126e-05
            ],
            [
                3.4663253846111126e-07,
                1.209865971934245e-06,
                1.7603438428660665e-06,
                3.7266379512857925e-06,
                2.9023119851635836e-06,
                1.067703251797684e-06,
                1.7603427935678977e-06,
                7.338208055579897e-07,
                1.5534983101393749e-06,
                8.315283250260307e-07
            ],
            [
                0.9999938558246656,
                0.9999921107374142,
                0.9999898700114355,
                0.9999945777790911,
                0.9999945777829693,
                0.9999984465026158,
                0.9999921107364739,
                0.9999885212359793,
                0.9999921107374143,
                0.9999962733620487
            ],
            [
                6.962253759581752e-06,
                2.902312331081799e-06,
                6.962253758916883e-06,
                1.4738983726908257e-05,
                7.484624510079911e-05,
                4.785093923916815e-06,
                1.4738981969240237e-05,
                3.1201926243586504e-05,
                8.939697369785323e-06,
                4.5397879462552736e-05
            ],
            [
                1.2098655392574583e-06,
                5.422220261948442e-06,
                1.2098652508144226e-06,
                1.670142781560441e-05,
                5.422217676575195e-06,
                1.067702615468225e-06,
                2.9023123310580418e-06,
                1.9947299591826594e-06,
                1.3709575336530204e-06,
                5.422220908560712e-06
            ],
            [
                0.9999977396751633,
                0.999988521233243,
                0.9999962733620487,
                0.9999952149049348,
                0.9999417087276724,
                0.9989677691921681,
                0.9999898700126428,
                0.999992110736474,
                0.9999970976890529,
                0.9999977396762411
            ],
            [
                7.889261645269683e-06,
                6.605214463743442e-05,
                2.4300252318589512e-05,
                1.892514372640862e-05,
                1.473897670007122e-05,
                6.962256249327861e-06,
                9.610241496111313e-05,
                4.006369696286016e-05,
                1.3007130013288297e-05,
                8.939699500164542e-06
            ],
            [
                2.7535704219423216e-05,
                6.144174601588856e-06,
                5.04347408197782e-07,
                3.466325797778739e-07,
                6.144172403715875e-06,
                6.144174601879434e-06,
                9.4224425692559e-07,
                8.315279285149107e-07,
                6.1441760667392215e-06,
                1.0677026154619133e-06
            ],
            [
                0.999972464315495,
                0.9999599362935387,
                0.00023050666035506282,
                0.9999251537727529,
                0.9993736658365711,
                0.9999852610110133,
                0.9994472213290531,
                0.5621765008857982,
                0.20181321505933414,
                0.20181322226037882
            ],
            [
                0.9997965729784852,
                0.9998766054104226,
                0.9999852610145146,
                0.9980732655838241,
                0.9992903297153246,
                0.998830489727737,
                0.9999151889182762,
                0.9999546021151283,
                0.9997965730274941,
                0.9998204720339836
            ],
            [
                0.9999938558246656,
                0.9999974387174841,
                0.9999995549147889,
                0.9999974387168733,
                0.9999970976880149,
                0.99999862904312,
                0.9999990577551814,
                0.9999962733602715,
                0.9999962733616045,
                0.999999057755743
            ],
            [
                3.120192624960245e-05,
                3.120192253242944e-05,
                2.4300249421932663e-05,
                NaN,
                3.535625070624499e-05,
                6.14417606031854e-06,
                2.1444953523537147e-05,
                1.1478764017720528e-05,
                0.0,
                1.3007134666431358e-05
            ],
            [
                0.999992110738355,
                0.9999599363173896,
                0.9999930377437503,
                0.9999251537817438,
                0.9999984465016899,
                0.9993736659811072,
                NaN,
                0.9999982396561572,
                0.9999994284997573,
                0.9992903296602172
            ],
            [
                0.7057850340255386,
                0.8807970811069351,
                0.9999885212318809,
                0.5,
                0.9399133458285746,
                0.9997965731028201,
                0.9999832985821646,
                0.9999910603069228,
                0.9999832985801492,
                0.9999945777790915
            ],
            [
                0.9999785550516765,
                0.9978172831631782,
                0.06754668644694546,
                0.18242551713899047,
                0.9579122708828602,
                0.5312093733737563,
                0.24508501313237172,
                0.8354835350552603,
                0.9999646437433654,
                0.9994472214130502
            ],
            [
                1.0129990979547237e-05,
                1.6701425825128124e-05,
                1.994729721265813e-06,
                2.2603251061664e-06,
                4.785095633999427e-06,
                1.5534983101393749e-06,
                2.144495607492721e-05,
                1.8925143728749452e-05,
                1.9947301970587145e-06,
                1.994730197071414e-06
            ],
            [
                2.260325375634003e-06,
                4.785093353687772e-06,
                1.9947290078746543e-06,
                1.012998977213635e-05,
                6.14417533430649e-06,
                5.422217676925328e-06,
                4.22283344433731e-06,
                2.56128159999123e-06,
                1.4738985485166298e-05,
                3.2887482812745586e-06
            ],
            [
                1.0129988561906404e-05,
                4.78509506499309e-06,
                1.0129989771288745e-05,
                6.9622579095833456e-06,
                1.9947306725669014e-06,
                1.7603434230312906e-06,
                0.9999756997476897,
                4.785096776251149e-06,
                2.561283126639892e-06,
                1.2098656834613962e-06
            ],
            [
                1.8925157261545463e-05,
                4.539787401825028e-05,
                2.1444940724775554e-05,
                1.4738976695459959e-05,
                NaN,
                5.422218323231539e-06,
                1.1478764018012839e-05,
                2.7535687806920664e-05,
                3.535624226936835e-05,
                2.753570422573402e-05
            ],
            [
                2.7535700933696396e-05,
                2.1444958637356654e-05,
                3.535626333088765e-05,
                6.96225956921868e-06,
                7.889266347248781e-06,
                1.6701419853184244e-05,
                2.144494329952946e-05,
                6.962257079376403e-06,
                1.4738985483128763e-05,
                3.726640172385136e-06
            ],
            [
                0.9999993524052789,
                0.9999987901337396,
                0.999998446502801,
                0.9999992661786696,
                0.9999962733589388,
                0.9999995549151072,
                0.9999989322972572,
                0.9999994284996893,
                0.9999984465016899,
                0.9999987901347491
            ],
            [
                6.962255419380732e-06,
                1.0129995809247506e-05,
                5.829128636782753e-05,
                2.9023126770343703e-06,
                5.422218969384951e-06,
                2.144495608105136e-05,
                5.422217030362759e-06,
                3.288747889178668e-06,
                4.2228344511197656e-06,
                4.785096205260165e-06
            ],
            [
                5.422221554581283e-06,
                4.785096776133645e-06,
                2.753568780802255e-05,
                5.422220261652556e-06,
                1.892515500808112e-05,
                4.2228344508893285e-06,
                1.1478773595657069e-05,
                3.120191880379252e-05,
                1.1478773598538445e-05,
                1.4738987240824012e-05
            ],
            [
                0.9999869928761882,
                0.9999724643154743,
                0.9999967112521109,
                0.9999945777784447,
                0.9999930377445801,
                0.9999810748585316,
                0.9999646437619555,
                0.9999832985701927,
                0.9999546021259399,
                0.9999930377462407
            ],
            [
                0.999948557786501,
                0.9999687980998067,
                0.9998601779761158,
                0.9999852610198081,
                0.9999810748495214,
                0.9996646499951802,
                0.9999599363131232,
                0.9999724642990576,
                0.9999724643025202,
                0.9991959139620928
            ],
            [
                0.999954602120557,
                0.9999832985761661,
                0.9999810748585286,
                0.9999967112513268,
                0.9999970976876693,
                0.9999810748517602,
                0.9999546021151431,
                0.9999599363030446,
                0.9999599363173673,
                0.999975699756372
            ],
            [
                7.889260703619978e-06,
                2.260324297702111e-06,
                6.144176065940129e-06,
                1.473898196677375e-05,
                5.422221554926484e-06,
                4.222834451065997e-06,
                5.422217676101776e-06,
                1.0129995808178788e-05,
                6.144172403928222e-06,
                1.0129989759919808e-05
            ],
            [
                1.0129990979381404e-05,
                1.1478773597870298e-05,
                7.889263525893087e-06,
                6.962259569117366e-06,
                1.6701421844085127e-05,
                3.535624649893211e-05,
                3.2887506332466845e-06,
                1.0129992187400498e-05,
                3.288750241500471e-06,
                4.7850933535659155e-06
            ],
            [
                0.017986209698896728,
                0.08509904848750825,
                0.9992903296260383,
                0.9998766054699474,
                0.32082128783705344,
                0.9999599363030355,
                0.9998766054692795,
                0.679178699175393,
                0.4073334000459302,
                0.998830489858967
            ],
            [
                2.4300249421932663e-05,
                2.7535700948722127e-05,
                3.288749849477628e-06,
                3.120191881321371e-05,
                1.147877223059538e-05,
                3.726641061027928e-06,
                1.0129995809763438e-05,
                1.6701423833436905e-05,
                2.902313023063532e-06,
                2.2603245673155757e-06
            ],
            [
                6.14417460073947e-06,
                6.962254589332388e-06,
                4.222833444283541e-06,
                8.939697369671496e-06,
                6.144173136019732e-06,
                3.2887490652810324e-06,
                3.1201907650801864e-05,
                6.962257079059797e-06,
                6.9622562487453084e-06,
                2.260324297702111e-06
            ],
            [
                5.14422197953122e-05,
                8.939698434820389e-06,
                1.3007128464559612e-05,
                4.7850939242083995e-06,
                3.120190765193695e-05,
                5.144220139179215e-05,
                6.962253759271479e-06,
                1.670142781520948e-05,
                2.144494329348333e-05,
                6.144173869240119e-06
            ],
            [
                2.9023119850527192e-06,
                3.72664017246987e-06,
                3.7266379512112265e-06,
                5.422221555069497e-06,
                1.1478764020372226e-05,
                1.4738978457336465e-05,
                1.5534981249291695e-06,
                4.785093923768848e-06,
                3.535625070624499e-05,
                7.889260704179641e-06
            ],
            [
                0.9999993524052789,
                0.9999994284994167,
                0.9999992661789321,
                0.999999266178757,
                0.9999945777829693,
                0.9999990577554061,
                0.9999994956527121,
                0.9999990577555185,
                0.9999994284997573,
                0.9999967112493665
            ],
            [
                1.30071315640992e-05,
                1.3007131564903626e-05,
                1.6701417859519093e-05,
                6.962254588977791e-06,
                1.6701425825128124e-05,
                5.422220908560712e-06,
                5.144222591279097e-05,
                0.00026119021454731005,
                1.5534975693488444e-06,
                1.1478770861650256e-05
            ],
            [
                0.9999756997563752,
                0.9997965729306277,
                0.9999417087553398,
                0.9998601779261674,
                0.9999339478789374,
                0.9999785550541426,
                0.9999898700090202,
                0.9996646498498932,
                0.9706877672877218,
                0.9999785550439183
            ],
            [
                2.9023123311583482e-06,
                7.889260704531226e-06,
                1.892515500663531e-05,
                3.2887498494551953e-06,
                2.260324028281919e-06,
                2.2603248367512505e-06,
                6.144176799283803e-06,
                2.2603248367173307e-06,
                7.889264466230069e-06,
                NaN
            ],
            [
                9.610240346745984e-05,
                5.14422381473764e-05,
                6.605212884380361e-05,
                4.5397890268254766e-05,
                6.962256248871951e-06,
                1.0129987356191011e-05,
                6.144176798870286e-06,
                6.962256249517824e-06,
                1.4738985485166298e-05,
                6.962255416961874e-06
            ],
            [
                3.2887478889513447e-06,
                3.726641061058432e-06,
                4.22283193393364e-06,
                1.7603440526662173e-06,
                1.3709573702248741e-06,
                7.889266347356409e-06,
                1.7603432132784448e-06,
                1.994730672496148e-06,
                3.2887486729876365e-06,
                1.994729721396435e-06
            ],
            [
                3.726637951126493e-06,
                1.0129995809763438e-05,
                7.889264466445326e-06,
                8.939693106182721e-06,
                2.5612834318257725e-06,
                2.5612831265630198e-06,
                1.1478768124324254e-05,
                2.5612831266165976e-06,
                1.1478769493540482e-05,
                1.7603430033607189e-06
            ],
            [
                0.9999869928746435,
                0.9997694932299975,
                0.9999646437324528,
                0.9999646437451318,
                0.9999339478479851,
                0.5,
                0.9999852610197898,
                0.5926665999540698,
                0.9999546021314297,
                0.9999885212264205
            ],
            [
                2.144495351940237e-05,
                1.0129992186774007e-05,
                6.9622587393661365e-06,
                1.147877222702498e-05,
                NaN,
                6.144173869240119e-06,
                1.8925152751174644e-05,
                6.962257079173776e-06,
                1.3007125363057018e-05,
                1.994729721396435e-06
            ],
            [
                7.889259764445822e-06,
                8.93969310675186e-06,
                1.5534973841309562e-06,
                1.892514147143123e-05,
                3.726637950851956e-06,
                1.147876812538911e-05,
                1.6701429807964442e-05,
                6.962253759752719e-06,
                2.144495608222158e-05,
                1.6701423833831836e-05
            ],
            [
                0.9998415637836084,
                0.9975273763988732,
                0.9999038975392935,
                0.9986749773013401,
                0.9998911030528093,
                0.999933947839665,
                0.6224593312018546,
                4.539786846594105e-05,
                0.9999151889182596,
                0.999933947878961
            ],
            [
                0.010986945170704697,
                0.9971990731863534,
                0.40733340004593027,
                0.09534947261117098,
                0.9997388096303742,
                0.08509904152653235,
                NaN,
                0.7057850216484837,
                0.9992903295886395,
                0.6513548714339144
            ],
            [
                0.9995694430118022,
                0.9999967112501504,
                0.9998601778925937,
                0.9999910603036959,
                0.9999945777803838,
                0.9999885212332453,
                0.9999832985781559,
                0.9999832985721857,
                0.9999485577741262,
                0.9999957771675623
            ],
            [
                4.78509563509613e-06,
                4.006367785875045e-05,
                7.484625375785435e-05,
                6.9622537587775775e-06,
                8.481105141464207e-05,
                1.473897669838221e-05,
                6.962253759157502e-06,
                1.8925143724239906e-05,
                1.4738987241494252e-05,
                9.610243764498401e-05
            ],
            [
                0.9999885212346142,
                0.9998204720979046,
                0.9999810748495044,
                0.9999756997477172,
                7.484624478551196e-05,
                0.9999967112501507,
                0.9999832985821387,
                0.9986749775545959,
                0.9999687980774697,
                0.99997569974768
            ],
            [
                3.120191880504111e-05,
                7.889260703619978e-06,
                3.2887498491620677e-06,
                1.5534979396448094e-06,
                2.5612834317535587e-06,
                0.00048785717577364403,
                7.889266345397582e-06,
                1.0129992186589747e-05,
                5.422218969217281e-06,
                1.5534984952492866e-06
            ],
            [
                4.7850950649408664e-06,
                8.481103122174425e-05,
                2.9023112930659533e-06,
                1.5534981249496567e-06,
                4.0063701700885974e-05,
                4.222832941034507e-06,
                7.889264465555602e-06,
                4.5397874029150114e-05,
                1.1478768125201194e-05,
                1.8925145983348442e-05
            ],
            [
                0.9999952149049349,
                0.9999967112493666,
                0.9997965730087802,
                0.9999869928699887,
                0.9999967112513268,
                0.9999957771680659,
                0.9999785550490354,
                0.999975699765066,
                0.9999910602994339,
                0.9999785550413836
            ],
            [
                0.9999724643187469,
                0.9999982396565769,
                0.9999785550490304,
                0.9999724643023337,
                0.9999869928715355,
                0.9999910603068931,
                0.9999885212318744,
                0.9999957771655487,
                0.9999485577863506,
                0.9999921107336525
            ],
            [
                0.9999869928699849,
                0.999903897608017,
                0.9999945777803838,
                0.9999151889384297,
                0.9998766053663363,
                0.9995694429612494,
                0.9999970976890528,
                0.9999885212346115,
                0.9999756997534747,
                0.9999869928668892
            ]
        ]
    },
    {
        "q_id": "8917_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            5,
            6,
            7,
            8,
            9,
            12,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            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,
            55,
            56,
            57,
            58,
            59,
            60,
            62,
            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,
            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,
            21,
            22,
            61,
            63,
            64
        ],
        "rewards": [
            [
                0.9999998724809875,
                0.9999996072139402,
                0.9999996533674615,
                0.9999998144609203,
                0.9999998144609645,
                0.9999994956524716,
                0.9999996533672549,
                0.9999996533674201,
                0.9999997897566589,
                0.9999996072136592
            ],
            [
                0.9999994956525317,
                0.999999554914842,
                0.9999994956526519,
                0.9999994284992805,
                0.999998446502801,
                0.9999996072138934,
                0.9999992661791944,
                0.9999994284997573,
                0.9999996533674614,
                0.9999992661792819
            ],
            [
                0.9999990577552937,
                0.9999987901344607,
                0.9999987901341723,
                0.9999992661788445,
                0.9999993524050474,
                0.999999168471675,
                0.9999974387168734,
                0.9999990577549568,
                0.9999987901344607,
                0.9999974387168734
            ],
            [
                0.9999989322970028,
                0.999998446502801,
                0.9999991684715759,
                0.999993855822469,
                0.9999982396572065,
                0.9999974387177893,
                0.9999962733602719,
                0.999997438716568,
                0.9999957771660523,
                0.9999982396567867
            ],
            [
                0.9999994284992805,
                0.9999994956526519,
                0.9999996940976636,
                0.9999997897567341,
                0.9999994956527721,
                0.9999994956525918,
                0.999999554914895,
                0.9999997300421903,
                0.9999996072136592,
                0.9999996940978825
            ],
            [
                0.9999989322972572,
                0.9999962733611604,
                0.999999057755743,
                0.9999994284993486,
                0.9999986290421394,
                0.9999967112493665,
                0.9999984465026158,
                0.9999977396748938,
                0.9999974387180947,
                0.9999986290421394
            ],
            [
                3.9278629390507954e-07,
                8.31528325021115e-07,
                6.475947981975644e-07,
                5.715006514040971e-07,
                9.422450431860582e-07,
                9.422442569208767e-07,
                7.338209805040511e-07,
                1.209866116170145e-06,
                7.338212429537553e-07,
                8.315283249923769e-07
            ],
            [
                0.9999996533674614,
                0.9999996940977002,
                0.999999554914789,
                0.9999996072137529,
                0.9999996072138465,
                0.9999996533673375,
                0.9999995549147359,
                0.9999995549151073,
                0.9999995549150542,
                0.9999996533672135
            ],
            [
                0.9999989322973845,
                0.9999982396567867,
                0.9999992661790195,
                0.9999992661786695,
                0.999999057755743,
                0.9999982396565769,
                0.9999990577550693,
                0.9999995549149481,
                0.9999994284996211,
                0.9999986290424663
            ],
            [
                0.9999987901344607,
                0.9999992661786695,
                0.9999990577557432,
                0.999999352404893,
                0.9999991684722698,
                0.9999991684720715,
                0.9999989322975119,
                0.9999986290431201,
                0.999998005269803,
                0.9999990577549568
            ],
            [
                0.9999970976883609,
                0.999999266178757,
                0.9999986290426297,
                0.9999991684718732,
                0.9999987901346049,
                0.9999977396751633,
                0.9999991684719723,
                0.999995214904935,
                0.9999994956527722,
                0.9999982396574163
            ],
            [
                0.9999991684717741,
                0.9999990577550691,
                0.9999990577556308,
                0.9999986290421394,
                0.9999984465024306,
                0.9999962733616046,
                0.99999893229713,
                0.9999987901343165,
                0.9999990577555185,
                0.9999991684722698
            ],
            [
                0.9999996533674202,
                0.9999997300421903,
                0.9999994956527121,
                0.9999997897566089,
                0.9999994956525317,
                0.9999993524054335,
                0.9999995549151072,
                0.9999995549147359,
                0.9999997617630616,
                0.9999996533673788
            ],
            [
                0.9999990577550691,
                0.999999266178932,
                0.999999352405279,
                0.9999984465024306,
                0.999998629042303,
                0.9999993524054335,
                0.9999977396765105,
                0.9999990577554061,
                0.9999986290421394,
                0.9999991684720715
            ],
            [
                0.999999887464811,
                0.9999989322968754,
                0.9999996072137529,
                0.9999998555020307,
                0.9999997300422547,
                0.9999996072137529,
                0.9999997897567091,
                0.9999998555020135,
                0.9999996940977366,
                0.9999996072137061
            ],
            [
                0.9999996940978095,
                0.9999997617631752,
                0.9999998362622552,
                0.9999996533672549,
                0.9999989322970027,
                0.9999996533672549,
                0.9999992661786695,
                0.9999996072138465,
                0.9999994284996211,
                0.9999994284997573
            ],
            [
                0.9999995549147358,
                0.9999993524050474,
                0.9999982396565769,
                0.9999992661792819,
                0.9999977396751634,
                0.9999957771660523,
                0.9999986290426297,
                0.9999982396561572,
                0.999998446502801,
                0.9999987901343165
            ],
            [
                0.9999986290432834,
                0.9999980052693274,
                0.9999997897566089,
                0.9999962733616047,
                0.9999991684715759,
                0.9999990577554061,
                0.9999996533673375,
                0.9999993524053562,
                0.9999993524053562,
                0.9999990577550691
            ],
            [
                0.9999990577555185,
                0.9999994284994168,
                0.9999987901337396,
                0.9999991684721706,
                0.9999974387171787,
                0.9999974387180948,
                0.9999989322967481,
                0.999999168471675,
                0.9999993524052789,
                0.9999989322972572
            ],
            [
                0.9999991684721706,
                0.9999986290421394,
                0.9999990577557432,
                0.9999986290432834,
                0.9999977396762411,
                0.9999994284996211,
                0.9999994956524115,
                0.9999994284997573,
                0.9999993524050474,
                0.9999991684717742
            ],
            [
                0.9999993524053562,
                0.9999990577557432,
                0.9999990577551814,
                0.9999986290426297,
                0.9999989322972572,
                0.9999989322972572,
                0.999998005269803,
                0.9999977396757022,
                0.9999996533673375,
                0.9999993524051246
            ],
            [
                0.9999996072136592,
                0.9999990577551814,
                0.9999996072136125,
                0.9999984465026158,
                0.9999994956524715,
                0.9999996940977002,
                0.999999266178757,
                0.9999994284995529,
                0.9999992661791945,
                0.9999989322975118
            ],
            [
                0.99999211073366,
                0.009708476929171176,
                0.8807970904940926,
                0.5926665999540698,
                0.8354835432479663,
                0.999941708755328,
                0.14804719427274568,
                0.9998911030707252,
                0.9997388095816756,
                0.009708474977211935
            ],
            [
                0.9999982396559474,
                0.999997438716568,
                0.9999987901337396,
                0.9999967112505427,
                0.999998446502801,
                0.999998790134028,
                0.9999987901343165,
                0.9999967112509347,
                0.9999990577556307,
                0.9999986290429566
            ],
            [
                0.9999993524054335,
                0.9999991684720715,
                0.9999996072137998,
                0.9999989322968754,
                0.9999995549151073,
                0.9999984465016899,
                0.9999982396569966,
                0.999999057755743,
                0.9999991684720715,
                0.9999992661789321
            ],
            [
                0.9999980052695652,
                0.9999938558253986,
                0.9999982396565769,
                0.9999989322971299,
                0.9999982396565769,
                0.9999989322970027,
                0.9999989322973845,
                0.9999980052705163,
                0.9999984465026158,
                0.999997097686631
            ],
            [
                0.9999984465016899,
                0.9999991684718733,
                0.99999893229713,
                0.9999998874648514,
                0.9999974387187053,
                0.9999986290427931,
                0.9999991684718732,
                0.9999987901347491,
                0.9999992661788446,
                0.9999986290423029
            ],
            [
                0.9999986290424663,
                0.999997438717484,
                0.999998790134028,
                0.9999977396765105,
                0.9999993524054335,
                0.9999987901344607,
                0.9999994284995529,
                0.9999986290432834,
                0.9999992661792819,
                0.999999554914895
            ],
            [
                0.99999862904312,
                0.9999993524053562,
                0.9999996940976272,
                0.999999266178757,
                0.999999352405279,
                0.999999653367379,
                0.9999991684715758,
                0.9999995549150011,
                0.9999989322970027,
                0.9999993524049702
            ],
            [
                0.9999993524054335,
                0.9999995549150542,
                0.9999990577552939,
                0.9999996940977002,
                0.9999986290424663,
                0.9999986290424663,
                0.9999990577552939,
                0.9999992661790196,
                0.9999989322968754,
                0.9999986290427931
            ],
            [
                0.9999996072136125,
                0.9999984465022456,
                0.9999994956527721,
                0.9999996072136592,
                0.9999980052702786,
                0.9999990577555185,
                0.999998629042303,
                0.9999995549151073,
                0.9999996940978825,
                0.9999990577555185
            ],
            [
                0.9999984465026159,
                0.9999898700078138,
                0.999986992869987,
                0.9999970976890528,
                0.999997097689053,
                0.9999930377420909,
                0.9999869928684354,
                0.9999952149072171,
                0.9999957771675624,
                0.9999987901347492
            ],
            [
                0.9999996940977731,
                0.9999989322970027,
                0.9999986290421394,
                0.9999995549148419,
                0.9999987901341723,
                0.9999994956524715,
                0.9999994956526519,
                0.9999993524054334,
                0.9999995549151072,
                0.9999994956527121
            ],
            [
                0.999999057755743,
                0.9999991684715759,
                0.999999168471675,
                0.9999992661787571,
                0.9999996072138934,
                0.9999994284996893,
                0.9999994956527721,
                0.999999168471675,
                0.999999057755743,
                0.9999998144608319
            ],
            [
                0.9999980052702786,
                0.9999986290431201,
                0.9999989322975118,
                0.9999989322967482,
                0.999999554914842,
                0.9999987901337396,
                0.9999977396759716,
                0.9999986290421394,
                0.9999938558253986,
                0.9999967112521109
            ],
            [
                0.9999989322968754,
                0.9999999006880312,
                0.9999990577552937,
                0.9999987901347492,
                0.9999984465016899,
                0.9999995549150542,
                0.9999989322968754,
                0.9999991684722698,
                0.9999982396572065,
                0.999999266178932
            ],
            [
                0.999995214903224,
                0.9999977396762411,
                0.9999982396572065,
                0.9999921107364758,
                0.9999992661788446,
                0.9999962733611604,
                0.9999974387180947,
                0.9999987901343165,
                0.9999992661786696,
                0.9999967112509348
            ],
            [
                0.9999996072139402,
                0.9999982396565769,
                0.9999977396765105,
                0.9999991684718732,
                0.999998790134028,
                0.9999998362623528,
                0.9999991684718733,
                0.9999995549147889,
                0.9999996072138465,
                0.999998239656367
            ],
            [
                0.9999970976873229,
                0.9999810748495139,
                0.9999982396559474,
                0.9999977396759716,
                0.9999987901337396,
                0.9999994956525918,
                0.9999970976869772,
                0.999999352405279,
                0.9999992661791944,
                0.9999994956527121
            ],
            [
                5.71500651413193e-07,
                3.059022998558814e-07,
                3.059021904543821e-07,
                4.450848927637999e-07,
                6.47594798194325e-07,
                5.715005151485975e-07,
                1.5534983100016177e-06,
                5.715002426343175e-07,
                1.3709572068079696e-06,
                2.102433410343832e-07
            ],
            [
                9.422444815220956e-07,
                2.3823702358748722e-07,
                5.715004470170917e-07,
                3.9278605977939997e-07,
                9.422445938642879e-07,
                2.6995787399686675e-07,
                2.102433911580983e-07,
                2.3823690998803445e-07,
                3.927863875492102e-07,
                5.04347528431602e-07
            ],
            [
                0.9999977396757022,
                0.9999990577552937,
                0.9999982396565769,
                0.9999987901341723,
                0.9999995549148419,
                0.9999994284992805,
                0.999999057755069,
                0.9999989322971299,
                0.99999893229713,
                0.9999990577557432
            ],
            [
                0.9999993524053562,
                0.9999993524048931,
                0.9999982396569966,
                0.9999996533674201,
                0.9999989322975118,
                0.9999990577557432,
                0.9999987901338838,
                0.9999987901346049,
                0.9999996072137998,
                0.9999986290432835
            ],
            [
                0.999999554914842,
                0.9999987901346049,
                0.9999990577556307,
                0.9999991684717742,
                0.9999986290429567,
                0.9999957771665557,
                0.9999982396567867,
                0.9999987901344607,
                0.9999987901338838,
                0.9999970976880149
            ],
            [
                0.999999814460876,
                0.9999995549147889,
                0.9999998724809723,
                0.9999997617631752,
                0.9999998144609202,
                0.9999996533672962,
                0.9999998362622747,
                0.9999998144609202,
                0.9999994956524115,
                0.9999993524052019
            ],
            [
                0.9999996940978095,
                0.999999057755743,
                0.9999993524050474,
                0.9999957771650461,
                0.9999996940977366,
                0.9999980052700408,
                0.9999993524052019,
                0.9999994284995529,
                0.9999998362622942,
                0.9999982396574163
            ],
            [
                0.999997097686977,
                0.9999989322975118,
                0.9999984465015047,
                0.9999957771645421,
                0.9999910603026313,
                0.9999987901338838,
                0.9999984465026158,
                0.9999992661792819,
                0.9999977396762412,
                0.9999991684720715
            ],
            [
                0.9999921107402364,
                0.9999962733607162,
                0.9999992661790195,
                0.9999992661789321,
                0.9999991684718732,
                0.9999997300420937,
                0.9999990577556307,
                0.9999987901338838,
                0.99999893229713,
                0.9999986290426298
            ],
            [
                0.9999989322968754,
                0.9999987901347492,
                0.9999993524050474,
                0.9999996533674201,
                0.9999994284995529,
                0.9999994956527721,
                0.9999994284994167,
                0.9999977396748939,
                0.9999980052693275,
                0.9999987901343165
            ],
            [
                0.9999785550569471,
                0.8175744850834649,
                0.9999930377437677,
                0.9579122728353318,
                0.9999930377404582,
                0.9669140236373025,
                0.05340332565681314,
                0.9669140244715405,
                0.9999546021498709,
                0.9796676481043166
            ],
            [
                0.9999992661787571,
                0.9999992661788446,
                0.9999987901347491,
                0.9999994956525317,
                0.9999989322972572,
                0.9999993524052019,
                0.9999992661786696,
                0.9999996072137998,
                0.999999352404893,
                0.9999996533675028
            ],
            [
                0.9999991684718732,
                0.9999994284993485,
                0.9999991684717742,
                0.9999992661786696,
                0.9999994956527121,
                0.9999994284992805,
                0.99999862904312,
                0.9999996072138934,
                0.9999990577554061,
                0.9999986290424663
            ],
            [
                0.9999994956523514,
                0.9999992661789321,
                0.9999996533672549,
                0.9999991684715758,
                0.9999991684722698,
                0.9999994284996893,
                0.9999996072139402,
                0.9999996940976272,
                0.9999990577549568,
                0.9999996533672549
            ],
            [
                0.9999977396762411,
                0.9999990577552937,
                0.9999980052709919,
                0.9999991684720715,
                0.9999995549151073,
                0.9999990577554061,
                0.9999987901347492,
                0.999998790134028,
                0.9999992661786696,
                0.9999992661788445
            ],
            [
                0.9999980052693275,
                0.9999990577551814,
                0.9999989322971299,
                0.9999995549150542,
                0.9999994956526519,
                0.999999266178932,
                0.9999991684718733,
                0.999999495652712,
                0.9999994284996211,
                0.9999991684722698
            ],
            [
                0.9999810748427421,
                0.999998005269803,
                0.9999930377404321,
                0.9999984465016899,
                0.999998005269803,
                0.9999962733620489,
                0.9999989322973846,
                0.9999980052700407,
                0.9999977396765106,
                0.9999952149055054
            ],
            [
                0.9999986290427932,
                0.9999977396748938,
                0.9999982396565769,
                0.9999995549151073,
                0.9999990577551814,
                0.9999991684718732,
                0.9999994956527721,
                0.9999987901337396,
                0.9999989322966208,
                0.9999995549151073
            ],
            [
                0.9999989322975118,
                0.9999977396748938,
                0.9999995549147358,
                0.9999996072139402,
                0.9999977396757023,
                0.9999989322970027,
                0.999999554914895,
                0.9999996940978461,
                0.9999995549150011,
                0.9999995549150011
            ],
            [
                0.9999995549147359,
                0.999999554914789,
                0.9999967112501507,
                0.9999990577556307,
                0.9999994284996211,
                0.9999938558275957,
                0.9999962733593833,
                0.9999952149066464,
                0.9999994284992805,
                0.9999994956524716
            ],
            [
                0.9999990577554061,
                0.9999984465024306,
                0.9999977396748938,
                0.9999993524051246,
                0.9999993524051246,
                0.9999980052693274,
                0.9999995549150542,
                0.9999993524050473,
                0.9999992661792819,
                0.999999057755069
            ],
            [
                0.9999993524052018,
                0.9999994284997573,
                0.9999996533674614,
                0.9999994284994167,
                0.9999995549149481,
                0.9999993524052018,
                0.9999980052707541,
                0.9999991684717741,
                0.99999862904312,
                0.9999970976880148
            ],
            [
                0.9999982396559474,
                0.9999994284992805,
                0.9999986290421395,
                0.9999995549149481,
                0.9999994956524716,
                0.999998239656367,
                0.9999987901338838,
                0.9999996072138934,
                0.9999994284993485,
                0.999996711251327
            ],
            [
                0.999998446502801,
                0.9999957771655493,
                0.9999986290431201,
                0.9999989322968754,
                0.9999992661788446,
                0.9999993524052018,
                0.9999991684718733,
                0.9999994956527722,
                0.9999974387180947,
                0.9999993524054335
            ],
            [
                0.9999994956527721,
                0.999999266179107,
                0.9999994284995529,
                0.9999994956527722,
                0.9999995549150541,
                0.9999994284994849,
                0.9999992661791944,
                0.9999977396759716,
                0.9999994956524716,
                0.9999994284992805
            ],
            [
                0.9999991684720715,
                0.9999982396565769,
                0.9999989322972572,
                0.9999989322970027,
                0.9999987901338838,
                0.9999990577550691,
                0.9999994284993485,
                0.9999957771655489,
                0.9999987901337396,
                0.9999989322973845
            ],
            [
                0.9999994956525317,
                0.9999970976866313,
                0.9999984465016899,
                0.9999994284996211,
                0.9999990577555185,
                0.9999994284997573,
                0.9999989322973846,
                0.9999986290426298,
                0.9999995549150011,
                0.9999977396759717
            ],
            [
                0.9999990577551814,
                0.9999991684718732,
                0.9999984465018751,
                0.9999977396748938,
                0.9999991684720715,
                0.9999982396574163,
                0.999998005270992,
                0.9999993524051246,
                0.9999982396572065,
                0.9999987901344607
            ],
            [
                0.999999554914895,
                0.9999995549147358,
                0.9999994284996211,
                0.9999993524051246,
                0.99999893229713,
                0.9999982396572065,
                0.9999993524049702,
                0.9999977396759716,
                0.999999057755743,
                0.9999990577551815
            ],
            [
                0.9999993524053563,
                0.9999994284993485,
                0.9999991684719725,
                0.9999994284993485,
                0.9999987901347491,
                0.9999986290423029,
                0.9999994284996211,
                0.9999992661792819,
                0.9999993524053563,
                0.9999990577555185
            ],
            [
                0.999999057755743,
                0.9999980052707541,
                0.9999982396565767,
                0.9999986290426297,
                0.9999990577554061,
                0.9999980052702785,
                0.9999986290427931,
                0.9999974387187053,
                0.9999982396559473,
                0.9999989322970028
            ],
            [
                0.9999993524050474,
                0.9999994956524114,
                0.9999974387177893,
                0.9999989322968754,
                0.9999990577557432,
                0.9999987901343166,
                0.9999989322966208,
                0.9999989322973845,
                0.9999993524052018,
                0.9999989322972572
            ],
            [
                0.9999990577551815,
                0.9999989322975118,
                0.9999990577552939,
                0.9999982396574163,
                0.9999952149032236,
                0.9999989322967482,
                0.9999945777784449,
                0.9999982396565769,
                0.9999992661791071,
                0.9999984465020603
            ],
            [
                0.9999994284992805,
                0.9999970976869772,
                0.9999991684718732,
                0.9999996940978095,
                0.9999994284993485,
                0.9999994284996211,
                0.9999993524051246,
                0.999998446502801,
                0.9999987901344607,
                0.9999992661791944
            ],
            [
                0.99999893229713,
                0.9999995549151073,
                0.9999970976876692,
                0.9999994284996891,
                0.9999974387187053,
                0.9999993524052019,
                0.9999995549149481,
                0.9999992661790196,
                0.9999994956525317,
                0.9999986290427931
            ],
            [
                0.9999989322975118,
                0.9999991684721706,
                0.9999991684716749,
                0.9999980052709919,
                0.9999994284994849,
                0.9999989322966208,
                0.9999991684721706,
                0.9999984465020603,
                0.9999991684718732,
                0.999999168471675
            ],
            [
                0.9999993524052018,
                0.9999977396751633,
                0.9999987901346049,
                0.999997097688707,
                0.9999962733611605,
                0.9999910602994339,
                0.9999952149043648,
                0.9999885212264029,
                0.9999989322975118,
                0.9999990577555185
            ],
            [
                0.9999980052709919,
                0.9999986290424663,
                0.9999994284995529,
                0.9999989322970028,
                0.9999991684719723,
                0.9999984465024306,
                0.9999967112513267,
                0.999999057755743,
                0.9999989322973846,
                0.9999993524052019
            ],
            [
                0.9999997300422868,
                0.9999970976876691,
                0.9999990577552937,
                0.999999554914895,
                0.9999977396754327,
                0.9999991684720715,
                0.999997438717484,
                0.9999994284994849,
                0.9999995549149481,
                0.9999997300422225
            ],
            [
                0.9999995549147359,
                0.9999997300422868,
                0.9999994956527722,
                0.999997097687323,
                0.9999995549147889,
                0.9999992661790196,
                0.9999995549148419,
                0.9999996533672962,
                0.9999977396762412,
                0.9999993524050473
            ],
            [
                0.9999945777829694,
                0.9999687980997877,
                0.9999832985741766,
                0.9999885212264015,
                0.9999885212318748,
                0.9999921107364742,
                0.9999930377454105,
                0.9999921107392953,
                0.9999977396762411,
                0.9999962733616045
            ],
            [
                0.9999990577551815,
                0.9999991684722697,
                0.9999990577552937,
                0.9999987901347491,
                0.9999996072137998,
                0.9999996072138465,
                0.9999990577555185,
                0.9999990577556308,
                0.9999994956524114,
                0.9999993524050474
            ],
            [
                0.9999982396561571,
                0.9999885212359824,
                0.9999724643154692,
                0.999986992873089,
                0.9999898700078134,
                0.9999952149032237,
                0.9999885212305076,
                0.9999970976890529,
                0.9999756997476862,
                0.9999546021476133
            ],
            [
                0.9999987901337396,
                0.9999991684722697,
                0.9999990577556308,
                0.9999982396569966,
                0.9999996533673788,
                0.9999991684717742,
                0.999998790134028,
                0.9999980052693275,
                0.9999957771655489,
                0.9999980052707541
            ],
            [
                0.9999938558261309,
                0.9999982396565769,
                0.9999957771670589,
                0.999999554914895,
                0.9999982396561572,
                0.9999989322968754,
                0.9999984465022455,
                0.9999990577550691,
                0.9999977396754327,
                0.999989870009021
            ],
            [
                0.9999994956526519,
                0.9999990577555183,
                0.9999992661788445,
                0.999999168471675,
                0.9999994956525317,
                0.9999992661789321,
                0.9999994284994849,
                0.9999996072138465,
                0.9999991684720715,
                0.9999986290421394
            ],
            [
                0.9999952149032237,
                0.9999984465015047,
                0.9999994284996893,
                0.999998446502801,
                0.9999986290427931,
                0.9999970976887068,
                0.999991060304763,
                0.9999974387177893,
                0.9999957771645421,
                0.9999992661789321
            ],
            [
                0.9999993524052018,
                0.9999982396565769,
                0.9999989322975118,
                0.9999993524051246,
                0.9999995549150541,
                0.9999994956525918,
                0.99999862904312,
                0.9999982396572065,
                0.9999992661786696,
                0.9999991684718733
            ],
            [
                0.9999984465018751,
                0.9999989322970027,
                0.9999991684717741,
                0.9999986290432834,
                0.9999989322975118,
                0.9999993524050474,
                0.9999984465015046,
                0.9999992661788446,
                0.9999938558224688,
                0.999996273358939
            ],
            [
                0.9999970976883609,
                0.9999991684721706,
                0.9999991684722698,
                0.9999967112513268,
                0.9999990577550691,
                0.9999989322973845,
                0.9999994284996211,
                0.9999987901341723,
                0.999999554914895,
                0.999998005269803
            ],
            [
                0.9999992661792819,
                0.999999168471675,
                0.9999984465018751,
                0.9999989322966208,
                0.9999995549150011,
                0.9999982396565769,
                0.9999995549150542,
                0.9999993524051246,
                0.9999991684720715,
                0.9999997300422225
            ],
            [
                0.9999987901346049,
                0.9999996533673375,
                0.9999996072138934,
                0.9999967112493665,
                0.9999984465024307,
                0.9999996072138934,
                0.9999987901347491,
                0.9999930377437514,
                0.9999974387165681,
                0.999999057755743
            ],
            [
                0.999933947871151,
                0.9999251537914328,
                0.14804719803168945,
                0.9525741278322102,
                0.46879062662624377,
                0.9999485577621218,
                0.9669140244715405,
                0.9046505312448598,
                0.7057850154599563,
                0.9796676448393464
            ],
            [
                0.9999990577556308,
                0.9999982396569966,
                0.9999991684715759,
                0.9999994284993486,
                0.999999554914842,
                0.9999994956523514,
                0.9999986290426297,
                0.9999993524052019,
                0.999999554914842,
                0.999999352404893
            ],
            [
                0.9999996072139402,
                0.9999997300422547,
                0.9999989322970027,
                0.9999989322968754,
                0.9999987901343165,
                0.9999994284994849,
                0.9999992661786696,
                0.9999996072138934,
                0.9999994956524716,
                0.9999989322968754
            ],
            [
                0.9999992661790196,
                0.9999970976887069,
                0.9999977396751633,
                0.999999266179107,
                0.999999352405279,
                0.999999352404893,
                0.9999991684722698,
                0.9999996072138465,
                0.999999730042319,
                0.9999984465022455
            ],
            [
                0.9999984465024306,
                0.9999986290426298,
                0.9999984465026158,
                0.999997438716568,
                0.9999989322973846,
                0.9999993524052018,
                0.9999980052707541,
                0.9999994956523514,
                0.9999990577555185,
                0.9999982396572065
            ],
            [
                0.9999992661792819,
                0.9999987901347491,
                0.9999980052709919,
                0.9999997300422225,
                0.9999986290421395,
                0.9999996533675028,
                0.9999986290432835,
                0.999999653367379,
                0.999997097689053,
                0.9999990577554061
            ],
            [
                0.9999997300421581,
                0.9999995549150011,
                0.9999991684717741,
                0.9999994956523514,
                0.9999997617630049,
                0.999999554914895,
                0.9999994284993485,
                0.9999995549150542,
                0.9999995549150011,
                0.9999997617631752
            ],
            [
                0.999998005269803,
                0.9999990577550691,
                0.9999938558268633,
                0.999999266179107,
                0.9999991684721706,
                0.9999992661791944,
                0.9999994284993486,
                0.9999993524054335,
                0.9999994284996893,
                0.9999957771650455
            ],
            [
                0.9999984465015047,
                0.9999974387168733,
                0.9999921107364745,
                0.99999893229713,
                0.9999977396751633,
                0.9999982396559474,
                0.9999991684715759,
                0.9999993524053563,
                0.9999991684715758,
                0.9999987901338838
            ],
            [
                0.9999756997535116,
                0.9994472214539876,
                0.6224593382055109,
                0.9999251537528098,
                0.9859363703352994,
                0.06008665459220631,
                0.8354835350552603,
                0.9999251537912791,
                0.999981074842747,
                0.9992903295642024
            ],
            [
                0.9999996072137061,
                0.9999998555019274,
                0.999999266179107,
                0.999998005270992,
                0.9999996533674614,
                0.9999996072138934,
                0.9999991684718732,
                0.9999994956524716,
                0.9999994284997573,
                0.9999996072136592
            ],
            [
                0.9999992661792819,
                0.9999991684719723,
                0.9999996072138465,
                0.9999977396751635,
                0.9999994956524115,
                0.9999996072137061,
                0.9999994284997573,
                0.99999893229713,
                0.9999994956524114,
                0.9999994956524716
            ],
            [
                0.8175744850834649,
                0.6791787121629466,
                0.9999957771665555,
                0.9626731110495138,
                0.9996646498105836,
                0.6224593312018546,
                0.9998766054415836,
                0.4687906266262437,
                0.9999151889704233,
                0.9998766053758465
            ],
            [
                0.9999995549150011,
                0.99999844650169,
                0.9999991684715759,
                0.9999982396574163,
                0.999999057755743,
                0.9999993524051246,
                0.9999994956525918,
                0.9999989322971301,
                0.9999990577556308,
                0.9999994284993485
            ],
            [
                0.9999990577549568,
                0.9999984465018751,
                0.999999057755743,
                0.9999984465016898,
                0.9999984465026158,
                0.9999989322973846,
                0.9999910603068934,
                0.9999993524053562,
                0.9999991684719723,
                0.9999982396567867
            ],
            [
                0.9999994284996211,
                0.9999921107402364,
                0.9999992661790195,
                0.9999994956524115,
                0.9999989322967482,
                0.999999266178757,
                0.999999352405279,
                0.999999266179107,
                0.999993037740431,
                0.9999984465018751
            ],
            [
                0.9999986290427931,
                0.9999974387187054,
                0.9999989322966208,
                0.9999982396567867,
                0.9999984465016899,
                0.999999168471675,
                0.999999352405279,
                0.9999994956523514,
                0.9999986290421394,
                0.9999995549150011
            ],
            [
                0.999999653367379,
                0.9999996072137998,
                0.9999997300422225,
                0.9999991684721706,
                0.999999554914895,
                0.9999995549147358,
                0.999999057755743,
                0.999999352405279,
                0.9999996940978095,
                0.9999997617631184
            ],
            [
                0.9999997617630049,
                0.9999991684722698,
                0.999999057755743,
                0.9999989322966208,
                0.9999997300420937,
                0.9999962733602719,
                0.9999986290432835,
                0.9999982396574163,
                0.9999987901343165,
                0.9999992661791071
            ],
            [
                0.9999996072137529,
                0.9999994284996891,
                0.9999994284996211,
                0.9999989322968754,
                0.9999967112505432,
                0.9999994284996211,
                0.9999994956524114,
                0.999999789756684,
                0.9999991684719725,
                0.9999996072137061
            ],
            [
                0.9999990577556307,
                0.9999986290424663,
                0.9999986290429566,
                0.9999982396565769,
                0.9999992661786696,
                0.9999982396572065,
                0.9999989322975118,
                0.9999996072139402,
                0.9999984465026159,
                0.9999987901343166
            ],
            [
                0.9999977396748939,
                0.9999989322975118,
                0.9999987901341723,
                0.9999995549151073,
                0.9999990577549569,
                0.9999987901343165,
                0.9999984465018751,
                0.9999995549148419,
                0.9999982396559474,
                0.9999991684717742
            ],
            [
                0.9999992661789321,
                0.9999987901344608,
                0.9999977396754327,
                0.999997438716568,
                0.9999989322975118,
                0.9999991684719725,
                0.9999991684722698,
                0.9999991684719725,
                0.9999993524053562,
                0.9999994956525918
            ],
            [
                0.9999986290424664,
                0.9999986290429567,
                0.999998629042303,
                0.9999995549150011,
                0.999998005269803,
                0.9999984465022455,
                0.9999992661792819,
                0.9999991684718732,
                0.9999989322967482,
                0.9999997300422868
            ],
            [
                0.9999987901338838,
                0.9999962733593833,
                0.999999057755743,
                0.999998446502801,
                0.9999984465022455,
                0.9999996533673375,
                0.9999989322970028,
                0.9999991684718733,
                0.999999266178932,
                0.999999352405279
            ],
            [
                0.9999974387180947,
                0.9999921107345937,
                0.9999546021313795,
                0.999986992873089,
                0.9999885212277713,
                0.9999930377445804,
                0.9999785550413702,
                0.9999417087414357,
                0.9999930377404306,
                0.9999687980737552
            ],
            [
                0.999997097686977,
                0.9999974387180947,
                0.999999352404893,
                0.9999989322970027,
                0.9999994284996891,
                0.999999352405279,
                0.9999994956524114,
                0.9999994956527121,
                0.9999974387187053,
                0.9999989322973846
            ],
            [
                0.9999989322970027,
                0.9999930377437508,
                0.9999982396561572,
                0.9999990577557432,
                0.9999992661790195,
                0.9999987901344607,
                0.9999991684722697,
                0.999999266179107,
                0.9999984465015047,
                0.9999993524048929
            ],
            [
                0.9999962733616046,
                0.9999987901341724,
                0.9999957771670592,
                0.9999989322971299,
                0.9999984465026158,
                0.9999982396565767,
                0.9999987901338839,
                0.9999995549150011,
                0.999997097687669,
                0.9999980052695652
            ],
            [
                0.320821300824607,
                0.22270013882530884,
                0.46879062662624377,
                0.9999038975506963,
                0.9984988179214258,
                0.01798620640896166,
                0.20181322946142374,
                0.029312231387330967,
                0.7772998663336158,
                0.9999339478241627
            ],
            [
                0.999998790134028,
                0.9999993524051246,
                0.9999987901346049,
                0.9999991684718732,
                0.9999991684719723,
                0.9999996072137061,
                0.9999993524052018,
                0.9999995549151073,
                0.9999982396565769,
                0.9999993524054335
            ]
        ]
    },
    {
        "q_id": "9039_mmlu_math",
        "cot_ids": [
            0,
            1,
            3,
            7,
            8,
            9,
            10,
            11,
            12,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            23,
            24,
            25,
            26,
            30,
            31,
            32,
            33,
            34,
            36,
            37,
            38,
            39,
            40,
            42,
            43,
            45,
            50,
            53,
            54,
            55,
            56,
            57,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            70,
            71,
            73,
            77,
            78,
            79,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            89,
            92,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            121,
            122,
            124,
            126,
            127
        ],
        "rewards": [
            [
                0.9998415637966696,
                NaN,
                NaN,
                0.997817283787411,
                0.9996646497198657,
                0.8175744739711883,
                0.9999910603047634,
                NaN,
                0.9999970976873229,
                0.9998911030784605
            ],
            [
                0.7772998611746912,
                0.9046505318875315,
                0.7981867705385762,
                0.9914225138734983,
                0.03732688828117087,
                0.5926665999540698,
                5.42222155426567e-06,
                0.999664649814896,
                0.9984988177279072,
                2.7535684497254823e-05
            ],
            [
                0.867035763237924,
                0.7057850340255386,
                0.9999898700102323,
                0.9999910603027778,
                0.9999810748450375,
                4.222832437109582e-06,
                0.651354857898194,
                0.9998766053959857,
                0.9999967112497633,
                0.999981074844998
            ],
            [
                1.1478768123280277e-05,
                1.3007134661628471e-05,
                1.1478765382092217e-05,
                3.12019225022362e-05,
                3.535624635706345e-05,
                6.605214466242357e-05,
                7.889264465842609e-06,
                1.3007134663521234e-05,
                8.481103091322968e-05,
                3.120190015868497e-05
            ],
            [
                2.561282514884537e-06,
                4.785095062634308e-06,
                NaN,
                1.3007128457012223e-05,
                7.889262576917293e-06,
                1.1478765386623071e-05,
                NaN,
                5.422217657855405e-06,
                2.9023116390421582e-06,
                1.300712380555121e-05
            ],
            [
                2.2603248367358324e-06,
                6.144175334239434e-06,
                4.22283193320392e-06,
                6.475947981904966e-07,
                1.3007126912542439e-05,
                1.4738980213020151e-05,
                4.450849458179853e-07,
                5.829129313731541e-05,
                1.0129987355988324e-05,
                6.9622562492265485e-06
            ],
            [
                NaN,
                1.0129993392342568e-05,
                3.4663274507287414e-07,
                2.4300252306390083e-05,
                NaN,
                NaN,
                1.4738976687631543e-05,
                1.0129994601301684e-05,
                1.8925145970336176e-05,
                6.962256249606473e-06
            ],
            [
                0.9999962733593833,
                0.999992110737415,
                0.9997694931756702,
                0.9999852610233015,
                0.9999852610180385,
                0.9999810748540229,
                0.9993736657685477,
                0.9999970976869769,
                0.999993855824666,
                0.9999910603047755
            ],
            [
                0.8354835350552603,
                0.0001584361939990617,
                0.999964643745125,
                0.9998911030780644,
                0.999993037741262,
                0.9986749777146523,
                0.9994472212593662,
                NaN,
                0.9997388096308225,
                0.9999910602994342
            ],
            [
                2.753569761771817e-05,
                7.8892625849535e-06,
                1.8925152735477297e-05,
                7.889261643899223e-06,
                1.892514370117584e-05,
                3.535623803067304e-05,
                1.3007126909537681e-05,
                1.4738980202162242e-05,
                NaN,
                2.7535684528909006e-05
            ],
            [
                5.1442232005568484e-05,
                3.288750240564259e-06,
                1.147876673608695e-05,
                3.535626331056557e-05,
                1.9947301952490574e-06,
                6.144175311943072e-06,
                0.0006263341295811198,
                3.120190758848578e-05,
                NaN,
                3.1201915067096954e-05
            ],
            [
                0.00317268322833478,
                0.9626731134590488,
                0.7310585786300049,
                NaN,
                6.144173133136295e-06,
                0.999512142947239,
                0.5,
                0.8519527963298946,
                0.16451646699291614,
                0.9998766054411923
            ],
            [
                1.3007131545384517e-05,
                0.00010889694781813752,
                0.0001584361968298286,
                6.605212855402547e-05,
                6.605214466242357e-05,
                NaN,
                0.00012339455912557665,
                0.0001398220568556284,
                2.144494838463716e-05,
                NaN
            ],
            [
                2.260323488925638e-06,
                NaN,
                0.9999885212317227,
                0.7772998714925403,
                0.9997694933529115,
                0.9999885212266914,
                0.9999832985702966,
                0.9992903297348908,
                0.5621765008857981,
                2.144495857014705e-05
            ],
            [
                0.0002034269707034362,
                0.02931223064536054,
                0.9997965729549589,
                NaN,
                8.48110810406911e-05,
                0.04742586796038571,
                NaN,
                0.015906395414714686,
                0.0009110512902977914,
                0.18242553047372242
            ],
            [
                0.9999996940978095,
                NaN,
                0.9982992774958652,
                0.9999980052705163,
                3.120191483099956e-05,
                NaN,
                0.00013982210440553267,
                2.4300249381886717e-05,
                0.9999974387168735,
                0.9995694429210051
            ],
            [
                1.7603432131855856e-06,
                3.726638385711703e-06,
                2.4300243598740258e-05,
                5.422218969601935e-06,
                NaN,
                0.16451646699291614,
                2.9023130222373278e-06,
                4.22283294098842e-06,
                8.939698434820389e-06,
                2.1024340785415065e-07
            ],
            [
                1.6701415866188347e-05,
                3.5356254919217684e-05,
                7.484624502565293e-05,
                1.0129987350147233e-05,
                4.539789026296999e-05,
                4.5397874023865346e-05,
                1.1478765384430723e-05,
                1.6701423829123058e-05,
                0.9959298628258425,
                4.006371119588617e-05
            ],
            [
                1.3007133106487501e-05,
                8.93970056529743e-06,
                NaN,
                6.1441738667590205e-06,
                1.1478770861441461e-05,
                1.1478773596283455e-05,
                6.14417460073947e-06,
                2.902311984915459e-06,
                6.962259569003389e-06,
                NaN
            ],
            [
                2.5612825140179756e-06,
                6.144176066443055e-06,
                1.0129993393945642e-05,
                2.1444953516281788e-05,
                7.889264463216492e-06,
                8.939694168225243e-06,
                1.3007131561804229e-05,
                1.4738978450419574e-05,
                4.785095634930755e-06,
                6.144172403335888e-06
            ],
            [
                NaN,
                8.93969843377968e-06,
                3.726639727526609e-06,
                7.889265404759017e-06,
                2.9023133686360798e-06,
                NaN,
                NaN,
                9.610238041093959e-05,
                5.829126545120912e-05,
                3.288749456838667e-06
            ],
            [
                NaN,
                8.315283248524667e-07,
                0.5621765008857981,
                NaN,
                NaN,
                NaN,
                NaN,
                2.4300231912844124e-05,
                2.144495603467167e-05,
                0.999195914070123
            ],
            [
                NaN,
                0.1066905996264336,
                0.1066905854244781,
                0.9579122749379932,
                0.06754668597767712,
                NaN,
                NaN,
                0.0021827161664434926,
                0.9978172832960369,
                NaN
            ],
            [
                0.9995694430182779,
                0.014063628244207642,
                0.9998415637082289,
                3.2887482776673045e-06,
                0.9999546021422393,
                0.9964063966224019,
                0.0031726824728354353,
                0.0,
                NaN,
                0.9998204719606828
            ],
            [
                0.9999938558254199,
                0.9998415637837214,
                NaN,
                0.7981867801399695,
                0.9995694429694661,
                NaN,
                0.9999910603058302,
                0.9999982396565771,
                0.9999921107364793,
                1.3007128448589436e-05
            ],
            [
                0.9999921107346011,
                0.9999852610233075,
                0.9999756997650822,
                NaN,
                0.9999930377445835,
                0.9999687980998114,
                NaN,
                0.9999921107393007,
                0.9999724643056662,
                0.9999930377404326
            ],
            [
                NaN,
                5.1442213596242845e-05,
                NaN,
                3.1201926219749737e-05,
                5.1442213603354026e-05,
                NaN,
                NaN,
                5.1442195225848094e-05,
                NaN,
                NaN
            ],
            [
                6.144173136019732e-06,
                8.939695231991565e-06,
                1.3007126911974612e-05,
                NaN,
                6.962259562531989e-06,
                3.2887498492936755e-06,
                6.962258732597129e-06,
                1.7603440525701563e-06,
                1.5534979396815448e-06,
                8.939696303010449e-06
            ],
            [
                0.9999756997621788,
                0.9999938558254001,
                0.9999986290431201,
                0.9999980052702786,
                0.999993855827596,
                0.9999952149060769,
                0.9999962733611605,
                0.9999938558224699,
                NaN,
                0.9998911031300973
            ],
            [
                3.2887482811908074e-06,
                7.484622689092787e-05,
                4.006371116615417e-05,
                7.484623558174233e-05,
                NaN,
                NaN,
                NaN,
                5.422217676200406e-06,
                5.1442201350809364e-05,
                1.670141983431876e-05
            ],
            [
                8.315279285012978e-07,
                5.715007195353674e-07,
                1.9947304347570075e-06,
                6.144176799227922e-06,
                2.144495863045236e-05,
                3.2887482812506295e-06,
                6.1441731363550164e-06,
                1.994730672496148e-06,
                5.4222202621161125e-06,
                1.1478770847848893e-05
            ],
            [
                0.9999687980923667,
                5.422220905887864e-06,
                0.9992903295320048,
                0.7549149868676283,
                6.605213628817054e-05,
                3.288748671031464e-06,
                0.16451646289656316,
                0.9991959140836852,
                0.7310585727705126,
                1.0129988545820372e-05
            ],
            [
                NaN,
                0.9997388096315978,
                0.9997694933126087,
                0.9999599363174791,
                0.9999910603005051,
                0.9980732653371203,
                0.9999957771650454,
                0.9997694931760726,
                0.06754669817865513,
                0.9999646437366749
            ],
            [
                0.9999938558224782,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999910603015668,
                0.9999957771660521,
                NaN,
                NaN
            ],
            [
                0.9997040430077203,
                0.9999984465015049,
                0.9999898700114362,
                0.9999990577549569,
                NaN,
                0.9999945777829696,
                0.9999984465024306,
                0.9999930377429298,
                NaN,
                0.9999910603058306
            ],
            [
                0.9999993524049703,
                0.9999724642990753,
                0.9996200155656276,
                0.9999980052702787,
                0.9999986290426298,
                0.999992110740237,
                0.9999984465024307,
                0.9999994284996211,
                0.999988521231878,
                0.9999970976883641
            ],
            [
                6.144176065940129e-06,
                1.8925150458536325e-05,
                0.9998415638399794,
                6.962259560581704e-06,
                NaN,
                0.999903897539223,
                1.994730434058543e-06,
                1.1478766753751021e-05,
                NaN,
                5.422218968714274e-06
            ],
            [
                1.0129988557318292e-05,
                2.4300232030064617e-05,
                1.370956879727337e-06,
                1.4738983715299675e-05,
                6.962254587951994e-06,
                2.2603240281606297e-06,
                1.2098656834195822e-06,
                1.0677031245710902e-06,
                2.5612834317116285e-06,
                4.222833444106873e-06
            ],
            [
                NaN,
                1.3007123806876143e-05,
                1.670141983261753e-05,
                NaN,
                NaN,
                2.430024359741423e-05,
                NaN,
                3.120191875680005e-05,
                NaN,
                1.4738988988010078e-05
            ],
            [
                1.670142184171555e-05,
                6.144174598593655e-06,
                2.561283125931734e-06,
                1.6701415853489846e-05,
                1.6701425809239798e-05,
                6.962255418658875e-06,
                NaN,
                2.753568450797317e-05,
                6.605213581722095e-05,
                4.539789006380022e-05
            ],
            [
                NaN,
                1.1478768116515313e-05,
                NaN,
                4.0063677713879955e-05,
                5.42221702886853e-06,
                NaN,
                NaN,
                2.1444955989891277e-05,
                2.1444953517061932e-05,
                1.3007128455545335e-05
            ],
            [
                1.0129990974572174e-05,
                0.9999885212264029,
                0.9626731103801985,
                0.9999898700102344,
                0.9999921107345955,
                0.9999980052705444,
                0.9999938558246945,
                0.9999646437410852,
                0.9706877686656669,
                0.9999938558269261
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999869928687767,
                0.9999921107336561,
                0.9999921107402892,
                NaN
            ],
            [
                NaN,
                4.222832934824211e-06,
                NaN,
                NaN,
                NaN,
                6.144176797115634e-06,
                NaN,
                0.0008040860069946537,
                NaN,
                NaN
            ],
            [
                2.753570422373059e-05,
                1.8925152752586028e-05,
                0.00010889696091391995,
                1.4738980211116665e-05,
                5.8291265427035414e-05,
                3.7266388397382506e-06,
                2.144494329348333e-05,
                1.3007126911004571e-05,
                3.535625492063251e-05,
                8.481102055701339e-05
            ],
            [
                5.144220115918209e-05,
                3.535624219412524e-05,
                4.2228324370327694e-06,
                4.539785229818853e-05,
                NaN,
                6.962257075488498e-06,
                NaN,
                1.994730433488886e-06,
                NaN,
                NaN
            ],
            [
                1.9947304347098384e-06,
                6.144172404380855e-06,
                NaN,
                1.300713001414004e-05,
                3.2887502413389517e-06,
                3.7266388395620047e-06,
                3.120190018853766e-05,
                1.0129994602057158e-05,
                1.0129987350921133e-05,
                3.2887498493325602e-06
            ],
            [
                0.9995694429638422,
                0.9890130549912148,
                0.9986749777206603,
                0.9999687980774912,
                0.9947798736462945,
                0.9997694933134538,
                0.9999485577618847,
                0.9992903295501676,
                NaN,
                0.9997694933145873
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999810748517651,
                NaN,
                0.9999885212291474,
                0.9999852610215523,
                0.9999962733602739,
                0.9999869928715392
            ],
            [
                0.18242552602881165,
                6.144176065582494e-06,
                NaN,
                0.2942149597859341,
                1.994729007841999e-06,
                0.977022628291917,
                0.9990889486639258,
                0.029312232394290857,
                1.2098661156320662e-06,
                NaN
            ],
            [
                1.9947306710466073e-06,
                9.422442568951678e-07,
                1.473898021366358e-05,
                3.5356267459872465e-05,
                1.5534979397140412e-06,
                1.0677028700130727e-06,
                1.4738987220234187e-05,
                1.0129989767695646e-05,
                4.222833444283541e-06,
                8.315282258158941e-07
            ],
            [
                2.753568124348506e-05,
                2.7535697652678035e-05,
                2.430024360519357e-05,
                3.2887478889034873e-06,
                6.96225707894582e-06,
                7.484621829540844e-05,
                3.726638394957837e-06,
                1.3007128456539035e-05,
                NaN,
                1.0129994599901296e-05
            ],
            [
                2.9023130226068764e-06,
                2.902311292960369e-06,
                9.422444815323792e-07,
                3.535626315261925e-05,
                6.9622554171645e-06,
                NaN,
                3.288748673035494e-06,
                2.7535704227537108e-05,
                1.553497754476329e-06,
                1.0129995799905438e-05
            ],
            [
                0.999997739675972,
                0.9999687980816488,
                0.9999599363081078,
                0.9999151889487513,
                0.9999417087206824,
                0.9999952149043908,
                0.9999898700078147,
                0.9999869928653489,
                0.5926665999540698,
                0.7549149758396752
            ],
            [
                5.144219521911119e-05,
                2.144495863201265e-05,
                4.006371124922888e-05,
                2.9023112927307205e-06,
                3.120192250053358e-05,
                2.1444945836212564e-05,
                4.006369682600557e-05,
                1.6701429783083866e-05,
                2.260323489266892e-06,
                8.481102092352864e-05
            ],
            [
                1.553497198801472e-06,
                1.5534981248133121e-06,
                1.9947301960400456e-06,
                7.8892625810789e-06,
                6.962259567217739e-06,
                1.5534983100595462e-06,
                1.5534975689659495e-06,
                1.3709570433387154e-06,
                1.8925150487521332e-05,
                1.1478764018012839e-05
            ],
            [
                1.6701429806475863e-05,
                2.5612828212676906e-06,
                4.222832436955956e-06,
                6.1441775290176756e-06,
                1.012999460108057e-05,
                NaN,
                NaN,
                3.120191506039996e-05,
                4.785095064601411e-06,
                2.4300243618542217e-05
            ],
            [
                0.9324533088603709,
                0.9999921107355351,
                0.9999952149060821,
                0.9999945777784469,
                NaN,
                0.9999785550480047,
                0.9999832985702237,
                0.7310585727705127,
                0.9324533018213449,
                0.9999417087160042
            ],
            [
                NaN,
                4.785093350245343e-06,
                0.999664649973335,
                3.726640167504477e-06,
                NaN,
                0.9999485577989726,
                0.9999687980952867,
                0.9999869928658977,
                0.99999577716808,
                0.9999687981001394
            ],
            [
                0.9999785550592712,
                0.9999930377429205,
                4.785093922776592e-06,
                4.7850950506227934e-06,
                0.9999945777810356,
                3.5356254898252494e-05,
                0.9998204720129281,
                1.0129989754502517e-05,
                0.9982992773665998,
                0.9998415637273435
            ],
            [
                0.9993736658404696,
                1.0,
                2.43002436174814e-05,
                NaN,
                0.2018132198600306,
                0.9995694429703554,
                0.025957356491382,
                6.144176793248695e-06,
                3.1201922517673344e-05,
                3.5356259082286005e-05
            ],
            [
                2.4300252299759956e-05,
                1.3007123812317831e-05,
                7.889262584006375e-06,
                2.144494073569759e-05,
                6.962257078249291e-06,
                0.0011695100593031374,
                2.144494327335557e-05,
                3.535625066508635e-05,
                3.535625064399255e-05,
                2.1444950957402623e-05
            ],
            [
                7.88926446430712e-06,
                0.00020342706690983656,
                6.9622595668378125e-06,
                6.144176064185479e-06,
                2.4300232036606334e-05,
                6.962259564254318e-06,
                NaN,
                1.1478773595343877e-05,
                0.0021827164189762924,
                3.1201907583945445e-05
            ],
            [
                2.144495096387783e-05,
                4.785093923116048e-06,
                0.9999038975743402,
                0.9986749774412162,
                0.2942149659744614,
                1.3709575336530204e-06,
                0.9999546021205469,
                4.539788484079622e-05,
                4.785093922393616e-06,
                0.7310585844894971
            ],
            [
                NaN,
                NaN,
                0.9999938558254025,
                NaN,
                NaN,
                NaN,
                NaN,
                0.999983298570227,
                NaN,
                NaN
            ],
            [
                1.6701423801721013e-05,
                NaN,
                4.222832939978334e-06,
                NaN,
                NaN,
                1.670141586454787e-05,
                NaN,
                2.430023202476052e-05,
                NaN,
                7.88925976316864e-06
            ],
            [
                NaN,
                NaN,
                0.9999852610111993,
                NaN,
                0.04742587519712089,
                NaN,
                4.785095061642053e-06,
                NaN,
                NaN,
                6.144173868670137e-06
            ],
            [
                1.5534981248881956e-06,
                3.466327037512053e-07,
                2.902313023063532e-06,
                2.102433660952354e-07,
                1.0129990976451642e-05,
                1.0129987351289655e-05,
                7.338208929998139e-07,
                3.726640616477725e-06,
                4.450851049941403e-07,
                1.7603436326432711e-06
            ],
            [
                NaN,
                0.9999930377429225,
                NaN,
                0.9999852610215458,
                NaN,
                NaN,
                0.9998204719499815,
                0.9999962733602736,
                NaN,
                0.9959298619197987
            ],
            [
                0.9999417087487913,
                0.9998766054089144,
                0.9999646437369827,
                2.7535690976547145e-05,
                0.2018132270610754,
                0.9999869928685222,
                0.9999687980775394,
                0.9992903294858962,
                0.9999687980894787,
                0.14804719803168948
            ],
            [
                2.9023119844508833e-06,
                5.422218323019487e-06,
                1.7603436328033735e-06,
                4.785095064044355e-06,
                1.3007128461838766e-05,
                1.7603430033607189e-06,
                1.0129990978220553e-05,
                NaN,
                2.1444945842219688e-05,
                1.0129994601688632e-05
            ],
            [
                1.8925145979561802e-05,
                0.9999945777791097,
                0.3775406687981454,
                0.9999546021097568,
                0.9998911030910002,
                0.9999646437366584,
                0.9999930377437717,
                0.9999724643155111,
                0.999933947848033,
                NaN
            ],
            [
                2.430023493485234e-05,
                2.753568448703733e-05,
                2.144495606813994e-05,
                1.6701417781292666e-05,
                2.7535704195382043e-05,
                2.753569417502338e-05,
                1.4738987229134998e-05,
                2.1444943290362748e-05,
                6.962258737650141e-06,
                1.0129993390610508e-05
            ],
            [
                4.7850950648799385e-06,
                1.4738978424038878e-05,
                7.88926070293116e-06,
                3.535625480152969e-05,
                NaN,
                NaN,
                1.4738985474764149e-05,
                NaN,
                1.670141584741401e-05,
                1.1478769487046951e-05
            ],
            [
                0.004609571478567864,
                0.7057850340255386,
                0.9999038975510578,
                1.444980381787736e-07,
                0.3486451488696663,
                0.037326885336183654,
                NaN,
                0.9999930377412731,
                0.9999546021376096,
                0.9999885212332675
            ],
            [
                0.999996273362049,
                0.9999885212346421,
                0.9999974387174843,
                0.9999938558246667,
                0.9999852610233173,
                0.9999984465020604,
                0.9999957771680661,
                0.9999982396565775,
                0.9999962733611626,
                0.9999785550567221
            ],
            [
                1.1478764017720528e-05,
                1.1478768123823146e-05,
                2.7535694357535878e-05,
                NaN,
                NaN,
                1.0129989771473008e-05,
                3.1201918779615236e-05,
                6.14417460073947e-06,
                1.670142977403086e-05,
                6.9622570786798724e-06
            ],
            [
                0.999769493370209,
                0.22270014398423357,
                NaN,
                0.9999151889266648,
                0.0,
                NaN,
                0.9994472214022129,
                NaN,
                0.320821300824607,
                NaN
            ],
            [
                1.0129989758408864e-05,
                8.315279277064584e-07,
                5.715004469401647e-07,
                NaN,
                3.726640616670918e-06,
                0.00012339452903099176,
                3.288749849209925e-06,
                7.88925975770115e-06,
                2.1444940660803607e-05,
                2.9023123307122503e-06
            ],
            [
                3.7266392835764795e-06,
                7.338209804773549e-07,
                3.059022633778138e-07,
                2.69957713081915e-07,
                5.715005832442471e-07,
                6.475951069561228e-07,
                3.059021539864825e-07,
                8.315281267248819e-07,
                3.466326624233938e-07,
                5.715003106756178e-07
            ],
            [
                0.999996273358939,
                0.999664649851591,
                0.9995121429543916,
                0.9999910602994373,
                0.9999930377429215,
                NaN,
                0.9995121428366298,
                0.9999982396559474,
                1.8925157255968775e-05,
                0.9999921107355338
            ],
            [
                NaN,
                NaN,
                0.9998766053959677,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.1478773597118638e-05,
                1.7603430032374404e-06,
                2.7535681215036362e-05,
                1.0129990977262395e-05,
                3.7266410608720178e-06,
                1.994729229692276e-06,
                1.2098656833689656e-06,
                2.561283431888668e-06,
                3.7266388394569345e-06,
                1.760343422928825e-06
            ],
            [
                1.0129989768027317e-05,
                1.3007123806024402e-05,
                2.260324028306588e-06,
                3.726641059702693e-06,
                2.902312330759764e-06,
                8.939697368500698e-06,
                1.9947290076496946e-06,
                1.5534971986912662e-06,
                1.1478773583860136e-05,
                1.760344052331604e-06
            ],
            [
                0.9999810748449939,
                0.9999885212332477,
                0.9999938558275957,
                0.999925153772803,
                0.9999417087345395,
                0.9999687980737659,
                0.9999832985781992,
                0.9999921107345933,
                0.9999970976880149,
                0.9999898700041923
            ],
            [
                NaN,
                NaN,
                6.144176798132662e-06,
                6.9622570747539755e-06,
                4.0063696885178056e-05,
                NaN,
                8.939693089726528e-06,
                NaN,
                2.144494829640266e-05,
                NaN
            ],
            [
                NaN,
                0.9669140231605952,
                NaN,
                0.9999869928761935,
                0.9999910602994719,
                0.999991060303714,
                0.9999930377412624,
                0.9999967112521146,
                NaN,
                0.9999810748495079
            ],
            [
                0.999447221469327,
                0.9999869928700037,
                0.999195913990667,
                1.1478768119146135e-05,
                3.5356267537559426e-05,
                0.9996200155230335,
                8.481103054054409e-05,
                0.9992903294585282,
                0.9999339478322975,
                0.999876605370841
            ],
            [
                0.9988304899566076,
                0.9997040429674642,
                0.0075772407881289985,
                0.2689414272294874,
                0.24508501864634827,
                0.9999339478711793,
                0.9399133435142799,
                NaN,
                0.46879062662624377,
                NaN
            ],
            [
                1.1478765384430723e-05,
                0.5621765008857981,
                NaN,
                0.06008665438181588,
                4.222834954403545e-06,
                0.9998911030670159,
                0.9999485578047742,
                NaN,
                0.9998415637091209,
                NaN
            ],
            [
                0.9796676445796328,
                0.9999910603026345,
                0.9999546021211231,
                0.9999417087276058,
                0.7549149978955811,
                0.8670357529306639,
                0.9046505254608135,
                0.9999646437636062,
                0.3775406687981454,
                0.9999970976887083
            ],
            [
                0.9999832985801649,
                0.9875683470086664,
                2.4300249356780647e-05,
                0.9997040427954434,
                NaN,
                7.484626275143474e-05,
                0.9999687980814832,
                0.9626731129235966,
                0.9997694931860327,
                1.1478773583860136e-05
            ]
        ]
    },
    {
        "q_id": "8717_mmlu_math",
        "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,
            29,
            30,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            55,
            56,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            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,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                0.9999930377429238,
                0.9999485577986705,
                0.9999785550515947,
                0.9999599363221695,
                0.999985261018032,
                0.9999898700078153,
                0.9999687980886737,
                0.9999756997679753,
                0.9999485577803072,
                0.9999756997505882
            ],
            [
                2.9023109467070445e-06,
                9.422448183036206e-07,
                2.2603245672497918e-06,
                1.553498495281783e-06,
                5.42221961567159e-06,
                2.5612831266165976e-06,
                2.561282210618905e-06,
                1.3007131558917768e-05,
                3.7266410607194972e-06,
                5.715002426202836e-07
            ],
            [
                0.9999991684722698,
                0.9999984465015047,
                0.9999945777797384,
                0.9999756997563796,
                0.999997097686631,
                0.9999982396572066,
                0.9999852610198012,
                0.9999962733598291,
                0.9997965730763432,
                0.9999977396759716
            ],
            [
                0.9999990577550691,
                0.9999646437492923,
                0.9999910603058326,
                0.9999952149037942,
                0.9999910603047626,
                0.9999977396762411,
                0.9999687980812239,
                0.999993855826132,
                0.9988304897864846,
                0.9999980052698031
            ],
            [
                0.9999957771670607,
                0.9999852610197931,
                0.9999977396759717,
                0.9999980052693274,
                0.9999952149055057,
                0.9999970976883613,
                0.9999967112521116,
                0.9999957771660521,
                0.9999646437450808,
                0.9999984465015048
            ],
            [
                0.9999785550516165,
                0.9999832985841359,
                0.9999646437408798,
                0.9999970976866311,
                0.999997438718706,
                0.9999967112501507,
                0.9999957771650457,
                0.9999938558275957,
                0.9999982396574163,
                0.9999938558253982
            ],
            [
                0.9999485577679679,
                0.9999756997621809,
                0.9999339478789965,
                0.9995694428608203,
                0.9998204720985001,
                0.9999687980849942,
                0.9996200155202918,
                0.9999417087554167,
                0.9999251537818603,
                0.9996200154249663
            ],
            [
                0.9999930377462429,
                0.9999957771665564,
                0.9999970976869771,
                0.9999952149066473,
                0.9999921107383561,
                0.9999967112509355,
                0.999997097688015,
                0.9999967112501537,
                0.9999945777784454,
                0.9999962733598282
            ],
            [
                3.466327863961242e-07,
                3.2887478888496478e-06,
                1.370957370247318e-06,
                2.1024329090781183e-07,
                7.338208055579897e-07,
                3.05902226923399e-07,
                1.7603434230921292e-06,
                5.04347528440776e-07,
                1.3709568799592562e-06,
                5.043472278255469e-07
            ],
            [
                0.9999810748562947,
                0.9999810748495058,
                0.9999938558275958,
                0.9999869928730893,
                0.9999898700053997,
                0.9999724643056468,
                0.9999957771645444,
                0.9999910603058282,
                0.999986992869988,
                0.9999687980737645
            ],
            [
                0.9999989322975119,
                0.9999910603005008,
                0.9999990577554061,
                0.9999957771680661,
                0.999997097689053,
                0.9999982396574163,
                0.9999957771650455,
                0.9999974387184001,
                0.9999993524052019,
                0.9999993524051246
            ],
            [
                0.9999898700066082,
                0.9999980052702786,
                0.9999989322967482,
                0.9999989322968759,
                0.9999970976883622,
                0.9999987901338839,
                0.999996273362049,
                0.9999952149066482,
                0.9999921107355353,
                0.9999898700041916
            ],
            [
                0.9999967112505433,
                0.9999967112521115,
                0.9999898700041907,
                0.9999938558232017,
                0.9999938558275958,
                0.9999930377404315,
                0.9999967112509349,
                0.9999952149043648,
                0.9999945777823239,
                0.9999984465016899
            ],
            [
                0.999997438718095,
                0.9999962733616047,
                0.9998601778761578,
                0.9998204720148193,
                0.9999724642957742,
                0.9999982396574164,
                0.9999756997679753,
                0.9999910603037013,
                0.9999485577802911,
                0.9999810748585568
            ],
            [
                0.9999945777790913,
                0.9999974387187054,
                0.9999987901337396,
                0.999998790134028,
                0.9999945777810308,
                0.9999957771655491,
                0.9999992661790195,
                0.9999991684719726,
                0.9999962733607195,
                0.9999952149072167
            ],
            [
                0.9999989322966208,
                0.9999930377404308,
                0.9999967112505429,
                0.9999980052707542,
                0.9999986290427931,
                0.9999938558261308,
                0.9999869928746405,
                0.9999974387177895,
                0.9999962733593832,
                0.999997097686977
            ],
            [
                0.9999930377412631,
                0.9999993524051246,
                0.9999993524049703,
                0.9999994284997574,
                0.9999970976876693,
                0.9999910603036964,
                0.999997097686977,
                0.9999869928746405,
                0.9999990577554062,
                0.9996200155182245
            ],
            [
                3.2887482809933958e-06,
                2.902313023039776e-06,
                9.422450431654909e-07,
                1.2098661161861e-06,
                1.994729483680993e-06,
                9.422450431860582e-07,
                6.475947982002148e-07,
                6.475947209985977e-07,
                9.422444815679433e-07,
                8.315277302788957e-07
            ],
            [
                5.422218323093458e-06,
                6.144173136645595e-06,
                1.2098653950551882e-06,
                6.1441738691562974e-06,
                4.785094494402695e-06,
                5.715007195353674e-07,
                8.315282258956806e-07,
                5.043474683156057e-07,
                4.222831934052698e-06,
                6.475945665900901e-07
            ],
            [
                0.9999930377429216,
                0.9999977396757024,
                0.9999952149032239,
                0.9999810748562796,
                0.9999990577551816,
                0.9999990577554061,
                0.9999991684720715,
                0.9999987901338838,
                0.9999967112497591,
                0.9999987901346051
            ],
            [
                0.9999970976880151,
                0.9999974387187054,
                0.9999938558224688,
                0.9999832985801506,
                0.9999957771650456,
                0.9999952149037942,
                0.9999756997621788,
                0.9999952149072169,
                0.9999945777829697,
                0.9999921107392993
            ],
            [
                0.9994472214599368,
                0.9990889489950624,
                0.9999546021097453,
                0.9978172839238192,
                0.9992903294657108,
                0.9993736657550304,
                0.9997965730819428,
                0.999841563802806,
                0.9996200155156378,
                0.9994472214706455
            ],
            [
                0.9999930377404312,
                0.9999785550516044,
                0.9999938558275983,
                0.999998239656577,
                0.9999910603036972,
                0.9999967112501505,
                0.9999898700102291,
                0.9999962733616049,
                0.999993037740431,
                0.9999970976880149
            ],
            [
                0.9999885212318793,
                0.9999984465026159,
                0.9999938558254008,
                0.9999910603058298,
                0.9999785550490615,
                0.9999991684719725,
                0.9999984465020606,
                0.9999980052709919,
                0.9999921107355344,
                0.9999986290421395
            ],
            [
                3.466327037472645e-07,
                9.42244930849811e-07,
                1.2098652508056196e-06,
                1.3709573702566696e-06,
                1.2098652508056196e-06,
                5.04347468309184e-07,
                7.33821067986608e-07,
                1.0677031245851707e-06,
                1.9947299592407137e-06,
                2.5612819053166966e-06
            ],
            [
                0.9999967112501507,
                0.9999952149043646,
                0.9999910603058296,
                0.9999982396569967,
                0.9999987901344609,
                0.999997438716568,
                0.9999980052700413,
                0.9999885212291474,
                0.9999938558261309,
                0.9999930377420919
            ],
            [
                0.9999980052698033,
                0.9999724643154788,
                0.9999970976883611,
                0.999996273362049,
                0.9999967112513268,
                0.9999852610110074,
                0.9999852610110026,
                0.9999980052702787,
                0.9999952149072195,
                0.9999852610110037
            ],
            [
                6.47595029750346e-07,
                9.422450431800595e-07,
                3.2887502409830123e-06,
                5.715004469963006e-07,
                9.422447059159823e-07,
                9.422450430566563e-07,
                8.31527829351332e-07,
                4.4508505192091017e-07,
                9.422444815323792e-07,
                4.4508505188933554e-07
            ],
            [
                0.9999957771650495,
                0.9999967112497589,
                0.999997097687669,
                0.9999938558246669,
                0.9999974387165689,
                0.9999982396572065,
                0.9999832985821414,
                0.9999938558261324,
                0.9999930377429208,
                0.9999987901341723
            ],
            [
                0.9999952149049355,
                0.999996273362049,
                0.9999938558268644,
                0.9999832985841314,
                0.999997097686977,
                0.9999832985721927,
                0.99999671125172,
                0.999986992873088,
                0.9999986290432834,
                0.9999910603037002
            ],
            [
                0.9986749775978836,
                0.9997694932034779,
                0.9996646498952815,
                0.9995694429109848,
                0.9999810748472621,
                0.9999724643089107,
                0.9996646499713251,
                0.9999756997621677,
                0.7549149868676284,
                0.9999885212318776
            ],
            [
                0.9999832985741892,
                0.9999724643089233,
                0.9999930377412646,
                0.9999724642990808,
                0.9999724642990699,
                0.9999485577680569,
                0.9999982396572065,
                0.9999832985761699,
                0.9999987901338839,
                0.9999724643122128
            ],
            [
                0.9999810748427385,
                0.999998005269803,
                0.9999967112513268,
                0.9999957771665561,
                0.999998790134605,
                0.9999957771665556,
                0.999992110736478,
                0.9999962733620488,
                0.9999957771665564,
                0.9999962733620488
            ],
            [
                0.9999977396748938,
                0.999997097686977,
                0.9999974387177896,
                0.9999977396746245,
                0.999998239656367,
                0.9999810748585336,
                0.9999974387180948,
                0.9999986290424665,
                0.9999982396563669,
                0.9999982396561572
            ],
            [
                0.9999910603047624,
                0.999998005269803,
                0.999993037743751,
                0.9999952149072177,
                0.9999151889689875,
                0.9999945777810323,
                0.9999898700126449,
                0.9999852610197916,
                0.9999930377429213,
                0.9999952149032237
            ],
            [
                0.9999485577863629,
                0.9999962733616061,
                0.9999967112501507,
                0.9999982396559474,
                0.9999910603068943,
                0.9999977396751637,
                0.9999852610162734,
                0.9999980052693277,
                0.9999957771645422,
                0.9999832985781587
            ],
            [
                0.999993037741261,
                0.999995777166053,
                0.9999724642957795,
                0.9999977396754335,
                0.9999832985741829,
                0.9999945777784451,
                0.9999970976866313,
                0.9999967112517193,
                0.9999993524049703,
                0.999981074849526
            ],
            [
                0.9999962733593839,
                0.9999977396748938,
                0.99997569975349,
                0.9999724642990652,
                0.999993037742095,
                0.9999957771645426,
                0.9999982396572065,
                0.9999724642990779,
                0.999941708734492,
                0.9999957771660523
            ],
            [
                0.9999989322972572,
                0.9999687980960721,
                0.9999987901338838,
                0.9999982396567868,
                0.9998911031167544,
                0.9999832985701994,
                0.9999980052693275,
                0.9999967112501507,
                0.9999984465018751,
                0.9999952149037941
            ],
            [
                0.9999832985701989,
                0.9999938558268634,
                0.9999993524052019,
                0.999997097687323,
                0.9999982396565767,
                0.9999977396751634,
                0.9999910603015666,
                0.9999970976873238,
                0.99999862904312,
                0.9999945777829702
            ],
            [
                4.2228349546493465e-06,
                7.338207180601138e-07,
                3.7266383952696564e-06,
                1.5534983101061718e-06,
                6.475945665853783e-07,
                1.0677033791000363e-06,
                9.422443691996268e-07,
                1.5534977544932838e-06,
                1.209865971934245e-06,
                5.715004470170917e-07
            ],
            [
                3.7266392839832006e-06,
                1.76034363298589e-06,
                4.222832437497486e-06,
                6.962255419279419e-06,
                6.962256249517824e-06,
                1.2098661161789477e-06,
                4.785096205434246e-06,
                1.0129995809247506e-05,
                3.726637951028202e-06,
                1.7603430034655858e-06
            ],
            [
                0.9999930377445806,
                0.9999852610233015,
                0.9999980052695653,
                0.999994577781031,
                0.999964643736671,
                0.9999938558246689,
                0.9999921107402366,
                0.9999986290423029,
                0.9999921107374156,
                0.9999952149049355
            ],
            [
                1.76034300345598e-06,
                4.222832941111319e-06,
                2.2603245673279107e-06,
                1.3709576971160984e-06,
                1.9947301970106386e-06,
                4.7850950649408664e-06,
                1.3709567165087443e-06,
                1.9947306726358406e-06,
                7.338208930391909e-07,
                6.962256248606003e-06
            ],
            [
                0.9999832985841366,
                0.9999984465026159,
                0.9999945777810335,
                0.9999977396762412,
                0.999998005269803,
                0.9999977396748939,
                0.999997097686977,
                0.9999898700066082,
                0.9999987901343166,
                0.9999990577550693
            ],
            [
                0.9999898700090257,
                0.9999852610232993,
                0.9999957771680661,
                0.9999546021097423,
                0.9999417087345128,
                0.9999990577549568,
                0.9999646437535161,
                0.9997388096953664,
                0.9999599363125955,
                0.9999756997592687
            ],
            [
                0.9999977396748941,
                0.999995777165549,
                0.9999952149072171,
                0.9999991684720715,
                0.9999990577556308,
                0.9999982396565769,
                0.9999646437619575,
                0.9999930377437511,
                0.9999832985702012,
                0.999998446502801
            ],
            [
                5.043475885453117e-07,
                7.338210679909462e-07,
                1.067702742726318e-06,
                1.5534975693347152e-06,
                2.9023130230133794e-06,
                6.962259568775433e-06,
                5.42221767672807e-06,
                6.475946437781423e-07,
                6.475949525834513e-07,
                3.726640616630245e-06
            ],
            [
                0.9999938558224687,
                0.9999977396746245,
                0.9999984465028012,
                0.9999957771680659,
                0.9999987901338839,
                0.9999982396559474,
                0.9999995549148419,
                0.9999945777790932,
                0.9999991684720715,
                0.9999930377404309
            ],
            [
                0.9968273174667835,
                0.6224593382055109,
                0.7549149813536518,
                0.9982992776156433,
                0.9988304897919242,
                0.7310585786300049,
                0.8354835350552603,
                0.9964063970709295,
                0.9241418231126367,
                0.9984988175726036
            ],
            [
                0.9465966688819449,
                0.997527376332257,
                0.8354835350552604,
                0.7310585669110202,
                0.9933071505709586,
                0.8933093982432729,
                0.9978172832564836,
                0.9986749775718494,
                0.8807970779778824,
                0.9991959141651522
            ],
            [
                0.9999967112493678,
                0.9999952149043648,
                0.9999974387168735,
                0.9999957771660526,
                0.9999982396572065,
                0.9999938558253995,
                0.9999974387180948,
                0.9999957771675634,
                0.9999989322968754,
                0.9999952149049355
            ],
            [
                0.9999989322968754,
                0.9999994284996891,
                0.999998932296621,
                0.9999938558239339,
                0.9999977396748944,
                0.9999970976880159,
                0.9999952149043656,
                0.9999993524050474,
                0.9999984465015048,
                0.9999986290424664
            ],
            [
                7.889262584006375e-06,
                5.144223816384438e-05,
                2.2603251060985603e-06,
                2.9023116389761676e-06,
                3.120192624233791e-05,
                0.00015843627322597727,
                1.0129993393945642e-05,
                3.7266406162947e-06,
                1.473898723042186e-05,
                1.4738980211920955e-05
            ],
            [
                0.9999810748585329,
                0.9999646437408712,
                0.9999991684716749,
                0.9999977396751633,
                0.9999910603015663,
                0.9999756997476862,
                0.9997965731000796,
                0.9999885212318764,
                0.9999967112497585,
                0.9999967112521114
            ],
            [
                0.9999724643187635,
                0.9999984465026159,
                0.9999910603015686,
                0.9999987901337396,
                0.99999893229713,
                0.999995214903224,
                0.9999977396762411,
                0.9999982396561572,
                0.9999952149043648,
                0.9999986290426298
            ],
            [
                0.9999952149055057,
                0.9999885212291401,
                0.9999957771665562,
                0.99993394785544,
                0.9999869928699912,
                0.9999938558261314,
                0.9999756997563826,
                0.9999898700126433,
                0.9999485577863596,
                0.9998766053813334
            ],
            [
                9.422449308566668e-07,
                3.2887490652451393e-06,
                4.222833444037741e-06,
                1.0677031245905116e-06,
                1.5534977545497995e-06,
                3.927860597935108e-07,
                1.7603438428460541e-06,
                7.338209805090567e-07,
                5.422218322851817e-06,
                5.043472879504592e-07
            ],
            [
                0.9998601778764243,
                0.9999910603036978,
                0.999995777167059,
                0.999876605439851,
                0.9999151889183183,
                0.9998601778931329,
                0.9997965730510352,
                0.999964643732451,
                0.9999687980998067,
                0.9999599362887218
            ],
            [
                0.9999957771675627,
                0.9999885212264057,
                0.999954602115177,
                0.9999910603015666,
                0.9999945777784449,
                0.9999987901337396,
                0.9999974387180949,
                0.9999957771675626,
                0.999991060302631,
                0.9999952149043654
            ],
            [
                0.9997388096604004,
                0.9998601779766122,
                0.999964643736671,
                0.9998766053958151,
                0.9999151889690362,
                0.9999756997650734,
                0.9998204719484429,
                0.9999485577679911,
                0.9999957771665557,
                0.9992903297155723
            ],
            [
                0.999981074849511,
                0.999991060302634,
                0.9999869928684462,
                0.999998239656367,
                0.9999599363079457,
                0.9999687980960844,
                0.9999898700054121,
                0.9999989322975119,
                0.9997694932864577,
                0.999978555046523
            ],
            [
                0.9999974387180948,
                0.9999957771650457,
                0.9999980052709929,
                0.9999852610215582,
                0.9999990577557432,
                0.999998005269803,
                0.9999810748540229,
                0.9999986290432843,
                0.9999990577551818,
                0.9999989322971301
            ],
            [
                2.2603242977555607e-06,
                1.370957533676711e-06,
                2.9023109470871505e-06,
                1.7603427935518875e-06,
                9.422444815628016e-07,
                1.9947299589105305e-06,
                9.422442568951678e-07,
                1.2098661161789477e-06,
                2.561282515988704e-06,
                9.422450431800595e-07
            ],
            [
                0.9999546021421996,
                0.9999910603047628,
                0.9999251537819502,
                0.9999962733607161,
                0.9999980052698033,
                0.9999993524052019,
                0.9999957771680659,
                0.9999832985721839,
                0.9999910603015658,
                0.9997965730277251
            ],
            [
                0.9999151889187001,
                0.9999038975623201,
                0.9999832985801487,
                0.9999339478396766,
                0.9999810748540244,
                0.9999417087067342,
                0.999948557798623,
                0.9999485577618885,
                0.999964643757743,
                0.9999885212346117
            ],
            [
                0.9999952149043672,
                0.9999970976876695,
                0.999998005270041,
                0.9999977396748939,
                0.9999945777816769,
                0.9999832985781592,
                0.9999962733598275,
                0.9999974387165682,
                0.9999982396569966,
                0.999993037744583
            ],
            [
                0.9997388097859695,
                0.9999151889586775,
                0.9998766054259134,
                0.9999251537550157,
                0.9993736659087481,
                0.9999910603015856,
                0.999933947831744,
                0.9999251537549547,
                0.9984988178130623,
                0.9999038976286769
            ],
            [
                0.9999910603058282,
                0.9999987901343166,
                0.9999785550567057,
                0.999995214903224,
                0.9999930377437514,
                0.9999957771675624,
                0.9999980052695653,
                0.9999967112509348,
                0.9999852610127743,
                0.9999724643121964
            ],
            [
                9.422450431800595e-07,
                1.2098658275740208e-06,
                9.42244256915735e-07,
                3.726641060536473e-06,
                3.7266388397382506e-06,
                9.42244930862237e-07,
                3.2887502413389517e-06,
                5.043472879240838e-07,
                5.04347348070562e-07,
                1.7603432132624344e-06
            ],
            [
                0.9999970976883613,
                0.9999991684719725,
                0.9999921107374157,
                0.9999974387177893,
                0.9999832985781617,
                0.9999980052693276,
                0.9999930377454143,
                0.9999989322975119,
                0.9999991684716751,
                0.9999852610198124
            ],
            [
                2.382369667914917e-07,
                3.7266397273639203e-06,
                1.553497939625029e-06,
                1.209865827698362e-06,
                5.043472879240838e-07,
                2.3823693838429036e-07,
                1.994729959224386e-06,
                3.726638839656906e-06,
                3.9278634072866033e-07,
                1.2098656834195822e-06
            ],
            [
                0.9999869928668906,
                0.9999938558253989,
                0.9999957771655493,
                0.9999785550439346,
                0.9999982396572065,
                0.9999980052700409,
                0.9999977396762412,
                0.9999992661787571,
                0.9999938558232017,
                0.9999980052695653
            ],
            [
                1.994729721004569e-06,
                6.144174600862407e-06,
                6.962257908348587e-06,
                2.1444945846588504e-05,
                1.2098653947630415e-06,
                1.3007126911974612e-05,
                1.1478769489343698e-05,
                1.147876538716594e-05,
                2.2603234893594005e-06,
                7.8892625830162e-06
            ],
            [
                3.7266383950256237e-06,
                1.5534981249164537e-06,
                8.31528424146183e-07,
                1.2098653950480359e-06,
                1.0677032518316716e-06,
                1.1478765387667046e-05,
                1.2098655392464547e-06,
                5.422217676654099e-06,
                7.889259763010786e-06,
                1.7603430034151537e-06
            ],
            [
                2.1444943292703185e-05,
                1.147876949187012e-05,
                2.1444945849006956e-05,
                4.222834450328596e-06,
                2.144494329566774e-05,
                4.785093923516432e-06,
                5.422218967491273e-06,
                2.1444948402034417e-05,
                4.7850933535006355e-06,
                5.829126549573962e-05
            ],
            [
                0.9999810748517634,
                0.9999974387184004,
                0.9999982396559479,
                0.9999986290432835,
                0.999995214904936,
                0.9999977396754329,
                0.9999952149066478,
                0.9999921107355351,
                0.9999810748472732,
                0.9999756997679812
            ],
            [
                0.9999810748427396,
                0.9999967112505455,
                0.9999977396748938,
                0.999993855826131,
                0.9999984465018752,
                0.9999986290421395,
                0.9999945777810305,
                0.9999869928715408,
                0.9999898700041931,
                0.9999952149043652
            ],
            [
                0.9999251537728504,
                0.9999977396746246,
                0.9999646437324458,
                0.999738809723432,
                0.9999921107345966,
                0.9999930377420909,
                0.9999832985801496,
                0.9999938558239336,
                0.9999417087484215,
                0.9999938558268638
            ],
            [
                0.9998911031038947,
                0.9992903295501676,
                0.999447221269271,
                0.7057850340255386,
                0.7772998663336158,
                0.754914975839675,
                0.9989677691837651,
                0.9990889487852543,
                0.9986749778542203,
                0.9999151889840855
            ],
            [
                0.999994577779738,
                0.9999869928730934,
                0.9999982396574165,
                0.9999832985761689,
                0.9999974387171792,
                0.9999930377454134,
                0.9999957771665575,
                0.999968798092358,
                0.9999756997592822,
                0.9999952149043658
            ],
            [
                0.999985261023302,
                0.9999885212318821,
                0.999996711252111,
                0.9999869928699997,
                0.9999945777797378,
                0.9999957771680659,
                0.9999810748449961,
                0.9999038975507264,
                0.9999921107393028,
                0.99998526101803
            ],
            [
                0.9999930377429215,
                0.9999785550515979,
                0.9999938558275964,
                0.9999957771650454,
                0.9999990577551815,
                0.9999952149037943,
                0.999925153799634,
                0.9999898700066069,
                0.999997097687323,
                0.9999938558268638
            ],
            [
                0.999975699753483,
                0.9999869928762035,
                0.9999952149037943,
                0.9999930377412619,
                0.9999852610180459,
                0.9999869928761901,
                0.9999952149072168,
                0.9999724643089218,
                0.9998766053960036,
                0.9999962733598275
            ],
            [
                0.999991060299446,
                0.9999687980998022,
                0.9999724643056309,
                0.9999957771670591,
                0.9999921107355353,
                0.999995777168066,
                0.9999921107364745,
                0.9999996533673375,
                0.9999687980811937,
                0.9999599363030746
            ],
            [
                0.9996646498109543,
                0.999991060305834,
                0.9999646437451655,
                0.9998911031300515,
                0.9995694428163172,
                0.9999151889486693,
                0.9999485577680569,
                0.9995694428191731,
                0.9999599363126329,
                0.9998204720985366
            ],
            [
                4.222832940500659e-06,
                3.2887498493983645e-06,
                1.067702615468225e-06,
                6.47594643784032e-07,
                9.42244818532859e-07,
                1.370956716519966e-06,
                6.475950297709604e-07,
                1.5534979397394734e-06,
                8.31528126775552e-07,
                7.338209805133949e-07
            ],
            [
                0.9999945777784451,
                0.9999756997505828,
                0.9999952149055065,
                0.9999151889890266,
                0.9999945777784448,
                0.9999339478397065,
                0.9999339478396593,
                0.999891103039086,
                0.9999938558239337,
                0.9999977396765105
            ],
            [
                0.9999980052705164,
                0.999997438717484,
                0.9999980052709921,
                0.9999930377437508,
                0.9999990577549569,
                0.9999952149072169,
                0.9999930377462416,
                0.9998204719705692,
                0.9999994284994848,
                0.9999982396569966
            ],
            [
                0.9999945777829717,
                0.999989870005401,
                0.9999957771655504,
                0.9999599363221586,
                0.9999982396559474,
                0.9999974387174841,
                0.9999756997621694,
                0.9999982396574167,
                0.9999986290429567,
                0.9999962733602717
            ],
            [
                0.9999982396559474,
                0.999993855826864,
                0.9999977396751637,
                0.9999957771670593,
                0.9999992661790195,
                0.9999970976869772,
                0.9999977396765106,
                0.9999910602994379,
                0.9999980052700408,
                0.9999952149043662
            ],
            [
                3.4663249714325014e-07,
                4.222834451215781e-06,
                1.2098662604192665e-06,
                9.422442569208767e-07,
                6.144176066521288e-06,
                7.889264466545779e-06,
                1.3709568799823232e-06,
                1.7603427935967163e-06,
                1.0677026154619133e-06,
                1.0677026154473471e-06
            ],
            [
                0.9999977396748938,
                0.999964643757743,
                0.9999785550515963,
                0.9999646437366584,
                0.9999417087347078,
                0.9998766053665213,
                0.9999869928653352,
                0.999860177893202,
                0.9997388096918022,
                0.9999251537817047
            ],
            [
                0.9999756997476897,
                0.9999962733620489,
                0.9999930377445819,
                0.9999962733593835,
                0.9999832985781602,
                0.9999832985801496,
                0.999993037740431,
                0.999981074856281,
                0.9999339478396708,
                0.999986992869987
            ],
            [
                0.9999724643122083,
                0.9999938558224688,
                0.9999898700066064,
                0.9999930377445808,
                0.9999921107402363,
                0.9999910603015666,
                0.9999810748472566,
                0.9999898700078167,
                0.9999869928668853,
                0.9999967112497585
            ],
            [
                1.3007125361755747e-05,
                3.288748673295719e-06,
                8.939700566143004e-06,
                8.939695237813028e-06,
                1.6701429804744246e-05,
                7.889266347133978e-06,
                3.726640172385136e-06,
                6.962259568648793e-06,
                1.1478765387667046e-05,
                3.120190392670705e-05
            ],
            [
                0.9999417087345488,
                0.999954602147616,
                0.9971990734542832,
                0.9999038976082164,
                0.9998601779096583,
                0.9984988180582324,
                0.9998766054107439,
                0.9999962733607163,
                0.999948557786415,
                0.9996200155200596
            ],
            [
                0.9999962733616046,
                0.9999921107336532,
                0.9999980052695653,
                0.9999962733589393,
                0.999999266179107,
                0.9999938558224705,
                0.9999962733598279,
                0.9999977396754328,
                0.9999921107374157,
                0.9999986290426298
            ],
            [
                0.9999869928699991,
                0.9999038976081016,
                0.9999984465028017,
                0.999964643732444,
                0.9999952149049353,
                0.9999974387174841,
                0.9999957771665557,
                0.9999898700054161,
                0.9999984465018751,
                0.9999885212305073
            ],
            [
                0.9999962733589393,
                0.999998790133884,
                0.9999952149049353,
                0.999997097686631,
                0.9999990577557432,
                0.999995214907218,
                0.9999986290423029,
                0.9999987901343166,
                0.999996273360272,
                0.9999990577555187
            ],
            [
                0.9999970976873229,
                0.9999898700078131,
                0.9999810748562937,
                0.9999967112505427,
                0.9999982396574163,
                0.9999885212318754,
                0.9999898700053986,
                0.9999938558261312,
                0.999994577781677,
                0.9999952149060761
            ],
            [
                0.9975273773923757,
                0.9980732654880081,
                0.9999485577834867,
                0.5926665999540697,
                0.9770226289191464,
                0.9968273177789977,
                0.9997040428673362,
                0.9997965730024703,
                0.9992903296617858,
                0.9997040429012288
            ],
            [
                0.9999646437451394,
                0.9999832985721862,
                0.9999687980737659,
                0.9999599362887198,
                0.9999485577740872,
                0.9998911030388833,
                0.9999885212332453,
                0.9999898700066067,
                0.9999930377445821,
                0.9999832985701989
            ],
            [
                0.9999885212318783,
                0.9999921107392962,
                0.9999984465024306,
                0.999989870004194,
                0.9999785550567023,
                0.9999952149032239,
                0.9999986290424663,
                0.9999974387168741,
                0.9999997300421261,
                0.999998239656577
            ],
            [
                0.9999952149049357,
                0.9999982396574164,
                0.9999938558232014,
                0.9999967112497591,
                0.999995777168066,
                0.9999982396574163,
                0.9999724643121909,
                0.9999599363173789,
                0.9999251537907204,
                0.9993736659895965
            ],
            [
                0.9999910603026316,
                0.9999970976866309,
                0.999997097689053,
                0.9999930377437511,
                0.9999957771675623,
                0.9999967112521118,
                0.9999910603026316,
                0.9999970976883609,
                0.9999852610233055,
                0.9999974387174841
            ],
            [
                0.9999952149032237,
                0.9999687980737751,
                0.9999992661789321,
                0.9999977396765106,
                0.9999977396748941,
                0.9999885212305084,
                0.9999962733593835,
                0.9999977396754328,
                0.9999810748495118,
                0.9999970976869773
            ],
            [
                0.9999970976866315,
                0.9999952149066474,
                0.9999952149037962,
                0.9999938558254018,
                0.9999921107393026,
                0.9999832985742131,
                0.9999992661791071,
                0.999998005269328,
                0.9999930377429269,
                0.9999977396759719
            ],
            [
                0.9999952149055095,
                0.9999990577555185,
                0.999998005270041,
                0.999996273360272,
                0.9999898700066067,
                0.9999982396574163,
                0.9999852610215463,
                0.9999970976883611,
                0.9999980052707549,
                0.9999994284994849
            ],
            [
                0.9999910603036988,
                0.9999982396569966,
                0.9999885212305113,
                0.999993855823938,
                0.999996273361161,
                0.9999970976866317,
                0.9999980052698036,
                0.9999982396563671,
                0.9999980052707543,
                0.9999852610110108
            ],
            [
                0.9999885212318764,
                0.9999987901346049,
                0.9999974387177897,
                0.9999832985841344,
                0.9999885212332564,
                0.9999952149043648,
                0.999994577782974,
                0.9999970976866316,
                0.999996273362049,
                0.9999957771645425
            ],
            [
                0.9999485577863896,
                0.9999991684718733,
                0.9999832985841333,
                0.9999982396559477,
                0.9999921107374175,
                0.9999945777803859,
                0.9999921107336536,
                0.9999952149032239,
                0.9999599363221524,
                0.999995777168067
            ],
            [
                0.9999989322973847,
                0.9999957771670591,
                0.9999989322973848,
                0.9999852610233045,
                0.9999967112509349,
                0.999996273361161,
                0.9999962733593835,
                0.9999980052702789,
                0.9999957771650456,
                0.9999982396574163
            ],
            [
                2.2603234893861252e-06,
                1.3709575336405514e-06,
                7.889261644057078e-06,
                1.2098653949688097e-06,
                8.315283249923769e-07,
                1.370956716450141e-06,
                1.3709578604495207e-06,
                1.1478770859019436e-05,
                5.715005151296257e-07,
                9.422442567854761e-07
            ],
            [
                0.9999962733611624,
                0.9999982396567868,
                0.9999970976890532,
                0.9999930377404361,
                0.9999832985741862,
                0.9999945777784455,
                0.9999980052702788,
                0.9999962733593862,
                0.9999646437619519,
                0.9999957771675629
            ],
            [
                0.999997097686631,
                0.9999982396567867,
                0.9999952149055056,
                0.9999962733620488,
                0.9999151889790765,
                0.999985261014516,
                0.9999885212359854,
                0.9999724643089097,
                0.9999724643056545,
                0.9999952149055067
            ],
            [
                9.422445937837332e-07,
                3.927862470840049e-07,
                5.043473480678099e-07,
                2.26032429753354e-06,
                3.927862002370363e-07,
                3.4663253846111126e-07,
                8.315280276263186e-07,
                3.9278624707257336e-07,
                5.715005151446993e-07,
                3.0590222691672177e-07
            ]
        ]
    },
    {
        "q_id": "8220_mmlu_math",
        "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,
            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,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999998874648245,
                0.999999814460876,
                0.9999999226557684,
                0.9999999317439872,
                0.9999996533672136,
                0.9999999317439464,
                0.999999887464744,
                0.999999887464744,
                0.9999999006880194,
                0.9999998724808964
            ],
            [
                8.31527730252048e-07,
                1.0677024881382882e-06,
                2.9023116390104826e-06,
                1.9947292458004866e-06,
                1.7603432132464244e-06,
                5.7150044702099e-07,
                1.2098652507847127e-06,
                1.7603436328994344e-06,
                1.5534971989258068e-06,
                2.561281599914358e-06
            ],
            [
                0.9999885212359809,
                0.999983298580152,
                0.9999885212307013,
                0.9999921107364741,
                0.9999885212346111,
                0.9999938558239335,
                0.9999898700126449,
                0.9999938558261305,
                0.9999930377412607,
                0.99998526101803
            ],
            [
                6.475945665800774e-07,
                8.315284241333265e-07,
                6.475948753847607e-07,
                1.3709567164962755e-06,
                3.059023363172604e-07,
                8.315284241333265e-07,
                3.059021539845349e-07,
                3.4663249713489575e-07,
                4.450852641596248e-07,
                8.315284241257637e-07
            ],
            [
                0.9999998874648379,
                0.9999999123574732,
                0.9999999123574419,
                0.9999999317439383,
                0.9999999123574836,
                0.9999998362623528,
                0.999999931743971,
                0.9999998362622746,
                0.9999999226557776,
                0.9999999317439708
            ],
            [
                0.9999997617630332,
                0.9999998724809723,
                0.9999998724809571,
                0.9999998144609423,
                0.999999887464811,
                0.9999996533674615,
                0.9999996533673375,
                0.9999998724809116,
                0.999999887464744,
                0.9999997617630332
            ],
            [
                9.42244818532859e-07,
                3.7266388396128453e-06,
                7.33820718037422e-07,
                1.0677032518578904e-06,
                8.939694171135975e-06,
                8.315279284937352e-07,
                5.715005832762133e-07,
                7.338209805040511e-07,
                3.0590211752039556e-07,
                1.3007134663876127e-05
            ],
            [
                0.9999998874648379,
                0.9999998362622942,
                0.999999730042126,
                0.9999997617631469,
                0.9999998724809723,
                0.9999999226557316,
                0.9999998874649051,
                0.9999999317439383,
                0.9999999123574836,
                0.9999998874649318
            ],
            [
                7.338207180661203e-07,
                1.7603427935678977e-06,
                7.889263525893087e-06,
                4.222833947674739e-06,
                1.2098662603862553e-06,
                1.994730434798734e-06,
                2.902312330759764e-06,
                9.422443692261927e-07,
                9.422450431654909e-07,
                1.0677024881761599e-06
            ],
            [
                0.9999998362622746,
                0.9999998555019274,
                0.9999997300421903,
                0.9999996940976636,
                0.9999992661791944,
                0.9999996533672135,
                0.9999994956524715,
                0.9999991684717742,
                0.9999993524049703,
                0.9999997897567342
            ],
            [
                5.715005832624392e-07,
                1.209865971732878e-06,
                1.0129987356191011e-05,
                4.785096776251149e-06,
                5.043472277838052e-07,
                2.2603245671202796e-06,
                6.475947981625199e-07,
                6.475951069561228e-07,
                1.0677032518316716e-06,
                8.31528027618756e-07
            ],
            [
                7.338212429504183e-07,
                7.338213304243302e-07,
                2.2603253755949437e-06,
                9.422447061336517e-07,
                8.315281267706361e-07,
                8.31528424151477e-07,
                5.4222202621161125e-06,
                9.42244593835151e-07,
                9.422442569028803e-07,
                2.753569437266178e-05
            ],
            [
                0.9999996940976636,
                0.9999998874648245,
                0.9999998144608098,
                0.9999998874648379,
                0.9999999123574941,
                0.9999998874647709,
                0.999999900688043,
                0.9999999006879957,
                0.9999998362622746,
                0.9999998724809571
            ],
            [
                0.999983298578157,
                0.9999885212264015,
                0.9999938558253993,
                0.9999832985841309,
                0.9999921107392964,
                0.9999898700078157,
                0.9999945777823235,
                0.9999980052705164,
                0.9999898700090223,
                0.999975699767969
            ],
            [
                0.9999999006880785,
                0.9999999006881141,
                0.9999999468421059,
                0.9999999006881496,
                0.9999999123575359,
                0.999999931743971,
                0.9999999397642365,
                0.9999999226558146,
                0.9999999006881141,
                0.9999999006880549
            ],
            [
                5.422218323231539e-06,
                1.0677029972920738e-06,
                1.0677028700130727e-06,
                4.2228329408924035e-06,
                1.3007131565140219e-05,
                1.4738987241172537e-05,
                1.3709568799243436e-06,
                9.422445938797133e-07,
                3.2887502409830123e-06,
                5.422217676575195e-06
            ],
            [
                3.7266379505740294e-06,
                8.939697368842181e-06,
                1.3709575336654889e-06,
                1.9947299591354906e-06,
                3.2887482811220126e-06,
                1.2098659719232413e-06,
                1.5534979396645902e-06,
                3.2887494573232236e-06,
                1.5534975693488444e-06,
                2.2603251060142746e-06
            ],
            [
                0.9999998724809116,
                0.9999999123574523,
                0.9999997897567342,
                0.999999789756684,
                0.9999998874649184,
                0.9999998874649318,
                0.9999998555019274,
                0.9999999006879838,
                0.9999998144608317,
                0.9999997897567342
            ],
            [
                0.9999997617631468,
                0.999999814460876,
                0.9999999397642508,
                0.9999999123575151,
                0.9999998874649051,
                0.9999998362623332,
                0.9999999006880194,
                0.9999998362623332,
                0.9999997300422869,
                0.999999887464811
            ],
            [
                0.9999998874648917,
                0.9999999226558423,
                0.9999999317439546,
                0.9999998874647976,
                0.9999999006881496,
                0.9999998555019274,
                0.9999998874647306,
                0.9999999226557316,
                0.9999999397642437,
                0.9999999634651662
            ],
            [
                0.9999999123574732,
                0.9999999226558238,
                0.9999999397642293,
                0.999999855502048,
                0.9999999397642293,
                0.9999998362622943,
                0.9999999226557224,
                0.9999998144609423,
                0.9999998724810027,
                0.9999999123574628
            ],
            [
                0.9999999123575359,
                0.9999999226558053,
                0.9999998555020307,
                0.9999998555020307,
                0.9999998362623528,
                0.9999999317439302,
                0.9999999226557224,
                0.9999998724810027,
                0.999999789756684,
                0.9999999226557131
            ],
            [
                0.9999993524052019,
                0.9999996533673375,
                0.9999999123574941,
                0.9999997300421903,
                0.9999998724810027,
                0.9999999226557408,
                0.9999996072137998,
                0.9999996940976271,
                0.9999998362622747,
                0.9999995549150541
            ],
            [
                0.9999998362623528,
                0.9999998724809875,
                0.999999900688043,
                0.999999789756634,
                0.9999999123574628,
                0.9999999317439708,
                0.9999998724809115,
                0.9999998724809419,
                0.9999999006880194,
                0.9999999586005999
            ],
            [
                4.7850944943330625e-06,
                3.5356246482211416e-05,
                2.1444950958338794e-05,
                1.0129987355122296e-05,
                2.4300252317086683e-05,
                0.00013982212398861956,
                9.610242631353545e-05,
                7.88926258532661e-06,
                1.8925150493166868e-05,
                1.3007123810638006e-05
            ],
            [
                1.0129987355564522e-05,
                6.962254588281262e-06,
                1.892515500560259e-05,
                3.12019076377484e-05,
                8.93969523678858e-06,
                6.605216040319643e-05,
                0.00017952800800186987,
                8.93969417199781e-06,
                1.0129987353832463e-05,
                5.144220748924517e-05
            ],
            [
                0.9999998874648379,
                0.9999998724809723,
                0.9999998362622747,
                0.9999998144609203,
                0.9999999226557869,
                0.9999996940977366,
                0.9999999468421629,
                0.9999999123575464,
                0.9999996940976272,
                0.9999997300422225
            ],
            [
                0.999993855822498,
                0.999989870010302,
                0.999978555043919,
                0.999941708748388,
                0.9999251537906851,
                0.7549149923816048,
                0.9999898700078227,
                0.99477987459178,
                0.9999599363221524,
                0.9999921107336526
            ],
            [
                6.144175333289463e-06,
                6.605214452354149e-05,
                1.2098652507715085e-06,
                1.670141985166528e-05,
                6.475950297768503e-07,
                3.53562675293277e-05,
                7.889263525261671e-06,
                1.2098655392354511e-06,
                1.7603436329394601e-06,
                6.962257906968191e-06
            ],
            [
                0.9999998724810027,
                0.999999814460876,
                0.9999999226557592,
                0.9999999226558146,
                0.9999999006881496,
                0.9999998724809116,
                0.9999998362623138,
                0.9999998144609202,
                0.9999998144608319,
                0.9999999123574628
            ],
            [
                4.539789026296999e-05,
                1.1478768121401121e-05,
                2.561283126304449e-06,
                NaN,
                2.902311984915459e-06,
                7.484621830793279e-05,
                4.785094493836935e-06,
                5.144219522247965e-05,
                4.539785780805251e-05,
                1.1478764018012839e-05
            ],
            [
                3.2887494567788457e-06,
                5.043472879291295e-07,
                1.2098656834349874e-06,
                1.3709576970949014e-06,
                1.20986611609532e-06,
                2.9023112927307205e-06,
                8.315278293899016e-07,
                3.726638395320497e-06,
                1.994730434735237e-06,
                1.0677031245050577e-06
            ],
            [
                1.7603434231241496e-06,
                3.288748673265808e-06,
                2.4300249415479343e-05,
                5.422219615898437e-06,
                3.288747889038086e-06,
                1.0129987355785634e-05,
                4.222832940715735e-06,
                7.889264466344872e-06,
                4.222834954514924e-06,
                2.9023119851055122e-06
            ],
            [
                0.9999910603004992,
                0.9999724642990605,
                0.999975699747687,
                0.9999957771675626,
                0.9999930377412606,
                0.9999910603015658,
                0.9999898700102282,
                0.9999921107402365,
                0.9999930377445809,
                0.9999151889688184
            ],
            [
                0.9999999226557592,
                0.999999789756634,
                0.999999855501979,
                0.9999999123575987,
                0.9999999317439627,
                0.9999999317439872,
                0.9999999226557131,
                0.999999931743971,
                0.9999998362622942,
                0.999999900687972
            ],
            [
                4.222832939310065e-06,
                1.5534979396815448e-06,
                3.1201926243586504e-05,
                2.5612828206736765e-06,
                2.2603248358025224e-06,
                1.012998856048759e-05,
                1.9947301968963442e-06,
                4.222834450666572e-06,
                4.222834954403545e-06,
                1.2098655392222467e-06
            ],
            [
                0.9999998874647574,
                0.9999999317439464,
                0.999999946842182,
                0.9999999006880312,
                0.9999999006881496,
                0.9999999317439627,
                0.9999998724809875,
                0.9999999317439627,
                0.9999998555020135,
                0.9999999123574732
            ],
            [
                1.7603436329554703e-06,
                6.144175334015912e-06,
                2.1444940738662144e-05,
                1.760342793515064e-06,
                1.3007133115667397e-05,
                2.561283431627768e-06,
                5.422217676299034e-06,
                1.4738978456719842e-05,
                6.962253759670401e-06,
                8.315282259051341e-07
            ],
            [
                0.9999999226558146,
                0.9999999317439058,
                0.9999998724809419,
                0.9999998555019962,
                0.9999999586005999,
                0.999999939764215,
                0.9999999530883564,
                0.999999939764215,
                0.9999998874647709,
                0.9999999530883452
            ],
            [
                0.9999999226557131,
                0.999999855501979,
                0.9999998555020134,
                0.9999999123575255,
                0.9999998724809571,
                0.9999999468421376,
                0.9999999123574523,
                0.9999999123574941,
                0.9999999468421122,
                0.9999999397642868
            ],
            [
                0.9999898700102325,
                0.999993855827596,
                0.9999952149049353,
                0.9999599363221695,
                0.9999945777797471,
                0.9999989322972574,
                0.9999974387171968,
                0.9999930377420905,
                0.9999910603036976,
                0.999994577778445
            ],
            [
                0.9999997617629764,
                0.9999999123574419,
                0.9999998144609202,
                0.9999998874648648,
                0.9999999123574523,
                0.999999789756634,
                0.9999999226557408,
                0.9999998874648917,
                0.9999998724810027,
                0.9999997300421903
            ],
            [
                0.9999999123575987,
                0.9999999006881141,
                0.9999999006880075,
                0.9999997897565838,
                0.9999998724809419,
                0.9999998555019962,
                0.9999998874647306,
                0.9999998555019446,
                0.9999999006880312,
                0.9999998724809116
            ],
            [
                0.9999852610145155,
                0.9999910603015654,
                0.9999251537460211,
                0.9999984465022456,
                0.9999898700053982,
                0.9999967112517189,
                0.9999967112493665,
                0.9999989322973845,
                0.9999987901341723,
                0.9999485577679945
            ],
            [
                0.9999869928684365,
                0.9999921107374152,
                0.999986992869989,
                0.9999417087414693,
                0.9999810748517607,
                0.9999832985701962,
                0.9999417087344762,
                0.9999910603047625,
                0.9999724643192932,
                0.9999957771670592
            ],
            [
                0.9999999123575568,
                0.9999999123575672,
                0.999999814460876,
                0.9999999530883452,
                0.9999999123575777,
                0.9999998874648246,
                0.9999999226558146,
                0.9999999123575881,
                0.9999999226558515,
                0.9999999123575777
            ],
            [
                0.9999999397642653,
                0.9999999586006245,
                0.9999999397642365,
                0.9999999530883843,
                0.9999999226557684,
                0.9999999677581336,
                0.999999931743979,
                0.9999999006881022,
                0.9999999123575255,
                0.9999999123575255
            ],
            [
                0.9999999123575672,
                0.9999997897566589,
                0.9999998724809267,
                0.9999999226558053,
                0.9999999586006443,
                0.9999999123575359,
                0.9999998724809267,
                0.9999999226557776,
                0.9999999006880785,
                0.9999998555020307
            ],
            [
                0.9999999634651531,
                0.9999998362622357,
                0.9999999006880312,
                0.9999999006881141,
                0.9999999123574628,
                0.99999992265575,
                0.9999998144609424,
                0.9999997300422225,
                0.9999999397642725,
                0.9999999226557776
            ],
            [
                0.9999986290424663,
                0.9999996072139402,
                0.9999984465018751,
                0.9999982396567868,
                0.999998790134028,
                0.999991060306894,
                0.9999977396751634,
                0.9999982396561572,
                0.999983298580152,
                0.999999168471675
            ],
            [
                0.9999998874647709,
                0.9999999397643011,
                0.9999999006880904,
                0.9999997897566589,
                0.9999999123574628,
                0.999999814460854,
                0.9999998362622746,
                0.9999998724809723,
                0.9999999006880075,
                0.9999998144609423
            ],
            [
                0.9999999226558238,
                0.9999998874648112,
                0.9999999226558053,
                0.9999998144608097,
                0.9999999226557131,
                0.9999999006880668,
                0.9999999317439302,
                0.9999999123575359,
                0.999999931743971,
                0.9999999226557316
            ],
            [
                1.0129988561372045e-05,
                4.53978848619353e-05,
                1.3007131561804229e-05,
                1.6701419846288166e-05,
                1.6701425821573757e-05,
                4.5397857784436206e-05,
                1.8925143715978147e-05,
                2.4300246516082393e-05,
                3.535625068579429e-05,
                1.147876401711502e-05
            ],
            [
                0.9999996072136125,
                0.9999997617631184,
                0.9999998724809115,
                0.9999998362623528,
                0.9999999006880785,
                0.9999998874647709,
                0.9999999226557869,
                0.9999998362622747,
                0.9999996940978095,
                0.9999997300422869
            ],
            [
                0.9999785550464814,
                0.9999785550592586,
                0.9999869928730875,
                0.9999687980774743,
                0.9999869928699874,
                0.9999852610233023,
                0.9999151889385265,
                0.9999984465015047,
                0.9999962733598277,
                0.9999977396754328
            ],
            [
                0.9999999397642868,
                0.9999999586006196,
                0.9999999226557869,
                0.9999999123574942,
                0.9999999468420996,
                0.9999999226557776,
                0.9999999397642653,
                0.9999999226557684,
                0.9999999468421249,
                0.9999999123575672
            ],
            [
                0.9999999468421186,
                0.9999999006880785,
                0.9999999397642222,
                0.9999999123575568,
                0.9999999530883172,
                0.9999999226558238,
                0.9999999226557684,
                0.9999998874648379,
                0.9999999468421502,
                0.9999999468421947
            ],
            [
                6.144174601208867e-06,
                6.962255417721724e-06,
                8.939700566143004e-06,
                4.222833947428939e-06,
                3.726641060956752e-06,
                1.5534983099564047e-06,
                6.962257909007124e-06,
                2.260323489192885e-06,
                1.6701425825492673e-05,
                1.670142781520948e-05
            ],
            [
                5.422219615395428e-06,
                4.22283193393364e-06,
                4.222831934248571e-06,
                1.1478773598099973e-05,
                1.2098652507715085e-06,
                2.561283126535066e-06,
                2.5612825159677387e-06,
                2.2603237588597026e-06,
                1.7603434230921292e-06,
                6.144173869312763e-06
            ],
            [
                0.9999998724809571,
                0.9999999123574419,
                0.9999998555020307,
                0.9999999226558423,
                0.9999999006879838,
                0.9999998362623528,
                0.9999995549150542,
                0.9999997617631469,
                0.99999976176309,
                0.9999998724809723
            ],
            [
                0.999998629042303,
                0.9999869928700029,
                0.9999724643089074,
                0.999998446502801,
                0.999992110736476,
                0.9999852610110167,
                0.9999687980961541,
                0.9999869928653495,
                0.9999962733616048,
                0.9964063968191539
            ],
            [
                0.9999921107383561,
                0.9999938558261897,
                0.9999938558261314,
                0.9999852610110006,
                0.9999687980849142,
                0.9999885212291395,
                0.9999938558261311,
                0.9999952149043647,
                0.9999938558253989,
                0.9999967112517191
            ],
            [
                1.3007133114011233e-05,
                1.30071315640992e-05,
                1.3007134665674251e-05,
                2.9023109471188266e-06,
                1.7603440526133836e-06,
                1.760343842833246e-06,
                8.93969417167259e-06,
                8.939694171135975e-06,
                2.9023109470554753e-06,
                1.8925143719695944e-05
            ],
            [
                0.9999996940976636,
                0.9999998724808963,
                0.9999997617630049,
                0.9999998362623723,
                0.9999998555020306,
                0.9999997617630049,
                0.9999998874647306,
                0.9999999530883508,
                0.9999999006880075,
                0.9999998874648782
            ],
            [
                0.999999814460876,
                0.999999912357515,
                0.9999998555019962,
                0.9999999226557408,
                0.9999999123574419,
                0.9999998874648647,
                0.999999789756634,
                0.9999999123575987,
                0.9999999317439708,
                0.9999998874649318
            ],
            [
                0.9999999123574941,
                0.9999999397642508,
                0.9999998555019962,
                0.9999996533672549,
                0.9999998874649318,
                0.9999999397643083,
                0.9999999006880075,
                0.9999999123575045,
                0.9999998724809267,
                0.9999999123574628
            ],
            [
                0.9999998555020307,
                0.9999999317439384,
                0.9999999006881141,
                0.9999999006880549,
                0.9999998362623723,
                0.9999999006879838,
                0.9999999317439546,
                0.999999855502048,
                0.9999998362622357,
                0.9999998724809875
            ],
            [
                0.999999887464811,
                0.9999998724809115,
                0.9999999317439546,
                0.9999998362623722,
                0.9999999006880904,
                0.9999999226557224,
                0.9999999226558238,
                0.9999999226557776,
                0.9999999226557408,
                0.9999999123574628
            ],
            [
                0.9999998555019618,
                0.9999994956525318,
                0.999999855502048,
                0.9999994284996212,
                0.9999997897567342,
                0.9999997617629763,
                0.9999998362623332,
                0.9999999123574523,
                0.9999997300421903,
                0.9999997300422547
            ],
            [
                1.7603425836870455e-06,
                5.715005832762133e-07,
                1.5534973840377051e-06,
                4.785096205434246e-06,
                5.04347287945184e-07,
                4.450851049941403e-07,
                1.3709578604831862e-06,
                2.902313023039776e-06,
                4.4508505193123265e-07,
                1.3709567163715878e-06
            ],
            [
                0.9999998362622357,
                0.9999999123575045,
                0.9999997617629764,
                0.9999996533672549,
                0.999999168471675,
                0.9999997897565838,
                0.9999998144608319,
                0.9999998144609203,
                0.9999997897567091,
                0.9999998144608981
            ],
            [
                0.9999999123575151,
                0.9999998555019962,
                0.9999998362622552,
                0.9999998555019274,
                0.9999999468421567,
                0.9999998874647709,
                0.9999998555020134,
                0.9999998362622747,
                0.9999999006880785,
                0.9999998555020134
            ],
            [
                0.9999999397642078,
                0.9999999123574523,
                0.9999999226557592,
                0.9999999123574419,
                0.9999998555019962,
                0.9999998724809267,
                0.9999999123575881,
                0.9999998362623528,
                0.9999999123574732,
                0.9999997897565587
            ],
            [
                0.9999999530883564,
                0.9999999123575568,
                0.9999999397643156,
                0.9999999123575777,
                0.9999999226557316,
                0.999999922655833,
                0.999999855501979,
                0.9999998724809571,
                0.9999999123574419,
                0.999999730042126
            ],
            [
                0.9999970976880154,
                0.9999990577554063,
                0.9999977396746244,
                0.9999938558232014,
                0.9999885212264029,
                0.9999832985838758,
                0.9999852610215436,
                0.9999970976880156,
                0.9999646437324566,
                0.9999921107364745
            ],
            [
                0.9999999006879957,
                0.9999999317440197,
                0.9999998724809723,
                0.9999999226557224,
                0.9999999006880785,
                0.9999998874648648,
                0.9999999677581222,
                0.9999998555019446,
                0.9999998724809419,
                0.9999999226558053
            ],
            [
                8.93969417150998e-06,
                4.2228339475595195e-06,
                1.5534977544932838e-06,
                2.56128221029278e-06,
                8.939699499823059e-06,
                1.892515726099468e-05,
                2.753568781022632e-05,
                1.3709572066982443e-06,
                2.9023109470871505e-06,
                5.422218321855664e-06
            ],
            [
                0.9999998144609424,
                0.9999998724809419,
                0.9999998362623332,
                0.9999998362623528,
                0.9999997617630049,
                0.999999789756684,
                0.999999789756684,
                0.9999998874647574,
                0.9999998724809723,
                0.9999998724809115
            ],
            [
                0.9999999006879838,
                0.9999998724809267,
                0.9999998724810027,
                0.999999887464811,
                0.9999998555019962,
                0.9999998555019446,
                0.9999998874648917,
                0.9999998874649184,
                0.9999998874648648,
                0.9999999006879721
            ],
            [
                0.9999987901344608,
                0.957912276139514,
                0.9999251537848286,
                0.9999993524050474,
                0.9999910602994343,
                0.9999885212347116,
                0.9999967112517196,
                0.9999898700041934,
                0.9999962733598277,
                0.9999986290426298
            ],
            [
                0.9999999317439221,
                0.999999855502048,
                0.9999998724809875,
                0.9999999317439383,
                0.9999999397642365,
                0.9999999006880904,
                0.9999999006879721,
                0.9999998724809116,
                0.9999999226557961,
                0.9999999123574732
            ],
            [
                0.9999998874647842,
                0.9999998874649184,
                0.9999997300422225,
                0.9999999123574941,
                0.999999730042319,
                0.9999999123574836,
                0.9999998874649051,
                0.999999855502048,
                0.9999998555020135,
                0.9999997897565587
            ],
            [
                2.7535687806920664e-05,
                2.902312676941983e-06,
                1.5534984952662413e-06,
                1.4738981968864903e-05,
                4.785095635413826e-06,
                4.78509563550957e-06,
                1.5534979397267575e-06,
                1.6701425823882575e-05,
                1.2098655392662613e-06,
                7.338207180761315e-07
            ],
            [
                0.9999998362623723,
                0.9999999123574732,
                0.9999998874647843,
                0.9999999468421502,
                0.999999922655833,
                0.9999999317439627,
                0.9999998724808963,
                0.9999998724810027,
                0.9999999317440197,
                0.9999999317439464
            ],
            [
                6.144177529855884e-06,
                1.3007126910294786e-05,
                2.561282515988704e-06,
                1.370957370146321e-06,
                1.012998977022003e-05,
                2.5612834318257725e-06,
                4.2228344508893285e-06,
                3.7266388397382506e-06,
                2.5612812938854287e-06,
                1.670141785809127e-05
            ],
            [
                0.9999999397642293,
                0.9999999586006048,
                0.9999998724809267,
                0.9999999317439708,
                0.9999999397642293,
                0.9999999468421059,
                0.9999999468421312,
                0.9999999397643083,
                0.9999998555019963,
                0.999999922655833
            ],
            [
                0.9999998724809267,
                0.9999998555019618,
                0.9999997897566089,
                0.9999997897565587,
                0.9999998362622943,
                0.9999998555019618,
                0.9999999317439464,
                0.9999997617630899,
                0.9999994956525317,
                0.9999998874647976
            ],
            [
                6.9622570784012604e-06,
                0.9999987901337427,
                0.9999930377454104,
                0.9999869928668906,
                1.3007133110320344e-05,
                0.999994577779738,
                0.999941708706721,
                0.9999339478648488,
                0.9875683499586242,
                0.9998911030978516
            ],
            [
                1.4738976698757546e-05,
                6.144176066443055e-06,
                1.7603438428028262e-06,
                1.8925152752999112e-05,
                8.939695238089467e-06,
                5.144220749598207e-05,
                0.0004878571867295483,
                5.8291258543467846e-05,
                5.422218969217281e-06,
                1.2098658277181688e-06
            ],
            [
                0.9999999468420996,
                0.9999999123575568,
                0.9999999006879957,
                0.9999999226558053,
                0.9999999006880075,
                0.9999999397642293,
                0.9999997300423191,
                0.9999999006880312,
                0.9999999468421312,
                0.9999999226557224
            ],
            [
                1.147876538789672e-05,
                4.222835457906302e-06,
                2.9023109469842055e-06,
                4.222834954461155e-06,
                5.4222170304318e-06,
                1.994729245842213e-06,
                5.422217676866151e-06,
                2.902312677084523e-06,
                7.88926634687567e-06,
                3.927862002582919e-07
            ],
            [
                0.9999998555019446,
                0.9999999317440279,
                0.9999999397643156,
                0.9999998362623722,
                0.9999998874648246,
                0.9999998555019446,
                0.9999999317439139,
                0.9999999317439627,
                0.9999999006880668,
                0.9999999123574732
            ],
            [
                5.71500583272315e-07,
                1.0677029972833341e-06,
                9.422444815495185e-07,
                4.4508489275752546e-07,
                2.260325105981383e-06,
                6.475950297868629e-07,
                8.315283250082584e-07,
                5.715006513952608e-07,
                7.338208930265102e-07,
                1.5534981249397663e-06
            ],
            [
                0.9999994956524716,
                0.9999945777797384,
                0.9999992661788445,
                0.9999993524054334,
                0.9999996072138465,
                0.9999998144609645,
                0.9859363727759646,
                0.9999992661791945,
                0.999993037742097,
                0.9999898700127252
            ],
            [
                0.9999998144609645,
                0.9999998724809571,
                0.9999999123575464,
                0.9999998555019274,
                0.9999998724809875,
                0.9999999123575045,
                0.999999887464744,
                0.9999998874648245,
                0.9999996533672549,
                0.9999999006881496
            ],
            [
                0.9999999226557869,
                0.9999998724809875,
                0.9999999397642222,
                0.9999998144608981,
                0.9999998362623723,
                0.9999998555019962,
                0.9999997300420937,
                0.9999999530883508,
                0.9999999006879721,
                0.9999998724809116
            ],
            [
                0.9999998724809419,
                0.9999997897566089,
                0.9999998874649051,
                0.9999999317439383,
                0.9999998144609645,
                0.9999999123574419,
                0.9999998874648782,
                0.9999999123574628,
                0.999999900688043,
                0.9999998144608981
            ],
            [
                0.9999999226558515,
                0.9999996940978095,
                0.9999998362623332,
                0.9999997617630616,
                0.9999999226557592,
                0.9999998874648112,
                0.999999855502048,
                0.9999998362623528,
                0.999999814460876,
                0.9999997897565587
            ],
            [
                9.422445938454347e-07,
                5.422219615750493e-06,
                9.422447061876404e-07,
                1.1478766755985128e-05,
                8.939698433145498e-06,
                5.422221554926484e-06,
                1.2098661161602417e-06,
                1.3709567164663505e-06,
                1.2098656832853378e-06,
                6.144172399334838e-06
            ],
            [
                8.939694171331106e-06,
                7.338211554464836e-07,
                5.715006513843456e-07,
                3.2887502412970765e-06,
                1.0129988562901417e-05,
                4.4508499887035535e-07,
                9.422450431474948e-07,
                1.7603432132079998e-06,
                5.043475885453117e-07,
                2.2603245671490605e-06
            ],
            [
                0.9999996072138934,
                0.9999945777797375,
                0.9999993524053562,
                0.9999995549151073,
                0.9999984465015047,
                0.999999653367379,
                0.9999996533674615,
                0.999999814460854,
                0.999999653367379,
                0.9999991684719725
            ],
            [
                0.9999999123575881,
                0.999999922655833,
                0.9999998724809571,
                0.9999998874648782,
                0.9999999123574628,
                0.9999999226557684,
                0.9999998724808964,
                0.9999999123575881,
                0.99999976176309,
                0.9999999123574942
            ],
            [
                0.9999998874648648,
                0.9999998724809571,
                0.9999998724809571,
                0.9999998874648917,
                0.999999855501979,
                0.9999999317439139,
                0.9999999226557131,
                0.9999998874648112,
                0.9999998874647977,
                0.9999999226558423
            ],
            [
                0.9999997897565587,
                0.9999999317439627,
                0.9999998144608317,
                0.9999998724809115,
                0.9999998362623722,
                0.9999998362622357,
                0.9999997617629763,
                0.9999998362622746,
                0.9999999226557684,
                0.9999998362622943
            ],
            [
                0.9999999226557224,
                0.9999999123575672,
                0.9999998874647574,
                0.9999999317439221,
                0.999999946842182,
                0.9999998874648648,
                0.9999998555019446,
                0.9999998724809419,
                0.9999999317439302,
                0.9999999123575151
            ],
            [
                0.9999999006880075,
                0.9999998874647977,
                0.9999999226557131,
                0.9999997617631468,
                0.9999998724809571,
                0.9999999226558423,
                0.9999999317439058,
                0.9999998724809419,
                0.9999998724809723,
                0.9999997897566589
            ],
            [
                0.9999998362622552,
                0.9999999123575882,
                0.999999974890015,
                0.9999998874649184,
                0.9999999123574836,
                0.9999996940976271,
                0.9999998144608538,
                0.9999997897565838,
                0.9999998724808963,
                0.9999998724808964
            ],
            [
                7.889264466230069e-06,
                2.260325375615501e-06,
                3.2887478892055875e-06,
                2.5612828212676906e-06,
                5.4222202624563834e-06,
                4.222834451065997e-06,
                8.315281267800897e-07,
                1.0129988564099116e-05,
                1.0677033791291683e-06,
                6.96225873895455e-06
            ],
            [
                6.962258739169842e-06,
                4.222833444429485e-06,
                5.422221555069497e-06,
                3.2887502414436403e-06,
                4.222834451254188e-06,
                5.715003107655392e-07,
                1.892515500715167e-05,
                3.2887478889034873e-06,
                8.31528424146183e-07,
                2.2603253755476615e-06
            ],
            [
                0.999999730042319,
                0.9999998362623332,
                0.999999855502048,
                0.9999999006881496,
                0.9999998362623722,
                0.9999998874647976,
                0.999999887464744,
                0.9999998555019446,
                0.9999998555020306,
                0.9999997897566589
            ],
            [
                6.962254589104433e-06,
                1.994729483608425e-06,
                1.7603436329714805e-06,
                2.561283431669698e-06,
                2.561283431916622e-06,
                1.2098652508144226e-06,
                1.3709578605243332e-06,
                1.5534981249291695e-06,
                6.9622554187981796e-06,
                3.7266410609160796e-06
            ],
            [
                0.9999999006880312,
                0.9999998555019274,
                0.999999730042319,
                0.9999998362622942,
                0.9999998362623332,
                0.9999998874648782,
                0.9999999317439383,
                0.9999997617630332,
                0.9999997617630899,
                0.9999998874648782
            ],
            [
                0.9999998362623138,
                0.9999998362623722,
                0.9999998144609202,
                0.9999998724808964,
                0.9999998362623332,
                0.9999998555020135,
                0.9999998555020307,
                0.9999998555020306,
                0.9999999317439627,
                0.9999998874647306
            ],
            [
                0.9999999006880668,
                0.9999999006879957,
                0.9999999123574628,
                0.9999999226557592,
                0.9999999226558515,
                0.9999999006880075,
                0.9999999006880312,
                0.9999997897565587,
                0.999999789756634,
                0.9999998362623332
            ],
            [
                0.9999999226558515,
                0.9999999397642078,
                0.9999997617629764,
                0.9999999006879721,
                0.9999999397643011,
                0.9999998555019274,
                0.9999999123574732,
                0.9999998724809571,
                0.9999998874647574,
                0.9999999530883396
            ],
            [
                0.9999991684721706,
                0.9999756997643006,
                0.9999995549150011,
                0.9999982396567868,
                0.9999990577555185,
                0.9999991684717741,
                0.9999974387168734,
                0.9999996072137529,
                0.9999991684722698,
                0.9999986290424663
            ],
            [
                0.9999646437408679,
                0.9999993524049706,
                0.9999832985841466,
                0.9999957771655488,
                0.9999869928761876,
                0.999995777164542,
                0.9999921107345934,
                0.9999810748472645,
                0.9999687980923779,
                0.9999930377412608
            ],
            [
                0.9999999123575464,
                0.9999998874649051,
                0.999999887464744,
                0.9999998874649318,
                0.9999999123575568,
                0.999999922655833,
                0.9999999123574732,
                0.9999998724809723,
                0.9999998874647306,
                0.9999998724808963
            ],
            [
                0.999999554914895,
                0.9999991684719723,
                0.9999994956525317,
                0.9999977396748941,
                0.9999999006880549,
                0.9999997300422225,
                0.9999992661788445,
                0.9999994956525318,
                0.9999989322970028,
                0.999999266178845
            ],
            [
                0.9999999006880785,
                0.9999999226557408,
                0.9999996533675028,
                0.9999999317439627,
                0.9999998362622357,
                0.9999999006881377,
                0.9999999397642437,
                0.9999999226557131,
                0.9999998874648782,
                0.9999998555020307
            ],
            [
                0.9999997617631468,
                0.9999999226558053,
                0.9999999397643083,
                0.999999912357515,
                0.9999999397642508,
                0.9999999226557316,
                0.9999998724809116,
                0.9999997897567091,
                0.9999998724810027,
                0.999999887464744
            ],
            [
                0.9999930377437506,
                0.9998415637458471,
                0.9999546021476212,
                0.999989870005401,
                0.9997694932051076,
                0.9999869928668956,
                0.9999885212305093,
                0.9999687980849181,
                0.9998601779595598,
                0.9999898700066082
            ],
            [
                0.9999999006881496,
                0.999999789756634,
                0.9999998724809419,
                0.999999939764258,
                0.9999998724809419,
                0.9999997300421581,
                0.9999998144608097,
                0.9999998555020134,
                0.9999998362623528,
                0.9999996533672962
            ],
            [
                7.338208055436404e-07,
                3.2887494572873306e-06,
                8.939694171135975e-06,
                1.300713311517055e-05,
                1.4738981965326028e-05,
                8.31528325021115e-07,
                2.430024072648329e-05,
                7.88925976126004e-06,
                5.422217030288788e-06,
                1.0677026154055912e-06
            ],
            [
                0.9999998362623723,
                0.9999999317440279,
                0.9999999226557131,
                0.9999999317439383,
                0.9999999123575777,
                0.999999789756684,
                0.9999999397642078,
                0.9999999468421059,
                0.9999999317440279,
                0.9999997897567342
            ],
            [
                0.9999991684719723,
                0.999999653367379,
                0.9999996072136592,
                0.9999967112513268,
                0.9999994956525317,
                0.9999993524052018,
                0.9999997897567091,
                0.9999980052693275,
                0.9999986290424667,
                0.999999266178932
            ]
        ]
    },
    {
        "q_id": "7777_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            6,
            7,
            9,
            10,
            12,
            15,
            16,
            17,
            18,
            19,
            20,
            22,
            24,
            25,
            26,
            27,
            28,
            29,
            31,
            33,
            35,
            36,
            38,
            39,
            40,
            41,
            43,
            44,
            45,
            46,
            47,
            48,
            50,
            53,
            55,
            56,
            57,
            59,
            60,
            62,
            63,
            64,
            66,
            68,
            69,
            70,
            72,
            73,
            74,
            75,
            77,
            78,
            79,
            80,
            83,
            85,
            87,
            88,
            89,
            91,
            92,
            95,
            97,
            99,
            100,
            101,
            102,
            104,
            105,
            106,
            107,
            108,
            109,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            126,
            127
        ],
        "rewards": [
            [
                8.939694170062744e-06,
                2.4300232038993178e-05,
                1.7603430033991435e-06,
                3.288747889229516e-06,
                6.962255419728997e-06,
                3.120190021339598e-05,
                1.0677033791000363e-06,
                3.120191509059319e-05,
                8.939693106020111e-06,
                4.785095634460739e-06
            ],
            [
                4.539787945561647e-05,
                3.7266388397382506e-06,
                7.889259763728304e-06,
                3.7266401719174067e-06,
                1.4738988998117324e-05,
                6.9622587393661365e-06,
                1.1478769490700865e-05,
                2.1444945852673643e-05,
                6.962256249606473e-06,
                1.8925152750176348e-05
            ],
            [
                6.962255419279419e-06,
                1.553497939144644e-06,
                1.209865827221904e-06,
                1.7603440526662173e-06,
                9.422445938557184e-07,
                6.475946437657736e-07,
                1.3007128462477575e-05,
                2.2603237589028734e-06,
                2.902311293034278e-06,
                9.422445938557184e-07
            ],
            [
                6.144172403827636e-06,
                4.78509563550957e-06,
                1.0129994602057158e-05,
                6.962257908880483e-06,
                1.9947301967693507e-06,
                1.7603436330091044e-06,
                1.012999460251781e-05,
                2.4300237830711845e-05,
                6.962255419570695e-06,
                8.93969736456552e-06
            ],
            [
                4.222832941034507e-06,
                6.144175334239434e-06,
                1.0677032518413822e-06,
                1.8925157262578186e-05,
                5.422220261849814e-06,
                1.1478768122987964e-05,
                1.9947306725669014e-06,
                6.1441775312976045e-06,
                2.260324297702111e-06,
                2.7535697610305477e-05
            ],
            [
                2.902310946944611e-06,
                5.4222176759932836e-06,
                1.3709578603659798e-06,
                8.939695237813028e-06,
                1.0677033790883835e-06,
                1.5534977543661227e-06,
                1.7603425835749741e-06,
                1.76034279349265e-06,
                3.7266392835764795e-06,
                6.144173135762683e-06
            ],
            [
                NaN,
                NaN,
                3.7266410605974813e-06,
                8.939699498587217e-06,
                1.1478766756444477e-05,
                2.9023123310580418e-06,
                1.7603436329714805e-06,
                NaN,
                1.7603440526662173e-06,
                3.7266406160845606e-06
            ],
            [
                1.6701425824307884e-05,
                1.3007125362323574e-05,
                1.1478764018827141e-05,
                1.8925155005051806e-05,
                3.7266383946527958e-06,
                2.1444956078515887e-05,
                1.6701417860795016e-05,
                2.5612819052072116e-06,
                4.785095635017795e-06,
                8.939698434332555e-06
            ],
            [
                2.2603242977555607e-06,
                2.144494329496561e-05,
                1.370956716529941e-06,
                6.1441724044534996e-06,
                1.0129995809597604e-05,
                5.4222202623972055e-06,
                3.7266383954560706e-06,
                4.222833947728508e-06,
                7.889264465067689e-06,
                8.939700564890901e-06
            ],
            [
                1.209865827698362e-06,
                1.2098655391947376e-06,
                1.5534975692866768e-06,
                0.00020342689751130886,
                6.475948753794598e-07,
                4.785095634843714e-06,
                7.889263525405172e-06,
                1.2098659719122375e-06,
                2.561282821239737e-06,
                8.93970056529743e-06
            ],
            [
                NaN,
                8.939699500636112e-06,
                1.9947304346535984e-06,
                NaN,
                6.962259566635186e-06,
                1.3007128462477575e-05,
                0.005220126510883465,
                1.760342793266906e-06,
                NaN,
                2.430023493052066e-05
            ],
            [
                NaN,
                1.0129990977004428e-05,
                NaN,
                4.785096775580942e-06,
                4.222834450589758e-06,
                1.0129989771473008e-05,
                NaN,
                3.2887498464940156e-06,
                NaN,
                4.222832940834793e-06
            ],
            [
                4.222832437639588e-06,
                4.785095065045315e-06,
                4.785092783319532e-06,
                1.760342583722268e-06,
                3.2887502407138142e-06,
                0.00015843626566266239,
                6.1441746016670885e-06,
                1.2098659719441482e-06,
                6.144174601309452e-06,
                7.88925976397226e-06
            ],
            [
                1.1478769488633793e-05,
                7.889262585541864e-06,
                4.2228319341064674e-06,
                3.120192623972722e-05,
                8.939693106182721e-06,
                1.0129994600859455e-05,
                1.5534979397394734e-06,
                4.222832437443716e-06,
                8.93969736929749e-06,
                2.9023133686835932e-06
            ],
            [
                1.3709573685927124e-06,
                1.9947292447863536e-06,
                4.222834954280646e-06,
                0.9996646500093275,
                1.1478769490053603e-05,
                8.481104091280437e-05,
                5.144223199097187e-05,
                6.14417460073947e-06,
                1.3007134662054344e-05,
                6.962255418658875e-06
            ],
            [
                1.3007126911974612e-05,
                4.785092782936557e-06,
                2.9023123310290063e-06,
                7.889260703619978e-06,
                2.9023126754426735e-06,
                3.7266401722360055e-06,
                4.222832941034507e-06,
                6.96225541916544e-06,
                1.1478773597118638e-05,
                2.561281599881745e-06
            ],
            [
                0.0005527786529383661,
                1.6701427813872793e-05,
                1.3007128464346676e-05,
                4.785092783149804e-06,
                3.726640172337686e-06,
                5.422217030209884e-06,
                7.889266347004826e-06,
                6.144172403827636e-06,
                5.829127220118597e-05,
                8.315282258832022e-07
            ],
            [
                0.0015011820141844186,
                2.1444958547990893e-05,
                7.889264451449183e-06,
                NaN,
                NaN,
                0.000379984481698006,
                NaN,
                NaN,
                1.6701421790617727e-05,
                NaN
            ],
            [
                8.939697366289195e-06,
                1.6701425819447213e-05,
                NaN,
                0.0010322309354381378,
                1.4738987240100149e-05,
                NaN,
                5.829128567272729e-05,
                0.00033535025585961425,
                NaN,
                3.2887498492936755e-06
            ],
            [
                1.1478769490387674e-05,
                1.1478765386894505e-05,
                0.0006263341062629698,
                6.962257079059797e-06,
                2.561282821176841e-06,
                1.0129994600859455e-05,
                5.4222196143006464e-06,
                2.5612815993296616e-06,
                3.1201907645920996e-05,
                NaN
            ],
            [
                8.939694171135975e-06,
                1.2098656834834034e-06,
                1.0129992187105678e-05,
                1.0129993394314164e-05,
                2.9023126770343703e-06,
                4.785092783454444e-06,
                1.4738980213020151e-05,
                6.144175333926503e-06,
                5.422220908402905e-06,
                2.902312676941983e-06
            ],
            [
                2.9023133687786197e-06,
                2.7535697643963113e-05,
                0.037326884131416216,
                6.144177530146464e-06,
                8.939698433584547e-06,
                7.484622716319649e-05,
                3.726641060956752e-06,
                1.0129989770662257e-05,
                5.422218322565793e-06,
                2.561281294369958e-06
            ],
            [
                6.144173136131494e-06,
                8.93970056668775e-06,
                8.315284241597959e-07,
                1.0129993388915298e-05,
                8.939699494895954e-06,
                2.561282515853595e-06,
                7.889261644982674e-06,
                6.962255419475714e-06,
                6.144173869379821e-06,
                4.7850927830148924e-06
            ],
            [
                1.209866116137134e-06,
                2.2603251061458426e-06,
                1.4738985479697128e-05,
                1.7603430032662588e-06,
                1.3709570433075437e-06,
                2.9023109470554753e-06,
                1.2098652508144226e-06,
                2.561283432005142e-06,
                6.475948753076037e-07,
                3.288749065077638e-06
            ],
            [
                1.2098662602861223e-06,
                0.005911069222906048,
                8.3152773023541e-07,
                5.422217676654099e-06,
                7.8892654060075e-06,
                0.998299277822191,
                4.222831933726245e-06,
                2.2603251060738913e-06,
                1.0129992299302578e-05,
                1.8925141457627214e-05
            ],
            [
                NaN,
                0.9999599363223673,
                0.8354835411997897,
                NaN,
                0.5621765008857981,
                0.9999546021153329,
                NaN,
                0.999903897539618,
                NaN,
                NaN
            ],
            [
                1.0129990978847043e-05,
                2.5612828212909852e-06,
                NaN,
                6.962259569313662e-06,
                4.0063696885178056e-05,
                1.147876812106705e-05,
                1.300713464913624e-05,
                2.7535687813231466e-05,
                0.005220125819300707,
                3.288749848677511e-06
            ],
            [
                4.222834954134701e-06,
                1.7603438428188364e-06,
                NaN,
                1.1478765388314311e-05,
                4.7850950646797465e-06,
                7.889264466115267e-06,
                9.42244930849811e-07,
                2.5612816000331606e-06,
                2.902311292960369e-06,
                NaN
            ],
            [
                1.370957370247318e-06,
                2.5612822106654943e-06,
                6.144177531532303e-06,
                6.962258739169842e-06,
                4.2228344508893285e-06,
                1.4738980213020151e-05,
                2.26032402841657e-06,
                6.144172403928222e-06,
                8.315280276338815e-07,
                3.726639728262097e-06
            ],
            [
                1.994729959270648e-06,
                2.2603242978377903e-06,
                2.9023133689317184e-06,
                8.31527829351332e-07,
                9.422448184287376e-07,
                2.902312330849511e-06,
                1.3709572068422585e-06,
                4.785096205651846e-06,
                4.785095635296322e-06,
                6.962254588724508e-06
            ],
            [
                6.144172402452975e-06,
                NaN,
                0.9525741285053949,
                NaN,
                1.8925145981283003e-05,
                NaN,
                0.4073334000459302,
                0.2942149783515162,
                0.5621765008857981,
                NaN
            ],
            [
                0.9995694428372849,
                NaN,
                6.475950297868629e-07,
                2.902312677007974e-06,
                7.33820893021171e-07,
                2.9023119851055122e-06,
                2.2603245672867952e-06,
                1.760343842833246e-06,
                4.785094494576774e-06,
                0.999373665906307
            ],
            [
                0.9999339478491652,
                0.01798621085037414,
                2.4300246520590875e-05,
                0.8175744761936437,
                NaN,
                2.1444953513707305e-05,
                0.9997040428103318,
                2.430024941459533e-05,
                0.9995694429639425,
                0.817574471748733
            ],
            [
                0.24508501864634827,
                NaN,
                5.144223177651387e-05,
                2.14449483869776e-05,
                NaN,
                3.535625482005107e-05,
                5.144223809160982e-05,
                0.9991959138793632,
                NaN,
                4.539787395384217e-05
            ],
            [
                0.999915188959239,
                0.34864513533394575,
                1.7603438427660027e-06,
                0.7981867873410141,
                0.9999646437540898,
                0.9999724643155028,
                6.605217004373086e-05,
                0.9999724643187554,
                0.9998415637147201,
                0.00010889693489823463
            ],
            [
                1.4738980211920955e-05,
                6.144176798691468e-06,
                5.422217676866151e-06,
                3.927861534257969e-07,
                4.222831933864508e-06,
                6.475945665523951e-07,
                5.422219614951598e-06,
                4.450851049890802e-07,
                9.422445938557184e-07,
                6.962257079173776e-06
            ],
            [
                2.144495861188488e-05,
                1.553497754476329e-06,
                5.422219615395428e-06,
                1.3007126909916233e-05,
                6.962255419279419e-06,
                7.88926634644516e-06,
                2.9023126770343703e-06,
                5.42221767672807e-06,
                8.93969630317306e-06,
                2.9023133690188264e-06
            ],
            [
                3.2887482812506295e-06,
                5.422218968714274e-06,
                1.2098656834834034e-06,
                4.78509563546605e-06,
                5.422217030362759e-06,
                5.4222183221120994e-06,
                4.785096205651846e-06,
                1.7603440527046419e-06,
                6.1441753335241615e-06,
                3.726639283752725e-06
            ],
            [
                0.999954602142788,
                2.9023133690425823e-06,
                0.4687906266262437,
                0.9999485577987147,
                0.9999251537823814,
                4.22283394786293e-06,
                0.999925153765113,
                NaN,
                2.260324028331257e-06,
                2.430023782222529e-05
            ],
            [
                3.7266392838544054e-06,
                5.422219614576807e-06,
                8.31528424151477e-07,
                3.2887506334560605e-06,
                2.9023112931213857e-06,
                6.962255419051463e-06,
                1.3007125359792008e-05,
                1.5534977545603963e-06,
                2.1444940740066406e-05,
                6.144173136885882e-06
            ],
            [
                2.5612831265630198e-06,
                3.2887498493983645e-06,
                5.422218969463855e-06,
                1.300712846361323e-05,
                3.7266397281434697e-06,
                6.962254589705982e-06,
                3.7266401725681614e-06,
                3.288749065209246e-06,
                6.144172404380855e-06,
                1.994730196482709e-06
            ],
            [
                8.93969310662177e-06,
                5.422220908703723e-06,
                1.7603438428460541e-06,
                8.939697368500698e-06,
                3.2887490653647836e-06,
                2.4300234497176063e-05,
                7.88926634755014e-06,
                1.370957206783032e-06,
                2.5612825160271407e-06,
                9.610244859678454e-05
            ],
            [
                6.475950297768503e-07,
                1.7603434230088762e-06,
                2.5612815995532906e-06,
                0.0002959570576883814,
                1.012998977022003e-05,
                8.315278293762888e-07,
                1.9947290081177566e-06,
                4.22283394762097e-06,
                1.300712381094558e-05,
                2.1444953521586782e-05
            ],
            [
                2.9023116390421582e-06,
                4.222834954211514e-06,
                2.2603240282243575e-06,
                7.88925976359915e-06,
                1.5534983100228109e-06,
                3.2887486731252264e-06,
                1.7603436329394601e-06,
                1.9947290080125335e-06,
                2.902311293147782e-06,
                0.001926734905554037
            ],
            [
                1.3007126905042372e-05,
                2.902311639126627e-06,
                6.144176066264237e-06,
                3.288749849114211e-06,
                NaN,
                6.144173868558375e-06,
                9.61023802445372e-05,
                6.962256246035174e-06,
                1.0129993392342568e-05,
                1.1478773593548236e-05
            ],
            [
                3.2887506334201674e-06,
                0.0015011823324692418,
                3.726639282763036e-06,
                1.670142183934597e-05,
                6.9622554187981796e-06,
                0.0031726822732834944,
                1.4738985480608657e-05,
                6.144173136019732e-06,
                3.2887482810382622e-06,
                2.5612825157045092e-06
            ],
            [
                1.99472900796355e-06,
                1.6701427809710842e-05,
                1.3007126880057919e-05,
                1.147876675548402e-05,
                2.4300246508833455e-05,
                1.8925157261545463e-05,
                2.5612828212676906e-06,
                1.9947294833780224e-06,
                NaN,
                3.7266406163624873e-06
            ],
            [
                7.889266347356409e-06,
                1.3709572068179446e-06,
                1.4738981970312625e-05,
                6.962254588724508e-06,
                3.7266379512857925e-06,
                1.994730434816876e-06,
                2.260324297570543e-06,
                1.7603432132079998e-06,
                1.7603436329394601e-06,
                7.889263525261671e-06
            ],
            [
                1.3007126913346863e-05,
                5.422218969532895e-06,
                7.889266347248781e-06,
                2.753570421481532e-05,
                6.962254589617333e-06,
                1.1478773597640625e-05,
                6.144172404218801e-06,
                2.561281905293402e-06,
                1.1478773597870298e-05,
                7.88926164421493e-06
            ],
            [
                3.2887498492936755e-06,
                1.1478768125201194e-05,
                1.5534973840984598e-06,
                4.785093353874907e-06,
                2.2603242976404388e-06,
                1.2098658276598493e-06,
                5.422217030209884e-06,
                6.605217605747206e-05,
                6.144177531208195e-06,
                1.3709572068354007e-06
            ],
            [
                2.7535681216639104e-05,
                2.2603251060985603e-06,
                1.1478770860982112e-05,
                1.6701419853184244e-05,
                1.1478765388314311e-05,
                1.9947294835630703e-06,
                6.144172404380855e-06,
                1.8925152750176348e-05,
                6.962256248871951e-06,
                2.4300237834601515e-05
            ],
            [
                1.3709578605617394e-06,
                2.561282210618905e-06,
                6.144175333926503e-06,
                3.72664061671159e-06,
                3.927863875584984e-07,
                3.927862002625787e-07,
                5.715007195228928e-07,
                9.422442568660309e-07,
                8.315280276338815e-07,
                3.2887490652810324e-06
            ],
            [
                6.962255419279419e-06,
                1.0129990977004428e-05,
                6.962254589104433e-06,
                5.422217676575195e-06,
                6.962257907158154e-06,
                4.785094494463623e-06,
                7.889264465842609e-06,
                2.43002523020584e-05,
                0.00029595722943352596,
                1.012999218340202e-05
            ],
            [
                8.939697368842181e-06,
                8.31528424146183e-07,
                2.260324028255194e-06,
                2.9023126768680736e-06,
                1.3007130014873483e-05,
                4.006367785525258e-05,
                1.6701415869924985e-05,
                1.0129989771473008e-05,
                7.889266346287306e-06,
                2.9023130227599746e-06
            ],
            [
                1.7603427933309468e-06,
                1.5534971988707037e-06,
                8.315279284309647e-07,
                3.7266406165319545e-06,
                5.422221555069497e-06,
                3.726637951079042e-06,
                1.3007133113703658e-05,
                4.222832939978334e-06,
                1.0129993393319151e-05,
                2.5612812946681295e-06
            ],
            [
                6.962254589528684e-06,
                3.535625489632318e-05,
                1.0129988564099116e-05,
                1.6701429805655623e-05,
                4.539789028064095e-05,
                1.3007123812554424e-05,
                1.6701425824307884e-05,
                6.962257906132355e-06,
                7.88926070020459e-06,
                6.96225790542316e-06
            ],
            [
                2.2603242977802297e-06,
                8.315284240879503e-07,
                1.2098658276598493e-06,
                5.422221555069497e-06,
                3.7266397282926013e-06,
                1.670142781025767e-05,
                3.7266388396975786e-06,
                1.7603440525925705e-06,
                1.1478768124324254e-05,
                1.9947301970287804e-06
            ],
            [
                3.726640171768275e-06,
                2.9023119850210436e-06,
                7.889263524257144e-06,
                1.0129989771473008e-05,
                2.260324567177841e-06,
                1.3709575335919232e-06,
                1.5534979396024226e-06,
                7.889265406567165e-06,
                4.222832940834793e-06,
                1.0129987351621326e-05
            ],
            [
                8.939694170729447e-06,
                9.42244481487817e-07,
                9.42244818532859e-07,
                2.5612825157045092e-06,
                1.3709570433536782e-06,
                1.0677026154619133e-06,
                1.2098653949842147e-06,
                2.9023130230133794e-06,
                2.9023123310290063e-06,
                3.726639284017094e-06
            ],
            [
                0.0002305067340055242,
                4.785096205830278e-06,
                3.726640172385136e-06,
                3.2887494572095624e-06,
                3.726638839656906e-06,
                1.370957697068717e-06,
                3.2887478882574116e-06,
                8.315277302444853e-07,
                2.5612831265909735e-06,
                6.144173868558375e-06
            ],
            [
                1.670141586949968e-05,
                5.422218322565793e-06,
                1.2098662603752517e-06,
                2.1444940736477737e-05,
                2.4300243626409964e-05,
                3.2887486732358968e-06,
                1.0129993393319151e-05,
                NaN,
                2.4300240723831244e-05,
                0.000626334064654648
            ],
            [
                1.3007134659924986e-05,
                0.999978555051946,
                3.12019150514328e-05,
                2.4300246516082393e-05,
                1.6701427815999337e-05,
                4.539787933043351e-05,
                7.484624482853042e-05,
                1.4738987241172537e-05,
                6.144173864881432e-06,
                0.0005527787415662793
            ],
            [
                1.5534971988904843e-06,
                6.144172404520556e-06,
                6.962255418924822e-06,
                4.7850950643402904e-06,
                4.539787404186659e-05,
                1.1478768122695653e-05,
                NaN,
                7.889265407004852e-06,
                2.14449458497871e-05,
                3.2887482812506295e-06
            ],
            [
                3.7266397280485686e-06,
                1.892514822538295e-05,
                1.3709573702248741e-06,
                1.3007134663876127e-05,
                1.9947299592407137e-06,
                6.475945665900901e-07,
                NaN,
                5.4222183222304545e-06,
                NaN,
                8.315282259051341e-07
            ],
            [
                4.785092783415276e-06,
                1.1478769493331685e-05,
                2.1444945843077847e-05,
                NaN,
                1.6701419845680582e-05,
                1.0129995809929273e-05,
                6.605215242107913e-05,
                2.5612834317116285e-06,
                6.1441753308083655e-06,
                6.1441731363550164e-06
            ],
            [
                2.260324567227179e-06,
                6.144172404218801e-06,
                1.3007126913583456e-05,
                4.222834954607099e-06,
                7.889260704423598e-06,
                1.300713156215912e-05,
                0.001032231278642435,
                7.889259763728304e-06,
                4.450848927437622e-07,
                2.9023116391477434e-06
            ],
            [
                2.5612825160096693e-06,
                NaN,
                2.9023119851055122e-06,
                1.7603434231241496e-06,
                5.043474683050556e-07,
                2.9023112926251358e-06,
                6.144174600985344e-06,
                1.3709576971160984e-06,
                8.31528424151477e-07,
                1.0129993393742954e-05
            ],
            [
                3.5356238059741304e-05,
                0.0024726235471444883,
                0.0007096703681413848,
                5.1442213596242845e-05,
                0.00048785719229265,
                0.5621765008857981,
                6.605213678939545e-05,
                0.00015843617868571992,
                0.0008040857463659321,
                4.006370172507966e-05
            ],
            [
                1.1478768123280277e-05,
                NaN,
                NaN,
                3.726640172337686e-06,
                6.47594952559303e-07,
                0.0010322310523604706,
                2.1444948397509574e-05,
                2.561281599881745e-06,
                5.4222215552470286e-06,
                1.2098659718990333e-06
            ],
            [
                1.012998856312253e-05,
                4.785093923768848e-06,
                1.2098655392090423e-06,
                9.422450431800595e-07,
                1.6701427809710842e-05,
                7.338210679061856e-07,
                4.22283193320392e-06,
                3.7266406167827664e-06,
                3.9278610661366994e-07,
                1.9947292457750883e-06
            ],
            [
                2.902311637529651e-06,
                NaN,
                3.2887490648622804e-06,
                NaN,
                2.260323758939877e-06,
                NaN,
                6.9622587372828785e-06,
                1.6701417859944398e-05,
                1.5534977533516638e-06,
                3.120191134459038e-05
            ],
            [
                4.222832437639588e-06,
                1.2098659719601033e-06,
                2.9023130230846496e-06,
                2.902311984989368e-06,
                1.3709576970213355e-06,
                1.0129995809929273e-05,
                4.785094494402695e-06,
                2.1444940734059286e-05,
                1.0129988563343644e-05,
                8.939699499627926e-06
            ],
            [
                3.726638395320497e-06,
                5.422221554670048e-06,
                3.2887486731252264e-06,
                2.1444948406091176e-05,
                1.9947294835630703e-06,
                5.422220908402905e-06,
                7.889263523869684e-06,
                4.2228319341064674e-06,
                3.726637951170554e-06,
                6.962259568775433e-06
            ],
            [
                8.939698434657777e-06,
                3.120191508185304e-05,
                6.144176798255599e-06,
                0.9999151889604422,
                4.222832437497486e-06,
                2.902313368897403e-06,
                1.0129993393319151e-05,
                0.9998911030657308,
                6.144173869072478e-06,
                6.962254588281262e-06
            ],
            [
                5.422220908018252e-06,
                1.6701425819447213e-05,
                3.1201900183543295e-05,
                NaN,
                1.0129989771473008e-05,
                5.144220131787343e-05,
                6.962254589617333e-06,
                6.962257079059797e-06,
                1.209866116149238e-06,
                7.889264465555602e-06
            ],
            [
                3.288750241473551e-06,
                1.670142781478417e-05,
                4.785096205830278e-06,
                NaN,
                2.9023116388969785e-06,
                2.9023116390104826e-06,
                3.120192252437034e-05,
                0.0004305570607578018,
                5.422217030495909e-06,
                1.3007131564383116e-05
            ],
            [
                2.56128282048266e-06,
                6.144172404380855e-06,
                4.222834451169694e-06,
                2.902313022952668e-06,
                1.5534983100228109e-06,
                1.9947297205401364e-06,
                1.0677031244234877e-06,
                3.288748280658394e-06,
                3.7266406160845606e-06,
                4.222834450950777e-06
            ],
            [
                9.422445938861406e-07,
                1.760344052650207e-06,
                3.726639727994339e-06,
                3.7266379512857925e-06,
                3.726640172385136e-06,
                1.4738976697229395e-05,
                1.5534971989427613e-06,
                6.9622570786798724e-06,
                3.2887482810382622e-06,
                4.222831934052698e-06
            ],
            [
                1.3007133114602719e-05,
                4.785092783210732e-06,
                2.90231163910023e-06,
                8.939693106020111e-06,
                2.2603242976404388e-06,
                4.785095064819011e-06,
                5.422218969601935e-06,
                1.209865827698362e-06,
                3.059021904484005e-07,
                1.4738983726184394e-05
            ],
            [
                4.222834451169694e-06,
                1.1478766344136694e-05,
                2.5612828212676906e-06,
                4.785095065045315e-06,
                2.2603242978213447e-06,
                1.994729959160889e-06,
                4.22283394786293e-06,
                8.939695238089467e-06,
                1.2098662604049616e-06,
                1.0129992186939844e-05
            ],
            [
                8.939700564890901e-06,
                4.785096205778054e-06,
                1.2098655392354511e-06,
                3.7266406165827946e-06,
                2.902313022802209e-06,
                2.9023130224960116e-06,
                1.209865395009523e-06,
                3.2887490653109436e-06,
                9.422445937186037e-07,
                1.994729245822257e-06
            ],
            [
                0.99989110314049,
                0.9999339478478042,
                0.9999251537645414,
                0.03732688841503393,
                0.010986942347234163,
                0.4378234991142019,
                0.6513548714339145,
                0.5926665999540698,
                0.9999417087284626,
                0.9669140220880034
            ],
            [
                4.222835457794923e-06,
                3.2887494570181325e-06,
                3.5356246413913815e-05,
                4.222833444429485e-06,
                2.561281905293402e-06,
                4.222833947774596e-06,
                0.00029595712515506325,
                5.4222196154940574e-06,
                2.902313368897403e-06,
                2.561282210618905e-06
            ],
            [
                1.0129987356706945e-05,
                1.1478773597870298e-05,
                1.4738978442537537e-05,
                2.2603234891558813e-06,
                2.4300246512104316e-05,
                0.0001233945894966614,
                1.0129989768322136e-05,
                1.99472924590571e-06,
                7.889259763728304e-06,
                2.753569437145972e-05
            ],
            [
                1.0677029972134173e-06,
                6.9622545872301346e-06,
                NaN,
                NaN,
                4.222831933296096e-06,
                3.726637951028202e-06,
                3.28875024125221e-06,
                1.1478764016112805e-05,
                NaN,
                NaN
            ],
            [
                8.939698435226916e-06,
                2.9023109466489728e-06,
                6.144173135896795e-06,
                1.1478772229781076e-05,
                0.008577486712573284,
                4.785092782188013e-06,
                1.3007131563815288e-05,
                2.4300252299759956e-05,
                1.8925157257345735e-05,
                0.00033535006020848636
            ],
            [
                0.9998911030782942,
                0.9999756997621831,
                0.9999599362945313,
                0.9999646437324796,
                0.999964643753523,
                0.6513548646660543,
                0.9997694933519323,
                0.9988304899084673,
                0.9994472214639244,
                0.9999339478318522
            ],
            [
                1.8925143725341476e-05,
                6.144173134868593e-06,
                6.962255419380732e-06,
                2.9023126757171947e-06,
                1.3007133107528522e-05,
                1.4738978452886064e-05,
                0.001700722617587818,
                4.785093919486482e-06,
                7.889262582112126e-06,
                3.120190020862863e-05
            ],
            [
                1.473898548194914e-05,
                2.561281905100056e-06,
                NaN,
                4.222832437186393e-06,
                1.2098656832611296e-06,
                2.5612834315811786e-06,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.7603436328994344e-06,
                2.4300243626409964e-05,
                1.0129992186939844e-05,
                7.889263525893087e-06,
                2.2603245672497918e-06,
                4.222831934202483e-06,
                6.962257907880012e-06,
                1.9947306725669014e-06,
                1.1478766754941153e-05,
                1.3007123812554424e-05
            ],
            [
                0.9998911031202942,
                0.9999724643187635,
                0.999989870004349,
                0.5926665999540698,
                NaN,
                0.43782349911420193,
                0.9999852610233081,
                0.9999646437412065,
                0.9994472214760802,
                0.9996200154400783
            ]
        ]
    },
    {
        "q_id": "8215_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            7,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            24,
            25,
            26,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            55,
            56,
            57,
            58,
            60,
            61,
            62,
            63,
            64,
            66,
            67,
            68,
            69,
            71,
            72,
            73,
            74,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            106,
            107,
            108,
            109,
            112,
            114,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999852610181188,
                0.9999151889969642,
                0.9999910603026321,
                0.9999938558268634,
                0.9999832985761808,
                0.9999869928684441,
                0.9999038975969108,
                0.9999852610197999,
                0.9999756997650872,
                0.9998766054406608
            ],
            [
                0.999997097686631,
                0.9999991684721706,
                0.999998629042303,
                0.9999994956527721,
                0.9999970976873229,
                0.9999984465020603,
                0.9999984465022455,
                0.9999970976880148,
                0.9999994284993485,
                0.9999970976880149
            ],
            [
                2.7535684521195802e-05,
                2.4300240725599276e-05,
                0.999991060300499,
                1.8925141469400216e-05,
                6.1441753335241615e-06,
                3.5356246490314526e-05,
                3.120191880379252e-05,
                8.939693105076969e-06,
                2.7535694358938284e-05,
                3.5356250699942575e-05
            ],
            [
                5.422220908314139e-06,
                6.9622562484666964e-06,
                1.4738978445218503e-05,
                4.539787943778038e-05,
                1.1478770856952364e-05,
                4.7850967754851966e-06,
                4.0063701710213663e-05,
                8.481108176384966e-05,
                1.0129989769722525e-05,
                1.0129995801637498e-05
            ],
            [
                1.3007133113372426e-05,
                2.1444958637356654e-05,
                7.484626280425489e-05,
                3.120190392534495e-05,
                0.9997040428308861,
                2.4300246525276163e-05,
                4.0063682625048554e-05,
                4.5397868592445174e-05,
                4.53978740152776e-05,
                1.012998977022003e-05
            ],
            [
                8.939695237341456e-06,
                0.0001233946027539403,
                5.422220907909759e-06,
                1.0129990979381404e-05,
                8.93969523573161e-06,
                3.535626334953767e-05,
                8.481106126736618e-05,
                0.9999987901338838,
                1.1478765376997616e-05,
                1.3007125359034903e-05
            ],
            [
                2.430023480941048e-05,
                1.8925157260443894e-05,
                3.120191134118513e-05,
                3.1201907474069375e-05,
                3.5356242262551455e-05,
                3.535626754334737e-05,
                5.1442201347440924e-05,
                7.889262577634811e-06,
                0.00013982202309079152,
                2.753570421601738e-05
            ],
            [
                9.610242453974122e-05,
                3.1201900119184085e-05,
                1.473897845240349e-05,
                0.00017952800870449983,
                4.5397879071810136e-05,
                0.00010889687012128086,
                3.120190386246134e-05,
                0.0035936031983537266,
                6.605213666925526e-05,
                0.0003799845709213209
            ],
            [
                3.535626334490732e-05,
                5.1442238170207006e-05,
                5.1442219765744705e-05,
                0.00015843615975093505,
                0.00017952803016475351,
                6.605214457784486e-05,
                1.3007126910649678e-05,
                1.4738983723664288e-05,
                2.7535694343912553e-05,
                4.0063687306232136e-05
            ],
            [
                0.00017952790042899172,
                2.753568781423318e-05,
                9.610241484924595e-05,
                8.939699497335115e-06,
                4.7850956352353935e-06,
                0.00010889692208924732,
                5.8291272482788436e-05,
                5.8291265499980624e-05,
                3.535626754900668e-05,
                2.4300249411766472e-05
            ],
            [
                0.9999984465016899,
                0.9999977396757023,
                0.9999962733611605,
                0.9999974387187053,
                0.9999977396751634,
                0.9999986290426298,
                0.9999938558224687,
                0.9999957771670591,
                0.9999967112517189,
                0.9999974387165681
            ],
            [
                0.5,
                0.4378234991142019,
                0.9998766054556021,
                0.9465966690702636,
                0.005911069310467187,
                0.9999785550439215,
                0.9998204719935575,
                0.00757724142543696,
                0.43782349911420193,
                NaN
            ],
            [
                3.5356254919217684e-05,
                4.00636778475281e-05,
                7.484624490966648e-05,
                0.0009110513805788705,
                0.9999921107345933,
                4.006369693473136e-05,
                2.1444940741392653e-05,
                1.8925143715978147e-05,
                4.222833946077037e-06,
                8.481107159890629e-05
            ],
            [
                0.9999984465015053,
                0.9999986290421394,
                0.9999910603004997,
                0.9999952149072167,
                0.9999980052695652,
                0.9999982396563669,
                0.9999994284992805,
                0.9999962733607163,
                0.9999989322967481,
                0.9999986290424663
            ],
            [
                1.4738976694494812e-05,
                8.315282135007954e-07,
                7.88926258381982e-06,
                7.889260703763482e-06,
                4.006370167494336e-05,
                2.7535694369155778e-05,
                1.4738978457041559e-05,
                1.0129994599072117e-05,
                1.4738976700366126e-05,
                6.962256249112569e-06
            ],
            [
                3.72663839473414e-06,
                2.561281904969606e-06,
                1.6701427815999337e-05,
                8.93969417214416e-06,
                3.120191135264947e-05,
                4.539785777882115e-05,
                2.1444940736477737e-05,
                5.829124466437278e-05,
                3.535625913039018e-05,
                1.6701421840318107e-05
            ],
            [
                0.9999938558261324,
                0.9999785550414858,
                0.9999687980997938,
                0.9999989322972572,
                0.999998446502801,
                0.9999785550541467,
                0.999994577780384,
                0.9999974387171787,
                0.9999957771665557,
                0.9999832985701989
            ],
            [
                0.9999995549147889,
                0.9999990577556307,
                0.9999989322975118,
                0.9999987901347491,
                0.9999986290421394,
                0.9999991684721706,
                0.9999986290426297,
                0.9999994956526519,
                0.999999057755743,
                0.9999993524051246
            ],
            [
                3.5356246487099006e-05,
                3.1201922520397544e-05,
                1.670142980608093e-05,
                2.561282210562998e-06,
                3.535623804623613e-05,
                1.67014178590634e-05,
                6.605212101402784e-05,
                4.006370649866785e-05,
                1.892515500715167e-05,
                1.6701429805199933e-05
            ],
            [
                0.9999930377412611,
                0.9999957771645419,
                0.9999957771675625,
                0.9999974387180947,
                0.9999957771680658,
                0.999988521233246,
                0.9999952149043648,
                0.9999967112521108,
                0.9999945777816771,
                0.9999980052695652
            ],
            [
                5.144223814063949e-05,
                2.7535694378772238e-05,
                4.222832434513317e-06,
                6.1441775291964935e-06,
                5.144220133284431e-05,
                1.01299933920846e-05,
                5.422220259709562e-06,
                4.0063692178050736e-05,
                1.0129993384861544e-05,
                7.889263524615903e-06
            ],
            [
                9.610243743663133e-05,
                2.753569764776963e-05,
                8.939699497042417e-06,
                1.892514371900746e-05,
                3.5356242260622145e-05,
                0.00013982204002712035,
                2.1444943278894603e-05,
                4.5397857790051276e-05,
                4.539787943778038e-05,
                2.430024360996726e-05
            ],
            [
                3.1201907620154606e-05,
                4.0063711246896956e-05,
                0.00013982210693632,
                1.1478772230198667e-05,
                5.144223815074485e-05,
                1.300712846115264e-05,
                4.006367783047594e-05,
                5.8291244647832884e-05,
                2.7535694379773952e-05,
                2.144494074201677e-05
            ],
            [
                2.430023782222529e-05,
                4.5397857795336036e-05,
                2.7535681249595513e-05,
                3.12019076377484e-05,
                7.889266344981421e-06,
                4.539787399744151e-05,
                2.4300234892861585e-05,
                2.14449535222109e-05,
                1.6701417853595148e-05,
                5.8291286317783706e-05
            ],
            [
                1.473897670007122e-05,
                6.1441753317695124e-06,
                6.9622554185195676e-06,
                6.605212888657352e-05,
                3.535625489632318e-05,
                1.8925145966893773e-05,
                2.7535684514885004e-05,
                6.962257079059797e-06,
                1.1478769492642663e-05,
                4.5397874031792504e-05
            ],
            [
                0.9999952149037942,
                0.9999970976880149,
                0.9999992661790195,
                0.9999970976876689,
                0.9999967112521109,
                0.9999991684721706,
                0.9999989322966208,
                0.9999974387177893,
                0.999991060304764,
                0.9999989322971299
            ],
            [
                0.9999546021098639,
                0.9999687980887236,
                0.999925153737382,
                0.9999898700102473,
                0.9999756997592744,
                0.9999785550567123,
                0.9999810748518011,
                0.9999756997505873,
                0.9999921107336531,
                0.9999485577743548
            ],
            [
                1.6701427803088173e-05,
                7.48462181396708e-05,
                6.962255417721724e-06,
                NaN,
                NaN,
                1.0129988562164371e-05,
                0.0013250223820900982,
                4.539788481371178e-05,
                0.0002611902651685853,
                2.1444953481409255e-05
            ],
            [
                0.9999995549151072,
                0.999997438717484,
                0.9999997300422547,
                0.9999989322970027,
                0.9999996940977366,
                0.9999987901344607,
                0.9999982396569966,
                0.9999986290423029,
                0.9999970976890528,
                0.9999994284994849
            ],
            [
                4.222834450743383e-06,
                5.422218321993744e-06,
                2.9023116382740264e-06,
                1.300713156215912e-05,
                8.939698434495167e-06,
                6.9622537576631295e-06,
                3.120192622962497e-05,
                4.222832939978334e-06,
                4.785095064523075e-06,
                1.0129990978220553e-05
            ],
            [
                4.222835457733473e-06,
                1.3007130004439633e-05,
                0.9999980052702785,
                2.1444940740066406e-05,
                2.1444945852673643e-05,
                3.120190020068305e-05,
                7.889265396651054e-06,
                1.3007130012673148e-05,
                2.1444943284979742e-05,
                1.1478765386038447e-05
            ],
            [
                7.88925976126004e-06,
                1.892515726099468e-05,
                1.8925143724239906e-05,
                1.012999580884213e-05,
                6.962256249112569e-06,
                1.0129987356706945e-05,
                1.3007133114886634e-05,
                1.4738987240824012e-05,
                7.88926164299515e-06,
                8.939693106873817e-06
            ],
            [
                1.1478768122695653e-05,
                9.610242630304791e-05,
                5.422220908402905e-06,
                4.222834953420345e-06,
                2.7535700739063095e-05,
                3.7266410604686857e-06,
                3.535623801986889e-05,
                4.0063677800452475e-05,
                5.829124467582348e-05,
                1.012998855982425e-05
            ],
            [
                2.144494073796001e-05,
                2.144494074076854e-05,
                1.3007131564383116e-05,
                3.7266397276079535e-06,
                1.4738980211920955e-05,
                3.726640616423495e-06,
                6.14417460073947e-06,
                7.88925976283858e-06,
                4.539786317192547e-05,
                4.22283344433731e-06
            ],
            [
                3.5356254910985954e-05,
                4.539786319009186e-05,
                3.120191879981973e-05,
                4.006368735403649e-05,
                2.753569108573408e-05,
                2.753569437266178e-05,
                2.144494329496561e-05,
                4.539785780309804e-05,
                1.3007125361755747e-05,
                7.88926634687567e-06
            ],
            [
                1.1478768118728544e-05,
                1.3007128457485415e-05,
                7.889266345584138e-06,
                6.962257078249291e-06,
                6.144176798691468e-06,
                1.0129989767695646e-05,
                3.7266410587943476e-06,
                6.96225956643256e-06,
                1.473897844934719e-05,
                6.962259566635186e-06
            ],
            [
                8.481103106008262e-05,
                1.0129988559492579e-05,
                4.53978847572308e-05,
                5.1442225828205446e-05,
                5.829127225207798e-05,
                2.753568452349975e-05,
                3.288749849209925e-06,
                1.892514823013346e-05,
                5.1442207485876726e-05,
                2.4300243621371074e-05
            ],
            [
                0.9997388096944696,
                0.1645164608483867,
                0.9999546021476569,
                0.9999251537908458,
                0.9999038975869546,
                0.9999038975394474,
                0.9997694933688542,
                0.999738809567259,
                0.9996200154756637,
                0.999891103039235
            ],
            [
                0.9999987901344607,
                0.9999987901343165,
                0.999999057755743,
                0.9999986290426297,
                0.9999994956526519,
                0.999999352405279,
                0.9999986290431201,
                0.9999986290424663,
                0.9999970976883609,
                0.9999980052693274
            ],
            [
                1.3007125359792008e-05,
                1.300712691308661e-05,
                2.7535704222728874e-05,
                2.4300237821252875e-05,
                7.484622719042334e-05,
                2.7535687813231466e-05,
                2.144495608046625e-05,
                2.753569765908901e-05,
                2.753570422573402e-05,
                2.4300240729754152e-05
            ],
            [
                1.0129990979031306e-05,
                4.539785238406597e-05,
                8.4811071529799e-05,
                2.4300234917879235e-05,
                1.4738981968864903e-05,
                2.430025231469984e-05,
                1.892514372640862e-05,
                3.535626754334737e-05,
                2.4300240727367308e-05,
                1.012998856048759e-05
            ],
            [
                3.120192252437034e-05,
                1.4738978456719842e-05,
                2.4300243628620005e-05,
                3.1201922523121745e-05,
                2.753570419688461e-05,
                0.00010889693578396252,
                3.535626333809042e-05,
                1.4738978455325741e-05,
                8.93969310647542e-06,
                2.43002436174814e-05
            ],
            [
                0.9999687980812753,
                0.9999869928715501,
                0.9999756997505882,
                0.9999810748562833,
                0.9999945777784452,
                0.9999810748450029,
                0.9999832985801479,
                0.9999832985841328,
                0.9999417087140235,
                0.9999646437450824
            ],
            [
                4.7850956352353935e-06,
                1.30071315602427e-05,
                3.120192239179253e-05,
                5.829125851717365e-05,
                NaN,
                9.610246025055319e-05,
                4.785096203449735e-06,
                4.5397863201321984e-05,
                6.605212097077738e-05,
                8.48110816015709e-05
            ],
            [
                0.9999898700114365,
                0.9999546021259963,
                0.9999599363126186,
                0.99998107485629,
                0.9999417087346539,
                0.9998204719491037,
                0.9999869928653352,
                0.9999546021367883,
                0.9999852610162764,
                0.9999756997476845
            ],
            [
                4.5397874048967995e-05,
                2.4300243624818735e-05,
                6.962253756004122e-06,
                1.1478770861211786e-05,
                3.7266397278791014e-06,
                3.7266410604686857e-06,
                1.4738978449883382e-05,
                5.829129325648758e-05,
                2.753568124348506e-05,
                3.120190392795564e-05
            ],
            [
                7.889266344981421e-06,
                7.889259763469998e-06,
                1.1478770860481005e-05,
                1.012998977108606e-05,
                4.7850950646797465e-06,
                2.430023493485234e-05,
                5.4222183231674305e-06,
                5.422217676486429e-06,
                8.939699499823059e-06,
                2.753569434872079e-05
            ],
            [
                0.9998415638023241,
                0.9999938558239339,
                0.9998911030391304,
                0.9999599363030446,
                0.9999687980737689,
                0.9999417087415957,
                0.9999810748495163,
                0.9999930377462417,
                0.9999810748472581,
                0.9999832985741806
            ],
            [
                0.9999952149032237,
                0.9999989322968754,
                0.9999970976869769,
                0.9999977396757022,
                0.9999994956525917,
                0.9999984465022455,
                0.9999987901347491,
                0.9999994284994167,
                0.9999990577551815,
                0.9999980052702786
            ],
            [
                0.9999986290429566,
                0.9999987901347491,
                0.9999980052702786,
                0.9999996072138465,
                0.9999991684719723,
                0.9999921107383618,
                0.9999980052705164,
                0.9999986290427932,
                0.9999996072136125,
                0.9999987901346049
            ],
            [
                2.7535684525803696e-05,
                4.006368262694324e-05,
                0.00012339453067199209,
                1.892514823364471e-05,
                3.535626333989112e-05,
                4.539785780309804e-05,
                1.8925150493717652e-05,
                2.753568124769226e-05,
                5.829128636782753e-05,
                3.53562591237019e-05
            ],
            [
                0.9579122737364724,
                0.9998601779004037,
                0.8933094152856196,
                0.7057850340255386,
                8.939697367703906e-06,
                0.6224593241981982,
                0.999915188929081,
                0.1066905911052601,
                0.999195913982249,
                0.9999339478318334
            ],
            [
                2.430025231469984e-05,
                1.1478765388105516e-05,
                9.61024145807647e-05,
                NaN,
                3.1201922525618933e-05,
                4.0063696566579386e-05,
                4.222831932888989e-06,
                1.1478772167434815e-05,
                1.892514597494899e-05,
                1.3007133113017532e-05
            ],
            [
                3.2887494570181325e-06,
                2.7535691097454142e-05,
                1.3007128461838766e-05,
                1.6701419842521146e-05,
                1.1478773596575768e-05,
                1.0129992184802409e-05,
                4.539789026032761e-05,
                6.962257079376403e-06,
                4.5397884837823535e-05,
                6.605216825123819e-05
            ],
            [
                0.9999991684715759,
                0.999995777166052,
                0.999998239656367,
                0.9999967112497586,
                0.9999990577549568,
                0.9999977396762411,
                0.9999980052707541,
                0.9999982396567867,
                0.9999986290426298,
                0.9999987901338838
            ],
            [
                5.8291286290217195e-05,
                2.430024941804299e-05,
                1.6701419845680582e-05,
                2.753569764776963e-05,
                2.1444958628814052e-05,
                1.6701423831188846e-05,
                2.1444945844014022e-05,
                1.4738976697631541e-05,
                2.561282210530385e-06,
                1.3007130012980722e-05
            ],
            [
                NaN,
                0.7549149868676283,
                0.9999339478241396,
                0.0031726823800548266,
                0.9980732650528062,
                0.7772998611746912,
                0.6791786926816161,
                0.9996200154520174,
                0.9997965730287874,
                0.015906388387952462
            ],
            [
                2.1444958632714784e-05,
                0.9999945777797377,
                6.605214454228335e-05,
                4.5397852403718694e-05,
                4.78509506425325e-06,
                4.006369212397934e-05,
                4.539785237613882e-05,
                4.22283193338827e-06,
                1.4738981968060613e-05,
                3.1201922511884416e-05
            ],
            [
                0.9999546021206142,
                0.9997965730617995,
                0.6224593241981982,
                0.9999646437537482,
                0.9046505261034854,
                0.9997965729783136,
                0.1329642281726931,
                0.00020342689922790518,
                0.22270014398423357,
                0.9997388097690222
            ],
            [
                0.9999993524052018,
                0.9999994284993486,
                0.9999996072137529,
                0.9999977396746244,
                0.999998790134605,
                0.9999994284996893,
                0.9999994284994167,
                0.999999057755743,
                0.99999893229713,
                0.9999986290421395
            ],
            [
                NaN,
                0.37754066179448903,
                0.9998601778761151,
                0.2942149597859341,
                0.9998911031183247,
                0.5,
                0.7772998508568416,
                0.8354835289107307,
                0.9999417087276058,
                0.7981867777396211
            ],
            [
                2.4300234936443568e-05,
                1.6701417848187652e-05,
                2.7535681246690542e-05,
                4.539785238142359e-05,
                8.481101080610379e-05,
                0.00012339458912680775,
                4.539786862564012e-05,
                2.1444943296369872e-05,
                1.8925150492616083e-05,
                4.5397868609620665e-05
            ],
            [
                0.9999938558239335,
                0.9999957771675626,
                0.9999930377454106,
                0.9999756997476821,
                0.9999974387168734,
                0.9999952149043646,
                0.9999898700126444,
                0.9999810748540608,
                0.999992110738356,
                0.9999945777784451
            ],
            [
                0.9999885212346146,
                0.9999952149043647,
                0.9999885212277727,
                NaN,
                0.9999910602994367,
                0.9999952149066468,
                0.999860177910232,
                0.9999952149043648,
                0.9999945777823245,
                0.9998766053670707
            ],
            [
                0.9999995549150542,
                0.9999989322966208,
                0.9999996072137529,
                0.9999993524051246,
                0.9999945777803863,
                0.9999991684719723,
                0.9999984465018751,
                0.9999930377420927,
                0.9999991684717741,
                0.9999991684719723
            ],
            [
                0.00013982214037567387,
                0.0008040861103950187,
                0.0005527785597761664,
                0.00023050682381337665,
                0.000335350144545397,
                0.008577485880985234,
                0.00012339456008432324,
                0.00026119021498049007,
                0.00033535026779206337,
                0.00012339457475817416
            ],
            [
                0.9998911030789376,
                0.867035758084294,
                0.9998204719930925,
                0.9999251537741666,
                0.9241418126663686,
                0.9046505453836382,
                NaN,
                0.9324533144915912,
                NaN,
                0.7981867729389246
            ],
            [
                6.605212846944677e-05,
                2.753568780461672e-05,
                8.481102097906127e-05,
                0.005911069102509486,
                4.006367785146321e-05,
                2.1444940742640888e-05,
                3.120191508707442e-05,
                2.430023783150746e-05,
                8.481107150203266e-05,
                2.144494074201677e-05
            ],
            [
                6.144175330383673e-06,
                9.610241459334976e-05,
                6.605217610793098e-05,
                1.8925152749659986e-05,
                3.120191508060445e-05,
                3.288750632678377e-06,
                6.962258737472841e-06,
                1.0129992185060374e-05,
                7.889260701237816e-06,
                6.9622570777680525e-06
            ],
            [
                0.9999967112517189,
                0.9999984465028011,
                0.9999952149072168,
                0.9999977396754327,
                0.9999952149066462,
                0.9999957771645421,
                0.999998790134028,
                0.9999967112505427,
                0.9999980052700407,
                0.9999962733616045
            ],
            [
                0.43782349911420193,
                0.9999485577987787,
                0.9999251537728095,
                0.9999339478477053,
                0.9999546021205913,
                0.9999687980812959,
                0.9998911030521819,
                0.8933094159957174,
                0.37754066879814546,
                0.9999339478557087
            ],
            [
                4.785092782396909e-06,
                3.7266383950934104e-06,
                6.9622562492265485e-06,
                6.144176065314267e-06,
                2.9023126764615702e-06,
                4.785095064601411e-06,
                4.785095064601411e-06,
                7.889264465397747e-06,
                2.5612828211442287e-06,
                1.9947299591100915e-06
            ],
            [
                0.9999938558254007,
                0.9999930377462417,
                0.9999945777829697,
                0.9999869928761882,
                0.9999852610197916,
                0.9999938558254,
                0.9999977396759716,
                0.9999938558261313,
                0.9999982396572066,
                0.9999910603047625
            ],
            [
                0.9999986290429567,
                0.9999987901338838,
                0.9999970976887068,
                0.9999990577555185,
                0.9999977396754328,
                0.99999862904312,
                0.999998005269803,
                0.9999990577557432,
                0.999999057755743,
                0.9999991684720715
            ],
            [
                4.539789027320923e-05,
                6.144175333837093e-06,
                6.605216824066585e-05,
                1.3007126911004571e-05,
                1.670142980687079e-05,
                5.422220261198862e-06,
                2.144495352474637e-05,
                6.605217612378949e-05,
                1.8925152747388e-05,
                6.605212100345552e-05
            ],
            [
                3.2887502411026557e-06,
                4.785096204650886e-06,
                6.144176064185479e-06,
                5.422218966465532e-06,
                2.5612828200447207e-06,
                8.93969630317306e-06,
                4.222834450236421e-06,
                1.99472972129484e-06,
                6.144173136019732e-06,
                1.6701425819447213e-05
            ],
            [
                1.670141983431876e-05,
                2.7535700934898458e-05,
                4.00637017209988e-05,
                4.0063706476368846e-05,
                1.4738985483504099e-05,
                2.1444958627955892e-05,
                1.300712844986705e-05,
                4.78509277781861e-06,
                2.1444945740332642e-05,
                8.93969416295666e-06
            ],
            [
                4.222832437186393e-06,
                7.88926164064169e-06,
                7.889261644057078e-06,
                NaN,
                NaN,
                2.7535704217219437e-05,
                5.422218321589366e-06,
                3.726637950329997e-06,
                2.7535691083329963e-05,
                6.605215240233725e-05
            ],
            [
                2.7535691095550887e-05,
                4.0063687392367425e-05,
                2.753569765708558e-05,
                6.605212887648175e-05,
                4.539789026032761e-05,
                4.222835457733473e-06,
                6.962256248606003e-06,
                2.7535684525803696e-05,
                3.535624225110421e-05,
                2.430023783309869e-05
            ],
            [
                7.889266344321303e-06,
                2.4300246516082393e-05,
                4.2228339467453066e-06,
                2.561281903390228e-06,
                1.147877084843352e-05,
                6.962255419051463e-06,
                1.670142781086525e-05,
                2.4300249417247375e-05,
                6.1441753327418334e-06,
                4.785093353274332e-06
            ],
            [
                0.4073334000459302,
                0.9999485577803241,
                0.9998415637285121,
                0.9995121429052035,
                0.7310585727705126,
                0.7772998611746911,
                0.9999810748585362,
                0.9998415637091209,
                0.9998766053670096,
                0.9999485577927784
            ],
            [
                1.1478770861650256e-05,
                7.889266347356409e-06,
                2.9023119850210436e-06,
                6.962259568889411e-06,
                1.994730196992497e-06,
                1.1478773597118638e-05,
                1.994729245693449e-06,
                7.889262585082652e-06,
                7.889262580791891e-06,
                1.3709578605355551e-06
            ],
            [
                3.120190019330501e-05,
                3.535624225316214e-05,
                2.4300249412738893e-05,
                0.0008040857531470478,
                3.5356254898252494e-05,
                0.00012339463329919025,
                1.8925152750692706e-05,
                0.9992903295180526,
                5.829125852607975e-05,
                2.7535684521195802e-05
            ],
            [
                5.422218320464995e-06,
                8.481102092352864e-05,
                4.006367785700152e-05,
                8.939697367492512e-06,
                8.93969630333567e-06,
                1.4738985485166298e-05,
                7.889263524443698e-06,
                7.889264465986113e-06,
                3.288750241204353e-06,
                1.6701427807280505e-05
            ],
            [
                0.9999982396567868,
                0.9999980052695652,
                0.9999974387168734,
                0.9999898700078136,
                0.9999992661792819,
                0.9999987901347492,
                0.9149009549929797,
                0.9999977396759716,
                0.9999967112501507,
                0.9999967112521109
            ],
            [
                4.006370171458602e-05,
                1.4738976700366126e-05,
                2.4300240728958537e-05,
                1.9947301968382903e-06,
                1.8925143725892257e-05,
                3.1201915085825835e-05,
                3.2887498491620677e-06,
                1.1478773598538445e-05,
                1.8925141470949294e-05,
                7.889263524443698e-06
            ],
            [
                0.9999339478766514,
                0.9998766053671335,
                0.9997040429022191,
                0.9999810748587046,
                0.1480471999111614,
                0.9993736657157539,
                0.9993736659232855,
                0.9959298616121213,
                NaN,
                0.5312093733737563
            ],
            [
                NaN,
                0.9999687980850682,
                0.999968798096175,
                0.9999687980850526,
                0.9999756997477295,
                0.320821300824607,
                0.9999546021477371,
                0.9999546021315849,
                0.999983298574187,
                0.9999785550516154
            ],
            [
                3.1201922531407855e-05,
                4.0063711272110856e-05,
                3.120190763332158e-05,
                1.300712380997554e-05,
                1.89251527491092e-05,
                2.4300232034838305e-05,
                1.3007123803043302e-05,
                0.9999810748517645,
                8.939696301140427e-06,
                7.48462449913471e-05
            ],
            [
                1.3007134663521234e-05,
                4.53978794604058e-05,
                1.012998856078241e-05,
                2.753568781022632e-05,
                2.7535704221626983e-05,
                8.939695232316787e-06,
                6.962257908753841e-06,
                3.535625913514915e-05,
                2.430023204129162e-05,
                1.0129994599901296e-05
            ],
            [
                2.430025231469984e-05,
                2.1444945851269378e-05,
                1.6701427813872793e-05,
                7.889262583633267e-06,
                4.006369214992195e-05,
                2.144495863411905e-05,
                2.144495096161541e-05,
                2.144494840531103e-05,
                7.48462272160166e-05,
                6.605214464272057e-05
            ],
            [
                0.9999251537918727,
                0.1480472036701053,
                0.46879062662624377,
                0.24508501313237174,
                0.43782349911420193,
                0.9997694932319493,
                0.9997694932380528,
                0.999933947824102,
                0.9999687980923667,
                0.9999599363085439
            ],
            [
                9.610245952900953e-05,
                3.1201907541266314e-05,
                0.00023050679532838784,
                2.753568452349975e-05,
                0.00012339462872808493,
                3.1201900204769344e-05,
                1.3007130000938025e-05,
                1.300713311517055e-05,
                4.006368260129212e-05,
                0.00010889696029755459
            ],
            [
                4.5397868609620665e-05,
                1.670142380876899e-05,
                1.892515045220231e-05,
                0.00013982214014578718,
                5.8291265491498626e-05,
                5.829129325648758e-05,
                3.535623800340544e-05,
                2.1444953521586782e-05,
                1.1478763993688211e-05,
                1.4738985475943776e-05
            ],
            [
                4.539788485169606e-05,
                5.144222588434628e-05,
                2.4300243625614346e-05,
                4.006370171895837e-05,
                0.9999869928668857,
                1.8925152744083297e-05,
                1.473898372275276e-05,
                1.0129995807165349e-05,
                4.5397863134932104e-05,
                3.535625913514915e-05
            ],
            [
                1.8925155005051806e-05,
                2.1444943297072005e-05,
                5.144219521911119e-05,
                4.006370172318498e-05,
                5.1442225840182154e-05,
                1.892514147143123e-05,
                4.5397879462552736e-05,
                3.120190392534495e-05,
                2.9023109470554753e-06,
                2.753568781022632e-05
            ],
            [
                0.00023050677817837393,
                2.561281597335639e-06,
                2.753569765708558e-05,
                1.892514591732323e-05,
                0.002800926980777589,
                2.1444950888983815e-05,
                1.0129993372000081e-05,
                4.006367778354606e-05,
                5.42221702886853e-06,
                1.670142771978837e-05
            ],
            [
                3.53562591336057e-05,
                0.00029595697243152815,
                6.605214462205646e-05,
                5.8291286359769625e-05,
                2.1444948393530826e-05,
                5.8291251603919903e-05,
                1.4738983727900215e-05,
                2.7535694373763664e-05,
                3.5356267547205986e-05,
                6.605216034600967e-05
            ],
            [
                5.144220138000259e-05,
                4.006367784956852e-05,
                1.892515726357648e-05,
                4.539787944306515e-05,
                1.0129987357020188e-05,
                8.93969523387785e-06,
                1.4738980214280206e-05,
                5.422218969532895e-06,
                6.962253755041645e-06,
                3.5356259136692605e-05
            ],
            [
                4.22283294098842e-06,
                7.889262582571338e-06,
                4.2228354571957855e-06,
                2.561282210194942e-06,
                4.785092781709294e-06,
                2.9023130228444433e-06,
                1.3007126906509262e-05,
                6.144173135628569e-06,
                8.939695237666677e-06,
                3.288749848677511e-06
            ],
            [
                0.0001584362918011666,
                1.4738988990959142e-05,
                0.00010889692219382342,
                8.93969949923766e-06,
                6.60521604084826e-05,
                2.144495094975719e-05,
                1.8925148223661747e-05,
                6.605212103421139e-05,
                7.484624448057106e-05,
                3.12019113163268e-05
            ],
            [
                0.3775406687981454,
                0.705785040214066,
                0.24508501864634824,
                0.5,
                0.1066905911052601,
                0.11920292828022305,
                0.9997040427688529,
                0.32082129433083023,
                0.4073334000459302,
                0.2942149721629888
            ],
            [
                0.9999151889591206,
                0.9997694931764818,
                0.817574478416099,
                0.8354835411997897,
                0.7549149813536518,
                0.9999599362983042,
                0.8807970842359877,
                0.9999756997563815,
                0.999981074851773,
                0.9953904267437769
            ],
            [
                0.9999687980886555,
                0.9999417087485551,
                0.9999921107336567,
                0.9999038975397915,
                0.9994472214197712,
                0.999988521233248,
                0.9999599362982967,
                0.9999646437577874,
                0.9999832985761824,
                0.9999251537372105
            ],
            [
                4.785095632554564e-06,
                2.90231233014737e-06,
                6.144177530291754e-06,
                4.785093922889744e-06,
                1.3709570433536782e-06,
                5.422217026609926e-06,
                2.902313368139829e-06,
                4.006367783266211e-05,
                1.892514372479069e-05,
                2.9023133678283525e-06
            ],
            [
                5.1442232005568484e-05,
                8.93969310584124e-06,
                2.7535681241281285e-05,
                1.3007134665130082e-05,
                7.484623598143269e-05,
                1.3007133114886634e-05,
                3.1201903930339314e-05,
                0.9999898700053984,
                5.144219522921654e-05,
                1.1478770859624945e-05
            ],
            [
                0.4378234991142019,
                NaN,
                0.18242551936144574,
                0.9994472212958015,
                NaN,
                0.9999339478319819,
                0.13296425222296632,
                0.29421497216298875,
                0.1824255326961778,
                0.003593602318806479
            ],
            [
                0.9999974387184,
                0.9999938558268633,
                0.9999952149037942,
                0.9999982396569966,
                0.9999967112517189,
                0.9999938558275963,
                0.9999992661792819,
                0.9999910603036972,
                0.9999952149066468,
                0.9999962733598274
            ],
            [
                0.9999989322967482,
                0.99999862904312,
                0.9999980052693275,
                0.9999984465015048,
                0.999998790134028,
                0.999998629042303,
                0.999997097687323,
                0.9999994956527121,
                0.9999921107392957,
                0.9999945777797375
            ]
        ]
    },
    {
        "q_id": "8757_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            22,
            23,
            24,
            25,
            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,
            78,
            79,
            80,
            81,
            82,
            83,
            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,
            21,
            26,
            31
        ],
        "rewards": [
            [
                0.9999999006880312,
                0.9999999226558238,
                0.9999998874647574,
                0.9999999226557408,
                0.9999999006880785,
                0.9999999677581222,
                0.9999999226557316,
                0.9999999634651617,
                0.9999998724809723,
                0.9999999123575255
            ],
            [
                0.9999999397642725,
                0.9999999397642437,
                0.9999998874647976,
                0.999999887464744,
                0.9999999468421502,
                0.9999999226558423,
                0.9999998874647306,
                0.999999900688043,
                0.9999999317439627,
                0.9999998724810027
            ],
            [
                0.9999998144608317,
                0.9999999226557592,
                0.9999999123574941,
                0.9999999586006295,
                0.999999789756684,
                0.9999999397642796,
                0.9999998874648915,
                0.9999999123574941,
                0.9999998362623137,
                0.9999999468421565
            ],
            [
                0.9999999468421629,
                0.9999998144608981,
                0.999999887464744,
                0.9999998555020135,
                0.9999998144608981,
                0.9999998874648782,
                0.9999998144609202,
                0.999999814460876,
                0.9999999634651662,
                0.999999855501979
            ],
            [
                0.9999999123575881,
                0.9999999226557684,
                0.9999998724808963,
                0.9999999226557776,
                0.9999999006879957,
                0.9999998724809875,
                0.9999998144608319,
                0.999999855501979,
                0.9999999317439708,
                0.9999998724809723
            ],
            [
                0.9999998724809419,
                0.999999855501979,
                0.9999998144608317,
                0.9999999317439708,
                0.9999999123575672,
                0.9999999530883787,
                0.9999998724810027,
                0.9999999226557224,
                0.9999998724809875,
                0.9999999317439708
            ],
            [
                0.9999999123575568,
                0.9999998144609203,
                0.9999999317440034,
                0.9999999226558053,
                0.9999996072136592,
                0.9999999226558053,
                0.9999999123575986,
                0.9999999317440116,
                0.9999996940978095,
                0.9999999468421439
            ],
            [
                0.9999998874647976,
                0.999999953088334,
                0.999999855501979,
                0.9999998874648379,
                0.9999999006881377,
                0.9999998555019618,
                0.999999900688043,
                0.9999998724809419,
                0.9999998555019618,
                0.999999855502048
            ],
            [
                0.9999999006880075,
                0.9999999634651879,
                0.9999996533673788,
                0.9999996072139402,
                0.9999999397643083,
                0.9999999317439384,
                0.999999168471675,
                0.9999999677581529,
                0.9999999006879957,
                0.999999789756634
            ],
            [
                0.9999999226557961,
                0.999999887464744,
                0.9999999226558145,
                0.999999855502048,
                0.9999998724809875,
                0.9999999468421756,
                0.9999999006881496,
                0.9999999317439546,
                0.9999998555019962,
                0.9999999397642653
            ],
            [
                0.9999998362623528,
                0.9999999677581375,
                0.9999999397642365,
                0.9999999226558053,
                0.9999999006881141,
                0.9999999530883732,
                0.9999999317440034,
                0.9999999397642365,
                0.9999999468421312,
                0.9999999226557776
            ],
            [
                0.9999999317439872,
                0.9999998555019618,
                0.9999998362623137,
                0.999999789756684,
                0.9999998874647976,
                0.999999946842182,
                0.9999998724810027,
                0.9999999586006443,
                0.9999999468421756,
                0.9999998362623137
            ],
            [
                0.999999814460854,
                0.9999999397642725,
                0.9999999006880075,
                0.9999999123574523,
                0.9999999226557961,
                0.9999997897566589,
                0.9999999123574732,
                0.9999999317439708,
                0.9999997897567342,
                0.9999999123574419
            ],
            [
                0.9999998874648245,
                0.9999999715466629,
                0.9999998555020306,
                0.9999999530883843,
                0.9999999123575045,
                0.9999998874647709,
                0.9999999226557224,
                0.9999999123574732,
                0.9999999226558421,
                0.99999992265575
            ],
            [
                5.829126550803852e-05,
                4.785093353739995e-06,
                6.144176798691468e-06,
                1.0677031245851707e-06,
                1.994729721469003e-06,
                3.2887494573561262e-06,
                6.962253759670401e-06,
                2.753569108924008e-05,
                2.561283431942246e-06,
                2.5612819053586272e-06
            ],
            [
                0.9999999006880075,
                0.9999998724809723,
                0.9999999123574836,
                0.9999999226557869,
                0.9999998555019963,
                0.9999999006880312,
                0.9999998362623528,
                0.9999999006880194,
                0.9999999006880312,
                0.9999999586005851
            ],
            [
                0.9999997617631753,
                0.9999998874647842,
                0.9999998555019274,
                0.9999998874649051,
                0.9999999123575464,
                0.999999922655833,
                0.9999998874649051,
                0.9999999317439872,
                0.9999999586006443,
                0.999999789756634
            ],
            [
                0.9999999006879957,
                0.9999999006881141,
                0.9999998724809723,
                0.9999997897565838,
                0.9999999715466426,
                0.9999999677581451,
                0.9999999123575672,
                0.9999998362622552,
                0.9999998874648379,
                0.9999998874649051
            ],
            [
                0.9999999006879838,
                0.9999999123575987,
                0.9999999530883564,
                0.9999999397642868,
                0.9999998874647709,
                0.9999999530883843,
                0.9999999317439953,
                0.9999998724809723,
                0.9999999123574732,
                0.9999999226557408
            ],
            [
                0.9999999586006245,
                0.9999999397642222,
                0.9999999677581414,
                0.9999999586006542,
                0.9999998874648647,
                0.9999999586006295,
                0.9999999397642222,
                0.9999999530883732,
                0.9999999006879957,
                0.9999999317439953
            ],
            [
                0.9999999586006245,
                0.9999999226558237,
                0.9999999634651879,
                0.999999974890021,
                0.9999999677581375,
                0.9999999123575568,
                0.9999999586006196,
                0.9999999397642508,
                0.999999953088362,
                0.9999999397642293
            ],
            [
                0.9999999123574732,
                0.9999998874647574,
                0.999999931743979,
                0.9999999226557776,
                0.999999939764294,
                0.9999998874647709,
                0.9999999123574836,
                0.9999999530884011,
                0.9999999397642868,
                0.9999999123574628
            ],
            [
                0.9999999226558145,
                0.9999999006880549,
                0.9999999468421376,
                0.9999998874647842,
                0.999999855502048,
                0.9999997897566089,
                0.9999999226557869,
                0.9999997300421581,
                0.9999999006879838,
                0.9999998874649318
            ],
            [
                0.9999999226557592,
                0.9999999123575464,
                0.9999999634651923,
                0.9999999123574941,
                0.9999999468421629,
                0.9999999530883675,
                0.9999999468421756,
                0.9999999468421502,
                0.9999999397642868,
                0.9999999715466561
            ],
            [
                0.9999999530883564,
                0.9999998362623723,
                0.9999999397642365,
                0.9999998555020307,
                0.999999939764294,
                0.9999999226558329,
                0.9999999226557316,
                0.9999999006880312,
                0.9999998362622357,
                0.9999999317439464
            ],
            [
                0.9999997617631468,
                0.9999998144608098,
                0.9999998362623137,
                0.999999730042319,
                0.9999999006880904,
                0.9999997617630048,
                0.9999998362623332,
                0.9999998724808963,
                0.9999998362623332,
                0.9999998555019446
            ],
            [
                0.999999939764294,
                0.9999999317439302,
                0.9999999468421756,
                0.9999999317439953,
                0.999999939764258,
                0.9999999397642725,
                0.9999999006880075,
                0.9999999226558515,
                0.9999999226557316,
                0.9999998724809875
            ],
            [
                0.994088931439275,
                0.9999986290426298,
                0.9999977396751634,
                0.9947798743161141,
                0.9999980052695671,
                0.984093606422157,
                0.9999992661790197,
                0.9999982396572074,
                0.9740426437911839,
                0.9947798738832704
            ],
            [
                0.9999999006880904,
                0.999999900688043,
                0.9999999634651574,
                0.9999999006881141,
                0.9999999317439954,
                0.9999999317439872,
                0.9999998724809267,
                0.9999999123575568,
                0.9999998144609423,
                0.9999998362622746
            ],
            [
                0.9999998144609202,
                0.9999999123574941,
                0.9999998362622552,
                0.9999999006881022,
                0.9999998724808964,
                0.9999999397643083,
                0.999999900688043,
                0.9999996940978825,
                0.9999999397642725,
                0.9999999006879838
            ],
            [
                0.9999999123575359,
                0.9999998874647306,
                0.9999999006879838,
                0.9999999123574836,
                0.9999999586006394,
                0.9999999226557408,
                0.9999999586006394,
                0.9999998874648782,
                0.9999999317439139,
                0.9999999226558145
            ],
            [
                0.9999999006879957,
                0.9999998362623528,
                0.9999998874647842,
                0.9999999827421744,
                0.9999999677581375,
                0.9999999123575987,
                0.9999999317440279,
                0.9999999006881022,
                0.9999999123575359,
                0.9999999715466696
            ],
            [
                0.9999999317439953,
                0.9999999397642796,
                0.999999855502048,
                0.9999998724809571,
                0.999999912357515,
                0.9999999226557316,
                0.9999998724809723,
                0.9999998144608097,
                0.9999999123574523,
                0.9999998555019274
            ],
            [
                0.9999999397643083,
                0.9999998874647306,
                0.99999992265575,
                0.9999999006880549,
                0.9999999123575464,
                0.9999999317439627,
                0.9999999634652097,
                0.9999999468421883,
                0.999999855501979,
                0.9999998555019618
            ],
            [
                0.9999999530883564,
                0.9999998874649184,
                0.9999999530883452,
                0.99999992265575,
                0.9999999226558515,
                0.9999998724809419,
                0.9999998724809723,
                0.9999999006879957,
                0.9999999226557408,
                0.9999998362623137
            ],
            [
                0.9999999317439384,
                0.9999999123575359,
                0.9999999397643083,
                0.9999999317440197,
                0.9999999397642222,
                0.9999999397642796,
                0.99999992265575,
                0.9999999715466527,
                0.9999999530884012,
                0.9999999226557776
            ],
            [
                0.9999997897567091,
                0.9999996940976636,
                0.9999997897566589,
                0.9999999006880668,
                0.9999998874648514,
                0.9999999530883172,
                0.9999998144608097,
                0.999999814460854,
                0.9999997617631468,
                0.9999999226557592
            ],
            [
                0.9999998874647976,
                0.9999998724809723,
                0.9999999123575045,
                0.9999999715466426,
                0.9999999677581028,
                0.9999998874649184,
                0.9999999006880549,
                0.9999999397642725,
                0.9999997617629764,
                0.9999999226557869
            ],
            [
                0.999999953088362,
                0.9999998144608317,
                0.999999887464905,
                0.9999998362622943,
                0.9999999468421502,
                0.9999999468421629,
                0.9999999677581106,
                0.9999999317439464,
                0.9999999006881259,
                0.9999999468421439
            ],
            [
                0.9999999468421059,
                0.9999999006880075,
                0.999999953088334,
                0.9999999586006146,
                0.9999998362623137,
                0.9999999397642222,
                0.9999999317439627,
                0.9999999677581414,
                0.9999999397642437,
                0.999999974890027
            ],
            [
                0.9999999226557592,
                0.9999999123575987,
                0.9999998555019962,
                0.9999999397642653,
                0.9999998362622747,
                0.9999999317439953,
                0.9999998724809723,
                0.9999997617631183,
                0.9999999006880194,
                0.9999999226557684
            ],
            [
                0.9999999226557869,
                0.9999999586006394,
                0.999999855501979,
                0.9999999586006098,
                0.9999992661788445,
                0.9999998724809115,
                0.9999998362622746,
                0.9999992661791944,
                0.9999998724809723,
                0.999999789756684
            ],
            [
                0.9999999123575568,
                0.9999999634651574,
                0.999999974890012,
                0.9999998874649318,
                0.9999999006880668,
                0.9999999226558238,
                0.9999999317439872,
                0.9999999123575464,
                0.9999999468421565,
                0.9999999634651923
            ],
            [
                0.9999998874649051,
                0.9999998724809419,
                0.9999997897565838,
                0.999999887464744,
                0.999999814460854,
                0.9999998874649318,
                0.9999996533675028,
                0.9999999317439464,
                0.9999998874647574,
                0.9999998555019446
            ],
            [
                0.9999999317440116,
                0.9999997617630616,
                0.999999900688043,
                0.9999999586005949,
                0.9999999226557961,
                0.9999995549147889,
                0.9999999123574941,
                0.9999999715466256,
                0.9988304897546629,
                0.999999855502048
            ],
            [
                0.9999998874647574,
                0.9999999317439302,
                0.9999999586006344,
                0.9999999634651792,
                0.9999999006879838,
                0.9999999397642796,
                0.9999998555020135,
                0.9999999123575987,
                0.9999999226557961,
                0.999999912357515
            ],
            [
                0.9999999123574732,
                0.9999999006881496,
                0.9999997617631752,
                0.9999998362622943,
                0.9999999397642653,
                0.999999855502048,
                0.9999998555019446,
                0.9999998555020307,
                0.9999998144608317,
                0.9999997897565587
            ],
            [
                0.9999998362623528,
                0.9999999317439464,
                0.9999999317440035,
                0.9999998362623332,
                0.9999998362622552,
                0.9999998555019962,
                0.9999999226557961,
                0.9999999586006245,
                0.9999999397642796,
                0.9999998874648379
            ],
            [
                0.9999998362622942,
                0.9999999317439627,
                0.9999999123574523,
                0.9999999468421122,
                0.9999999634651836,
                0.9999999006881259,
                0.9999999226557776,
                0.9999998144609645,
                0.9999999586006394,
                0.9999999006880194
            ],
            [
                0.9999999586006443,
                0.9999998874648514,
                0.9999999586006245,
                0.999999912357515,
                0.9999999123574941,
                0.9999998362623332,
                0.9999998724809267,
                0.9999998555019446,
                0.9999999123574732,
                0.9999999317439708
            ],
            [
                0.9999997617630616,
                0.99999995308839,
                0.9999998144608097,
                0.99999976176309,
                0.9999999317440116,
                0.9999998724809419,
                0.9999999397643156,
                0.9999998144608981,
                0.9999999634651792,
                0.9999999226557408
            ],
            [
                7.889265406438011e-06,
                7.338209805040511e-07,
                8.93969949923766e-06,
                1.994729721436347e-06,
                2.260325106045111e-06,
                8.939695237959376e-06,
                4.785096205434246e-06,
                1.994729483666479e-06,
                1.1478769489719528e-05,
                5.422217030209884e-06
            ],
            [
                0.9999999226558146,
                0.9999998724809723,
                0.9999999006881496,
                0.999999939764294,
                0.9999999586006245,
                0.9999998144608538,
                0.9999998362623722,
                0.9999997617631468,
                0.9999999006880668,
                0.9999999006880075
            ],
            [
                0.9999999586006295,
                0.9999996940978095,
                0.9999999778405292,
                0.9999998724809571,
                0.9999998362623723,
                0.9999998874648379,
                0.9999998555019446,
                0.9999999006879721,
                0.9999999226557776,
                0.9999999006880785
            ],
            [
                0.9999999317439302,
                0.9999999006879957,
                0.999999912357515,
                0.9999998362623138,
                0.9999998724809571,
                0.9999998874647842,
                0.9999998724809571,
                0.9999999530883508,
                0.9999999226558237,
                0.9999999317439953
            ],
            [
                0.9999995549148419,
                0.9999998874649184,
                0.999999912357515,
                0.9999999226557131,
                0.9999999123575359,
                0.99999992265575,
                0.999999900688043,
                0.9999997617631469,
                0.9999999397642508,
                0.9999998724810027
            ],
            [
                0.9999999586006245,
                0.99999995308839,
                0.999999967758149,
                0.9999998555020307,
                0.9999998724809116,
                0.99999992265575,
                0.9999994284994168,
                0.9999999317439302,
                0.9999999468421439,
                0.9999999123575255
            ],
            [
                0.999999730042126,
                0.9999996072138465,
                0.9999998362623332,
                0.999999855501979,
                0.9999997300422225,
                0.9999999226557131,
                0.999999912357515,
                0.9999998144608538,
                0.9999999634651443,
                0.9999998874648917
            ],
            [
                0.99999992265575,
                0.9999999468421946,
                0.9999999317439546,
                0.9999998555020135,
                0.9999998724810027,
                0.9999999123575986,
                0.9999999123574941,
                0.9999998362623137,
                0.9999999006881141,
                0.9999999123574836
            ],
            [
                0.9999999006880312,
                0.999999963465201,
                0.9999999226557131,
                0.999999814460876,
                0.999999266179107,
                0.9999997617630332,
                0.9999999006880785,
                0.999999855502048,
                0.9999999468421439,
                0.9999998724809267
            ],
            [
                0.999999855501979,
                0.9999999468421567,
                0.9999999468421502,
                0.9999999226557869,
                0.9999999530883675,
                0.9999999317439872,
                0.9999999123574836,
                0.9999999123574628,
                0.999999912357515,
                0.999999939764258
            ],
            [
                1.9947299592824403e-06,
                2.902311984952413e-06,
                8.315279285012978e-07,
                2.902312677060767e-06,
                3.2887494573232236e-06,
                7.338208055302923e-07,
                2.90231163910023e-06,
                1.5534981249496567e-06,
                2.9023126770343703e-06,
                8.315284241560147e-07
            ],
            [
                0.9999998874648379,
                0.999999887464744,
                0.9999998362622357,
                0.9999998144608538,
                0.9999999468421756,
                0.9999998874647709,
                0.9999998362623723,
                0.9999999530883732,
                0.9999999468421439,
                0.9999999586006394
            ],
            [
                0.9999999804443286,
                0.999999953088362,
                0.9999999468421249,
                0.9999999397642508,
                0.9999998144608981,
                0.9999999317439464,
                0.9999998724809116,
                0.999999931743979,
                0.9999999006879721,
                0.9999998874648514
            ],
            [
                0.9999999317440034,
                0.9999999226558237,
                0.9999999226557869,
                0.999999939764294,
                0.9999998362622357,
                0.9999998724809267,
                0.9999999123574836,
                0.9999999778405081,
                0.999999939764258,
                0.9999998724809115
            ],
            [
                0.9999999397643083,
                0.9999999123574419,
                0.9999998555019446,
                0.999999789756634,
                0.9999998724809116,
                0.9999999317439302,
                0.9999999530883732,
                0.999999953088362,
                0.9999998362622746,
                0.9999998874648917
            ],
            [
                0.9999999397643156,
                0.9999999123575046,
                0.9999999226557224,
                0.9999999317439546,
                0.9999999123575987,
                0.9999999317439708,
                0.9999998362623528,
                0.9999999226557684,
                0.999999887464744,
                0.9999999397642437
            ],
            [
                0.9999998874649318,
                0.999999900688043,
                0.9999998144608317,
                0.9999998555019446,
                0.9999999468421883,
                0.9999999006880904,
                0.9999998874647709,
                0.9999999317439872,
                0.9999998874649184,
                0.9999999586006542
            ],
            [
                0.9999999006880194,
                0.999999912357515,
                0.9999999468421565,
                0.9999998362623332,
                0.9999999226558515,
                0.999999855501979,
                0.999999939764294,
                0.9999998362622943,
                0.9999999634651792,
                0.9999998874649184
            ],
            [
                0.9999999006880549,
                0.9999998555019962,
                0.999999855501979,
                0.9999997897567342,
                0.9999998724810027,
                0.9999998724808963,
                0.9999999634652097,
                0.999999963465201,
                0.9999998555020307,
                0.9999999226557408
            ],
            [
                0.9999998874648245,
                0.9999999006881259,
                0.9999999530883787,
                0.9999999006880785,
                0.999999887464811,
                0.9999999586006245,
                0.9999998362622357,
                0.9999999123574836,
                0.9999998144609644,
                0.9999999123574628
            ],
            [
                0.999999789756634,
                0.9999998874647976,
                0.9999999006881141,
                0.9999998874649051,
                0.99999992265575,
                0.9999998874648917,
                0.9999999226558145,
                0.9999998724809419,
                0.9999999123575881,
                0.9999999123575255
            ],
            [
                0.9999999006879957,
                0.9999998724809723,
                0.9999998874648245,
                0.9999998362622357,
                0.9999998362622552,
                0.999999939764294,
                0.9999998724809723,
                0.9999999006879957,
                0.999999912357515,
                0.999999953088362
            ],
            [
                0.9999998874647709,
                0.9999999586006344,
                0.9999998874648245,
                0.9999999468421629,
                0.9999998724809116,
                0.999999912357515,
                0.9999998362622357,
                0.9999999468421565,
                0.9999999715466595,
                0.9999999634652054
            ],
            [
                0.9999999123574419,
                0.9999999586006492,
                0.9999998555019274,
                0.999999855502048,
                0.9999999397642653,
                0.9999999530883508,
                0.999999939764258,
                0.9999999317439953,
                0.9999998362622746,
                0.999999953088362
            ],
            [
                0.9999999468421376,
                0.9999998724809267,
                0.9999998555019274,
                0.999999939764258,
                0.9999999397642725,
                0.9999998874647976,
                0.999999653367379,
                0.9999999226557684,
                0.9999998724809115,
                0.9999998724809875
            ],
            [
                0.9999998724809419,
                0.9999999006880785,
                0.9999998874647842,
                0.9999998724808963,
                0.9999998874647976,
                0.9999998362623137,
                0.9999999317439546,
                0.9999998144608981,
                0.9999999226557592,
                0.9999999530883843
            ],
            [
                0.9999999715466561,
                0.9999998724809571,
                0.9999999123575255,
                0.9999999468421565,
                0.999999900688043,
                0.9999998724809419,
                0.9999998874648245,
                0.9999998724809875,
                0.9999999715466629,
                0.9999997617630332
            ],
            [
                0.9999997300421903,
                0.9999999317439708,
                0.9999998724809571,
                0.9999998362622746,
                0.9999999226557776,
                0.9999998874647709,
                0.9999997897567091,
                0.9999999006879957,
                0.9999998724808963,
                0.999999855502048
            ],
            [
                0.9999999397643011,
                0.9999999006880904,
                0.9999999123574523,
                0.9999998874647842,
                0.9999998874648917,
                0.999999946842182,
                0.9999998555019963,
                0.9999999530883396,
                0.9999998724809875,
                0.9999998724808964
            ],
            [
                0.999999814460876,
                0.9999999226557316,
                0.99999992265575,
                0.9999999317440279,
                0.9999998724809875,
                0.9999999006879838,
                0.9999998724809419,
                0.9999999123574628,
                0.999999814460876,
                0.9999999530883787
            ],
            [
                0.9999999468421502,
                0.9999998874648915,
                0.9999998362622942,
                0.9999998362623528,
                0.9999999226557869,
                0.9999998724809419,
                0.9999998724809115,
                0.9999999226557776,
                0.9999998555019446,
                0.9999999317439383
            ],
            [
                0.9999996072137998,
                0.9999999123574836,
                0.9999999006880904,
                0.9999996533673788,
                0.9999998724809267,
                0.9999998555020134,
                0.9999999317439302,
                0.9999998724809723,
                0.9999999468421756,
                0.9999998144609423
            ],
            [
                0.9999999468421439,
                0.9999999006879957,
                0.9999998724809875,
                0.9999999586006245,
                0.9999998362622357,
                0.9999999317439464,
                0.9999999317439627,
                0.9999999468421883,
                0.9999999123575045,
                0.9999999226557316
            ],
            [
                0.9999999123575255,
                0.9999999397642725,
                0.9999999123575045,
                0.9999998144608981,
                0.9999998874648112,
                0.9999999634651574,
                0.9999999006881259,
                0.9999999006880194,
                0.9999999123575568,
                0.9999999317439221
            ],
            [
                0.9999998555019446,
                0.999999939764258,
                0.9999999397643083,
                0.9999999317439953,
                0.9999998724808963,
                0.9999998144608981,
                0.9999999317439465,
                0.9999997897567091,
                0.9999998362623528,
                0.9999997300420937
            ],
            [
                0.999999939764258,
                0.9999999317440034,
                0.9999999530883452,
                0.9999998874648647,
                0.9999998874648782,
                0.9999999586006443,
                0.9999999006880312,
                0.9999999123575672,
                0.9999999530883564,
                0.9999999226557776
            ],
            [
                0.9999999317439872,
                0.9999998362622747,
                0.9999999586006146,
                0.9999997300420937,
                0.9999998362623332,
                0.9999998724809571,
                0.9999998874648917,
                0.9999999586006196,
                0.9999998724809419,
                0.99999992265575
            ],
            [
                0.9999999715466696,
                0.9999999677581529,
                0.9999996072138466,
                0.9999999317439302,
                0.9999999226558515,
                0.9999998724809723,
                0.9999999226557776,
                0.9999998874649184,
                0.9999999006881259,
                0.9999998555019962
            ],
            [
                0.9999997897565587,
                0.9999998874649051,
                0.9999998362623528,
                0.9999999226557592,
                0.9999999006880312,
                0.9999998362623138,
                0.9999998555020307,
                0.9999999530883732,
                0.9999998724809115,
                0.9999997300420937
            ],
            [
                0.9999997897565587,
                0.9999998144609423,
                0.9999997897567091,
                0.9999998555020307,
                0.9999999226557776,
                0.999999887464744,
                0.9999998555019962,
                0.999999900688043,
                0.999999789756684,
                0.9999998874648781
            ],
            [
                0.9999991684718732,
                0.9999996072137529,
                0.9999992661790196,
                0.9999982396569966,
                0.9999984465016899,
                0.9999989322968755,
                0.9999991684718732,
                0.9999990577556308,
                0.9999970976866309,
                0.9999986290427932
            ],
            [
                0.9999999006879721,
                0.9999999586006245,
                0.9999999530883955,
                0.99999992265575,
                0.9999999123575987,
                0.9999998724809115,
                0.9999999468421439,
                0.9999999123574419,
                0.999999939764258,
                0.9999999468421376
            ],
            [
                0.9999996533672962,
                0.9999999586006295,
                0.9999999006880904,
                0.9999999123575672,
                0.9999999677581414,
                0.9999998724810027,
                0.9999998724809115,
                0.9999999123574523,
                0.9999998874648782,
                0.999999789756634
            ],
            [
                0.9999999226557316,
                0.9999999530883396,
                0.9999999397642437,
                0.9999999804443169,
                0.9999999468421502,
                0.9999999865595998,
                0.9999999397642653,
                0.999999974890018,
                0.999999939764215,
                0.9999999530883508
            ],
            [
                0.9999998362622552,
                0.9999999397642293,
                0.9999998555020135,
                0.9999999397642796,
                0.999999977840516,
                0.9999997617630048,
                0.9999998724809115,
                0.9999999123575359,
                0.9999998555020135,
                0.9999996072137061
            ],
            [
                0.9999999006881141,
                0.999999953088362,
                0.9999998874649318,
                0.9999997897567091,
                0.9999999468421629,
                0.9999999226558053,
                0.9999999006880904,
                0.9999999804443286,
                0.9999999006881023,
                0.9999999677581451
            ],
            [
                0.9999997897565587,
                0.9999998555019618,
                0.999999939764258,
                0.9999997617630332,
                0.9999998874647574,
                0.9999997300421903,
                0.9999998362623528,
                0.999999855501979,
                0.999999855501979,
                0.9999999226557684
            ],
            [
                0.9999998724809723,
                0.999999855501979,
                0.9999999634651836,
                0.9999999634651444,
                0.999999887464744,
                0.9999998724809571,
                0.9999998144609423,
                0.9999999226558515,
                0.9999998874648782,
                0.999999939764294
            ],
            [
                0.9999998724809267,
                0.9999997617631183,
                0.9999998144608981,
                0.9999997897565587,
                0.9999998555019446,
                0.9999998555019446,
                0.9999999226557776,
                0.9999999468421249,
                0.9999999006881141,
                0.9999998144608981
            ],
            [
                0.9999999123575359,
                0.999999814460876,
                0.9999999677581259,
                0.9999998362623528,
                0.9999999006881496,
                0.9999998724809116,
                0.9999999006881259,
                0.9999999317439627,
                0.999999855502048,
                0.99999992265575
            ],
            [
                0.9999999317439708,
                0.9999999006880194,
                0.99999992265575,
                0.9999999468421502,
                0.999999939764258,
                0.9999999468421439,
                0.9999998874647976,
                0.9999999317439464,
                0.9999999226557592,
                0.9999997300422869
            ],
            [
                0.9999997897567091,
                0.9999997300422547,
                0.9999998144608319,
                0.9999997897565838,
                0.9999998555019962,
                0.9999997300422225,
                0.9999999006881142,
                0.9999999123574732,
                0.9999998555019274,
                0.9999997617630332
            ],
            [
                0.9999999123575568,
                0.9999998724810027,
                0.9999999634651879,
                0.9999998874648514,
                0.9999999226557776,
                0.9999999006880904,
                0.999999974890012,
                0.9999999006881141,
                0.999999912357515,
                0.9999999006880549
            ],
            [
                0.9999999226558515,
                0.9999999397642653,
                0.9999999317439221,
                0.9999999317440279,
                0.9999999586006344,
                0.9999999530883732,
                0.9999999397642365,
                0.9999999677581144,
                0.9999999006879838,
                0.9999999586006542
            ],
            [
                0.9999999468421376,
                0.9999998362623332,
                0.9999999397642508,
                0.999999963465201,
                0.9999999123574628,
                0.9999998724808963,
                0.9999999226558053,
                0.9999999530883396,
                0.9999999123574836,
                0.9999999634652097
            ],
            [
                0.9999999468421502,
                0.9999999123574836,
                0.9999999634651792,
                0.9999999123574628,
                0.9999999317440197,
                0.999999931743979,
                0.9999999006881259,
                0.9999999006881496,
                0.9999998874647306,
                0.9999999226557776
            ],
            [
                0.9999999006880194,
                0.9999998874647709,
                0.9999997617631753,
                0.9999999123575987,
                0.9999998724810027,
                0.9999998874647709,
                0.9999998144608317,
                0.9999999226557961,
                0.9999999006881377,
                0.9999999317439464
            ],
            [
                0.9999756997564142,
                0.995390428354777,
                0.9999990577549568,
                0.9840936080840885,
                0.9999967112509383,
                0.9999992661788449,
                0.9999930377429209,
                0.9975273764109331,
                0.999996273360716,
                0.9999921107355387
            ],
            [
                0.9999999006880312,
                0.99999992265575,
                0.9999998724808963,
                0.9999999397642508,
                0.9999999123574419,
                0.9999999530883508,
                0.9999999226558237,
                0.9999999006879957,
                0.9999998724809419,
                0.9999998724809875
            ],
            [
                0.9999999123575672,
                0.9999999226558238,
                0.9999999006881259,
                0.9999998555020134,
                0.9999999006880904,
                0.9999999397643156,
                0.9999999397643083,
                0.9999998724809267,
                0.9999999226558423,
                0.9999999123574836
            ],
            [
                0.9999998362622357,
                0.9999999397642437,
                0.9999999317439627,
                0.9999999006879838,
                0.999999730042319,
                0.999999887464811,
                0.9999999468421883,
                0.9999999317439546,
                0.9999999397643083,
                0.9999999634651923
            ],
            [
                6.962258739454786e-06,
                1.0129995809431767e-05,
                1.473897845240349e-05,
                2.4300246522270504e-05,
                2.7535681249595513e-05,
                4.006369217615605e-05,
                7.889261644631091e-06,
                1.1478765387416494e-05,
                1.3007134666431358e-05,
                1.012998735687278e-05
            ],
            [
                0.9999999634651748,
                0.9999999006880312,
                0.9999999715466629,
                0.9999999317439627,
                0.9999999468421692,
                0.9999999397642653,
                0.9999998555019274,
                0.9999999397642653,
                0.9999999006879957,
                0.9999999123574941
            ],
            [
                0.9999998555020135,
                0.9999998874648514,
                0.9999999226557408,
                0.9999998362622357,
                0.9999998874647574,
                0.9999996533673375,
                0.999999900688043,
                0.9999999317439302,
                0.9999999226557961,
                0.9999998874648246
            ],
            [
                0.9999999634651748,
                0.9999999530883285,
                0.999999855501979,
                0.9999999123574732,
                0.999999953088334,
                0.9999999468421376,
                0.9999998555019274,
                0.9999998724809875,
                0.999999900688043,
                0.9999999468421439
            ],
            [
                0.9999998874647842,
                0.9999999123574732,
                0.9999998362622552,
                0.999999887464744,
                0.9999998555020134,
                0.9999999317440116,
                0.9999999468421756,
                0.9999998555020307,
                0.999999887464811,
                0.9999999006880549
            ],
            [
                0.9999999317439708,
                0.9999999715466289,
                0.9999999226558237,
                0.9999998874647574,
                0.9999999226557869,
                0.9999999226558053,
                0.9999998874648379,
                0.9999999530883732,
                0.9999999226557224,
                0.9999999226557408
            ],
            [
                0.9999998555019446,
                0.9999998555019446,
                0.999999974890024,
                0.9999999317439546,
                0.9999999317439627,
                0.9999999317439464,
                0.9999998555020307,
                0.9999998724810027,
                0.9999998362623722,
                0.9999999123574836
            ],
            [
                0.9999999123574941,
                0.9999999226557869,
                0.9999998362623723,
                0.9999999317439627,
                0.9999998874647306,
                0.9999999468421376,
                0.9999999123574628,
                0.9999998724809267,
                0.9999999006881141,
                0.9999999715466663
            ],
            [
                0.9999999530883732,
                0.9999999586006295,
                0.9999999006880785,
                0.9999999634651748,
                0.9999999317439383,
                0.9999999226558145,
                0.999999946842182,
                0.9999999804443286,
                0.9999999123575359,
                0.999999855501979
            ],
            [
                0.9999997897566589,
                0.9999998362622942,
                0.9999999530883787,
                0.9999999586006394,
                0.9999999006880312,
                0.9999999226557684,
                0.9999998555020135,
                0.9999998555020307,
                0.9999999226557224,
                0.9999998144609202
            ],
            [
                5.422221554926484e-06,
                6.14417606659952e-06,
                2.260325375615501e-06,
                1.994729721436347e-06,
                3.72664017246987e-06,
                4.222831934156396e-06,
                2.260323758939877e-06,
                3.726638839656906e-06,
                8.939697369671496e-06,
                2.260325375572331e-06
            ],
            [
                0.999999912357515,
                0.9999998874649051,
                0.9999999468421186,
                0.9999999226557131,
                0.9999997617631184,
                0.9999999123575359,
                0.9999997897565587,
                0.9999999530883787,
                0.9999998874649318,
                0.9999998724809267
            ],
            [
                0.9999998555019962,
                0.9999997897567091,
                0.9999998724809419,
                0.999999939764258,
                0.9999998555020307,
                0.9999999006881377,
                0.999999900688043,
                0.9999998724808963,
                0.9999998724808964,
                0.9999999634651966
            ],
            [
                0.9999999317439708,
                0.9999999530883787,
                0.9999998874647306,
                0.9999999586006146,
                0.9999998724809571,
                0.999999855501979,
                0.9999998874648514,
                0.9999999226557869,
                0.9999999226557776,
                0.9999999468421439
            ]
        ]
    },
    {
        "q_id": "8170_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            42,
            43,
            44,
            46,
            47,
            49,
            50,
            51,
            53,
            54,
            56,
            57,
            58,
            59,
            60,
            61,
            63,
            65,
            66,
            67,
            69,
            70,
            71,
            72,
            73,
            74,
            76,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            94,
            95,
            96,
            97,
            98,
            100,
            101,
            102,
            103,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            115,
            116,
            117,
            118,
            119,
            121,
            122,
            124,
            125,
            127
        ],
        "rewards": [
            [
                0.9999980052698031,
                0.9999977396746245,
                0.9999546021372838,
                0.9999977396762411,
                0.9999982396567868,
                0.9999974387180947,
                0.9999952149043669,
                0.9999957771660528,
                0.9999038976236093,
                0.9999982396565769
            ],
            [
                0.9999993524052018,
                0.9999998144609645,
                0.9999996940978095,
                0.9999996072136125,
                0.999997097686977,
                0.9999996072138934,
                0.9999996072138465,
                0.9999996072136593,
                0.9999997300421581,
                0.9999998724808963
            ],
            [
                0.999994577783002,
                0.9999957771660523,
                0.9999980052695658,
                0.9999980052702795,
                0.9999986290427935,
                0.9999962733593835,
                0.9999986290424665,
                0.9324533036984185,
                0.9999967112513735,
                0.9999952149055101
            ],
            [
                0.9999996940977731,
                0.9999996940976636,
                0.9999997897567091,
                0.9999998555019963,
                0.9999999006880785,
                0.9999996072138465,
                0.9999997897565587,
                0.999999912357515,
                0.9999998874648647,
                0.9999997897565838
            ],
            [
                0.9999989322973846,
                0.9999994956527121,
                0.9999989322975118,
                0.9999998362623137,
                0.9999994284996891,
                0.9999995549150011,
                0.9999986290421394,
                0.9999997300422868,
                0.9999997617630049,
                0.9999994284994849
            ],
            [
                5.422217030614265e-06,
                3.2887482811908074e-06,
                9.422447062202052e-07,
                1.4738981969240237e-05,
                3.7266406167827664e-06,
                2.5612831266608576e-06,
                6.144177531599359e-06,
                3.726640616748873e-06,
                1.0677031245710902e-06,
                1.99472924590571e-06
            ],
            [
                0.9999997897566338,
                0.9999997300422225,
                0.9999998874648379,
                0.9999987901343165,
                0.9999996533672549,
                0.9999998555019618,
                0.9999999226558053,
                0.9999997300421261,
                0.9999999317439627,
                0.9999996533673375
            ],
            [
                0.9999995549148419,
                0.9999998362622357,
                0.9999998144609644,
                0.9999998362622943,
                0.9999993524053562,
                0.999999653367379,
                0.9999998144608098,
                0.9999999677581451,
                0.9999996533674614,
                0.9999998144608981
            ],
            [
                0.9999993524051246,
                0.9999993524052789,
                0.9999992661787571,
                0.999999266179107,
                0.9999998724809875,
                0.9999993524052019,
                0.9999984465016899,
                0.999999789756684,
                0.9999987901344607,
                0.9999994284993486
            ],
            [
                0.9999952149072172,
                0.9669140238756563,
                0.9999989322971304,
                0.9999990577552942,
                0.9999970976880148,
                0.9999832985721941,
                0.9999974387171787,
                0.9999977396757024,
                0.7772998611746912,
                0.9999921107355588
            ],
            [
                0.9999038976195779,
                0.9999810748449967,
                NaN,
                0.9999930377420999,
                0.9999980052693275,
                0.9997694931797079,
                0.9999339478412936,
                0.9999417087282794,
                0.9999869928654836,
                0.999941708748413
            ],
            [
                0.9999921107345953,
                0.9820137861557843,
                NaN,
                0.9999785550441218,
                0.9999646437324686,
                0.9999869928656789,
                0.9999945777799004,
                0.9999251537522631,
                0.9999938558232364,
                0.9999962733616066
            ],
            [
                0.04208772671409797,
                0.9999756997506734,
                NaN,
                NaN,
                0.4687906266262437,
                0.5926665999540697,
                0.22270013882530884,
                0.679178699175393,
                0.9999756997536534,
                0.7981867729389246
            ],
            [
                0.9999994284992805,
                0.9999982396569966,
                0.9999980052695652,
                0.9999974387184,
                0.9999996533675028,
                0.9999993524052019,
                0.9999990577550691,
                0.9999992661787571,
                0.999998446502801,
                0.999998005270041
            ],
            [
                0.9999996940977002,
                0.9999996533675028,
                0.9999992661792819,
                0.9999994956527121,
                0.9999991684721706,
                0.9999994956524716,
                0.9999996940978095,
                0.9999997617630616,
                0.9999994284996211,
                0.9999996533674201
            ],
            [
                0.999999057755743,
                0.9999990577552939,
                0.9999996072138934,
                0.9999921107365378,
                0.999999168471675,
                0.9999992661791071,
                0.9999962733616061,
                0.9999986290427932,
                0.9999962733620545,
                NaN
            ],
            [
                0.9999998362623332,
                0.999999694097773,
                0.9999999123575464,
                0.9999998144609645,
                0.9999996533673788,
                0.9999998362623137,
                0.9999998362623722,
                0.9999999123575777,
                0.99999976176309,
                0.9999999226557961
            ],
            [
                0.9999992661787571,
                0.9999996940976272,
                0.9999998555019446,
                0.99999976176309,
                0.999999554914895,
                0.9999997897565587,
                0.9999992661791944,
                0.9999987901341723,
                0.9999995549148419,
                0.9999997897567091
            ],
            [
                2.260324028255194e-06,
                1.8925148238808306e-05,
                2.260325375634003e-06,
                1.8925145981283003e-05,
                1.2098661161861e-06,
                6.475946437928669e-07,
                1.994729008074216e-06,
                1.994729008105057e-06,
                2.9023119847359636e-06,
                1.0677028700053041e-06
            ],
            [
                NaN,
                0.0,
                1.0,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                0.9999646437332099,
                0.9990889489454714,
                0.9999938558276186,
                0.9999852610197986,
                0.6791787056691698,
                0.46879062662624377,
                NaN,
                0.5926665999540698,
                0.9999646437409938,
                0.9324533158993963
            ],
            [
                0.9999957771665603,
                NaN,
                0.9999962733598279,
                0.9999930377454109,
                0.9999986290426297,
                NaN,
                0.999993855822471,
                NaN,
                0.9999898700041968,
                0.9999982396567867
            ],
            [
                0.999998005269803,
                0.9999995549150542,
                0.9999987901337396,
                0.9999999006879838,
                0.9999996072138934,
                0.9999977396765105,
                0.9999991684722697,
                0.9999995549147889,
                0.9999998362623332,
                0.9999945777816805
            ],
            [
                3.2887502414436403e-06,
                1.3007130014376633e-05,
                1.3709570433661467e-06,
                2.6995768090561445e-07,
                1.3709570433885908e-06,
                2.5612815995532906e-06,
                2.56128159999123e-06,
                6.962259569313662e-06,
                1.5534975693488444e-06,
                2.2603253755949437e-06
            ],
            [
                0.9999992661789321,
                0.9999991684720715,
                0.9999997617630049,
                0.9999996940976636,
                0.9999869928715381,
                0.999999855501979,
                0.9999998724809875,
                0.9999998144608319,
                0.9999997617630332,
                0.9999997617630616
            ],
            [
                0.9999974387187054,
                0.9999957771650504,
                0.9999974387165681,
                0.9999991684722698,
                0.999998005269803,
                0.999999266178932,
                0.9999977396754328,
                0.9999997300421903,
                0.9999982396572064,
                0.9999957771665574
            ],
            [
                0.9999938558224699,
                0.9999930377445854,
                0.9999339478554703,
                5.144220124077339e-05,
                0.9999852610215446,
                0.9999962733611605,
                0.8670357494949105,
                0.9999151889182282,
                0.9999417087554858,
                0.9999980052702786
            ],
            [
                0.9999996533672135,
                0.9999998874649184,
                0.9999994956524114,
                0.9999998724809116,
                0.9999998144608981,
                0.999999730042319,
                0.9999997300422868,
                0.9999995549150542,
                0.9999995549151073,
                0.9999998555019618
            ],
            [
                0.9999945777829718,
                0.9999991684721706,
                0.9999993524052018,
                0.9999996072137529,
                0.9999989322967481,
                0.99999893229713,
                0.9999993524051246,
                0.9999993524051246,
                0.9999989322973846,
                0.9999991684721706
            ],
            [
                0.817574478416099,
                0.9999921107393127,
                0.999997739674896,
                0.5,
                0.9999785550490653,
                0.9999339478438791,
                0.9999885212346301,
                0.9998204720941564,
                0.46879062662624377,
                0.9999869928699903
            ],
            [
                0.9999869928684816,
                0.9999938558275997,
                0.9999974387187054,
                NaN,
                0.9999974387184085,
                0.9999687980929685,
                0.9999930377412775,
                0.9999724643203354,
                0.9999885212319797,
                0.9999910603047849
            ],
            [
                0.9996646500096982,
                0.9999930377446277,
                0.9999930377404601,
                0.9890130591404006,
                0.9999251537744334,
                0.9999852610163604,
                0.999993037742924,
                0.9999910603026424,
                0.9999832985821991,
                0.9999687980738715
            ],
            [
                0.9999038975620991,
                0.9999339478817992,
                0.7057850216484838,
                0.6791787056691698,
                0.5621765008857981,
                0.5621765008857981,
                NaN,
                0.9859363696896206,
                0.9995121429397742,
                0.999876605371534
            ],
            [
                0.9999998874647574,
                0.9999998362623528,
                0.9999997897566589,
                0.9999998144608097,
                0.9999997897566089,
                0.9999998362622552,
                0.9999998555020135,
                0.9999999123575045,
                0.9999998144609644,
                0.9999997617629764
            ],
            [
                0.9999992661788446,
                0.9999997617631184,
                0.9999987901341723,
                0.9999997617631184,
                0.9999987901347492,
                0.9999997617631183,
                0.9999994956524114,
                0.999999495652712,
                0.9999996940977366,
                0.999998790134605
            ],
            [
                NaN,
                0.999996273360272,
                0.999998005270041,
                0.9770226276646877,
                NaN,
                0.9999982396561573,
                NaN,
                0.9999898700078644,
                NaN,
                0.99999862904263
            ],
            [
                0.9999869928669104,
                0.8175744695262775,
                0.9999852610128248,
                0.9999646437536532,
                0.9999869928731351,
                0.9999724643122014,
                0.9999038975542908,
                NaN,
                0.8519527982093666,
                0.999968798074797
            ],
            [
                0.999959936289197,
                NaN,
                0.9999251537819589,
                0.9997694933153385,
                NaN,
                NaN,
                0.9999724643216433,
                NaN,
                0.9999885212277727,
                0.9999251538001214
            ],
            [
                0.9999998144609424,
                0.9999996533673375,
                0.9999996533674615,
                0.9999994284994167,
                0.9999996533673375,
                0.9999997300420937,
                0.9999991684717741,
                0.9999996072138465,
                0.999999730042126,
                0.9999974387184007
            ],
            [
                0.999999554914895,
                0.9999990577556308,
                0.999999352405279,
                0.9999993524054335,
                0.9999997300422225,
                0.999999887464744,
                0.99999976176309,
                0.9999992661792819,
                0.9999998724809419,
                0.9999992661786696
            ],
            [
                1.0,
                0.9999485577927487,
                0.5312093733737563,
                0.9999339478320198,
                0.9999945777829775,
                0.9999898700114783,
                0.9999251537695728,
                0.9999339478443289,
                0.9996646498907445,
                0.9999977396751671
            ],
            [
                0.9989677687274797,
                0.999985261018101,
                0.033085976958581766,
                NaN,
                0.012431649046622646,
                0.003172682483144392,
                0.03732688399755318,
                0.02595735889319258,
                0.6224593312018546,
                0.8354835330070839
            ],
            [
                0.5312093733737562,
                0.9999038975527442,
                0.22270012850745968,
                0.9998415637156607,
                0.9999852610165288,
                0.7310585844894971,
                0.9465966728366374,
                0.9999885212359807,
                0.6224593312018545,
                0.9999962733598308
            ],
            [
                0.9999986290432834,
                0.9999986290426298,
                0.9999967112517187,
                0.9999962733602717,
                0.9999982396569966,
                0.9999756997679619,
                0.9999994284996893,
                0.9999986290423029,
                0.9999938558268661,
                0.9999945777823231
            ],
            [
                0.9999998724809723,
                0.9999997897567341,
                0.999999653367379,
                0.9999999226558421,
                0.9999999123575568,
                0.999999939764258,
                0.999999554914789,
                0.9999998874648514,
                0.9999998144608538,
                0.999999814460854
            ],
            [
                0.9999910603005013,
                0.8519527982093666,
                NaN,
                0.9999989322970027,
                0.6513548646660542,
                NaN,
                0.9999756997535033,
                NaN,
                0.9999986290429567,
                NaN
            ],
            [
                0.9998415638138431,
                NaN,
                0.9999756997652363,
                0.9999852610164298,
                0.851952809486198,
                0.03732688868276006,
                0.8519527982093666,
                NaN,
                0.14804719239327382,
                NaN
            ],
            [
                0.9999995549147359,
                0.9999996940978095,
                0.999999266178757,
                0.9999992661788446,
                0.9999994956525918,
                0.9999998362622746,
                0.99999976176309,
                0.9999996940976636,
                0.9999995549147358,
                0.9999995549149481
            ],
            [
                0.9999952149060773,
                0.9890130564889699,
                0.9626731086399786,
                0.9999984465022457,
                NaN,
                0.999997438718404,
                0.9999974387177897,
                0.9999952149066471,
                0.9999984465022456,
                0.9999982396561574
            ],
            [
                0.9999599363036602,
                0.017986207165646678,
                0.9999599362887481,
                0.999954602142306,
                0.5312093733737562,
                0.9999151889913468,
                NaN,
                0.9991959138920836,
                0.24508500210441886,
                0.9997965730606333
            ],
            [
                0.9999974387171787,
                0.999999814460854,
                0.9999990577552937,
                0.9999998144608983,
                0.9999997617629764,
                0.9999997300422225,
                0.9999987901343166,
                0.9999996940977366,
                0.999999855502048,
                0.9999994284994848
            ],
            [
                0.9999980052693288,
                0.9999885212306221,
                0.962673111451103,
                0.999996273362054,
                0.9999974387177912,
                0.9999869928748851,
                0.9324533093296393,
                0.9999993524051248,
                NaN,
                0.9999977396748939
            ],
            [
                0.999993037740435,
                0.9999910603026367,
                0.9999952149043908,
                0.999997097686631,
                0.9999687980905584,
                0.9999989322973846,
                0.9999967112493665,
                0.9999984465028029,
                0.99999862904312,
                0.9999952149043654
            ],
            [
                0.9999999123575359,
                0.9999991684722698,
                0.9999990577549569,
                0.9999993524051246,
                0.99999976176309,
                0.9999996533673375,
                0.9999998362622747,
                0.9999997897565838,
                0.9999996940978825,
                0.9999997897566089
            ],
            [
                0.9999869928715381,
                0.9999724643022861,
                0.9999898700090238,
                0.9706877690896499,
                NaN,
                NaN,
                NaN,
                0.9999599363079457,
                NaN,
                NaN
            ],
            [
                0.9999996072138465,
                0.9999996940978095,
                0.999999789756684,
                0.9999999468421376,
                0.9999998362622552,
                0.9999998362622552,
                0.999999855501979,
                0.9999999123575672,
                0.9999998362622357,
                0.9999998724809419
            ],
            [
                8.939697368842181e-06,
                2.5612812945260317e-06,
                1.1478766751997141e-05,
                6.962254585938389e-06,
                4.78509449410676e-06,
                5.422220262333096e-06,
                1.892515048889829e-05,
                1.0129987352284668e-05,
                4.222831934156396e-06,
                7.8892654060075e-06
            ],
            [
                0.9998911030400431,
                0.9999785550465805,
                0.914900959053549,
                0.7057850340255386,
                0.9796676459153025,
                0.99984156385494,
                0.7549149868676283,
                0.9984988174291661,
                0.9998766053700798,
                0.04742587014823577
            ],
            [
                0.9999991684716749,
                0.9999995549150011,
                0.999999730042126,
                0.999999352405279,
                0.999999266178757,
                0.9999994956526519,
                0.9999996533672549,
                0.9999997617630617,
                0.9999996533673788,
                0.999995777164544
            ],
            [
                0.9999962733611611,
                0.9999989322972573,
                0.9999977396746245,
                0.9999996940978095,
                0.9999996072136125,
                0.999999495652712,
                0.9999852610180385,
                0.9998911031303208,
                0.9999485577744345,
                0.9999869928746405
            ],
            [
                0.9465966677520327,
                0.0,
                NaN,
                NaN,
                NaN,
                0.9999832985782006,
                0.999959936323197,
                0.9999810748519721,
                0.9999785550597448,
                0.8519528000888387
            ],
            [
                0.9999992661787571,
                0.9999991684716749,
                0.9999997300421581,
                0.999998446502801,
                0.9999921107364745,
                0.9999990577550691,
                0.9999993524054335,
                0.9999982396565769,
                0.9999994284992805,
                0.9999980052702787
            ],
            [
                0.9999869928670596,
                0.9999921107402364,
                0.9999967112497598,
                0.9999987901344627,
                0.9999970976876716,
                0.9999952149072315,
                0.9999962733611603,
                0.9999646437330526,
                0.9999982396565821,
                0.9999898700055075
            ],
            [
                0.999999352405279,
                0.9999997617631468,
                0.9999997617630617,
                0.9999997617630616,
                0.9999994956524715,
                0.9999992661792819,
                0.999999730042319,
                0.9999998555019274,
                0.9999991684719723,
                0.9999994284996893
            ],
            [
                0.9999952149032242,
                0.7057850340255386,
                0.2689414272294874,
                0.999986992868465,
                0.9999832985845791,
                NaN,
                NaN,
                NaN,
                0.9999251537642843,
                NaN
            ],
            [
                0.9999251537728575,
                0.999995777167563,
                0.9999832985703174,
                0.9999687980997952,
                0.9999599363221586,
                0.9999869928653495,
                0.9999921107345936,
                0.9999724643056297,
                0.9999687980849583,
                0.9999945777823259
            ],
            [
                0.9999957771680668,
                0.9999992661792819,
                0.9999986290427931,
                0.9999990577550691,
                0.9999993524052018,
                0.9999984465015047,
                0.99999862904312,
                0.9999996533674202,
                0.9999997897566589,
                0.9999993524054335
            ],
            [
                0.9999974387171977,
                0.9999967112517568,
                0.9999938558232084,
                NaN,
                0.2689414213699951,
                0.9999832985782017,
                0.9149009526726544,
                0.9999945777784651,
                0.8519527944504227,
                0.7772998560157665
            ],
            [
                0.9999993524054334,
                0.9999994956527121,
                0.9999994956526519,
                0.9999993524050474,
                0.9999994284994849,
                0.999999352404893,
                0.9999998362622942,
                0.9999991684720715,
                0.9999996533673375,
                0.9999996072139402
            ],
            [
                0.999664649816018,
                0.8175744739711883,
                0.9999251537671638,
                0.8670357683915537,
                0.999996711250544,
                0.9999756997621748,
                0.9995121429059415,
                0.9998911030766003,
                0.3486451217982255,
                0.999948557774137
            ],
            [
                3.7266388395620047e-06,
                2.9023109471452223e-06,
                5.422217030614265e-06,
                2.260324028281919e-06,
                4.222835458002318e-06,
                7.338208055489796e-07,
                5.715004470272272e-07,
                2.561281294644835e-06,
                7.338212429464139e-07,
                2.902312677084523e-06
            ],
            [
                0.9999810748585614,
                0.9999885212346207,
                0.9999989322971301,
                0.9820137871427651,
                0.9999952149060771,
                0.9999977396748938,
                0.9999910602995492,
                0.5312093733737562,
                NaN,
                0.9399133443558415
            ],
            [
                0.9993736659562223,
                0.9046505248181417,
                0.9999869928653405,
                0.9999869928761898,
                0.9999945777804015,
                0.9579122734360922,
                NaN,
                0.9149009602137116,
                0.9998766054279242,
                0.9999885212277717
            ],
            [
                0.9999998362623332,
                0.9999998555020135,
                0.9999994956525918,
                0.9999999226557961,
                0.9999997897566089,
                0.9999997897565587,
                0.9999997897565838,
                0.9999997617630616,
                0.9999998555019962,
                0.999999855502048
            ],
            [
                0.9999977396762411,
                0.99999893229713,
                0.9999977396757023,
                0.9999982396574163,
                0.9999986290423029,
                0.9999832985801483,
                0.9999832985741741,
                0.9999996533675028,
                0.9999952149032235,
                0.9999994956524715
            ],
            [
                0.9999996072136592,
                0.9999996072136125,
                0.9999989322971299,
                0.9999987901338839,
                0.9999994956524716,
                0.9999995549150011,
                0.9999991684721705,
                0.9999998362622552,
                0.9999995549150011,
                0.9999986290427931
            ],
            [
                0.904650541527608,
                0.9999687980877987,
                NaN,
                NaN,
                0.9999957771680706,
                0.9999996940978825,
                NaN,
                0.9999832985841355,
                0.9999885212318776,
                0.9999417087093018
            ],
            [
                0.9999910603026354,
                0.9999898700078736,
                0.8354835289107307,
                0.9999810748428879,
                0.9999938558232304,
                0.9998766054400844,
                0.9999810748478158,
                NaN,
                0.5926665999540698,
                NaN
            ],
            [
                2.3823693839154895e-07,
                1.0677031245851707e-06,
                1.5534979397394734e-06,
                2.6995774527577444e-07,
                1.444980726319581e-07,
                2.2603248367358324e-06,
                4.450849458179853e-07,
                5.7150044702099e-07,
                1.994729721436347e-06,
                1.2098659719661556e-06
            ],
            [
                0.9999999006880194,
                0.9999998724808963,
                0.9999998144608983,
                0.9999999123575359,
                0.9999998362623137,
                0.9999999397642653,
                0.9999998362623137,
                0.9999998362623137,
                0.9999997897566089,
                0.9999999123575568
            ],
            [
                0.9999994956527121,
                0.9999992661788446,
                0.9999991684717741,
                0.9999984465016899,
                0.9999999006880904,
                0.999999495652652,
                0.9999998362622746,
                0.9999995549147358,
                0.9999980052700408,
                0.9999994284997573
            ],
            [
                2.2603237589542675e-06,
                3.927861534406222e-07,
                1.76034300345598e-06,
                1.7603427935967163e-06,
                2.90231163910023e-06,
                1.994729245878497e-06,
                1.0677026154774503e-06,
                5.043476486764593e-07,
                9.422444815628016e-07,
                1.3709568799823232e-06
            ],
            [
                0.9999996940978095,
                0.999999730042319,
                0.9999999317439708,
                0.9999997617630333,
                0.9999997300421903,
                0.9999997897566089,
                0.9999998144608981,
                0.9999998724809875,
                0.9999999123575881,
                0.9999998724810027
            ],
            [
                0.9579122677288677,
                NaN,
                0.9999989322967482,
                0.9999997897566589,
                0.9999910603005019,
                0.999992110735552,
                0.9999599363031364,
                0.9999998724809723,
                0.999994577780384,
                0.9999997617629764
            ],
            [
                NaN,
                0.9999945777823449,
                0.999915188949517,
                0.9999832985802396,
                0.9999898700114467,
                0.9999994284996213,
                0.999983298574185,
                0.999996711251327,
                0.8175744850834648,
                0.9999910603049348
            ],
            [
                0.9999994284994168,
                0.9999996533672962,
                0.9999998144609645,
                0.9999997897566589,
                0.999999887464811,
                0.9999998362623137,
                0.999999855502048,
                0.9999999317440034,
                0.9999998724809723,
                0.9999998144608097
            ],
            [
                0.9999852610110065,
                0.9999869928726067,
                0.9999991684718732,
                0.9999938558261311,
                0.9999417087067342,
                0.9999687980812105,
                0.9999938558261402,
                0.9999982396574163,
                0.9999938558275956,
                0.9999810748450007
            ],
            [
                0.9999987901344608,
                0.9999995549150011,
                0.9999996940978095,
                0.9999992661788445,
                0.9999997300422869,
                0.9999997300422225,
                0.999996273358939,
                0.9999997300422868,
                0.999998790134028,
                0.9999994956525918
            ],
            [
                0.9999994956524716,
                0.999999900688043,
                0.9999999317439953,
                0.999999730042126,
                0.9999992661790196,
                0.9999998144608319,
                0.999999694097773,
                0.9999994956527721,
                0.9999997300422547,
                0.9999996533674615
            ],
            [
                NaN,
                0.999993855825399,
                0.9999869928699935,
                0.9999930377454244,
                0.9999151889794307,
                0.99997855505931,
                0.9999977396759719,
                0.999997097686977,
                0.9999832985821435,
                0.43782349911420193
            ],
            [
                8.93969310662177e-06,
                1.760343842833246e-06,
                1.2098662603631479e-06,
                4.78509563550957e-06,
                7.338207180661203e-07,
                1.7603434231705793e-06,
                1.370957860466977e-06,
                5.043472879481655e-07,
                4.785092783371756e-06,
                1.2098662603961589e-06
            ],
            [
                0.9999998724810027,
                0.9999998362623332,
                0.9999980052707541,
                0.9999999226558053,
                0.9999998144608319,
                0.9999997300421581,
                0.9999998555019446,
                0.9999999123575464,
                0.9999998144609202,
                0.9999996940977731
            ],
            [
                0.9999982396559487,
                0.9999994284997573,
                0.9999945777784456,
                0.9999962733616046,
                0.9999930377420911,
                0.9999970976873299,
                0.999985261012762,
                0.9999980052695658,
                0.99999893229713,
                0.9999957771675646
            ],
            [
                0.9998766053736059,
                0.9706877723755188,
                0.9998766053744677,
                0.9999984465020646,
                0.8175744806385543,
                0.9999756997653012,
                0.9999151889817285,
                0.9999980052705317,
                0.8670357666736772,
                0.9999984465024306
            ],
            [
                0.9999962733620503,
                0.9999994284995529,
                0.9999986290427932,
                0.9999970976880151,
                0.999997438718095,
                0.9999997300422225,
                0.9999974387165685,
                0.9998911030474331,
                0.9999991684715758,
                0.9999962733589404
            ],
            [
                0.9999998362622747,
                0.9999994956523512,
                0.9999990577555183,
                0.9999989322968755,
                0.999999814460876,
                0.9999994956525918,
                0.9999996940977731,
                0.9999990577549568,
                0.9999986290424663,
                0.9999997300422547
            ],
            [
                0.932453310268176,
                0.679178699175393,
                NaN,
                0.9980732649560948,
                0.9999646437518945,
                0.9999724642990853,
                0.9999967112509439,
                0.8670357701094303,
                0.9999687980775065,
                0.9999832985841604
            ],
            [
                0.9996646498734362,
                0.9999756997517221,
                0.9399133557169235,
                0.9999898700042195,
                0.9998415637990439,
                0.999993037740476,
                0.9999974387174861,
                0.9999945777810428,
                0.9999938558240066,
                0.9999930377446649
            ],
            [
                0.012431651836505122,
                0.0013250223021389195,
                0.9999546021512885,
                0.002472622598435702,
                0.9999810748563934,
                0.01098694352115014,
                0.22270013882530884,
                0.18242552158390105,
                0.053403335449385296,
                0.0010322311527168157
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999921107365005
            ],
            [
                0.9999980052700407,
                0.9999997897567341,
                0.9999998362622552,
                0.999999694097773,
                0.9999982396572065,
                0.9999997300421581,
                0.999999266178757,
                0.9999995549147889,
                0.9999996940978095,
                0.999999352404893
            ],
            [
                0.9999998362622747,
                0.9999999226557869,
                0.9999997300422547,
                0.9999998362623137,
                0.9999999123575672,
                0.9999998724810026,
                0.9999999123575255,
                0.9999996940978095,
                0.999999694097846,
                0.9999998144608538
            ],
            [
                0.8519527963298946,
                NaN,
                0.9999980052705189,
                0.9999977396757035,
                0.9999810748541595,
                0.999769493176247,
                0.6791786926816161,
                0.9999885212333479,
                0.9999852610134816,
                0.9999910603058524
            ],
            [
                0.5926665999540698,
                0.9998766054511566,
                0.9997040430199736,
                0.9990889488751116,
                0.9999485577804095,
                0.0009110512988808512,
                0.6224593312018546,
                0.9992903294526255,
                0.914900952092573,
                0.01243165309423923
            ],
            [
                0.9999938558268656,
                NaN,
                0.9999930377454104,
                NaN,
                0.8354835391516133,
                NaN,
                0.9999756997505934,
                0.9796676476961953,
                0.9999599362995998,
                0.9999832985782204
            ],
            [
                0.9999921107336536,
                0.9999982396565769,
                0.9999945777784451,
                0.8933094124452287,
                0.9999687980785628,
                0.9998911030923565,
                0.9999646437366789,
                0.9999945777816768,
                0.999993037742097,
                0.9999832985824336
            ],
            [
                0.9999989322968755,
                0.9999997300422547,
                0.9999997300421903,
                0.9999999226557131,
                0.9999996072136125,
                0.999999789756684,
                0.9999997897566338,
                0.9999998144608538,
                0.999999694097846,
                0.9999999530883564
            ],
            [
                0.9999599363222054,
                0.06754669254743426,
                0.7549149758396752,
                0.7057850278370112,
                0.3486451285660856,
                0.8519528076067262,
                0.40733340004593027,
                0.9999724643163278,
                0.798186787341014,
                0.5621765008857981
            ]
        ]
    },
    {
        "q_id": "8492_mmlu_math",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            7,
            8,
            9,
            10,
            12,
            13,
            14,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            28,
            29,
            31,
            32,
            33,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            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": [
            [
                0.9986749778825652,
                0.9992903294603446,
                0.9991959142472738,
                0.9995694429684766,
                0.9997040430079959,
                0.9986749776350093,
                0.9998766054105537,
                0.989013057015208,
                0.999820471970005,
                0.9971990727669001
            ],
            [
                0.9998415637837214,
                0.9990889488780785,
                0.9980732649587811,
                0.9988304897318168,
                0.9999785550475816,
                0.9992903294482086,
                0.9770226318880316,
                0.9995121428220125,
                0.9978172834167253,
                0.9997388096692921
            ],
            [
                1.012999581021488e-05,
                4.4508505193791187e-07,
                7.889262585541864e-06,
                4.785092783415276e-06,
                2.260325375634003e-06,
                1.7603434231241496e-06,
                2.5612819053399912e-06,
                2.5612822106654943e-06,
                1.0677028700266676e-06,
                8.93969310675186e-06
            ],
            [
                1.0129988564578197e-05,
                4.785092783319532e-06,
                2.4300243628620005e-05,
                1.8925155008528632e-05,
                4.2228329411708495e-06,
                3.120192252686752e-05,
                1.4738980214280206e-05,
                1.4738978457872657e-05,
                9.61024264149151e-05,
                9.422443692446175e-07
            ],
            [
                1.5534971989568904e-06,
                4.222833444506298e-06,
                2.5612816000331606e-06,
                7.338210679949506e-07,
                2.9023123311055552e-06,
                1.9947306726213275e-06,
                1.7603425837366772e-06,
                3.927860597935108e-07,
                1.2098662604247682e-06,
                1.5534979397592542e-06
            ],
            [
                3.7266406167827664e-06,
                2.5612822106841303e-06,
                5.422220262505697e-06,
                8.939696304002375e-06,
                2.7535694382378416e-05,
                1.4738983727256784e-05,
                5.422221555192784e-06,
                4.2228349547223175e-06,
                3.288749457432399e-06,
                2.4300249421225448e-05
            ],
            [
                0.9997388097847384,
                0.999991060302631,
                0.9999038975736865,
                0.9996646500107031,
                0.9995121429524331,
                0.999915188948652,
                0.9999038975508551,
                0.9999339478711182,
                0.9988304894716684,
                0.9997694932303799
            ],
            [
                0.9999687980737504,
                0.9998204720558539,
                0.9998766053664531,
                0.9994472214536338,
                0.9999417087275647,
                0.9997040429359567,
                0.9999687980960733,
                0.9995121428843703,
                0.9991959140559061,
                0.999941708727552
            ],
            [
                0.9993736658990929,
                0.9953904280748818,
                0.99640639657905,
                0.9947798751503658,
                0.9706877661217682,
                0.9959298629523111,
                0.9992903295368345,
                0.9933071499518102,
                0.9992903297080182,
                0.9964063981797425
            ],
            [
                2.2603251062147097e-06,
                6.962255419804982e-06,
                4.785095065132354e-06,
                1.3007128463069061e-05,
                8.939693106987645e-06,
                5.422220908703723e-06,
                4.222832437747125e-06,
                8.93970056668775e-06,
                6.962258739454786e-06,
                1.0129990979842057e-05
            ],
            [
                2.430025231469984e-05,
                0.7772998508568417,
                2.1444950969026795e-05,
                3.535625913514915e-05,
                2.430023203740195e-05,
                1.147877223059538e-05,
                1.0129987357158383e-05,
                2.7535704228438656e-05,
                7.889260704631679e-06,
                1.6701421842961097e-05
            ],
            [
                0.999447221255861,
                0.16451646289656316,
                0.9924227595480334,
                0.9997040428908958,
                0.6224593312018546,
                0.9982992777283057,
                0.9964063976436773,
                0.9988304894582054,
                0.9990889487765653,
                0.9933071476733436
            ],
            [
                2.260325375664839e-06,
                3.7266397283231055e-06,
                3.288750633518874e-06,
                4.78509563550957e-06,
                2.9023109472244114e-06,
                2.9023112931873767e-06,
                6.144176799166453e-06,
                4.222834451254188e-06,
                3.726638839806038e-06,
                4.222833947897496e-06
            ],
            [
                0.9998204720784973,
                0.9996200155200596,
                0.9995121428326562,
                0.9996200154770897,
                0.9991959140750335,
                0.9997040429390825,
                0.999512142828569,
                0.9992903295571438,
                0.9990889487443523,
                0.9995694429203037
            ],
            [
                0.9999599362934862,
                0.9999687980923528,
                0.9998204720773533,
                0.9995121428858179,
                0.9999251537460951,
                0.9998415638024325,
                0.9999417087136322,
                0.9993736658258594,
                0.9999339478711234,
                0.9996646498521764
            ],
            [
                0.9996646499303471,
                0.9999151889182842,
                0.9997040428305244,
                0.9999687980997913,
                0.9999038975965836,
                0.9999724642990595,
                0.9999910603026306,
                0.999933947839665,
                0.9998766053812794,
                0.9999646437324408
            ],
            [
                0.9997694932309433,
                0.9999151889285935,
                0.9999687980849129,
                0.9999417087136483,
                0.9988304897378002,
                0.999992110737415,
                0.9999485577740902,
                0.9999546021097568,
                0.9999724643121954,
                0.9999485577864075
            ],
            [
                0.9999962733607161,
                0.9999910603058279,
                0.999988521229139,
                0.9999339478240112,
                0.9998911031042987,
                0.9999962733620493,
                0.9999869928746399,
                0.9999599362983224,
                0.999941708748388,
                0.9999251537996128
            ],
            [
                0.996827316507314,
                0.9999151889284437,
                0.998299277510887,
                0.9994472214533443,
                0.9997388097843887,
                0.9997694931770182,
                0.9875683482320986,
                0.9975273769674095,
                0.9998204719914993,
                0.9997388096294927
            ],
            [
                6.962255419570695e-06,
                1.473897670007122e-05,
                2.2603237589542675e-06,
                5.144223204748698e-05,
                2.4300232040584407e-05,
                1.892514372737249e-05,
                7.889261644875049e-06,
                2.7535697662094155e-05,
                1.0129995810076682e-05,
                5.829129331925442e-05
            ],
            [
                6.9622537593854575e-06,
                6.96225375833433e-06,
                5.422221554758815e-06,
                4.7850939242083995e-06,
                6.475947210012481e-07,
                7.338208930443633e-07,
                2.2603251061664e-06,
                2.5612825159421147e-06,
                1.553498495295912e-06,
                2.9023133690425823e-06
            ],
            [
                1.1478772229989872e-05,
                1.6701421843720577e-05,
                1.0129995809929273e-05,
                8.939694172290508e-06,
                1.1478765388898939e-05,
                1.300712691403299e-05,
                1.4738983728490028e-05,
                2.144494840687132e-05,
                1.892515275165658e-05,
                3.7266406167827664e-06
            ],
            [
                7.889266347456862e-06,
                2.902311293147782e-06,
                6.9622587396067566e-06,
                5.422218323019487e-06,
                8.939693106873817e-06,
                2.9023126771227976e-06,
                4.22283294098842e-06,
                1.6701429808632785e-05,
                6.1441767989541075e-06,
                1.8925155007633607e-05
            ],
            [
                0.9999724643089131,
                0.9999756997621777,
                0.9999151889688949,
                0.9999756997592754,
                0.9999599363030427,
                0.9998911031038139,
                0.999993855822469,
                0.999975699762171,
                0.9999687980997993,
                0.9998601778763104
            ],
            [
                0.9999151889488002,
                0.999975699747687,
                0.9999151889385431,
                0.999447221328442,
                0.999933947863251,
                0.9990889488890987,
                0.9997040428316094,
                0.9999756997621702,
                0.9998204720135786,
                0.9999485577986424
            ],
            [
                0.9980732651839936,
                0.9998204720347122,
                0.998830489874198,
                0.9997388096606815,
                0.9999151889890027,
                0.9999832985801496,
                0.999704042867517,
                0.9999038975395677,
                0.999290329628804,
                0.9996200155142007
            ],
            [
                3.2887506335906595e-06,
                2.26032402841657e-06,
                8.939698435226916e-06,
                1.147877359926923e-05,
                3.2887482810801374e-06,
                2.4300246525276163e-05,
                8.939697369785323e-06,
                8.939697369671496e-06,
                1.0129990979215566e-05,
                6.605214464752619e-05
            ],
            [
                6.962254589781966e-06,
                1.8925150496609267e-05,
                2.4300249423965898e-05,
                1.8925155007633607e-05,
                2.2603251062270446e-06,
                1.1478770862255766e-05,
                6.9622587396067566e-06,
                4.222831934321543e-06,
                8.939695238333382e-06,
                1.670141586949968e-05
            ],
            [
                0.9999417087067299,
                0.9999038976080584,
                0.9999599363221651,
                0.999088948687238,
                0.999796573027361,
                0.9999599363173831,
                0.9998415637080859,
                0.999738809566689,
                0.9999151889285072,
                0.9997965729542457
            ],
            [
                0.9996200155609736,
                0.998967769089651,
                0.9989677687991458,
                0.9995121428826957,
                0.9988304897224335,
                0.9982992774940863,
                0.9997040429358706,
                0.34864514210180597,
                0.9982992775023879,
                0.9997694932585831
            ],
            [
                3.288750633569722e-06,
                1.4738985484871391e-05,
                3.288747889229516e-06,
                2.1444953524161264e-05,
                1.8925155008941717e-05,
                6.1441760667392215e-06,
                1.300713466619476e-05,
                6.962259569484628e-06,
                4.006370174184034e-05,
                2.1444945854624007e-05
            ],
            [
                1.4738987242137685e-05,
                2.561282210701601e-06,
                8.939698435226916e-06,
                1.1478772230929451e-05,
                1.9947301970587145e-06,
                4.22283344433731e-06,
                5.422217676979575e-06,
                6.144176066795103e-06,
                1.300712846361323e-05,
                1.9947297214944016e-06
            ],
            [
                1.8925155008528632e-05,
                1.3007133115903994e-05,
                4.2228324377164004e-06,
                1.0677029973114952e-06,
                4.785094494628999e-06,
                2.5612831266946347e-06,
                3.7266392839425286e-06,
                6.962253759670401e-06,
                5.4222202623972055e-06,
                3.288748281220719e-06
            ],
            [
                0.9992903295458333,
                0.9997694932301049,
                0.9989677688049078,
                0.9975273769553497,
                0.9991959141648248,
                0.9984988179723793,
                0.9997694931767768,
                0.9999724642957943,
                0.9997694932591733,
                0.9991959142488639
            ],
            [
                0.9994472214537946,
                0.9980732655771081,
                0.9988304897579268,
                0.9996646498504494,
                0.9994472213276703,
                0.9994472213319151,
                0.9999151889789512,
                0.9947798741565181,
                0.9996200154254749,
                0.998830490004612
            ],
            [
                0.9992903295607763,
                0.9990889486628662,
                0.9997388097871854,
                0.9971990731844024,
                0.999820472056068,
                0.9998766054400844,
                0.999903897585194,
                0.9991959139987576,
                0.9998601779100326,
                0.9996646498913104
            ],
            [
                0.00010889689607832474,
                2.902311293147782e-06,
                8.939700566565793e-06,
                2.1444956075707356e-05,
                1.3007134665130082e-05,
                3.726640172537657e-06,
                0.939913349615602,
                6.144176066672166e-06,
                1.300713466685723e-05,
                2.9023116389365734e-06
            ],
            [
                0.9999151889183534,
                0.999769493286337,
                0.9996200155631845,
                0.999738809568209,
                0.9998911030781548,
                0.9998601778764243,
                0.9999546021476443,
                0.999841563784104,
                0.9998415637270507,
                0.999941708748396
            ],
            [
                4.785093924251918e-06,
                6.962257079629686e-06,
                6.962257909323729e-06,
                7.889266347356409e-06,
                2.5612815999423112e-06,
                4.222831934156396e-06,
                1.3709572068354007e-06,
                3.7266379512857925e-06,
                8.93969736955767e-06,
                0.8519527982093666
            ],
            [
                0.9993736659811072,
                0.9999785550567096,
                0.9999151889691188,
                0.9998415637836361,
                0.9996200154290014,
                0.9995121429453657,
                0.999972464299064,
                0.9999921107402361,
                0.9999546021313986,
                0.9992903296308266
            ],
            [
                0.9999339478711133,
                0.8807970748488297,
                0.9999251537371326,
                0.9997965730278168,
                0.9997694933401279,
                0.9988304897172658,
                0.9997694932025857,
                0.9998601778594738,
                0.9999546021151331,
                0.9997694932858139
            ],
            [
                5.422217676866151e-06,
                8.939696304002375e-06,
                3.2887486733420804e-06,
                5.422218969769604e-06,
                3.7266401725681614e-06,
                2.5612825160562587e-06,
                3.7266388396975786e-06,
                1.8925141472773765e-05,
                4.2228334445658276e-06,
                1.7603440527222532e-06
            ],
            [
                1.2098658277264215e-06,
                2.9023109469842055e-06,
                1.9947306726213275e-06,
                1.994729008105057e-06,
                1.0129988564099116e-05,
                2.902312677060767e-06,
                2.5612812946890944e-06,
                3.2887482811579057e-06,
                1.2098653950480359e-06,
                1.7603438428660665e-06
            ],
            [
                1.670141985166528e-05,
                3.535625913206225e-05,
                4.0063692172075196e-05,
                4.006368262111344e-05,
                1.3007123811797321e-05,
                1.892515275165658e-05,
                2.753568453191415e-05,
                0.0010322311992936874,
                4.0063677853357896e-05,
                1.473898899908247e-05
            ],
            [
                0.9991959142549903,
                0.9999852610180298,
                0.9999756997563805,
                0.9995694430166496,
                0.9998601778931797,
                0.999933947863225,
                0.9998601779766366,
                0.999891103039086,
                0.9999038975625899,
                0.9999485577802578
            ],
            [
                7.889266346746518e-06,
                2.753569108453202e-05,
                1.8925145983348442e-05,
                8.481108174040254e-05,
                5.144222589744581e-05,
                1.6701415868193372e-05,
                3.726641061027928e-06,
                1.4738980212296288e-05,
                5.422217676797111e-06,
                3.120191881094355e-05
            ],
            [
                0.9997388096287858,
                0.9996200153958148,
                0.9980732653823419,
                0.9978172834719985,
                0.999796572954595,
                0.9990889486628662,
                0.46879062662624377,
                0.998073265590988,
                0.9994472213894782,
                0.6791786926816161
            ],
            [
                6.144175334367959e-06,
                7.889264466344872e-06,
                1.2098662604192665e-06,
                3.726639728262097e-06,
                1.994729483694599e-06,
                4.0063696959216535e-05,
                3.1201918809808464e-05,
                1.8925157264023994e-05,
                2.144495608105136e-05,
                3.288750241473551e-06
            ],
            [
                0.9999756997679652,
                0.9998766053667189,
                0.9953904282180343,
                0.9995694429669987,
                0.9997040427640738,
                0.9995121427696172,
                0.9986749775944945,
                0.9998911030780502,
                0.9982992772474149,
                0.9991959140684862
            ],
            [
                7.889266347456862e-06,
                4.006370650653807e-05,
                2.4300240730549767e-05,
                1.2098661161982042e-06,
                5.422218323349895e-06,
                3.2887490652810324e-06,
                7.889264466545779e-06,
                2.2603251062270446e-06,
                4.785096205973894e-06,
                2.561281294616881e-06
            ],
            [
                1.4738983728490028e-05,
                1.6701429805655623e-05,
                9.610239198289712e-05,
                6.6052152530647e-05,
                4.7850967763512445e-06,
                7.889263526093993e-06,
                4.785095065045315e-06,
                7.889263525778283e-06,
                7.484624503872184e-05,
                0.00012339460431414831
            ],
            [
                1.6701427813417103e-05,
                0.0002959571316304878,
                2.7535700933696396e-05,
                6.144175334367959e-06,
                1.147877223059538e-05,
                2.7535697655983693e-05,
                6.962259569484628e-06,
                1.6701421842140854e-05,
                5.144220138599094e-05,
                1.0129987357158383e-05
            ],
            [
                7.338212429537553e-07,
                8.315283250343497e-07,
                7.88926258532661e-06,
                8.939694172420599e-06,
                2.902311293147782e-06,
                4.785093924047376e-06,
                6.962256249517824e-06,
                3.7266379513434106e-06,
                5.422219615967477e-06,
                2.5612828213818346e-06
            ],
            [
                3.120190765307203e-05,
                2.4300232036606334e-05,
                6.144177531660828e-06,
                2.9023116391675407e-06,
                2.2603234894745224e-06,
                1.0129987356541108e-05,
                4.006370651382533e-05,
                2.2603251061849014e-06,
                4.785093924156175e-06,
                5.8291293334097926e-05
            ],
            [
                0.9982992778925557,
                0.9990889489999898,
                0.9953904279295926,
                0.9992903297045509,
                0.9997040427963476,
                0.9975273772826886,
                0.9996646498131788,
                0.999447221467719,
                0.999620015518302,
                0.9999038976195121
            ],
            [
                0.9996200155668878,
                0.999569442914855,
                0.9999417087345216,
                0.9999810748472692,
                0.9997388096929878,
                0.9999151889688683,
                0.9998766054105878,
                0.9999485577925789,
                0.9999898700066052,
                0.9999485577802993
            ],
            [
                0.9997965729789262,
                0.9998911031169858,
                0.9998415637266933,
                0.9999832985781634,
                0.9999546021151405,
                0.9999852610233015,
                0.9999724642990652,
                0.9995121428836323,
                0.9998204720768701,
                0.9997965729783551
            ],
            [
                1.892514147143123e-05,
                1.473898372822193e-05,
                4.7850950649408664e-06,
                1.1478772229989872e-05,
                2.7535681254003062e-05,
                0.9241418205010699,
                1.1478764019787597e-05,
                5.1442219775101506e-05,
                1.0129992185981682e-05,
                1.4738988999940381e-05
            ],
            [
                0.9999038975851088,
                0.9924227594324776,
                0.9998601779760731,
                0.9999810748585295,
                0.9999756997650621,
                0.9999756997476967,
                0.9999885212264013,
                0.9998766053812794,
                0.9997040427946599,
                0.9998766054104549
            ],
            [
                1.0677031245905116e-06,
                3.726638395493353e-06,
                3.726641061027928e-06,
                1.8925150495232307e-05,
                2.561283431986506e-06,
                3.726641061058432e-06,
                4.785092783149804e-06,
                7.889259764273619e-06,
                1.7603440527046419e-06,
                3.2887502415243994e-06
            ],
            [
                1.1478765388314311e-05,
                2.5612834320214477e-06,
                6.962254589705982e-06,
                1.6701423834591316e-05,
                6.1441746017453204e-06,
                1.6701417861189946e-05,
                7.889264466230069e-06,
                8.939694172420599e-06,
                8.939696304002375e-06,
                7.88925976397226e-06
            ],
            [
                0.9990889486624953,
                0.9998766054547905,
                0.6513548646660543,
                0.9990889486914235,
                0.9996200154733421,
                0.9994472214664327,
                0.999664649851708,
                0.9982992779431549,
                0.9998415637643255,
                0.9914225151565198
            ],
            [
                0.9992903296330969,
                0.9999417087557543,
                0.9999251537995529,
                0.7057850216484838,
                0.6791787056691698,
                0.9997388096596329,
                0.9999785550465308,
                0.9991959138783811,
                0.9971990725204307,
                0.9997694933677074
            ],
            [
                0.9998601779761361,
                0.9999957771650455,
                0.9999485577618361,
                0.9999546021097627,
                0.9997965730280062,
                0.9998766053960377,
                0.9997040429023138,
                0.9999546021206008,
                0.9999599363078994,
                0.9999599363221917
            ],
            [
                5.422218969661113e-06,
                7.889266347356409e-06,
                1.2098661161927025e-06,
                4.222832941072913e-06,
                2.9023119851055122e-06,
                6.962256249606473e-06,
                3.726637951028202e-06,
                4.222835458044565e-06,
                3.288747889229516e-06,
                6.1441767989541075e-06
            ],
            [
                3.120190764966677e-05,
                7.88926164518358e-06,
                0.00010889689614645761,
                3.726639284050988e-06,
                3.120190764467241e-05,
                4.006370651207639e-05,
                7.889261645090304e-06,
                1.6701423834591316e-05,
                1.6701421843356024e-05,
                1.670142781636389e-05
            ],
            [
                0.9998601778595816,
                0.9999151889487143,
                0.9998601778595592,
                0.9997040429036314,
                0.9999038976082275,
                0.9999038975737515,
                0.999948557761846,
                0.9999756997650714,
                0.9997965730270946,
                0.9998601778760724
            ],
            [
                0.9994472213253549,
                0.9998415638211505,
                0.9999869928684375,
                0.9996200155609736,
                0.9998911031298644,
                0.9998766054693442,
                0.998967769048356,
                0.9999646437493104,
                0.9996646498921203,
                0.9989677690514772
            ],
            [
                0.999512142833167,
                0.9975273764384985,
                0.999195914255645,
                0.9993736657583825,
                0.9997694933683847,
                0.9991959139763565,
                0.9997965730276775,
                0.9988304895048499,
                0.999664649735613,
                0.9996200154778857
            ],
            [
                0.9998766054547045,
                0.9999599363078342,
                0.9999832985801496,
                0.9999785550439201,
                0.9999646437577411,
                0.9999151889492061,
                0.9999785550515996,
                0.9999599363126119,
                0.9998911030390591,
                0.9999417087137148
            ],
            [
                2.260323758923431e-06,
                2.2603234895053587e-06,
                1.0129987357020188e-05,
                5.422218969818919e-06,
                7.338209805200689e-07,
                4.22283545808297e-06,
                1.012999339449843e-05,
                1.892515049702235e-05,
                5.144223816721283e-05,
                5.422220908925639e-06
            ],
            [
                0.9998204719489601,
                0.9999687980737855,
                0.9999251537639581,
                0.9999546021205493,
                0.9996200154284596,
                0.9986749774290464,
                0.999769493257624,
                0.9999151889789432,
                0.9996646499720179,
                0.9997694932304871
            ],
            [
                0.9992903296228185,
                0.9986749778388154,
                0.9995694428603443,
                0.998299277900857,
                0.9988304899084673,
                0.999290329628061,
                0.9998415637455221,
                0.9996646497702103,
                0.9992903296188558,
                0.9997694932031357
            ],
            [
                0.9999756997679594,
                0.9999832985761689,
                0.99997569975349,
                0.9999646437577528,
                0.9999952149043646,
                0.9999852610215443,
                0.9999038975737402,
                0.999959936317411,
                0.9999869928715396,
                0.9999646437535344
            ],
            [
                0.9999485577740995,
                0.9999756997476837,
                0.9999151889790031,
                0.999978555046477,
                0.999993855822469,
                0.9999646437366584,
                0.999933947831744,
                0.9999952149060758,
                0.9996646499712081,
                0.9997965730515117
            ],
            [
                3.288750633518874e-06,
                4.222834954753043e-06,
                4.006371129120346e-05,
                7.88926352599354e-06,
                5.422221555133606e-06,
                3.2887490653872164e-06,
                1.4738988999672284e-05,
                4.222832941034507e-06,
                1.0677031245851707e-06,
                4.222834451327159e-06
            ],
            [
                0.999925153790678,
                0.999995214906076,
                0.9999151889892037,
                0.9996200155630407,
                0.9998204720770059,
                0.9999546021260151,
                0.9982992777101215,
                0.9999921107345933,
                0.9994472214700023,
                0.9997965730527784
            ],
            [
                1.473898197063434e-05,
                7.889265407090955e-06,
                6.605216041280767e-05,
                1.0129989771823107e-05,
                3.535625913514915e-05,
                4.006370650653807e-05,
                1.147876949310201e-05,
                4.0063696957321844e-05,
                5.1442238170207006e-05,
                0.00013982204065167932
            ],
            [
                0.9996646499726131,
                0.9995121428380489,
                0.4378234991142019,
                0.8807970842359877,
                0.08509905370824053,
                0.7549149923816048,
                0.5621765008857982,
                0.3208213073183839,
                0.32082130731838393,
                0.08509904442693891
            ],
            [
                0.9997040430093133,
                0.9997694932595356,
                0.9998204719717002,
                0.9999756997505924,
                0.9999417087554314,
                0.9999417087275736,
                0.9999038975967038,
                0.9999546021476268,
                0.9999869928761915,
                0.9998204719703524
            ],
            [
                2.1444953521586782e-05,
                1.3007130014376633e-05,
                7.889266347456862e-06,
                6.144173869379821e-06,
                4.78509506499309e-06,
                1.1478768125201194e-05,
                2.4300232033865884e-05,
                1.8925143727854426e-05,
                3.1201915085825835e-05,
                1.3007128463873485e-05
            ],
            [
                0.9998911030650431,
                0.9999938558239332,
                0.999985261016273,
                0.9999339478790019,
                0.9999646437619537,
                0.999820472055611,
                0.9999852610233051,
                0.999903897619545,
                0.9999485577802313,
                0.9999810748472588
            ],
            [
                0.9999339478397439,
                0.9998415637459024,
                0.999933947839654,
                0.999447221399801,
                0.9992903297219292,
                0.9998204720987822,
                0.9999151889185471,
                0.99987660541069,
                0.9997388097233559,
                0.9997694933133399
            ],
            [
                0.9997388096919465,
                0.999860177893019,
                0.9997388096599749,
                0.999903897573785,
                0.9998204719490306,
                0.999704042901401,
                0.9999724643122518,
                0.9998204720572695,
                0.9993736657513141,
                0.9999546021260356
            ],
            [
                2.1444940743772097e-05,
                4.785096205930373e-06,
                5.8291251623852595e-05,
                4.5397863219323224e-05,
                1.1478770861859053e-05,
                1.3007134666431358e-05,
                2.144495352474637e-05,
                0.9465966739665495,
                5.422219616085833e-06,
                1.670142980687079e-05
            ],
            [
                0.9988304899213863,
                0.9998766053812275,
                0.1480471999111614,
                0.9978172838071877,
                0.9990889486056458,
                0.9994472213271879,
                0.9947798734963709,
                0.9940889320987197,
                0.9995121429435492,
                0.34864513533394575
            ],
            [
                5.422221555192784e-06,
                1.3007126913583456e-05,
                6.962255419868303e-06,
                2.26032402841657e-06,
                2.9023119851055122e-06,
                3.7266379512518984e-06,
                2.5612825160562587e-06,
                6.144176066795103e-06,
                2.5612828213818346e-06,
                1.5534979397677313e-06
            ],
            [
                6.962255419728997e-06,
                1.300712846411008e-05,
                1.1478765389065974e-05,
                1.300712846477255e-05,
                3.12019002110123e-05,
                2.1444945855248125e-05,
                4.006370173294989e-05,
                1.147876402018431e-05,
                2.7535700945316292e-05,
                8.939696304002375e-06
            ],
            [
                0.9995121428867828,
                0.9999038975392328,
                0.999796573099902,
                0.99997569975928,
                0.9996646500122057,
                0.9992903296372249,
                0.9993736657565971,
                0.9997694932575704,
                0.9990889489905589,
                0.9982992778478861
            ],
            [
                0.7772998560157665,
                0.999985261023348,
                0.3775406687981454,
                0.4378234991142019,
                0.2942149659744614,
                0.9984988178566868,
                0.6791786926816161,
                0.6224593382055109,
                0.9994472213241329,
                0.2942149721629888
            ],
            [
                5.144220136091472e-05,
                4.78509563550957e-06,
                1.4738981969615573e-05,
                4.785096776394765e-06,
                1.147877223059538e-05,
                5.422217677078203e-06,
                8.939698435226916e-06,
                2.430023493228869e-05,
                1.8925143725341476e-05,
                3.726639284103523e-06
            ],
            [
                1.14787708624228e-05,
                2.2603234895053587e-06,
                7.889263525893087e-06,
                7.889263525893087e-06,
                8.939700566801578e-06,
                1.0129994602222992e-05,
                1.5534975693792215e-06,
                1.892514372737249e-05,
                6.1441760667392215e-06,
                2.5612825160562587e-06
            ],
            [
                1.6701425824307884e-05,
                6.962257079553702e-06,
                7.88926164518358e-06,
                7.889265407090955e-06,
                3.288749457409966e-06,
                8.939695238211425e-06,
                1.8925148238291944e-05,
                2.4300246523066122e-05,
                0.9997694932849286,
                1.4738987242700688e-05
            ],
            [
                0.9999546021259963,
                0.9995121428940773,
                0.9999251537906448,
                0.9984988178828615,
                0.9984988177783373,
                0.9975273767020927,
                0.9924227605039952,
                0.9994472213897998,
                0.998299277693321,
                0.9975273770725026
            ],
            [
                7.889266345957247e-06,
                3.2887490653408545e-06,
                5.422221555133606e-06,
                8.93970056668775e-06,
                6.962257079553702e-06,
                3.726641061058432e-06,
                4.222832941072913e-06,
                1.8925141469950998e-05,
                6.962257079465052e-06,
                5.422218969661113e-06
            ],
            [
                0.99962001556471,
                0.9999869928684411,
                0.9999832985781617,
                0.9998911031302717,
                0.9999251537462013,
                0.9998911030648926,
                0.9996646498161449,
                0.9999339478555707,
                0.9999546021097508,
                0.9999832985761665
            ],
            [
                0.9999810748517645,
                0.9999869928684351,
                0.9999810748585336,
                0.9999724642957817,
                0.9999599363030772,
                0.9999038976080479,
                0.9999810748540259,
                0.999948557774109,
                0.9999546021313743,
                0.9999921107383551
            ],
            [
                8.481108174842393e-05,
                1.0129992187253088e-05,
                1.1478770862255766e-05,
                1.01299946023704e-05,
                1.1478773599102191e-05,
                1.1478766757404937e-05,
                4.006367785146321e-05,
                2.7535687811228037e-05,
                7.889264466725156e-06,
                1.4738987242432592e-05
            ],
            [
                1.994729483705484e-06,
                6.144177531459659e-06,
                6.9622537593854575e-06,
                5.422218969769604e-06,
                4.222833444467892e-06,
                2.1444945854624007e-05,
                6.9622562489985925e-06,
                1.7603425837606927e-06,
                2.2603245673155757e-06,
                1.670141985245514e-05
            ],
            [
                1.4738981970312625e-05,
                2.7535697662094155e-05,
                2.1444945853999886e-05,
                0.00013982205718926903,
                2.7535687811228037e-05,
                3.535623806128476e-05,
                2.1444956079218013e-05,
                1.0129987357020188e-05,
                7.889260704423598e-06,
                4.006368262111344e-05
            ],
            [
                0.9999339478474795,
                0.9992903297150356,
                0.9984988174584818,
                0.9933071476052373,
                0.9875683476146655,
                0.9982992777368048,
                0.9959298626219827,
                0.9997694932586972,
                0.9982992779052055,
                0.999512142825305
            ],
            [
                0.060086646807761206,
                0.10669058897496682,
                0.14804719427274568,
                0.9988304900126354,
                0.0059110691709166234,
                0.8354835411997897,
                0.9998911031041102,
                0.32082130731838393,
                0.9998204720402549,
                0.2942149783515162
            ],
            [
                0.9998601778593477,
                0.9998601779765166,
                0.996406397892118,
                0.9999756997476936,
                0.9996646500133961,
                0.9997694931758446,
                0.9998766054693945,
                0.9996200154718387,
                0.9999646437619467,
                0.9991959139753744
            ],
            [
                4.222834451327159e-06,
                2.9023112931873767e-06,
                1.4738981971250963e-05,
                4.222832437639588e-06,
                1.0129992186774007e-05,
                1.1478766756214804e-05,
                2.260325375664839e-06,
                2.4300246525983375e-05,
                1.6701425826191394e-05,
                1.553498124964492e-06
            ],
            [
                0.9995121428245953,
                0.9991959139624201,
                0.9975273772723515,
                0.9995121429462456,
                0.9990889486702307,
                0.9975273764534298,
                0.9978172830952277,
                0.9999485577925875,
                0.9997694932038869,
                0.9993736659815079
            ],
            [
                0.9992903297216815,
                0.9999810748449939,
                0.9997388096602561,
                0.9997040427974756,
                0.9997388097247163,
                0.9997388096297813,
                0.99997569975639,
                0.9999646437366584,
                0.9999251537995719,
                0.9999485577741227
            ],
            [
                0.9996200154259834,
                0.9975273772005666,
                0.9999038975394935,
                0.9999339478475265,
                0.9999724642990664,
                0.9999832985821414,
                0.9989677689350349,
                0.9993736658278268,
                0.9999038976080801,
                0.9997040428323499
            ],
            [
                0.9999832985841359,
                0.9999910603015649,
                0.9999957771680659,
                0.9999599363078239,
                0.999985261023306,
                0.9999852610233092,
                0.9999646437619653,
                0.999986992869988,
                0.9999687980737948,
                0.9999910602994342
            ],
            [
                5.8291244672006574e-05,
                2.75356878022126e-05,
                7.88925976418034e-06,
                1.892515726357648e-05,
                3.12019002122609e-05,
                2.7535697660090726e-05,
                2.4300252319296727e-05,
                3.120191509059319e-05,
                5.829129330780371e-05,
                1.3007123812767362e-05
            ],
            [
                8.93969950101825e-06,
                1.147877359872636e-05,
                0.0007096704604410937,
                6.144173869502757e-06,
                6.144173869379821e-06,
                3.120191881207863e-05,
                2.430024072471526e-05,
                5.422218323399208e-06,
                2.5612831266608576e-06,
                5.422217030555087e-06
            ],
            [
                0.9975273769691323,
                0.999972464295784,
                0.9997388097853083,
                0.9996646499712081,
                0.9984988180997629,
                0.9995694429655582,
                0.9999038975737075,
                0.9998415638214826,
                0.9998601779763111,
                0.9999756997563777
            ],
            [
                0.9990889486973045,
                0.9997694933131117,
                0.9988304898882049,
                0.997527376371308,
                0.9989677690556786,
                0.9964063968850158,
                0.9991959139567147,
                0.9978172832661183,
                0.9992903296298359,
                0.9924227589457424
            ],
            [
                0.9241418252018901,
                0.977022631511694,
                0.7981867729389246,
                0.9997388096285122,
                0.7981867801399695,
                0.7981867777396212,
                0.924141814233309,
                0.5926665999540698,
                0.9998415637833618,
                0.999860177975949
            ],
            [
                0.9998204720768021,
                0.9993736658231632,
                0.999769493257624,
                0.9999599362887259,
                0.9992903294558452,
                0.999373665973456,
                0.9982992772576929,
                0.9982992777623021,
                0.999860177976541,
                0.9999724643056241
            ],
            [
                3.2887498493983645e-06,
                4.785092783319532e-06,
                1.9947299592407137e-06,
                1.994729483694599e-06,
                6.962259568889411e-06,
                4.222831934286977e-06,
                4.222833444467892e-06,
                2.9023109471689794e-06,
                7.889265407004852e-06,
                5.422217030362759e-06
            ],
            [
                0.9997040428308861,
                0.8670357494949104,
                0.9980732652238424,
                1.994729483680993e-06,
                0.9998415637835254,
                0.2689414272294874,
                0.9998601779763558,
                0.9988304898822213,
                0.09534946232842245,
                0.9999251537906715
            ],
            [
                0.999738809629713,
                0.9998911031170887,
                0.9998415638400323,
                0.999981074845,
                0.9999339478790523,
                0.9999251537728232,
                0.999941708706721,
                0.9998911030910002,
                0.9999852610233023,
                0.9999251537906715
            ],
            [
                2.4300249423302888e-05,
                7.889264466545779e-06,
                1.0129989771288745e-05,
                2.4300234937239182e-05,
                1.6701427816728442e-05,
                0.0002034269243375671,
                1.1478773597870298e-05,
                2.1444940743772097e-05,
                3.1201900209877224e-05,
                1.3007134665934505e-05
            ]
        ]
    },
    {
        "q_id": "8110_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            7,
            8,
            10,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            23,
            24,
            26,
            27,
            29,
            30,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            40,
            41,
            42,
            43,
            46,
            47,
            48,
            49,
            51,
            52,
            53,
            54,
            55,
            56,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            70,
            71,
            75,
            77,
            78,
            79,
            80,
            81,
            83,
            84,
            85,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            95,
            96,
            97,
            98,
            100,
            101,
            103,
            105,
            106,
            107,
            109,
            110,
            111,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127,
            4,
            6,
            9,
            50,
            99,
            102
        ],
        "rewards": [
            [
                3.288750633518874e-06,
                1.760343423160973e-06,
                6.144173136243255e-06,
                3.120192624233791e-05,
                2.3823690999236795e-07,
                2.902311639073834e-06,
                1.9947306725451314e-06,
                2.9023133690637e-06,
                3.466327863961242e-07,
                2.5612825159677387e-06
            ],
            [
                0.9999251537907733,
                0.999447221468523,
                0.9947798742580792,
                4.0063706494441236e-05,
                0.9986749774447594,
                0.9525741298517642,
                0.995390427927456,
                0.9964063981805762,
                0.9933071485927794,
                0.9998766054258917
            ],
            [
                2.4300232036606334e-05,
                6.605216036763493e-05,
                5.829126551185543e-05,
                3.535626334799422e-05,
                3.535625490018181e-05,
                4.0063692187232674e-05,
                4.7850933538313875e-06,
                1.6701421843356024e-05,
                1.892514598427789e-05,
                8.481107159026786e-05
            ],
            [
                5.829128637885414e-05,
                1.4738987241494252e-05,
                1.8925152752999112e-05,
                1.892514598427789e-05,
                6.1441724044534996e-06,
                6.1441767990323395e-06,
                2.1444953522913026e-05,
                5.422217676299034e-06,
                8.93969630348202e-06,
                6.1441724044534996e-06
            ],
            [
                6.605216829977486e-05,
                0.9982992773656116,
                2.5612825159421147e-06,
                0.18242551491653522,
                0.9996200154123749,
                0.047425875028824706,
                0.02931222947940706,
                8.481106151541198e-05,
                0.37754067580180184,
                5.144221976237626e-05
            ],
            [
                0.9999038975735655,
                0.9998415637833087,
                0.9991959142353016,
                0.9992903294496533,
                0.9999898700053976,
                0.9968273177252438,
                0.9997040428299991,
                0.9999546021367712,
                0.9998415638209939,
                0.9999339478632105
            ],
            [
                8.939694172290508e-06,
                8.939695237813028e-06,
                3.288749849368453e-06,
                8.93970056668775e-06,
                1.4738988998787566e-05,
                3.7266383955882547e-06,
                1.5534977545497995e-06,
                1.4738981970956057e-05,
                6.14417313680765e-06,
                3.2887498494282754e-06
            ],
            [
                2.9023130230133794e-06,
                3.92786293909545e-07,
                6.475945666009864e-07,
                1.6373762769034363e-07,
                8.315278293687262e-07,
                7.338209804853638e-07,
                6.144176798870286e-06,
                2.9023116391477434e-06,
                4.4508489275469177e-07,
                3.9278615343901467e-07
            ],
            [
                2.430023783530873e-05,
                2.753569438157704e-05,
                1.6701429806475863e-05,
                2.7535681245588654e-05,
                2.14449509695729e-05,
                6.962255418658875e-06,
                4.5397852401406606e-05,
                3.535623805819787e-05,
                1.4738981970956057e-05,
                2.902313368963394e-06
            ],
            [
                3.120190020068305e-05,
                2.902312331125353e-06,
                1.0129990979547237e-05,
                7.889264466344872e-06,
                8.939695238439078e-06,
                4.22283394786293e-06,
                1.6701425826525565e-05,
                2.260324836651547e-06,
                6.962256249821764e-06,
                5.422218969661113e-06
            ],
            [
                1.1478765388523107e-05,
                1.300712846477255e-05,
                8.939694172290508e-06,
                4.222834451327159e-06,
                8.939695238333382e-06,
                4.785093353909723e-06,
                1.300713001414004e-05,
                3.726637951079042e-06,
                1.012998977198894e-05,
                1.3709567165461505e-06
            ],
            [
                0.0002959570626999455,
                0.005220126842166147,
                0.00017952790062228017,
                0.0002611903406407374,
                8.4811031131658e-05,
                9.610240349752414e-05,
                0.0015011824223358568,
                NaN,
                5.1442238170207006e-05,
                3.120191880867338e-05
            ],
            [
                0.9924227595480334,
                0.9993736658954131,
                0.9964063972551759,
                0.924141814233309,
                0.9840936105040935,
                0.9982992778743716,
                0.994088931209427,
                0.9988304897390242,
                0.9953904278740409,
                0.9986749777043311
            ],
            [
                0.9999251537727715,
                0.9998911030907222,
                0.9986749776770646,
                0.9995694428601689,
                0.9998766054692472,
                0.999876605425161,
                0.9990889488696014,
                0.9997040427949182,
                0.9997694933120754,
                0.996406397938805
            ],
            [
                4.785092783149804e-06,
                1.2098659719524008e-06,
                4.006370172712009e-05,
                4.0063706483364614e-05,
                3.726640172337686e-06,
                4.0063692178050736e-05,
                1.4738983725809062e-05,
                8.315278293838516e-07,
                7.889264466445326e-06,
                1.3709568799243436e-06
            ],
            [
                0.9975273773360965,
                0.012431648692170408,
                0.9978172836368041,
                0.999512142834047,
                0.03308597826952727,
                0.9971990732026113,
                0.37754066879814546,
                0.9968273169933078,
                0.9933071504409375,
                0.00857748632449885
            ],
            [
                1.5534983101301911e-06,
                4.22283545795623e-06,
                3.72664061671159e-06,
                2.561282821209454e-06,
                2.1444956081636468e-05,
                1.2098662604126641e-06,
                4.222834451254188e-06,
                2.5612834319655406e-06,
                7.338213304196583e-07,
                1.3709568798782093e-06
            ],
            [
                1.067702615468225e-06,
                1.0129987357158383e-05,
                4.222831934286977e-06,
                1.5534973841895917e-06,
                1.0129993395088066e-05,
                1.0677027427525368e-06,
                6.144177531660828e-06,
                5.42222090882208e-06,
                5.422218323349895e-06,
                4.78509563555309e-06
            ],
            [
                1.1478768124553928e-05,
                3.5356267569843254e-05,
                1.01299946023704e-05,
                1.300712846411008e-05,
                3.288750633518874e-06,
                9.610241496111313e-05,
                1.892515500808112e-05,
                1.0129988564578197e-05,
                6.962255419475714e-06,
                6.144177531599359e-06
            ],
            [
                0.9770226277065029,
                0.9994472212555717,
                0.9933071478621839,
                0.9971990726173277,
                0.9975273772149237,
                0.9978172831439087,
                0.9971990736552304,
                0.9998204719916403,
                0.9968273172046415,
                0.9989677691774027
            ],
            [
                0.9740426428492974,
                0.9669140241140101,
                0.9924227583014311,
                0.977022628877331,
                0.9924227604864868,
                0.9820137925053598,
                0.9940889302708812,
                0.998967768943438,
                0.9988304896249288,
                0.952574127663914
            ],
            [
                1.2098656835076114e-06,
                3.288748673319648e-06,
                3.288747889229516e-06,
                5.043475284430694e-07,
                1.7603434231705793e-06,
                1.76034300345598e-06,
                1.0129987357158383e-05,
                5.715003107738556e-07,
                1.7603438428740716e-06,
                1.7603440527222532e-06
            ],
            [
                0.002472623730339508,
                0.005911068631868398,
                0.9986749776829184,
                0.0009110511117489696,
                0.9706877690366522,
                0.9399133510883347,
                0.9740426441208442,
                0.9770226301317896,
                0.9399133462493554,
                0.0019267345200511504
            ],
            [
                3.7266406168403854e-06,
                1.0677032518748838e-06,
                3.4663262110425684e-07,
                1.3709578605355551e-06,
                7.338212429464139e-07,
                2.90231198483099e-06,
                1.0129995809929273e-05,
                9.422445938861406e-07,
                7.889266347636241e-06,
                1.9947306726594253e-06
            ],
            [
                1.994729245722476e-06,
                6.475947981904966e-07,
                2.561283431986506e-06,
                1.0129987356191011e-05,
                2.4300249416363357e-05,
                2.5612819053166966e-06,
                1.7603430033799313e-06,
                4.222834451292594e-06,
                1.6701427811412077e-05,
                6.962259569117366e-06
            ],
            [
                0.9990889488748466,
                0.9959298616649739,
                0.9988304900032522,
                0.9980732651136986,
                0.9998911031038282,
                0.998967769167079,
                0.9984988175087373,
                0.9991959139541894,
                0.9859363742997659,
                0.9991959141480825
            ],
            [
                0.9980732649207235,
                0.9990889487478491,
                0.9706877673407197,
                0.9992903294523778,
                0.9988304897437839,
                0.9968273170662069,
                0.9997694933670568,
                0.9997040429007811,
                0.9999646437366431,
                0.9959298614762147
            ],
            [
                0.9940889308783366,
                0.999704042936749,
                0.9579122723847614,
                0.9997965729781864,
                0.9953904287906443,
                0.9859363751391478,
                0.9984988180439235,
                0.9953904275642331,
                0.999841563783205,
                0.9933071477785989
            ],
            [
                0.999964643757729,
                0.0007096705257856623,
                0.004609571771282696,
                0.0015011824000000765,
                0.00012339455980783077,
                8.481106149073081e-05,
                0.9997694931766561,
                0.00015843627179906717,
                0.001926734350358266,
                0.9999898700066052
            ],
            [
                1.4738987240475486e-05,
                1.0129988563343644e-05,
                4.785094494576774e-06,
                7.88926634644516e-06,
                1.473898899742027e-05,
                1.8925152750176348e-05,
                3.1201922531407855e-05,
                8.93969736955767e-06,
                1.3007133114886634e-05,
                7.88925976418034e-06
            ],
            [
                0.9991959142080369,
                0.00020342692468384608,
                0.00020342707016545293,
                0.029312231864311963,
                0.9988304899474963,
                NaN,
                0.002182715984396773,
                1.8925155008941717e-05,
                0.0008040858445752018,
                0.24508501864634827
            ],
            [
                3.288750633518874e-06,
                3.288748673295719e-06,
                1.3007128464346676e-05,
                1.1478768125577027e-05,
                9.422448185015797e-07,
                3.92786293909545e-07,
                4.222831933864508e-06,
                5.71500242637956e-07,
                2.902313023063532e-06,
                1.6701417862648148e-05
            ],
            [
                2.561282515914161e-06,
                3.7266383954560706e-06,
                4.5397879450662006e-05,
                7.889264466639056e-06,
                4.222834451215781e-06,
                6.144172404380855e-06,
                3.7266388396975786e-06,
                1.6701427816728442e-05,
                8.93969736929749e-06,
                2.1444945853375776e-05
            ],
            [
                0.5,
                0.053403334131154334,
                0.9988304897224335,
                0.34864514210180597,
                NaN,
                0.09534946425643773,
                0.9995121427683967,
                0.0004305571069767681,
                0.18242551713899047,
                0.9999810748428052
            ],
            [
                0.9978172832473557,
                0.998674977545045,
                0.9971990730744992,
                0.001926734636015425,
                0.9999687980737504,
                0.009708478361802058,
                0.01406362688828262,
                0.9959298614139241,
                0.0006263342469370099,
                0.984093610737347
            ],
            [
                3.5356242264223526e-05,
                NaN,
                NaN,
                0.0002959570986850448,
                2.430023783309869e-05,
                2.1444945855248125e-05,
                2.753569436294514e-05,
                NaN,
                1.4738987237124277e-05,
                0.0024726232743619613
            ],
            [
                0.9997694932024248,
                0.9993736659724722,
                0.9997694933672178,
                0.9975273769542011,
                0.9998415638398986,
                0.9982992774996207,
                0.9875683498328509,
                0.9995121427637702,
                0.9959298622954295,
                0.9953904287991907
            ],
            [
                2.144495096457996e-05,
                1.6701419852819694e-05,
                0.0001584362735394825,
                0.00015843619780953218,
                1.8925152747938785e-05,
                9.610242636527403e-05,
                1.8925145982866508e-05,
                0.00017952798727559279,
                8.481104132251176e-05,
                5.14422258772351e-05
            ],
            [
                4.539789026561238e-05,
                0.0017007223843567695,
                0.001169510393293796,
                0.9859363722465081,
                0.00015843625447790115,
                0.00023050674264424667,
                0.00012339457491796526,
                0.0003799845748899956,
                7.484626286034225e-05,
                0.00043055708873969027
            ],
            [
                5.043472278255469e-07,
                2.6995771309523475e-07,
                3.05902226923399e-07,
                1.99473067264854e-06,
                5.422221555340727e-06,
                1.5534975693869924e-06,
                1.5534971989907999e-06,
                4.222834954687752e-06,
                2.260324028427877e-06,
                3.288750633545794e-06
            ],
            [
                1.3007130014376633e-05,
                6.962256249517824e-06,
                2.9023119851266288e-06,
                2.1444953525877587e-05,
                6.47594566594213e-07,
                2.4300252317882297e-05,
                1.1478769494083349e-05,
                1.3007133115903994e-05,
                2.1444958637941764e-05,
                1.3007123812057577e-05
            ],
            [
                0.989013054910255,
                0.00043055698828547057,
                0.0010322311564381636,
                0.0015011824045370317,
                0.0008040860517968003,
                0.0013250225657159451,
                0.00048785717693735405,
                0.00037998452991905404,
                0.0006263342457711021,
                0.000335350149892069
            ],
            [
                9.610242642470349e-05,
                4.006368262883792e-05,
                7.484621827634963e-05,
                0.00029595702843703724,
                0.00033535010857244324,
                6.605212890195146e-05,
                0.0001584361791352309,
                0.00023050679736063442,
                8.481106153947614e-05,
                6.605215253545261e-05
            ],
            [
                9.610243782956492e-05,
                9.610242625969935e-05,
                0.0009110510829268486,
                3.535624225316214e-05,
                0.00013982214054859745,
                4.539785238918559e-05,
                2.4300240727367308e-05,
                8.481106138460176e-05,
                9.610244922114349e-05,
                0.9706877720045337
            ],
            [
                1.2098652508287273e-06,
                6.1441760661636525e-06,
                1.99472900796355e-06,
                4.222834954607099e-06,
                1.0677027426709671e-06,
                1.7603427935518875e-06,
                2.5612819053166966e-06,
                1.5534981249574276e-06,
                5.04347528431602e-07,
                1.4738981970956057e-05
            ],
            [
                2.5612812946890944e-06,
                1.7603434231385591e-06,
                1.0129994602222992e-05,
                1.670141786231398e-05,
                1.892515049571424e-05,
                2.1444940743772097e-05,
                2.4300237834601515e-05,
                1.47389854857293e-05,
                6.1441746018123775e-06,
                8.93969736929749e-06
            ],
            [
                1.7603436329978976e-06,
                4.222834451254188e-06,
                1.3709572068354007e-06,
                6.144172404520556e-06,
                2.902313023039776e-06,
                4.222834451254188e-06,
                1.5534973841309562e-06,
                3.726639728184142e-06,
                1.209866116170145e-06,
                1.0677026154619133e-06
            ],
            [
                0.00029595713312879083,
                5.422220908762902e-06,
                0.0024726233708408304,
                1.8925148232267744e-05,
                1.6701421844419295e-05,
                0.22270012850745968,
                4.7850956351657615e-06,
                0.01798621177155612,
                0.0001088969092152976,
                2.753570422573402e-05
            ],
            [
                1.8925152750176348e-05,
                5.829127247176183e-05,
                5.144219521574275e-05,
                7.484626294855732e-05,
                7.484622714250407e-05,
                0.00012339458963849851,
                1.670141586907437e-05,
                0.00013982209068353965,
                1.1478768124783601e-05,
                2.1444943296369872e-05
            ],
            [
                1.1478765388898939e-05,
                2.9023133690425823e-06,
                1.0677033791437343e-06,
                3.2887498493983645e-06,
                1.3709567165530083e-06,
                4.785092783319532e-06,
                2.260324028404236e-06,
                1.994729959224386e-06,
                1.012999460150437e-05,
                2.561281600049467e-06
            ],
            [
                0.9978172831439087,
                0.9820137942161259,
                0.9971990732663422,
                0.998674977367119,
                0.9924227582033835,
                0.9991959140520712,
                0.9975273769542011,
                0.9998601779259395,
                0.9986749775203972,
                0.9996646497309396
            ],
            [
                0.9975273769823407,
                0.9968273175588278,
                0.9840936069178209,
                0.9964063981230513,
                0.9940889302654086,
                0.9992903296243045,
                0.9890130573390469,
                0.9953904276496974,
                0.9998204720767055,
                0.995929861719714
            ],
            [
                0.8933094032139577,
                0.9993736659099505,
                0.9971990732780477,
                0.9324533112067127,
                0.9995694429106089,
                0.9993736659744397,
                0.996406397464433,
                0.9989677689344347,
                0.9990889486640848,
                0.9998911031167164
            ],
            [
                2.1444953524161264e-05,
                3.5356238044435446e-05,
                9.610241478352397e-05,
                2.4300246527309398e-05,
                1.4738981971250963e-05,
                8.481102093340112e-05,
                0.0002034270657733305,
                6.605212085304002e-05,
                4.0063692179945426e-05,
                1.1478772229300848e-05
            ],
            [
                0.9968273176589719,
                0.5621765008857981,
                0.02595735828096633,
                0.997817283124639,
                0.009708475487586563,
                0.01798621190315355,
                0.008577485152355773,
                0.14804719427274568,
                0.9986749776668973,
                0.029312233030265544
            ],
            [
                8.315277302649045e-07,
                5.422220908876325e-06,
                1.7603430033607189e-06,
                1.5534971989258068e-06,
                5.422217676866151e-06,
                3.2887494564857185e-06,
                2.5612815998141903e-06,
                4.7850967763512445e-06,
                2.5612828212909852e-06,
                1.5534981248881956e-06
            ],
            [
                0.9982992776765205,
                0.9998601779258398,
                0.9984988176860276,
                0.9995694429614373,
                0.9968273172193686,
                0.9968273167326385,
                0.9995694429091561,
                0.9993736657468691,
                0.99408893027909,
                0.9964063979946625
            ],
            [
                2.9023130230133794e-06,
                4.450850519360903e-07,
                1.3709568798956654e-06,
                3.288748673265808e-06,
                3.2887482812506295e-06,
                5.422217030495909e-06,
                9.42244930862237e-07,
                6.475947981860793e-07,
                1.3709575336860625e-06,
                2.1024336609399248e-07
            ],
            [
                0.9999038975620929,
                0.999769493257463,
                0.9995694429091561,
                0.9995694428587786,
                0.9998766054398044,
                0.9997694933672178,
                0.9997040429709516,
                0.9998911030777436,
                0.9995121429386673,
                0.9993736658223981
            ],
            [
                0.00218271683530051,
                0.9953904273462995,
                0.9980732657414281,
                0.9971990735921499,
                0.9999038976195234,
                0.998830489595963,
                0.9875683485751169,
                0.999290329624057,
                0.0024726232680448925,
                0.9840936063055302
            ],
            [
                0.9991959139469405,
                0.9982992776806712,
                0.9940889320877746,
                0.9995694429086174,
                0.9986749773584921,
                0.9986749775160838,
                0.9999038975392132,
                0.9997694933120218,
                0.9982992776792876,
                0.9997388096595644
            ],
            [
                0.9997388096052421,
                0.00015843619764816923,
                2.1444945848226808e-05,
                6.962258739454786e-06,
                7.484620046617512e-05,
                2.7535704212311033e-05,
                1.3007128463069061e-05,
                0.00017952798717633654,
                0.0011695104807351773,
                3.726639283901856e-06
            ],
            [
                0.00017952792289224282,
                1.8925148238291944e-05,
                0.00026119024624545313,
                0.0001233946039963614,
                4.785096205882502e-06,
                0.00020342694913350932,
                4.539785778740889e-05,
                6.605215252536083e-05,
                0.0004305570361577904,
                0.0004878572301558034
            ],
            [
                9.61024378393533e-05,
                0.002800926593840173,
                0.8354835432479661,
                0.00026119040190915446,
                0.9964063979079583,
                0.0011695103879901978,
                0.9669140212537652,
                9.610242636527403e-05,
                0.9940889311464924,
                0.0007096702765021507
            ],
            [
                0.001700722057833355,
                0.0002611904277479851,
                2.4300249423302888e-05,
                0.0010322310503197314,
                0.0002034270699079633,
                5.8291251631486394e-05,
                1.3007123812767362e-05,
                1.0129989771657269e-05,
                5.829126552754713e-05,
                7.484623600430327e-05
            ],
            [
                2.699577130944368e-07,
                3.288750241410738e-06,
                5.715003107715166e-07,
                5.4222202624563834e-06,
                3.927862939075802e-07,
                1.7603440527222532e-06,
                6.962258739530771e-06,
                1.3709572068079696e-06,
                8.315283250305684e-07,
                1.3709572068179446e-06
            ],
            [
                0.9998204719482471,
                0.9996200155142007,
                0.9978172831510079,
                0.9998415637454944,
                0.9975273772034381,
                0.9995121428802264,
                0.9999417087483575,
                0.998073265094222,
                0.9997040427589675,
                0.9968273172046415
            ],
            [
                1.5534971989258068e-06,
                2.260323758923431e-06,
                5.422221555133606e-06,
                1.4738978457604563e-05,
                3.12019113570763e-05,
                2.7535704220525098e-05,
                6.96225541916544e-06,
                4.785096776394765e-06,
                3.2887482812745586e-06,
                1.0129987357020188e-05
            ],
            [
                2.7535684528909006e-05,
                1.147876538789672e-05,
                1.670141985166528e-05,
                8.939700566289352e-06,
                1.0129987355988324e-05,
                4.222834954514924e-06,
                4.7850967763512445e-06,
                1.8925157262061825e-05,
                4.785093924156175e-06,
                1.300712536350655e-05
            ],
            [
                5.144221975938208e-05,
                5.829128636782753e-05,
                1.8925148232956223e-05,
                3.2887502414436403e-06,
                1.3007131562514014e-05,
                1.67014178554179e-05,
                5.422217029509618e-06,
                1.4738987241494252e-05,
                5.422218967649081e-06,
                1.3007125358230479e-05
            ],
            [
                0.9984988178818146,
                0.8933094152856196,
                0.9579122768904645,
                0.9770226306753883,
                0.9971990726589478,
                0.9978172837012049,
                0.00043055709111952873,
                0.8933094103149354,
                0.9953904272586986,
                0.9992903295365868
            ],
            [
                0.9998204720125233,
                0.9968273169498629,
                0.9968273175514643,
                0.9993736659738567,
                0.9984988175218247,
                0.9982992779135069,
                0.9984988180810916,
                0.9997694932576776,
                0.998073265546438,
                0.9964063980255091
            ],
            [
                0.9964063982589434,
                0.9997965729782308,
                0.9986749773467845,
                0.9995694429604353,
                0.9984988176785242,
                0.9995121428210758,
                0.9994472213184087,
                0.9992903294486627,
                0.9984988180439235,
                0.9999251537370873
            ],
            [
                0.9968273164145334,
                0.9324533116759811,
                0.00029595706110692254,
                0.9465966741548683,
                0.9241418189341296,
                0.0010322309521241782,
                0.0008040859279127915,
                0.9996200155601777,
                0.9840936069469776,
                0.9626731122542813
            ],
            [
                0.00023050663267494372,
                0.9993736659738567,
                0.9959298625408164,
                0.9975273770277088,
                0.0013250222939743487,
                0.00015843625434420038,
                0.9626731135929119,
                0.6513548782017745,
                0.9241418121440552,
                0.9940889309768428
            ],
            [
                0.89330940889474,
                0.9998204720553105,
                0.9998204719910003,
                0.9995121427628619,
                0.0031726821179128037,
                0.9859363703998673,
                0.0028009271017361875,
                0.9997965730509908,
                0.9997388097213952,
                0.9902915248974329
            ],
            [
                0.9995121428792897,
                0.999954602115151,
                0.9982992778939392,
                0.9994472213863268,
                0.9984988175118783,
                0.9996200154695835,
                0.9999339478553145,
                0.9933071476485776,
                0.9999251537370689,
                0.9998204720980979
            ],
            [
                6.962255419804982e-06,
                6.475945666009864e-07,
                9.422443692390473e-07,
                6.144173136952939e-06,
                8.939698435454571e-06,
                1.300713466619476e-05,
                8.315281267800897e-07,
                4.222833947932061e-06,
                3.288749457432399e-06,
                1.7603440526662173e-06
            ],
            [
                0.9953904273206602,
                0.03732688319437491,
                3.120191507912884e-05,
                0.10669059252545564,
                0.00020342697299124553,
                1.4738976700366126e-05,
                0.00020342704557963122,
                0.0002959572407741338,
                0.0002611904023347352,
                2.430024072188641e-05
            ],
            [
                0.9953904287991907,
                0.02297736894827407,
                0.24508501864634827,
                0.017986209731796078,
                0.009708478272262622,
                0.9706877717395442,
                0.9999599363126541,
                0.0035936030266127306,
                0.7057850402140659,
                0.03308597767364294
            ],
            [
                0.999972464302337,
                0.9999832985721826,
                0.9959298624464367,
                0.9999038976079185,
                0.9999885212359796,
                0.9999038975964549,
                0.9982992774828201,
                0.999796573026544,
                0.996827316785656,
                0.9999910603036963
            ],
            [
                0.9968273173740029,
                0.9669140226838876,
                0.9890130572580872,
                0.9994472213256443,
                0.9933071479550563,
                0.9859363700770278,
                0.9241418267688303,
                0.9959298619820892,
                0.9890130598791579,
                0.7549149813536518
            ],
            [
                0.7057850340255386,
                0.0850990438468576,
                7.484621833189242e-05,
                0.9990889490064004,
                0.0015011822790727699,
                9.610242643449187e-05,
                0.0007096704526393737,
                0.04208772746504851,
                0.04742587435564,
                0.0008040860359430134
            ],
            [
                0.9991959139569953,
                0.9975273772826886,
                0.9902915253003602,
                0.9959298621934994,
                0.9940889310945031,
                0.994088929819394,
                0.9998204720772462,
                0.9982992774662173,
                0.9980732655410651,
                0.9953904275129546
            ],
            [
                0.05340332659840655,
                0.10669059678604235,
                0.22270013882530884,
                0.001700722028580655,
                0.09534945782972029,
                0.004070137138293195,
                0.0010322308204365133,
                0.9991959141879274,
                0.0024726232858475407,
                0.04208772686428807
            ],
            [
                0.9875683490439087,
                0.997817283900493,
                0.9994472213275094,
                0.9984988180580578,
                0.9992903297006293,
                0.999796573075402,
                0.9992903295353485,
                0.9996200155613383,
                0.9997388096629539,
                0.9978172834948178
            ],
            [
                0.995929861381835,
                0.9890130569241283,
                0.9890130560436913,
                0.9971990726706534,
                0.9953904283376841,
                0.9980732651929485,
                0.9579122672782974,
                0.9859363701415957,
                0.9990889488809396,
                0.9924227601608294
            ],
            [
                1.5534977545497995e-06,
                7.338212429464139e-07,
                6.144175334015912e-06,
                3.927862002625787e-07,
                7.338208055489796e-07,
                7.889266347456862e-06,
                8.939698435226916e-06,
                9.42244930862237e-07,
                4.785092783415276e-06,
                5.422217030555087e-06
            ],
            [
                1.892514598469098e-05,
                1.8925145985104064e-05,
                3.5356254926549066e-05,
                7.338208930265102e-07,
                4.785095065093186e-06,
                1.4738980213341866e-05,
                7.889265407004852e-06,
                2.430023783530873e-05,
                2.9023112930659533e-06,
                1.4738980214280206e-05
            ],
            [
                6.9622595694023114e-06,
                1.067703379154416e-06,
                2.561282515988704e-06,
                1.1478772230198667e-05,
                2.90231094702116e-06,
                6.9622579095833456e-06,
                1.0129995809763438e-05,
                3.2887482811908074e-06,
                3.2887490653109436e-06,
                1.670142383495587e-05
            ],
            [
                0.00015843617908451683,
                6.962259569117366e-06,
                2.4300249421225448e-05,
                6.605213677497863e-05,
                5.8291293326888225e-05,
                7.889266347133978e-06,
                7.889264466344872e-06,
                2.144494585801764e-05,
                1.6701427817427163e-05,
                2.75356845363217e-05
            ],
            [
                0.00026119027707723974,
                0.9525741293468757,
                0.0007096705394077146,
                0.9840936096877063,
                0.8807970748488297,
                NaN,
                0.0001795279441800938,
                0.00013982212368956342,
                0.0017007226743143574,
                0.8354835309589074
            ],
            [
                1.994729959224386e-06,
                1.670142980726572e-05,
                3.2887486732000038e-06,
                1.012999339449843e-05,
                1.0129995809597604e-05,
                4.785095064819011e-06,
                1.6701429807630274e-05,
                2.753569765908901e-05,
                1.3007131564643372e-05,
                4.78509563535725e-06
            ],
            [
                0.966914018751051,
                0.9933071476052372,
                0.9980732653373441,
                0.9953904277821669,
                0.9984988175195562,
                0.9984988177352361,
                0.9669140218496496,
                0.9947798746159611,
                0.9959298621293213,
                0.9953904281688923
            ],
            [
                0.0006263341762538571,
                0.9997040428489347,
                0.025957357009419556,
                8.481108175582829e-05,
                0.025957356303004702,
                0.9996200155628086,
                0.9978172835505981,
                0.4073334000459302,
                0.9959298614384628,
                0.18242552825126704
            ],
            [
                0.999876605395702,
                0.99781728396033,
                0.9875683483235701,
                0.9994472213210779,
                0.9989677689199095,
                0.9988304895913394,
                0.9971990733794969,
                0.9997965729783551,
                0.9996200154705231,
                0.9978172834740269
            ],
            [
                4.539788485433845e-05,
                1.47389819699641e-05,
                0.9770226279155795,
                0.5621765008857981,
                0.9982992778980899,
                0.9953904271262292,
                0.9890130572479672,
                0.9933071485215772,
                0.004609571822561209,
                0.9796676484753358
            ],
            [
                0.00010889688334460505,
                0.00015843619756748776,
                1.1478769494083349e-05,
                4.0063706494441236e-05,
                2.7535704228438656e-05,
                2.7535697651475977e-05,
                7.88926164518358e-06,
                3.7266383953679482e-06,
                8.481108169042316e-05,
                3.53562633126235e-05
            ],
            [
                0.999569442962264,
                0.9998415637643762,
                0.9995121427642527,
                0.9997388096904798,
                0.9995121428222395,
                0.9999038975621404,
                0.9982992774842037,
                0.9997388095972548,
                0.9993736659703589,
                0.9959298627616644
            ],
            [
                0.0002611903076886401,
                6.605211631318335e-05,
                0.003172683537603568,
                0.00020342704540501178,
                0.0007096703744570623,
                0.8519527944504227,
                0.0006263340236292827,
                0.00037998448055936144,
                0.00015843625401225367,
                0.00012339453041524914
            ],
            [
                0.9982992772891197,
                0.9995694430134556,
                0.999841563745317,
                0.9989677691716407,
                0.9986749773695837,
                0.9997965730996415,
                0.9989677689224304,
                0.9988304899967246,
                0.9982992772920846,
                0.9940889306129168
            ],
            [
                0.9968273165014232,
                0.9924227575065467,
                0.995929861719714,
                0.996406396824156,
                0.9940889310917668,
                0.9971990732552868,
                0.9995121427660125,
                0.9982992776905538,
                0.9996200155593263,
                0.9914225143407716
            ],
            [
                0.999769493367164,
                0.9999151889586547,
                0.99986017797601,
                0.9991959140489378,
                0.9975273764591727,
                0.9997694932305475,
                0.9999251537549232,
                0.9995694429098825,
                0.9999546021314075,
                0.999915188928393
            ]
        ]
    },
    {
        "q_id": "8179_mmlu_math",
        "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,
            32,
            33,
            34,
            35,
            37,
            38,
            39,
            40,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            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,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            109,
            110,
            111,
            112,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.5612815999679353e-06,
                3.2887498491620677e-06,
                2.902310946944611e-06,
                1.0677027427413698e-06,
                2.5612819053166966e-06,
                1.760343632854606e-06,
                1.3709576970537545e-06,
                2.902313368897403e-06,
                1.5534975692866768e-06,
                1.760343842833246e-06
            ],
            [
                0.9999952149072171,
                0.9999952149032237,
                0.9999957771660523,
                0.999988521234614,
                0.9999977396759717,
                0.9999251537638889,
                0.9999756997621879,
                0.9999945777816769,
                0.9999546021421873,
                0.999996711249759
            ],
            [
                0.9999977396762413,
                0.9999962733602719,
                0.9999984465028011,
                0.9999987901344608,
                0.9999991684722698,
                0.9999962733589389,
                0.9999987901337396,
                0.9999994956527721,
                0.9999992661786696,
                0.9999910603068946
            ],
            [
                0.9999967112505471,
                0.999997097686631,
                0.9999785550413824,
                0.9999995549149481,
                0.9999974387168737,
                0.999998239656577,
                0.9999967112517189,
                0.9999980052700408,
                0.999985261011005,
                0.999993855825399
            ],
            [
                0.9999921107346014,
                0.9999930377462427,
                0.9525741301883566,
                0.9975273770386202,
                0.9999974387168734,
                0.9999910602994387,
                0.9999938558239344,
                0.9999810748562908,
                0.9999938558239343,
                0.9999869928762091
            ],
            [
                8.939695235243779e-06,
                1.3007131560621253e-05,
                1.7603434230729168e-06,
                1.0129995807165349e-05,
                4.222831934202483e-06,
                1.3709570433075437e-06,
                1.0129987356375273e-05,
                6.962255418367598e-06,
                6.144176796601534e-06,
                7.889265403654039e-06
            ],
            [
                0.9999938558239343,
                0.999992110737415,
                0.9999986290424664,
                0.9999984465022456,
                0.999997097688015,
                0.9999957771660524,
                0.9999967112517189,
                0.9999938558239341,
                0.9999832985781597,
                0.9999984465024306
            ],
            [
                9.422447061456491e-07,
                3.92786340734912e-07,
                3.4663249713741784e-07,
                4.4508510498604413e-07,
                1.067702488159652e-06,
                1.2098659719232413e-06,
                4.450851049941403e-07,
                1.3709568799243436e-06,
                4.4508505193791187e-07,
                7.338212429367364e-07
            ],
            [
                7.338207180661203e-07,
                1.760343632920248e-06,
                7.338211554591642e-07,
                2.561283431888668e-06,
                1.7603438428660665e-06,
                1.370957370236096e-06,
                2.9023116387069255e-06,
                5.422217030032353e-06,
                1.7603427935518875e-06,
                2.9023130230133794e-06
            ],
            [
                0.9999930377462409,
                0.9999977396759775,
                0.9999974387184005,
                0.9999646437535248,
                0.9999930377414166,
                0.999986992873093,
                0.9999485577928278,
                0.9999930377445817,
                0.9999599362982944,
                0.9999869928746445
            ],
            [
                0.9999785550464855,
                0.999996273360272,
                0.9964063982180924,
                0.9998601778763552,
                0.9997965729306721,
                0.9999724643056309,
                0.9999967112501505,
                0.9999945777816774,
                0.9989677690583195,
                0.9999485577986358
            ],
            [
                0.9999962733593833,
                0.9999962733611609,
                0.9999974387165681,
                0.9999910603047628,
                0.9999982396574163,
                0.9999957771660528,
                0.9999982396561572,
                0.9999977396751633,
                0.9999785550490354,
                0.9998911030778838
            ],
            [
                0.999941708741448,
                0.9999756997621677,
                0.999983298574179,
                0.9999485577925665,
                0.9997388096606132,
                0.999978555056715,
                0.9997965730046485,
                0.9999869928700547,
                0.9999852610145218,
                0.9999832985821396
            ],
            [
                1.994729721396435e-06,
                6.475951069855719e-07,
                9.422448185187191e-07,
                1.9947294836483373e-06,
                1.994729483608425e-06,
                2.2603245672497918e-06,
                2.5612822104977725e-06,
                9.422443692390473e-07,
                8.315283250150648e-07,
                8.315281267581578e-07
            ],
            [
                0.9999869928684397,
                0.999972464315471,
                0.9999687980849195,
                0.9999832985781587,
                0.9999898700041918,
                0.9999869928699874,
                0.9999984465026159,
                0.9999910603068934,
                0.999968798092358,
                0.9999151889789598
            ],
            [
                0.999983298577241,
                0.9399133473013075,
                0.9999974387184012,
                0.9999546021476294,
                0.9999756997564174,
                0.7772998663336157,
                0.9999151889185891,
                0.9999945777797377,
                0.9999945777829702,
                0.9999852610216979
            ],
            [
                4.5397884843438604e-05,
                5.829124463044478e-05,
                1.1478768124324254e-05,
                3.535626332509972e-05,
                2.4300237828059798e-05,
                8.481108174842393e-05,
                1.892514823364471e-05,
                0.00013982210717841299,
                4.0063682616886836e-05,
                9.610244917849409e-05
            ],
            [
                0.9999982396572065,
                0.9998911030520091,
                0.9999952149072174,
                0.999999352404893,
                0.9999832985841337,
                0.9999970976869773,
                0.9999980052705163,
                0.9999945777803844,
                0.9999967112517192,
                0.9999990577552939
            ],
            [
                6.475946437966953e-07,
                2.5612822106654943e-06,
                6.47594952595231e-07,
                7.338210679622478e-07,
                2.699578739999358e-07,
                6.47594643784032e-07,
                3.4663249713741784e-07,
                5.043475284228866e-07,
                6.475947981813674e-07,
                3.726637951126493e-06
            ],
            [
                5.42222025986737e-06,
                5.422218969601935e-06,
                1.760343422928825e-06,
                2.902313022984344e-06,
                2.2603248365343694e-06,
                1.2098658276862581e-06,
                1.5534975692866768e-06,
                3.2887482811220126e-06,
                6.144174601208867e-06,
                1.5534981249164537e-06
            ],
            [
                1.3007128462477575e-05,
                1.670142979997471e-05,
                2.561281904871769e-06,
                6.144172403827636e-06,
                6.144176066051891e-06,
                1.012998976522654e-05,
                0.9999151889789265,
                1.0129988561648438e-05,
                3.5356267555952205e-05,
                7.88926163685319e-06
            ],
            [
                1.760342793583908e-06,
                9.422448185264317e-07,
                9.422450431654909e-07,
                4.4508521110499674e-07,
                9.422445938728576e-07,
                3.4663249714325014e-07,
                1.0677031245783732e-06,
                6.475948753930064e-07,
                9.422448184912962e-07,
                8.315281267581578e-07
            ],
            [
                1.3709573702566696e-06,
                9.422442568763144e-07,
                1.9947297214182054e-06,
                8.315283250150648e-07,
                1.7603430033991435e-06,
                9.42244256886598e-07,
                1.7603430034151537e-06,
                1.7603430033991435e-06,
                1.0677029972993568e-06,
                8.315279285251204e-07
            ],
            [
                0.9999930377454107,
                0.9999977396751828,
                0.9999945777816783,
                0.99999743871718,
                0.9999962733593833,
                0.999997097689059,
                0.999988521235985,
                0.9999910603058294,
                0.9999967112521335,
                0.999993855825418
            ],
            [
                7.8892625830162e-06,
                5.4222215541571775e-06,
                5.043472277838052e-07,
                5.715007195057402e-07,
                1.0677028699489821e-06,
                7.889262585082652e-06,
                6.144175333155351e-06,
                1.553498495189945e-06,
                6.962256248871951e-06,
                3.7266406165319545e-06
            ],
            [
                3.9278605979011705e-07,
                3.466324971415162e-07,
                5.715003107525447e-07,
                1.7603425836246058e-06,
                5.043474081902134e-07,
                5.043472278255469e-07,
                4.4508489275145346e-07,
                2.699577130887897e-07,
                1.2098655392574583e-06,
                3.4663278639044955e-07
            ],
            [
                6.9622579086271995e-06,
                5.4222215537823875e-06,
                1.7603434230312906e-06,
                1.9947297213746646e-06,
                8.939700565996655e-06,
                3.2887482809933958e-06,
                6.1441738684354385e-06,
                5.4222196143006464e-06,
                1.0129990977759901e-05,
                2.260325105870372e-06
            ],
            [
                1.7603436329978976e-06,
                4.785093923603471e-06,
                1.0677031245710902e-06,
                3.2887498488809053e-06,
                2.2603245670174926e-06,
                1.2098652508056196e-06,
                2.902311984915459e-06,
                3.2887486732000038e-06,
                1.3709575336093795e-06,
                4.7850944943330625e-06
            ],
            [
                0.9999852610162746,
                0.9999869928684358,
                0.999997097687323,
                0.9999957771645427,
                0.9999970976869772,
                0.9999987901344608,
                0.9999974387168735,
                0.9902915236259733,
                0.9999974387165681,
                0.9999952149043653
            ],
            [
                5.043475885576967e-07,
                1.3709568799368123e-06,
                8.315284241083696e-07,
                1.3709578605542582e-06,
                1.2098653949842147e-06,
                1.7603432132912532e-06,
                1.0677026154376365e-06,
                4.222832940777184e-06,
                1.3007128460040644e-05,
                1.2098656833865714e-06
            ],
            [
                0.9999485577864307,
                1.4738985438624722e-05,
                0.9999151889693595,
                0.9999417087414922,
                0.999195914027285,
                0.999664649784377,
                0.9998766054435657,
                0.9998911030394917,
                0.9998911030414913,
                0.9995121427899395
            ],
            [
                5.4222202621161125e-06,
                1.012999459934851e-05,
                6.144173132912773e-06,
                7.889263524960312e-06,
                1.300713464095004e-05,
                6.9622570777680525e-06,
                6.144175333926503e-06,
                1.89251572481201e-05,
                6.962259568889411e-06,
                5.422219614951598e-06
            ],
            [
                1.2098661161239298e-06,
                3.2887486729337966e-06,
                1.2098662603499435e-06,
                3.288750633139005e-06,
                7.338208055369664e-07,
                3.2887482810801374e-06,
                1.0677033790757595e-06,
                3.2887486728201357e-06,
                3.466324971396247e-07,
                1.2098661161239298e-06
            ],
            [
                0.9999852610197902,
                0.9999898700078131,
                0.9999921107336532,
                0.9999687980737689,
                0.9149009474519223,
                0.9999945777823245,
                0.999981074851795,
                0.9999869928684394,
                0.9999756997563912,
                0.9999599363126541
            ],
            [
                3.2887486731641103e-06,
                1.7603436329394601e-06,
                1.9947292458004866e-06,
                1.9947301970287804e-06,
                2.902313022984344e-06,
                4.2228349539810764e-06,
                3.7266401722360055e-06,
                4.785096205717126e-06,
                1.99472995920443e-06,
                8.315282258756395e-07
            ],
            [
                1.7603438427852151e-06,
                1.7603434231241496e-06,
                7.338213304283347e-07,
                1.760344052632596e-06,
                1.9947292458930106e-06,
                1.9947306723745965e-06,
                1.2098655392354511e-06,
                1.7603438428028262e-06,
                1.994729721469003e-06,
                1.3709572068272963e-06
            ],
            [
                5.4222202617511845e-06,
                2.902311984989368e-06,
                3.2887506334560605e-06,
                1.4738983727900215e-05,
                9.422449308566668e-07,
                4.222833444429485e-06,
                1.0677028699858827e-06,
                4.785096205830278e-06,
                1.0129992186589747e-05,
                6.144173136729416e-06
            ],
            [
                0.99998329858015,
                0.9999980052707541,
                0.9999938558268643,
                0.999996273358939,
                0.9999945777829697,
                0.9999970976876693,
                0.999997097688361,
                0.999995214906076,
                0.9999687980737645,
                0.9999977396754329
            ],
            [
                6.144173135896795e-06,
                5.422220906065395e-06,
                1.4738976691331275e-05,
                8.939700565834043e-06,
                1.4738980207363312e-05,
                3.120190015664183e-05,
                3.1201926201134365e-05,
                3.535623801292338e-05,
                3.288747887916428e-06,
                3.120191132631554e-05
            ],
            [
                0.9999869928730934,
                0.9999930377404308,
                0.9999885212305079,
                0.9999898700102291,
                0.9999910603068963,
                0.9999810748495053,
                0.9999977396765105,
                0.9999785550515924,
                0.999981074847252,
                0.99995993630783
            ],
            [
                1.5534971989427613e-06,
                1.3709567165461505e-06,
                6.47594643788744e-07,
                4.4508489275469177e-07,
                8.315282258900085e-07,
                8.315280276263186e-07,
                1.994729007841999e-06,
                3.7266383952696564e-06,
                2.9023126768680736e-06,
                4.785096775676685e-06
            ],
            [
                1.2098652508144226e-06,
                7.889265406294507e-06,
                6.475948753794598e-07,
                4.222833443461647e-06,
                3.9278605976725394e-07,
                4.785095064819011e-06,
                7.889260703619978e-06,
                1.7603425837494853e-06,
                3.726640616670918e-06,
                4.222832437386106e-06
            ],
            [
                0.9982992775403373,
                0.9999910603036969,
                0.9999485577925392,
                0.9999756997505882,
                0.9999930377429205,
                0.999964643732436,
                0.9971990729977621,
                0.9999898700066134,
                0.9999945777816768,
                0.9999852610162746
            ],
            [
                0.9999785550515884,
                0.9999756997622014,
                0.9999038976081925,
                0.8354835330070839,
                0.9999977396755559,
                0.9999546021422361,
                0.9999251537817307,
                0.99998699287309,
                0.9999930377430093,
                0.999983298570206
            ],
            [
                4.539787398489018e-05,
                4.785096205512581e-06,
                8.939699485529578e-06,
                4.78509563535725e-06,
                1.1478768124992398e-05,
                0.9999869928700112,
                1.3007126910649678e-05,
                0.9993736658542783,
                1.300712380455751e-05,
                6.962256248871951e-06
            ],
            [
                6.962254589104433e-06,
                9.422444814458256e-07,
                1.5534984951673385e-06,
                2.9023130230133794e-06,
                2.5612819047646128e-06,
                5.422217029391264e-06,
                3.2887486729876365e-06,
                1.0129989769188164e-05,
                1.2098658276862581e-06,
                2.9023109469023766e-06
            ],
            [
                0.9986749778600742,
                0.9999869928669918,
                0.9999785550515972,
                0.9999952149066473,
                0.9999990577555185,
                0.9999980052705164,
                0.9999977396765105,
                0.999998239656367,
                0.9999991684718732,
                0.9999938558246659
            ],
            [
                3.7266379509129646e-06,
                7.889259762494174e-06,
                6.96225790542316e-06,
                4.222832435926668e-06,
                1.4738987238035806e-05,
                4.78509277928088e-06,
                5.422219612229437e-06,
                1.2098655391947376e-06,
                1.7603427931548347e-06,
                1.3007125355533295e-05
            ],
            [
                0.999972464302344,
                0.9999945777810637,
                0.9999546021314167,
                0.9999945777823233,
                0.9999832985801526,
                0.9999756997480622,
                0.9999957771675626,
                0.9999938558232027,
                0.9998204720353157,
                0.9998415637077078
            ],
            [
                8.939697366289195e-06,
                4.7850956352353935e-06,
                5.422220908314139e-06,
                3.726639283129085e-06,
                1.892514369215675e-05,
                0.9149009468718409,
                1.3007130012010681e-05,
                3.2887478880061605e-06,
                3.7266379512518984e-06,
                3.726640616670918e-06
            ],
            [
                0.9999785550541526,
                0.9999724643121858,
                0.9999957771665557,
                0.9999938558224686,
                0.9999994284996891,
                0.9999852610110026,
                0.9999852610162734,
                0.999981074854021,
                0.9998415638404197,
                0.999994577778445
            ],
            [
                1.3709576970824327e-06,
                4.222833946645451e-06,
                6.47594643784032e-07,
                3.2887498491620677e-06,
                1.994730434735237e-06,
                1.0677032518413822e-06,
                9.422448184681581e-07,
                3.726637951079042e-06,
                2.561281294558644e-06,
                5.715005832510042e-07
            ],
            [
                5.422217670657454e-06,
                5.422220907554695e-06,
                6.144176798870286e-06,
                1.147876812106705e-05,
                6.962259568078904e-06,
                2.2603253754284284e-06,
                1.99472900790731e-06,
                2.9023133684671433e-06,
                1.012999097276641e-05,
                6.144175333401224e-06
            ],
            [
                1.9947299591826594e-06,
                1.2098655392354511e-06,
                1.7603434230729168e-06,
                2.9023109468548636e-06,
                3.2887494573232236e-06,
                1.5534975692683091e-06,
                5.043472278159142e-07,
                7.338213304243302e-07,
                7.338209805170655e-07,
                1.760342583722268e-06
            ],
            [
                6.144172402765906e-06,
                6.144176065314267e-06,
                1.1478768119563723e-05,
                6.96225541916544e-06,
                0.00015843625401225367,
                0.00010889690897128673,
                7.484620931490225e-05,
                6.962259563139869e-06,
                0.9995694428675965,
                0.9990889488044867
            ],
            [
                0.9999885212264018,
                0.9999970976883611,
                0.9999970976890531,
                0.9999921107364758,
                0.9999980052702786,
                0.999997097686631,
                0.9999984465018751,
                0.9999869928699887,
                0.999978555056703,
                0.999998239656577
            ],
            [
                0.9999724643154788,
                0.9999810748517881,
                0.9999251537818522,
                0.9999785550567315,
                0.9999417087276304,
                0.9999952149037964,
                0.999948557792528,
                0.9999810748518191,
                0.9999251537996787,
                0.9999885212277717
            ],
            [
                1.6701415862785876e-05,
                6.144174601309452e-06,
                4.222833443553821e-06,
                6.144174601588856e-06,
                5.422221555192784e-06,
                4.22283193393364e-06,
                6.144177531208195e-06,
                0.9999251537370873,
                6.144175332596544e-06,
                4.785093923982095e-06
            ],
            [
                2.2603248367358324e-06,
                1.3709572068079696e-06,
                6.475949525878687e-07,
                2.9023133689924295e-06,
                2.9023112930949896e-06,
                2.2603242976733308e-06,
                1.5534979397267575e-06,
                4.785095634356291e-06,
                2.9023109471188266e-06,
                9.422443692090534e-07
            ],
            [
                0.9997040428307052,
                0.9999785550413645,
                0.9993736658323811,
                0.999996273360716,
                0.9999898700102285,
                0.9998204720128236,
                0.9999952149066464,
                0.999998005269803,
                0.999373665753063,
                0.9999986290424663
            ],
            [
                1.0129987355988324e-05,
                1.3007123808153756e-05,
                6.962255418924822e-06,
                1.300712846361323e-05,
                8.939697368663308e-06,
                1.0129989771823107e-05,
                3.288750241374845e-06,
                1.670142781432848e-05,
                1.0129988561906404e-05,
                6.144176799099397e-06
            ],
            [
                6.475947209826952e-07,
                1.3709570433075437e-06,
                8.315277302588544e-07,
                9.422443692261927e-07,
                8.315279285149107e-07,
                1.0677029973056687e-06,
                1.0677031245186523e-06,
                1.5534975693347152e-06,
                5.715005832762133e-07,
                2.561281294616881e-06
            ],
            [
                0.9999962733598278,
                0.6224593312018546,
                0.9999938558253997,
                0.9999974387168735,
                0.9999646437366672,
                0.9999982396559474,
                0.9999962733602719,
                0.9999952149066462,
                0.9999938558275958,
                0.9999962733598275
            ],
            [
                1.4738980205164923e-05,
                1.4738980212644815e-05,
                6.144176066051891e-06,
                2.430023493485234e-05,
                8.315283249833015e-07,
                3.288748673295719e-06,
                7.889263525405172e-06,
                3.7266392839832006e-06,
                1.0129988562661878e-05,
                6.962259564532931e-06
            ],
            [
                7.889261643727018e-06,
                6.144177530671741e-06,
                2.260324296176746e-06,
                6.962259568775433e-06,
                1.6701415855069562e-05,
                3.1201922508819695e-05,
                1.4738988986723215e-05,
                1.1478764012939119e-05,
                3.2887502407856003e-06,
                4.785092782396909e-06
            ],
            [
                0.9999910603036964,
                0.9999952149049351,
                0.9999967112497589,
                0.9999977396746245,
                0.9999910603015658,
                0.9999898700053989,
                0.9999885212359819,
                0.9999957771665557,
                0.999998629042303,
                0.9999910603026315
            ],
            [
                2.26032429753354e-06,
                2.260324028351814e-06,
                3.2887498492518007e-06,
                1.5534977544565482e-06,
                1.5534973840150989e-06,
                2.9023109471188266e-06,
                9.422444815006715e-07,
                1.9947299591826594e-06,
                7.889261644358435e-06,
                3.7266383955611403e-06
            ],
            [
                1.0677031245710902e-06,
                9.422443691893433e-07,
                9.422443692261927e-07,
                5.715004470077356e-07,
                7.338208055489796e-07,
                1.067703379136937e-06,
                1.5534983100016177e-06,
                1.067702488159652e-06,
                7.338211554591642e-07,
                6.47594566594213e-07
            ],
            [
                0.9999970976873236,
                0.999997438718411,
                0.9999546021422212,
                0.9999810748472503,
                0.9999957771645422,
                0.9999724643122221,
                0.9999930377404305,
                0.9999646437325401,
                0.9997965729306721,
                0.9999869928730883
            ],
            [
                0.9999995549150542,
                0.9999977396751633,
                0.9999970976890531,
                0.9999957771665562,
                0.9999977396762411,
                0.999992110739296,
                0.9999810748517634,
                0.9999957771665556,
                0.9999785550515884,
                0.9999984465026159
            ],
            [
                0.9999852610233037,
                0.9999898700066079,
                0.9999646437451138,
                0.9998415637650148,
                0.9997040429044063,
                0.9997965731002156,
                0.9999646437325226,
                0.9999852610127595,
                0.9998911030918368,
                0.9999945777805428
            ],
            [
                0.9999869928684356,
                0.9999869928715386,
                0.9999990577554334,
                0.9999952149060762,
                0.9465966645506148,
                0.9999417087415159,
                0.9999910603068942,
                0.9999952149066462,
                0.9999785550464798,
                0.9999938558268635
            ],
            [
                1.5534973840377051e-06,
                4.7850933535006355e-06,
                1.370956716519966e-06,
                4.785095064436034e-06,
                5.422219615582823e-06,
                1.760342793515064e-06,
                1.3709575333525227e-06,
                1.3709576970026324e-06,
                1.760344052632596e-06,
                2.2603242978007868e-06
            ],
            [
                0.9996200154340422,
                0.9999945777810749,
                0.9999967112513882,
                0.9999687980849468,
                0.8933094074745445,
                0.9999810748472581,
                0.970687767181726,
                0.9999869928653436,
                0.9999930377429491,
                0.999978555048373
            ],
            [
                1.6701429807630274e-05,
                7.889265406438011e-06,
                1.670142781025767e-05,
                1.0129993394314164e-05,
                1.3007134666431358e-05,
                1.6701423829669885e-05,
                1.0129994601688632e-05,
                8.939697368842181e-06,
                1.1478764019787597e-05,
                1.0129987354882753e-05
            ],
            [
                1.370957533625589e-06,
                5.715003788317969e-07,
                1.3709575335121232e-06,
                9.422449307649713e-07,
                5.043472879121577e-07,
                8.3152792848466e-07,
                3.7266392828579377e-06,
                2.5612822104232297e-06,
                2.2603248362013377e-06,
                2.2603253754921562e-06
            ],
            [
                0.9997388096936793,
                8.315284240508931e-07,
                2.90231302150879e-06,
                2.9023109470871505e-06,
                6.1441760654483806e-06,
                6.144173867284299e-06,
                6.962259567217739e-06,
                8.93969736547614e-06,
                2.2603253754284284e-06,
                4.785094493184135e-06
            ],
            [
                0.9999982396559483,
                0.9999417087067299,
                0.9999962733598274,
                0.9999970976869772,
                0.9999756997592735,
                0.9999970976880149,
                0.9999984465016899,
                0.9525741231199173,
                0.9999930377429208,
                0.9999869928715369
            ],
            [
                5.422217676101776e-06,
                5.422217674937953e-06,
                8.315280274463265e-07,
                2.260324567227179e-06,
                2.9023116387069255e-06,
                2.2603237587774727e-06,
                2.3823685318502406e-07,
                2.5612831264675113e-06,
                2.260324567177841e-06,
                1.2098661160237963e-06
            ],
            [
                9.422442568660309e-07,
                5.043474081739295e-07,
                5.04347528438253e-07,
                2.902311984783477e-06,
                4.222833444037741e-06,
                4.450849988758202e-07,
                1.3709570433661467e-06,
                3.4663262110425684e-07,
                3.7266392835086923e-06,
                4.450849458125204e-07
            ],
            [
                0.9999921107383638,
                0.9999251537461931,
                0.9999546021206818,
                0.9999485577682591,
                0.9982992772231034,
                0.9999417087067041,
                0.9997965729556724,
                0.9999417087417835,
                0.9997965729308586,
                0.9999599362935286
            ],
            [
                2.9023126767836054e-06,
                3.288748673035494e-06,
                3.7266401720529807e-06,
                8.315280276096808e-07,
                1.0677033791437343e-06,
                1.2098659718539182e-06,
                3.2887482810382622e-06,
                1.760344052650207e-06,
                1.553498495189945e-06,
                1.994729721469003e-06
            ],
            [
                0.9998601779265519,
                0.9997965731021218,
                0.9999251538000059,
                0.9999810748540635,
                0.9999832985762651,
                0.9998766053962621,
                0.9999038975853087,
                0.9994472214043354,
                0.9996646499723789,
                0.9999687980812332
            ],
            [
                0.9999485577992279,
                0.9241418152779358,
                0.9990889489597765,
                0.999993855823938,
                0.9999869928746643,
                0.9999251538034408,
                0.9999251537568284,
                0.9999962733611618,
                0.9991959141552845,
                0.9999151889501908
            ],
            [
                0.999997097686631,
                0.9998204720144014,
                0.9999930377462453,
                0.9999996940978095,
                0.9999996072138934,
                0.9999977396762411,
                0.9999989322968754,
                0.9999994284996211,
                0.9999980052707544,
                0.9999970976873231
            ],
            [
                1.209865394936899e-06,
                0.9999997617630616,
                4.222835457852533e-06,
                0.9999998724809571,
                3.7266410608245674e-06,
                NaN,
                1.9947290080343035e-06,
                3.7266397278180926e-06,
                3.2887478889513447e-06,
                3.726639727994339e-06
            ],
            [
                5.71500719531729e-07,
                1.7603427935342762e-06,
                9.422442568763144e-07,
                7.338211554725124e-07,
                5.422217030614265e-06,
                1.5534981249496567e-06,
                1.9947299592407137e-06,
                1.9947290080905435e-06,
                8.315279285012978e-07,
                1.553497384180408e-06
            ],
            [
                0.999948557774137,
                0.9997965730999907,
                0.9999810748472515,
                0.9998415638209939,
                0.9999687980998273,
                0.9999832985721934,
                0.9994472212699463,
                0.9994472212635469,
                0.9999599363078385,
                0.9998766053666093
            ],
            [
                0.9997040427983367,
                0.9046505286741726,
                0.9999687980774944,
                0.9999785550567315,
                0.7057850154599562,
                0.9993736659873375,
                0.9998766053824968,
                0.9999930377462836,
                0.9999417087077529,
                0.9998911031041261
            ],
            [
                0.9999898700103612,
                0.9999967112514797,
                0.999999168471675,
                0.9999952149049401,
                0.9999910603069206,
                0.9999938558261529,
                0.9999984465018754,
                0.9999930377462427,
                0.9999984465024307,
                0.9999938558254022
            ],
            [
                0.999985261012766,
                0.9914225157267514,
                0.9999921107364748,
                0.999964643745208,
                0.999975699762255,
                0.9999910603005098,
                0.9999038975631381,
                0.9996200155631845,
                0.9999546021422212,
                0.9998601779102848
            ],
            [
                4.2228324375512536e-06,
                1.3709575336860625e-06,
                1.5534973841705173e-06,
                8.315280276546789e-07,
                1.2098659718990333e-06,
                2.2603242976733308e-06,
                2.260324028331257e-06,
                0.9999984465016923,
                1.9947292458603553e-06,
                4.785096205173126e-06
            ],
            [
                0.9999967112509348,
                0.9999989322971301,
                0.9999930377429213,
                0.9999921107355341,
                0.9999982396574166,
                0.9999957771645432,
                0.9999980052705163,
                0.9999982396559474,
                0.914900952092573,
                0.9999974387171787
            ],
            [
                0.9999251537817928,
                0.99995460211518,
                0.9999785550516282,
                0.9999151889490716,
                0.9999852610162822,
                0.9999910603058326,
                0.9999546021313874,
                0.999991060304762,
                0.9999785550465079,
                0.9999485577987062
            ],
            [
                3.2887490645272776e-06,
                1.9947306720480425e-06,
                7.88926352407059e-06,
                2.56128282048266e-06,
                1.3007128463352975e-05,
                4.222834953520201e-06,
                1.9947299590810645e-06,
                1.370956879727337e-06,
                5.422218322565793e-06,
                3.7266388391993445e-06
            ],
            [
                0.9999952149060766,
                0.9999974387168733,
                0.9999945777829745,
                0.9999974387165683,
                0.9999832985821409,
                0.9669140180359896,
                0.9999984465022455,
                0.9999962733598318,
                0.9999984465028011,
                0.9525741261492485
            ],
            [
                2.561282210590951e-06,
                6.144172403335888e-06,
                6.144173136131494e-06,
                1.0129988563914856e-05,
                3.7266383951544193e-06,
                2.260323489435463e-06,
                7.88926446470893e-06,
                6.9622562478334885e-06,
                3.288749065167371e-06,
                1.2098656834613962e-06
            ],
            [
                2.561281905100056e-06,
                3.726638395493353e-06,
                1.7603432132784448e-06,
                1.9947304348595095e-06,
                0.9999724643089846,
                2.902310946944611e-06,
                3.726637951079042e-06,
                1.8925150489517924e-05,
                1.9947304347570075e-06,
                9.42244930862237e-07
            ],
            [
                0.9999646437535114,
                0.9999952149032237,
                0.9999885212305093,
                0.9999962733607161,
                0.9999810748450044,
                0.9999910603015651,
                0.9999921107374152,
                0.9999885212305084,
                0.9706877719515358,
                0.999983298578157
            ],
            [
                0.9399133561377043,
                0.999993037741262,
                0.9999945777791415,
                0.9999957771680733,
                0.9999546021205649,
                0.999988521227886,
                0.9999970976866326,
                0.999964643732473,
                0.9999974387168735,
                0.9999974387181093
            ],
            [
                2.2603242976733308e-06,
                2.561281294369958e-06,
                2.5612812938202033e-06,
                4.785095634930755e-06,
                1.8925150490826034e-05,
                3.7266392826613557e-06,
                2.9023126748197205e-06,
                6.962254585710433e-06,
                1.5534984947858565e-06,
                1.4738978445861935e-05
            ],
            [
                0.999997438718407,
                0.9999687980738113,
                0.9999687980998236,
                0.999985261012785,
                0.9999785550515924,
                0.9149009561531424,
                0.9999339478827796,
                0.9999869928653375,
                0.9999930377454446,
                0.9999852610145762
            ],
            [
                0.9999967112513343,
                0.9999989322967594,
                0.9999945777803847,
                0.9999994956524716,
                0.9890130591302806,
                0.9998911030418114,
                0.9999930377462447,
                0.9999980052702787,
                0.999996273358944,
                0.9999970976880166
            ],
            [
                4.785096775389454e-06,
                1.1478766753751021e-05,
                4.785096203588998e-06,
                1.012998856015592e-05,
                6.144175332887123e-06,
                1.3007128440734474e-05,
                1.0129988559160908e-05,
                0.9994472212675345,
                1.4738978441840487e-05,
                7.889265400898766e-06
            ],
            [
                5.422220260656402e-06,
                1.9947294835630703e-06,
                2.1024326583998928e-07,
                6.144173134868593e-06,
                1.55349719872235e-06,
                8.93970056565517e-06,
                5.715005150672525e-07,
                5.4222183221120994e-06,
                3.7266388396128453e-06,
                1.7603438427852151e-06
            ],
            [
                3.2887490645272776e-06,
                1.300712380408432e-05,
                5.422220258959982e-06,
                3.288750632678377e-06,
                1.0677026153784014e-06,
                1.9947290074138497e-06,
                1.5534975692471157e-06,
                9.422449306844166e-07,
                3.2887478881736613e-06,
                6.14417386791016e-06
            ],
            [
                6.9622554185195676e-06,
                4.222835458002318e-06,
                1.994729483630195e-06,
                6.14417313680765e-06,
                7.889262582571338e-06,
                6.144172403928222e-06,
                3.7266410607194972e-06,
                1.994729483508644e-06,
                1.1478772229989872e-05,
                3.2887478889513447e-06
            ],
            [
                1.1478768122695653e-05,
                4.222831934052698e-06,
                2.2603234893594005e-06,
                3.2887506332945414e-06,
                7.889264463890957e-06,
                1.0129994600638342e-05,
                6.144177530548804e-06,
                4.785092782936557e-06,
                1.0129989769722525e-05,
                2.5612834315811786e-06
            ],
            [
                3.288750241374845e-06,
                4.785093353352668e-06,
                6.962254588724508e-06,
                2.561281599881745e-06,
                2.9023133687786197e-06,
                4.222835457906302e-06,
                1.2098659718847284e-06,
                6.144174601588856e-06,
                1.2098656834723998e-06,
                1.0677027426709671e-06
            ],
            [
                1.5534979397140412e-06,
                1.3709572068079696e-06,
                5.715007195410849e-07,
                1.3709567164663505e-06,
                1.0677032518700286e-06,
                1.3709570433536782e-06,
                5.71500583272315e-07,
                1.209866116170145e-06,
                2.9023119851055122e-06,
                1.553498495308628e-06
            ],
            [
                0.9940889321151374,
                0.9999339478637023,
                0.9999546021260217,
                0.9994472212593662,
                0.9998601778614898,
                0.999959936307828,
                0.999620015569143,
                0.9996646499314886,
                0.9997040429040188,
                0.9991959139649924
            ],
            [
                6.144177530794679e-06,
                4.785093353352668e-06,
                2.5612819048205203e-06,
                5.4222183209778656e-06,
                3.288749065167371e-06,
                3.2887502411564953e-06,
                2.561283431942246e-06,
                3.2887498492936755e-06,
                6.962258738131379e-06,
                2.9023133689924295e-06
            ],
            [
                9.422447062202052e-07,
                1.3709570433075437e-06,
                1.760344052693435e-06,
                7.338209805133949e-07,
                2.2603237588597026e-06,
                1.7603432132624344e-06,
                7.338209804987119e-07,
                5.043476486883855e-07,
                3.466325384589045e-07,
                2.5612831265630198e-06
            ],
            [
                1.3709572067356507e-06,
                3.7266388392671313e-06,
                5.4222170304318e-06,
                1.2098656834834034e-06,
                1.2098659718363124e-06,
                2.9023133687311063e-06,
                2.902310946031299e-06,
                1.670142781244497e-05,
                2.260324836624822e-06,
                6.144173869072478e-06
            ],
            [
                0.9999938558224694,
                0.9999038975836001,
                0.9999930377452697,
                0.999998239656998,
                0.9999869928761882,
                0.9999930377429278,
                0.9999869928708465,
                0.9999832985841333,
                0.9999967112497586,
                0.9999832985782724
            ],
            [
                6.144176799099397e-06,
                6.144175333401224e-06,
                2.561282821176841e-06,
                7.889261643181705e-06,
                7.338209805090567e-07,
                4.222833947774596e-06,
                6.144175333289463e-06,
                3.726640616670918e-06,
                5.422220908762902e-06,
                1.5534973841705173e-06
            ],
            [
                0.9999957771660757,
                0.9994472213983538,
                0.9999810748541009,
                0.9999852610131515,
                0.999664650013162,
                0.9626731135929119,
                0.999948557792528,
                0.9626731125220075,
                0.9990889489403851,
                0.9999756997571019
            ],
            [
                1.9947292458004866e-06,
                1.553498310118888e-06,
                2.5612812945260317e-06,
                2.9023133689924295e-06,
                2.260325375650449e-06,
                1.9947306726049992e-06,
                4.222834450505264e-06,
                3.05902263389638e-07,
                6.475949525919915e-07,
                1.3709578604981489e-06
            ]
        ]
    },
    {
        "q_id": "8291_mmlu_math",
        "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": [
            [
                0.9999989322971299,
                0.9999992661792819,
                0.9999982396567868,
                0.9999977396751633,
                0.9999991684719723,
                0.9999982396561572,
                0.9999945777797377,
                0.999999057755743,
                0.9999982396567868,
                0.9999967112517189
            ],
            [
                0.9999957771660524,
                0.9999957771680658,
                0.9999945777829694,
                0.9999974387187053,
                0.99999862904312,
                0.9999991684722698,
                0.999998239656367,
                0.9999962733598274,
                0.9999952149055052,
                0.9999938558275956
            ],
            [
                0.9999977396765105,
                0.9999990577554061,
                0.9999992661786695,
                0.9999982396574163,
                0.9999982396574162,
                0.9999930377412608,
                0.9999977396757022,
                0.9999921107383553,
                0.9999945777790913,
                0.9999982396574162
            ],
            [
                0.9999977396762411,
                0.9999984465016899,
                0.9999967112505427,
                0.9999989322968753,
                0.9999952149055052,
                0.9999898700041907,
                0.9999980052702785,
                0.9999852610233005,
                0.9999986290423029,
                0.9999910603015649
            ],
            [
                3.2887482811908074e-06,
                5.422221555069497e-06,
                2.430023783601594e-05,
                1.147877086073156e-05,
                1.670141587031992e-05,
                1.7603427935678977e-06,
                8.939699500489763e-06,
                0.9999869928668849,
                1.3007123812057577e-05,
                2.1444953524161264e-05
            ],
            [
                0.9999962733589389,
                0.999992110739296,
                0.9999885212332433,
                0.999996273360716,
                0.9999885212305069,
                0.999989870011436,
                0.999997438716568,
                0.9999970976880148,
                0.9999986290426297,
                0.9999957771680656
            ],
            [
                0.999991060304762,
                0.9999952149055054,
                0.9999885212264011,
                0.9999970976890529,
                0.999995214904935,
                0.9999910603004997,
                0.9999986290421394,
                0.9999989322970027,
                0.9999967112509347,
                0.9999974387184
            ],
            [
                0.9999986290432834,
                0.9999957771675624,
                0.9999945777816769,
                0.9999974387184,
                0.999997097686977,
                0.9999945777823231,
                0.999997438716568,
                0.9999957771680658,
                0.9999970976887068,
                0.9999980052707542
            ],
            [
                0.9999957771660521,
                0.9999980052700407,
                0.9999921107383554,
                0.9999980052702785,
                0.9999957771650454,
                0.9999970976866309,
                0.9999990577552937,
                0.9999970976880149,
                0.9999962733602717,
                0.999996273358939
            ],
            [
                1.6701417861189946e-05,
                1.300712691308661e-05,
                2.753568778107642e-05,
                2.561283431942246e-06,
                5.1442232038504445e-05,
                0.9999910603015644,
                0.9999869928684346,
                6.144176066353646e-06,
                4.785096205582214e-06,
                4.539786862811735e-05
            ],
            [
                0.9997965729545062,
                0.9999910603036963,
                6.144176798590883e-06,
                5.422221554847581e-06,
                7.889263525663481e-06,
                1.01299933928585e-05,
                0.9999898700102287,
                3.120191137126484e-05,
                0.00013982214054859745,
                4.5397884856980825e-05
            ],
            [
                0.9999970976887068,
                0.9999974387177893,
                0.9999980052705163,
                0.9999992661791944,
                0.9999987901344607,
                0.9999984465022455,
                0.9999982396561572,
                0.999999168471675,
                0.999997438716568,
                0.9999990577552939
            ],
            [
                0.9999980052702785,
                0.9999952149066462,
                0.9999945777816768,
                0.999996273358939,
                0.9999974387168733,
                0.999997438717484,
                0.999997438717484,
                0.9999967112497585,
                0.9999982396572065,
                0.9999982396561572
            ],
            [
                0.999995214903224,
                0.9999982396574163,
                0.9999938558239333,
                0.9999989322967481,
                0.9999910603068939,
                0.999997438716568,
                0.9999970976866309,
                0.9999962733616045,
                0.9999957771655488,
                0.9999974387177893
            ],
            [
                4.006368262694324e-05,
                2.144494072680393e-05,
                4.539787944306515e-05,
                2.4300243620398656e-05,
                5.14422075023447e-05,
                3.120191137012976e-05,
                8.939694170729447e-06,
                0.9999898700102282,
                0.00017952794393195324,
                1.012999460108057e-05
            ],
            [
                0.9999957771650453,
                0.999999266179107,
                0.999997438717484,
                0.999998239656367,
                0.999997438716568,
                0.9999980052695652,
                0.9999992661786696,
                0.9999994956527721,
                0.9999977396757022,
                0.9999962733611603
            ],
            [
                4.785094494628999e-06,
                1.473898723610551e-05,
                8.481101097331865e-05,
                0.9999910603036969,
                0.9999910603026306,
                0.00020342692360949345,
                0.00012339460396224868,
                4.5397884859458064e-05,
                7.484623611811155e-05,
                8.481108168178473e-05
            ],
            [
                0.9999957771665555,
                0.9999980052702786,
                0.9999982396572065,
                0.9999967112493665,
                0.9999982396559473,
                0.9999980052695652,
                0.9999996940977002,
                0.9999980052709919,
                0.99999862904312,
                0.9999986290429567
            ],
            [
                2.430024362791279e-05,
                7.889265406151004e-06,
                3.120191136774608e-05,
                0.9999898700078131,
                0.9999687980923553,
                0.9996646497721616,
                0.9999852610110012,
                1.1478766754941153e-05,
                0.9999546021421896,
                2.7535681241281285e-05
            ],
            [
                0.9999945777810303,
                0.9999980052709919,
                0.9999885212305059,
                0.9999984465022455,
                0.9999930377404306,
                0.9999938558261305,
                0.9999898700078134,
                0.9999957771675625,
                0.9999952149032236,
                0.9999930377412608
            ],
            [
                0.00023050671360258008,
                4.539788485169606e-05,
                1.4738988999377379e-05,
                0.9999832985821384,
                6.605212102411961e-05,
                9.610240337377108e-05,
                0.9999810748472489,
                4.5397874044343825e-05,
                2.144495096387783e-05,
                0.9999938558246656
            ],
            [
                0.9999980052702786,
                0.9999974387177893,
                0.9999982396569966,
                0.9999984465024306,
                0.9999970976883609,
                0.9999980052695652,
                0.999998446502801,
                0.9999986290424663,
                0.9999921107355337,
                0.9999977396746244
            ],
            [
                0.9999962733611603,
                0.9999885212291383,
                0.999986992876188,
                0.9999962733611601,
                0.9999977396746244,
                0.9999957771650453,
                0.9999957771650454,
                0.9999930377454102,
                0.9999945777829694,
                0.9999945777816767
            ],
            [
                0.9999977396762411,
                0.9999970976869769,
                0.9999977396765105,
                0.9999938558261308,
                0.9999986290424663,
                0.999989870009021,
                0.9999974387168732,
                0.999997438716568,
                0.9999957771650453,
                0.9999970976876689
            ],
            [
                0.9999977396765105,
                0.9999967112501507,
                0.9999977396765105,
                0.9999993524054334,
                0.9999910603068949,
                0.9999986290426297,
                0.999999266178932,
                0.9999967112521109,
                0.9999970976873229,
                0.9999970976880148
            ],
            [
                0.9999945777829695,
                0.9999980052705163,
                0.9999967112517186,
                0.9999957771665555,
                0.9999952149066462,
                0.9999974387168733,
                0.9999977396754327,
                0.9999962733611603,
                0.9999952149032236,
                0.9999989322973845
            ],
            [
                0.9999984465018751,
                0.9999938558239335,
                0.9999938558239334,
                0.9999885212277699,
                0.9999982396563669,
                0.9999970976890528,
                0.9999910603058276,
                0.9999977396748938,
                0.9999967112493664,
                0.9999982396563669
            ],
            [
                0.9999977396748938,
                0.9999984465020603,
                0.9999810748449929,
                0.9999967112521109,
                0.9999957771655487,
                0.9999984465016898,
                0.999997097686631,
                0.9999967112509347,
                0.9999970976876689,
                0.9999987901344607
            ],
            [
                1.0129988563914856e-05,
                1.892514147143123e-05,
                0.9999977396748938,
                2.753568781423318e-05,
                3.288748281220719e-06,
                1.1478764018827141e-05,
                2.144494074201677e-05,
                5.1442195242316055e-05,
                6.1441746016670885e-06,
                3.7266410609940346e-06
            ],
            [
                0.9999986290421394,
                0.9999952149060758,
                0.9999989322975118,
                0.9999921107364741,
                0.9999980052702785,
                0.999998446502801,
                0.9999957771680658,
                0.9999989322967482,
                0.999995214904935,
                0.9999962733620488
            ],
            [
                0.9999962733602717,
                0.9999910603026305,
                0.9999962733593831,
                0.9999945777829696,
                0.9999962733598274,
                0.9999952149066462,
                0.9999952149037941,
                0.9999921107355337,
                0.9999970976869769,
                0.9999898700126431
            ],
            [
                0.9999989322970027,
                0.9999938558268633,
                0.9999986290421394,
                0.9999910603058279,
                0.9999977396757022,
                0.9999967112493664,
                0.9999987901344608,
                0.9999970976869773,
                0.9999991684720715,
                0.9999991684715759
            ],
            [
                0.999996273358939,
                0.9999980052700408,
                0.9999962733598274,
                0.999997438717484,
                0.9999990577551814,
                0.999972464302351,
                0.9999970976887068,
                0.9999957771655487,
                0.9999957771675624,
                0.9999869928715366
            ],
            [
                0.999995777166052,
                0.9999687980811937,
                0.00020342704517711867,
                7.484621827634963e-05,
                3.535626333989112e-05,
                0.9999952149055052,
                0.9999957771645419,
                9.610240323743297e-05,
                3.120192252437034e-05,
                5.144219522247965e-05
            ],
            [
                0.9999980052702785,
                0.9999962733602719,
                0.9999952149032237,
                0.9999992661789321,
                0.9999898700126435,
                0.9999980052693274,
                0.999998446502801,
                0.9999885212305062,
                0.9999974387177893,
                0.9999987901337396
            ],
            [
                0.999997438717484,
                0.9999987901341723,
                0.999999266178757,
                0.9999990577550691,
                0.9999982396567868,
                0.9999989322970027,
                0.9999984465024306,
                0.999999168471675,
                0.9999982396567867,
                0.9999995549147358
            ],
            [
                0.9999977396746244,
                0.9999989322967481,
                0.999996273358939,
                0.9999977396762411,
                0.9999957771655488,
                0.9999977396757022,
                0.9999957771680656,
                0.9999977396746244,
                0.9999993524050473,
                0.9999967112509347
            ],
            [
                0.9999977396746244,
                0.9999977396759716,
                0.9999984465018751,
                0.9999980052702785,
                0.9999991684719723,
                0.9999974387177893,
                0.9999986290423029,
                0.9999986290427931,
                0.9999970976890528,
                0.9999957771650453
            ],
            [
                0.9999984465016899,
                0.9999967112517189,
                0.9999962733602717,
                0.9999967112505427,
                0.99999893229713,
                0.999997097687669,
                0.9999989322973845,
                0.9999957771665557,
                0.9999930377412606,
                0.9999977396765105
            ],
            [
                0.9999977396754327,
                0.9999989322970027,
                0.9999992661788446,
                0.999999057755743,
                0.9999987901343165,
                0.9999989322972572,
                0.9999977396757023,
                0.9999984465026158,
                0.9999986290432834,
                0.9999982396574163
            ],
            [
                0.9999930377420909,
                0.9999938558246669,
                0.9999869928715386,
                0.9999952149055056,
                0.9999952149072165,
                0.999995214904935,
                0.9999967112517187,
                0.9999967112517189,
                0.999994577780384,
                0.9999957771665555
            ],
            [
                0.9999785550567016,
                5.144220137064579e-05,
                2.4300232039788792e-05,
                4.006369218184011e-05,
                4.0063696945516495e-05,
                6.605213677978425e-05,
                3.2887482811908074e-06,
                0.9999852610215426,
                4.785094494019719e-06,
                0.9999485578047914
            ],
            [
                0.9999984465026158,
                0.9999987901341723,
                0.9999984465018751,
                0.9999982396567867,
                0.9999977396759716,
                0.9999938558268632,
                0.9999970976887068,
                0.999997438716568,
                0.9999977396762411,
                0.9999991684720715
            ],
            [
                7.889260703117714e-06,
                1.0129989771473008e-05,
                2.4300252315495453e-05,
                1.0129988564099116e-05,
                2.5612816000331606e-06,
                1.6701415867707307e-05,
                3.2887486732000038e-06,
                1.4738980213985297e-05,
                2.7535684532815695e-05,
                1.553498310118888e-06
            ],
            [
                0.9999952149037942,
                0.9999957771660523,
                0.9999957771675623,
                0.9999921107336528,
                0.9999945777784449,
                0.99999893229713,
                0.9999977396751633,
                0.9999938558224686,
                0.9999989322975118,
                0.9999986290432834
            ],
            [
                0.9999977396748938,
                0.9999977396748938,
                0.9999957771655489,
                0.999995777164542,
                0.9999986290431201,
                0.9999967112497585,
                0.9999984465028011,
                0.9999980052707541,
                0.9999945777823233,
                0.9999967112497585
            ],
            [
                0.9999599363221565,
                0.9999974387165681,
                0.9999957771650456,
                0.9999980052709919,
                0.9999967112493665,
                0.9999974387187053,
                0.9999974387171787,
                0.9999977396754327,
                0.999993037746241,
                0.9999986290423029
            ],
            [
                0.9999962733611603,
                0.9999646437493181,
                0.9999930377429208,
                0.9999990577551815,
                0.9999938558275954,
                0.999993855825398,
                0.9999982396561571,
                0.9999945777784447,
                0.9999962733593831,
                0.9999945777816768
            ],
            [
                0.9999986290432834,
                0.9999977396757022,
                0.9999984465015047,
                0.999992110736476,
                0.9999982396572065,
                0.9999962733611603,
                0.9999977396754327,
                0.9999980052705163,
                0.999998005269803,
                0.9999987901346049
            ],
            [
                0.9999974387187053,
                0.9999921107392955,
                0.9999930377445804,
                0.9999984465015047,
                0.9999970976873229,
                0.999997438716568,
                0.9999885212359799,
                0.9999987901343165,
                0.9999885212264015,
                0.999995777164542
            ],
            [
                0.9999982396574162,
                0.9999994956524715,
                0.9999970976880149,
                0.9999982396567867,
                0.9999980052705163,
                0.999999057755069,
                0.9999957771645425,
                0.9999992661791071,
                0.9999967112497586,
                0.9999980052709919
            ],
            [
                0.9999984465015047,
                0.9999982396565769,
                0.999997438717484,
                0.9999967112497585,
                0.9999962733598274,
                0.9999952149043646,
                0.9999987901344607,
                0.999997097686977,
                0.9999921107345934,
                0.999995777166052
            ],
            [
                0.999999266179107,
                0.9999986290424664,
                0.9999984465022455,
                0.9999832985721865,
                0.9999982396572064,
                0.9999987901338838,
                0.9999957771665556,
                0.9999980052705163,
                0.9999980052707541,
                0.9999986290427931
            ],
            [
                0.9999885212277717,
                0.999997438717484,
                0.9999930377454105,
                0.9999984465022455,
                0.9999980052709919,
                0.9999980052700408,
                0.9999980052700407,
                0.9999967112501504,
                0.9999977396748938,
                0.9999984465016898
            ],
            [
                0.9999989322966208,
                0.9999986290421394,
                0.9999991684719723,
                0.9999977396748938,
                0.9999977396754327,
                0.9999986290431201,
                0.9999977396765105,
                0.9999989322971299,
                0.9999977396757023,
                0.9999990577550691
            ],
            [
                0.9999982396559474,
                0.9999984465016899,
                0.9999992661789321,
                0.999997097686631,
                0.9999982396574162,
                0.9999938558246657,
                0.9999962733593833,
                0.9999957771655488,
                0.9999785550413645,
                0.9999974387168733
            ],
            [
                0.9999986290427931,
                0.999998005269803,
                0.9999993524053562,
                0.9999970976880151,
                0.9999984465015047,
                0.9999984465015046,
                0.9999962733620488,
                0.9999984465015046,
                0.999995777164542,
                0.9999957771665556
            ],
            [
                0.9999980052693274,
                0.9999994956527722,
                0.9999996940976272,
                0.9999982396574162,
                0.9999970976887069,
                0.9999982396574162,
                0.9999984465015046,
                0.9999945777823231,
                0.999998790134028,
                0.9999989322970027
            ],
            [
                0.9999945777797377,
                0.9999980052709919,
                0.9999967112501507,
                0.9999989322970027,
                0.9999957771655488,
                0.9999987901338838,
                0.9999957771650454,
                0.9999980052700408,
                0.9999952149072167,
                0.999996273360716
            ],
            [
                0.9999990577554061,
                0.9999974387180947,
                0.9999980052705164,
                0.9999982396561572,
                0.9999990577554061,
                0.9999989322967482,
                0.9999994956525318,
                0.9999980052693275,
                0.9999980052698031,
                0.9999957771650453
            ],
            [
                2.1444950962395557e-05,
                6.962257079553702e-06,
                6.605216037292109e-05,
                1.3007130012341915e-05,
                2.4300246523066122e-05,
                2.9023116389365734e-06,
                4.222833444467892e-06,
                1.3007128463069061e-05,
                6.144172403827636e-06,
                7.889262583633267e-06
            ],
            [
                0.999988521234613,
                0.9999990577549568,
                0.9999938558253986,
                0.9999952149032239,
                0.9999967112513268,
                0.99999862904312,
                0.9999977396754328,
                0.9999990577554061,
                0.9999986290426298,
                0.9999984465020603
            ],
            [
                0.999997438717484,
                0.9999974387184,
                0.9999986290426298,
                0.9999952149060761,
                0.9999974387168733,
                0.9999832985721853,
                0.9999945777803843,
                0.9999987901344607,
                0.9999885212318752,
                0.999991060300499
            ],
            [
                7.484622710602007e-05,
                8.93969417167259e-06,
                1.1478769492392108e-05,
                4.785092783319532e-06,
                7.33820893021171e-07,
                1.3007128463352975e-05,
                7.889261645090304e-06,
                5.8291286364010624e-05,
                5.422221554758815e-06,
                3.2887494572095624e-06
            ],
            [
                0.9999930377404307,
                4.785094494672519e-06,
                1.8925152749659986e-05,
                3.120192251631124e-05,
                1.8925145982866508e-05,
                0.0001795279867897595,
                2.9023109471452223e-06,
                2.4300249419722622e-05,
                1.9947299591826594e-06,
                4.222832437677995e-06
            ],
            [
                0.9999990577556307,
                0.9999921107364745,
                0.9999982396572065,
                0.9999974387187053,
                0.9999986290426297,
                0.9999945777823231,
                0.9999967112517187,
                0.9999982396574163,
                0.9999921107383549,
                0.9999957771670589
            ],
            [
                0.9999952149049348,
                0.999993855826863,
                0.999997097686977,
                0.999999266178757,
                0.9999910602994336,
                0.9999984465016898,
                0.999998790134028,
                0.9999945777810304,
                0.9999724643121878,
                0.9999930377454104
            ],
            [
                2.1444940739364273e-05,
                7.88926634644516e-06,
                2.7535687793096995e-05,
                0.9999832985801475,
                0.9999910603026303,
                5.422218968083048e-06,
                4.006368738143655e-05,
                0.9999810748517598,
                1.300712536203966e-05,
                0.9999810748495047
            ],
            [
                5.14422381608502e-05,
                1.5534971989907999e-06,
                1.8925141466439755e-05,
                2.1444945853999886e-05,
                0.9999756997476807,
                7.889261644358435e-06,
                9.610242633451056e-05,
                0.9999724643121868,
                0.9999785550541431,
                4.7850933535006355e-06
            ],
            [
                3.535624227734284e-05,
                5.144223814063949e-05,
                8.939698433974813e-06,
                1.0129993392600532e-05,
                5.144220132535887e-05,
                0.9999724642990576,
                3.12019002110123e-05,
                3.288750241500471e-06,
                0.9999832985841293,
                0.9999852610180293
            ],
            [
                0.9999980052707541,
                0.9999910602994346,
                0.9999957771670589,
                0.9999980052695652,
                0.9999938558253983,
                0.9999967112505427,
                0.999985261014516,
                0.9999974387184,
                0.9999982396559474,
                0.9999967112513266
            ],
            [
                0.9999962733593832,
                0.9999945777803838,
                0.9999945777816766,
                0.9999810748472515,
                0.9999921107364738,
                0.9999921107402359,
                0.9999967112497584,
                0.9999974387180947,
                0.9999967112497585,
                0.9999967112513268
            ],
            [
                0.9999962733620488,
                0.9999967112509347,
                0.9999957771680656,
                0.9999938558239334,
                0.9999980052700407,
                0.9999970976883608,
                0.999996273360716,
                0.9999962733616046,
                0.9999945777816768,
                0.9999930377420906
            ],
            [
                0.9999962733602717,
                0.999997438717484,
                0.999998005269803,
                0.9999982396567867,
                0.9999990577554061,
                0.9999957771645419,
                0.9999992661788445,
                0.9999984465020603,
                0.999998629042303,
                0.999997438717484
            ],
            [
                8.939700566143004e-06,
                0.9999962733611601,
                1.8925141465820123e-05,
                0.9999785550515873,
                9.610246047009266e-05,
                2.7535681249595513e-05,
                2.7535681233968765e-05,
                0.9999785550490299,
                2.4300246517938825e-05,
                0.00012339457442243326
            ],
            [
                0.9999986290427931,
                0.999998005269803,
                0.9999970976866309,
                0.9999986290421394,
                0.9999970976876689,
                0.9999980052698031,
                0.9999980052700408,
                0.999999057755743,
                0.99999893229713,
                0.9999994956525918
            ],
            [
                0.9999957771665556,
                2.430023203740195e-05,
                0.9999952149060757,
                0.9999921107392955,
                2.144495096161541e-05,
                5.422218969217281e-06,
                4.5397879450662006e-05,
                2.7535684524701807e-05,
                5.144219522247965e-05,
                6.144175332283612e-06
            ],
            [
                0.9999980052695652,
                0.999999266179107,
                0.9999984465018751,
                0.9999982396569966,
                0.9999989322971299,
                0.999995214906076,
                0.9999977396748938,
                0.999997097688361,
                0.9999992661786696,
                0.9999910603047634
            ],
            [
                0.9999885212332436,
                0.9999945777790913,
                0.9999930377420906,
                0.9999957771670589,
                0.9999945777784448,
                0.9999952149055054,
                0.9999977396746244,
                0.9999984465018751,
                0.9999962733593833,
                0.9999957771660523
            ],
            [
                0.9999982396572065,
                0.9999967112509347,
                0.9999989322970027,
                0.9999970976887068,
                0.9999938558261307,
                0.9999970976887068,
                0.9999945777816768,
                0.9999930377429209,
                0.9999957771680656,
                0.9999967112501505
            ],
            [
                0.999998446502801,
                0.9999991684715759,
                0.9999980052693274,
                0.9999994284996211,
                0.9999962733602717,
                0.999999352405279,
                0.9999974387171787,
                0.9999980052693274,
                0.9999980052702786,
                0.999999352404893
            ],
            [
                0.9999994956524716,
                0.9999989322970027,
                0.9999962733589389,
                0.9999986290421394,
                0.9999980052702785,
                0.9999938558232009,
                0.9999974387180947,
                0.9999977396748938,
                0.9999974387171787,
                0.9999974387168733
            ],
            [
                0.9999980052695652,
                0.9999910603015654,
                0.9999984465018751,
                0.9999987901347491,
                0.9999982396559473,
                0.9999970976880149,
                0.9999977396754328,
                0.9999974387171787,
                0.9999977396762411,
                0.9999987901341723
            ],
            [
                0.9999984465015047,
                0.9999970976880149,
                0.9999977396751633,
                0.999999266178757,
                0.9999986290421394,
                0.9999869928715373,
                0.9999984465020603,
                0.9999991684720715,
                0.9999989322968753,
                0.9999989322973846
            ],
            [
                3.120191136400031e-05,
                5.14422075023447e-05,
                1.300712691308661e-05,
                1.994729483694599e-06,
                0.999972464302337,
                0.9999898700090204,
                4.539785780805251e-05,
                8.481108168178473e-05,
                8.93970056529743e-06,
                4.0063682630732606e-05
            ],
            [
                0.9999930377437504,
                4.5397890237206746e-05,
                4.006370170554982e-05,
                8.93969417150998e-06,
                5.82912862948823e-05,
                0.9999852610233002,
                0.00010889694805897948,
                0.9999599362887179,
                4.006369217615605e-05,
                2.753570421361326e-05
            ],
            [
                0.9999869928653335,
                0.9999852610145148,
                0.9999785550413627,
                2.753569437266178e-05,
                3.120191136774608e-05,
                1.3007133112307748e-05,
                5.144221363404434e-05,
                0.9999832985721833,
                0.999989870010228,
                0.9999756997563743
            ],
            [
                0.9999930377429204,
                1.8925143727854426e-05,
                3.1201903922734266e-05,
                3.726641060956752e-06,
                5.422220262195015e-06,
                0.0003353501474724072,
                9.610241492126045e-05,
                3.535624225316214e-05,
                2.7535684534618784e-05,
                6.1441775312976045e-06
            ],
            [
                0.9999990577554061,
                0.999998239656367,
                0.9999977396762411,
                0.9999962733611603,
                0.9999970976866309,
                0.9999910603047626,
                0.999998239656367,
                0.9999980052700408,
                0.9999977396746244,
                0.9999977396762411
            ],
            [
                0.9999930377420907,
                0.9999980052709919,
                0.9999980052705163,
                0.999997097687669,
                0.9999962733593832,
                0.9999938558224687,
                0.9999977396751633,
                0.9999945777790913,
                0.9999962733611601,
                0.9999962733616045
            ],
            [
                0.9999952149037942,
                0.9999993524051246,
                0.9999952149049349,
                0.9999986290429566,
                0.9999974387168733,
                0.9999952149055052,
                0.9999938558275957,
                0.9999991684721705,
                0.9999938558239335,
                0.9999970976883608
            ],
            [
                0.0001398221406320077,
                3.120191508321514e-05,
                1.6701425825492673e-05,
                7.889260704308795e-06,
                0.9999974387177893,
                5.8291272482788436e-05,
                2.4300240730549767e-05,
                3.120191880867338e-05,
                0.9999869928684351,
                3.2887482809933958e-06
            ],
            [
                0.9999982396561572,
                0.9999994956524716,
                0.9999982396574163,
                0.9999984465016899,
                0.999997097686977,
                0.9999974387171787,
                0.9999990577554061,
                0.9999984465016899,
                0.9999982396567867,
                0.9999986290423029
            ],
            [
                0.9999984465026158,
                0.9999952149066462,
                0.9999987901337396,
                0.9999952149066462,
                0.9999962733616043,
                0.9999984465015047,
                0.9999980052707541,
                0.9999967112501507,
                0.9999993524052018,
                0.9999974387187053
            ],
            [
                5.8291258539226846e-05,
                4.006367785146321e-05,
                2.430023783309869e-05,
                9.610241478352397e-05,
                9.610239198289712e-05,
                5.422217030495909e-06,
                3.535626335262457e-05,
                0.999995214906076,
                4.006367785146321e-05,
                6.605216828103296e-05
            ],
            [
                0.9999984465024306,
                0.9999974387171787,
                0.999999554914895,
                0.9999967112501507,
                0.9999977396754327,
                0.9999986290423029,
                0.9999982396561571,
                0.9999970976880149,
                0.9999992661790195,
                0.9999989322975118
            ],
            [
                0.9999987901344607,
                0.9999982396567867,
                0.9999982396565767,
                0.9999977396754327,
                0.9999930377404307,
                0.9999967112509347,
                0.9999974387168733,
                0.9999987901344607,
                0.9999970976890529,
                0.9999986290427931
            ],
            [
                0.9999832985801468,
                0.999988521231875,
                1.8925141462377723e-05,
                0.9999724643023399,
                3.7266383951544193e-06,
                0.9999898700078128,
                4.006369693910372e-05,
                1.6701427811898146e-05,
                5.144221363703851e-05,
                2.4300249412738893e-05
            ],
            [
                0.00012339458930993918,
                0.00013982210715806904,
                1.892514147143123e-05,
                0.9999785550413638,
                0.999981074842736,
                1.4738978449883382e-05,
                6.1441767987808774e-06,
                0.999954602136796,
                5.14422258772351e-05,
                1.8925157258585e-05
            ],
            [
                6.144176066443055e-06,
                1.994730434816876e-06,
                6.605215251046346e-05,
                0.999968798081203,
                3.1201918806289706e-05,
                0.9999990577549568,
                3.726639284017094e-06,
                6.962257909412379e-06,
                0.9999974387168733,
                9.610243789808358e-05
            ],
            [
                3.5356259128846735e-05,
                4.539785238142359e-05,
                0.9999921107355337,
                2.7535697660090726e-05,
                3.288749849114211e-06,
                3.120191136774608e-05,
                4.006368262883792e-05,
                1.4738985483128763e-05,
                2.1444940738662144e-05,
                1.8925152749659986e-05
            ],
            [
                0.9999984465022455,
                0.9999970976883608,
                0.9999984465024306,
                0.9999970976883609,
                0.9999990577556307,
                0.9999977396746245,
                0.9999967112509346,
                0.999993037743751,
                0.9999967112493665,
                0.9999987901338838
            ],
            [
                0.9999967112521109,
                0.9999967112509347,
                0.9999962733589389,
                0.9999984465015047,
                0.9999967112501504,
                0.9999869928653345,
                0.9999970976883608,
                0.9999945777816767,
                0.9999982396559473,
                0.9999984465020603
            ],
            [
                0.9999785550439179,
                0.9999785550413688,
                0.999738809629067,
                0.00010889696096937699,
                3.535624648542694e-05,
                8.4811031131658e-05,
                2.4300249412738893e-05,
                0.9999785550439195,
                9.610242637576158e-05,
                8.9396973679153e-06
            ],
            [
                0.9999980052705163,
                0.999996273360716,
                0.9999982396567867,
                0.999996273358939,
                0.999999352404893,
                0.9999970976873228,
                0.9999974387180947,
                0.9999970976876689,
                0.9999957771645418,
                0.9999962733602717
            ],
            [
                0.9999962733602716,
                0.9999984465020603,
                0.999997438716568,
                0.9999967112513268,
                0.9999962733598274,
                0.9999962733598274,
                0.9999957771675624,
                0.9999938558224686,
                0.9999930377420911,
                0.9999977396762411
            ],
            [
                0.9999977396748938,
                0.9999970976876689,
                0.9999945777797374,
                0.999998790134605,
                0.9999982396567868,
                0.9999989322971299,
                0.9999990577551815,
                0.9999994284996211,
                0.9999987901343165,
                0.9999982396559474
            ],
            [
                0.999998239656367,
                0.9999993524054334,
                0.9999945777816768,
                0.9999989322973845,
                0.999998446502801,
                0.9999986290427932,
                0.9999967112497585,
                0.9999970976873229,
                0.9999984465016899,
                0.9999970976883608
            ],
            [
                0.9999986290429566,
                0.9999989322968753,
                0.9999967112497585,
                0.9999974387177893,
                0.9999974387177893,
                0.9999977396748938,
                0.9999957771680656,
                0.999999057755743,
                0.9999982396561572,
                0.9999980052707542
            ],
            [
                0.9999977396759716,
                0.9999810748449934,
                0.9999996072138934,
                0.9999962733611604,
                0.999995214904935,
                0.9999952149032236,
                0.9999945777829695,
                0.9999970976880149,
                0.9999952149055054,
                0.9999992661790195
            ],
            [
                1.6701417860795016e-05,
                1.1478764016780948e-05,
                0.9998911031297583,
                3.1201918807538294e-05,
                0.9999756997621654,
                7.484620042097855e-05,
                0.9999910603058274,
                2.7535700932494338e-05,
                0.9999962733611603,
                0.9999687980774743
            ],
            [
                0.9999987901347491,
                0.9999930377437506,
                0.9999977396748938,
                0.9999990577550691,
                0.9999977396751633,
                0.999997097686977,
                0.9999970976890529,
                0.9999967112521106,
                0.9999938558239334,
                0.9999989322975118
            ],
            [
                0.999994577782323,
                0.9999910603036963,
                0.9999945777823235,
                0.9999962733620487,
                0.9999938558232011,
                0.9999910603047617,
                0.9999984465020603,
                0.999993037742921,
                0.9999938558224685,
                0.9999980052702786
            ],
            [
                0.9999485577741026,
                2.4300249419722622e-05,
                0.9999910602994335,
                7.484623610449812e-05,
                2.7535697652678035e-05,
                0.0004305570327007623,
                0.9999957771680658,
                2.9023130230133794e-06,
                0.999996273360716,
                2.144494585583323e-05
            ],
            [
                0.9999996072137061,
                0.999997438716568,
                0.9999980052707541,
                0.9999994956523512,
                0.999996273360716,
                0.9999962733620487,
                0.9999952149055054,
                0.9999921107336528,
                0.9999962733607161,
                0.999992110737415
            ],
            [
                2.9023130228444433e-06,
                5.422217676654099e-06,
                5.144223816384438e-05,
                0.9999832985761651,
                5.144223203551027e-05,
                4.0063711282021514e-05,
                7.889262583633267e-06,
                3.535625911829982e-05,
                7.484624504525627e-05,
                6.605215252055522e-05
            ],
            [
                0.9999982396563669,
                0.9999982396563669,
                0.9999990577555185,
                0.9999980052693274,
                0.9999982396561572,
                0.9999967112501504,
                0.9999974387184,
                0.9999989322975118,
                0.9999989322967482,
                0.9999982396559473
            ],
            [
                0.9999994284994167,
                0.9999986290426298,
                0.9999984465020603,
                0.9999989322967481,
                0.9999970976866309,
                0.9999991684720715,
                0.9999987901347492,
                0.9999980052700407,
                0.9999982396574162,
                0.9999986290429567
            ],
            [
                0.99999862904312,
                0.9999970976873228,
                0.9999993524052018,
                0.9999994956524114,
                0.999999057755743,
                0.999997438717484,
                0.9999982396559473,
                0.9999977396746244,
                0.9999967112521109,
                0.9999991684722698
            ],
            [
                0.999999266178932,
                0.999997438717484,
                0.999997097687669,
                0.9999910603058283,
                0.9999962733589389,
                0.9999986290429566,
                0.9999977396748938,
                0.9999974387165679,
                0.999998446502801,
                0.9999980052702785
            ],
            [
                0.9999982396561572,
                0.9999980052695652,
                0.9999974387171787,
                0.9999990577552937,
                0.9999921107383551,
                0.9999970976876689,
                0.9999957771680659,
                0.9999974387184,
                0.9999982396561572,
                0.9999986290429566
            ],
            [
                0.9999980052705163,
                0.9999990577556307,
                0.9999962733616046,
                0.9999980052702785,
                0.9999990577554061,
                0.9999970976890528,
                0.9999980052705164,
                0.9999984465026158,
                0.999998790134605,
                0.9999970976883609
            ],
            [
                0.9999952149055056,
                0.999998005269803,
                0.9999957771650454,
                0.9999962733620487,
                0.9999962733611603,
                0.9999970976866309,
                0.9999957771665555,
                0.9999810748472503,
                0.9999991684715759,
                0.9999938558253982
            ],
            [
                0.9999957771660521,
                0.9999930377429207,
                0.999996273360716,
                0.999997097686977,
                0.9999952149066467,
                0.9999980052695652,
                0.9999977396754328,
                0.999981074856281,
                0.9999980052700408,
                0.9999945777810304
            ],
            [
                0.9999992661792819,
                0.9999982396572065,
                0.9999996533674615,
                0.999998446502801,
                0.9999994284997573,
                0.9999980052702786,
                0.9999990577549569,
                0.9999989322975118,
                0.9999990577551814,
                0.9999990577552937
            ],
            [
                0.9999993524052789,
                0.9999898700102289,
                0.9999984465026158,
                0.9999962733620488,
                0.9999986290432834,
                0.9999987901343165,
                0.9999977396748938,
                0.99999862904312,
                0.9999994284992805,
                0.9999974387171787
            ],
            [
                0.999994577782323,
                0.00015843625403991587,
                0.9999756997650613,
                2.7535700939406174e-05,
                0.9999869928668841,
                8.481103115695619e-05,
                1.0129992186387057e-05,
                0.0002034270453576574,
                6.962256248314727e-06,
                0.9999646437324344
            ]
        ]
    },
    {
        "q_id": "8435_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            14,
            15,
            16,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            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,
            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,
            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": [
            [
                2.561282515406337e-06,
                3.288749849209925e-06,
                3.288749456563487e-06,
                2.902311292371731e-06,
                4.2228354571957855e-06,
                4.785096205173126e-06,
                2.9023112928785396e-06,
                5.422219614951598e-06,
                2.5612822104232297e-06,
                4.222834953896582e-06
            ],
            [
                1.0129992183070348e-05,
                2.2603242972087315e-06,
                1.994729007809344e-06,
                2.5612812943280275e-06,
                1.1478766744689312e-05,
                4.222833947121688e-06,
                4.785095064044355e-06,
                1.4738987238035806e-05,
                4.7850967718904455e-06,
                6.1441753327418334e-06
            ],
            [
                5.422217029844958e-06,
                1.9947290078746543e-06,
                6.144175333635923e-06,
                5.422218321441422e-06,
                3.726638839395927e-06,
                4.785096773996813e-06,
                3.2887502412970765e-06,
                7.889264463890957e-06,
                6.962254587597396e-06,
                4.222832939064264e-06
            ],
            [
                5.422218320642526e-06,
                2.9023126767836054e-06,
                7.889259754142258e-06,
                6.9622570780973205e-06,
                2.9023123297461457e-06,
                7.889260698453844e-06,
                1.012999218369684e-05,
                7.889259761905808e-06,
                3.726637950723161e-06,
                2.9023109466489728e-06
            ],
            [
                0.9999417087556228,
                0.9997965730044946,
                0.9999687980812931,
                0.9999417087556863,
                0.9999151889388597,
                0.9996646500167718,
                0.9997965729555717,
                0.9984988180151313,
                0.9995121427817936,
                0.995390428160346
            ],
            [
                0.9984988179259626,
                0.9998415637647267,
                0.999796573102175,
                0.9993736659863174,
                0.9998601779106021,
                0.9999485577926721,
                0.999964643753704,
                0.999769493234981,
                0.9996646498554546,
                0.9999417087346256
            ],
            [
                0.9999599363222975,
                0.9998601779286819,
                0.9997694932886712,
                0.995929862306755,
                0.9998415637839542,
                0.9978172834121615,
                0.9997965730289355,
                0.9998204720794298,
                0.9998911030793273,
                0.9997965729312374
            ],
            [
                5.422219612012453e-06,
                4.785093922115089e-06,
                4.7850933527085725e-06,
                4.222832436272325e-06,
                6.1441753313895225e-06,
                5.422220261544064e-06,
                3.7266397272757976e-06,
                0.13296424878721277,
                2.561283431627768e-06,
                4.222832939663403e-06
            ],
            [
                8.939693100361262e-06,
                3.2887482807780376e-06,
                6.96225873459807e-06,
                2.902311638205396e-06,
                3.726641060244989e-06,
                6.144172403201774e-06,
                2.2603242965714493e-06,
                2.9023116384746377e-06,
                2.5612815996930587e-06,
                5.422218968083048e-06
            ],
            [
                6.96225541655662e-06,
                8.939699495546396e-06,
                5.422218962835982e-06,
                4.78509449280116e-06,
                5.422218968931258e-06,
                3.288749456838667e-06,
                1.4738988982594524e-05,
                6.1441731309681274e-06,
                4.222832938926002e-06,
                2.561281599734989e-06
            ],
            [
                2.1444953507076064e-05,
                6.144175330383673e-06,
                6.1441738671166565e-06,
                2.9023109469023766e-06,
                1.3007133095130927e-05,
                1.3007128445182463e-05,
                2.144494834539582e-05,
                1.0129993356006171e-05,
                1.8925152655338222e-05,
                4.222834450029027e-06
            ],
            [
                1.3007134658978603e-05,
                1.147876948575242e-05,
                1.3007131549501275e-05,
                8.93969629982328e-06,
                6.962255416328664e-06,
                1.6701421837705495e-05,
                6.962255416961874e-06,
                8.939696299237883e-06,
                8.939694167932546e-06,
                8.939698432690187e-06
            ],
            [
                4.222834450505264e-06,
                1.0129993389984017e-05,
                1.147877222702498e-05,
                1.3007123795188342e-05,
                5.422218966071015e-06,
                6.962254588724508e-06,
                7.889261632490677e-06,
                2.753569103244284e-05,
                3.726640171131078e-06,
                1.1478769486170011e-05
            ],
            [
                1.3007128456065844e-05,
                4.785093346781154e-06,
                1.3007125355533295e-05,
                1.8925154983708924e-05,
                6.1441767949698196e-06,
                8.939700560549195e-06,
                1.0129994590964606e-05,
                8.939694158436083e-06,
                4.78509278100427e-06,
                1.0129990968417838e-05
            ],
            [
                1.8925157255280296e-05,
                1.1478769467545481e-05,
                1.4738981953476161e-05,
                1.4738978415674267e-05,
                2.75356811755688e-05,
                4.539789008758168e-05,
                1.3007129990338557e-05,
                2.1444956059090247e-05,
                2.7535700771318334e-05,
                1.0129988559492579e-05
            ],
            [
                1.0129988559160908e-05,
                2.9023130222373278e-06,
                3.726640171842841e-06,
                4.222835457364773e-06,
                4.785096775058701e-06,
                4.222833947359807e-06,
                8.939694170729447e-06,
                2.561282821176841e-06,
                8.939693097726971e-06,
                4.7850933509416626e-06
            ],
            [
                6.14417606400666e-06,
                1.0129988552896015e-05,
                1.8925141447437712e-05,
                1.892515273086448e-05,
                6.14417606112322e-06,
                2.561283125363344e-06,
                2.56128129449109e-06,
                6.962257907158154e-06,
                1.1478764013816059e-05,
                1.8925154997891613e-05
            ],
            [
                1.6701415848325384e-05,
                4.222833947029514e-06,
                4.222835455690258e-06,
                6.9622570784012604e-06,
                4.22283294025486e-06,
                6.144176796947993e-06,
                1.0129988550353205e-05,
                1.3709567163940317e-06,
                6.1441724029223715e-06,
                3.288748280520804e-06
            ],
            [
                0.9971990725067741,
                0.9996200154765259,
                0.9964063972176596,
                0.998830489832313,
                0.5,
                0.9996646497786694,
                0.9971990726465919,
                0.9988304899311776,
                0.9902915240915782,
                0.999447221272712
            ],
            [
                5.4222170296279735e-06,
                6.962253758182361e-06,
                6.144177523966067e-06,
                2.902311638759718e-06,
                6.144172390148071e-06,
                1.1478773595009805e-05,
                4.78509620374567e-06,
                5.422217024065297e-06,
                7.889266341307724e-06,
                7.889264450473357e-06
            ],
            [
                4.222832435266081e-06,
                8.939693092295774e-06,
                4.222833947029514e-06,
                1.7603430033607189e-06,
                6.144177529364136e-06,
                7.88926540454376e-06,
                2.2603240272766577e-06,
                3.7266406160845606e-06,
                5.4222183221120994e-06,
                8.93969523358515e-06
            ],
            [
                0.9982992775338148,
                0.9991959139926779,
                0.999941708748561,
                0.99989110307831,
                0.999088948602149,
                0.9997388095729511,
                0.999891103039376,
                0.9998766054402657,
                0.9999339478790071,
                0.9999687980886489
            ],
            [
                4.7850927818311495e-06,
                5.422218321589366e-06,
                6.962258737814774e-06,
                1.012998734896796e-05,
                3.2887486729337966e-06,
                3.7266406160032166e-06,
                8.939700563752626e-06,
                4.2228349536200574e-06,
                2.2603245661540776e-06,
                1.0129987345872367e-05
            ],
            [
                6.9622554171645e-06,
                7.889262581337206e-06,
                1.147876675082789e-05,
                1.0129992177321387e-05,
                6.962258737472841e-06,
                1.6701415858046724e-05,
                6.962255411668247e-06,
                1.3007130004960144e-05,
                6.9622562478334885e-06,
                1.1478768100020495e-05
            ],
            [
                6.1441731317504555e-06,
                3.726637950973972e-06,
                4.222834449337713e-06,
                4.22283495284425e-06,
                3.7266379500520703e-06,
                1.7603440525461408e-06,
                7.88925976283858e-06,
                4.222832939310065e-06,
                1.01299873472359e-05,
                5.422219614833243e-06
            ],
            [
                2.2603240280866228e-06,
                1.5534984946134832e-06,
                4.785094491582601e-06,
                6.14417460073947e-06,
                5.422219615395428e-06,
                2.5612825157045092e-06,
                2.9023126766305067e-06,
                2.5612825151640725e-06,
                4.222835456696504e-06,
                2.5612812941789413e-06
            ],
            [
                0.9999417087138841,
                0.9998911031172615,
                3.120190760732817e-05,
                4.006369215691771e-05,
                0.9998204719710603,
                4.785096205347206e-06,
                4.00637063504451e-05,
                1.300712380555121e-05,
                0.9995121428043866,
                5.829127930740772e-05
            ],
            [
                7.889261643382609e-06,
                6.962258738283349e-06,
                4.222832938926002e-06,
                3.7266401719851935e-06,
                4.222834954280646e-06,
                2.2603241727167277e-06,
                3.2887506328937356e-06,
                4.785092782501357e-06,
                2.561281904969606e-06,
                6.9622554171645e-06
            ],
            [
                5.422218967649081e-06,
                3.2887486726287055e-06,
                5.4222215532202016e-06,
                7.889262577634811e-06,
                8.93969736654937e-06,
                2.9023126758016634e-06,
                6.144174783178453e-06,
                6.962254588281262e-06,
                6.144173135025058e-06,
                6.962257906562937e-06
            ],
            [
                4.006368730302574e-05,
                4.539787396077843e-05,
                2.1444958621558693e-05,
                8.481107145513842e-05,
                0.00013982206527191757,
                0.00010889686987093214,
                2.7535681135500216e-05,
                2.753570417654979e-05,
                1.7603439078522935e-06,
                4.006368238500655e-05
            ],
            [
                1.3709570431803621e-06,
                8.939697367492512e-06,
                4.222833443154396e-06,
                6.962257077413455e-06,
                3.288750633192845e-06,
                4.5397851192021035e-05,
                3.726637950241874e-06,
                1.8925145958150083e-05,
                4.222833947121688e-06,
                6.962257902687696e-06
            ],
            [
                7.889261642578988e-06,
                6.144172403827636e-06,
                1.473898898859989e-05,
                5.422219614833243e-06,
                4.785095633337923e-06,
                2.2603248364233586e-06,
                4.222834953520201e-06,
                5.422217673931937e-06,
                7.88926446135094e-06,
                1.3007125355060104e-05
            ],
            [
                8.481104054258686e-05,
                3.5356267511063545e-05,
                9.61024341225653e-05,
                4.222833443891798e-06,
                3.535624222962456e-05,
                6.605214277670278e-05,
                8.481108106660633e-05,
                4.785094004124117e-06,
                7.48462447582851e-05,
                5.1442225761959264e-05
            ],
            [
                4.22283193338827e-06,
                4.222831932021007e-06,
                4.785096203449735e-06,
                4.785093923420688e-06,
                2.561281905058126e-06,
                7.889263520339493e-06,
                3.7266397271876744e-06,
                4.785093923516432e-06,
                2.9023116384746377e-06,
                2.9023130223693095e-06
            ],
            [
                5.4222183212934785e-06,
                4.222833947198501e-06,
                2.561281599269096e-06,
                4.222835457595211e-06,
                3.726639727092773e-06,
                2.5612825153504304e-06,
                5.422221553654169e-06,
                6.144176797439742e-06,
                4.785096775171854e-06,
                1.5534973839359769e-06
            ],
            [
                4.2228349539810764e-06,
                7.889262579615163e-06,
                2.5612831262578596e-06,
                5.422220906558541e-06,
                3.2887494557618747e-06,
                5.422219613689145e-06,
                3.726641059702693e-06,
                8.939696291139872e-06,
                6.144174598191315e-06,
                1.3007130004960144e-05
            ],
            [
                8.939698431942181e-06,
                6.962257076628275e-06,
                3.7266397278180926e-06,
                8.939696298945184e-06,
                6.144177530001174e-06,
                6.962257902054487e-06,
                5.422220260202708e-06,
                1.3007134660776729e-05,
                2.4300246452610016e-05,
                8.9396973639476e-06
            ],
            [
                0.9989677689631251,
                0.9991959140724146,
                0.9995694428706527,
                0.9995694429193769,
                0.9991959140694683,
                0.9995121429516668,
                0.9997694931780244,
                0.9991959138849751,
                0.9998766054108732,
                0.9994472213311112
            ],
            [
                1.8925143669299228e-05,
                2.1444948392516633e-05,
                2.430023779862206e-05,
                1.3007125359413455e-05,
                1.8925150469896243e-05,
                8.939697363264635e-06,
                7.889262582571338e-06,
                1.14787667504103e-05,
                1.8925154993072253e-05,
                1.4738978445218503e-05
            ],
            [
                4.222835457003754e-06,
                6.144174597967793e-06,
                6.962259568078904e-06,
                7.88926633625639e-06,
                6.1441753319483296e-06,
                6.962255418924822e-06,
                8.93969310000352e-06,
                8.939699497335115e-06,
                6.962259566204604e-06,
                8.939697366029015e-06
            ],
            [
                1.0129987346351444e-05,
                8.939698429568063e-06,
                8.939696300376156e-06,
                1.1478764002165291e-05,
                8.939698429893283e-06,
                6.9622587210727185e-06,
                6.1441723974572505e-06,
                2.9023123299942713e-06,
                8.939693102280066e-06,
                4.222833946937338e-06
            ],
            [
                5.422217675628357e-06,
                5.422218968714274e-06,
                2.4300249362084747e-05,
                6.96225707640032e-06,
                4.006368252433876e-05,
                1.0129989768322136e-05,
                7.889259758935282e-06,
                5.422218321441422e-06,
                2.144495860587775e-05,
                7.88926630511607e-06
            ],
            [
                2.7535694210283754e-05,
                2.7535694353228506e-05,
                5.144222580312921e-05,
                2.7535704207102113e-05,
                1.0129992179495674e-05,
                2.7535681206621957e-05,
                3.120191130543e-05,
                1.892515725225098e-05,
                4.539787358489929e-05,
                2.4300246504236573e-05
            ],
            [
                3.12019261530068e-05,
                1.1478764004044448e-05,
                8.93969736547614e-06,
                1.473898371326214e-05,
                6.962258737472841e-06,
                8.939697367492512e-06,
                2.1444948395559206e-05,
                3.7266406154676995e-06,
                6.9622562484666964e-06,
                1.012999097276641e-05
            ],
            [
                7.889260701926633e-06,
                4.222832436779288e-06,
                6.962258738435319e-06,
                6.144175333635923e-06,
                6.144173136455602e-06,
                1.0129987353537646e-05,
                6.144175328439027e-06,
                1.0129989770441144e-05,
                1.4738980204575109e-05,
                8.939700562695657e-06
            ],
            [
                5.1442231916491694e-05,
                0.9999038976095979,
                0.9999251537640834,
                0.9997965729821257,
                2.1444950954750122e-05,
                0.999968798084945,
                0.9999785550594845,
                0.9999417087143655,
                0.9999910603026352,
                1.4738981960929243e-05
            ],
            [
                0.9995694428769155,
                0.9999251537373385,
                7.484625308099433e-05,
                8.481101080610379e-05,
                0.9999785550492367,
                0.999954602110796,
                0.9998204720160312,
                0.9984988176526984,
                0.9997965730110593,
                0.9999546021371127
            ],
            [
                0.9996646498206426,
                0.9997694933708597,
                0.9998911030396486,
                0.9993736657692035,
                0.999860177860143,
                0.9999151889490357,
                0.9999546021477672,
                0.9998601779101831,
                0.9999546021314918,
                0.9999546021369236
            ],
            [
                6.9622545849505825e-06,
                1.0129989764821166e-05,
                1.1478766745190422e-05,
                4.222831932420432e-06,
                7.889265405146477e-06,
                1.1478765383679059e-05,
                6.1441738684354385e-06,
                5.422218321855664e-06,
                7.889264465239894e-06,
                3.5356267488169044e-05
            ],
            [
                6.962256248871951e-06,
                1.8925150443940552e-05,
                1.670142381757896e-05,
                2.7535700911558485e-05,
                6.1441723982842825e-06,
                2.902311984873224e-06,
                1.1478764012521528e-05,
                1.012998855982425e-05,
                1.1478772226690907e-05,
                7.889265401214474e-06
            ],
            [
                1.4738980203395485e-05,
                1.4738985468758785e-05,
                6.962255415644799e-06,
                3.5356254847833156e-05,
                1.012998855982425e-05,
                2.430024356187678e-05,
                1.147876812106705e-05,
                1.6701425777341625e-05,
                6.144177529531776e-06,
                1.4738987205381632e-05
            ],
            [
                0.9993736659303538,
                0.9996200155670426,
                0.9978172833198703,
                0.9998415637469468,
                0.9997694933422405,
                0.9995121429488568,
                0.9991959139916491,
                0.9991959140961719,
                0.9994472212498796,
                0.9996200154765259
            ],
            [
                4.222833946937338e-06,
                1.9947294829281026e-06,
                1.553498310118888e-06,
                5.422221554038823e-06,
                4.222833944648323e-06,
                4.222834953712232e-06,
                6.144173132912773e-06,
                6.144176062330242e-06,
                6.144177530548804e-06,
                5.422220907909759e-06
            ],
            [
                2.5612812943280275e-06,
                3.2887506329595395e-06,
                3.2887498477024157e-06,
                4.785095064601411e-06,
                6.1441775290176756e-06,
                5.42222025986737e-06,
                4.7850927784627044e-06,
                8.93969736518344e-06,
                5.422219614705025e-06,
                7.889259759509296e-06
            ],
            [
                1.4738983669616014e-05,
                6.144176797730321e-06,
                7.889260699630574e-06,
                4.222834450420771e-06,
                3.2887490645272776e-06,
                1.3007133101897553e-05,
                3.2887498470084827e-06,
                4.222834953896582e-06,
                7.889259754142258e-06,
                6.1441775291964935e-06
            ],
            [
                0.9995694429323031,
                0.9999151889718757,
                0.9998601778617096,
                0.9994472214700023,
                0.9996200155668105,
                0.9994472213555514,
                0.9997040427684051,
                0.9996200154818764,
                0.9994472213049987,
                0.9997388097012486
            ],
            [
                7.889263522291142e-06,
                6.962256248314727e-06,
                2.2603248359834287e-06,
                5.422219610907807e-06,
                7.889261642363733e-06,
                4.222831933649433e-06,
                5.4222196154940574e-06,
                3.726637950851956e-06,
                6.144176065828368e-06,
                1.4738983718463215e-05
            ],
            [
                2.9023133687311063e-06,
                3.726638394957837e-06,
                6.9622562472889285e-06,
                3.7266388395111645e-06,
                3.726640616423495e-06,
                7.889266341307724e-06,
                4.785096204868486e-06,
                2.561282210087786e-06,
                3.7266401714225625e-06,
                4.785093923324944e-06
            ],
            [
                3.7266392828579377e-06,
                3.7266388388875246e-06,
                1.0129990971550284e-05,
                5.422218969029887e-06,
                4.222834450236421e-06,
                3.2887502406420278e-06,
                6.144172402609439e-06,
                4.222832939548183e-06,
                4.222833945692974e-06,
                8.9396930985075e-06
            ],
            [
                4.785095634121282e-06,
                2.5612831258059426e-06,
                2.9023112927307205e-06,
                3.7266379491640618e-06,
                1.0129993386593603e-05,
                5.422218321855664e-06,
                4.785096204024198e-06,
                7.889266345196678e-06,
                6.962257909007124e-06,
                7.889263524443698e-06
            ],
            [
                0.9995694429251886,
                0.9999756997593292,
                0.999891103066615,
                0.5312093733737563,
                0.9997040429084448,
                0.9998204720358355,
                0.7981867849406659,
                0.9999417087553654,
                0.9999646437324686,
                0.9999417087151025
            ],
            [
                3.726639283291774e-06,
                3.288748280658394e-06,
                7.889264463890957e-06,
                7.88926070020459e-06,
                6.144176796042727e-06,
                5.4222202613172164e-06,
                7.8892663403606e-06,
                1.1478765381674627e-05,
                3.726639727526609e-06,
                6.962258734344787e-06
            ],
            [
                6.144172400743029e-06,
                1.1478768115053749e-05,
                8.939698428559877e-06,
                4.785093913219607e-06,
                4.785095633041987e-06,
                1.147876674819707e-05,
                1.1478768123823146e-05,
                7.889261641158302e-06,
                1.4738983706452486e-05,
                1.6701417853595148e-05
            ],
            [
                6.144176794276899e-06,
                1.4738978443234588e-05,
                5.42221702914469e-06,
                3.726638838528254e-06,
                3.726639282342757e-06,
                2.561283431669698e-06,
                6.962259567027776e-06,
                3.288748280449018e-06,
                5.422219614438727e-06,
                2.902311984318902e-06
            ],
            [
                0.9998415637468153,
                0.9999417087485212,
                0.9997694932625872,
                0.9998766054402837,
                0.9999417087206676,
                0.9997388096959516,
                0.9999251537907967,
                0.9996646499377914,
                0.9999646437577489,
                0.9995121429058563
            ],
            [
                2.144495092658685e-05,
                1.8925152719091475e-05,
                1.3007131555463476e-05,
                3.5356250658398075e-05,
                5.422220260656402e-06,
                2.430023489445281e-05,
                3.2887478882574116e-06,
                5.144223190264361e-05,
                6.144177528838857e-06,
                7.889263521487523e-06
            ],
            [
                2.4300237708275628e-05,
                6.144173135762683e-06,
                7.88925975770115e-06,
                8.93969630089651e-06,
                6.144177525933064e-06,
                1.0129994559013632e-05,
                4.78509563466093e-06,
                5.422219613846953e-06,
                4.7850967744320136e-06,
                1.300712844986705e-05
            ],
            [
                0.9989677690045401,
                4.5397879411686836e-05,
                0.9991959141183858,
                2.1444950947650794e-05,
                0.999860177862446,
                0.9988304898656306,
                8.93970056424046e-06,
                0.9959298629145593,
                0.00012339457346548197,
                1.0129988557318292e-05
            ],
            [
                0.9999785550541502,
                0.999941708706802,
                0.9997965730525831,
                0.9999724643056561,
                0.9999832985702132,
                0.9999339478556144,
                0.9998911030652998,
                0.9997965731028201,
                0.9999151889490482,
                0.9999038975511627
            ],
            [
                1.670142582254589e-05,
                6.144175792963343e-06,
                4.0063701341770154e-05,
                0.5,
                3.120191502237466e-05,
                0.00015843628868686006,
                6.605212068147983e-05,
                7.889264459829802e-06,
                2.1444940676874607e-05,
                0.0002611902700171631
            ],
            [
                3.7266397266860513e-06,
                6.962259567914269e-06,
                2.561282820785491e-06,
                5.422217676101776e-06,
                2.260324297262181e-06,
                6.962253755776166e-06,
                5.422217674464535e-06,
                3.288749456964293e-06,
                2.561281905100056e-06,
                4.222832940577472e-06
            ],
            [
                6.962259568078904e-06,
                3.7266401714225625e-06,
                3.7266388391247794e-06,
                2.9023133684090715e-06,
                7.889263523869684e-06,
                2.9023119845723063e-06,
                8.939695235243779e-06,
                2.902311984783477e-06,
                5.422217676397663e-06,
                3.7266388391993445e-06
            ],
            [
                7.889264465842609e-06,
                3.726640172120768e-06,
                2.260324836567261e-06,
                1.1478770858372173e-05,
                4.2228324364874005e-06,
                3.2887498489407274e-06,
                5.422218321993744e-06,
                1.300712380555121e-05,
                7.889264462728577e-06,
                3.2887506262116375e-06
            ],
            [
                6.1441753319483296e-06,
                2.9023112926779284e-06,
                1.1478773590625104e-05,
                6.962259567217739e-06,
                8.939699498814873e-06,
                6.144176796601534e-06,
                6.1441731319963306e-06,
                2.1444948396573396e-05,
                5.422218967491273e-06,
                3.2887482796653523e-06
            ],
            [
                0.9999339478713671,
                0.999891103104912,
                0.9997694933503696,
                0.9992903296759033,
                0.9992903297347258,
                0.9992903296880805,
                0.9992903294896114,
                0.9982992778020303,
                0.9998601779792854,
                0.9997040427669843
            ],
            [
                6.962258737472841e-06,
                7.889259762666377e-06,
                1.1478764007552206e-05,
                2.260323758676741e-06,
                6.144177530291754e-06,
                6.962257909121104e-06,
                4.785095633877571e-06,
                3.2887498489407274e-06,
                6.144172403067661e-06,
                6.962255415644799e-06
            ],
            [
                NaN,
                1.8925150482908516e-05,
                1.8925143716804326e-05,
                1.8925148223661747e-05,
                0.0007096705292118148,
                2.7535704156916166e-05,
                0.00010889688138380408,
                3.1201922469432284e-05,
                4.539786858947248e-05,
                6.962257908487893e-06
            ],
            [
                0.9996646498569864,
                0.9999687980961222,
                0.18242551713899047,
                0.9982992774264888,
                0.9988304897765574,
                0.679178699175393,
                0.9993736657799517,
                0.9998415638229095,
                0.9998204721000125,
                0.9996200154391164
            ],
            [
                7.889260701926633e-06,
                6.144177525933064e-06,
                7.889264464508026e-06,
                1.0129993380918345e-05,
                7.889263515001153e-06,
                1.0129987350147233e-05,
                8.939699495221176e-06,
                1.4738980202162242e-05,
                6.962254587597396e-06,
                8.93970056350871e-06
            ],
            [
                5.422217029006611e-06,
                6.9622562484666964e-06,
                4.222833443046859e-06,
                7.889266344981421e-06,
                1.0129990975235516e-05,
                4.222831933649433e-06,
                3.7266388395111645e-06,
                2.561282515783711e-06,
                4.222832436871463e-06,
                7.889265405333033e-06
            ],
            [
                8.939696297644297e-06,
                1.3007134641707146e-05,
                6.1441775291964935e-06,
                4.222832940423847e-06,
                1.9947304340041172e-06,
                5.422218321993744e-06,
                4.2228354568040404e-06,
                6.962257077033528e-06,
                8.939698431129126e-06,
                8.939697320270368e-06
            ],
            [
                8.939700561817559e-06,
                8.939697366289195e-06,
                3.726639283291774e-06,
                2.9023130227124616e-06,
                4.222832437186393e-06,
                5.42222090767305e-06,
                4.22283495296715e-06,
                4.222833442816421e-06,
                4.222832436779288e-06,
                7.889265404959923e-06
            ],
            [
                2.4300249381886717e-05,
                6.9622570736395275e-06,
                1.0129993391808207e-05,
                7.88926164299515e-06,
                2.430024649530801e-05,
                7.889261640899994e-06,
                1.0129994586247505e-05,
                1.0129992179495674e-05,
                1.892514371356847e-05,
                7.889259760025908e-06
            ],
            [
                4.222834450420771e-06,
                6.144173864389683e-06,
                3.726639727940109e-06,
                3.7266383941918447e-06,
                7.889260702744606e-06,
                1.994729720866691e-06,
                7.889264464106214e-06,
                1.0677026153919963e-06,
                2.902311292831027e-06,
                5.422217027024168e-06
            ],
            [
                6.144173134868593e-06,
                7.889262580504884e-06,
                4.222833946845163e-06,
                3.7266410591603975e-06,
                6.9622579075254155e-06,
                1.3007128450482197e-05,
                1.6701423799533713e-05,
                6.962257077932685e-06,
                5.422218320642526e-06,
                1.0129993371336739e-05
            ],
            [
                6.144176798132662e-06,
                1.9947304346245714e-06,
                3.7266383953679482e-06,
                1.9947299589504427e-06,
                4.222835455828521e-06,
                6.144176794522774e-06,
                2.902311638596061e-06,
                4.785093923768848e-06,
                1.0129992171240752e-05,
                1.0129989758924796e-05
            ],
            [
                1.8925154962572585e-05,
                1.8925152706698834e-05,
                2.4300231991521528e-05,
                2.1444948393530826e-05,
                1.3007126897471327e-05,
                1.1478770854029233e-05,
                3.120190387358516e-05,
                3.726638394564673e-06,
                4.006370163238581e-05,
                1.0129989769962063e-05
            ],
            [
                0.9998415637839542,
                0.9982992777905665,
                0.9999724643122417,
                0.9998415637477858,
                0.9990889487118215,
                0.9995121427791822,
                0.9999151889390239,
                0.9996646499755498,
                0.9996200155194406,
                0.9999852610180489
            ],
            [
                1.0129993384382464e-05,
                2.4300231988162266e-05,
                8.93969629829474e-06,
                4.222832939870796e-06,
                7.88926446135094e-06,
                1.1478769489343698e-05,
                8.939695234723424e-06,
                2.1444940727740105e-05,
                1.670141778603182e-05,
                1.670142780235907e-05
            ],
            [
                0.9999417087072278,
                0.9999869928715392,
                0.9997040429786325,
                0.9999417087347464,
                0.999769493268503,
                0.9998204720781395,
                0.995929861936787,
                0.9997388096028559,
                0.9996200155384438,
                0.999769493233673
            ],
            [
                5.422218967797024e-06,
                3.288749849000549e-06,
                6.9622562481627565e-06,
                5.422218322348809e-06,
                2.9023119850210436e-06,
                4.785093352595421e-06,
                2.5612812945260317e-06,
                6.144174597967793e-06,
                4.222831933649433e-06,
                1.3007125358230479e-05
            ],
            [
                0.9998601778807189,
                0.9990889489642271,
                0.9999038975557786,
                0.9997388096663054,
                0.9995121429610616,
                0.9998911030532656,
                0.9999339478581555,
                0.9995121428205933,
                0.9997388098038059,
                0.9998601778935194
            ],
            [
                4.7850956293340845e-06,
                2.4300243546318093e-05,
                1.1478770847306026e-05,
                6.9622562472889285e-06,
                1.1478764007552206e-05,
                1.6701417851043295e-05,
                4.785092781709294e-06,
                8.939697364890742e-06,
                8.939699497042417e-06,
                8.93969630089651e-06
            ],
            [
                0.9999251537373908,
                0.9999251537552417,
                0.9998204720589569,
                0.9968273169204087,
                0.9993736659491905,
                0.9997965731014529,
                0.9999724643188698,
                0.9999339478243318,
                0.9996200154811137,
                0.9999038975513151
            ],
            [
                2.561282821176841e-06,
                6.962259565976648e-06,
                1.9947299590810645e-06,
                3.288749065209246e-06,
                4.7850962047640385e-06,
                4.222833946845163e-06,
                3.726638394957837e-06,
                0.005220126034513514,
                6.962255418924822e-06,
                4.222831932021007e-06
            ],
            [
                0.10669059252545562,
                0.9993736657032568,
                0.9986749777913685,
                0.060086648911665194,
                0.9984988180697493,
                0.9994472213433313,
                0.9998766054255219,
                0.9997694932357724,
                0.9997694933135142,
                0.9971990730556402
            ],
            [
                1.3007130011655787e-05,
                3.120191875680005e-05,
                2.4300237794201987e-05,
                0.0001088968943623266,
                0.00033534997463249654,
                6.605213645060008e-05,
                4.5397852275067685e-05,
                0.00012339455760486813,
                2.4300246506623417e-05,
                0.00012339458606923134
            ],
            [
                6.962255416328664e-06,
                1.4738985470903557e-05,
                1.8925150481256165e-05,
                7.889259755290287e-06,
                8.939699496489538e-06,
                1.0129987351289655e-05,
                1.01299933928585e-05,
                1.147876401711502e-05,
                1.1478765382092217e-05,
                3.7266388388061806e-06
            ],
            [
                4.785093923116048e-06,
                6.144174599867732e-06,
                6.144173136131494e-06,
                4.222834954134701e-06,
                2.14449482896934e-05,
                1.0129995805027913e-05,
                7.889261639493659e-06,
                4.785094493184135e-06,
                1.1478772221888615e-05,
                2.90231336806592e-06
            ],
            [
                1.1478768121401121e-05,
                8.939700557166892e-06,
                8.939700564890901e-06,
                5.422218968595919e-06,
                5.4222196143006464e-06,
                0.9997388097280145,
                6.144173133762157e-06,
                1.9947294833780224e-06,
                1.3007134651738787e-05,
                1.4738988996240646e-05
            ],
            [
                0.9997965731011095,
                0.999512142977013,
                0.9993736658515093,
                0.9991959140191945,
                0.9994472214118603,
                0.9992903296602172,
                0.9975273767141525,
                0.9997694933466605,
                0.9980732651638454,
                0.9995694429224581
            ],
            [
                2.144494837847401e-05,
                1.3007128454504315e-05,
                5.42222155426567e-06,
                6.1441724019276964e-06,
                6.962258731989248e-06,
                6.144173864881432e-06,
                1.1478770856158943e-05,
                8.939693103158165e-06,
                1.012999218277553e-05,
                7.889259758016858e-06
            ],
            [
                6.1441724019276964e-06,
                2.26032402791394e-06,
                5.4222196143006464e-06,
                5.422218967491273e-06,
                2.7535700647706655e-05,
                6.962254586824882e-06,
                1.147876947531266e-05,
                3.7266383921379016e-06,
                1.0129995795409453e-05,
                3.726640171842841e-06
            ],
            [
                0.025957359976362126,
                0.16451645880021026,
                0.0008040861228816308,
                0.9999967112521709,
                0.9998911031331538,
                0.9998415638415146,
                0.999569442869325,
                0.9997965729562228,
                0.9995121429002649,
                0.999876605396781
            ],
            [
                4.785095633999427e-06,
                1.0129994599072117e-05,
                1.4738978429722525e-05,
                4.222834953712232e-06,
                4.78509449306228e-06,
                8.939699492326704e-06,
                4.785092781300206e-06,
                3.2887478884069663e-06,
                6.144173864143809e-06,
                5.42221702914469e-06
            ],
            [
                2.2603240281236263e-06,
                6.962257907348116e-06,
                6.144173134700951e-06,
                7.889266342226149e-06,
                5.422220262037209e-06,
                7.88926258381982e-06,
                1.670141785596473e-05,
                6.1441775296994185e-06,
                1.0129987350147233e-05,
                6.962254584165403e-06
            ],
            [
                0.999860177927744,
                0.9992903297310519,
                0.9988304898336731,
                0.99883048979546,
                0.9997388097863419,
                0.9997040429001439,
                0.9995121428974549,
                0.9995121429658868,
                0.9994472212770211,
                0.9997694932083806
            ],
            [
                4.785096204024198e-06,
                4.222831931129981e-06,
                6.14417606400666e-06,
                6.144176063224333e-06,
                3.2887506326006084e-06,
                6.144172402285332e-06,
                3.288749064802458e-06,
                3.2887502403130076e-06,
                6.962255417721724e-06,
                5.422220907298259e-06
            ],
            [
                3.7266392824512166e-06,
                3.2887502412970765e-06,
                4.222832436379863e-06,
                5.42221702886853e-06,
                5.422220908481809e-06,
                5.42222155426567e-06,
                1.012998976633211e-05,
                6.962257895722395e-06,
                7.889263520655201e-06,
                1.9947299590810645e-06
            ],
            [
                0.26894141551050293,
                0.0011695103836385273,
                0.09534946554178127,
                0.9988304899510321,
                0.9997965730776749,
                0.9971990731440828,
                0.017986208646117444,
                0.13296423504419935,
                0.020332351339154456,
                0.9978172837159107
            ],
            [
                1.3007126895436607e-05,
                4.222832437109582e-06,
                7.889262581337206e-06,
                1.760343213227212e-06,
                7.889266338208041e-06,
                5.422218321993744e-06,
                5.422217674464535e-06,
                1.1478768102943628e-05,
                3.2887486728201357e-06,
                2.561282820785491e-06
            ],
            [
                6.962253755776166e-06,
                1.3007134620224291e-05,
                6.144173135483279e-06,
                1.3007134659924986e-05,
                7.889259758332567e-06,
                1.4738985478142165e-05,
                1.0129993386593603e-05,
                6.9622562481627565e-06,
                4.785094489458826e-06,
                4.222834446418836e-06
            ],
            [
                7.484623580173539e-05,
                3.120191127387468e-05,
                1.670142581883963e-05,
                2.7535684488840414e-05,
                2.7535700868484725e-05,
                2.7535694345515298e-05,
                1.3007126910294786e-05,
                2.753568450797317e-05,
                8.4811010448844e-05,
                2.1444950935948603e-05
            ],
            [
                6.144174594369081e-06,
                6.962259567027776e-06,
                1.3007123782743439e-05,
                8.939696297644297e-06,
                1.0129994595718555e-05,
                6.962253756232077e-06,
                1.0129989766700635e-05,
                0.9991959140904196,
                1.1478773591543802e-05,
                1.0129993375169382e-05
            ],
            [
                4.785096204868486e-06,
                1.1478770844215855e-05,
                7.889263523238269e-06,
                6.144176787593577e-06,
                6.144173865104955e-06,
                6.144176057613919e-06,
                6.9622554126053955e-06,
                2.5612822101436936e-06,
                7.889265395847433e-06,
                7.88926634383339e-06
            ],
            [
                1.4738976693529666e-05,
                1.3007125357804606e-05,
                4.785093352238557e-06,
                5.422217675223978e-06,
                7.889259758619574e-06,
                1.0129989753323244e-05,
                4.222834953082369e-06,
                6.144176063805491e-06,
                1.012998976633211e-05,
                1.0129990968896918e-05
            ],
            [
                4.222832939432965e-06,
                8.939694164159978e-06,
                6.962255417544426e-06,
                5.422217029736466e-06,
                4.222834450420771e-06,
                7.889265401214474e-06,
                7.889262582112126e-06,
                4.222832435803769e-06,
                1.7603427931548347e-06,
                5.422217029509618e-06
            ],
            [
                5.422217676299034e-06,
                6.144175332115971e-06,
                3.7266392829528392e-06,
                4.785092782597101e-06,
                1.3007125356952865e-05,
                3.7266379509129646e-06,
                0.9993736657458488,
                8.939700550629937e-06,
                3.2887486729876365e-06,
                1.0129992174446906e-05
            ],
            [
                3.2887478887958082e-06,
                2.5612825151640725e-06,
                5.422218966071015e-06,
                2.2603245669804887e-06,
                5.4222215520465154e-06,
                1.3709576970026324e-06,
                2.9023119844508833e-06,
                4.785092782396909e-06,
                4.22283293878774e-06,
                3.7266383948154845e-06
            ],
            [
                0.9968273169174634,
                0.9997694932859279,
                0.999569442865818,
                0.9995121427683967,
                0.9995121427775077,
                0.9997388096045126,
                0.9994472214594544,
                0.9975273763718822,
                0.9997040430110785,
                0.9975273764919065
            ]
        ]
    },
    {
        "q_id": "8729_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            4,
            9,
            17,
            19,
            20,
            21,
            23,
            24,
            25,
            31,
            34,
            35,
            36,
            37,
            38,
            41,
            42,
            43,
            44,
            47,
            49,
            50,
            54,
            57,
            59,
            60,
            62,
            65,
            67,
            69,
            70,
            74,
            75,
            78,
            79,
            80,
            81,
            84,
            85,
            86,
            88,
            90,
            91,
            93,
            94,
            95,
            96,
            97,
            100,
            104,
            105,
            109,
            110,
            111,
            113,
            114,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124
        ],
        "rewards": [
            [
                NaN,
                1.3709573701637772e-06,
                1.4738987236641703e-05,
                NaN,
                NaN,
                NaN,
                5.8291244479465225e-05,
                NaN,
                NaN,
                2.9023130220947882e-06
            ],
            [
                NaN,
                3.7266388368200243e-06,
                1.1478773595343877e-05,
                NaN,
                2.430023765134499e-05,
                NaN,
                1.9947304346826253e-06,
                2.7535691064898404e-05,
                2.2603245667050187e-06,
                NaN
            ],
            [
                NaN,
                3.120192249712832e-05,
                5.144223809535255e-05,
                1.473898548194914e-05,
                0.0013250225740345661,
                NaN,
                NaN,
                1.8925152747388e-05,
                NaN,
                7.889263515001153e-06
            ],
            [
                1.6701419845073e-05,
                NaN,
                3.288749455331158e-06,
                1.3709568798782093e-06,
                1.1478772218923723e-05,
                5.14422074125194e-05,
                6.144172403470001e-06,
                1.6701419833468143e-05,
                NaN,
                6.962255418367598e-06
            ],
            [
                NaN,
                1.6701415856588526e-05,
                4.5397873902976276e-05,
                5.144222579414667e-05,
                3.12019076269651e-05,
                2.7535694366751658e-05,
                NaN,
                NaN,
                NaN,
                7.889265403654039e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                2.7535697651475977e-05,
                NaN,
                0.0002611902635118612
            ],
            [
                NaN,
                NaN,
                2.2603245665981198e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.5534971987506078e-06,
                2.2603237572089375e-06,
                7.889260647682242e-06,
                1.0129990964843162e-05,
                NaN,
                1.0129989754502517e-05,
                NaN,
                1.3709578604981489e-06,
                2.561281294123034e-06,
                1.8925141461620395e-05
            ],
            [
                1.4738976685647628e-05,
                3.120191134118513e-05,
                1.3007126904001353e-05,
                1.892515048042999e-05,
                NaN,
                1.3007133109847152e-05,
                1.3007130011300897e-05,
                NaN,
                2.902310945302762e-06,
                0.002472623273213403
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                1.5534973831504068e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                1.8925143700143116e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                0.03308597624352061,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                6.144172402106516e-06,
                NaN
            ],
            [
                NaN,
                4.785095061816132e-06,
                1.7603430033991435e-06,
                7.88926446430712e-06,
                3.288750240486491e-06,
                3.2887482786364177e-06,
                1.3007128456065844e-05,
                2.5612825157045092e-06,
                NaN,
                8.481105969764351e-05
            ],
            [
                2.9023130228444433e-06,
                5.4222176759932836e-06,
                2.9023116389761676e-06,
                6.144174600325954e-06,
                1.5534971985217185e-06,
                8.939700562110258e-06,
                1.0129994600638342e-05,
                NaN,
                8.939698419908987e-06,
                1.6701415867707307e-05
            ],
            [
                NaN,
                NaN,
                1.3007123797175743e-05,
                NaN,
                NaN,
                NaN,
                7.889263519736775e-06,
                NaN,
                3.7266410592824143e-06,
                5.422220261070644e-06
            ],
            [
                1.7603436326080487e-06,
                NaN,
                1.4738980211116665e-05,
                8.939698432917844e-06,
                NaN,
                NaN,
                NaN,
                3.7266406160845606e-06,
                NaN,
                NaN
            ],
            [
                6.1441753313895225e-06,
                NaN,
                1.6701429790860943e-05,
                NaN,
                NaN,
                1.2098662590889244e-06,
                4.785092781160942e-06,
                7.889264461637948e-06,
                NaN,
                0.0035936019511474565
            ],
            [
                8.481102028675467e-05,
                0.9947798736874025,
                3.120190386019117e-05,
                NaN,
                0.7310585669110202,
                NaN,
                NaN,
                NaN,
                0.9399133544545811,
                0.2942149783515162
            ],
            [
                NaN,
                3.120190388402792e-05,
                NaN,
                1.5534971985923634e-06,
                2.9023116373395974e-06,
                NaN,
                0.00012339461314395656,
                NaN,
                1.01299933920846e-05,
                1.1478764007009336e-05
            ],
            [
                0.9997965730335348,
                0.9999599362911139,
                0.0035936022020893253,
                NaN,
                NaN,
                0.9997694933533945,
                NaN,
                2.753569107251144e-05,
                NaN,
                5.829127930740772e-05
            ],
            [
                0.00037998445156261785,
                6.605214428278049e-05,
                9.610239160884131e-05,
                1.3007125340580479e-05,
                1.1478773559681642e-05,
                NaN,
                3.535625069312567e-05,
                NaN,
                8.939698425502796e-06,
                NaN
            ],
            [
                NaN,
                NaN,
                4.785095063939907e-06,
                NaN,
                NaN,
                1.0,
                0.00023050665530463134,
                NaN,
                2.2603237582655916e-06,
                NaN
            ],
            [
                1.6701425819447213e-05,
                NaN,
                NaN,
                4.222831932666232e-06,
                3.535623799851786e-05,
                NaN,
                6.962253758916883e-06,
                4.5397890183368146e-05,
                NaN,
                NaN
            ],
            [
                4.2228339464303755e-06,
                NaN,
                NaN,
                NaN,
                6.962256246263128e-06,
                NaN,
                4.785095063826755e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                1.6701417848916754e-05,
                1.670141984792864e-05,
                6.962259565976648e-06,
                1.0677032518413822e-06,
                NaN,
                1.7603430033607189e-06,
                2.9023126768680736e-06,
                NaN,
                3.288749065209246e-06,
                5.144219505967133e-05
            ],
            [
                2.2603245668530326e-06,
                6.144176065828368e-06,
                1.3709575334098791e-06,
                1.0677031236524586e-06,
                3.2887498488809053e-06,
                1.8925148179392492e-05,
                9.422443690736529e-07,
                1.370957533574467e-06,
                2.1444953514565465e-05,
                8.939696302457574e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                7.484621790388621e-05,
                NaN,
                NaN,
                1.1478766753751021e-05,
                8.481101079623133e-05,
                NaN
            ],
            [
                1.6701421797058122e-05,
                9.422444814132609e-07,
                2.4300249406550775e-05,
                NaN,
                8.939693094247102e-06,
                7.484620008227652e-05,
                2.5612828212676906e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                5.144223807888457e-05,
                NaN,
                NaN,
                NaN,
                2.753569763394596e-05,
                2.4300243587159647e-05,
                2.7535700890722806e-05,
                NaN,
                0.00010889687012128086,
                2.7535700942411318e-05
            ],
            [
                5.422217672965374e-06,
                NaN,
                NaN,
                0.00010889693471601869,
                8.481102074088805e-05,
                NaN,
                1.0129989768911772e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                1.3007126906982452e-05,
                NaN,
                4.22283193320392e-06,
                1.473897844934719e-05,
                4.222833438852893e-06,
                1.0129993367798916e-05,
                1.7603430031445813e-06,
                0.0,
                4.5397890237206746e-05,
                NaN
            ],
            [
                1.1478765380839446e-05,
                NaN,
                2.5612828212676906e-06,
                4.5397857795336036e-05,
                NaN,
                4.539787391519731e-05,
                NaN,
                NaN,
                4.785095061276484e-06,
                NaN
            ],
            [
                NaN,
                NaN,
                0.0,
                1.2098662603499435e-06,
                2.2603237579654523e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.473898021151881e-05,
                NaN,
                4.785095063713602e-06,
                4.222833947359807e-06,
                NaN,
                4.006367774885875e-05,
                1.5534975685957707e-06,
                4.539787399744151e-05,
                1.9947306716053792e-06,
                NaN
            ],
            [
                6.962253750457213e-06,
                3.7266379505740294e-06,
                1.4738981968462759e-05,
                3.2887478889962107e-06,
                1.7603427927866002e-06,
                NaN,
                1.1478763989762862e-05,
                3.535626332111248e-05,
                NaN,
                4.539786314219866e-05
            ],
            [
                NaN,
                6.962257052642312e-06,
                5.4222170304318e-06,
                1.8925155005051806e-05,
                3.2887502406420278e-06,
                NaN,
                5.422219615898437e-06,
                NaN,
                NaN,
                1.6701423816789103e-05
            ],
            [
                NaN,
                1.0129992173930973e-05,
                NaN,
                1.4738983705648196e-05,
                NaN,
                NaN,
                3.2887490642879904e-06,
                NaN,
                1.8925150490826034e-05,
                NaN
            ],
            [
                NaN,
                NaN,
                0.00012339461710641851,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.2098662600198338e-06,
                1.147876947531266e-05,
                2.9023126759653203e-06,
                1.3709576970537545e-06,
                9.422447060908033e-07,
                1.1478773573796204e-05,
                3.5356254708665494e-05,
                1.9947292449169753e-06,
                4.222832940339353e-06,
                1.0677027424398527e-06
            ],
            [
                NaN,
                4.222833946645451e-06,
                4.222834450505264e-06,
                0.015906392586515418,
                6.962253756890615e-06,
                1.4738981964843453e-05,
                NaN,
                6.605217610793098e-05,
                3.535626720160189e-05,
                7.889261640899994e-06
            ],
            [
                4.222831930976356e-06,
                1.1478766713704111e-05,
                4.785093353013212e-06,
                1.3709578572088868e-06,
                3.120192236999894e-05,
                8.939700562110258e-06,
                1.4738976690741464e-05,
                NaN,
                1.7603438426747447e-06,
                6.962258738701267e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                8.939700558760474e-06,
                2.1444956065331412e-05,
                NaN,
                2.260325373849613e-06,
                3.535624642960554e-05,
                6.962257904663309e-06
            ],
            [
                NaN,
                NaN,
                3.7266383948154845e-06,
                2.9023112930949896e-06,
                8.939699493107236e-06,
                3.288748262005961e-06,
                NaN,
                1.2098658276290391e-06,
                NaN,
                3.7266383940901643e-06
            ],
            [
                5.4222176711703245e-06,
                1.0129990977759901e-05,
                1.670142580759932e-05,
                1.892515048889829e-05,
                2.144494329192304e-05,
                4.539789019426799e-05,
                5.8291251402896515e-05,
                0.0008040858084716022,
                6.144175328707254e-06,
                1.1478772227338172e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                5.422217022704215e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                6.96225624580722e-06,
                NaN,
                1.4738980200821758e-05,
                6.144175329690753e-06,
                6.962259568775433e-06,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.3007125356952865e-05,
                NaN,
                2.4300243590165296e-05,
                0.0
            ],
            [
                4.222835457449267e-06,
                NaN,
                1.5534984946586959e-06,
                NaN,
                NaN,
                NaN,
                1.553497754391555e-06,
                1.8925150485318196e-05,
                1.3007131549501275e-05,
                9.422447061062286e-07
            ],
            [
                0.0010322309527243956,
                4.539786856370925e-05,
                0.0001398220567132208,
                NaN,
                NaN,
                NaN,
                5.8291250869378786e-05,
                0.0003353500765119296,
                5.829127933751884e-05,
                6.144173864389683e-06
            ],
            [
                2.2603248355311635e-06,
                3.2887486726287055e-06,
                2.902312329915082e-06,
                1.7603432132079998e-06,
                1.6701423819948542e-05,
                6.9622545823924185e-06,
                6.1441753308083655e-06,
                NaN,
                2.561283431478682e-06,
                1.2098653948576728e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                1.0129992183070348e-05,
                3.1201922486004504e-05,
                1.473898718951031e-05,
                4.785093353013212e-06,
                NaN,
                NaN
            ],
            [
                6.605214371283532e-05,
                2.4300234910365097e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                2.4300234903469775e-05,
                NaN,
                5.144223199471459e-05,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                4.785095633999427e-06,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                2.4300234914166368e-05,
                NaN,
                1.3007131563176482e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                5.422218968931258e-06,
                1.0129989761836128e-05,
                NaN,
                NaN,
                2.753569108573408e-05,
                NaN,
                1.7603434229832599e-06,
                1.2098653949842147e-06,
                6.962253757840428e-06,
                1.1478763999534472e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                1.0129988556912918e-05,
                NaN,
                2.1444948171267246e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                3.7266388366708923e-06,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                1.4738980193475914e-05,
                0.00013982205703668945,
                5.829128622320936e-05,
                7.88926634305847e-06,
                6.962259565976648e-06,
                NaN,
                3.1201926095344524e-05,
                1.147877222702498e-05
            ],
            [
                NaN,
                4.539789017213801e-05,
                4.222833443154396e-06,
                4.785095064436034e-06,
                4.222834953712232e-06,
                1.0129992182112188e-05,
                1.8925157254522964e-05,
                5.144223173496965e-05,
                4.539787385904664e-05,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.2098662602046953e-06,
                NaN
            ],
            [
                1.0129989769188164e-05,
                NaN,
                NaN,
                3.535624222267904e-05,
                4.222834953197588e-06,
                1.0129992180674948e-05,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.994729245842213e-06,
                2.4300240723831244e-05,
                2.9023116390104826e-06,
                2.260324836295902e-06,
                8.315284241174449e-07,
                6.1441753327418334e-06,
                4.7850939232204965e-06,
                1.7603427934206038e-06,
                1.553497198908852e-06,
                1.3007131560621253e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                0.00033535009402520434,
                NaN
            ],
            [
                0.9984988177333166,
                6.605215973089162e-05,
                0.9999339478717613,
                NaN,
                NaN,
                0.012431648029001732,
                7.88926634687567e-06,
                0.03308597636269747,
                NaN,
                0.002182716654775017
            ],
            [
                NaN,
                NaN,
                NaN,
                2.4300240619163735e-05,
                NaN,
                NaN,
                8.939698433373153e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                8.93969949923766e-06,
                7.484621722974924e-05,
                5.4222170296279735e-06,
                NaN,
                6.9622579059043994e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.670141979300305e-05,
                NaN,
                1.9947304341673947e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ]
        ]
    },
    {
        "q_id": "8936_mmlu_math",
        "cot_ids": [
            1,
            2,
            3,
            5,
            7,
            8,
            11,
            12,
            13,
            15,
            16,
            17,
            18,
            21,
            22,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            34,
            35,
            38,
            41,
            42,
            43,
            46,
            48,
            49,
            51,
            52,
            53,
            56,
            57,
            58,
            59,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            70,
            71,
            72,
            73,
            74,
            75,
            77,
            78,
            79,
            80,
            83,
            86,
            87,
            88,
            89,
            90,
            91,
            93,
            95,
            96,
            98,
            99,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                NaN,
                1.670142975094265e-05,
                NaN,
                2.1444958627955892e-05,
                4.006368255290478e-05,
                2.4300249330967372e-05,
                NaN,
                8.481105072973957e-05,
                7.88926350369306e-06,
                5.422221547075608e-06
            ],
            [
                5.8291251358366035e-05,
                3.120190386700167e-05,
                0.0001398221049670257,
                0.00015843617759767281,
                3.5356259112640515e-05,
                4.539787926569509e-05,
                NaN,
                0.00010889692119876608,
                0.0001584362516102502,
                7.484626243723662e-05
            ],
            [
                NaN,
                0.9997694932099634,
                NaN,
                0.0015011822309112482,
                NaN,
                NaN,
                0.9998204720992628,
                0.9999485577759848,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                4.785095635017795e-06,
                0.705785040214066,
                2.430023489445281e-05,
                NaN,
                NaN,
                3.120192608898806e-05,
                3.1201900133940165e-05,
                4.539789011896001e-05
            ],
            [
                0.9998415637885506,
                0.34864514210180597,
                0.014063624951247102,
                0.9999251537959895,
                0.9999485577931638,
                0.9999038976086695,
                0.9998601779037931,
                0.9995694428659182,
                0.9999546021167011,
                0.9998204720563633
            ],
            [
                NaN,
                0.5312093733737563,
                NaN,
                0.015906388621205934,
                0.5621765008857981,
                0.24508500210441886,
                0.9999417087280621,
                NaN,
                NaN,
                0.0019267344134893901
            ],
            [
                7.484620908565215e-05,
                5.422218322457301e-06,
                8.93970055837021e-06,
                8.939698432446272e-06,
                1.892514371900746e-05,
                4.539789014868685e-05,
                4.539787397465094e-05,
                5.829126462209352e-05,
                0.000335350050266411,
                6.144176798479122e-06
            ],
            [
                3.5356263223617915e-05,
                1.4738978437390084e-05,
                2.753568448703733e-05,
                0.00015843627131036773,
                1.1478773595009805e-05,
                NaN,
                7.48462357636178e-05,
                0.00020342694423232976,
                8.481105110736149e-05,
                3.5356267347200643e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                7.889260701467423e-06,
                1.670142182342727e-05,
                NaN,
                NaN,
                3.120191133017482e-05,
                1.0129993382466144e-05
            ],
            [
                1.6701427786379604e-05,
                NaN,
                6.9622562313447225e-06,
                8.93969310367852e-06,
                1.3007131538428617e-05,
                2.753569757965299e-05,
                1.1478769487046951e-05,
                1.3007131561047124e-05,
                NaN,
                5.829125142113282e-05
            ],
            [
                NaN,
                0.2689414272294874,
                0.02595735653847632,
                0.651354857898194,
                0.9992903295357612,
                0.9890130591910004,
                0.9770226296300062,
                1.553498309557968e-06,
                NaN,
                5.422219607475515e-06
            ],
            [
                1.892514812830729e-05,
                1.6701415859504925e-05,
                NaN,
                2.1444943194872906e-05,
                1.8925152703944913e-05,
                NaN,
                1.892514145232592e-05,
                2.4300252249459416e-05,
                2.4300234819134658e-05,
                1.4738988967205773e-05
            ],
            [
                3.2887482798567817e-06,
                1.9947290074646476e-06,
                7.88926351104045e-06,
                2.4300237810821485e-05,
                6.475947981904966e-07,
                1.4738978433261398e-05,
                3.7266388373758766e-06,
                4.785095633477187e-06,
                4.7850944937411915e-06,
                3.2887486722518283e-06
            ],
            [
                5.422217661169341e-06,
                1.0129995798468197e-05,
                2.1444943256504422e-05,
                1.0677026151871005e-06,
                2.26032402791394e-06,
                4.539786297407701e-05,
                2.7535681168957485e-05,
                7.889266341939142e-06,
                3.2887498477024157e-06,
                6.475947208513517e-07
            ],
            [
                4.5397868092043744e-05,
                NaN,
                2.2603240279591663e-06,
                1.6701417835367632e-05,
                1.6701423811563878e-05,
                NaN,
                NaN,
                1.1478766743561818e-05,
                NaN,
                1.3007134656423374e-05
            ],
            [
                5.144223787827462e-05,
                NaN,
                NaN,
                0.0003799845693625935,
                NaN,
                0.0,
                NaN,
                1.3007126899411407e-05,
                1.4738983701251412e-05,
                NaN
            ],
            [
                0.00010889690678152709,
                NaN,
                4.5397873923454754e-05,
                NaN,
                4.006368732517898e-05,
                1.4738981951974817e-05,
                NaN,
                4.2228354478707355e-06,
                NaN,
                NaN
            ],
            [
                1.3007133108474901e-05,
                NaN,
                1.3007129994928505e-05,
                1.1478768078973942e-05,
                8.939700559833708e-06,
                2.561281903185235e-06,
                2.4300243529168176e-05,
                1.4738985417069753e-05,
                6.605217579700796e-05,
                7.889262573329699e-06
            ],
            [
                8.939698431129126e-06,
                NaN,
                8.481106980581877e-05,
                3.535625028797033e-05,
                8.939699467902573e-06,
                2.1444956037636224e-05,
                2.7535681227157105e-05,
                5.8291244525692116e-05,
                3.1201926101701e-05,
                2.1444945771070387e-05
            ],
            [
                9.422445937974445e-07,
                2.1444945812730175e-05,
                4.539785234013636e-05,
                2.902312330891746e-06,
                8.939694153069933e-06,
                0.00013982212301617865,
                1.3007125351889727e-05,
                1.4738985478142165e-05,
                6.144174601499446e-06,
                2.1444958609544435e-05
            ],
            [
                0.005220126743023153,
                0.970687770520593,
                0.9924227599647347,
                NaN,
                0.4687906266262437,
                0.033085981844833426,
                0.9914225144912494,
                0.7057850216484838,
                0.0009110512285209547,
                1.994730196482709e-06
            ],
            [
                0.004609573194261634,
                0.2942149783515162,
                0.16451646084838667,
                0.00048785713691708397,
                0.939913352771458,
                8.93969629205049e-06,
                1.0129987341781759e-05,
                0.06754669442450784,
                0.9999646437366789,
                0.9992903297371198
            ],
            [
                NaN,
                7.484623608435025e-05,
                0.00023050663091098183,
                0.00023050668601635373,
                2.753569433890398e-05,
                9.610246027712167e-05,
                6.962254586622255e-06,
                0.007577241761599423,
                4.539789022498571e-05,
                NaN
            ],
            [
                0.9820137872414632,
                0.11920293140927592,
                NaN,
                0.0011695100533195926,
                NaN,
                0.26894141551050293,
                0.0953494732538428,
                0.029312227359491745,
                0.00857748494643876,
                0.0010322308061513437
            ],
            [
                1.6701429778283947e-05,
                3.5356237993373034e-05,
                0.00012339452988740005,
                1.1478772221888615e-05,
                2.144494327452579e-05,
                4.785095617218121e-06,
                1.3007133065414559e-05,
                1.4738976690741464e-05,
                3.7266397249778205e-06,
                1.6701417824917187e-05
            ],
            [
                8.481105055450325e-05,
                NaN,
                0.0001584361748614188,
                NaN,
                0.00043055702573660467,
                NaN,
                9.610241468004681e-05,
                NaN,
                NaN,
                0.00010889690894276599
            ],
            [
                0.00280092637923625,
                0.9980732657284437,
                0.43782349911420193,
                0.5621765008857981,
                6.605214447116035e-05,
                7.48462260381826e-05,
                0.9998766054389444,
                0.007577242910154616,
                0.9975273771735755,
                0.20181321505933414
            ],
            [
                9.610244742357704e-05,
                4.006371079013184e-05,
                2.753569426377534e-05,
                NaN,
                NaN,
                0.00010889689556653582,
                4.539788959973136e-05,
                4.006371116615417e-05,
                5.1442237984942225e-05,
                1.1478773565861984e-05
            ],
            [
                0.0002034270608662288,
                6.605216020953037e-05,
                5.1442201281194775e-05,
                0.00012339460210938942,
                0.0009110511316701421,
                1.4738985475943776e-05,
                8.481103036654188e-05,
                9.61023906118253e-05,
                5.829126537996031e-05,
                9.610241461851987e-05
            ],
            [
                4.222833443645997e-06,
                0.0002034269176605987,
                0.0002034269198093039,
                5.8291265119138775e-05,
                5.422218321855664e-06,
                9.610238018161194e-05,
                1.1478769489343698e-05,
                2.561282209249179e-06,
                6.605216790811762e-05,
                7.484622660667945e-05
            ],
            [
                2.9023133676594165e-06,
                5.144219514537961e-05,
                5.8291279270086916e-05,
                1.473897659433397e-05,
                3.120189991782034e-05,
                NaN,
                NaN,
                1.4738976635620825e-05,
                NaN,
                6.144174580086001e-06
            ],
            [
                1.1478765345427792e-05,
                4.006367780569929e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                2.1444945797595342e-05,
                NaN,
                NaN
            ],
            [
                2.4300232030064617e-05,
                NaN,
                2.4300249397180202e-05,
                1.4738976610741475e-05,
                NaN,
                4.539786301371276e-05,
                NaN,
                3.535624215888317e-05,
                2.7535700619257942e-05,
                4.00637110314857e-05
            ],
            [
                NaN,
                NaN,
                0.00048785704078329966,
                0.03732688841503393,
                NaN,
                0.9968273167164386,
                NaN,
                0.020332355531672928,
                0.001169510439666285,
                NaN
            ],
            [
                5.144223804819424e-05,
                NaN,
                NaN,
                NaN,
                0.00037998451939488164,
                4.539785768600744e-05,
                9.610237980126365e-05,
                NaN,
                5.829128595432984e-05,
                NaN
            ],
            [
                1.1478766749115769e-05,
                NaN,
                NaN,
                2.4300237795616407e-05,
                NaN,
                1.4738985463343232e-05,
                8.939700551150293e-06,
                NaN,
                2.1444956061196638e-05,
                2.144495092658685e-05
            ],
            [
                2.5612831240122525e-06,
                2.144495092658685e-05,
                4.006367778354606e-05,
                1.6701427741296855e-05,
                1.3007125332346968e-05,
                4.78509391743234e-06,
                5.144219511843204e-05,
                1.9947290073086266e-06,
                4.006368725318095e-05,
                9.422445936997504e-07
            ],
            [
                NaN,
                3.726640170066823e-06,
                1.1478766740638685e-05,
                7.484625325306817e-05,
                NaN,
                2.144494835538169e-05,
                1.012999338147113e-05,
                4.006370163879859e-05,
                1.670142581574095e-05,
                1.5534983097812057e-06
            ],
            [
                0.9999485577928809,
                0.05340333450779175,
                NaN,
                0.0002034270011404774,
                0.29421497216298875,
                0.9933071475649926,
                0.20181322946142374,
                0.999088948751028,
                0.042087725963147436,
                0.16451646904109268
            ],
            [
                0.00015843615669656593,
                3.120192248986379e-05,
                2.753568116675371e-05,
                1.892515048820981e-05,
                2.4300243621371074e-05,
                2.430024069059224e-05,
                1.892514593646297e-05,
                0.9988304899075154,
                2.4300252291096595e-05,
                7.889264464106214e-06
            ],
            [
                4.006369689100785e-05,
                0.9964063967224454,
                0.9933071497072465,
                0.9947798748698639,
                0.9971990728755028,
                0.9840936094544528,
                0.9149009642742806,
                NaN,
                0.9740426404474868,
                0.00026119026623253646
            ],
            [
                4.006369194471296e-05,
                3.5356246161302705e-05,
                1.4738980142323096e-05,
                6.9622587329010695e-06,
                5.1442231916491694e-05,
                2.144495347235956e-05,
                1.760344051841692e-06,
                1.3007128460419196e-05,
                2.430024358097153e-05,
                3.5356242238628006e-05
            ],
            [
                NaN,
                NaN,
                9.610240303607204e-05,
                NaN,
                3.5356267453698665e-05,
                6.144177518065073e-06,
                0.00048785714429670795,
                4.22283344189467e-06,
                3.535624639127656e-05,
                NaN
            ],
            [
                7.484624474085991e-05,
                NaN,
                0.0,
                0.04742587435564,
                0.001700722771955165,
                5.144221342220632e-05,
                0.00033535027351924886,
                0.009708475675619324,
                0.0010322310913745989,
                0.2942149597859341
            ],
            [
                0.924141813188682,
                0.9947798743282047,
                0.40733340004593027,
                0.9964063967407867,
                0.9796676472138702,
                0.9465966681286702,
                0.987568351021981,
                6.605212868425745e-05,
                NaN,
                0.9890130591505205
            ],
            [
                0.9669140185126972,
                0.9953904276368778,
                0.9980732654562188,
                0.9986749777078743,
                0.9991959139859904,
                0.9989677689716482,
                0.9953904278120793,
                0.9968273178327516,
                0.9978172832448203,
                0.9986749775649172
            ],
            [
                3.535624633314e-05,
                0.0002959570902377168,
                0.0002305068195208422,
                0.00013982213881529257,
                0.0001088969602246682,
                NaN,
                NaN,
                0.00012339460347748901,
                0.0001233945555042436,
                0.00017952800229985793
            ],
            [
                3.120192617525444e-05,
                6.962253741668272e-06,
                0.00013982213881529257,
                4.0063711140794525e-05,
                1.1478770853569882e-05,
                NaN,
                3.120190757713495e-05,
                NaN,
                3.120192242062368e-05,
                3.120190006515413e-05
            ],
            [
                NaN,
                NaN,
                1.067702487806183e-06,
                4.785095632032323e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                1.5534973839642345e-06,
                NaN
            ],
            [
                NaN,
                1.7603425830466377e-06,
                1.7603432125227635e-06,
                2.753569107391384e-05,
                4.222833404840288e-06,
                NaN,
                NaN,
                3.7266388386231563e-06,
                NaN,
                3.7266410501989626e-06
            ],
            [
                1.0129989767695646e-05,
                1.4738978446451746e-05,
                1.2098656827747684e-06,
                1.4738985478678359e-05,
                4.785095063939907e-06,
                1.1478772229050293e-05,
                9.422442562627274e-07,
                6.962255419279419e-06,
                4.222832939548183e-06,
                1.6701419850389357e-05
            ],
            [
                7.484625378235853e-05,
                0.0015011819768417957,
                1.4738985452565748e-05,
                7.889266341623432e-06,
                2.4300234921326896e-05,
                5.1442207317454294e-05,
                6.144174595777273e-06,
                2.144494583410617e-05,
                0.00013982203921743158,
                0.0003353500007219022
            ],
            [
                1.012999097276641e-05,
                8.939697357670826e-06,
                6.144174594078502e-06,
                5.422217674464535e-06,
                2.144495860837422e-05,
                1.1478765379920747e-05,
                5.422220257026851e-06,
                1.4738976686988113e-05,
                1.14787667504103e-05,
                NaN
            ],
            [
                0.9997388096603245,
                0.1329642316084462,
                0.9980732650922073,
                0.9999898700042074,
                0.9986749778298807,
                0.9986749778964296,
                0.999860177877116,
                0.9997388097436166,
                1.1478773574547868e-05,
                NaN
            ],
            [
                2.430024939055008e-05,
                NaN,
                1.0129994593249448e-05,
                4.539789012358419e-05,
                1.012999097195566e-05,
                8.939699494895954e-06,
                7.889262570115216e-06,
                1.4738976691867467e-05,
                2.7535691022025e-05,
                3.120192231120158e-05
            ],
            [
                5.1442237890251334e-05,
                1.0129992184544441e-05,
                9.422448184681581e-07,
                2.144494072867628e-05,
                6.962255418063657e-06,
                2.4300249326547287e-05,
                2.2603253746225744e-06,
                1.473898193781932e-05,
                6.144177529531776e-06,
                2.144494071471167e-05
            ],
            [
                6.144173842998593e-06,
                NaN,
                5.8291272132905845e-05,
                0.00013982213935847615,
                0.00017952800665668606,
                0.00013982208666561016,
                0.0002959570253715448,
                0.0001584361958293784,
                7.484624486174719e-05,
                9.61023800487697e-05
            ],
            [
                2.56128281847e-06,
                3.7266410555812463e-06,
                5.422219615188307e-06,
                1.760342793362967e-06,
                NaN,
                NaN,
                NaN,
                2.1444953482813517e-05,
                7.889259747971602e-06,
                8.939696297644297e-06
            ],
            [
                0.00023050670429315055,
                0.24508501864634824,
                0.08509905312815914,
                NaN,
                0.0017007224163766233,
                0.0011695101343694335,
                0.9986749778844137,
                0.24508500210441886,
                0.999447221331272,
                0.05340333036478031
            ],
            [
                0.5312093733737563,
                0.9995694428183214,
                0.0675466911396291,
                0.9978172834811262,
                0.025957358092589027,
                0.0005527787239757597,
                0.02595735865772094,
                0.14804720179063335,
                0.320821300824607,
                0.00013982213713081316
            ],
            [
                0.008577485857225578,
                0.34864514210180597,
                1.6701417789191255e-05,
                7.484624444680974e-05,
                0.02297737016091733,
                1.8925157153316377e-05,
                0.001700722681429882,
                0.029312229161419755,
                0.7981867873410141,
                0.0001233946032189505
            ],
            [
                6.96225706707948e-06,
                1.8925148200184586e-05,
                1.3007125355060104e-05,
                3.726638838528254e-06,
                3.1201911339482505e-05,
                1.147876673608695e-05,
                2.7535691022025e-05,
                0.00010889690854506,
                0.0002959571961178017,
                7.889259761489647e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                3.1201915003305256e-05,
                NaN
            ],
            [
                3.466325797504462e-07,
                1.994729721004569e-06,
                6.4759464375046e-07,
                3.466325384292699e-07,
                3.28875024092319e-06,
                8.315283249923769e-07,
                1.5534979396024226e-06,
                1.0677032517015483e-06,
                1.9947301966967833e-06,
                9.422449307649713e-07
            ],
            [
                0.9978172839496809,
                0.9992903295566071,
                9.610237923213957e-05,
                0.9980732651307128,
                0.9241418210233833,
                0.817574478416099,
                0.8175744828610095,
                0.989013055831172,
                0.9890130559222517,
                0.9820137910248891
            ],
            [
                1.1478773588244838e-05,
                1.7603440517840551e-06,
                1.7603440518929245e-06,
                2.561281599502042e-06,
                1.30071253513219e-05,
                2.5612812940671274e-06,
                3.7266410596010127e-06,
                4.2228339475595195e-06,
                1.3007131559816827e-05,
                2.561282209165318e-06
            ],
            [
                2.144495859792026e-05,
                0.00017952800307823608,
                7.484626247644333e-05,
                0.00029595708417561804,
                0.014063627818059764,
                NaN,
                0.0002034269946766013,
                0.0040701384803707216,
                2.753569422530948e-05,
                0.0008040859783736596
            ],
            [
                NaN,
                0.006692849859349476,
                0.0953494616857507,
                0.9992903295171858,
                0.09534946425643773,
                0.966914017797636,
                0.9991959141915284,
                0.7981867777396211,
                NaN,
                NaN
            ],
            [
                4.5397868326555305e-05,
                0.0,
                3.120191506868607e-05,
                0.00015843617624913987,
                0.00017952796077939538,
                1.8925152721432305e-05,
                3.535624629609723e-05,
                6.605215209573939e-05,
                5.1442194994173735e-05,
                0.00017952791598871082
            ],
            [
                3.535626333809042e-05,
                5.144219519029225e-05,
                0.0001233946333189397,
                8.481104097820946e-05,
                2.1444958620544503e-05,
                3.535625478866761e-05,
                1.4738985481091229e-05,
                2.4300246512104316e-05,
                5.144223802461508e-05,
                6.605213642657204e-05
            ],
            [
                NaN,
                0.24508500761839525,
                0.9992903297082246,
                NaN,
                1.9947299579961775e-06,
                0.08509904732734555,
                0.03308597958047282,
                3.5356267471448335e-05,
                NaN,
                0.9820137866492746
            ],
            [
                NaN,
                NaN,
                0.00023050664181669338,
                NaN,
                NaN,
                3.5356263103743346e-05,
                NaN,
                5.144222560364213e-05,
                6.605216803979133e-05,
                NaN
            ],
            [
                NaN,
                2.430024645649969e-05,
                1.3007129991947403e-05,
                8.93969735984981e-06,
                5.1442207158762935e-05,
                2.1444958609544435e-05,
                1.3007123801954964e-05,
                NaN,
                1.0129987348562583e-05,
                NaN
            ],
            [
                NaN,
                0.9940889317156398,
                NaN,
                0.0004305571534963506,
                3.120190748405811e-05,
                0.07585817218654307,
                0.9999417087226439,
                NaN,
                0.9971990734152643,
                NaN
            ],
            [
                0.9990889489397494,
                0.0008040858983097073,
                0.9940889324216013,
                0.0046095714059233095,
                1.0129994586247505e-05,
                0.0003353500513494045,
                5.8291250727729406e-05,
                0.0035936019328061913,
                5.422218966071015e-06,
                NaN
            ],
            [
                6.14417460073947e-06,
                1.5534975691524517e-06,
                6.144173135181524e-06,
                1.2098658274595828e-06,
                6.144175333021237e-06,
                7.889266341623432e-06,
                6.475948752604851e-07,
                3.726637951028202e-06,
                2.5612831266165976e-06,
                4.222832940500659e-06
            ],
            [
                NaN,
                1.0129990958320302e-05,
                1.4738988983291576e-05,
                8.939694168517944e-06,
                1.0129990968417838e-05,
                6.962255413213276e-06,
                2.9023109470554753e-06,
                1.3007129991190302e-05,
                2.2603251058292572e-06,
                2.9023116352595695e-06
            ],
            [
                6.9622570736395275e-06,
                1.147877222702498e-05,
                3.2887502413389517e-06,
                1.4738985482351282e-05,
                4.785096775920397e-06,
                1.0677024881140118e-06,
                6.962253756004122e-06,
                1.4738983724575818e-05,
                5.715005151233884e-07,
                1.6701415869924985e-05
            ],
            [
                2.1444956062288846e-05,
                NaN,
                1.8925145960215522e-05,
                NaN,
                NaN,
                6.1441731317504555e-06,
                2.4300246489738706e-05,
                NaN,
                NaN,
                1.4738976678033687e-05
            ],
            [
                0.00012339455965881214,
                5.829125846925035e-05,
                2.7535681075998364e-05,
                4.5397889980895396e-05,
                3.1201926072415836e-05,
                NaN,
                5.8291264568656914e-05,
                NaN,
                9.610245968422533e-05,
                5.8291258386974944e-05
            ],
            [
                NaN,
                3.535625903418184e-05,
                6.605212761789317e-05,
                NaN,
                4.53978575978179e-05,
                NaN,
                1.4738980186612642e-05,
                6.962253744454392e-06,
                1.3007133093616717e-05,
                1.3007123784446925e-05
            ],
            [
                0.00020342705960541742,
                7.484621794200383e-05,
                NaN,
                8.481107091893984e-05,
                NaN,
                NaN,
                0.0002034269229820478,
                NaN,
                3.535625487947387e-05,
                0.017986213844215747
            ],
            [
                0.0017007226330047868,
                0.9149009613738741,
                0.009708478128999526,
                0.9902915252914062,
                0.01098694194243558,
                0.010986941740036293,
                0.02931223064536054,
                0.320821300824607,
                0.9964063974419234,
                NaN
            ],
            [
                6.1441724013465395e-06,
                4.5397890105748086e-05,
                5.829127915557987e-05,
                4.539785775768208e-05,
                7.889266342226149e-06,
                5.8291244123645406e-05,
                5.144221955353239e-05,
                0.00020342706618176238,
                2.144495349709019e-05,
                0.00010889689520527302
            ],
            [
                NaN,
                0.004070137912205639,
                3.12019038195552e-05,
                NaN,
                NaN,
                2.1444958618516124e-05,
                NaN,
                4.539787910814292e-05,
                NaN,
                NaN
            ],
            [
                0.9993736657365945,
                NaN,
                0.9999646437409061,
                0.9997040428021342,
                0.9993736657114547,
                0.9995694428684232,
                0.9994472213042591,
                0.999738809688899,
                0.09534945847239203,
                0.999903897574494
            ],
            [
                1.473898722420202e-05,
                NaN,
                5.422218320820059e-06,
                4.785096200855943e-06,
                6.962257076830902e-06,
                NaN,
                6.144173129559937e-06,
                NaN,
                1.6701417821514717e-05,
                NaN
            ],
            [
                NaN,
                0.16451646699291614,
                0.06008665480259673,
                NaN,
                0.00020342705945743488,
                0.14804719427274568,
                0.00010889695172072805,
                0.9994472213077,
                1.0129993386593603e-05,
                0.9875683502902086
            ],
            [
                1.8925152739677025e-05,
                8.481106134696298e-05,
                NaN,
                1.1478772207774056e-05,
                NaN,
                4.006367779491416e-05,
                5.8291279181025874e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                4.539786853530362e-05,
                0.000123394617029216,
                0.00015843615685792883,
                NaN,
                2.4300240698017976e-05,
                0.06754669630158146,
                0.9998415638053416,
                0.025957355031458025,
                0.9902915218441386,
                5.1442219615661567e-05
            ],
            [
                6.144176794522774e-06,
                5.422218319320898e-06,
                1.0129988544567392e-05,
                3.7266388388061806e-06,
                1.0129992182443859e-05,
                1.0129993389652346e-05,
                2.1444950950771382e-05,
                1.4738985479214553e-05,
                8.939697361443396e-06,
                1.553497383500805e-06
            ],
            [
                2.7535691026232207e-05,
                8.939694161232988e-06,
                2.753570418897106e-05,
                1.892515272253387e-05,
                3.120190017071685e-05,
                NaN,
                1.1478770854488583e-05,
                3.120190754943891e-05,
                NaN,
                4.5397873780435714e-05
            ]
        ]
    },
    {
        "q_id": "8569_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            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,
            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,
            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": [
            [
                0.9999898700041912,
                0.9999885212277715,
                0.9999869928653365,
                0.9999910603068948,
                0.9999898700126449,
                0.9999885212359833,
                0.9999832985721908,
                0.9999952149049351,
                0.999975699753489,
                0.9999962733616047
            ],
            [
                0.999986992865342,
                0.9999810748517707,
                0.9999910603058291,
                0.9999832985741811,
                0.9999921107374181,
                0.9999910603058315,
                0.9999898700078172,
                0.9999785550541526,
                0.9999852610110046,
                0.9999687980737836
            ],
            [
                0.9999885212359826,
                0.9999930377420909,
                0.9999898700102283,
                0.9999885212332451,
                0.9999930377420909,
                0.9999945777797378,
                0.9999930377445808,
                0.9999938558268634,
                0.9999974387171787,
                0.9999938558224687
            ],
            [
                0.9999930377412609,
                0.9999546021259933,
                0.9999945777823233,
                0.9999898700066059,
                0.9999898700090217,
                0.9999921107345942,
                0.9999687980998007,
                0.9999910603068942,
                0.9999869928761891,
                0.9999885212305079
            ],
            [
                0.9999921107383551,
                0.9999832985721882,
                0.999988521226404,
                0.9999417087554167,
                0.9999938558232019,
                0.9999898700126446,
                0.999981074854021,
                0.9999952149049353,
                0.9999810748517677,
                0.9999921107345937
            ],
            [
                0.9999417087553925,
                0.9999756997563846,
                0.9999485578048909,
                0.9999898700078136,
                0.9999945777816766,
                0.9999832985841309,
                0.999933947824018,
                0.9999852610145195,
                0.9999938558268631,
                0.9999339478475265
            ],
            [
                0.999915188928498,
                0.9999832985761709,
                0.9999930377420909,
                0.9999756997563805,
                0.9999810748495092,
                0.9999417087415308,
                0.9999646437324888,
                0.9999785550515947,
                0.9999810748517691,
                0.9999151889688949
            ],
            [
                0.9999832985841398,
                0.9999910603015663,
                0.9999984465022456,
                0.999986992873106,
                0.999996273360272,
                0.9999952149072169,
                0.9999938558246676,
                0.9999898700078145,
                0.9999938558275966,
                0.9999910602994351
            ],
            [
                0.9999898700066059,
                0.9999832985781587,
                0.999986992873089,
                0.9999785550541551,
                0.9999930377454126,
                0.9999898700102291,
                0.9999869928668871,
                0.9999687980960991,
                0.9999724643122003,
                0.9999687980960844
            ],
            [
                0.9999952149072175,
                0.9999852610215458,
                0.9999945777784455,
                0.9999970976876691,
                0.999997097687323,
                0.9999869928684397,
                0.9999962733616046,
                0.9999977396762412,
                0.9999957771655489,
                0.9999687980960907
            ],
            [
                0.9999756997650652,
                0.9999251537995159,
                0.9999485577986458,
                0.9999785550567011,
                0.9999546021259992,
                0.9999151889689127,
                0.9999339478396017,
                0.9999417087484639,
                0.9999756997563736,
                0.9998415637080306
            ],
            [
                0.9999945777803845,
                0.9999930377454112,
                0.9999938558253989,
                0.9999885212277727,
                0.9999977396765105,
                0.999991060302632,
                0.9999785550490401,
                0.9999921107355347,
                0.9999945777790913,
                0.9999921107402369
            ],
            [
                0.9999810748427421,
                0.9999910603005024,
                0.999994577779738,
                0.9999898700066084,
                0.9999599362887458,
                0.9999885212291424,
                0.9999852610215446,
                0.9999832985841355,
                0.9999646437535248,
                0.9999724643023574
            ],
            [
                0.9999910603058302,
                0.9999952149066464,
                0.9999832985801543,
                0.9999967112501505,
                0.9999938558239337,
                0.9999945777803845,
                0.9999938558268653,
                0.9999756997505845,
                0.9999832985721872,
                0.9999832985701943
            ],
            [
                0.9999921107402365,
                0.9999921107364745,
                0.9999910603058286,
                0.9999785550567081,
                0.9999930377404314,
                0.9999945777816768,
                0.9999898700078149,
                0.9999832985721898,
                0.9999687980998051,
                0.9999810748472532
            ],
            [
                0.9999921107392986,
                0.9999974387180948,
                0.9999885212346137,
                0.9999938558224696,
                0.9999930377454117,
                0.9999952149049356,
                0.9999957771650457,
                0.9999945777829696,
                0.9999970976873229,
                0.999995214903224
            ],
            [
                0.9999885212359813,
                0.9999885212291393,
                0.9999810748562803,
                0.9999885212332453,
                0.9999930377429213,
                0.999876605396149,
                0.9999832985781607,
                0.9999810748427448,
                0.9999945777816768,
                0.9999910603026312
            ],
            [
                0.9999930377445809,
                0.9999832985761679,
                0.9999646437535213,
                0.9999852610127615,
                0.9999869928715381,
                0.999991060305829,
                0.9999938558224688,
                0.999860177859783,
                0.9999756997650743,
                0.9999810748495063
            ],
            [
                0.9999810748517645,
                0.9999785550592668,
                0.9999910603047628,
                0.9999898700114408,
                0.9999921107364751,
                0.9999957771680663,
                0.9999810748472558,
                0.9999485577741519,
                0.9999687980923682,
                0.9999957771680661
            ],
            [
                0.999992110737415,
                0.9999967112497588,
                0.9999869928699907,
                0.9999930377462418,
                0.9999962733616049,
                0.9999921107392983,
                0.9999910603026313,
                0.9999970976883609,
                0.9999910603058298,
                0.9999869928684382
            ],
            [
                0.9999962733589393,
                0.9999869928761919,
                0.9999724643056253,
                0.9999930377462418,
                0.9999885212305126,
                0.9999687980737786,
                0.9999810748540398,
                0.9999898700102369,
                0.9999869928715416,
                0.999991060302634
            ],
            [
                0.999993037745411,
                0.9999832985721882,
                0.9999967112497585,
                0.9999974387177893,
                0.9999810748427421,
                0.999997097688707,
                0.9999785550541578,
                0.9999957771680661,
                0.9999921107383557,
                0.9999945777816774
            ],
            [
                0.9999810748585336,
                0.9999832985721898,
                0.9999945777823233,
                0.9999967112501507,
                0.9999417087136911,
                0.9999832985821445,
                0.9999967112517189,
                0.9999962733607161,
                0.9999945777823234,
                0.9999785550490375
            ],
            [
                0.9999885212318752,
                0.9999930377429209,
                0.9999938558232012,
                0.9999687980774782,
                0.9999921107374157,
                0.9999898700078143,
                0.9999832985841337,
                0.9999869928684368,
                0.9999938558232014,
                0.9999832985761683
            ],
            [
                0.9999974387165681,
                0.9999885212277729,
                0.9999938558232029,
                0.9999832985841349,
                0.9999952149032239,
                0.9999921107392991,
                0.9999938558275963,
                0.999992110735536,
                0.9999852610197911,
                0.9999974387168735
            ],
            [
                0.9999832985841333,
                0.9999756997592901,
                0.9999810748495092,
                0.99997246431548,
                0.9999810748472526,
                0.9999974387171787,
                0.9999852610197902,
                0.9999885212359899,
                0.9999921107364749,
                0.9999832985702033
            ],
            [
                0.9999952149037944,
                0.9999945777803845,
                0.9999930377445815,
                0.9999977396751634,
                0.999989870007817,
                0.9999938558246664,
                0.9999974387174841,
                0.9999967112521111,
                0.9999921107345938,
                0.9999982396561572
            ],
            [
                0.9999982396569966,
                0.9999967112521108,
                0.9999910603068942,
                0.9999930377420911,
                0.9999910603004999,
                0.9999910603026325,
                0.9999974387168733,
                0.9999910603058294,
                0.9999952149066464,
                0.9999898700066062
            ],
            [
                0.9999852610233015,
                0.9999869928746389,
                0.999985261018041,
                0.9999038975393901,
                0.9999785550567065,
                0.9999885212264035,
                0.9999546021259761,
                0.9999945777784452,
                0.9999724642990652,
                0.9999756997505873
            ],
            [
                0.9999945777823231,
                0.9999646437577591,
                0.9999898700126446,
                0.9999832985701962,
                0.9999898700114362,
                0.9999687980737719,
                0.9999852610127611,
                0.9999910602994346,
                0.9999687980886537,
                0.9999898700090213
            ],
            [
                0.9999869928668871,
                0.9999869928653405,
                0.9999898700078167,
                0.9999832985841355,
                0.9999898700126444,
                0.999988521226404,
                0.9999898700090215,
                0.9999898700126462,
                0.999994577781031,
                0.9999945777823231
            ],
            [
                0.9999756997621702,
                0.9999832985701949,
                0.9999885212305081,
                0.9999898700126444,
                0.9999546021313769,
                0.999985261014516,
                0.9999417087276202,
                0.9999646437535129,
                0.9999898700053982,
                0.9999251537817438
            ],
            [
                0.679178699175393,
                0.8807970889295664,
                0.9968273169535448,
                0.9999869928671412,
                0.9914225139685369,
                0.8670357477770336,
                0.9971990726277328,
                0.9990889489881217,
                0.9999962733589426,
                0.9999852610234629
            ],
            [
                0.9999898700090227,
                0.9999869928653431,
                0.9999930377429219,
                0.9999910603058304,
                0.9999724643023462,
                0.9999852610215467,
                0.9999852610110059,
                0.9999832985801516,
                0.9999599363078789,
                0.9999852610197902
            ],
            [
                0.9999785550464855,
                0.9999852610215486,
                0.9999898700053997,
                0.9999962733616047,
                0.9999832985721898,
                0.9999977396757023,
                0.9999921107336539,
                0.9999832985821503,
                0.9999756997477003,
                0.9999910603026321
            ],
            [
                0.9999832985761661,
                0.9999952149066467,
                0.9999945777823236,
                0.9999785550541535,
                0.999993855822469,
                0.9999921107402364,
                0.9999945777816774,
                0.9999687980849754,
                0.999997097688361,
                0.9999599363030898
            ],
            [
                0.9999785550515924,
                0.9999832985721903,
                0.9999852610233111,
                0.9999832985741818,
                0.999991060306894,
                0.9999910603026323,
                0.9999785550592659,
                0.9999646437324707,
                0.9999930377462409,
                0.9999962733602719
            ],
            [
                0.9999930377454128,
                0.9999974387184001,
                0.9999921107392975,
                0.9999952149072175,
                0.999983298582147,
                0.9999974387168735,
                0.9999938558246666,
                0.9999962733589395,
                0.9999785550490417,
                0.9999921107383557
            ],
            [
                0.9999810748585312,
                0.9999810748517638,
                0.999989870009022,
                0.9999898700078147,
                0.999972464312199,
                0.9999599363222107,
                0.9999945777797381,
                0.9999810748540229,
                0.9999417087206578,
                0.9999869928684362
            ],
            [
                0.9999852610215476,
                0.9999910603005003,
                0.9999952149055057,
                0.9999930377429216,
                0.9999938558224688,
                0.9999967112501508,
                0.9999910603026313,
                0.9999952149043648,
                0.9999885212332448,
                0.9999970976880149
            ],
            [
                0.9999982396572065,
                0.9999810748495105,
                0.999964643757743,
                0.9999852610180324,
                0.9999885212318783,
                0.9999945777784452,
                0.999993855827596,
                0.9999952149055058,
                0.9999869928653365,
                0.9999852610233032
            ],
            [
                0.9999930377420916,
                0.9999910603047628,
                0.9999980052700408,
                0.9999970976869771,
                0.9999869928761919,
                0.9999921107374165,
                0.9999885212332453,
                0.9999898700041923,
                0.9999977396765106,
                0.9999952149060761
            ],
            [
                0.9999938558253991,
                0.9999930377445815,
                0.9999921107383563,
                0.9999852610180342,
                0.9999810748449992,
                0.99998699287309,
                0.9999974387184001,
                0.999993855823202,
                0.9999952149060758,
                0.9999910603005003
            ],
            [
                0.9999832985801581,
                0.9999957771645427,
                0.9999852610145203,
                0.9999852610127629,
                0.9999898700066088,
                0.9999885212277733,
                0.9999756997476926,
                0.9999785550541559,
                0.9999885212305091,
                0.9999485577802874
            ],
            [
                2.2603234895053587e-06,
                1.7603436330091044e-06,
                4.222832437677995e-06,
                2.9023133690821773e-06,
                1.1478773598914277e-05,
                1.3709568799823232e-06,
                1.99472900813862e-06,
                1.9947292458930106e-06,
                2.7535697662094155e-05,
                1.0677024881980089e-06
            ],
            [
                0.9999945777803847,
                0.999993855827596,
                0.9999869928715378,
                0.9999977396754328,
                0.9999756997534811,
                0.9999977396746245,
                0.9999938558261308,
                0.9999938558261319,
                0.9999970976880149,
                0.9999974387187053
            ],
            [
                0.9999832985701962,
                0.9999921107336527,
                0.999964643736673,
                0.9999417087205921,
                0.9999921107345936,
                0.9999810748517658,
                0.9999869928715366,
                0.9999687980737603,
                0.9999417087345535,
                0.9999785550439215
            ],
            [
                0.9999852610162773,
                0.9999869928761908,
                0.9999962733593835,
                0.9999756997534839,
                0.9999910603005013,
                0.9999852610197907,
                0.9999885212291416,
                0.9999962733607163,
                0.999993855822469,
                0.9999921107383554
            ],
            [
                0.9999957771650456,
                0.9999938558275969,
                0.999972464312199,
                0.9999921107374157,
                0.999891103039086,
                0.9999785550439292,
                0.9999852610197874,
                0.9999945777790915,
                0.9999967112513267,
                0.9999921107383555
            ],
            [
                0.9999967112493665,
                0.9999921107345934,
                0.9999785550439309,
                0.9999785550413738,
                0.999981074851781,
                0.9999910603015649,
                0.9999930377462407,
                0.999991060303697,
                0.9999599362983339,
                0.9999962733593833
            ],
            [
                0.9999962733620489,
                0.9999945777810308,
                0.9999957771650454,
                0.9999921107364749,
                0.9999980052709919,
                0.999992110737415,
                0.9999957771675626,
                0.9999898700041934,
                0.9999885212305111,
                0.999995214906076
            ],
            [
                0.9999852610215486,
                0.9999910602994357,
                0.9999938558253987,
                0.999994577778445,
                0.999991060301566,
                0.9999952149072169,
                0.9999756997563937,
                0.9999982396559474,
                0.9999898700078175,
                0.999989870007814
            ],
            [
                1.760343213322473e-06,
                3.288750633569722e-06,
                7.889260704531226e-06,
                6.962257909501028e-06,
                3.2887494572873306e-06,
                6.144174601879434e-06,
                1.4738988999377379e-05,
                8.939698434495167e-06,
                1.4738980214280206e-05,
                1.3007134666431358e-05
            ],
            [
                0.9999869928668863,
                0.9999910603047634,
                0.9999952149032239,
                0.9999921107392958,
                0.999996273361605,
                0.9999921107336535,
                0.9999756997534859,
                0.9999910603058282,
                0.9999898700053989,
                0.9999885212264024
            ],
            [
                0.9999945777829695,
                0.999983298574178,
                0.9999952149060758,
                0.9999885212359804,
                0.9999785550464814,
                0.999989870006606,
                0.9999930377462409,
                0.9999970976880149,
                0.9999687980737675,
                0.9999930377429208
            ],
            [
                0.9999930377445814,
                0.9999957771655488,
                0.9999810748562752,
                0.9999869928668873,
                0.9999898700078163,
                0.9999810748585392,
                0.9999945777797379,
                0.9999921107383563,
                0.9999832985701989,
                0.9999945777790913
            ],
            [
                0.9999898700053977,
                0.9999885212346129,
                0.9999869928684378,
                0.9999921107345936,
                0.9999599363078454,
                0.9999869928730875,
                0.999986992866886,
                0.9999852610162734,
                0.9999898700041906,
                0.9999832985701943
            ],
            [
                0.9999945777829704,
                0.9999952149066466,
                0.9999852610145189,
                0.9999977396765105,
                0.9999952149055058,
                0.9999869928746427,
                0.9999910603026323,
                0.9999967112513269,
                0.9999938558232017,
                0.9999957771645421
            ],
            [
                0.9999852610215458,
                0.9999910602994345,
                0.9999921107374159,
                0.9999967112517189,
                0.9999930377420911,
                0.9999852610215446,
                0.9999945777790913,
                0.9999869928699895,
                0.999988521234617,
                0.9999952149072169
            ],
            [
                0.9999938558232032,
                0.9999982396572065,
                0.9999952149043648,
                0.9999974387171787,
                0.9999957771660524,
                0.9999982396561572,
                0.999991060302632,
                0.999997097687323,
                0.9999930377429223,
                0.9999967112513269
            ],
            [
                0.9999974387171787,
                0.9999910603005011,
                0.9999417087276151,
                0.9999921107355341,
                0.9999921107345936,
                0.9999930377412607,
                0.999991060302631,
                0.9999885212305111,
                0.9999546021259933,
                0.9999921107383554
            ],
            [
                0.9999885212318759,
                0.9999974387177893,
                0.9999967112497589,
                0.9999945777810307,
                0.9999898700041934,
                0.999993037743751,
                0.9999952149060765,
                0.9999938558253989,
                0.999993855823934,
                0.9999952149043656
            ],
            [
                0.9999967112497588,
                0.9999945777810308,
                0.9999898700066073,
                0.9999938558275969,
                0.9999957771670593,
                0.9999898700114378,
                0.9999869928715404,
                0.999991060301568,
                0.9999977396762412,
                0.9999910602994357
            ],
            [
                0.9999546021314647,
                0.9999910603015684,
                0.9999945777790914,
                0.999991060300501,
                0.9999687980998433,
                0.9999938558253991,
                0.9999869928668873,
                0.9999417087276669,
                0.9999785550439356,
                0.999993855822469
            ],
            [
                0.9999810748562796,
                0.9999251537728369,
                0.9999756997621767,
                0.9999417087067125,
                0.9999599362982833,
                0.9999852610197885,
                0.99998329858015,
                0.9999832985741784,
                0.9999977396757022,
                0.9999546021259992
            ],
            [
                0.999995777165549,
                0.9999945777829703,
                0.9999785550490401,
                0.999993037742092,
                0.9999485577803031,
                0.9999952149037947,
                0.9999921107364758,
                0.999996711252111,
                0.999997097686977,
                0.9999910603047633
            ],
            [
                0.99998852123051,
                0.9999898700066079,
                0.9999921107336531,
                0.9999957771680659,
                0.999997097688707,
                0.9999898700066072,
                0.9999869928668877,
                0.9999869928699903,
                0.9999938558261308,
                0.999992110738357
            ],
            [
                0.9999952149049355,
                0.9999957771680661,
                0.9999898700114366,
                0.9999938558224694,
                0.9999885212277715,
                0.999993855825399,
                0.9999984465018752,
                0.9999898700066077,
                0.9999921107345945,
                0.9999967112505427
            ],
            [
                0.9999910603015673,
                0.9999967112505429,
                0.9999970976876692,
                0.9999945777784456,
                0.9999921107364772,
                0.9999930377404314,
                0.9999952149032242,
                0.9999869928684375,
                0.9999885212346149,
                0.9999810748472546
            ],
            [
                0.999981074854028,
                0.9999957771645425,
                0.9999930377462407,
                0.999996273358939,
                0.9999869928746399,
                0.999981074845,
                0.9999898700102291,
                0.9999930377462407,
                0.9999921107345942,
                0.9999930377437507
            ],
            [
                0.999997097688707,
                0.999988521231877,
                0.9999810748450022,
                0.9999957771645421,
                0.9999970976880151,
                0.9999982396569966,
                0.9999810748427433,
                0.9999832985721969,
                0.9999810748495086,
                0.9999974387184
            ],
            [
                0.999989870006606,
                0.9999921107345944,
                0.9999251537728793,
                0.9999546021314167,
                0.9999852610162783,
                0.9999938558261311,
                0.9999885212318768,
                0.9999921107355342,
                0.9999810748562757,
                0.9999921107345944
            ],
            [
                0.9999810748427478,
                0.9999957771655492,
                0.9999646437493104,
                0.999989870007817,
                0.999978555054151,
                0.9999485577925665,
                0.9999869928668885,
                0.999993037743751,
                0.9999910603036981,
                0.9999957771675627
            ],
            [
                0.9999910603036983,
                0.9999885212318821,
                0.9999785550413756,
                0.9999921107355337,
                0.9999957771670592,
                0.9999921107336536,
                0.9999945777784456,
                0.9999921107336541,
                0.9999952149072169,
                0.9999952149066464
            ],
            [
                0.9999967112505428,
                0.9999974387171787,
                0.9999974387180947,
                0.9999977396746245,
                0.9999977396759716,
                0.9999869928761911,
                0.9999957771670591,
                0.9999885212264068,
                0.9999977396765106,
                0.9999921107383561
            ],
            [
                0.9999869928699883,
                0.9999810748427463,
                0.9999898700114366,
                0.9999852610162764,
                0.9999852610162749,
                0.9999785550413764,
                0.9999810748472552,
                0.9999930377437508,
                0.9999785550592643,
                0.99998329858015
            ],
            [
                0.9999967112497589,
                0.9999910603005013,
                0.9999832985821441,
                0.9999952149060765,
                0.999986992866886,
                0.9999921107374157,
                0.9999910603058293,
                0.999993037745411,
                0.9999957771650456,
                0.9999970976880149
            ],
            [
                0.9999962733611605,
                0.9999869928761891,
                0.9999869928684385,
                0.9999724643122128,
                0.9999910602994373,
                0.9999785550464919,
                0.9999646437324707,
                0.999978555046489,
                0.999988521231877,
                0.9999599363126486
            ],
            [
                0.9999852610110034,
                0.9999785550515979,
                0.9999910603026316,
                0.9999898700078157,
                0.9999930377462417,
                0.9999756997505913,
                0.9999724643154838,
                0.9999952149043647,
                0.9999921107402382,
                0.9999945777823236
            ],
            [
                0.999996711251327,
                0.9999869928653368,
                0.9999980052700408,
                0.9999921107345939,
                0.9999910603047634,
                0.9999952149060765,
                0.9999970976869771,
                0.9999980052693275,
                0.9999852610145172,
                0.9999938558224697
            ],
            [
                0.9999910603058294,
                0.9999832985761721,
                0.9999957771665559,
                0.9999945777810307,
                0.9999921107364751,
                0.9999869928746395,
                0.9999810748517638,
                0.9999785550541659,
                0.9999852610162758,
                0.9999970976876689
            ],
            [
                0.9999810748517685,
                0.9999485577864734,
                0.9999810748540259,
                0.9999945777784459,
                0.9999930377454112,
                0.9999756997592855,
                0.9999810748472588,
                0.9999885212359829,
                0.9999930377454106,
                0.999981074842744
            ],
            [
                0.9999962733602719,
                0.9999957771675624,
                0.9999938558246662,
                0.9999967112497586,
                0.999993037740431,
                0.9999962733589393,
                0.9999967112493666,
                0.9999980052695652,
                0.9999785550567073,
                0.9999869928684406
            ],
            [
                0.9999974387165683,
                0.9999952149032239,
                0.9999967112501509,
                0.9999921107374152,
                0.9999930377404319,
                0.9999930377445809,
                0.9999930377462418,
                0.9999962733620492,
                0.9999984465022455,
                0.9999986290429567
            ],
            [
                0.9999921107355355,
                0.9999898700041923,
                0.9999898700126456,
                0.999988521234614,
                0.999989870004196,
                0.9999910603036986,
                0.9999945777797385,
                0.9999938558232011,
                0.9999977396757023,
                0.999995214905506
            ],
            [
                0.9999832985821457,
                0.9999910603068948,
                0.9999921107336536,
                0.9999921107345942,
                0.9999898700054003,
                0.9999869928668906,
                0.9999977396757022,
                0.9999938558246662,
                0.9999945777823239,
                0.9999945777797379
            ],
            [
                0.999995777166052,
                0.9999785550515878,
                0.9999724642990546,
                0.9999599362887179,
                0.9999724643056274,
                0.9999967112493664,
                0.9999869928746369,
                0.999933947855328,
                0.9999967112493664,
                0.9999990577555183
            ],
            [
                0.9999957771680665,
                0.9999967112513269,
                0.999983298574187,
                0.9999962733593835,
                0.9999921107392965,
                0.9999885212291397,
                0.9999852610127665,
                0.9999852610215467,
                0.9999930377445828,
                0.9999810748495098
            ],
            [
                0.9999952149072172,
                0.9999930377445815,
                0.9999910603058296,
                0.999995777168066,
                0.9999945777810306,
                0.9999898700053994,
                0.9999952149060765,
                0.9999962733611607,
                0.9999938558224694,
                0.9999977396746245
            ],
            [
                0.9999885212359836,
                0.99999457778297,
                0.9999885212305086,
                0.9999832985821435,
                0.999995777165549,
                0.9999810748495098,
                0.9999852610127639,
                0.9999930377454112,
                0.9999930377420916,
                0.9999852610215451
            ],
            [
                0.9999687980774769,
                0.9999910603058276,
                0.9999952149060757,
                0.9999646437366552,
                0.9999910602994334,
                0.9999832985801483,
                0.9999832985761654,
                0.9999952149032236,
                0.9999724643056286,
                0.9999785550490333
            ],
            [
                0.9999967112497589,
                0.9999938558232021,
                0.9999957771660527,
                0.9999921107402375,
                0.999993037741262,
                0.9999921107402366,
                0.9999852610162815,
                0.9999921107336538,
                0.9999980052705163,
                0.9999930377404355
            ],
            [
                0.9999910603047626,
                0.9999898700102293,
                0.9999930377462409,
                0.9999938558232031,
                0.9999869928699877,
                0.9999930377429206,
                0.9999599363078577,
                0.9999546021098202,
                0.9999869928715408,
                0.9999810748562789
            ],
            [
                0.999996273360272,
                0.9999930377454109,
                0.9999930377420916,
                0.999996273360716,
                0.9999832985781612,
                0.9999938558246669,
                0.999996711252111,
                0.9999921107392977,
                0.9999785550592643,
                0.9999599363078501
            ],
            [
                0.9999832985761689,
                0.9999962733598278,
                0.9999952149043647,
                0.9999945777816771,
                0.9999910603036983,
                0.9999930377412614,
                0.9999898700126449,
                0.9999930377412609,
                0.9999970976873229,
                0.9999921107364755
            ],
            [
                0.9999967112517189,
                0.999996273360272,
                0.9999967112513268,
                0.9999952149060761,
                0.9999810748450013,
                0.9999952149049355,
                0.9999687980923908,
                0.9999945777816774,
                0.9999869928668889,
                0.9999852610127683
            ],
            [
                0.9999869928715404,
                0.9999832985801581,
                0.9999810748585377,
                0.9999832985801554,
                0.9999869928653388,
                0.9999599363030677,
                0.9999724643154813,
                0.9999852610110074,
                0.9999852610110065,
                0.9999910603047638
            ],
            [
                0.9999970976880153,
                0.9999970976883609,
                0.9999852610215436,
                0.9999898700041907,
                0.9999921107392958,
                0.9999910603036981,
                0.9999962733611605,
                0.9999910603058286,
                0.9999930377420913,
                0.9999957771670591
            ],
            [
                0.9999938558232031,
                0.999995777165046,
                0.9999974387180947,
                0.9999832985702053,
                0.999992110736476,
                0.9999910603047633,
                0.999997438717484,
                0.9999885212359836,
                0.9999852610110074,
                0.9999921107355351
            ],
            [
                0.999992110733653,
                0.9999898700114378,
                0.999994577779738,
                0.9999898700078147,
                0.9999898700102318,
                0.9999952149060763,
                0.9999546021422423,
                0.9999921107402366,
                0.9999938558253983,
                0.9999832985821414
            ],
            [
                0.9999599362887636,
                0.9999785550592695,
                0.9999898700078145,
                0.9999599363078678,
                0.9999898700126456,
                0.9999952149037942,
                0.9999724643023806,
                0.9999957771665557,
                0.999993855826131,
                0.9999687980923798
            ],
            [
                0.9999832985801516,
                0.9999938558268638,
                0.9999945777784451,
                0.9999945777829696,
                0.9999930377412614,
                0.9999952149055054,
                0.9999910603015668,
                0.999991060301566,
                0.9999910603015656,
                0.9999921107336532
            ],
            [
                0.9999785550464798,
                0.9999945777803845,
                0.9999957771645422,
                0.9999756997563889,
                0.9999599362887583,
                0.9999724643089143,
                0.999991060304763,
                0.9999885212305076,
                0.9999810748517677,
                0.9999885212277709
            ],
            [
                0.9999869928715373,
                0.9999921107336535,
                0.9999785550592651,
                0.9999832985801537,
                0.9999832985702012,
                0.9999869928730883,
                0.9999869928684368,
                0.9999785550439274,
                0.9999910603068943,
                0.9999938558232014
            ],
            [
                0.9999952149060768,
                0.9999832985701977,
                0.9999970976876693,
                0.9999938558275958,
                0.9999756997592781,
                0.9999945777810311,
                0.9999962733598278,
                0.9999930377420916,
                0.9999756997650764,
                0.9999938558268636
            ],
            [
                0.9999687980923697,
                0.9999852610197864,
                0.999968798081203,
                0.9999852610110139,
                0.9999869928653345,
                0.9999957771675624,
                0.9999938558275957,
                0.999985261021549,
                0.9999785550567011,
                0.9999251537995594
            ],
            [
                0.9999832985781628,
                0.9999756997592926,
                0.999996711251327,
                0.9999869928715396,
                0.9999930377445815,
                0.9999898700114374,
                0.9999885212359814,
                0.9999852610197992,
                0.9999938558246664,
                0.9999869928761926
            ],
            [
                0.9999898700066067,
                0.9999930377462408,
                0.9999957771655488,
                0.999995777165549,
                0.9999687980774897,
                0.9999885212305084,
                0.9999785550567073,
                0.9999810748449961,
                0.9999852610145259,
                0.9999885212332453
            ],
            [
                0.9999898700078145,
                0.9999989322973845,
                0.9999852610110019,
                0.9999930377404305,
                0.9999785550515884,
                0.9999952149037941,
                0.9999930377420904,
                0.9999990577549568,
                0.9999832985701949,
                0.9999646437408728
            ],
            [
                0.9999962733607163,
                0.9999898700041907,
                0.9999910603058293,
                0.9999832985741811,
                0.9999785550541569,
                0.9999724643023546,
                0.9999938558261315,
                0.9999832985821424,
                0.9999952149055058,
                0.9999898700066094
            ],
            [
                0.9999930377445811,
                0.9999945777797381,
                0.9999898700066079,
                0.9999898700114371,
                0.99997246431548,
                0.9999921107345953,
                0.9999910602994355,
                0.9999957771660526,
                0.9999945777784452,
                0.9999977396746245
            ],
            [
                0.9999930377445808,
                0.9999910603058286,
                0.9999957771675629,
                0.9999957771660524,
                0.9999952149043648,
                0.9999974387168734,
                0.999997097686631,
                0.9999898700078154,
                0.9999687980961101,
                0.999996273358939
            ],
            [
                0.999993855825399,
                0.9999957771675624,
                0.9999756997534879,
                0.999992110739296,
                0.9999957771670593,
                0.9999974387171788,
                0.9999921107336531,
                0.9999962733620487,
                0.9999885212264037,
                0.9999952149055057
            ],
            [
                0.9999785550439215,
                0.9999756997621719,
                0.9999832985721847,
                0.999975699750582,
                0.9999546021151592,
                0.9999869928653343,
                0.9999646437324458,
                0.9999810748449944,
                0.9999687980774823,
                0.9999599363173789
            ],
            [
                0.9999970976880148,
                0.9999930377420916,
                0.9999952149066469,
                0.9999921107355346,
                0.999997097689053,
                0.9999977396751635,
                0.9999974387180949,
                0.9999974387184,
                0.9999957771665557,
                0.999995777166556
            ],
            [
                0.9999921107355344,
                0.9999930377420906,
                0.9999910603026315,
                0.9999251537906921,
                0.9999938558253987,
                0.9999810748585306,
                0.9999938558253983,
                0.9999885212291387,
                0.999993855826131,
                0.9998415637844151
            ],
            [
                0.9999724643122028,
                0.9999938558246664,
                0.9999938558246659,
                0.9999967112509349,
                0.9999885212359814,
                0.9999832985741784,
                0.9999832985841393,
                0.9999921107355346,
                0.999988521227772,
                0.9999938558224687
            ],
            [
                0.9999599363126119,
                0.9999885212318773,
                0.9999938558275958,
                0.9999930377445817,
                0.999997097688015,
                0.999985261016284,
                0.9999930377404315,
                0.9999980052695652,
                0.999981074842744,
                0.9999898700126446
            ],
            [
                0.9999910602994353,
                0.999995214906076,
                0.999978555043942,
                0.9999810748585323,
                0.9999974387177893,
                0.999988521229142,
                0.9999869928653365,
                0.9999930377412611,
                0.9999938558224692,
                0.999993855826132
            ],
            [
                0.9999967112513269,
                0.9999417087554069,
                0.9999974387168734,
                0.9999938558224699,
                0.9999952149072169,
                0.9999986290427931,
                0.9999885212359819,
                0.9999980052709919,
                0.9999810748495125,
                0.9999852610127608
            ],
            [
                0.999995214906076,
                0.9999957771675627,
                0.9999599362935339,
                0.9999938558268638,
                0.9999938558239343,
                0.9999938558232018,
                0.9999967112493667,
                0.9999885212264044,
                0.9999898700054003,
                0.9999852610145198
            ],
            [
                0.9999810748562776,
                0.9999930377437511,
                0.9999952149055057,
                0.9999962733607161,
                0.9999962733593835,
                0.9999945777810304,
                0.999993037740431,
                0.999996711251327,
                0.9999832985781607,
                0.9999885212277724
            ],
            [
                0.9999898700066073,
                0.9999982396565769,
                0.9999962733607161,
                0.9999852610197902,
                0.999994577780384,
                0.9999852610162742,
                0.9999898700102311,
                0.9999885212359844,
                0.9999885212346152,
                0.9999869928715381
            ],
            [
                0.9999938558246665,
                0.9999938558232011,
                0.9999885212332448,
                0.9999785550464871,
                0.9999869928699874,
                0.9999930377437515,
                0.9999930377420913,
                0.9999898700102303,
                0.9999810748495125,
                0.9999852610127634
            ],
            [
                0.9999982396565769,
                0.9999974387165681,
                0.9999945777810307,
                0.9999724643023523,
                0.9999938558268635,
                0.9999952149072168,
                0.9999945777784459,
                0.9999938558261309,
                0.9999930377412646,
                0.9999967112513268
            ]
        ]
    },
    {
        "q_id": "8979_mmlu_math",
        "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": [
            [
                0.0008040861193273892,
                1.5534971989992774e-06,
                4.5397857775848465e-05,
                3.120191508446373e-05,
                2.902313023063532e-06,
                1.892515498859713e-05,
                4.006370650070828e-05,
                1.4738988998787566e-05,
                8.9396941718352e-06,
                8.93969736955767e-06
            ],
            [
                0.9953904285257054,
                0.999620015472734,
                0.9997040428666903,
                0.9997965729552876,
                0.9990889487721148,
                0.9975273773958215,
                0.9994472213461933,
                0.9998415637642217,
                0.9999417087348291,
                0.9980732651602635
            ],
            [
                0.999738809568741,
                0.9998601778762006,
                0.9999724643121909,
                0.9997040428302661,
                0.9998415637271959,
                0.0007096704576754045,
                0.999948557798626,
                0.9999038975392132,
                0.999948557792504,
                0.9999898700078143
            ],
            [
                6.475947982022763e-07,
                4.2228324375973415e-06,
                1.760343423160973e-06,
                4.785096776303374e-06,
                1.7603430034743913e-06,
                1.8925148239290237e-05,
                8.315278294072958e-07,
                2.2603245672867952e-06,
                1.4738983726908257e-05,
                4.222833444506298e-06
            ],
            [
                0.9990889486843239,
                0.9998415637836937,
                0.998967768927112,
                0.9999485577986358,
                0.9998415637839242,
                0.9995121428854489,
                0.9999756997476957,
                0.93991335382341,
                0.9964063976478457,
                0.9959298629674119
            ],
            [
                0.00013982212368956342,
                1.4738985485461206e-05,
                5.422218969720291e-06,
                3.1201903922734266e-05,
                3.1201911372399926e-05,
                6.60521210438226e-05,
                0.00010889687014821711,
                9.610238058922784e-05,
                1.0129988564430787e-05,
                4.222832437677995e-06
            ],
            [
                0.9999417087483646,
                0.9999038975621116,
                0.9998204720339836,
                0.9997965729539469,
                0.9999785550439243,
                0.9999646437535082,
                0.999796572978145,
                0.9997040427956243,
                0.9999599362982728,
                0.9999646437366446
            ],
            [
                8.481106121553572e-05,
                0.998830489753847,
                0.9902915219157702,
                0.977022630048159,
                4.5397874046655906e-05,
                0.999738809568665,
                0.998674977526251,
                0.9994472213265769,
                0.9902915242348412,
                7.484626278955236e-05
            ],
            [
                0.9993736657528445,
                0.9999417087206531,
                0.999373665830778,
                0.9996646498102713,
                0.9999646437366584,
                0.9999599363173749,
                0.9997694932852572,
                0.9989677689401968,
                0.9995694429613496,
                0.9999810748427478
            ],
            [
                4.539785780557527e-05,
                4.222833444106873e-06,
                1.0129995809929273e-05,
                1.3709578605542582e-06,
                0.00010889692196407291,
                4.539785239182798e-05,
                1.892514372479069e-05,
                5.422218968931258e-06,
                0.00020342706950841037,
                1.4738978457336465e-05
            ],
            [
                2.4300232040584407e-05,
                0.9999982396572064,
                0.9999832985721876,
                0.999995777165549,
                0.9999869928761908,
                8.93969630317306e-06,
                0.005911069181861766,
                0.9998911030391162,
                0.9999970976869773,
                0.9999898700054063
            ],
            [
                3.726641061109272e-06,
                1.3709573702778664e-06,
                2.430024651705481e-05,
                3.1201926246083686e-05,
                8.481108166450792e-05,
                6.605215252055522e-05,
                8.939695237959376e-06,
                6.605216038349344e-05,
                2.4300243624818735e-05,
                0.00020342689978431914
            ],
            [
                4.5397852361605714e-05,
                3.2887478890769702e-06,
                4.2228329408924035e-06,
                2.4300249410794055e-05,
                8.93969417167259e-06,
                7.484625397240209e-05,
                1.8925145981283003e-05,
                4.785095065045315e-06,
                4.2228324377164004e-06,
                1.3007131565376817e-05
            ],
            [
                0.9399133466701362,
                0.9859363724660388,
                2.144494329952946e-05,
                0.9046505338155469,
                9.610241487022105e-05,
                9.610241443673568e-05,
                0.000804085828300522,
                4.785093353687772e-06,
                3.5356250696598434e-05,
                3.5356246488642456e-05
            ],
            [
                0.9999977396762414,
                0.9999832985721898,
                0.9999599363126035,
                0.9999967112501533,
                0.996406396935871,
                7.484624505832518e-05,
                0.9998911030662013,
                0.9999756997593006,
                0.9999910603005032,
                0.00033535006686255466
            ],
            [
                0.9914225128755926,
                0.9796676477703992,
                0.9840936065096272,
                0.9933071501251718,
                0.998498817747451,
                0.9989677692011713,
                0.9706877682946817,
                0.9980732652202604,
                0.9902915240289006,
                0.9959298630787797
            ],
            [
                4.222831934286977e-06,
                4.0063706496627415e-05,
                1.1478770862255766e-05,
                1.6701419853184244e-05,
                0.00013982213972873613,
                1.670142980687079e-05,
                0.00023050668643219275,
                2.430023782010365e-05,
                1.0129993394664264e-05,
                1.9947299592824403e-06
            ],
            [
                4.222835458117536e-06,
                6.962257079629686e-06,
                1.1478769492893215e-05,
                4.78509563555309e-06,
                8.481105145413196e-05,
                5.144222591279097e-05,
                4.0063696932399445e-05,
                5.422219616140078e-06,
                2.2603251062147097e-06,
                1.4738976700366126e-05
            ],
            [
                0.9999756997534821,
                0.9999546021205596,
                0.9999852610180342,
                0.9998601779602719,
                0.9998911031040516,
                0.9999832985841328,
                0.9999910603047715,
                0.9999687980998067,
                0.999994577778445,
                0.9999810748517677
            ],
            [
                4.0063692159249626e-05,
                4.00636778475281e-05,
                0.00048785721006051625,
                5.1442232038504445e-05,
                0.0008040857950496685,
                6.605216824595201e-05,
                4.006370650464339e-05,
                0.9840936060722768,
                6.605215248979934e-05,
                4.539786861787811e-05
            ],
            [
                3.288749457432399e-06,
                8.93969736929749e-06,
                3.53562591336057e-05,
                4.7850933535659155e-06,
                5.422220908925639e-06,
                3.5356259098234985e-05,
                2.7535697660090726e-05,
                1.30071315602427e-05,
                0.00026119030876019115,
                2.430023782717578e-05
            ],
            [
                0.015906389466749788,
                0.00020342694892337422,
                0.0002305067140117121,
                8.481101095665886e-05,
                3.2887498494551953e-06,
                4.006368741175151e-05,
                0.00013982204067405766,
                2.753569109925723e-05,
                3.120190021453107e-05,
                0.993307150038491
            ],
            [
                0.9990889486592105,
                0.00010889687024170175,
                5.829127245607013e-05,
                0.00020342706876257823,
                0.00015843629205243188,
                0.9986749777034069,
                0.995390427386895,
                0.995929861885822,
                0.9992903296223232,
                0.9996200154711754
            ],
            [
                6.475949526003845e-07,
                2.5612831266608576e-06,
                2.4300246524568948e-05,
                3.288749849498565e-06,
                1.9947297215043796e-06,
                1.1478768125201194e-05,
                0.9149009474519223,
                3.53562675670136e-05,
                2.90231233114251e-06,
                1.1478769493331685e-05
            ],
            [
                0.0008040861117044762,
                0.00033535018283069285,
                0.9984988175469525,
                0.9992903296213326,
                0.9993736659883576,
                0.9999417087141331,
                0.9991959140992583,
                0.0008040858292826146,
                0.9999546021422242,
                0.9997694932305475
            ],
            [
                0.9999151889284437,
                0.9999832985722059,
                0.9999810748472566,
                0.999954602136903,
                0.9999885212332446,
                9.610238054937517e-05,
                0.9997694933126624,
                0.9999885212332457,
                0.9990889488245669,
                0.99979657307687
            ],
            [
                6.962254587597396e-06,
                6.962254589914941e-06,
                9.610240348773577e-05,
                8.93969310662177e-06,
                1.0129990979381404e-05,
                0.8807970842359877,
                1.3007133115903994e-05,
                1.8925150496161756e-05,
                2.4300237828943813e-05,
                2.9023116391978967e-06
            ],
            [
                5.715003789033962e-07,
                2.260324836776948e-06,
                1.3709575337016483e-06,
                3.7266383955882547e-06,
                8.939696303758459e-06,
                2.561281600076256e-06,
                1.2098662604291696e-06,
                4.785095065093186e-06,
                5.42222090882208e-06,
                4.222834451327159e-06
            ],
            [
                0.9999967112501504,
                0.9999962733611603,
                0.9999952149043645,
                0.9999930377454104,
                0.9999987901344608,
                0.9999885212264016,
                0.9999938558224682,
                0.9999938558253983,
                0.9999970976873229,
                0.9999646437493034
            ],
            [
                3.1201922525618933e-05,
                0.9982992777368048,
                9.61023804983358e-05,
                1.1478769493728398e-05,
                9.610244913374722e-05,
                6.962254589705982e-06,
                1.994729959270648e-06,
                1.8925141466439755e-05,
                1.0129990979547237e-05,
                6.962256249682458e-06
            ],
            [
                0.9953904273249334,
                0.9968273176773809,
                0.9924227593554404,
                0.9968273176611809,
                0.9840936072093877,
                0.679178699175393,
                4.2228349547223175e-06,
                4.785093353687772e-06,
                0.9740426436969953,
                0.9947798749665887
            ],
            [
                1.892515500663531e-05,
                3.1201907597112416e-05,
                6.144177531660828e-06,
                2.5612812946890944e-06,
                5.144219523894761e-05,
                3.2887486733420804e-06,
                2.2603245673279107e-06,
                5.422218969720291e-06,
                2.144495608222158e-05,
                3.535626334799422e-05
            ],
            [
                0.9991959139522719,
                0.9992903294578266,
                0.9998911031171505,
                0.9986749775476639,
                0.9998415637267211,
                0.9984988176450205,
                0.9998415638410881,
                0.9995121427713202,
                0.9978172836986695,
                0.9998601778594941
            ],
            [
                1.3007133114886634e-05,
                2.430023493228869e-05,
                2.2603251061849014e-06,
                2.1444950959977102e-05,
                2.7535704212311033e-05,
                6.605213678458984e-05,
                1.892514147046736e-05,
                5.144221977210733e-05,
                6.605217593396786e-05,
                3.5356242243001115e-05
            ],
            [
                0.00010889694789102389,
                0.9978172835921798,
                0.998299277693321,
                0.0008040858680518957,
                0.0021827166781013445,
                0.9986749775416558,
                0.9796676466944432,
                0.9770226304663119,
                0.9859363705935708,
                0.9740426422841656
            ],
            [
                0.9980732649171415,
                2.9023130230846496e-06,
                3.535626333641835e-05,
                0.000335350188587147,
                4.7850967763512445e-06,
                0.9971990734373749,
                0.00026119043252816905,
                0.9465966749081429,
                0.00033535006650155686,
                0.00013982212394793165
            ],
            [
                0.9525741298517643,
                0.0003799844349914718,
                0.00026119043274095945,
                0.00033535006637471973,
                5.144223809160982e-05,
                0.0008040860935123711,
                5.829128635171172e-05,
                7.484625397893652e-05,
                1.6701421842140854e-05,
                0.9525741313664297
            ],
            [
                0.00017952798700133205,
                0.9840936108248172,
                0.9999756997476829,
                0.9993736658732607,
                0.9999756997679586,
                0.9999417087136521,
                0.9999687980849298,
                0.9999832985761699,
                0.999769493312555,
                0.999841563745628
            ],
            [
                6.605214463262879e-05,
                0.0002034268997399244,
                0.00015843621641929045,
                4.539789026032761e-05,
                7.889265406567165e-06,
                2.144494073796001e-05,
                2.1444950957402623e-05,
                3.120190391251851e-05,
                1.670142383015595e-05,
                1.892514372640862e-05
            ],
            [
                0.00010889690922797348,
                8.481106150677358e-05,
                5.144220750870732e-05,
                2.1444943300075563e-05,
                8.481103079352604e-05,
                2.753570094621784e-05,
                4.539785781961294e-05,
                0.0011695102306501248,
                2.144494329952946e-05,
                2.144494329952946e-05
            ],
            [
                0.9998601779784391,
                0.9994472213245831,
                0.00029595706158913485,
                0.9999885212305069,
                0.999996711250935,
                0.9998415637266403,
                0.0010322309359183115,
                0.9999910603005003,
                0.9999485577679911,
                0.005220124602985797
            ],
            [
                0.999981074844992,
                0.9999962733611603,
                0.9999952149032236,
                0.9999962733620488,
                0.9999967112493665,
                0.9999938558232008,
                0.9999957771645418,
                0.99995460213136,
                0.9999957771655487,
                0.9999982396572064
            ],
            [
                0.9999687980886374,
                0.9999945777810322,
                0.9999869928668994,
                0.9999810748517772,
                0.9999810748495139,
                0.9999970976866311,
                0.9988304897618704,
                0.9999546021260319,
                0.9999339478789562,
                0.182425528251267
            ],
            [
                2.2603242978377903e-06,
                1.0129989769722525e-05,
                6.9622579096593295e-06,
                6.962256249682458e-06,
                0.00013982205705906782,
                5.144223201604811e-05,
                5.8291286270284484e-05,
                4.006369694959736e-05,
                8.481103097369854e-05,
                6.144175334172377e-06
            ],
            [
                6.962253759581752e-06,
                3.120191136774608e-05,
                0.00020342699714494958,
                2.1444943298944354e-05,
                2.260324297853209e-06,
                0.9989677691722408,
                5.1442195245310235e-05,
                2.9023109470871505e-06,
                4.006369694755693e-05,
                2.1444940743772097e-05
            ],
            [
                0.9933071496855764,
                0.9914225132161477,
                0.9465966734015935,
                0.9890130594237595,
                0.9980732655587508,
                0.9964063968033137,
                0.9984988176279196,
                0.991422513263667,
                0.9875683502101711,
                0.9890130577640854
            ],
            [
                6.605215251574962e-05,
                0.0001398220906631957,
                3.5356246482211416e-05,
                2.7535691095550887e-05,
                2.5612812945889277e-06,
                4.006369694755693e-05,
                2.2603251061664e-06,
                2.1444943300075563e-05,
                6.144172404380855e-06,
                4.539787405128009e-05
            ],
            [
                6.144176066672166e-06,
                1.0129989769188164e-05,
                0.9968273168850638,
                5.144220748250827e-05,
                1.3007133114602719e-05,
                2.9023109471689794e-06,
                3.53562591237019e-05,
                9.610241487022105e-05,
                8.481105105429698e-05,
                6.144173136885882e-06
            ],
            [
                0.9978172840292948,
                0.9964063972676812,
                2.7535704218321328e-05,
                9.610241470381859e-05,
                0.0005527785896832567,
                0.99752737679972,
                0.9980732649614676,
                3.535624646150348e-05,
                0.9947798736390401,
                0.9989677690720046
            ],
            [
                5.829127242638312e-05,
                3.1201926246083686e-05,
                7.889266347456862e-06,
                5.144220137700842e-05,
                3.1201903929204235e-05,
                7.889263525893087e-06,
                2.2603245673279107e-06,
                2.4300243625614346e-05,
                1.3007131565140219e-05,
                2.5612812947240366e-06
            ],
            [
                1.300712381094558e-05,
                0.9840936070636043,
                1.6701423831188846e-05,
                0.00010889693460193567,
                2.4300237821252875e-05,
                5.144223806615931e-05,
                1.4738987240100149e-05,
                2.753568451618723e-05,
                3.535626333809042e-05,
                4.222832940777184e-06
            ],
            [
                1.3007131565376817e-05,
                1.4738980203395485e-05,
                1.670141585178861e-05,
                1.0129987356706945e-05,
                6.144177531208195e-06,
                1.1478764018305152e-05,
                6.144176066051891e-06,
                3.5356263314938686e-05,
                4.539787938592359e-05,
                4.006370172318498e-05
            ],
            [
                0.9924227595480335,
                0.9971990726478925,
                0.9953904279808712,
                1.2098655392921197e-06,
                0.00017952790156782624,
                4.539786321684599e-05,
                1.8925141469950998e-05,
                1.1478766757049986e-05,
                0.9947798748601914,
                0.9796676488463552
            ],
            [
                5.715005832872586e-07,
                3.2887490652810324e-06,
                2.1444943290362748e-05,
                3.2887502415243994e-06,
                2.2603248367512505e-06,
                6.962255419570695e-06,
                1.370956879949281e-06,
                1.8925141472360678e-05,
                4.222835458148261e-06,
                3.120190764966677e-05
            ],
            [
                0.0002959571681150299,
                4.785093923768848e-06,
                0.00029595706121025373,
                1.892515725149365e-05,
                0.9947798755300109,
                1.4738987240824012e-05,
                8.481105129493839e-05,
                3.120191880504111e-05,
                0.9975273764947779,
                2.7535681246690542e-05
            ],
            [
                0.9990889489191924,
                0.8354835330070838,
                0.989013058735602,
                0.00048785711333067103,
                0.9996646497720446,
                0.9959298614837649,
                4.539786323088365e-05,
                0.9997965729303111,
                5.144221971634078e-05,
                0.966914023160595
            ],
            [
                0.9984988177516388,
                0.9996646498962863,
                0.999959936322189,
                0.9984988174248037,
                0.9997040428350882,
                0.9993736659871554,
                0.9875683509876791,
                0.9706877719515358,
                0.9996646498522934,
                0.9997694932610044
            ],
            [
                2.9023133690425823e-06,
                8.939695237813028e-06,
                1.9947299592824403e-06,
                8.939699500489763e-06,
                4.785094494628999e-06,
                1.670142781560441e-05,
                3.2887498494282754e-06,
                7.88926258532661e-06,
                1.1478770859332632e-05,
                2.4300252310279753e-05
            ],
            [
                4.006368736190672e-05,
                2.1444940740066406e-05,
                5.829127222705607e-05,
                6.605214456006411e-05,
                6.962253759752719e-06,
                1.3007126912542439e-05,
                2.260324028331257e-06,
                8.939700565834043e-06,
                4.006368733421517e-05,
                2.5612828213352452e-06
            ],
            [
                0.9940889316089246,
                0.9978172839694577,
                0.00017952794374911278,
                0.0004878571662085154,
                0.9988304898962282,
                0.00023050676829213258,
                0.0002611903689494498,
                0.9959298622331388,
                0.00023050673996141355,
                0.9980732656111363
            ],
            [
                2.5612816000331606e-06,
                7.889261645090304e-06,
                3.7266379513434106e-06,
                1.5534979397677313e-06,
                6.144176066521288e-06,
                3.288747889229516e-06,
                1.300713466619476e-05,
                4.222832437639588e-06,
                1.300712846361323e-05,
                1.7603430034439723e-06
            ],
            [
                0.9998601779093998,
                0.9989677688206335,
                0.9999417087344882,
                0.9999984465026159,
                0.999997097689053,
                0.9999974387184001,
                0.9999832985741752,
                0.9999646437493,
                0.9999921107392965,
                0.999915188928401
            ],
            [
                3.288748281295496e-06,
                1.8925157262061825e-05,
                1.3709573702778664e-06,
                4.222832941142044e-06,
                2.2603251062270446e-06,
                1.0129993394664264e-05,
                1.7603434231705793e-06,
                1.7603440527222532e-06,
                2.902313023101807e-06,
                2.561283126679493e-06
            ],
            [
                0.9968273174226023,
                0.9770226296718215,
                0.9995694429161077,
                0.9975273770443628,
                0.977022630466312,
                0.9990889488159838,
                0.998830489887525,
                0.9995121428876343,
                0.9465966694469009,
                0.7057850340255386
            ],
            [
                0.9959298630240396,
                0.9933071506050118,
                0.994088931420121,
                0.9999038975393901,
                0.9995121429439182,
                0.9975273772476576,
                0.9996200154309469,
                0.9902915242079794,
                0.9902915249601105,
                0.9947798754913209
            ],
            [
                0.9968273166420668,
                0.9953904274723592,
                0.9995121429410231,
                0.996827316860764,
                0.9986749777345245,
                0.9875683506675288,
                0.9875683489181353,
                0.9982992773284528,
                0.9982992775067362,
                0.9991959140714325
            ],
            [
                1.4738988999377379e-05,
                0.9997040429548318,
                5.422218969661113e-06,
                0.0009110511162524262,
                4.0063687409856826e-05,
                0.9988304900112754,
                0.00043055708781280583,
                7.484620042805751e-05,
                7.484623615568462e-05,
                0.9980732656111363
            ],
            [
                2.2603234894745224e-06,
                4.785094494716039e-06,
                2.753568124458694e-05,
                7.338211554783522e-07,
                1.3007125360809367e-05,
                4.006369216362198e-05,
                2.2603242978778778e-06,
                7.88925976418034e-06,
                8.481102108148808e-05,
                9.422443692527585e-07
            ],
            [
                1.670142582300158e-05,
                2.144495608046625e-05,
                4.785094494672519e-06,
                3.535625066302841e-05,
                1.994729245878497e-06,
                3.2887486731641103e-06,
                3.120191880867338e-05,
                1.3007131564383116e-05,
                4.222834953712232e-06,
                1.7603436329978976e-06
            ],
            [
                3.535624224505904e-05,
                0.00015843619767583143,
                0.0006263340175082692,
                6.144177531459659e-06,
                9.610239195213367e-05,
                0.9924227586971223,
                0.9997694933127764,
                0.0002305067143001166,
                0.00023050676962013515,
                0.0008040860343529581
            ],
            [
                0.0010322309401198325,
                7.484622713542509e-05,
                8.9396941718352e-06,
                0.9959298617083884,
                6.605212879046137e-05,
                8.939698434820389e-06,
                8.481105106540349e-05,
                NaN,
                9.610239186473745e-05,
                7.484623607727125e-05
            ],
            [
                0.9999756997534777,
                0.9978172839562732,
                0.9999785550439397,
                0.9999724642990885,
                0.9999810748449955,
                0.9999869928761882,
                0.9999485577925467,
                0.9999832985801479,
                0.9998911030655344,
                0.9999251537906992
            ],
            [
                0.9999980052709919,
                0.9999991684721707,
                0.9999967112521109,
                0.9999991684715758,
                0.9999898700078128,
                0.9999974387187053,
                0.999997438716568,
                0.9999989322970028,
                0.9999977396759716,
                0.999996273358939
            ],
            [
                0.9914225151565198,
                0.9914225147526056,
                0.9978172837884252,
                0.9914225160831462,
                0.9986749772733033,
                9.610239199338466e-05,
                0.9993736659201885,
                0.9924227602273615,
                0.9968273165595952,
                0.9953904277351616
            ],
            [
                0.9994472214551452,
                0.9999785550515917,
                0.9996200154736516,
                0.9998911030777935,
                0.9998601779593259,
                0.999512142940427,
                0.9999785550490328,
                0.9999898700102289,
                0.9999810748427356,
                0.9995121428836323
            ],
            [
                0.9933071481005561,
                0.9968273167002388,
                4.006368262300812e-05,
                0.9975273771138506,
                0.9982992779714193,
                0.9840936080549317,
                0.9859363750100122,
                0.9046505248181418,
                0.9968273176015363,
                0.18242552602881168
            ],
            [
                0.9998766053664029,
                0.9999832985701962,
                0.9999785550413652,
                0.9999945777797378,
                0.9999869928761882,
                0.9999952149072169,
                0.9999938558224687,
                0.9999910603058294,
                0.9999885212346119,
                0.9999921107374152
            ],
            [
                6.144172404520556e-06,
                4.5397863201321984e-05,
                4.0063682625048554e-05,
                1.8925152752138513e-05,
                5.829126537996031e-05,
                2.26032402841657e-06,
                0.00010889690911072151,
                0.00023050668648584945,
                1.6701427815999337e-05,
                2.1444948408977715e-05
            ],
            [
                1.3709576971379186e-06,
                3.1201922517673344e-05,
                5.144220138599094e-05,
                4.0063682603624035e-05,
                8.939697369671496e-06,
                3.2887490653647836e-06,
                0.00012339460406817764,
                0.0009110510000102739,
                0.00020342694900920405,
                2.9023116391675407e-06
            ],
            [
                2.4300249422639878e-05,
                1.892515049702235e-05,
                4.785096206013061e-06,
                1.2098658277451275e-06,
                8.939700566801578e-06,
                7.889265407090955e-06,
                0.00010889694804630358,
                4.785093353909723e-06,
                3.2887502415438413e-06,
                4.785096206047877e-06
            ],
            [
                0.999981074856277,
                0.9999869928746395,
                0.9999785550541502,
                0.9999898700041926,
                0.9999982396559474,
                0.9999957771675625,
                0.999995777165549,
                0.9999898700041907,
                0.9999832985741766,
                0.9999970976869773
            ],
            [
                2.430023201503635e-05,
                1.3007125363057018e-05,
                1.7603440527222532e-06,
                5.422218323349895e-06,
                3.288748673295719e-06,
                2.430024940080467e-05,
                2.902313023039776e-06,
                0.0001795280089030124,
                2.1444956079218013e-05,
                3.7266406167827664e-06
            ],
            [
                0.9997388096302221,
                0.9875683487923619,
                0.9947798750850766,
                0.9975273766136535,
                0.9982992779038219,
                0.991422513334946,
                0.992422757128364,
                0.9890130571973674,
                0.998498817485529,
                0.9940889311355473
            ],
            [
                0.9465966730249561,
                0.99330714805412,
                0.9971990732910541,
                0.994088932438019,
                0.9947798752035645,
                0.9933071506483522,
                0.9796676484753358,
                0.9940889324434916,
                0.9940889302271005,
                0.9980732654306975
            ],
            [
                0.8354835391516133,
                1.1478765385746131e-05,
                1.2098653950656417e-06,
                1.994729959224386e-06,
                6.144173136556186e-06,
                1.6701415871049018e-05,
                7.88925976397226e-06,
                4.785092782936557e-06,
                1.4738981963234875e-05,
                8.939695236593446e-06
            ],
            [
                2.2603245673155757e-06,
                4.222834954403545e-06,
                1.1478773598538445e-05,
                0.8519527944504227,
                1.3007128462785148e-05,
                1.3709576971316842e-06,
                4.0063696941289896e-05,
                6.962256248871951e-06,
                3.466326624322211e-07,
                3.288749849368453e-06
            ],
            [
                0.9997694932025321,
                0.9999251537639091,
                0.9998204720767708,
                0.9995121428247089,
                0.9999251537550016,
                0.9998911030388706,
                0.9999151889586775,
                0.9994472213930157,
                0.9947798738542528,
                0.9998601779426847
            ],
            [
                0.00017952805148918532,
                1.1478773598914277e-05,
                1.8925152750692706e-05,
                1.1478764019996392e-05,
                2.902313023063532e-06,
                4.539788485169606e-05,
                1.0129988564430787e-05,
                1.6701423834591316e-05,
                1.892515048820981e-05,
                4.006368260595596e-05
            ],
            [
                1.8925152751174644e-05,
                6.144176799227922e-06,
                2.5612816000646084e-06,
                6.144176799099397e-06,
                3.72664017246987e-06,
                1.300712691308661e-05,
                1.7603440527222532e-06,
                1.4738978457041559e-05,
                1.1478764019787597e-05,
                1.670142781636389e-05
            ],
            [
                3.535624646947797e-05,
                2.75357009220765e-05,
                3.7266410609160796e-06,
                0.00023050671371660047,
                1.3007130012980722e-05,
                3.535623801986889e-05,
                4.785092783319532e-06,
                2.1444948409679848e-05,
                9.610240332972338e-05,
                1.670141786036971e-05
            ],
            [
                0.00015843629153837536,
                2.430023783309869e-05,
                2.4300252313020203e-05,
                6.14417313680765e-06,
                0.00017952794432114216,
                0.00043055702225452584,
                1.3007130014376633e-05,
                0.00013982210691394165,
                4.222834451254188e-06,
                4.539788483220847e-05
            ],
            [
                0.9996646498110714,
                0.9796676448764484,
                0.996406397205988,
                0.9953904279851443,
                0.9991959141522446,
                0.9859363733570753,
                1.147877223059538e-05,
                0.9988304896039865,
                0.9953904278184892,
                0.9968273170323346
            ],
            [
                0.9669140218496496,
                0.9947798741927899,
                0.9971990727805568,
                0.9986749777433054,
                0.9994472213917935,
                0.9796676484011321,
                0.995390427570643,
                0.9975273767761746,
                0.9953904281646192,
                0.9947798735108796
            ],
            [
                0.9982992777872064,
                0.974042643367335,
                0.9940889324517005,
                0.9953904284701536,
                0.9914225126617556,
                0.9241418178895028,
                1.4738980212644815e-05,
                0.9324533065140289,
                0.9626731151992686,
                0.9953904284787001
            ],
            [
                0.00012339455958160968,
                1.4738988999377379e-05,
                1.4738988998787566e-05,
                0.00020342692455362147,
                0.00012339458936200595,
                0.0010322308183957748,
                1.4738985485166298e-05,
                5.8291251623852595e-05,
                0.9998766053957809,
                0.0010322308787776282
            ],
            [
                0.00017952802964757599,
                7.88926258532661e-06,
                0.9626731122542813,
                1.6701425825128124e-05,
                0.984093607938305,
                3.120191509172827e-05,
                0.990291524870571,
                7.889259764079887e-06,
                0.9399133525610676,
                0.0001795280507499871
            ],
            [
                5.144223201941656e-05,
                8.939699495221176e-06,
                5.422220908402905e-06,
                5.829128607647069e-05,
                4.006371126555232e-05,
                5.144220736274121e-05,
                2.4300240714549077e-05,
                5.8291258551949844e-05,
                0.00015843617876870657,
                1.8925152741191683e-05
            ],
            [
                5.422220908762902e-06,
                4.006369693006752e-05,
                0.9980732649337078,
                7.484623613063591e-05,
                0.9947798730925446,
                0.8807970842359877,
                0.9840936108539737,
                0.9997965729561221,
                1.1478772229551402e-05,
                0.9996646500161377
            ],
            [
                0.9999962733593833,
                0.9999938558246659,
                0.9999921107336538,
                0.9999417087136483,
                0.9999832985841359,
                0.9999687980886335,
                0.9996646500123227,
                0.9999785550490333,
                0.9999910603036983,
                0.9999724642990605
            ],
            [
                0.9999546021368129,
                0.0007096702757178511,
                0.999447221256472,
                0.9999485577680443,
                0.9998911031301592,
                0.9986749777137282,
                0.99994170874838,
                0.9997040428678959,
                0.9988304898808614,
                0.9996200155609736
            ],
            [
                4.22283294098842e-06,
                2.5612834319655406e-06,
                8.93969310647542e-06,
                1.7603425837606927e-06,
                1.7603436330091044e-06,
                1.1478772230407462e-05,
                1.3007133109421283e-05,
                1.1478772230198667e-05,
                8.939698435096828e-06,
                2.9023133690188264e-06
            ],
            [
                0.9998204720127244,
                2.144494329769612e-05,
                4.539786863059458e-05,
                4.00636778475281e-05,
                5.829127246412803e-05,
                2.1444950969026795e-05,
                0.00033534998826260085,
                9.610238061859297e-05,
                1.300713311614059e-05,
                0.9940889313352961
            ],
            [
                0.999975699753489,
                0.9999921107355343,
                0.9999885212264024,
                0.999993037740431,
                0.9999980052702786,
                0.9999938558246686,
                0.9999810748540359,
                0.9999885212346129,
                0.9999898700090233,
                0.996406396903357
            ],
            [
                4.5397857790051276e-05,
                3.72664061671159e-06,
                2.430023782717578e-05,
                3.5356267555952205e-05,
                5.422218969661113e-06,
                4.0063696932399445e-05,
                5.422217030614265e-06,
                4.006368262111344e-05,
                0.0002034269963280861,
                2.753568122996191e-05
            ],
            [
                2.9023119851266288e-06,
                1.3007133115903994e-05,
                4.2228324377164004e-06,
                1.5534975693933505e-06,
                6.144173869502757e-06,
                4.2228349547223175e-06,
                4.785094494672519e-06,
                1.5534971990126997e-06,
                1.9947292459265734e-06,
                1.994730434879465e-06
            ],
            [
                5.422217675628357e-06,
                1.6701423825538316e-05,
                4.006371126992468e-05,
                1.1478769483372156e-05,
                2.4300237829827827e-05,
                3.288750241473551e-06,
                6.962259565292781e-06,
                4.222832437386106e-06,
                6.144177531532303e-06,
                8.93969736942758e-06
            ],
            [
                0.9947798738663435,
                0.9953904272330594,
                0.98201378585969,
                0.9525741310298373,
                0.9706877696196289,
                0.9859363736282603,
                0.9046505261034854,
                0.9770226289191464,
                0.817574478416099,
                0.995390428662448
            ],
            [
                1.892515273885085e-05,
                6.962257078819179e-06,
                4.222831934202483e-06,
                1.553498495338299e-06,
                3.2887478892055875e-06,
                1.2098661161861e-06,
                1.8925150487521332e-05,
                4.785093924103951e-06,
                5.043475885657239e-07,
                2.9023133689317184e-06
            ],
            [
                3.726640172503764e-06,
                6.144173869240119e-06,
                4.785093353787868e-06,
                5.422218969818919e-06,
                1.5534983101549167e-06,
                1.2098659719716573e-06,
                1.5534971990126997e-06,
                2.9023123311055552e-06,
                8.93969630348202e-06,
                6.475945666051092e-07
            ],
            [
                0.999978555056703,
                0.00033535026538215743,
                0.9999930377437504,
                0.9999832985702006,
                0.9999898700053982,
                0.9999251537995099,
                0.9998204720559609,
                0.9999687980775012,
                0.9998204720988919,
                0.999941708734573
            ],
            [
                0.9947798752567631,
                0.00033535022760420067,
                4.006371126336615e-05,
                5.422217030663578e-06,
                1.4738983728490028e-05,
                0.9924227598491789,
                5.829124465207388e-05,
                1.4738981971250963e-05,
                0.00029595723730392506,
                2.7535697663897248e-05
            ],
            [
                2.902312677104321e-06,
                5.144223812641715e-05,
                1.99472900813862e-06,
                3.7266388397721442e-06,
                3.9278638756099906e-07,
                1.0677031245905116e-06,
                1.3709573702722555e-06,
                3.7266379512518984e-06,
                1.3709572068179446e-06,
                1.0677031245905116e-06
            ],
            [
                0.997199073598653,
                0.9994472213201774,
                0.9968273165492862,
                0.9971990729593935,
                0.9924227582419022,
                0.9982992779698382,
                0.99937366584251,
                0.9995121427681696,
                0.9875683466999498,
                0.9902915256137481
            ],
            [
                1.7603430032918752e-06,
                0.9740426401178265,
                6.60521444778882e-05,
                1.4738976699749503e-05,
                1.147876538789672e-05,
                0.00010889693506777467,
                8.481103097369854e-05,
                8.481105063718517e-05,
                0.9982992773039437,
                3.120191507027519e-05
            ],
            [
                4.006367785146321e-05,
                0.00033535018598210753,
                7.484626288049013e-05,
                2.1444940741392653e-05,
                7.48462093285157e-05,
                0.0003353501841088208,
                0.0002611904312590264,
                7.88926258532661e-06,
                5.422217029943586e-06,
                4.539789026032761e-05
            ],
            [
                0.995929862195387,
                0.9859363727113967,
                0.9994472214086445,
                0.9902915220769412,
                0.9980732651786207,
                0.9964063978796126,
                0.9399133534026293,
                0.9997388095676162,
                0.9988304899200264,
                0.9840936080840884
            ],
            [
                1.892514147046736e-05,
                0.0010322308067515608,
                8.481108129984348e-05,
                6.605213676969247e-05,
                0.0002034270202361419,
                0.00017952794407561355,
                9.610240332972338e-05,
                0.9525741300200603,
                0.9399133561377043,
                1.6701427803088173e-05
            ],
            [
                2.4300240719941574e-05,
                4.5397879445707534e-05,
                5.829127933751884e-05,
                1.0129995809431767e-05,
                2.430023203740195e-05,
                1.4738978455325741e-05,
                2.902312677060767e-06,
                2.5612819053166966e-06,
                0.00033535018706510147,
                4.5397884834850856e-05
            ],
            [
                4.0063692185483734e-05,
                1.892514372737249e-05,
                3.5356254892335935e-05,
                1.473898724181597e-05,
                1.0129988564430787e-05,
                7.484625397893652e-05,
                7.889259764079887e-06,
                0.00010889696091391995,
                1.760344052714248e-06,
                1.4738980214280206e-05
            ],
            [
                1.9947297215043796e-06,
                1.892515726099468e-05,
                8.481102104878554e-05,
                1.0129988564716393e-05,
                2.90231163910023e-06,
                7.889265407090955e-06,
                5.144221974927673e-05,
                1.1478769493916314e-05,
                8.939698435454571e-06,
                4.006369696286016e-05
            ],
            [
                0.9980732654938288,
                0.0002034270667440961,
                5.829125851717365e-05,
                7.484623608435025e-05,
                5.82912723385944e-05,
                0.000335350104845384,
                0.00015843615887957543,
                5.829125851250855e-05,
                7.484621821481694e-05,
                0.000261190370286989
            ],
            [
                0.999985261016273,
                0.9999945777803846,
                0.9999984465022456,
                0.999985261018032,
                0.9999967112521109,
                0.9999977396759719,
                0.9999898700066057,
                0.9999977396748938,
                0.9999970976887069,
                0.9999952149032242
            ],
            [
                0.9988304894595653,
                0.00012339453003282785,
                0.0003799845666431117,
                6.605215247346026e-05,
                4.0063682616886836e-05,
                0.9992903297376565,
                0.9994472213893174,
                5.8291258543467846e-05,
                0.9984988177306992,
                0.9995121428896212
            ],
            [
                0.00013982207397912565,
                0.00020342697277223143,
                6.605213668751657e-05,
                9.610239184236401e-05,
                7.484626290608339e-05,
                0.997527376515452,
                0.9984988174450455,
                0.0013250223129223154,
                0.0001398220571038245,
                1.3007131562514014e-05
            ],
            [
                0.9996200154748787,
                0.0009110511925992626,
                0.9999251537995654,
                0.9999962733616051,
                0.9999151889589378,
                0.9999852610110065,
                0.9999417087136648,
                0.9999756997563835,
                0.9999869928684358,
                0.9996646499752961
            ],
            [
                1.2098653950551882e-06,
                1.3709568799823232e-06,
                5.42221767672807e-06,
                1.7603438428460541e-06,
                2.9023126770343703e-06,
                2.5612816000331606e-06,
                1.892514145136205e-05,
                2.5612812947240366e-06,
                6.144173136455602e-06,
                1.3709573702647743e-06
            ],
            [
                7.48462093682669e-05,
                4.539786320924914e-05,
                4.006370646616669e-05,
                5.8291251591196906e-05,
                0.00013982205541527727,
                6.1441775312976045e-06,
                1.8925150496609267e-05,
                3.5356246488642456e-05,
                1.9947304348595095e-06,
                0.00013982210700345504
            ],
            [
                6.962257079376403e-06,
                4.539788486936701e-05,
                2.902312331081799e-06,
                1.3007123812057577e-05,
                2.2603251062147097e-06,
                5.422220908925639e-06,
                4.222834451292594e-06,
                2.9023119851635836e-06,
                3.7266379512857925e-06,
                1.2098656835076114e-06
            ]
        ]
    },
    {
        "q_id": "8272_mmlu_math",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            12,
            13,
            15,
            16,
            17,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            37,
            38,
            39,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            60,
            61,
            62,
            63,
            64,
            65,
            67,
            69,
            70,
            71,
            72,
            74,
            75,
            76,
            78,
            79,
            80,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            111,
            112,
            113,
            114,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126
        ],
        "rewards": [
            [
                0.9999987901341724,
                0.9999970976883612,
                0.9999952149037956,
                0.999999814460854,
                0.9999967112513267,
                0.9999977396757024,
                0.9999945777817105,
                0.999999266178757,
                0.9999986290431202,
                0.9999986290429567
            ],
            [
                0.9999993524049703,
                0.999999814460876,
                0.9999996940977002,
                0.9999996940978825,
                0.999998932296621,
                0.9999997897565587,
                0.9999996533673788,
                0.9999996072137998,
                0.9999987901341723,
                0.99999844650169
            ],
            [
                1.5534975693488444e-06,
                1.0677028700053041e-06,
                6.475946437722523e-07,
                2.260323758882316e-06,
                3.2887482810801374e-06,
                7.338208930265102e-07,
                9.422443692261927e-07,
                1.7603436328289897e-06,
                4.4508489275145346e-07,
                9.422449308138184e-07
            ],
            [
                0.999983298580152,
                0.999995777167059,
                0.9999921107345964,
                0.999995214905506,
                0.9999945777829696,
                0.9999962733611607,
                0.9999832985781597,
                0.9999984465022455,
                0.999993037742092,
                0.9999930377420916
            ],
            [
                1.4738985482753428e-05,
                3.7266397280485686e-06,
                1.0129993393540266e-05,
                1.2098662604049616e-06,
                3.466327450744504e-07,
                1.067702615468225e-06,
                1.4738978454172926e-05,
                1.370956716529941e-06,
                4.7850950647493785e-06,
                1.0677024881683915e-06
            ],
            [
                3.7266388390502134e-06,
                4.222833443891798e-06,
                3.726640171517464e-06,
                2.1444943256504422e-05,
                4.785095061990212e-06,
                4.006370648569653e-05,
                6.962259568775433e-06,
                1.0129993393319151e-05,
                6.605216803979133e-05,
                5.422220260656402e-06
            ],
            [
                1.012999460150437e-05,
                1.1478773595343877e-05,
                1.8925157259824262e-05,
                2.1444948383466943e-05,
                2.4300243611116483e-05,
                4.5397868553139715e-05,
                1.4738983723664288e-05,
                8.939698434966738e-06,
                1.3007130013288297e-05,
                1.1478770858706246e-05
            ],
            [
                8.93969630333567e-06,
                1.670142582254589e-05,
                2.1444945847446664e-05,
                1.6701429806475863e-05,
                4.785092782936557e-06,
                1.473897845457507e-05,
                1.8925143711847272e-05,
                6.962257907348116e-06,
                1.3007123810638006e-05,
                8.939700564468113e-06
            ],
            [
                0.9999852610197867,
                0.9999930377429216,
                0.9924227604409648,
                0.9999962733620488,
                0.9999938558232023,
                0.9999970976866372,
                0.9999852610185175,
                0.9999810748495053,
                0.999991060306896,
                0.9046505395995927
            ],
            [
                2.2603242977802297e-06,
                7.889266346129453e-06,
                3.2887498493983645e-06,
                3.7266383954560706e-06,
                2.9023133690188264e-06,
                3.2887502414436403e-06,
                3.288749065125496e-06,
                5.043473480730849e-07,
                9.422442568428928e-07,
                4.2228344508893285e-06
            ],
            [
                4.785094494463623e-06,
                5.144221977210733e-05,
                6.962257078249291e-06,
                4.222834451065997e-06,
                1.9947304346535984e-06,
                1.6701415868193372e-05,
                1.8925157259824262e-05,
                2.753570092878799e-05,
                6.144173136556186e-06,
                4.222832940834793e-06
            ],
            [
                1.1478769487840372e-05,
                1.3007128462477575e-05,
                1.473897845240349e-05,
                1.1478773596283455e-05,
                2.9023123309287002e-06,
                3.535624642703312e-05,
                4.222832436272325e-06,
                1.6701421836551084e-05,
                1.147876675466972e-05,
                8.9396941718352e-06
            ],
            [
                9.422447061679302e-07,
                5.422220259709562e-06,
                1.3007126912826352e-05,
                1.6701421841259862e-05,
                6.962254587420098e-06,
                2.902311292920774e-06,
                6.1441753335241615e-06,
                7.88925976359915e-06,
                1.6701425820540864e-05,
                1.8925150491445666e-05
            ],
            [
                0.9999992661786696,
                0.999999168471675,
                0.9999991684722698,
                0.9999989322968755,
                0.9999967112505427,
                0.9999984465015047,
                0.9999995549149481,
                0.9999957771650458,
                0.9999987901337396,
                0.9999986290432834
            ],
            [
                0.9999339478553626,
                0.9999810748474185,
                0.9999869928699859,
                0.9999151889182682,
                0.9999485577986293,
                0.9999938558224687,
                0.9999984465026158,
                0.9999921107402363,
                0.999997097687323,
                0.9999852610145229
            ],
            [
                1.473897845457507e-05,
                2.4300232034838305e-05,
                1.5534975693036317e-06,
                2.4300243618542217e-05,
                1.3007125360146898e-05,
                6.962257079059797e-06,
                1.473897845457507e-05,
                1.3007131561425676e-05,
                1.300713311155064e-05,
                1.3007131561804229e-05
            ],
            [
                6.962253759271479e-06,
                4.2228319341064674e-06,
                1.892515500663531e-05,
                2.9023126769762986e-06,
                4.785094494576774e-06,
                1.8925145979561802e-05,
                1.3709578605542582e-06,
                6.144175333635923e-06,
                2.5612816000145246e-06,
                1.0129990978847043e-05
            ],
            [
                2.561281294644835e-06,
                2.9023116390421582e-06,
                8.93969417150998e-06,
                2.2603248365014775e-06,
                3.2887478886821466e-06,
                5.422218969384951e-06,
                4.222833444283541e-06,
                1.5534984952662413e-06,
                1.7603438427852151e-06,
                5.422218969463855e-06
            ],
            [
                1.994729483608425e-06,
                8.939694169835089e-06,
                1.1478770859917257e-05,
                2.9023133687786197e-06,
                1.0129987355988324e-05,
                1.6701419847381817e-05,
                1.7603434230729168e-06,
                1.1478764017720528e-05,
                1.012999339309804e-05,
                7.889263525534328e-06
            ],
            [
                0.00012339460375757237,
                3.535623805163821e-05,
                3.5356242266024216e-05,
                0.00010889693514699898,
                5.14422258772351e-05,
                8.481107157360807e-05,
                2.4300232029003796e-05,
                7.48462182289749e-05,
                0.00048785717373005564,
                0.00029595702717122996
            ],
            [
                1.5534979395798164e-06,
                1.994729721265813e-06,
                1.0677031243632815e-06,
                1.3709572067356507e-06,
                4.222833947359807e-06,
                1.7603425837062577e-06,
                5.422218322851817e-06,
                9.422444815220956e-07,
                1.5534983100425914e-06,
                1.99472900796355e-06
            ],
            [
                6.962257909121104e-06,
                3.7266410609940346e-06,
                2.4300232040584407e-05,
                NaN,
                1.892514146382353e-05,
                NaN,
                2.144494073054863e-05,
                6.1441775312976045e-06,
                2.430024073333442e-05,
                NaN
            ],
            [
                6.962253758916883e-06,
                1.0129987356541108e-05,
                1.6701429804288556e-05,
                7.889265405677441e-06,
                9.422444815409489e-07,
                4.785093924103951e-06,
                1.6701427812931038e-05,
                1.4738987240475486e-05,
                1.0129992185981682e-05,
                7.889262583231455e-06
            ],
            [
                2.7535700933696396e-05,
                8.93969736929749e-06,
                2.561282210460501e-06,
                2.1444948398445745e-05,
                3.1201922523121745e-05,
                1.7603434230729168e-06,
                2.5612812943280275e-06,
                2.902311638596061e-06,
                0.00012339454386103924,
                2.902311984952413e-06
            ],
            [
                0.9999970976866313,
                0.999997097687669,
                0.999997438716568,
                0.9999962733598274,
                0.9999945777823233,
                0.9999995549147359,
                0.9999898700090223,
                0.9999980052700407,
                0.9999952149066466,
                0.9999984465015047
            ],
            [
                1.8925154986738235e-05,
                6.144174599867732e-06,
                2.1444943284979742e-05,
                8.939699487025595e-06,
                0.0002611902212274027,
                9.610243765756909e-05,
                3.120192617048709e-05,
                5.8291244639350886e-05,
                0.0001088969606556486,
                1.892514371900746e-05
            ],
            [
                0.9999974387168743,
                0.9999974387174848,
                0.9999957771665569,
                0.99999844650169,
                0.9999970976876694,
                0.9999990577555186,
                0.9999992661791945,
                0.9999945777797393,
                0.9999986290432837,
                0.9999967112493692
            ],
            [
                0.9999992661789322,
                0.99999976176309,
                0.9999984465028011,
                0.9999994956524115,
                0.9999997617630332,
                0.9999994956523514,
                0.9999992661788445,
                0.9999997300420937,
                0.9999997300421903,
                0.9999984465022456
            ],
            [
                1.300713156215912e-05,
                6.96225956921868e-06,
                1.6701421842140854e-05,
                1.1478768122695653e-05,
                1.4738988994015443e-05,
                1.4738978452886064e-05,
                1.147877086073156e-05,
                3.1201922520397544e-05,
                1.3007131563815288e-05,
                1.892514597632595e-05
            ],
            [
                0.9999952149060818,
                0.9999930377437727,
                0.9999910603007779,
                0.9999910603039678,
                0.9933071491221513,
                0.9999921107402454,
                0.962673116404036,
                0.9999910603037682,
                0.9999938558224962,
                0.9999910603068932
            ],
            [
                0.9999832985741829,
                0.9999994284994849,
                0.9999996072139402,
                0.9999998144608538,
                0.999999266178932,
                0.9999996940978825,
                0.9999997300422225,
                0.9999991684717742,
                0.999998005270041,
                0.9999982396574164
            ],
            [
                2.9023109466489728e-06,
                3.288749455965269e-06,
                3.7266388388875246e-06,
                2.5612815996930587e-06,
                1.4738987235622935e-05,
                3.288748672168078e-06,
                3.1201907628667734e-05,
                6.962259567914269e-06,
                4.0063701688351906e-05,
                3.7266410594993323e-06
            ],
            [
                0.9999997617631752,
                0.9999994956527722,
                0.9999994284994167,
                0.9999996533673375,
                0.9999997617630616,
                0.9999998362623528,
                0.9999997300422225,
                0.9999997617630333,
                0.9999997300421581,
                0.9999999006880668
            ],
            [
                0.9999994284996212,
                0.9999999123575046,
                0.999999922655787,
                0.9999986290432835,
                0.9999995549150011,
                0.9999996533675028,
                0.9999994284997574,
                0.9999999123575568,
                0.9999967112505429,
                0.9999984465028011
            ],
            [
                8.93969310662177e-06,
                2.9023109471689794e-06,
                1.6701423828576233e-05,
                0.0001233945893961187,
                1.4738983723235332e-05,
                2.144495862623957e-05,
                7.484620041444411e-05,
                3.535626334156318e-05,
                8.481106135683544e-05,
                3.5356254914330094e-05
            ],
            [
                2.753568124769226e-05,
                2.2603242978007868e-06,
                4.785093923982095e-06,
                8.939698435226916e-06,
                3.28874867308036e-06,
                4.222833444106873e-06,
                1.1478772229300848e-05,
                1.3007125359792008e-05,
                1.0129988564099116e-05,
                4.5397857772875786e-05
            ],
            [
                0.9999987901341724,
                0.9999974387168736,
                0.9999952149049366,
                0.9999962733598275,
                0.9999869928684385,
                0.9999785550464909,
                0.9999957771650472,
                0.99997569975639,
                0.9999980052700408,
                0.9999898700126487
            ],
            [
                0.9999989322973847,
                0.9999986290424667,
                0.9999980052698031,
                0.9999967112493814,
                0.9999980052708755,
                0.9999970976887069,
                0.9999982396574163,
                0.9999977396762422,
                0.9999982396569966,
                0.9999832985731327
            ],
            [
                0.9999970976869771,
                0.9999977396751635,
                0.9999982396569966,
                0.9999987901341724,
                0.9999982396572066,
                0.9999930377437514,
                0.999997438718095,
                0.9999984465020604,
                0.9999991684719723,
                0.999993855822469
            ],
            [
                0.9999952149072169,
                0.9999967112509347,
                0.9999987901344607,
                0.9999991684715759,
                0.999999789756684,
                0.9999980052709919,
                0.9999994284993486,
                0.9999994956524114,
                0.9999991684719726,
                0.999996711252111
            ],
            [
                6.9622587372828785e-06,
                1.300713156215912e-05,
                8.315283250150648e-07,
                1.4738985482351282e-05,
                2.4300246488324276e-05,
                4.2228319341064674e-06,
                8.93969630362837e-06,
                5.4222170304318e-06,
                1.1478770859917257e-05,
                1.670141586949968e-05
            ],
            [
                0.9999992661787571,
                0.9999910603068949,
                0.9999970976883614,
                0.9999977396746245,
                0.999998239656577,
                0.9999980052700408,
                0.9999974387168735,
                0.9999982396561572,
                0.9999970976880149,
                0.9999957771645424
            ],
            [
                1.1478773598099973e-05,
                1.6701421842961097e-05,
                1.14787681240737e-05,
                1.300712846115264e-05,
                5.422218323231539e-06,
                4.2228344508893285e-06,
                6.962257909121104e-06,
                6.9622579092224155e-06,
                5.422218969128516e-06,
                2.561281904923017e-06
            ],
            [
                0.9999989322971299,
                0.999998790134028,
                0.9999993524053563,
                0.9999962733607162,
                0.999999266178757,
                0.999995214903224,
                0.9999989322967482,
                0.9999974387184,
                0.9999990577551815,
                0.9999982396565769
            ],
            [
                0.9999974387165684,
                0.9999993524050474,
                0.9999945777797379,
                0.999998790134605,
                0.999993855827596,
                0.9999952149060761,
                0.9999952149055075,
                0.9999990577555185,
                0.9999962733620491,
                0.9999980052695654
            ],
            [
                0.9999945777810302,
                0.9999990577555185,
                0.999998790134028,
                0.9999982396563669,
                0.9999982396572065,
                0.9999986290431201,
                0.9999982396567867,
                0.999997097687669,
                0.9999251537728645,
                0.9999995549147889
            ],
            [
                0.9999997300422226,
                0.9999998555019618,
                0.9999997897565588,
                0.9999998362622747,
                0.9999998144609644,
                0.9999998144609645,
                0.9999997300420939,
                0.9999997300423191,
                0.9999996533672549,
                0.9999998555019963
            ],
            [
                0.999996711251719,
                0.9999898700102293,
                0.9999921107364749,
                0.9999724643089233,
                0.9999785550439309,
                0.9999724643187743,
                0.999985261023302,
                0.9999687980812002,
                0.9999952149055056,
                0.9999970976887069
            ],
            [
                0.9999987901347491,
                0.999998005270041,
                0.9859363714587801,
                0.999998629042303,
                0.9999987901343168,
                0.7310585844894971,
                0.9999938558261328,
                0.9999989322971302,
                0.999999266179107,
                0.9999967112517191
            ],
            [
                0.9999962733589393,
                0.9999977396757022,
                0.9999995549151072,
                0.9999998724809267,
                0.9999996533674615,
                0.9999986290424664,
                0.9999967112497585,
                0.999999554914895,
                0.9999984465015047,
                0.9999992661791944
            ],
            [
                0.9999980052693276,
                0.9999996940978461,
                0.9999957771680659,
                0.9999980052695652,
                0.9999967112521113,
                0.9999991684716749,
                0.9999977396748944,
                0.9999885212359799,
                0.9999999006880668,
                0.9999997300421903
            ],
            [
                0.9999993524049703,
                0.9999992661791945,
                0.9999989322967482,
                0.9999994284997574,
                0.9999998555019963,
                0.9999995549147889,
                0.9999993524054335,
                0.9999994284995531,
                0.9999974387171789,
                0.9999996533672135
            ],
            [
                1.6701423825538316e-05,
                2.2603242977555607e-06,
                1.5534984952111384e-06,
                3.2887482809455384e-06,
                1.0129993394129904e-05,
                5.422218968931258e-06,
                8.93969417199781e-06,
                1.9947294833780224e-06,
                1.9947290079889487e-06,
                1.147876949310201e-05
            ],
            [
                0.9999986290426298,
                0.9999992661791944,
                0.9999984465015047,
                0.999999266179107,
                0.9999930377445828,
                0.9999962733616046,
                0.999998790134605,
                0.9999987901341724,
                0.9999990577556308,
                0.9999990577556308
            ],
            [
                1.3007126906982452e-05,
                6.9622562492265485e-06,
                1.3007128457485415e-05,
                8.93969417199781e-06,
                2.144494585583323e-05,
                3.288750241374845e-06,
                7.889262584350785e-06,
                2.5612825157464395e-06,
                2.144494840531103e-05,
                7.889263525405172e-06
            ],
            [
                0.9999687980886489,
                0.9999952149072167,
                0.99998107485853,
                0.999997097689053,
                0.9999885212359807,
                0.99994855779862,
                0.9999832985721847,
                0.999978555054146,
                0.9999646437535068,
                0.9999869928715369
            ],
            [
                1.1478768124992398e-05,
                2.2603242978377903e-06,
                1.5534971989809095e-06,
                1.4738978454172926e-05,
                2.260324567177841e-06,
                2.9023126768680736e-06,
                1.994729245822257e-06,
                2.144494073483943e-05,
                1.9947299589105305e-06,
                2.260324567302214e-06
            ],
            [
                0.999954602136796,
                0.9998415638025179,
                0.9999485577618425,
                0.9999810748585323,
                0.9999885212264035,
                0.9992903294629039,
                0.9999832985741748,
                0.9999485577863896,
                0.9997694933405168,
                0.9999756997563835
            ],
            [
                1.1478769491306371e-05,
                6.9622537584863015e-06,
                1.4738985481520185e-05,
                1.0129988563546333e-05,
                5.144220747202866e-05,
                9.610241492126045e-05,
                4.006370650260296e-05,
                1.6701419842521146e-05,
                2.144495607789177e-05,
                1.1478769489343698e-05
            ],
            [
                0.00010889690897128673,
                7.484625391903742e-05,
                1.892515725920463e-05,
                1.3007125361448172e-05,
                0.00020342702134009156,
                7.48462093285157e-05,
                0.0001398220570143111,
                9.61024147499638e-05,
                0.00023050671441413696,
                3.120190020204515e-05
            ],
            [
                1.3709575336405514e-06,
                1.9947294833018263e-06,
                1.994729721436347e-06,
                9.422450431260706e-07,
                1.209865539274514e-06,
                1.5534981248133121e-06,
                5.715005832572414e-07,
                5.715007195275709e-07,
                4.450849458179853e-07,
                5.043473480678099e-07
            ],
            [
                2.260324297702111e-06,
                1.8925152747938785e-05,
                7.889262584350785e-06,
                2.260324567087388e-06,
                1.8925157257345735e-05,
                1.892515274614874e-05,
                4.222834450950777e-06,
                3.726638839395927e-06,
                2.56128221024619e-06,
                1.0129989767032304e-05
            ],
            [
                1.4738978451920916e-05,
                6.605217613436184e-05,
                4.006370640437078e-05,
                8.939694169330997e-06,
                4.785093353352668e-06,
                8.93969630333567e-06,
                1.0129992185060374e-05,
                5.1442232038504445e-05,
                3.120191507481552e-05,
                1.0129992184802409e-05
            ],
            [
                1.0677024881683915e-06,
                2.902313022984344e-06,
                3.2887498492936755e-06,
                4.7850933534310035e-06,
                1.3709576971160984e-06,
                4.785095064819011e-06,
                2.260324028372372e-06,
                2.902313368963394e-06,
                4.785096205882502e-06,
                4.7850933535006355e-06
            ],
            [
                0.9999989322975118,
                0.999998239656367,
                0.9999998724809419,
                0.9999996940977001,
                0.9999996940976636,
                0.9999996533672135,
                0.9999999123574732,
                0.9999980052700408,
                0.9999991684715759,
                0.9999998144609202
            ],
            [
                4.539789023423405e-05,
                7.889263524788109e-06,
                4.539786861523573e-05,
                6.605217614925922e-05,
                3.120191509172827e-05,
                1.300713466281145e-05,
                4.785096775842062e-06,
                3.535626333809042e-05,
                6.962257909412379e-06,
                3.2887490652451393e-06
            ],
            [
                0.9999989322968754,
                0.9999974387171787,
                0.9999952149043647,
                0.9820137905971974,
                0.9999992661790195,
                0.9999957771660523,
                0.9999989322967482,
                0.9999977396759716,
                0.9999989322968754,
                0.9999998144608981
            ],
            [
                0.9999945777816768,
                0.9999982396565769,
                0.9999987901344607,
                0.9999957771650453,
                0.9999974387180947,
                0.8519528000888386,
                0.9999957771655499,
                0.9999724643023589,
                0.9999952149049355,
                0.9999989322967483
            ],
            [
                2.56128159999123e-06,
                2.260323489435463e-06,
                1.5534977545603963e-06,
                2.9023112931688987e-06,
                1.3709578605118645e-06,
                6.962259568509485e-06,
                3.288749849368453e-06,
                2.902311984873224e-06,
                1.994729721436347e-06,
                1.9947297214544894e-06
            ],
            [
                1.6701415868193372e-05,
                1.1478764009640154e-05,
                6.962259568648793e-06,
                7.889264463216492e-06,
                8.939693106329072e-06,
                1.6701419851270353e-05,
                1.892514146086307e-05,
                3.120190391558324e-05,
                5.8291293278964903e-05,
                2.4300234933172706e-05
            ],
            [
                0.9999938558275967,
                0.99998852123051,
                0.9999785550413688,
                0.9999930377404321,
                0.999993855827596,
                0.9999910603015666,
                0.9999910603068946,
                0.9999417087275647,
                0.9999339478239727,
                0.9999832985761714
            ],
            [
                0.9999995549147889,
                0.9999995549148419,
                0.9999996940978461,
                0.9999996940977002,
                0.9999996072137061,
                0.9999998724809571,
                0.9999997617631468,
                0.99999976176309,
                0.9999998555019963,
                0.999999789756684
            ],
            [
                1.3007123809644304e-05,
                9.422448184424489e-07,
                5.71500378868701e-07,
                6.962255419279419e-06,
                7.338212429240558e-07,
                1.5534973839896667e-06,
                1.012999339309804e-05,
                5.422218968595919e-06,
                1.1478766756214804e-05,
                3.288750632678377e-06
            ],
            [
                1.3709578605455302e-06,
                4.222834451215781e-06,
                8.93969630226244e-06,
                1.0129993394811673e-05,
                1.670141587068447e-05,
                6.962257078819179e-06,
                3.2887482811220126e-06,
                6.144173869312763e-06,
                2.9023116389761676e-06,
                2.5612825159421147e-06
            ],
            [
                9.422444815563743e-07,
                1.4738980212644815e-05,
                7.33821067986608e-07,
                8.939698434966738e-06,
                5.829125853074485e-05,
                6.9622545892184106e-06,
                2.902312330965655e-06,
                1.209865394997419e-06,
                1.473898021366358e-05,
                1.5534975693347152e-06
            ],
            [
                0.9959298621425345,
                0.99999709768767,
                0.9999957771655489,
                0.9999993524053589,
                0.9999962733589403,
                0.9999646437408712,
                0.9999938558232012,
                0.9999995549148422,
                0.9999980052707541,
                0.9999984465020636
            ],
            [
                0.9999982396563671,
                0.9999921107374159,
                0.999993855823202,
                0.9999952149072174,
                0.9999852610215454,
                0.9999921107345944,
                0.999993855822469,
                0.9999962733598281,
                0.9999952149032242,
                0.9999952149032243
            ],
            [
                4.539787403691212e-05,
                2.753570094040789e-05,
                4.0063692167994334e-05,
                5.8291251569143705e-05,
                7.889265406294507e-06,
                7.889263524257144e-06,
                2.144495096387783e-05,
                1.4738988998787566e-05,
                7.88926164421493e-06,
                3.120192623836512e-05
            ],
            [
                6.144173136556186e-06,
                1.209866116149238e-06,
                7.889260701697028e-06,
                7.889261644982674e-06,
                5.04347348020793e-07,
                1.553497754476329e-06,
                1.9947297213746646e-06,
                1.7603436328289897e-06,
                1.7603438428460541e-06,
                1.0677028699955933e-06
            ],
            [
                0.9999984465020603,
                0.999998790134605,
                0.9999977396751634,
                0.9999987901344607,
                0.9999987901337396,
                0.9999986290429568,
                0.9999977396759719,
                0.9999991684721706,
                0.9999989322972572,
                0.999997097686631
            ],
            [
                0.9999996940977002,
                0.9999991684721706,
                0.9999994284997574,
                0.999999554914895,
                0.9999996940978095,
                0.9999996940978825,
                0.9999997617631753,
                0.9999996072139402,
                0.9999995549147889,
                0.9999994284994167
            ],
            [
                0.9324533144915912,
                0.9999952149066468,
                0.9999852610127615,
                0.9840936108539737,
                0.999998446502431,
                0.9999957771675654,
                0.8670357494949105,
                0.9999967112505541,
                0.9959298631448454,
                0.9999984465018755
            ],
            [
                0.9999952149049351,
                0.9999599363104992,
                0.9999967112497968,
                0.9999910603005002,
                0.9999957771675627,
                0.9999957771645426,
                0.9999885212318793,
                0.9999910603047628,
                0.9999982396561572,
                0.9999980052695656
            ],
            [
                2.2603242977802297e-06,
                3.288748280520804e-06,
                1.5534983099027147e-06,
                1.994729959160889e-06,
                4.222834953804408e-06,
                1.5534981248528732e-06,
                1.5534973835460175e-06,
                2.9023116385379885e-06,
                1.067702742683591e-06,
                4.7850956351657615e-06
            ],
            [
                0.9999852610197931,
                0.9999546021259903,
                0.99998329857418,
                0.9999869928653375,
                0.9999485577618699,
                0.9998766054695488,
                0.9999910602994342,
                0.999981074844995,
                0.9999970976880155,
                0.9999687980849222
            ],
            [
                1.8925150490826034e-05,
                4.7850944943330625e-06,
                5.422220908703723e-06,
                2.9023116388547446e-06,
                1.7603438426203097e-06,
                2.9023116383479355e-06,
                1.3007125356952865e-05,
                1.1478765386330758e-05,
                1.3007134661628471e-05,
                2.753569437266178e-05
            ],
            [
                3.5356267541418054e-05,
                1.3007134661628471e-05,
                6.1441753337365085e-06,
                4.785093923420688e-06,
                7.889259763728304e-06,
                5.1442213603354026e-05,
                5.422218322940583e-06,
                3.120191877609648e-05,
                5.829128612863501e-05,
                4.7850967749455485e-06
            ],
            [
                0.9999992661792819,
                0.9999990577554062,
                0.9999989322970027,
                0.9999980052709919,
                0.9999980052707542,
                0.9999938558224699,
                0.9999984465018752,
                0.9999989322971301,
                0.9999832985821441,
                0.9999852610197926
            ],
            [
                0.9999967112505427,
                0.9999996072138934,
                0.9999989322966208,
                0.9999984465018751,
                0.9999986290421394,
                0.9999989322972572,
                0.9999994956527721,
                0.9999987901337396,
                0.9999989322971299,
                0.9999990577552937
            ],
            [
                2.430023783309869e-05,
                3.5356250699942575e-05,
                2.7535700934898458e-05,
                1.4738981963771067e-05,
                4.539787401825028e-05,
                8.48110715112881e-05,
                2.430024362791279e-05,
                8.9397005654763e-06,
                3.2887498491620677e-06,
                7.484620030608123e-05
            ],
            [
                0.9999967112497592,
                0.9999995549150011,
                0.9999998724809267,
                0.9999997300422225,
                0.9999987901344608,
                0.9999982396565773,
                0.9999992661792819,
                0.9999994956525919,
                0.9999995549149481,
                0.999999730042126
            ],
            [
                0.9999984465018751,
                0.9999984465022455,
                0.9999987901340283,
                0.9999967112521253,
                0.9999957771680663,
                0.9999974387171788,
                0.9940889321561818,
                0.9999938558276111,
                0.9999962733620532,
                0.9999980052702855
            ],
            [
                0.00020342699731660927,
                2.4300249416363357e-05,
                0.00017952792201460878,
                0.00026119030761264354,
                1.8925154986738235e-05,
                1.1478769489343698e-05,
                5.829126546520442e-05,
                0.9669140244715406,
                0.00023050663126645703,
                3.535625067383256e-05
            ],
            [
                0.9999982396572065,
                0.9999957771675625,
                0.9999921107383568,
                0.9999945777810304,
                0.9999930377429218,
                0.9999987901343166,
                0.9999980052705217,
                0.9999898700126446,
                0.999998239656367,
                0.9999930377409897
            ],
            [
                5.422220908703723e-06,
                3.7266388391247794e-06,
                1.300712846115264e-05,
                1.3007131562845248e-05,
                1.994730434816876e-06,
                2.1444948408977715e-05,
                1.3007134665413997e-05,
                1.0129987353832463e-05,
                1.1478768124992398e-05,
                1.3007131562514014e-05
            ],
            [
                6.144176798590883e-06,
                8.93969417167259e-06,
                3.28874906467085e-06,
                1.4738985482753428e-05,
                1.6701425822059825e-05,
                1.0129995808639442e-05,
                9.422449308241022e-07,
                1.473897845457507e-05,
                1.4738985480179701e-05,
                8.939699500164542e-06
            ],
            [
                0.9999599363031778,
                6.144177530425867e-06,
                2.561282515820982e-06,
                1.89251482372248e-05,
                2.5612831265630198e-06,
                1.3709576970824327e-06,
                1.3007130012010681e-05,
                2.5612834317908303e-06,
                6.144176799099397e-06,
                1.1478773597870298e-05
            ],
            [
                0.9999724643089275,
                0.9999945777823236,
                0.9999930377404334,
                0.9999930377429208,
                0.9999869928699895,
                0.9999987901337397,
                0.9999910603036983,
                0.9999910603004997,
                0.9999962733589395,
                0.9999921107402366
            ],
            [
                1.2098658275740208e-06,
                8.93969630333567e-06,
                1.760344052650207e-06,
                2.144494585197151e-05,
                1.9947292457750883e-06,
                1.1478768123280277e-05,
                2.2603242976404388e-06,
                1.6701421842140854e-05,
                5.422218323231539e-06,
                6.144173136729416e-06
            ],
            [
                0.9999993524051246,
                0.999999266179107,
                0.9999998874648379,
                0.9999994284996893,
                0.9999995549148419,
                0.9999994284996893,
                0.9999986290424664,
                0.9999962733617408,
                0.9999996533672963,
                0.9999996072136593
            ],
            [
                5.42221961567159e-06,
                1.3007123808910861e-05,
                4.785096775842062e-06,
                3.726639727526609e-06,
                1.370957860466977e-06,
                7.889265405849647e-06,
                1.0129990976156825e-05,
                1.2098658275938276e-06,
                9.422443691233569e-07,
                3.7266401719174067e-06
            ],
            [
                2.7535697660090726e-05,
                1.147876675686207e-05,
                3.726640172503764e-06,
                2.4300234937239182e-05,
                3.120191880504111e-05,
                1.670141587031992e-05,
                1.3007126911974612e-05,
                2.561283431888668e-06,
                2.1444950966608343e-05,
                6.144176798590883e-06
            ],
            [
                0.9999996072136125,
                0.9999977396759726,
                0.9999982396565774,
                0.9999995549147359,
                0.9999994284996893,
                0.9999995549148419,
                0.9999898700041944,
                0.9999997617630048,
                0.999999352405279,
                0.9999996940977002
            ],
            [
                2.260323758806253e-06,
                9.422450429675318e-07,
                3.2887506329595395e-06,
                3.2887498489407274e-06,
                5.144220132947586e-05,
                5.422220261849814e-06,
                8.939694168810643e-06,
                5.4222215532202016e-06,
                1.3007123808153756e-05,
                1.553497568892479e-06
            ],
            [
                0.9999852610127615,
                0.9999974387180953,
                0.9999952149043647,
                0.999995777165046,
                0.9999724643195701,
                0.9999930377437518,
                0.9999967112517198,
                0.9999970976890686,
                0.9999962733602804,
                0.9999921107345985
            ],
            [
                1.1478769489009626e-05,
                8.939695237504067e-06,
                1.012998977108606e-05,
                8.939700553134145e-06,
                8.939695237341456e-06,
                1.4738981968060613e-05,
                5.1442201250130194e-05,
                1.3007133110320344e-05,
                6.962253756004122e-06,
                5.422220262037209e-06
            ],
            [
                3.2887490652810324e-06,
                3.726639728262097e-06,
                3.2887494570719725e-06,
                7.88925976283858e-06,
                5.422217030032353e-06,
                6.1441760654483806e-06,
                3.2887486729876365e-06,
                6.1441775309064404e-06,
                1.9947290080125335e-06,
                1.473898021366358e-05
            ],
            [
                1.7603425836678333e-06,
                1.553497569203316e-06,
                4.785092782936557e-06,
                2.9023119845723063e-06,
                4.785094493932679e-06,
                1.670141786036971e-05,
                3.726638839395927e-06,
                1.994729245842213e-06,
                1.9947301970287804e-06,
                6.962259568509485e-06
            ],
            [
                3.5356246475137275e-05,
                7.889265405677441e-06,
                2.7535700932494338e-05,
                1.892515499637696e-05,
                3.726637950851956e-06,
                8.9397005654763e-06,
                1.8925155005051806e-05,
                5.144220134032976e-05,
                4.2228334433617906e-06,
                1.0129992186387057e-05
            ],
            [
                4.785095064601411e-06,
                3.28875024125221e-06,
                2.9023116388072315e-06,
                2.753568780461672e-05,
                4.222833947029514e-06,
                1.4738976699749503e-05,
                2.9023126767360923e-06,
                8.93969523678858e-06,
                6.144172403335888e-06,
                4.7850933535006355e-06
            ]
        ]
    },
    {
        "q_id": "8853_mmlu_math",
        "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": [
            [
                0.999999789756684,
                0.9999999123574941,
                0.9999998362622747,
                0.9999996072138465,
                0.9999996940978095,
                0.9999996533674615,
                0.9999999317439954,
                0.9999996072138934,
                0.9999999397642725,
                0.9999998555020307
            ],
            [
                0.9999998362622357,
                0.9999997300421903,
                0.9999998874647709,
                0.9999994956524716,
                0.9999997897567091,
                0.9999996072137529,
                0.9999997897566089,
                0.9999998874647574,
                0.9999996940977366,
                0.999999730042126
            ],
            [
                3.2887498494551953e-06,
                8.939695237813028e-06,
                4.222833947728508e-06,
                1.670142980687079e-05,
                2.260324028331257e-06,
                1.3709572068179446e-06,
                1.300712846361323e-05,
                7.3382080556433e-07,
                3.2887490653109436e-06,
                6.475945666009864e-07
            ],
            [
                0.9999997897567091,
                0.9999997300421583,
                0.9999998362622552,
                0.9999997300420939,
                0.9999996072136592,
                0.9999997897567091,
                0.9999997300422869,
                0.9999999226557684,
                0.9999998874648781,
                0.9999993524049703
            ],
            [
                0.9999996533674202,
                0.9999994284996893,
                0.9999997617631469,
                0.999999554914842,
                0.9999994284996211,
                0.9999997617630616,
                0.9999997617631752,
                0.9999994956524114,
                0.9999995549148419,
                0.9999992661786696
            ],
            [
                0.9999998144608097,
                0.9999998362623138,
                0.9999999006880312,
                0.999999789756684,
                0.9999998362622357,
                0.999999855502048,
                0.999999266178932,
                0.9999997617631183,
                0.9999998555019962,
                0.9999999123575255
            ],
            [
                0.999999887464744,
                0.9999994956524114,
                0.9999992661791945,
                0.9999996533674614,
                0.9999998724809116,
                0.9999998144609645,
                0.9999998362623137,
                0.9999996533672549,
                0.999999694097846,
                0.99999976176309
            ],
            [
                6.962257909501028e-06,
                8.481101096529726e-05,
                3.535625492217596e-05,
                1.300713001414004e-05,
                4.0063687394553603e-05,
                1.300712536203966e-05,
                1.3007123810306773e-05,
                6.962257079275089e-06,
                3.1201903922734266e-05,
                1.0129994602057158e-05
            ],
            [
                0.9999998362623332,
                0.9999998362623332,
                0.9999997300422547,
                0.9999995549148419,
                0.999999953088334,
                0.9999995549151073,
                0.9999998555020307,
                0.9999999123574628,
                0.999999855502048,
                0.9999997300423191
            ],
            [
                0.9999994284997573,
                0.9999996533673375,
                0.9999996940977002,
                0.9999995549150542,
                0.9999995549151073,
                0.9999998724809267,
                0.9999998874648647,
                0.99999976176309,
                0.9999996072138465,
                0.9999998362622552
            ],
            [
                0.999999653367379,
                0.9999992661791945,
                0.9999996940976638,
                0.9999996940977366,
                0.9999997897566589,
                0.9999995549149481,
                0.9999996940976272,
                0.9999997617631468,
                0.9999998144608981,
                0.9999996533674202
            ],
            [
                0.9999996072138465,
                0.999999814460854,
                0.9999996940977002,
                0.9999994284992804,
                0.9999997300422869,
                0.9999997617629764,
                0.9999997300420939,
                0.9999996940978461,
                0.9999997897565587,
                0.9999997897566089
            ],
            [
                0.9999998362623137,
                0.9999998874649318,
                0.9999999317439221,
                0.9999999317439464,
                0.9999998724810026,
                0.9999999006879721,
                0.999999814460876,
                0.9999998724809419,
                0.9999998874647709,
                0.9999998362623528
            ],
            [
                0.9999989322968755,
                0.9999987901343166,
                0.9999986290421394,
                0.9999987901343165,
                0.9999970976866309,
                0.9999982396561572,
                0.9999980052705164,
                0.9999977396754328,
                0.9999997300421581,
                0.9999957771645424
            ],
            [
                0.9999998144609202,
                0.9999996072139402,
                0.9999997617630899,
                0.999999554914895,
                0.9999998724809723,
                0.9999998724809875,
                0.9999996940977366,
                0.999999789756634,
                0.9999997897565587,
                0.9999997617630616
            ],
            [
                2.56128282131428e-06,
                8.939695237959376e-06,
                6.9622579092224155e-06,
                4.785096205717126e-06,
                6.144173869072478e-06,
                1.0129987355988324e-05,
                2.2603242978007868e-06,
                3.726638395527247e-06,
                6.144175334094145e-06,
                1.994730434847717e-06
            ],
            [
                0.9999998724809116,
                0.9999994956524715,
                0.9999998874648782,
                0.9999998555019618,
                0.9999998362623137,
                0.999999789756684,
                0.9999998362623528,
                0.9999997300421581,
                0.9999998144608317,
                0.9999998874648917
            ],
            [
                1.3709576970949014e-06,
                1.3709568799823232e-06,
                7.88926258532661e-06,
                9.422448185264317e-07,
                1.994730434816876e-06,
                1.9947299592570416e-06,
                4.2228349546493465e-06,
                6.962256248871951e-06,
                1.370957370236096e-06,
                2.9023126769762986e-06
            ],
            [
                4.785093353100252e-06,
                1.3709576971061233e-06,
                2.561282210701601e-06,
                1.7603427936079236e-06,
                1.0677024881887838e-06,
                1.2098662604049616e-06,
                6.962254589617333e-06,
                2.260324028404236e-06,
                3.726638395415398e-06,
                2.561282515988704e-06
            ],
            [
                0.9999995549151073,
                0.9999996940977002,
                0.9999998724809267,
                0.9999996533672962,
                0.9999999123575881,
                0.9999998724809116,
                0.999999730042126,
                0.9999996940978825,
                0.9999998362623138,
                0.9999998555019963
            ],
            [
                0.9999999226557131,
                0.9999999006880785,
                0.9999998555019791,
                0.9999999226557776,
                0.9999999123575672,
                0.9999998362622552,
                0.9999998874648917,
                0.9999999123574732,
                0.9999996072137529,
                0.9999998362623528
            ],
            [
                0.9999994284997574,
                0.9999997300420939,
                0.9999992661792819,
                0.9999993524050474,
                0.9999992661790196,
                0.9999997300421903,
                0.9999996072136125,
                0.9999992661792819,
                0.9999997617631469,
                0.999999168471675
            ],
            [
                0.9999990577549568,
                0.9999998724809723,
                0.9999999317439058,
                0.9999994956524716,
                0.9999993524052019,
                0.9999998874648917,
                0.9999997897566089,
                0.9999998724809419,
                0.9999990577550691,
                0.9999997897565838
            ],
            [
                0.9999997897567341,
                0.9999997300422547,
                0.999999814460854,
                0.999999789756634,
                0.9999998362623332,
                0.9999984465020604,
                0.9999999317439221,
                0.9999990577552939,
                0.9999989322966208,
                0.9999999317439464
            ],
            [
                0.9999938558224699,
                0.9999984465024307,
                0.9999952149066464,
                0.9999930377445821,
                0.9999982396574163,
                0.9999885212359814,
                0.9999984465020603,
                0.9999957771680662,
                0.9999962733620493,
                0.9999984465024306
            ],
            [
                0.9999982396561572,
                0.999998932296621,
                0.999998446502801,
                0.9999994284996211,
                0.9999987901344607,
                0.9999990577554062,
                0.9999989322968755,
                0.9999945777797387,
                0.999999168471675,
                0.9999977396746245
            ],
            [
                0.9999998144608098,
                0.9999994956527721,
                0.9999996940977731,
                0.999999694097773,
                0.9999997897565838,
                0.9999997617630332,
                0.9999992661786696,
                0.9999992661790196,
                0.9999997300421581,
                0.999999554914895
            ],
            [
                0.9999990577549568,
                0.9999986290427931,
                0.9999997300421903,
                0.9999997300421581,
                0.9999989322972573,
                0.9999995549149481,
                0.9999987901338839,
                0.9999997617630616,
                0.9999996533672136,
                0.9999994956525918
            ],
            [
                0.9999996533672963,
                0.9999998874647842,
                0.9999998362622942,
                0.9999998362623723,
                0.9999997300421903,
                0.9999999123575672,
                0.9999998362622746,
                0.9999998144609423,
                0.9999998144609202,
                0.9999998555019274
            ],
            [
                0.9999997300422547,
                0.9999997617630048,
                0.9999998362623137,
                0.9999998144608097,
                0.9999998362622357,
                0.9999997617630332,
                0.9999999123575881,
                0.9999998144608983,
                0.9999997300421903,
                0.9999998362623723
            ],
            [
                0.9999998555020135,
                0.999999554914895,
                0.9999998362622943,
                0.9999998144609424,
                0.9999998555020306,
                0.9999997897565838,
                0.999999789756634,
                0.9999999006880668,
                0.9999997897567091,
                0.9999997300422869
            ],
            [
                0.9999999006880785,
                0.9999998144609645,
                0.9999998555019618,
                0.9999997617630616,
                0.9999999006880312,
                0.9999996533675028,
                0.9999998724809723,
                0.9999998874647976,
                0.9999997617630332,
                0.9999996072137061
            ],
            [
                1.3007130013856124e-05,
                1.0129988563730593e-05,
                8.939693105272102e-06,
                5.422218969532895e-06,
                6.9622562489985925e-06,
                1.3007131564383116e-05,
                3.7266397282926013e-06,
                4.2228324375512536e-06,
                6.144175333635923e-06,
                6.9622537593854575e-06
            ],
            [
                0.9999996940977002,
                0.9999998362622942,
                0.9999998874648112,
                0.9999998362622747,
                0.9999998724809875,
                0.9999999317439953,
                0.9999998724809723,
                0.9999996072139402,
                0.9999998555020135,
                0.9999999226557592
            ],
            [
                0.9999998144608981,
                0.9999998874649051,
                0.9999997617630049,
                0.999999352405279,
                0.9999998362622552,
                0.9999998362623137,
                0.9999992661790195,
                0.99999976176309,
                0.9999994956523514,
                0.9999998555019446
            ],
            [
                0.9999996072138934,
                0.9999999530883172,
                0.9999999226557869,
                0.9999997300421903,
                0.9999998724808964,
                0.9999996940978095,
                0.9999986290432835,
                0.9999998874648514,
                0.9999995549150011,
                0.9999999006879721
            ],
            [
                0.9999998874649184,
                0.9999996940978095,
                0.9999997617630333,
                0.9999997300422547,
                0.9999996072137529,
                0.9999996072139402,
                0.9999997617630049,
                0.999999428499553,
                0.9999996072136125,
                0.9999998144608317
            ],
            [
                1.0677031245953668e-06,
                3.2887498493325602e-06,
                2.9023133690425823e-06,
                6.144176798590883e-06,
                2.2603251061458426e-06,
                3.2887478891487563e-06,
                2.260323489490968e-06,
                4.22283294098842e-06,
                1.7603438428564603e-06,
                6.1441746017453204e-06
            ],
            [
                0.9999997897565587,
                0.9999998362622552,
                0.9999998724809723,
                0.9999997617631468,
                0.9999996072138934,
                0.999999789756634,
                0.9999996533672549,
                0.9999998724809116,
                0.999999814460854,
                0.9999996940978095
            ],
            [
                0.9999998144608981,
                0.9999994284996893,
                0.9999994284996211,
                0.9999997617631183,
                0.9999998144609644,
                0.9999994284997574,
                0.9999990577557432,
                0.9999996940978095,
                0.9999997300420937,
                0.9999992661789321
            ],
            [
                0.9998766054105537,
                0.9975273773923757,
                0.9996200154744144,
                4.222831934052698e-06,
                7.889261644760245e-06,
                1.8925148231579266e-05,
                0.9947798743765671,
                3.535625062547117e-05,
                3.5356254914330094e-05,
                0.9982992775630675
            ],
            [
                0.99999893229713,
                0.999999814460876,
                0.9999997617629764,
                0.9999996940977366,
                0.9999990577556308,
                0.9999996533674615,
                0.9999993524050474,
                0.9999993524053563,
                0.9999989322973846,
                0.9999989322975119
            ],
            [
                0.9999997897566589,
                0.9999997897567342,
                0.999999855502048,
                0.9999997897566089,
                0.9999998874648379,
                0.9999997617630616,
                0.9999999317439464,
                0.9999999006880194,
                0.9999994956525317,
                0.9999999123574836
            ],
            [
                0.9999994956527722,
                0.999999352404893,
                0.9999986290429567,
                0.9999996072137529,
                0.999999694097846,
                0.999999855502048,
                0.9999994284996893,
                0.9999996072139402,
                0.9999994956524716,
                0.9999990577551815
            ],
            [
                0.9999997897567341,
                0.999999789756684,
                0.999999855501979,
                0.9999992661789321,
                0.9999998724810027,
                0.9999997300423191,
                0.9999994956524716,
                0.9999998555020135,
                0.9999996940977731,
                0.9999997617630899
            ],
            [
                2.2603242978665707e-06,
                4.222832941034507e-06,
                4.222831934202483e-06,
                2.902311639073834e-06,
                9.422444815628016e-07,
                1.7603438427660027e-06,
                8.315284241560147e-07,
                9.422444815628016e-07,
                3.288750241473551e-06,
                6.144175333837093e-06
            ],
            [
                0.9999998362623332,
                0.9999998144609423,
                0.9999999006881022,
                0.9999999226558145,
                0.9999999006879957,
                0.9999998874647574,
                0.9999998874647574,
                0.9999999397642365,
                0.9999997617630616,
                0.9999998362622552
            ],
            [
                0.999999814460854,
                0.999999855501979,
                0.9999998555020135,
                0.999999855501979,
                0.9999998874647306,
                0.999999855501979,
                0.9999998724808963,
                0.9999996072137529,
                0.9999998362623723,
                0.9999998724809419
            ],
            [
                0.9999999006880785,
                0.9999996072139402,
                0.9999989322966208,
                0.999999266178932,
                0.9999996072137529,
                0.9999992661792819,
                0.9999994284994849,
                0.9999994284996211,
                0.9999997300421581,
                0.9999989322973847
            ],
            [
                0.999999814460876,
                0.9999998144608317,
                0.9999996940977731,
                0.9999997300421903,
                0.9999997617631184,
                0.9999994956527721,
                0.999999653367503,
                0.9999990577549569,
                0.9999997617630332,
                0.9999997300421903
            ],
            [
                0.9999996940977731,
                0.999999789756684,
                0.9999996533675028,
                0.999999887464811,
                0.9999998874648917,
                0.9999998724809267,
                0.9999999006880075,
                0.9999997897566089,
                0.9999999006880549,
                0.9999998362622942
            ],
            [
                0.9999997897567342,
                0.9999999226557684,
                0.9999999006880904,
                0.9999998144609423,
                0.9999998144608317,
                0.9999998144609202,
                0.9999998362623138,
                0.9999998362623137,
                0.9999996940976636,
                0.9999998362623723
            ],
            [
                0.9999998555020307,
                0.9999994956527721,
                0.9999995549147889,
                0.9999997300422225,
                0.999999266178757,
                0.9999993524051246,
                0.9999996533672549,
                0.9999998874648648,
                0.9999996072137998,
                0.9999987901341723
            ],
            [
                0.999999789756634,
                0.9999997897567342,
                0.9999997617630048,
                0.9999996533672136,
                0.9999998144608097,
                0.999999352404893,
                0.99999976176309,
                0.9999998555019618,
                0.9999998144608097,
                0.9999998144608098
            ],
            [
                0.999999855501979,
                0.9999998555020134,
                0.9999996072137998,
                0.9999996940976636,
                0.9999997897567341,
                0.9999998362622746,
                0.9999997617630332,
                0.9999998555020307,
                0.9999997897565838,
                0.9999996533674614
            ],
            [
                0.9999997897565587,
                0.9999998362623332,
                0.9999996533673375,
                0.999999554914789,
                0.9999997897567342,
                0.9999999006881377,
                0.9999997300421903,
                0.9999995549151073,
                0.9999996533672136,
                0.9999997617631469
            ],
            [
                0.9999997617629764,
                0.999999789756684,
                0.9999996533672549,
                0.9999962733607165,
                0.9999810748427433,
                0.9999938558232018,
                0.9999945777784454,
                0.9999962733616046,
                0.9999993524049702,
                0.9999993524050474
            ],
            [
                0.9999997300422869,
                0.9999852610145198,
                0.9999980052695652,
                0.9999998362623528,
                0.9999990577554061,
                0.9999967112517189,
                0.9999938558239345,
                0.9999962733620489,
                0.9999996072139402,
                0.9999974387171787
            ],
            [
                0.9999998724809116,
                0.9999990577549568,
                0.9999989322966208,
                0.9999999123575464,
                0.9999993524052789,
                0.9999998724809875,
                0.9999997300422225,
                0.9999999317439627,
                0.999999266179107,
                0.9999998362623528
            ],
            [
                0.9999996940978095,
                0.9999993524053562,
                0.9999994284994167,
                0.9999986290424665,
                0.9999990577554061,
                0.9999996940976271,
                0.9999997617631183,
                0.9999993524052018,
                0.9999970976873231,
                0.9999997617630332
            ],
            [
                0.999999694097773,
                0.9999997617630332,
                0.9999997617631183,
                0.9999998144609424,
                0.9999998144609202,
                0.9999998724810027,
                0.9999998555019619,
                0.9999997617629764,
                0.9999998724809723,
                0.9999996533675028
            ],
            [
                6.1441738691562974e-06,
                1.4738985483128763e-05,
                3.726640616748873e-06,
                2.7535687799708318e-05,
                1.7603440526806268e-06,
                6.144173136645595e-06,
                5.422218322940583e-06,
                1.012999460108057e-05,
                1.0129993393742954e-05,
                4.785093353739995e-06
            ],
            [
                0.9999999468421249,
                0.9999998874648379,
                0.9999997897565587,
                0.9999998874648782,
                0.9999998874649184,
                0.9999999397643156,
                0.9999999317440116,
                0.9999996533674202,
                0.9999998144609202,
                0.9999997897566589
            ],
            [
                0.9999999123575255,
                0.9999998362622747,
                0.9999995549150011,
                0.9999970976869769,
                0.9999996533672136,
                0.9999996072139402,
                0.9999991684718732,
                0.9999997300421581,
                0.9999999006880194,
                0.9999810748472552
            ],
            [
                0.9999996533672962,
                0.9999996940978825,
                0.9999997300421903,
                0.9999993524050476,
                0.9999996072137529,
                0.9999994284992805,
                0.9999996940976271,
                0.9999996533672549,
                0.999999352405279,
                0.9999996072136125
            ],
            [
                0.9999998144609645,
                0.9999995549150542,
                0.9999996072136592,
                0.9999996072138934,
                0.9999999006879957,
                0.9999996940976636,
                0.999999789756684,
                0.9999995549147889,
                0.9999998144609202,
                0.9999996072136592
            ],
            [
                0.9999996533675028,
                0.9999998144609202,
                0.9999997617631752,
                0.9999998144608981,
                0.99999976176309,
                0.9999996533673788,
                0.9999995549150541,
                0.9999994956525918,
                0.9999990577549569,
                0.9999996533674614
            ],
            [
                1.8925145980181433e-05,
                1.4738983726908257e-05,
                5.422220908314139e-06,
                7.889265405505236e-06,
                1.7603440526662173e-06,
                1.5534971989809095e-06,
                1.6701425824307884e-05,
                3.726638839395927e-06,
                2.9023130229209922e-06,
                1.300712846217e-05
            ],
            [
                0.9999996940978825,
                0.9999995549148419,
                0.9999998724809875,
                0.9999996072138934,
                0.9999996940977002,
                0.9999995549148419,
                0.9999998555019274,
                0.9999994956524115,
                0.999999694097846,
                0.9999998362623723
            ],
            [
                0.9999998555019274,
                0.9999997300420939,
                0.9999998144609424,
                0.9999997300421581,
                0.9999997300420937,
                0.9999998362622747,
                0.9999997897567091,
                0.9999997897567091,
                0.9999998362622552,
                0.9999992661791071
            ],
            [
                0.999997097686977,
                0.9999996533672549,
                0.99999976176309,
                0.999999495652652,
                0.9999995549150011,
                0.9999997617630616,
                0.9999995549148419,
                0.9999996940978825,
                0.9999996533674202,
                0.9999997300422547
            ],
            [
                0.9999998144608098,
                0.9999998555019618,
                0.9999999397642508,
                0.9999997897566089,
                0.999999814460876,
                0.999999730042319,
                0.9999998724808964,
                0.9999998144608097,
                0.9999999226557131,
                0.999999554914789
            ],
            [
                0.9999998724809267,
                0.9999997617630616,
                0.9999997897567091,
                0.999999694097773,
                0.99999976176309,
                0.9999996940978095,
                0.9999998144608981,
                0.9999995549150011,
                0.9999998874648246,
                0.9999998724809875
            ],
            [
                0.9999997617630049,
                0.9999998724809875,
                0.9999998874648917,
                0.9999998555019446,
                0.9999998724809267,
                0.9999997617631184,
                0.9999998874647574,
                0.9999995549147889,
                0.9999998874648917,
                0.9999998144609645
            ],
            [
                1.0677027427525368e-06,
                2.9023119851266288e-06,
                2.2603234895053587e-06,
                2.561283431942246e-06,
                2.902311292960369e-06,
                1.7603430034439723e-06,
                2.2603251061458426e-06,
                1.0677024881761599e-06,
                1.5534973841154145e-06,
                1.994729245822257e-06
            ],
            [
                0.9999998362622552,
                0.9999995549150542,
                0.999999352405279,
                0.9999999226558145,
                0.9999998874648514,
                0.9999995549149481,
                0.9999993524054334,
                0.999999931743979,
                0.9999994956523514,
                0.9999998144608981
            ],
            [
                0.9999998362623528,
                0.9999999006880904,
                0.9999998724809571,
                0.9999999006881141,
                0.9999998144609644,
                0.9999999530883396,
                0.9999998555019962,
                0.9999999468421313,
                0.9999999317439627,
                0.9999997897565587
            ],
            [
                4.222833947674739e-06,
                4.222831934202483e-06,
                4.7850967763512445e-06,
                1.5534983100920427e-06,
                3.7266410608720178e-06,
                4.785095065045315e-06,
                2.56128159999123e-06,
                1.7603430033799313e-06,
                6.14417753110761e-06,
                2.5612815999679353e-06
            ],
            [
                0.9999998555019274,
                0.9999996940977002,
                0.9999998144608097,
                0.9999996072137061,
                0.9999993524051246,
                0.9999996533672136,
                0.9999998874648647,
                0.999999814460876,
                0.9999992661791944,
                0.9999998362622747
            ],
            [
                0.9999998362623332,
                0.9999998555020135,
                0.9999999317439627,
                0.9999998555020307,
                0.9999995549150542,
                0.9999999006879957,
                0.9999999006879838,
                0.9999999226557316,
                0.9999999123575881,
                0.9999998724809874
            ],
            [
                4.2228319339950885e-06,
                5.4222196154940574e-06,
                2.5612831266165976e-06,
                1.7603427935678977e-06,
                1.0129994601301684e-05,
                2.9023119850210436e-06,
                1.1478768124324254e-05,
                4.7850944942634305e-06,
                4.2228344511197656e-06,
                6.962256248871951e-06
            ],
            [
                0.999993855826131,
                0.9999970976887069,
                0.9999957771650455,
                0.9999962733593833,
                0.9999869928746369,
                0.9999980052705167,
                0.999996273360272,
                0.9999962733611607,
                0.9999989322973846,
                0.9999832985821384
            ],
            [
                0.9999998555019618,
                0.9999998724808964,
                0.9999998144608981,
                0.9999998362622747,
                0.9999992661788446,
                0.9999996940976272,
                0.9999997300421903,
                0.9999996533674615,
                0.9999996940977001,
                0.9999997897566338
            ],
            [
                0.9999997897567342,
                0.999999730042126,
                0.9999999006879721,
                0.9999999397642078,
                0.9999998874647574,
                0.9999998144608317,
                0.9999999006881022,
                0.9999998362622552,
                0.99999976176309,
                0.9999996940976272
            ],
            [
                0.9999996940977002,
                0.9999997897566589,
                0.9999990577555185,
                0.9999994956525918,
                0.9999996072136125,
                0.9999999226557778,
                0.9999993524052019,
                0.9999994956523514,
                0.9999997897565587,
                0.9999992661786695
            ],
            [
                0.999999814460876,
                0.9999998362622357,
                0.9999998555019962,
                0.9999993524049703,
                0.9999997300421581,
                0.9999996533674615,
                0.9999994956527722,
                0.9999994284995529,
                0.9999993524051246,
                0.9999995549147358
            ],
            [
                0.9999994956524716,
                0.9999994284995529,
                0.9999996533675028,
                0.9999994284997573,
                0.9999997300422868,
                0.9999996940978095,
                0.9999995549148419,
                0.9999996072137529,
                0.9999997617630332,
                0.9999994284994849
            ],
            [
                0.9999998874649051,
                0.9999997300423191,
                0.9999998874647843,
                0.9999998362623723,
                0.9999997300422225,
                0.999999855502048,
                0.9999998555019962,
                0.9999997617630616,
                0.9999997617631184,
                0.9999998144608981
            ],
            [
                0.9999998724810027,
                0.9999995549150542,
                0.9999997617631752,
                0.9999998362622552,
                0.9999998144609203,
                0.9999998555019618,
                0.9999997300421903,
                0.9999998555019446,
                0.9999994956525317,
                0.9999997617630048
            ],
            [
                0.9999998874647306,
                0.9999998874648245,
                0.9999997617630332,
                0.9999998874649051,
                0.9999998144609202,
                0.9999997617630332,
                0.9999996533674201,
                0.999999694097846,
                0.9999998144609202,
                0.9999998724809571
            ],
            [
                0.9999996072136125,
                0.9999998555019274,
                0.9999995549149481,
                0.9999997617630332,
                0.9999996533673788,
                0.9999998144608097,
                0.9999998144609203,
                0.99999976176309,
                0.9999997300420939,
                0.9999998362622552
            ],
            [
                0.9999996533675028,
                0.999999352404893,
                0.9999997300422547,
                0.9999998362622746,
                0.9999996072137529,
                0.9999997300420937,
                0.99999976176309,
                0.9999997617629763,
                0.9999997897566589,
                0.9999995549150011
            ],
            [
                0.9999998555020135,
                0.9999996072137061,
                0.9999997617630332,
                0.9999998144608538,
                0.9999995549150011,
                0.9999995549148419,
                0.9999997617631468,
                0.9999997617630048,
                0.9999996940978095,
                0.9999999123574523
            ],
            [
                0.999999694097846,
                0.999999855501979,
                0.9999999006880312,
                0.9999998724809115,
                0.999999855501979,
                0.9999998874647843,
                0.9999997300422547,
                0.9999998362622552,
                0.9999998724809419,
                0.9999996940977002
            ],
            [
                0.9999996072138466,
                0.9999996533674201,
                0.9999997300422547,
                0.9999998555019446,
                0.9999997300422547,
                0.9999996533672962,
                0.9999997617631469,
                0.9999997617631184,
                0.9999998144609202,
                0.9999998144608097
            ],
            [
                0.9999980052695652,
                0.9999974387168775,
                0.9999921107374152,
                0.9999962733611608,
                0.9324533154301279,
                0.9999986290427932,
                0.9999952149060761,
                0.9999832985841317,
                0.9999987901343166,
                0.999999057755294
            ],
            [
                0.9999994956524716,
                0.9999997617631752,
                0.9999996940978825,
                0.9999994284992805,
                0.9999996072137529,
                0.9999997300422225,
                0.9999994284996891,
                0.9999992661790196,
                0.9999986290431201,
                0.9999996940977001
            ],
            [
                4.22283294098842e-06,
                1.7603436330091044e-06,
                5.4222183231674305e-06,
                0.9999994284996891,
                3.2887478892055875e-06,
                2.9023133690188264e-06,
                2.9023109470871505e-06,
                1.5534983101301911e-06,
                1.4738983726559732e-05,
                2.9023123310290063e-06
            ],
            [
                0.9999997300421581,
                0.9999996533674202,
                0.9999997617630048,
                0.9999999123575255,
                0.9999994956525918,
                0.9999998724809723,
                0.9999995549151073,
                0.9999997617630332,
                0.9999996533674201,
                0.9999996533674615
            ],
            [
                0.9999995549150011,
                0.999999554914895,
                0.9999995549150542,
                0.9999998555019446,
                0.9999991684715759,
                0.9999970976890531,
                0.9999996072139402,
                0.9999997617630616,
                0.9999997300421903,
                0.9999996940977366
            ],
            [
                0.9999994956524115,
                0.9999997617630899,
                0.9999998555019274,
                0.9999998362623723,
                0.9999998724809875,
                0.999999554914895,
                0.9999996533672963,
                0.999999653367503,
                0.9999996940978825,
                0.9999994284996893
            ],
            [
                0.9999999123575046,
                0.9999998555019618,
                0.9999999123574942,
                0.9999998555019274,
                0.9999997617631468,
                0.9999999226557224,
                0.9999996940978825,
                0.999999789756634,
                0.9999998724809875,
                0.9999997897565838
            ],
            [
                0.9999993524054335,
                0.9999996533673788,
                0.9999996533672136,
                0.9999996533672135,
                0.9999997897565587,
                0.9999995549147889,
                0.9999996072138466,
                0.9999970976873229,
                0.9999991684720715,
                0.9999994284995529
            ],
            [
                0.9999997617631752,
                0.9999991684720715,
                0.9999998555019618,
                0.9999993524052018,
                0.9999989322970027,
                0.9999996072138934,
                0.9999993524050474,
                0.9999995549150011,
                0.9999994956523514,
                0.9999993524051246
            ],
            [
                0.9999996533674202,
                0.9999995549147889,
                0.9999997617630616,
                0.9999995549149481,
                0.9999997300422869,
                0.9999994956523514,
                0.9999996940978095,
                0.9999996072138934,
                0.9999996940976636,
                0.9999994284997574
            ],
            [
                0.9999996533675028,
                0.999999266178757,
                0.9999996533675028,
                0.9999997617631752,
                0.9999996072138465,
                0.9999998724809723,
                0.9999997897567341,
                0.9999997300422547,
                0.9999996533674615,
                0.9999995549148419
            ],
            [
                1.7603440527046419e-06,
                2.902311985146426e-06,
                3.2887498494551953e-06,
                3.726641061027928e-06,
                4.2228329408924035e-06,
                1.0677024881761599e-06,
                1.994730196992497e-06,
                2.902311639126627e-06,
                6.144175334015912e-06,
                2.5612831265630198e-06
            ],
            [
                0.9999994956527722,
                0.9999994956524716,
                0.9999996940978825,
                0.999999266178757,
                0.9999995549150011,
                0.9999997300422547,
                0.9999995549149481,
                0.9999990577556308,
                0.9999997300422547,
                0.999999266178932
            ],
            [
                0.9999998362623332,
                0.9999996072137061,
                0.9999997617630049,
                0.9999996940976636,
                0.9999998144609423,
                0.999999912357515,
                0.9999998144608097,
                0.9999998724808963,
                0.9999997617630332,
                0.999999814460876
            ],
            [
                0.9999997300422869,
                0.9999997897567091,
                0.9999997617631184,
                0.9999991684720716,
                0.9999998724809723,
                0.9999995549150011,
                0.9999998362623138,
                0.9999998874647709,
                0.9999998144608981,
                0.9999996072137529
            ],
            [
                0.9999996533672549,
                0.9999997300421581,
                0.9999992661789322,
                0.999999814460876,
                0.9999997300422869,
                0.9999996533672136,
                0.9999999123574523,
                0.9999998144609424,
                0.9999993524052018,
                0.9999996072138465
            ],
            [
                5.422219616026655e-06,
                5.422220908481809e-06,
                5.422218322664422e-06,
                2.9023112931213857e-06,
                3.7266379512857925e-06,
                2.902311639126627e-06,
                2.902311639126627e-06,
                1.0129990979381404e-05,
                6.144172404028807e-06,
                7.889265406438011e-06
            ],
            [
                0.9999998362623723,
                0.9999998874647842,
                0.9999997617631752,
                0.9999999226557961,
                0.9999996533675028,
                0.9999997617630616,
                0.999999789756684,
                0.999999789756684,
                0.9999997897567091,
                0.999999730042126
            ],
            [
                1.994730434847717e-06,
                1.994729721482609e-06,
                0.999664649732569,
                8.315282259089153e-07,
                8.315280276580819e-07,
                3.7266388397721442e-06,
                3.7266392838544054e-06,
                1.9947306726049992e-06,
                2.2603251061458426e-06,
                1.5534979397394734e-06
            ],
            [
                0.999999887464744,
                0.9999987901341724,
                0.999998790134028,
                0.9999996072137061,
                0.9999997617631469,
                0.9999984465020603,
                0.9999997300423191,
                0.9999996072138465,
                0.9999994956524715,
                0.9999992661791944
            ],
            [
                0.9999998874648917,
                0.9999996940976272,
                0.9999998144608317,
                0.9999994956527121,
                0.9999998362623332,
                0.9999997300422869,
                0.999999814460876,
                0.9999998362622357,
                0.9999997300420937,
                0.9999993524053562
            ],
            [
                0.9999998362623722,
                0.9999997897567342,
                0.9999998555019274,
                0.9999997617631184,
                0.9999998362622747,
                0.9999998874648782,
                0.9999999317439221,
                0.9999998874648782,
                0.9999998724809419,
                0.9999999123574628
            ],
            [
                0.9999997617630048,
                0.9999997617631753,
                0.999999495652712,
                0.9999998362622746,
                0.9999998362622747,
                0.9999998724810027,
                0.9999997300421903,
                0.9999997300420937,
                0.9999997897567091,
                0.999999057755743
            ],
            [
                0.9999991684718732,
                0.9999997617631469,
                0.9999997300421903,
                0.9999998874647306,
                0.9999990577556308,
                0.9999984465020603,
                0.9999996072137061,
                0.9999997617630333,
                0.9999998555019446,
                0.9999982396572065
            ],
            [
                0.9999999123574523,
                0.9999996072139402,
                0.9999998724810027,
                0.9999998724810027,
                0.9999996533674202,
                0.9999997897565838,
                0.999999730042126,
                0.999999789756684,
                0.9999999317439383,
                0.9999999530883396
            ],
            [
                0.9999999468421376,
                0.9999999530883675,
                0.9999999123574836,
                0.9999997300421581,
                0.9999998874648917,
                0.9999999006879957,
                0.9999998144608981,
                0.999999900688043,
                0.9999998144608098,
                0.9999999006881377
            ],
            [
                0.9999999123574836,
                0.9999999006880785,
                0.9999996533672136,
                0.9999998362623332,
                0.9999990577554061,
                0.9999997300421581,
                0.99999976176309,
                0.9999998362622943,
                0.9999998555019619,
                0.9999998362622357
            ],
            [
                2.26032348933062e-06,
                2.2603251060985603e-06,
                4.7850956351657615e-06,
                2.260324028255194e-06,
                6.144172404218801e-06,
                7.889264465842609e-06,
                3.726640172503764e-06,
                6.96225707894582e-06,
                1.9947299592570416e-06,
                2.561282515853595e-06
            ],
            [
                7.889265405677441e-06,
                1.8925157259824262e-05,
                1.473897669838221e-05,
                1.1478764019996392e-05,
                7.889261644501938e-06,
                1.6701417860795016e-05,
                2.4300234933172706e-05,
                1.1478766755985128e-05,
                3.7266379512518984e-06,
                1.4738985478678359e-05
            ],
            [
                0.9999998362622942,
                0.9999998362623722,
                0.9999999530883452,
                0.9999994284996211,
                0.9999998724809115,
                0.99999976176309,
                0.9999997617630899,
                0.9999998724809723,
                0.9999997300421581,
                0.9999997617630616
            ],
            [
                0.9999997617631468,
                0.999999789756634,
                0.9999998362623528,
                0.9999996533672963,
                0.999999814460854,
                0.9999995549147889,
                0.9999993524054335,
                0.9999996533674614,
                0.9999998144609202,
                0.9999996072136593
            ],
            [
                6.1441738691562974e-06,
                1.6701415867707307e-05,
                4.785092783319532e-06,
                1.6701419850845044e-05,
                7.88925976359915e-06,
                5.422221555133606e-06,
                2.430024072091399e-05,
                2.1444950959196957e-05,
                1.3007134664514934e-05,
                8.939693106873817e-06
            ],
            [
                0.9999997897565838,
                0.9999996940976272,
                0.999999855501979,
                0.9999998144608317,
                0.9999999006881141,
                0.9999996940978461,
                0.9999996940977366,
                0.9999995549150011,
                0.9999996072139402,
                0.9999991684719723
            ]
        ]
    },
    {
        "q_id": "8306_mmlu_math",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            31,
            32,
            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,
            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,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            125,
            126,
            127
        ],
        "rewards": [
            [
                3.535626751800907e-05,
                1.8925143705306717e-05,
                6.60521600278783e-05,
                6.962257908044647e-06,
                5.829126547411052e-05,
                9.610239091526496e-05,
                1.147876538716594e-05,
                1.473898021151881e-05,
                3.535625483162694e-05,
                6.605216036763493e-05
            ],
            [
                4.0063682540662206e-05,
                NaN,
                7.484625365166955e-05,
                0.00020342689829265615,
                0.00020342692317738462,
                0.0001398220735885219,
                3.53562422342549e-05,
                NaN,
                5.829126536893371e-05,
                NaN
            ],
            [
                NaN,
                1.6701419848475466e-05,
                3.120192622803585e-05,
                3.120190387585532e-05,
                3.120190012417845e-05,
                1.8925148230890784e-05,
                4.539785231635491e-05,
                NaN,
                6.962254588433232e-06,
                1.1478772220928159e-05
            ],
            [
                4.5397852361605714e-05,
                7.48462267449919e-05,
                0.00010889689596424175,
                6.605216011534042e-05,
                7.484620918748056e-05,
                0.0006263341632102658,
                1.1478765387667046e-05,
                1.6701421840804172e-05,
                8.481105120978835e-05,
                0.00012339453003282785
            ],
            [
                3.535626332895835e-05,
                4.5397868604005595e-05,
                4.0063706494441236e-05,
                6.605212076750022e-05,
                3.120192616072537e-05,
                3.5356242249174894e-05,
                5.422220259709562e-06,
                5.8291272451829125e-05,
                7.484621804982218e-05,
                9.610238045498727e-05
            ],
            [
                0.7310585844894971,
                0.9998766054259546,
                0.9999038975399801,
                0.9241418225903233,
                0.9997965729633023,
                0.9999038976082527,
                0.8807970795424088,
                0.9999832985702152,
                0.9982992776443029,
                0.999620015569961
            ],
            [
                1.473898722977843e-05,
                1.1478769492141554e-05,
                2.2603253753174176e-06,
                6.962257079376403e-06,
                3.466326850720213e-07,
                4.222832436587256e-06,
                3.2887502413389517e-06,
                1.1478769493728398e-05,
                5.4222215552470286e-06,
                4.785093923603471e-06
            ],
            [
                7.484621828887399e-05,
                3.120191880379252e-05,
                3.535625066945945e-05,
                7.484624490966648e-05,
                0.00020342689662341423,
                4.539787938262061e-05,
                3.535626749614353e-05,
                4.539785234013636e-05,
                0.0002034269486658847,
                0.0001795280073906601
            ],
            [
                4.785094494402695e-06,
                3.7266383952696564e-06,
                3.726639728184142e-06,
                1.0129988562901417e-05,
                2.2603240282243575e-06,
                1.5534979397140412e-06,
                2.561283431888668e-06,
                6.962258739454786e-06,
                4.7850933534310035e-06,
                1.1478772229050293e-05
            ],
            [
                2.430024356187678e-05,
                2.7535704170940182e-05,
                2.4300237766974286e-05,
                1.6701423810652505e-05,
                0.00015843628952133746,
                0.00010889693486971388,
                7.484620870992156e-05,
                9.610242595625959e-05,
                2.4300252288444548e-05,
                1.4738978434119307e-05
            ],
            [
                8.939695237341456e-06,
                1.9947292457750883e-06,
                1.300712535865635e-05,
                2.5612831263510383e-06,
                2.9023126768680736e-06,
                3.288748672760313e-06,
                5.1442195178315546e-05,
                3.7266379509129646e-06,
                1.3007128461507534e-05,
                3.5356238042506135e-05
            ],
            [
                NaN,
                1.8925148220012804e-05,
                1.4738980203395485e-05,
                0.00010889688174031335,
                4.539789007833334e-05,
                0.9999952149043648,
                1.670142781244497e-05,
                1.1478773596575768e-05,
                9.610242504454196e-05,
                6.962254589104433e-06
            ],
            [
                2.561282515914161e-06,
                5.422217676575195e-06,
                7.484623573530184e-05,
                3.1201918806289706e-05,
                8.481102069646196e-05,
                4.5397874009662535e-05,
                3.535625068000635e-05,
                6.962257909121104e-06,
                0.0001233945450100987,
                0.00013982210670236459
            ],
            [
                0.5,
                0.9998766054698092,
                0.9999546021422488,
                0.012431649412508837,
                0.9988304897961399,
                0.08509904790742691,
                0.939913352771458,
                0.012431649423942781,
                0.9998415638411849,
                0.999620015408572
            ],
            [
                2.1444953517061932e-05,
                4.222834450743383e-06,
                2.260324028306588e-06,
                7.338208930265102e-07,
                1.8925143721072897e-05,
                5.422217029943586e-06,
                1.8925143724239906e-05,
                3.7266383951544193e-06,
                4.222832940577472e-06,
                6.475950297709604e-07
            ],
            [
                1.1478765375285496e-05,
                5.422219615582823e-06,
                1.0129990978441666e-05,
                2.4300249417247375e-05,
                2.561282515662579e-06,
                2.1444950959196957e-05,
                1.3007130010117919e-05,
                1.994730434735237e-06,
                1.670141586454787e-05,
                1.0129989767032304e-05
            ],
            [
                0.9999910603058279,
                0.9999885212332431,
                0.9999945777829695,
                0.9999832985821387,
                0.9999599362982833,
                0.9999832985761661,
                0.999988521231875,
                0.9999962733598274,
                0.9999921107374146,
                0.9999810748517602
            ],
            [
                1.0129993386593603e-05,
                1.892514597632595e-05,
                8.939695233292452e-06,
                7.484626271168351e-05,
                1.0129993391531815e-05,
                8.48110813566102e-05,
                7.889262583633267e-06,
                0.0001584362900100369,
                9.610244829753971e-05,
                1.147876812238246e-05
            ],
            [
                0.00013982214046315286,
                0.9997694931928269,
                0.00023050663097134552,
                3.535626333088765e-05,
                NaN,
                4.006367783047594e-05,
                6.605217601422157e-05,
                6.6052176080539e-05,
                0.9999869928715471,
                5.144223190264361e-05
            ],
            [
                8.939698433373153e-06,
                6.144176797585032e-06,
                1.9947301969707264e-06,
                2.5612819050161955e-06,
                6.962255418215627e-06,
                3.726640616630245e-06,
                2.561282515853595e-06,
                2.4300240725599276e-05,
                2.9023112929973233e-06,
                4.785093353626844e-06
            ],
            [
                0.00013982210695869836,
                6.605212089917383e-05,
                0.00017952800792612165,
                8.48110715470758e-05,
                NaN,
                0.00026119036543080965,
                3.120191129612231e-05,
                0.0002611902123358118,
                NaN,
                1.4738985481091229e-05
            ],
            [
                3.726638395320497e-06,
                1.994729245822257e-06,
                3.288748672760313e-06,
                8.939693106329072e-06,
                3.2887494571676872e-06,
                5.422220908634683e-06,
                1.994730672496148e-06,
                6.962258738827909e-06,
                4.785095064601411e-06,
                3.2887478890769702e-06
            ],
            [
                8.481105137391814e-05,
                9.610240318988942e-05,
                0.00037998443286895014,
                0.00012339463273902334,
                0.0019267342415578233,
                0.00013982208989216013,
                6.605215252055522e-05,
                0.00012339456001789326,
                0.0005527785286792258,
                0.00020342689960378053
            ],
            [
                2.902312330891746e-06,
                6.144176798255599e-06,
                3.726638839656906e-06,
                2.902312677007974e-06,
                1.7603440525701563e-06,
                7.889266343316778e-06,
                1.0677029972270124e-06,
                1.0129995808639442e-05,
                7.889263521487523e-06,
                2.260324297607547e-06
            ],
            [
                5.82912860964034e-05,
                2.1444953280287583e-05,
                1.0129987352284668e-05,
                2.7535684518791692e-05,
                3.1201900207380036e-05,
                3.726639726103083e-06,
                0.00010889692189118655,
                4.785093923847183e-06,
                0.00013982214035329548,
                0.00017952798547330796
            ],
            [
                0.00020342699570064025,
                8.481101095665886e-05,
                6.605216819645424e-05,
                0.000179527965324287,
                1.300713311155064e-05,
                8.48110715384374e-05,
                2.144494838924002e-05,
                8.48110310785935e-05,
                0.00020342699678979154,
                0.0002959570624243955
            ],
            [
                1.4738988991495334e-05,
                1.0129993393540266e-05,
                1.0129990975862006e-05,
                5.144220129392002e-05,
                5.829127243062412e-05,
                1.3007126909537681e-05,
                7.484624497718912e-05,
                1.0129992182443859e-05,
                3.2887494572514376e-06,
                5.144220745705777e-05
            ],
            [
                2.1444945846588504e-05,
                5.829124465207388e-05,
                NaN,
                3.53562506877236e-05,
                8.93969843377968e-06,
                NaN,
                4.006369216362198e-05,
                0.000179527900998409,
                3.5356246478738656e-05,
                5.144220746828593e-05
            ],
            [
                5.715006513843456e-07,
                7.338213304016384e-07,
                2.902310946944611e-06,
                1.99472900796355e-06,
                6.1441775309064404e-06,
                2.90231233014737e-06,
                5.715003107619008e-07,
                8.939693106329072e-06,
                5.422221554670048e-06,
                1.5534971988904843e-06
            ],
            [
                1.8925145972677006e-05,
                1.9947301970587145e-06,
                2.561282515988704e-06,
                7.88925976359915e-06,
                1.2098662603202336e-06,
                1.3709570432501875e-06,
                5.422218969601935e-06,
                2.5612822103393692e-06,
                9.422448184561605e-07,
                4.222835457733473e-06
            ],
            [
                4.785093353352668e-06,
                2.561283431124603e-06,
                5.422218320642526e-06,
                1.9947299591354906e-06,
                1.553497198908852e-06,
                6.962255411668247e-06,
                1.4738980213341866e-05,
                1.3007130008887624e-05,
                6.144174601309452e-06,
                2.4300249410794055e-05
            ],
            [
                4.0063706476368846e-05,
                5.144221974927673e-05,
                2.430025024256514e-05,
                9.610246043233746e-05,
                0.0007096704051685921,
                0.00043055708733683826,
                7.484620040083068e-05,
                7.484625388309796e-05,
                0.00010889694815087969,
                0.00013982209057978554
            ],
            [
                1.2098659718539182e-06,
                7.338212429307298e-07,
                1.5534975693205863e-06,
                1.8925157257965367e-05,
                1.5534979397267575e-06,
                1.2098655391947376e-06,
                9.422449308566668e-07,
                8.315284241333265e-07,
                3.2887494570181325e-06,
                1.2098662603862553e-06
            ],
            [
                5.829127239415151e-05,
                0.0001088968960910006,
                6.605216023019448e-05,
                9.610243721709193e-05,
                8.481107132371116e-05,
                5.829128623423597e-05,
                9.610238046617398e-05,
                0.00020342689854718592,
                9.610239109704907e-05,
                0.00026119036832627807
            ],
            [
                1.3709572067680694e-06,
                9.42244593835151e-07,
                3.7266406165319545e-06,
                1.0677033791000363e-06,
                1.2098655392354511e-06,
                6.96225956837018e-06,
                3.2887486729337966e-06,
                5.422221554926484e-06,
                1.5534971989427613e-06,
                1.9947292458603553e-06
            ],
            [
                1.7603436329394601e-06,
                8.315283249742262e-07,
                8.315279285205827e-07,
                2.561283126639892e-06,
                1.9947306726049992e-06,
                5.715005832510042e-07,
                1.2098662603862553e-06,
                6.475948753794598e-07,
                1.2098659718990333e-06,
                2.2603248365343694e-06
            ],
            [
                2.260323758835034e-06,
                1.5534971988495103e-06,
                8.315279285088606e-07,
                2.260324028306588e-06,
                4.785095635413826e-06,
                1.0677032518209896e-06,
                1.5534979396815448e-06,
                8.315284241333265e-07,
                5.422218969029887e-06,
                1.3709578605243332e-06
            ],
            [
                5.1442231976000976e-05,
                2.4300252300909177e-05,
                1.4738980202752053e-05,
                7.484624476808677e-05,
                2.1444950942033742e-05,
                2.4300249387721226e-05,
                4.006370169826257e-05,
                2.4300249384892373e-05,
                1.3007126902913016e-05,
                2.4300232006903406e-05
            ],
            [
                NaN,
                1.6701417850314193e-05,
                7.48462625995088e-05,
                1.892515048042999e-05,
                5.829129305079897e-05,
                0.9999938558275985,
                2.753568450356562e-05,
                0.999994577779092,
                6.962257079275089e-06,
                7.484621796051808e-05
            ],
            [
                3.7266401724291984e-06,
                2.753569436805389e-05,
                7.889265403395731e-06,
                3.535624642703312e-05,
                3.535624646549072e-05,
                4.7850944943330625e-06,
                6.962259567914269e-06,
                7.889263523238269e-06,
                3.5356267465789024e-05,
                3.12019075573845e-05
            ],
            [
                0.00010889689603554361,
                0.00020342692222437763,
                0.0003799845262046402,
                0.0001795280507865552,
                0.00010889693466689962,
                2.7535681222849733e-05,
                0.00026119039864890215,
                4.0063706494441236e-05,
                4.0063687388140825e-05,
                5.8291244643591885e-05
            ],
            [
                1.0129990973503458e-05,
                3.5356246340085515e-05,
                2.1444953504969666e-05,
                1.670142979875954e-05,
                1.4738985464147524e-05,
                1.0129990975235516e-05,
                3.535624222267904e-05,
                1.8925154993072253e-05,
                2.753568780802255e-05,
                3.535626752263942e-05
            ],
            [
                7.889259761030436e-06,
                5.422218322664422e-06,
                1.3007123800819306e-05,
                2.9023112926251358e-06,
                4.222832436587256e-06,
                2.260325375091285e-06,
                2.4300249411766472e-05,
                1.3007126906036072e-05,
                2.1444956072586775e-05,
                3.2887506332466845e-06
            ],
            [
                1.6701419852090592e-05,
                2.14449535222109e-05,
                1.012999460150437e-05,
                9.610246057636654e-05,
                1.6701429795417824e-05,
                1.1478765388314311e-05,
                2.4300249374107374e-05,
                1.3007128461838766e-05,
                4.222833443968609e-06,
                5.144220138599094e-05
            ],
            [
                7.88926540454376e-06,
                2.260325375391425e-06,
                3.7266388395620047e-06,
                2.902312330849511e-06,
                6.144173868178388e-06,
                3.2887498485279564e-06,
                1.5534973841154145e-06,
                7.889259762307618e-06,
                1.300712536258383e-05,
                1.1478768123823146e-05
            ],
            [
                0.9999646437492984,
                0.9999885212318744,
                0.9986749777397623,
                0.9999599362982898,
                0.9999251537995218,
                0.9999417087553654,
                0.9998911030777682,
                0.9997694933128299,
                0.999373665746104,
                0.9999251537995654
            ],
            [
                0.6513548714339144,
                0.7981867753392728,
                0.999860177876933,
                0.4378234991142019,
                0.3208213138121609,
                0.9997965730987299,
                0.04208772491181672,
                0.798186768138228,
                0.8933093975331751,
                0.9997965729588214
            ],
            [
                1.994729245822257e-06,
                2.260323758557508e-06,
                2.9023133689317184e-06,
                8.9396973679153e-06,
                1.0677028699858827e-06,
                1.370957206783032e-06,
                1.553497198908852e-06,
                5.422219615395428e-06,
                2.561282210618905e-06,
                3.2887478854876635e-06
            ],
            [
                1.3007126908733257e-05,
                1.892515726099468e-05,
                1.6701417853595148e-05,
                2.144494328685209e-05,
                5.144222585927004e-05,
                1.0129987354366822e-05,
                0.00017952790125438557,
                1.6701415866188347e-05,
                6.605216035177641e-05,
                7.484621779388972e-05
            ],
            [
                6.962259568648793e-06,
                6.475950297942253e-07,
                6.962258738827909e-06,
                3.726639283752725e-06,
                1.0677026154376365e-06,
                9.422444815495185e-07,
                6.144175334015912e-06,
                2.2603248365343694e-06,
                2.5612834318257725e-06,
                6.14417606659952e-06
            ],
            [
                4.222833947728508e-06,
                4.222835457595211e-06,
                1.994730434798734e-06,
                7.889260704531226e-06,
                4.785096776133645e-06,
                2.902311984989368e-06,
                1.5534983099564047e-06,
                1.5534979395798164e-06,
                1.5534983100595462e-06,
                6.475951069631906e-07
            ],
            [
                8.481105140662068e-05,
                2.1444956065331412e-05,
                3.120191508446373e-05,
                5.829124465207388e-05,
                4.785095063069508e-06,
                0.00020342694780166703,
                6.605212085976786e-05,
                0.00017952800622309288,
                4.006368256456438e-05,
                1.8925152739677025e-05
            ],
            [
                0.24508501864634827,
                0.7549149923816048,
                0.8933094152856196,
                0.29421497835151617,
                0.14804720554957732,
                0.9999417087347333,
                0.0005527787163542734,
                0.8807970826714614,
                0.3775406687981454,
                0.679178699175393
            ],
            [
                2.4300252309307336e-05,
                1.994729721396435e-06,
                1.3007134657464394e-05,
                6.962258729962979e-06,
                5.8291286249927666e-05,
                2.902313368897403e-06,
                4.2228334433617906e-06,
                3.535624609030406e-05,
                8.939693103938694e-06,
                1.3709572066982443e-06
            ],
            [
                1.67014178576052e-05,
                2.4300231994703987e-05,
                2.753569434711804e-05,
                4.006368253424943e-05,
                1.4738985479214553e-05,
                7.889261644057078e-06,
                2.1444950965906214e-05,
                4.785093352360413e-06,
                1.300712846115264e-05,
                6.962259569117366e-06
            ],
            [
                2.9023109464641985e-06,
                1.4738978452886064e-05,
                2.144495608046625e-05,
                NaN,
                0.9999930377429203,
                1.06770312455264e-06,
                6.1441738667590205e-06,
                3.726639728224814e-06,
                8.315278293899016e-07,
                6.962257909323729e-06
            ],
            [
                4.539786313856538e-05,
                0.00010889688255473898,
                4.006368729282359e-05,
                0.00037998448055936144,
                5.8291265233645785e-05,
                1.6701419825205004e-05,
                5.829124449727741e-05,
                7.484624503872184e-05,
                7.889266345584138e-06,
                4.539789017213801e-05
            ],
            [
                9.422445938557184e-07,
                1.5534973840786793e-06,
                3.28875024125221e-06,
                3.2887494572095624e-06,
                7.338208930355202e-07,
                9.422450431569214e-07,
                1.7603438426203097e-06,
                4.7850933534310035e-06,
                6.962257079275089e-06,
                2.5612819051373276e-06
            ],
            [
                0.9999038975622327,
                0.9998601779096806,
                0.9999810748450022,
                0.9999810748472489,
                0.9999957771655488,
                0.9999910602994334,
                0.9999930377437505,
                0.9999910603047628,
                0.9999646437492923,
                0.9999898700102289
            ],
            [
                7.889265402362503e-06,
                1.4738978450955768e-05,
                5.1442225851784594e-05,
                1.892515499864894e-05,
                3.12019113163268e-05,
                7.88926258381982e-06,
                1.670142780594382e-05,
                1.670142581762446e-05,
                7.889260694177436e-06,
                3.120192241767245e-05
            ],
            [
                8.939695237504067e-06,
                6.962253759157502e-06,
                6.1441760661636525e-06,
                1.147877222879974e-05,
                3.2887478889513447e-06,
                2.5612822104977725e-06,
                1.6701423831188846e-05,
                1.3007123808532309e-05,
                1.99472900796355e-06,
                4.785096776068365e-06
            ],
            [
                3.120190761845198e-05,
                2.7535687798506256e-05,
                1.4738980213341866e-05,
                7.484620899308084e-05,
                7.889264465842609e-06,
                0.00012339463347873087,
                5.4222202623972055e-06,
                4.78509563466093e-06,
                4.5397884800499855e-05,
                1.4738976689561836e-05
            ],
            [
                4.222831933564939e-06,
                5.829128634789482e-05,
                4.5397879445707534e-05,
                5.1442213617576366e-05,
                1.1478772227338172e-05,
                7.484620020860911e-05,
                0.0001584362153243275,
                7.484621677560526e-05,
                0.0002611903076886401,
                2.7535694360340682e-05
            ],
            [
                8.939699500164542e-06,
                9.422443692090534e-07,
                1.9947301970106386e-06,
                1.0129990978847043e-05,
                8.939693106020111e-06,
                1.0129989771657269e-05,
                1.892514597343433e-05,
                0.9999151889283764,
                1.0129990970260453e-05,
                1.0129989771288745e-05
            ],
            [
                NaN,
                NaN,
                0.9999687980742322,
                0.9999485577632445,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999485577805591
            ],
            [
                1.0677033791204289e-06,
                8.939699500766203e-06,
                1.5534983100920427e-06,
                1.5534971989696065e-06,
                3.7266379507909478e-06,
                1.5534983100425914e-06,
                9.422444815409489e-07,
                1.0129993394129904e-05,
                1.994730434798734e-06,
                9.422444815495185e-07
            ],
            [
                3.120192251631124e-05,
                1.3709575335919232e-06,
                8.93969310418261e-06,
                3.288747889178668e-06,
                1.0129987355564522e-05,
                1.1478765387416494e-05,
                2.902313368820854e-06,
                7.889262584809997e-06,
                5.144222577580734e-05,
                6.962253758182361e-06
            ],
            [
                4.78509506425325e-06,
                2.260324028281919e-06,
                2.43002465110435e-05,
                6.144176066051891e-06,
                7.889265405677441e-06,
                1.6701429804744246e-05,
                4.222832436587256e-06,
                3.1201903922734266e-05,
                1.6701427813417103e-05,
                2.144494328404357e-05
            ],
            [
                3.7266379507909478e-06,
                2.260323488974976e-06,
                2.1444940734059286e-05,
                1.6701417851711638e-05,
                1.0129992183070348e-05,
                5.4222196154940574e-06,
                4.785095063939907e-06,
                2.9023116389365734e-06,
                2.2603245670174926e-06,
                8.939694170062744e-06
            ],
            [
                0.9999724643089085,
                0.9999151889586936,
                0.9999945777784449,
                0.9999832985701935,
                0.9999151889485459,
                0.9997965730753162,
                0.9998766054398833,
                0.9999417087484042,
                0.9998204719483437,
                0.9999038975621606
            ],
            [
                1.8925148230890784e-05,
                2.4300252316291068e-05,
                9.610244920016838e-05,
                4.006370172916052e-05,
                5.1442213498932095e-05,
                1.6701421837705495e-05,
                6.60521761026448e-05,
                1.670142781244497e-05,
                7.889261642134126e-06,
                4.006368737677271e-05
            ],
            [
                2.7535694357535878e-05,
                1.6701419849447602e-05,
                8.939696304002375e-06,
                1.3007133114318805e-05,
                2.14449458497871e-05,
                1.8925143721072897e-05,
                2.561283126639892e-06,
                4.0063701703217896e-05,
                6.14417533430649e-06,
                2.2603251060738913e-06
            ],
            [
                0.00020342704362330194,
                3.120191877428034e-05,
                0.00012339461790178356,
                0.0007096702623434774,
                0.0002034268988431508,
                0.0002611903000053911,
                0.00026119039790413587,
                0.00013982208945273084,
                NaN,
                2.7535687767453096e-05
            ],
            [
                0.00010889687017515336,
                0.00012339454510166436,
                2.430023782222529e-05,
                0.00010889687006423939,
                4.5397852367551086e-05,
                3.120192623700302e-05,
                0.0001088969605241362,
                3.120190018524592e-05,
                3.1201907614819715e-05,
                3.120191136899467e-05
            ],
            [
                1.147876949187012e-05,
                5.144223195990727e-05,
                6.605212090542114e-05,
                2.4300243593170955e-05,
                8.481102095191198e-05,
                2.7535704183762137e-05,
                1.670142979997471e-05,
                4.006367779491416e-05,
                2.430024072471526e-05,
                1.4738988975463152e-05
            ],
            [
                1.9947306725669014e-06,
                5.422219614951598e-06,
                1.0677027426418351e-06,
                2.56128282131428e-06,
                2.260325375391425e-06,
                1.2098656834195822e-06,
                1.553497939625029e-06,
                2.26032348933062e-06,
                5.422218968595919e-06,
                1.3709568796749682e-06
            ],
            [
                1.892514823426434e-05,
                2.430023782717578e-05,
                3.2887506330851655e-06,
                1.4738987238893715e-05,
                7.889259761905808e-06,
                8.939700563248534e-06,
                2.144494328685209e-05,
                6.1441753335241615e-06,
                6.962257076628275e-06,
                4.785092781709294e-06
            ],
            [
                8.939697367492512e-06,
                1.9947306725451314e-06,
                2.902313022952668e-06,
                2.430024941804299e-05,
                1.5534971989258068e-06,
                1.2098661160788147e-06,
                1.6701423829123058e-05,
                1.2098658275740208e-06,
                1.3007134665130082e-05,
                1.7603440525205244e-06
            ],
            [
                1.8925143723000643e-05,
                2.260325375391425e-06,
                3.7266392836374875e-06,
                2.4300249408672413e-05,
                1.8925145974191664e-05,
                8.315279285205827e-07,
                6.962253759486771e-06,
                2.26032537546132e-06,
                6.962254585710433e-06,
                2.5612815998491325e-06
            ],
            [
                2.1444943292703185e-05,
                2.1444953513707305e-05,
                4.5397879408714157e-05,
                NaN,
                7.484621820011444e-05,
                2.7535704221626983e-05,
                3.120192250393883e-05,
                1.0129989768027317e-05,
                0.00010889689599276248,
                NaN
            ],
            [
                1.892515492029991e-05,
                3.535624639719312e-05,
                4.539789021837975e-05,
                1.6701419843189485e-05,
                8.481107108430372e-05,
                2.4300246519706854e-05,
                0.999975699765308,
                NaN,
                1.4738985479214553e-05,
                0.0001233945446133141
            ],
            [
                3.288749849368453e-06,
                3.288747889038086e-06,
                4.222832437497486e-06,
                5.715003788801361e-07,
                8.315280276263186e-07,
                1.3709568798956654e-06,
                1.553497198908852e-06,
                1.2098656833491588e-06,
                3.7266410608720178e-06,
                4.222835457595211e-06
            ],
            [
                0.9999810748540167,
                0.9999885212264018,
                0.9999785550490354,
                0.9999885212264015,
                0.9999756997505767,
                0.999959936317373,
                0.9999930377454107,
                0.999975699753477,
                0.9999921107402359,
                0.9999957771680661
            ],
            [
                0.9999967112497796,
                6.962255418063657e-06,
                6.962254589104433e-06,
                6.962259565520738e-06,
                1.9947306725451314e-06,
                1.8925145981833788e-05,
                1.14787708580381e-05,
                8.939697367492512e-06,
                1.4738988990369329e-05,
                1.0129992184802409e-05
            ],
            [
                2.4300234929636645e-05,
                2.430025230320762e-05,
                7.889261643382609e-06,
                NaN,
                3.535623804803683e-05,
                3.1201922514835635e-05,
                4.0063677818524845e-05,
                1.4738976691867467e-05,
                4.7850927822924614e-06,
                1.012999459934851e-05
            ],
            [
                4.785096205512581e-06,
                1.2098661161602417e-06,
                1.2098661161239298e-06,
                2.9023130229209922e-06,
                2.5612819052374947e-06,
                5.715003788933905e-07,
                1.3709576969826825e-06,
                1.994729483508644e-06,
                1.209865395009523e-06,
                1.3709568799106278e-06
            ],
            [
                1.994730196992497e-06,
                1.670142383015595e-05,
                5.422220262195015e-06,
                2.5612812946890944e-06,
                7.889263525663481e-06,
                6.96225458885115e-06,
                2.260323489024314e-06,
                7.889261642794245e-06,
                1.300712379968365e-05,
                2.260325375391425e-06
            ],
            [
                1.1478770854906172e-05,
                4.006369215458579e-05,
                1.0129988550353205e-05,
                1.4738980203985296e-05,
                5.829128633941282e-05,
                1.4738976659963988e-05,
                2.753569437266178e-05,
                3.120191504167108e-05,
                2.430023202582134e-05,
                0.0001398221069810767
            ],
            [
                1.1478765385432939e-05,
                8.939695234983602e-06,
                3.1201915067096954e-05,
                0.00010889690840404075,
                2.1444940717130123e-05,
                2.4300246508833455e-05,
                1.4738978446451746e-05,
                1.8925157260443894e-05,
                1.8925148231579266e-05,
                9.610238019419699e-05
            ],
            [
                1.012998977022003e-05,
                1.4738981968060613e-05,
                2.7535681173365028e-05,
                1.9947294834469616e-06,
                1.8925152741191683e-05,
                7.88926069905656e-06,
                4.539785234013636e-05,
                4.539789002383415e-05,
                6.962257908487893e-06,
                1.1478769487464542e-05
            ],
            [
                1.2098658276114334e-06,
                1.994730434735237e-06,
                1.2098661160612089e-06,
                1.0677024881683915e-06,
                1.760343842556269e-06,
                1.06770312455264e-06,
                9.422448185264317e-07,
                6.962253758017727e-06,
                2.5612831264675113e-06,
                6.962257079173776e-06
            ],
            [
                2.753569109034197e-05,
                1.1478764018012839e-05,
                1.14787681240737e-05,
                0.00023050671354221634,
                2.144494073796001e-05,
                5.144220737696355e-05,
                6.96225956643256e-06,
                5.829126546520442e-05,
                1.670142578341747e-05,
                1.0129995809044816e-05
            ],
            [
                1.3709570433536782e-06,
                1.5534975693347152e-06,
                7.889261643727018e-06,
                1.994730196733067e-06,
                1.370957533676711e-06,
                1.0677031244759254e-06,
                6.9622562484666964e-06,
                1.5534984952662413e-06,
                5.715005832510042e-07,
                1.0677031245186523e-06
            ],
            [
                8.481104113061569e-05,
                0.00017952805071341898,
                3.5356237990800615e-05,
                2.1444953493423506e-05,
                6.605212884380361e-05,
                0.00013982212238755054,
                2.753569763394596e-05,
                2.430024650299895e-05,
                3.1201907614819715e-05,
                2.7535697638353506e-05
            ],
            [
                8.481102092352864e-05,
                3.120191135412508e-05,
                0.0001795279213798913,
                0.0002611902111958643,
                0.0001233945451214138,
                1.6701421832054962e-05,
                1.892515048820981e-05,
                2.430023193901099e-05,
                0.001325022575112906,
                4.5397857625893214e-05
            ],
            [
                2.561282515853595e-06,
                1.8925157259824262e-05,
                3.726639283752725e-06,
                1.2098655392574583e-06,
                3.726638395215427e-06,
                5.422221554482653e-06,
                2.144495096083526e-05,
                1.2098662602861223e-06,
                8.315281267513512e-07,
                6.962253758916883e-06
            ],
            [
                4.53978575370431e-05,
                6.14417313533799e-06,
                4.222833947498071e-06,
                7.889263525103816e-06,
                1.147876401711502e-05,
                5.144221350342337e-05,
                3.2887478890769702e-06,
                1.370957697068717e-06,
                2.7535684525803696e-05,
                1.8925157263094544e-05
            ],
            [
                4.006371122853307e-05,
                7.484625386839543e-05,
                3.120190015664183e-05,
                8.481103109648735e-05,
                0.0010322308913821904,
                4.006370166036886e-05,
                0.00010889688180369276,
                2.75357041747467e-05,
                1.6701423828576233e-05,
                9.610246054140802e-05
            ],
            [
                1.8925155002022494e-05,
                3.72664017246987e-06,
                6.144176066443055e-06,
                2.9023119847359636e-06,
                6.144176066264237e-06,
                1.012998977022003e-05,
                2.9023126765777146e-06,
                5.422218969601935e-06,
                6.962254586824882e-06,
                8.939697368110433e-06
            ],
            [
                1.6701423829669885e-05,
                2.7535694333695055e-05,
                4.785096205077381e-06,
                1.1478765386038447e-05,
                2.902313368897403e-06,
                5.8291272374642915e-05,
                2.260325375615501e-06,
                1.892515500450102e-05,
                2.7535704154912737e-05,
                5.422220262333096e-06
            ],
            [
                5.829129321322935e-05,
                1.4738988994015443e-05,
                6.9622570786798724e-06,
                1.1478769492893215e-05,
                4.785095634843714e-06,
                1.1478769493331685e-05,
                2.90231163910023e-06,
                5.422221554847581e-06,
                6.9622562487453084e-06,
                1.6701419846288166e-05
            ],
            [
                2.1444940737257882e-05,
                6.962257909323729e-06,
                2.4300252308334918e-05,
                1.147876675466972e-05,
                2.9023109470871505e-06,
                1.4738978454950406e-05,
                2.5612831265630198e-06,
                6.144174601588856e-06,
                1.6701423833436905e-05,
                4.2228344511197656e-06
            ],
            [
                7.484620927188383e-05,
                0.00015843623355142708,
                5.422218968595919e-06,
                2.4300237801450912e-05,
                0.5,
                7.484624487808333e-05,
                2.1444956070012293e-05,
                0.00026119043216338555,
                7.484623604187633e-05,
                5.8291279342183934e-05
            ],
            [
                1.5534979397140412e-06,
                2.56128129423019e-06,
                2.9023123307122503e-06,
                2.260324028306588e-06,
                1.0677024879984545e-06,
                7.3382115538308e-07,
                1.209865827698362e-06,
                8.315279284755847e-07,
                2.2603245667543567e-06,
                5.422220261849814e-06
            ],
            [
                1.1478766754941153e-05,
                5.422218322940583e-06,
                1.3007126911643378e-05,
                1.6701425819447213e-05,
                5.043474562292902e-07,
                5.422220908402905e-06,
                1.3007134652353935e-05,
                7.889260703906985e-06,
                8.93969417150998e-06,
                6.962254589332388e-06
            ],
            [
                4.785093923847183e-06,
                3.1201907603241865e-05,
                4.5397868609620665e-05,
                3.535624646356141e-05,
                8.939693106020111e-06,
                3.5356259106723956e-05,
                1.892514821808506e-05,
                4.5397879256116455e-05,
                0.0001088968695065005,
                1.670142581075876e-05
            ],
            [
                6.144176058865644e-06,
                2.4300240719941574e-05,
                8.481102105680693e-05,
                0.00010889693501231766,
                0.00020342702075408075,
                1.8925157255968775e-05,
                NaN,
                0.0001233946041687204,
                7.484622712072259e-05,
                1.8925143723620274e-05
            ],
            [
                1.2098656834723998e-06,
                1.7603425836005905e-06,
                1.6701419846288166e-05,
                5.715003788933905e-07,
                1.7603436329394601e-06,
                5.4222202617511845e-06,
                2.9023112925670636e-06,
                4.785095635296322e-06,
                1.7603427934206038e-06,
                3.7266383952696564e-06
            ],
            [
                1.0129995799426358e-05,
                2.144495607640949e-05,
                2.1444948360062566e-05,
                3.7266397276757403e-06,
                6.605217614925922e-05,
                0.00013982212291039007,
                1.0129987353537646e-05,
                1.8925155003330605e-05,
                5.8291279411736364e-05,
                8.939698433145498e-06
            ],
            [
                0.9995121428840013,
                0.9999339478475265,
                4.5397884843438604e-05,
                2.7535687801010546e-05,
                5.144220739530288e-05,
                0.0001233946333728019,
                6.605216818444021e-05,
                5.829127241747701e-05,
                5.829129319796175e-05,
                7.484619997336912e-05
            ],
            [
                8.481107143601051e-05,
                2.1444940717130123e-05,
                0.00010889688298571906,
                3.120191508185304e-05,
                8.48110513393645e-05,
                0.0001795280284225444,
                6.605213668751657e-05,
                1.6701419846834993e-05,
                4.78509677368347e-06,
                3.120192621804711e-05
            ],
            [
                0.00048785722354252375,
                0.00020342692201128287,
                0.00017952790073720844,
                0.0002034269408820066,
                0.0009110512124144731,
                7.484623577341946e-05,
                0.00029595722872742883,
                0.0003799845119660543,
                0.000430557021502998,
                0.0006263341527170977
            ],
            [
                2.561282515662579e-06,
                4.5397879378987325e-05,
                3.12019225022362e-05,
                8.481104119602078e-05,
                8.481102080505906e-05,
                8.481108155405963e-05,
                5.8291258551949844e-05,
                1.4738983721733992e-05,
                6.144175332596544e-06,
                9.610243765756909e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                2.4300240706150922e-05,
                NaN,
                0.6513548511303338,
                NaN,
                NaN
            ],
            [
                0.9999756997679586,
                0.9999756997476829,
                0.9999945777810302,
                0.9999910603026303,
                0.9999869928668839,
                0.9999957771660523,
                0.9999687980849142,
                0.9999251537818369,
                0.9999151889689492,
                0.9999646437577169
            ]
        ]
    },
    {
        "q_id": "7759_mmlu_math",
        "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,
            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,
            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": [
            [
                8.315279285088606e-07,
                2.260323758835034e-06,
                4.222833444229772e-06,
                4.222834451292594e-06,
                1.209866116149238e-06,
                4.785093923847183e-06,
                4.785095064436034e-06,
                7.33821330394297e-07,
                1.2098655392574583e-06,
                3.927862938991851e-07
            ],
            [
                4.2228334438149845e-06,
                2.561282821352716e-06,
                1.9947306725868575e-06,
                2.260323489435463e-06,
                9.422442569208767e-07,
                4.450849458200093e-07,
                1.0677024881829577e-06,
                1.2098655392871682e-06,
                1.9947304348595095e-06,
                2.2603234893861252e-06
            ],
            [
                1.553498495308628e-06,
                6.144173136131494e-06,
                0.9999938558253987,
                5.422219615898437e-06,
                1.3709568799592562e-06,
                7.8892654060075e-06,
                3.7266397283231055e-06,
                2.9023130230133794e-06,
                2.561283431916622e-06,
                9.422444815679433e-07
            ],
            [
                2.26032429753354e-06,
                7.33821330394297e-07,
                6.962256249112569e-06,
                5.04347648680129e-07,
                8.939698435226916e-06,
                1.370957533676711e-06,
                8.31528325021115e-07,
                6.962253758916883e-06,
                8.315283249742262e-07,
                4.2228319339950885e-06
            ],
            [
                5.043472278280699e-07,
                6.475948753965404e-07,
                1.3709572067955008e-06,
                9.422445938964242e-07,
                6.47594566597747e-07,
                5.715003107715166e-07,
                1.553498495281783e-06,
                5.715005832827105e-07,
                4.450852111120808e-07,
                8.315282259009745e-07
            ],
            [
                7.889262585441413e-06,
                1.473898724181597e-05,
                1.76034300345598e-06,
                1.3007134665413997e-05,
                1.9947290081286418e-06,
                4.222834451327159e-06,
                1.7603425837791042e-06,
                4.539785779797843e-05,
                1.0129993394314164e-05,
                1.994729721482609e-06
            ],
            [
                7.338208055579897e-07,
                2.9023133690425823e-06,
                4.450848927637999e-07,
                1.5534984953298217e-06,
                1.7603434231385591e-06,
                2.902312677060767e-06,
                8.315283250305684e-07,
                3.726637951079042e-06,
                2.9023109471689794e-06,
                5.043476486902204e-07
            ],
            [
                2.2603245673155757e-06,
                5.043472278299047e-07,
                3.7266379513434106e-06,
                2.5612816000331606e-06,
                6.475949525919915e-07,
                1.0677031245851707e-06,
                1.3709578605355551e-06,
                7.889260704732132e-06,
                2.5612822106841303e-06,
                9.422450431954847e-07
            ],
            [
                0.999999352405279,
                0.9999997897565587,
                0.9999996940978095,
                0.9999989322968754,
                0.9999986290421395,
                0.9999986290429566,
                0.9999994284997573,
                0.9999980052709918,
                0.9999995549147889,
                0.9999996072137998
            ],
            [
                1.370956716519966e-06,
                4.7850956351657615e-06,
                1.3007134666431358e-05,
                1.7603440526133836e-06,
                1.0677033791204289e-06,
                8.315279285251204e-07,
                1.5534971988904843e-06,
                1.0677028700053041e-06,
                3.7266379512518984e-06,
                8.315280276546789e-07
            ],
            [
                9.422447062240614e-07,
                4.222831934156396e-06,
                1.2098661161982042e-06,
                1.3709568799760888e-06,
                6.144176066353646e-06,
                2.5612819053399912e-06,
                2.902313368897403e-06,
                1.3709568799760888e-06,
                1.209866116170145e-06,
                2.5612815999423112e-06
            ],
            [
                0.9999945777797377,
                0.9999921107402358,
                0.9999994284992805,
                0.9999989322966208,
                1.2098653950315304e-06,
                1.2098655392222467e-06,
                1.4738978455701077e-05,
                0.9999982396574162,
                6.475947981695877e-07,
                0.9999991684722697
            ],
            [
                1.67014158650947e-05,
                4.785096205651846e-06,
                7.889260703117714e-06,
                1.3007123809644304e-05,
                5.422220908402905e-06,
                2.5612825159421147e-06,
                1.30071346612026e-05,
                4.539786321436876e-05,
                4.222834451169694e-06,
                4.785093353274332e-06
            ],
            [
                0.9999997300421581,
                0.9999992661788445,
                0.9999996940977731,
                0.999999789756634,
                0.9999998144609644,
                0.9999992661791944,
                0.999999730042126,
                0.9999997300421903,
                0.9999993524053562,
                0.9999990577552939
            ],
            [
                3.7266379513162962e-06,
                1.147876402018431e-05,
                1.8925150494750372e-05,
                1.5534983101301911e-06,
                1.5534979397394734e-06,
                1.0129988563730593e-05,
                4.22283545808297e-06,
                1.012998977088337e-05,
                2.7535691097454142e-05,
                2.9023109471452223e-06
            ],
            [
                1.3007123807727885e-05,
                8.939694171135975e-06,
                8.939695237162584e-06,
                1.1478769493331685e-05,
                8.939698435226916e-06,
                1.147877086073156e-05,
                1.6701415867221242e-05,
                3.120191136774608e-05,
                3.5356250699942575e-05,
                0.9999687980997966
            ],
            [
                0.9999996533675028,
                0.9999997897566589,
                0.9999997617629764,
                0.9999993524050473,
                0.9999997300421903,
                0.9999992661791944,
                0.9999998144609424,
                0.9999999006880194,
                0.9999996072137061,
                0.9999997897566338
            ],
            [
                6.144172403928222e-06,
                1.3007126910294786e-05,
                0.999999352404893,
                3.2887506333812835e-06,
                5.422218969532895e-06,
                4.785093353352668e-06,
                1.2098661161602417e-06,
                0.9999996533674202,
                0.9999990577551815,
                6.144175334239434e-06
            ],
            [
                0.999999730042126,
                0.9999982396572065,
                0.9999996940977731,
                0.9999999006880194,
                0.9999996940978095,
                0.9999994956523514,
                0.9999998144608981,
                0.9999995549150011,
                0.9999998874648782,
                0.9999997300421903
            ],
            [
                3.288750633488963e-06,
                5.422217030362759e-06,
                2.4300240715698294e-05,
                1.370957533676711e-06,
                1.8925145983795953e-05,
                1.2098655392662613e-06,
                8.939698435340743e-06,
                4.222833444037741e-06,
                5.422219615582823e-06,
                2.1444940734059286e-05
            ],
            [
                4.785095635413826e-06,
                4.785092783149804e-06,
                1.8925157259824262e-05,
                2.902313368897403e-06,
                3.120190392670705e-05,
                4.539786862316288e-05,
                1.300713311517055e-05,
                1.1478770862255766e-05,
                1.6701429805655623e-05,
                8.939699498587217e-06
            ],
            [
                4.7850927830845245e-06,
                1.1478772229300848e-05,
                3.7266410608720178e-06,
                2.5612831266165976e-06,
                3.7266383954560706e-06,
                3.288748673265808e-06,
                8.939695237666677e-06,
                3.2887502412970765e-06,
                2.2603237589028734e-06,
                4.222833947820683e-06
            ],
            [
                0.9999977396765105,
                0.999999730042126,
                0.9999992661788446,
                0.9999996940976271,
                0.9999957771670589,
                0.9999984465015047,
                0.9999996940978825,
                0.9999998555019962,
                0.9999994284996891,
                0.999999730042126
            ],
            [
                7.88925976397226e-06,
                1.4738976699427788e-05,
                6.962257909501028e-06,
                8.939699500896292e-06,
                1.9947290081177566e-06,
                8.939700565834043e-06,
                5.422220908925639e-06,
                1.8925145983795953e-05,
                1.4738978457604563e-05,
                1.8925141468298646e-05
            ],
            [
                7.338208055579897e-07,
                1.2098659719601033e-06,
                2.2603251062147097e-06,
                3.726640616630245e-06,
                4.450848927599543e-07,
                1.7603434231241496e-06,
                2.902312676941983e-06,
                1.5534975693205863e-06,
                6.144173135762683e-06,
                5.043472278255469e-07
            ],
            [
                0.9999996072137998,
                0.9999999006880904,
                0.9999996940978825,
                0.9999996533675028,
                0.9999998724809267,
                0.9999998144609644,
                0.9999996533672962,
                0.9999998555019274,
                0.9999994284994167,
                0.9999998555020307
            ],
            [
                2.4300246525276163e-05,
                4.006367784956852e-05,
                0.00010889693525870529,
                1.892514598469098e-05,
                3.535624649172935e-05,
                2.5612828212909852e-06,
                3.2887478892055875e-06,
                2.1444950969026795e-05,
                2.5612815999679353e-06,
                4.222834451065997e-06
            ],
            [
                1.2098662604247682e-06,
                1.5534984953199313e-06,
                5.715005832827105e-07,
                1.0677032518209896e-06,
                4.450848927621807e-07,
                1.5534973841450852e-06,
                6.475947209918244e-07,
                9.42244930862237e-07,
                1.5534983100765009e-06,
                1.5534983101061718e-06
            ],
            [
                6.475947209953583e-07,
                3.726637951126493e-06,
                4.450851580555361e-07,
                1.5534984953298217e-06,
                8.315282259089153e-07,
                9.422445938964242e-07,
                2.260324028351814e-06,
                1.3709578605355551e-06,
                1.9947290080125335e-06,
                5.043475284430694e-07
            ],
            [
                0.9999998555019274,
                0.9999995549151073,
                0.9999996072136592,
                0.9999997617631469,
                0.9999997897566589,
                0.9999992661792819,
                0.9999998724808963,
                0.9999996533672136,
                0.9999994284996891,
                0.9999996940976272
            ],
            [
                1.06770312455264e-06,
                5.422219615967477e-06,
                3.288749849368453e-06,
                6.9622562489985925e-06,
                1.5534984953199313e-06,
                3.288748673265808e-06,
                1.994729245878497e-06,
                8.939695237666677e-06,
                1.9947306726049992e-06,
                3.2887498494282754e-06
            ],
            [
                2.260323758923431e-06,
                6.962258739454786e-06,
                2.5612816000145246e-06,
                4.785092783267308e-06,
                2.9023130227124616e-06,
                9.422450431800595e-07,
                8.315278294038928e-07,
                2.9023123309973302e-06,
                8.93969310662177e-06,
                5.422217676979575e-06
            ],
            [
                1.0677024881761599e-06,
                8.315283250260307e-07,
                1.5534981249164537e-06,
                8.315279285205827e-07,
                8.31528424151477e-07,
                7.338208930144969e-07,
                6.475947981904966e-07,
                9.422447062094932e-07,
                6.47594643788744e-07,
                5.715004470243685e-07
            ],
            [
                0.9999998362622943,
                0.9999994956524114,
                0.9999994284996893,
                0.9999980052705164,
                0.999998790134028,
                0.9999994284992805,
                0.9999991684719723,
                0.9999869928715365,
                0.9999998724809571,
                0.9999980052700408
            ],
            [
                0.0001398220404197584,
                4.0063706458587944e-05,
                0.00017952800825523456,
                0.00013982202321692388,
                6.605215246769354e-05,
                0.00017952802817440365,
                0.00013982205683325005,
                0.000108896909056849,
                4.006371122853307e-05,
                4.539786860136322e-05
            ],
            [
                0.9999810748472503,
                0.9999986290432834,
                0.9999938558224684,
                8.939698433584547e-06,
                0.9999945777810304,
                9.422443692090534e-07,
                0.9999962733620487,
                0.9999970976890528,
                0.9999980052707541,
                0.9999945777829693
            ],
            [
                1.7603436329554703e-06,
                9.422444815726566e-07,
                1.2098662604192665e-06,
                2.2603251061849014e-06,
                1.209865250822125e-06,
                5.422220908634683e-06,
                8.315281267800897e-07,
                8.939700564890901e-06,
                1.0677032518501217e-06,
                6.962259569560613e-06
            ],
            [
                9.422450431800595e-07,
                2.1024344128584085e-07,
                4.450851049959619e-07,
                3.288747889229516e-06,
                2.902312677007974e-06,
                4.450851049890802e-07,
                1.760344052693435e-06,
                6.475951069961737e-07,
                6.475946437996402e-07,
                8.3152792852928e-07
            ],
            [
                3.5356254919217684e-05,
                1.0129990979215566e-05,
                1.30071315640992e-05,
                1.760342793583908e-06,
                4.006369696286016e-05,
                4.222834954607099e-06,
                1.994729008105057e-06,
                6.962253757295868e-06,
                1.1478764018827141e-05,
                7.889264465842609e-06
            ],
            [
                1.2098658277335738e-06,
                7.338211554688417e-07,
                3.288750241204353e-06,
                4.2228344511197656e-06,
                5.715005151574337e-07,
                9.422450431954847e-07,
                4.785094494628999e-06,
                7.338208055579897e-07,
                9.422448185478557e-07,
                1.2098662604126641e-06
            ],
            [
                1.7603434230921292e-06,
                6.144177531208195e-06,
                0.9999986290427931,
                0.9999952149072167,
                3.2887494572514376e-06,
                0.9999990577549568,
                8.31528126775552e-07,
                1.0677027427471959e-06,
                9.422447061953531e-07,
                7.338209805090567e-07
            ],
            [
                1.2098662604192665e-06,
                7.338211554783522e-07,
                3.2887502411026557e-06,
                1.0677031245783732e-06,
                1.2098655392811161e-06,
                1.3709567165386693e-06,
                1.7603432132912532e-06,
                1.7603436329554703e-06,
                1.7603436329978976e-06,
                2.5612828211442287e-06
            ],
            [
                8.315277302747361e-07,
                6.96225956837018e-06,
                0.9999986290426298,
                1.9947290080125335e-06,
                5.422217030495909e-06,
                4.7850950649408664e-06,
                0.9999987901338838,
                1.9947292458930106e-06,
                0.9999991684717742,
                3.288749065209246e-06
            ],
            [
                1.7603436329978976e-06,
                6.962255419380732e-06,
                3.2887482811220126e-06,
                2.56128159999123e-06,
                1.0677031245783732e-06,
                3.726641060956752e-06,
                2.56128282131428e-06,
                1.553497384180408e-06,
                9.422447062150634e-07,
                2.902311985079115e-06
            ],
            [
                1.2098656834481918e-06,
                7.338213304243302e-07,
                8.315282258756395e-07,
                5.715004470272272e-07,
                9.422447062094932e-07,
                1.3709573702566696e-06,
                9.42244818532859e-07,
                1.2098661161107252e-06,
                9.422448185435711e-07,
                1.2098652508056196e-06
            ],
            [
                3.7266410609940346e-06,
                1.1478769493331685e-05,
                2.2603251061232293e-06,
                1.3709570433536782e-06,
                1.9947299590520376e-06,
                3.120191136774608e-05,
                3.2887506332466845e-06,
                5.4222196154940574e-06,
                7.889266346603015e-06,
                1.3007128463069061e-05
            ],
            [
                2.5612812946681295e-06,
                5.422220908703723e-06,
                1.067703251864202e-06,
                2.9023109471689794e-06,
                1.0677029973056687e-06,
                8.315279285088606e-07,
                1.9947304347570075e-06,
                1.0677029972639127e-06,
                1.300713466420736e-05,
                0.9999987901337396
            ],
            [
                0.9999996072139402,
                0.9999996072139402,
                0.9999995549151072,
                0.9999977396751634,
                0.9999996072136592,
                0.9999994956526519,
                0.9999995549151073,
                0.999999554914895,
                0.9999998555020135,
                0.9999987901344607
            ],
            [
                1.0677024881829577e-06,
                5.043472879504592e-07,
                0.9999984465024309,
                0.999999495652712,
                1.2098656835136636e-06,
                7.889264465986113e-06,
                1.0677032518700286e-06,
                1.5534977545603963e-06,
                5.715006513999389e-07,
                5.715007195410849e-07
            ],
            [
                8.315279285205827e-07,
                6.475947209953583e-07,
                5.715005151485975e-07,
                1.0677028700203557e-06,
                7.338211554688417e-07,
                1.0677028700203557e-06,
                8.315278294001114e-07,
                7.338212429504183e-07,
                5.043474081931949e-07,
                8.315279285251204e-07
            ],
            [
                1.7603436329394601e-06,
                6.47594566594213e-07,
                4.785095635413826e-06,
                1.7603430033399058e-06,
                2.561282821209454e-06,
                3.288750633518874e-06,
                0.9999996072136592,
                0.9999984465022455,
                0.9999990577549568,
                1.2098659719524008e-06
            ],
            [
                0.999996273360716,
                3.2887498493325602e-06,
                0.9999970976880148,
                3.288747889038086e-06,
                1.7603434231241496e-06,
                0.9999967112513267,
                0.9999984465016899,
                1.9947306725868575e-06,
                4.7850956351657615e-06,
                4.785093923768848e-06
            ],
            [
                7.338212429367364e-07,
                6.47594720987407e-07,
                4.2228344511197656e-06,
                0.9999980052709919,
                8.315284241257637e-07,
                1.0677026154376365e-06,
                1.2098662603862553e-06,
                9.422448185264317e-07,
                1.209865250822125e-06,
                1.0129994601872894e-05
            ],
            [
                6.144176798870286e-06,
                3.726641060658489e-06,
                1.5534977545603963e-06,
                5.715003788933905e-07,
                4.22283394786293e-06,
                1.9947301970451086e-06,
                4.785093923982095e-06,
                1.3709578605243332e-06,
                2.561283431942246e-06,
                1.7603438428188364e-06
            ],
            [
                7.889263520942206e-06,
                5.422218321855664e-06,
                8.939693101694668e-06,
                3.2887486718928972e-06,
                1.4738980205164923e-05,
                3.535623800597785e-05,
                8.93969417150998e-06,
                2.902311984318902e-06,
                4.00636969128696e-05,
                3.726638394957837e-06
            ],
            [
                0.9999994956523514,
                0.9999994284996211,
                0.9999997897566589,
                0.999999554914895,
                0.9999992661786695,
                0.9999994956527121,
                0.9999996533672962,
                0.9999996533672135,
                0.9999996940977366,
                0.9999998724809875
            ],
            [
                1.9947301970287804e-06,
                1.2098652508056196e-06,
                1.0677032518578904e-06,
                1.5534981249164537e-06,
                1.2098655392662613e-06,
                9.422444815679433e-07,
                6.47594798194325e-07,
                7.338212429420757e-07,
                1.7603425837366772e-06,
                5.043472278280699e-07
            ],
            [
                8.315277302444853e-07,
                1.2098659719441482e-06,
                1.5534971988495103e-06,
                2.5612831266165976e-06,
                1.0677029972745947e-06,
                1.2098659719441482e-06,
                6.962255419653012e-06,
                5.04347648672331e-07,
                9.42244930849811e-07,
                1.994729959270648e-06
            ],
            [
                3.726639728184142e-06,
                1.5534983101301911e-06,
                1.553498495308628e-06,
                1.994730196992497e-06,
                1.370957533625589e-06,
                2.2603251060985603e-06,
                3.7266406162269133e-06,
                1.7603432132624344e-06,
                2.26032537546132e-06,
                2.2603248366762157e-06
            ],
            [
                0.9999996072136125,
                0.9999997617630616,
                0.9999997300422547,
                0.9999992661790195,
                0.9999995549150542,
                0.999999730042319,
                0.999999814460876,
                0.9999996072138934,
                0.9999995549148419,
                0.9999997617630049
            ],
            [
                1.209865827740176e-06,
                1.3709567165461505e-06,
                6.475947209985977e-07,
                1.5534975693792215e-06,
                1.209865539274514e-06,
                2.9023130230846496e-06,
                5.422220262264056e-06,
                3.288749849060371e-06,
                6.475951069932288e-07,
                0.9999984465020603
            ],
            [
                2.9023133690637e-06,
                2.4300240719941574e-05,
                2.5612834320214477e-06,
                7.889260704631679e-06,
                2.902313023063532e-06,
                4.785094494672519e-06,
                6.14417313680765e-06,
                2.2603234895176927e-06,
                1.4738987240824012e-05,
                2.1444953522913026e-05
            ],
            [
                0.9999993524050474,
                0.9999994956527721,
                0.9999982396563669,
                0.9999986290427932,
                0.9999987901343165,
                0.9999992661792819,
                0.9999993524053563,
                0.9999992661786696,
                0.9999990577555185,
                0.9999986290424664
            ],
            [
                0.999978555054148,
                0.9999991684720715,
                0.9999980052702786,
                0.9999991684718733,
                0.9999991684715759,
                0.999998446502801,
                0.9999910603058293,
                0.9999997897567341,
                0.9999991684718732,
                0.9999962733607158
            ],
            [
                0.9999996533672962,
                0.9999998144608981,
                0.9999999123574941,
                0.9999998724809115,
                0.9999997617630899,
                0.9999994956525317,
                0.9999997617630332,
                0.99999976176309,
                0.9999997897566589,
                0.9999997617631184
            ],
            [
                2.561282515886208e-06,
                1.5534984952111384e-06,
                4.7850933535659155e-06,
                3.726637951028202e-06,
                3.288749065167371e-06,
                1.994729483680993e-06,
                4.222834954280646e-06,
                1.0677024881829577e-06,
                1.5534983100595462e-06,
                7.338210679909462e-07
            ],
            [
                3.288748281220719e-06,
                8.315282258832022e-07,
                9.422444815628016e-07,
                6.144172404520556e-06,
                1.3709570433786157e-06,
                1.9947297213746646e-06,
                5.043474683156057e-07,
                2.5612828212909852e-06,
                1.5534979397500702e-06,
                1.5534975693488444e-06
            ],
            [
                5.715007195410849e-07,
                8.315284241560147e-07,
                2.5612825160271407e-06,
                7.889265406151004e-06,
                2.260324567302214e-06,
                8.939698435340743e-06,
                2.5612831266608576e-06,
                2.902313022984344e-06,
                7.338213304283347e-07,
                6.144176065828368e-06
            ],
            [
                0.999999266179107,
                0.9999998555020135,
                0.999999789756684,
                0.9999998362623332,
                0.9999997897567091,
                0.9999991684722698,
                0.9999996533675028,
                0.999999554914895,
                0.9999996940978825,
                0.9999990577549568
            ],
            [
                5.422221554847581e-06,
                0.9999989322966208,
                6.144174601097106e-06,
                9.422450431912e-07,
                7.338208055613267e-07,
                1.0677033791204289e-06,
                0.9999970976873229,
                4.222832940834793e-06,
                1.7603425837494853e-06,
                2.902311985079115e-06
            ],
            [
                2.1444945852673643e-05,
                7.484626266158608e-05,
                6.605216817867347e-05,
                4.7850950648799385e-06,
                3.535623803273096e-05,
                5.829129330398681e-05,
                6.9622562492265485e-06,
                1.6701421840318107e-05,
                1.0129987354882753e-05,
                6.962253759271479e-06
            ],
            [
                9.422450431954847e-07,
                2.2603237588597026e-06,
                5.715003107715166e-07,
                2.2603242977555607e-06,
                1.2098662604049616e-06,
                1.9947297214182054e-06,
                1.5534971989809095e-06,
                1.553498495308628e-06,
                2.9023123310290063e-06,
                8.315279285149107e-07
            ],
            [
                7.889262585541864e-06,
                5.422220908703723e-06,
                7.338208055536515e-07,
                3.7266397281434697e-06,
                8.939695238536645e-06,
                1.99472900813862e-06,
                2.9023126769762986e-06,
                1.0129990979547237e-05,
                6.144174601410037e-06,
                1.1478765389065974e-05
            ],
            [
                0.9999910603068956,
                0.9999910603005017,
                0.9999930377412649,
                0.9999724643023419,
                0.9999832985761699,
                0.9999646437544448,
                0.9999974387174846,
                0.9820137916828761,
                0.9999970976890529,
                0.9933071492583639
            ],
            [
                3.120192252686752e-05,
                1.7603432133136672e-06,
                4.7850944943330625e-06,
                6.962257079376403e-06,
                6.144175334172377e-06,
                1.6701425824307884e-05,
                1.1478765388314311e-05,
                4.785095065093186e-06,
                1.1478764019996392e-05,
                1.6701423830702777e-05
            ],
            [
                0.9999996533673375,
                0.9999962733607162,
                0.9999977396751634,
                0.9999980052709921,
                0.9999967112513268,
                0.99999893229713,
                0.9999991684722698,
                0.9999945777784451,
                0.9999977396762412,
                0.9999984465024306
            ],
            [
                3.5356250691324983e-05,
                0.9999151889891026,
                0.9978172831865045,
                0.9999417087067002,
                0.9971990733990064,
                2.1444948408275583e-05,
                2.144495096083526e-05,
                3.726640616670918e-06,
                0.9999339478238921,
                0.9999038975967038
            ],
            [
                0.999998790134605,
                0.9999996940976636,
                0.999999352405279,
                0.9999996533672962,
                0.9999994284992805,
                0.9999992661792819,
                0.9999994284996211,
                0.9999994284995529,
                0.9999997897566089,
                0.999997438716568
            ],
            [
                0.9999997897566089,
                0.9999990577550691,
                0.9999994284997573,
                0.9999987901337396,
                0.9999991684717741,
                0.9999984465022455,
                0.9999997617631468,
                0.9999997300422868,
                0.9999996072137061,
                0.9999996072136592
            ],
            [
                1.2098661161982042e-06,
                1.3007123811229494e-05,
                7.889265406904397e-06,
                0.9999990577554061,
                1.5534979397592542e-06,
                1.0677032518700286e-06,
                2.260324567302214e-06,
                6.475947981904966e-07,
                5.422221555192784e-06,
                2.2603234895053587e-06
            ],
            [
                1.2098656834922064e-06,
                1.9947290080905435e-06,
                0.9999945777784447,
                0.9999989322975118,
                6.144173134522134e-06,
                0.9999977396759716,
                1.0129992185539456e-05,
                0.9999810748562722,
                3.2887478891487563e-06,
                1.7603427935678977e-06
            ],
            [
                3.2887502415243994e-06,
                1.0677024881829577e-06,
                5.043474081993875e-07,
                2.5612828212909852e-06,
                3.288747889178668e-06,
                1.067702615468225e-06,
                0.999993855825398,
                5.715003107738556e-07,
                1.3709576970949014e-06,
                0.9999980052700408
            ],
            [
                3.7266397283231055e-06,
                3.7266392839425286e-06,
                1.3007131564383116e-05,
                2.561282515988704e-06,
                8.93969950101825e-06,
                1.6701423833011596e-05,
                4.006369694755693e-05,
                1.3007123812767362e-05,
                2.902312331081799e-06,
                3.288749457383046e-06
            ],
            [
                1.209865250822125e-06,
                2.260324836696773e-06,
                4.785096775998733e-06,
                3.726638395493353e-06,
                4.785092783319532e-06,
                1.994729721482609e-06,
                7.889263525663481e-06,
                9.422448185388577e-07,
                8.315282259089153e-07,
                6.962255419380732e-06
            ],
            [
                0.999999855502048,
                0.9999997897567091,
                0.9999996533672549,
                0.9999995549151073,
                0.9999992661788445,
                0.9999997300422547,
                0.999999694097846,
                0.9999997897566589,
                0.9999994284992805,
                0.9999997300422547
            ],
            [
                1.2098659719601033e-06,
                1.067703251864202e-06,
                6.475950297942253e-07,
                7.338212429367364e-07,
                3.288748673265808e-06,
                1.76034300345598e-06,
                1.3709567165087443e-06,
                1.7603425837366772e-06,
                1.9947306725868575e-06,
                5.04347408197782e-07
            ],
            [
                3.726639728224814e-06,
                2.9023109470871505e-06,
                7.48462002984577e-05,
                7.484621828887399e-05,
                2.144495352533148e-05,
                1.1478770859332632e-05,
                2.1444958636771547e-05,
                4.22283394762097e-06,
                1.994729721436347e-06,
                2.9023133689924295e-06
            ],
            [
                1.5534981249397663e-06,
                6.475948753930064e-07,
                6.144176066264237e-06,
                7.338208055436404e-07,
                3.2887490652810324e-06,
                5.043472879525233e-07,
                4.785093353626844e-06,
                1.0677029972993568e-06,
                5.715003107738556e-07,
                3.4663257978465195e-07
            ],
            [
                3.2887498493325602e-06,
                2.260324567268294e-06,
                1.370957370247318e-06,
                7.88926258532661e-06,
                6.475946438022905e-07,
                4.222832940942332e-06,
                1.1478772228256871e-05,
                6.475951069896949e-07,
                9.422450431954847e-07,
                9.422447062240614e-07
            ],
            [
                2.9023123310580418e-06,
                8.31528424151477e-07,
                3.2887502413389517e-06,
                1.7603425837062577e-06,
                3.726641061027928e-06,
                5.71500242637956e-07,
                9.422447062202052e-07,
                1.994729483694599e-06,
                1.0677024881941248e-06,
                4.785096205930373e-06
            ],
            [
                9.422442569208767e-07,
                1.9947299592570416e-06,
                1.7603432132784448e-06,
                1.370956879949281e-06,
                8.939693104865575e-06,
                1.2098653950403334e-06,
                9.422447062094932e-07,
                1.067703379154416e-06,
                1.994730672439908e-06,
                3.2887486732000038e-06
            ],
            [
                6.47594798194325e-07,
                9.422442569097361e-07,
                6.475947981860793e-07,
                1.2098658277181688e-06,
                1.0677024881683915e-06,
                8.315280276338815e-07,
                8.315280276505193e-07,
                8.315280276263186e-07,
                6.475947209918244e-07,
                1.7603440526133836e-06
            ],
            [
                0.9999990577554062,
                0.9999993524049703,
                0.9999989322968754,
                0.9999996072138465,
                0.9999997897567091,
                0.9999996072139402,
                0.9999992661787571,
                0.9999990577549569,
                0.9999996072137061,
                0.9999996940976636
            ],
            [
                0.9999991684722698,
                0.999997739675442,
                0.9999997300421903,
                0.999999789756634,
                0.9999992661789321,
                0.9999996533672549,
                0.9999962733611809,
                0.9999852610232999,
                0.9947798731070533,
                0.9902915251123275
            ],
            [
                0.9999996533672135,
                0.9999982396569966,
                0.9999990577551815,
                0.9999997300420937,
                0.9999997617630048,
                0.9999996072137529,
                0.9999996533673375,
                0.9999998144609202,
                0.999999730042126,
                0.9999995549148419
            ],
            [
                2.4300252310279753e-05,
                1.1478768125201194e-05,
                4.785092783371756e-06,
                1.7603430034743913e-06,
                1.8925150493166868e-05,
                1.4738981970956057e-05,
                1.3007134665674251e-05,
                6.144172404520556e-06,
                6.962257079553702e-06,
                1.6701419850845044e-05
            ],
            [
                2.902313023039776e-06,
                0.9999993524053562,
                5.043474081931949e-07,
                1.3709570433885908e-06,
                1.3709567165386693e-06,
                9.422445939002803e-07,
                7.889264465699106e-06,
                1.4738978452886064e-05,
                3.288749849368453e-06,
                6.144172403715875e-06
            ],
            [
                7.338208055579897e-07,
                5.715007195353674e-07,
                3.2887482811908074e-06,
                2.260325375664839e-06,
                1.5534983101301911e-06,
                8.315279285205827e-07,
                3.288749849368453e-06,
                6.1441753337365085e-06,
                1.994730434816876e-06,
                1.760342793583908e-06
            ],
            [
                1.0677028700266676e-06,
                8.315277302747361e-07,
                1.3709575335919232e-06,
                1.0677033791437343e-06,
                5.043473480730849e-07,
                2.561281905058126e-06,
                6.475945666009864e-07,
                2.5612825160096693e-06,
                1.9947299592570416e-06,
                2.260324028372372e-06
            ],
            [
                0.9999921107345932,
                0.9999991684715759,
                0.9999998555020135,
                0.9999938558239332,
                0.9999910603058275,
                0.9999967112501504,
                0.9999910603026306,
                0.9999938558239333,
                0.9999724643187701,
                0.9999994284996211
            ],
            [
                0.9999996533672549,
                0.999999789756684,
                0.9999995549147358,
                0.9999996072138465,
                0.9999997897566338,
                0.9999996533673788,
                0.9999994284992805,
                0.9999998362623723,
                0.9999996533674201,
                0.9999998144609645
            ],
            [
                2.5612825156159896e-06,
                6.962255419475714e-06,
                2.561282210460501e-06,
                3.288749849368453e-06,
                1.7603440525461408e-06,
                7.889265405849647e-06,
                1.3709578605355551e-06,
                1.3709578605355551e-06,
                4.2228349546493465e-06,
                1.9947304348332037e-06
            ],
            [
                0.9999945777784449,
                0.999995777165549,
                0.999995214903224,
                0.9999921107345939,
                0.9998911031298375,
                0.9999977396757022,
                0.9999910603068956,
                0.9999910603047621,
                0.9999984465015047,
                0.9999952149049349
            ],
            [
                2.9023133690425823e-06,
                2.902313022984344e-06,
                1.3709576971242028e-06,
                2.5612819053399912e-06,
                1.0677027427413698e-06,
                1.7603427935967163e-06,
                1.3007133114602719e-05,
                7.889260703906985e-06,
                5.422220908560712e-06,
                2.561281599881745e-06
            ],
            [
                2.260323489435463e-06,
                1.4738987238464762e-05,
                2.2603234893861252e-06,
                2.5612819053586272e-06,
                1.9947304348332037e-06,
                9.422448185388577e-07,
                4.222834451292594e-06,
                2.260324028372372e-06,
                1.0677033791437343e-06,
                1.7603436329714805e-06
            ],
            [
                0.9999962733589389,
                9.422449308566668e-07,
                0.9999990577554061,
                0.9999984465015047,
                0.9999957771660521,
                0.9999885212346113,
                0.9999980052705163,
                0.9999982396559473,
                5.422219615967477e-06,
                0.9999977396757022
            ],
            [
                1.9947306725868575e-06,
                1.7603430033799313e-06,
                1.3709578605355551e-06,
                1.9947301970287804e-06,
                1.3709578605243332e-06,
                2.2603245672025095e-06,
                2.2603234894560207e-06,
                2.2603242977802297e-06,
                1.5534975693601474e-06,
                2.902311984952413e-06
            ],
            [
                0.9999998144609423,
                0.9999995549151073,
                0.9999997897565587,
                0.9999998362622942,
                0.9999997617631752,
                0.9999999006880312,
                0.9999997897567091,
                0.9999994956527121,
                0.9999997617630616,
                0.9999997300420937
            ],
            [
                1.760344052650207e-06,
                2.5612828212909852e-06,
                1.5534975693347152e-06,
                1.3709567164139816e-06,
                6.144176065314267e-06,
                1.7603438427660027e-06,
                1.20986611609532e-06,
                1.994730672305658e-06,
                9.422444815495185e-07,
                1.1478770861441461e-05
            ],
            [
                0.9999996072138465,
                0.9999997300421581,
                0.9999996533674202,
                0.9999996533673788,
                0.9999997617630616,
                0.9999995549151073,
                0.9999989322970027,
                0.9999991684721706,
                0.9999996940978825,
                0.9999997300421581
            ],
            [
                0.9999998362622942,
                0.999999887464744,
                0.9999998362623528,
                0.9999998555019962,
                0.999999855501979,
                0.9999998724809875,
                0.9999998874648245,
                0.9999999006880549,
                0.9999999397642365,
                0.9999997897565838
            ],
            [
                6.475947981975644e-07,
                9.422447062150634e-07,
                4.222835457852533e-06,
                1.3709573702647743e-06,
                1.5534983101393749e-06,
                5.715005151574337e-07,
                8.3152792852928e-07,
                1.370957533676711e-06,
                6.47594952595231e-07,
                5.715002426410745e-07
            ],
            [
                1.7603440526806268e-06,
                4.222834954607099e-06,
                4.450848927621807e-07,
                8.315282259051341e-07,
                1.7603430034439723e-06,
                1.0677027427525368e-06,
                0.9999980052695652,
                2.9023109471689794e-06,
                0.9999991684718732,
                6.475946437996402e-07
            ],
            [
                0.999981074845,
                0.9998766054116668,
                0.9999339478241318,
                0.9994472213309504,
                0.9999687980812632,
                0.9999599362935414,
                0.999841563746375,
                0.9995694428805729,
                0.9999038975852612,
                0.9999952149072197
            ],
            [
                8.31528424151477e-07,
                2.561281599881745e-06,
                3.7266392839832006e-06,
                1.5534981249164537e-06,
                1.7603438428460541e-06,
                3.2887506333812835e-06,
                4.222831934052698e-06,
                1.7603425837062577e-06,
                6.962257908487893e-06,
                1.3709578605542582e-06
            ],
            [
                2.5612819053399912e-06,
                1.370956716529941e-06,
                1.209866116149238e-06,
                5.715003788993679e-07,
                1.3709567165087443e-06,
                1.5534981249496567e-06,
                1.2098655392811161e-06,
                5.715005151574337e-07,
                1.994730434816876e-06,
                2.561281599914358e-06
            ],
            [
                8.939697366793286e-06,
                3.2887482811579057e-06,
                3.535623805163821e-05,
                1.5534981249023245e-06,
                2.144494074076854e-05,
                2.260324028281919e-06,
                1.5534971989809095e-06,
                1.473898548194914e-05,
                4.785096205778054e-06,
                2.9023126769762986e-06
            ],
            [
                1.3709572068272963e-06,
                5.715005151400212e-07,
                1.9947304348332037e-06,
                2.561283431916622e-06,
                0.9999989322971299,
                6.1441746016670885e-06,
                1.9947297214944016e-06,
                1.2098662604126641e-06,
                1.2098662604126641e-06,
                4.222832940777184e-06
            ],
            [
                0.9999989322973846,
                4.222831934156396e-06,
                0.9999986290432834,
                4.222834450950777e-06,
                0.9999996533672549,
                7.338207180761315e-07,
                1.2098662603862553e-06,
                0.9999984465020603,
                0.9999989322967481,
                0.9999987901341723
            ],
            [
                1.1478769490387674e-05,
                2.260323758835034e-06,
                4.539787945792856e-05,
                2.4300243622255085e-05,
                2.1444956079842134e-05,
                1.892515500663531e-05,
                5.422219615829396e-06,
                7.484625397240209e-05,
                6.144176796601534e-06,
                1.4738978453743973e-05
            ],
            [
                2.260324836696773e-06,
                1.3709567165087443e-06,
                2.561282210701601e-06,
                1.209865250822125e-06,
                3.2887494572514376e-06,
                1.5534973841592143e-06,
                5.4222202623972055e-06,
                7.889264466115267e-06,
                4.222832437186393e-06,
                4.785096776194573e-06
            ],
            [
                2.7535697658087296e-05,
                8.93969950101825e-06,
                5.144221975264518e-05,
                1.0129992187253088e-05,
                1.5534979397267575e-06,
                4.7850967763512445e-06,
                1.4738980210687712e-05,
                2.260323758835034e-06,
                1.9947304348332037e-06,
                5.422220262264056e-06
            ],
            [
                0.999999855502048,
                0.9999998362623528,
                0.9999997617630049,
                0.9999997617630616,
                0.9999998144609423,
                0.9999998724809267,
                0.9999997617631468,
                0.9999998874647709,
                0.9999996533672548,
                0.9999997897565838
            ],
            [
                0.9999999317439627,
                0.9999999123575045,
                0.9999999317439546,
                0.9999997300422547,
                0.9999997897565587,
                0.9999997617631752,
                0.9999998555020307,
                0.9999998874647976,
                0.999999694097846,
                0.9999999006880904
            ]
        ]
    },
    {
        "q_id": "8992_mmlu_math",
        "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,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            35,
            36,
            37,
            39,
            40,
            41,
            42,
            47,
            48,
            49,
            50,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            61,
            62,
            63,
            64,
            65,
            68,
            69,
            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,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            115,
            116,
            117,
            118,
            119,
            121,
            122,
            123,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.000261190339880772,
                0.0008040861216189398,
                0.7772998611746911,
                0.679178699175393,
                0.0017007222758450467,
                0.07585817793199001,
                3.5356250691324983e-05,
                1.1478764015361142e-05,
                0.00037998452243495244,
                4.5397852361605714e-05
            ],
            [
                8.481107160692766e-05,
                0.00013982210726385758,
                0.0002959571345668173,
                5.8291251595862005e-05,
                0.00017952805017795734,
                2.1444958633416914e-05,
                9.610239198289712e-05,
                6.605212890195146e-05,
                2.7535691098355687e-05,
                0.00023050671463547068
            ],
            [
                0.9999945777790911,
                0.00012339455973421916,
                0.00015843627314529571,
                0.9988304895754285,
                0.9999724643089007,
                0.0002959570282562076,
                0.9999546021475895,
                0.9999687980960685,
                0.00012339456011664052,
                0.9999962733593831
            ],
            [
                7.484624498426811e-05,
                0.00023050682493345987,
                0.00023050679762891778,
                0.9999921107383548,
                0.0002959570640432513,
                0.9999982396567867,
                0.00010889696117932149,
                0.0007096703739617149,
                5.1442195225848094e-05,
                4.006367785525258e-05
            ],
            [
                2.430023202688216e-05,
                1.1478766756214804e-05,
                6.605212099816935e-05,
                1.670142582254589e-05,
                5.422217676797111e-06,
                2.4300232029003796e-05,
                6.605217603921075e-05,
                2.4300246524568948e-05,
                9.610246058755327e-05,
                1.8925141468298646e-05
            ],
            [
                0.00010889694799084654,
                5.144219521911119e-05,
                1.670141786036971e-05,
                9.610243781907736e-05,
                6.605212891684883e-05,
                0.00010889690917726991,
                5.1442219768738885e-05,
                1.473898372822193e-05,
                8.481106149875219e-05,
                1.1478768122069266e-05
            ],
            [
                1.4738988995838502e-05,
                6.605214449759119e-05,
                5.1442213588757405e-05,
                7.889265406294507e-06,
                2.4300232039788792e-05,
                6.144174601410037e-06,
                2.1444945853375776e-05,
                5.144221973879711e-05,
                5.829128636782753e-05,
                2.7535687803514833e-05
            ],
            [
                0.0001398221240089635,
                0.000108896948112852,
                4.539786862811735e-05,
                0.0002305067141860962,
                0.0001233946336474991,
                2.144494585197151e-05,
                3.1201900209877224e-05,
                0.000261190246663434,
                6.605213675960068e-05,
                9.610242634499809e-05
            ],
            [
                7.484623609796368e-05,
                5.1442207526298114e-05,
                7.484620938678116e-05,
                7.484624505832518e-05,
                0.00010889687030508116,
                3.535626756251187e-05,
                1.473898197063434e-05,
                0.00017952798700133205,
                0.0001233946190203218,
                5.8291286375037224e-05
            ],
            [
                6.605216040319643e-05,
                5.8291286355952725e-05,
                5.144220137700842e-05,
                5.829125856424875e-05,
                0.0001233946336133864,
                9.610246072738731e-05,
                2.430023493865361e-05,
                4.539786863059458e-05,
                4.539786321436876e-05,
                4.0063711246896956e-05
            ],
            [
                0.00033535026848478935,
                0.00013982209055944157,
                2.7535697660090726e-05,
                1.3007126912542439e-05,
                0.00012339463372649704,
                5.829125844846945e-05,
                9.61024034059329e-05,
                0.0010322308041106052,
                0.0001584362545816345,
                0.00017952805142388512
            ],
            [
                0.0003353500691944056,
                0.00010889689621142153,
                0.0002611904021219448,
                2.1444948407573453e-05,
                0.0002611904319429955,
                6.60521524840326e-05,
                5.8291272451829125e-05,
                9.610246059873997e-05,
                5.144221975938208e-05,
                0.00012339463354695633
            ],
            [
                4.006370170554982e-05,
                2.1444945853999886e-05,
                2.144494073569759e-05,
                8.939693104637921e-06,
                5.1442219765744705e-05,
                1.2098662604126641e-06,
                5.829124461687359e-05,
                3.535625070920327e-05,
                1.4738985483128763e-05,
                6.962258738827909e-06
            ],
            [
                4.539785776395774e-05,
                1.4738985479214553e-05,
                5.422218968931258e-06,
                3.535625070778844e-05,
                1.8925152750692706e-05,
                0.00013982209034176134,
                0.00020342692356213902,
                6.962259568078904e-06,
                3.7266392840781026e-06,
                1.892514146884943e-05
            ],
            [
                2.7535684532815695e-05,
                6.144175334094145e-06,
                0.00010889696107712208,
                6.605216826661615e-05,
                4.539785239661729e-05,
                1.4738985485997396e-05,
                0.0001233945601004819,
                0.00013982209042924033,
                0.00012339457475817416,
                1.8925148239772175e-05
            ],
            [
                3.120192624846737e-05,
                0.022977369115535207,
                0.00020342699714494958,
                0.982013792242165,
                0.9890130589784811,
                0.9980732655679295,
                1.209865539274514e-06,
                1.3007130012980722e-05,
                0.00023050663267494372,
                0.9890130595654391
            ],
            [
                3.120190763491069e-05,
                9.610240346745984e-05,
                0.00015843615991460315,
                7.484620927188383e-05,
                6.605216824066585e-05,
                0.00015843627325363947,
                0.00015843623554541244,
                0.0001795279441800938,
                0.0001795279444569665,
                2.430023203740195e-05
            ],
            [
                1.6701425824733193e-05,
                0.00012339453024827647,
                4.006368740052914e-05,
                6.605216034600967e-05,
                9.610241479471069e-05,
                6.605216829064421e-05,
                5.144221359998557e-05,
                7.484625400997517e-05,
                0.00010889690926520891,
                1.4738980213341866e-05
            ],
            [
                3.120191135991401e-05,
                0.9999151889890187,
                0.00017952802897890205,
                4.0063706476368846e-05,
                0.00020342706955280511,
                4.5397884859458064e-05,
                6.605217612907568e-05,
                0.00013982207378789255,
                0.00017952798727559279,
                4.539785238406597e-05
            ],
            [
                3.726640616670918e-06,
                4.539787403691212e-05,
                2.753570091316123e-05,
                3.120190020613144e-05,
                2.4300232040584407e-05,
                6.6052121039017e-05,
                1.8925145981283003e-05,
                4.539788482296012e-05,
                6.96225541916544e-06,
                6.605212890675706e-05
            ],
            [
                0.00010889690894276599,
                5.829124465589078e-05,
                3.535624226936835e-05,
                9.610239204372489e-05,
                6.605212102411961e-05,
                8.481105133072609e-05,
                2.7535684534618784e-05,
                0.00012339460415256175,
                2.7535681242383173e-05,
                0.00012339458948050277
            ],
            [
                0.00020342692455362147,
                0.00010889693504083841,
                0.00010889687012128086,
                0.0002305067971996644,
                NaN,
                3.535625070624499e-05,
                0.00013982208969075504,
                9.610238036479439e-05,
                0.00020342694862148994,
                0.0011695101003720164
            ],
            [
                2.7535700941409604e-05,
                2.43002378338943e-05,
                5.144221971634078e-05,
                0.00020342690014243665,
                5.829124465207388e-05,
                4.0063696955427154e-05,
                4.539786321436876e-05,
                3.5356254902111115e-05,
                NaN,
                3.5356246476937965e-05
            ],
            [
                0.00029595699209028725,
                0.0006263341603683661,
                3.5356250704701545e-05,
                7.484626277430532e-05,
                5.1442195242316055e-05,
                5.8291286335171815e-05,
                0.00013982207393843773,
                7.484624508881928e-05,
                3.535625913514915e-05,
                0.00012339455986169293
            ],
            [
                2.4300252316291068e-05,
                3.120190765193695e-05,
                7.484621834387223e-05,
                3.120191136649749e-05,
                3.120192252800261e-05,
                6.605213673845602e-05,
                8.481108180210549e-05,
                4.5397863235342677e-05,
                0.00013982214048349683,
                1.6701417861189946e-05
            ],
            [
                5.144223816721283e-05,
                4.006369693473136e-05,
                4.006367784956852e-05,
                0.0001233945601004819,
                8.481106150677358e-05,
                0.00023050671480314775,
                0.00012339463353079768,
                1.670141985166528e-05,
                5.8291251603919903e-05,
                0.00013982214077238095
            ],
            [
                5.144220138599094e-05,
                4.539786321436876e-05,
                7.484624506431508e-05,
                2.4300243627117176e-05,
                3.120190020613144e-05,
                5.144221365519071e-05,
                9.610242636527403e-05,
                4.0063711272110856e-05,
                7.484622722854095e-05,
                5.144220136428317e-05
            ],
            [
                0.9999921107383547,
                0.0001398220907038836,
                0.9999910602994333,
                0.0013250226311865762,
                0.9999646437408576,
                0.00017952794435509826,
                0.0002959569934422037,
                0.9999810748472471,
                0.9999930377412604,
                0.00013982209060012945
            ],
            [
                5.14422381473764e-05,
                2.430024362999023e-05,
                8.939699500766203e-06,
                8.939695233292452e-06,
                NaN,
                2.1444940741392653e-05,
                1.147876675548402e-05,
                NaN,
                4.0063692183734794e-05,
                2.430025231213619e-05
            ],
            [
                9.610238030606413e-05,
                5.829126544654401e-05,
                4.0063711283916205e-05,
                1.3007125359034903e-05,
                NaN,
                0.0001398220572747136,
                4.0063711285810896e-05,
                0.00020342689918055078,
                4.006368260814213e-05,
                8.481105135664132e-05
            ],
            [
                9.610240323743297e-05,
                1.3007134656943884e-05,
                2.430025231213619e-05,
                1.892515500808112e-05,
                2.1444945852673643e-05,
                0.00010889688327092647,
                4.539785239182798e-05,
                0.00026119021432692016,
                0.00010889696117932149,
                6.605214448461604e-05
            ],
            [
                1.8925157259824262e-05,
                1.4738976700366126e-05,
                1.6701421842566163e-05,
                0.00010889690908378526,
                1.1478772229300848e-05,
                5.829126552754713e-05,
                4.006370173105521e-05,
                4.5397890257685224e-05,
                5.82912516276695e-05,
                0.00017952794385881705
            ],
            [
                7.889260704423598e-06,
                1.9947297215043796e-06,
                5.715003788993679e-07,
                2.7535704228438656e-05,
                1.0677032518700286e-06,
                2.1444956075707356e-05,
                2.1444945855248125e-05,
                2.9023126771227976e-06,
                2.753568453191415e-05,
                8.315284241597959e-07
            ],
            [
                1.8925155001402863e-05,
                0.00010889693508045057,
                0.00012339453076894396,
                8.481107156496966e-05,
                5.8291286317783706e-05,
                5.829127939562056e-05,
                3.1201918798457626e-05,
                2.7535704226635563e-05,
                3.1201922530272776e-05,
                4.0063682630732606e-05
            ],
            [
                2.1444948407573453e-05,
                2.561282821209454e-06,
                2.2603242978007868e-06,
                1.670142980726572e-05,
                1.6701415866188347e-05,
                8.93970056668775e-06,
                6.144176066443055e-06,
                2.561281600049467e-06,
                4.785092783454444e-06,
                1.8925150489517924e-05
            ],
            [
                0.0008040858585115657,
                0.00010889693517235078,
                0.00012339453075278531,
                2.1444956079218013e-05,
                0.00013982205714654678,
                1.3007126913583456e-05,
                5.8291279438030564e-05,
                4.0063696941289896e-05,
                9.610240352619009e-05,
                8.481108174842393e-05
            ],
            [
                0.9999982396572065,
                5.8291279365509446e-05,
                6.144177531532303e-06,
                4.0063706508432764e-05,
                3.5356246493272806e-05,
                0.00017952800832575876,
                0.0001584362163363038,
                2.7535694380675497e-05,
                3.1201922523121745e-05,
                0.00010889692202111441
            ],
            [
                0.00015843619767583143,
                1.3007134665130082e-05,
                0.00010889692212885947,
                9.610239195213367e-05,
                1.6701421837158667e-05,
                7.889266345397582e-06,
                8.481101083448713e-05,
                1.473898548194914e-05,
                5.8291258547708845e-05,
                8.481104098931598e-05
            ],
            [
                9.610239195213367e-05,
                0.00012339457465583602,
                0.00013982202384351717,
                3.5356242262551455e-05,
                0.0001088968833327214,
                0.0001584362546323486,
                5.1442207499350526e-05,
                7.484624504525627e-05,
                0.0002305066315012048,
                0.00010889692212885947
            ],
            [
                1.6701419848961534e-05,
                0.0001233945894966614,
                3.120192623972722e-05,
                2.7535691095550887e-05,
                2.4300249416363357e-05,
                2.430023203572232e-05,
                0.000261190401985151,
                3.120191880867338e-05,
                0.0002305067141860962,
                0.00013982210684477224
            ],
            [
                4.006367785525258e-05,
                0.0005527786102001648,
                8.93969630348202e-06,
                1.6701421844085127e-05,
                0.00023050665948314234,
                3.535626754900668e-05,
                3.535623805819787e-05,
                2.4300243618542217e-05,
                1.1478772229050293e-05,
                3.535624649468763e-05
            ],
            [
                5.82912515827149e-05,
                1.8925145983348442e-05,
                8.48110109406161e-05,
                5.144223816721283e-05,
                4.5397884864412536e-05,
                8.481101102761719e-05,
                1.8925148236674017e-05,
                4.539786321436876e-05,
                2.5612819053586272e-06,
                6.144173136556186e-06
            ],
            [
                0.0001584362730899713,
                0.999998446502801,
                3.53562506982705e-05,
                3.5356267564055315e-05,
                8.481101096529726e-05,
                0.0001795280507499871,
                0.0001088968831679349,
                0.00010889689618606975,
                1.892514597832254e-05,
                0.00012339458954513738
            ],
            [
                1.1478770862067849e-05,
                3.1201900207380036e-05,
                0.0001088969221019232,
                6.605215250037168e-05,
                9.61024377673388e-05,
                5.8291286359769625e-05,
                6.605213677497863e-05,
                1.6701425824733193e-05,
                2.1444958633416914e-05,
                1.300713466281145e-05
            ],
            [
                NaN,
                3.120191509274984e-05,
                NaN,
                NaN,
                4.0063687398634466e-05,
                NaN,
                4.00636826326273e-05,
                5.144221976237626e-05,
                5.8291286364010624e-05,
                1.4738980205754734e-05
            ],
            [
                0.9999852610145177,
                8.481102106544534e-05,
                0.0002611903704313824,
                0.00043055698355084587,
                0.00029595699172862804,
                0.0007096702874823467,
                4.539786862316288e-05,
                5.144220137401424e-05,
                0.9999910603026305,
                0.0010322308067515608
            ],
            [
                3.7266410609940346e-06,
                7.889263525778283e-06,
                2.9023119851055122e-06,
                1.4738976694977387e-05,
                1.3007130012980722e-05,
                1.670141587068447e-05,
                1.1478765381674627e-05,
                1.6701417861584877e-05,
                1.8925145983348442e-05,
                5.422218323231539e-06
            ],
            [
                2.4300249420429837e-05,
                2.753569765708558e-05,
                4.539786863769599e-05,
                8.48110109233393e-05,
                4.222832941072913e-06,
                5.422221554847581e-06,
                8.939694172656384e-06,
                4.2228319341064674e-06,
                6.605217616848166e-05,
                6.144174601208867e-06
            ],
            [
                0.00012339461872048888,
                2.4300249420429837e-05,
                1.8925152744771773e-05,
                2.1444940737257882e-05,
                4.539787401263522e-05,
                1.473898372500477e-05,
                0.0001584362545816345,
                2.7535694380675497e-05,
                0.00015843615988694095,
                0.00013982202401033748
            ],
            [
                3.120192622803585e-05,
                1.892515500560259e-05,
                7.484624506431508e-05,
                2.7535704222728874e-05,
                3.535623804983752e-05,
                2.4300252313904224e-05,
                5.1442238184803627e-05,
                0.00013982202382113886,
                4.0063711283916205e-05,
                7.484624505832518e-05
            ],
            [
                0.00015843623582664505,
                7.88926540454376e-06,
                2.9023109471188266e-06,
                4.5397852394305204e-05,
                6.605217614925922e-05,
                6.605216035177641e-05,
                4.539785782175987e-05,
                1.670142183934597e-05,
                1.4738976698006875e-05,
                5.144221363404434e-05
            ],
            [
                2.9023133690425823e-06,
                5.422217676299034e-06,
                3.5356238062828204e-05,
                1.8925141471913163e-05,
                1.3709576971379186e-06,
                3.120191137012976e-05,
                5.144223199471459e-05,
                1.300712846361323e-05,
                1.4738980214280206e-05,
                1.0129988564099116e-05
            ],
            [
                0.9947798733537018,
                0.9999038975736865,
                0.999993855827596,
                0.000552778540224005,
                0.0017007222206997478,
                0.00013982210724351363,
                0.9999832985721828,
                0.0008040859176709661,
                0.9999724643121813,
                0.00013982205749646256
            ],
            [
                6.605216827142175e-05,
                0.00010889690895702637,
                3.5356250694926364e-05,
                2.4300243627117176e-05,
                8.481106146543261e-05,
                9.610240348773577e-05,
                1.67014218359435e-05,
                0.00020342689987606823,
                6.144173136729416e-06,
                1.4738980212644815e-05
            ],
            [
                0.00043055698636907487,
                0.0007096705396553883,
                0.9999994284994167,
                0.0002305068251480866,
                0.0002611902758992937,
                0.00029595716875223935,
                0.9999986290429567,
                0.00043055708648510654,
                0.00013982202375603826,
                0.0002959570630702156
            ],
            [
                3.120190019330501e-05,
                1.8925155005051806e-05,
                8.93969523678858e-06,
                7.484623611811155e-05,
                4.5397863198349305e-05,
                5.829127935617924e-05,
                7.484620044058188e-05,
                1.4738988999377379e-05,
                NaN,
                4.785096775920397e-06
            ],
            [
                1.4738983726184394e-05,
                0.0001398220405479252,
                5.829126553475683e-05,
                6.605212102892523e-05,
                7.484625399799535e-05,
                0.00012339457485512604,
                9.610243785962923e-05,
                4.785092783319532e-06,
                0.00013982210717841299,
                1.4738985483504099e-05
            ],
            [
                3.535623805498234e-05,
                1.3007125360478133e-05,
                2.1444948408275583e-05,
                7.889260704631679e-06,
                7.484624501203951e-05,
                1.1478773598099973e-05,
                1.8925152747388e-05,
                5.144219522247965e-05,
                1.147876675341695e-05,
                4.5397879429522924e-05
            ],
            [
                8.48110513985993e-05,
                5.1442219756013625e-05,
                9.610239201366058e-05,
                2.1444953520182517e-05,
                0.00017952802939421127,
                0.00015843617879636877,
                5.1442238173201186e-05,
                6.605216827142175e-05,
                2.4300243621371074e-05,
                5.8291258534985854e-05
            ],
            [
                1.892515499389843e-05,
                3.5356254916002164e-05,
                0.000108896909056849,
                1.892514369904155e-05,
                6.605212102892523e-05,
                8.481102108148808e-05,
                8.481103115695619e-05,
                0.00012339460418487908,
                7.484622714250407e-05,
                1.4738983727900215e-05
            ],
            [
                1.4738988999672284e-05,
                8.481106154688048e-05,
                2.4300249421932663e-05,
                4.006370652067535e-05,
                3.120191509274984e-05,
                0.000487857232199392,
                0.0001233946042513091,
                8.93969630362837e-06,
                0.00017952790180290678,
                8.481101103563856e-05
            ],
            [
                8.48110109233393e-05,
                7.484620039429623e-05,
                5.8291286335171815e-05,
                4.539787405128009e-05,
                7.484620044711632e-05,
                1.4738978456049602e-05,
                5.144223811144626e-05,
                1.670141985245514e-05,
                6.144172404129392e-06,
                3.5356267541418054e-05
            ],
            [
                0.0004305571371005144,
                0.00029595713025273786,
                0.00013982204057030355,
                0.00020342697281662618,
                0.0006263340218804216,
                0.00015843623549239316,
                0.0004305570363456723,
                0.00013982209057978554,
                0.000335350227955442,
                0.0001233946038509335
            ],
            [
                6.1441724044534996e-06,
                1.3007130013572209e-05,
                1.3007133114886634e-05,
                2.260324028331257e-06,
                7.889261644358435e-06,
                5.422221554374162e-06,
                2.260324028331257e-06,
                1.9947306726049992e-06,
                4.785093353352668e-06,
                1.6701421843720577e-05
            ],
            [
                4.006369694755693e-05,
                0.0002611902147676999,
                9.610243785962923e-05,
                0.00010889692207498694,
                0.0013250224212184225,
                0.00023050679686431014,
                4.539787396804498e-05,
                0.00010889694800510692,
                5.144222587049821e-05,
                9.61024493518883e-05
            ],
            [
                0.00010889688297145868,
                4.539789021837975e-05,
                4.0063696955427154e-05,
                9.610239205281409e-05,
                5.8291293247581486e-05,
                2.7535681249595513e-05,
                5.82912516391202e-05,
                0.00010889692212885947,
                2.7535684525803696e-05,
                4.5397863224112544e-05
            ],
            [
                5.144223202914764e-05,
                5.144223202914764e-05,
                1.0129989771657269e-05,
                7.889264464895484e-06,
                1.670141587031992e-05,
                2.1444948411552198e-05,
                1.0129992181043471e-05,
                4.785096205651846e-06,
                5.422218969661113e-06,
                2.144495352474637e-05
            ],
            [
                2.753570422373059e-05,
                4.0063706494441236e-05,
                0.00013982202403068142,
                7.484626290608339e-05,
                4.539785238406597e-05,
                4.006369694347607e-05,
                0.00033535002798211347,
                0.00012339460406817764,
                0.00012339461884078114,
                0.00012339463353079768
            ],
            [
                0.9997040429714769,
                0.000295957203833203,
                6.605214465761795e-05,
                0.00015843625423585665,
                0.00023050668733764877,
                6.605217616848166e-05,
                0.00015843619788790842,
                0.00017952792285828674,
                0.00010889692215579573,
                3.5356254910985954e-05
            ],
            [
                4.006370172916052e-05,
                2.14449509695729e-05,
                4.539785238670836e-05,
                7.484624506431508e-05,
                8.481104132991612e-05,
                5.829126551609642e-05,
                4.0063687398634466e-05,
                1.3007123812057577e-05,
                1.6701421842140854e-05,
                1.6701419851270353e-05
            ],
            [
                0.0003799844380094323,
                0.00015843615934522262,
                4.0063701703217896e-05,
                6.605212103421139e-05,
                0.00015843623562378874,
                6.144175333289463e-06,
                0.00020342706968894909,
                8.481102104014715e-05,
                0.00017952794428457408,
                7.484620934866355e-05
            ],
            [
                0.00043055703653355426,
                0.00013982204069440157,
                6.605213677497863e-05,
                1.6701419848961534e-05,
                6.605214463262879e-05,
                0.00017952800867054373,
                3.535625066740153e-05,
                5.144221362768171e-05,
                4.006370172318498e-05,
                1.1478766756214804e-05
            ],
            [
                4.539785240603078e-05,
                7.48462538460694e-05,
                2.4300234934056724e-05,
                5.829128637885414e-05,
                7.484621828233953e-05,
                8.481105131283225e-05,
                3.535623804623613e-05,
                2.1444958636771547e-05,
                0.0001233945305391321,
                3.5356259112640515e-05
            ],
            [
                4.539787944042276e-05,
                0.9999832985701943,
                0.00048785716402301117,
                0.0002034269243375671,
                0.00012339457482280874,
                8.481108175582829e-05,
                0.0009110510972319453,
                0.9999921107345932,
                5.144221972045777e-05,
                0.00015843621604585045
            ],
            [
                0.0008040860317808097,
                8.481102101484894e-05,
                3.535626755929635e-05,
                7.484621826927065e-05,
                3.120192623110058e-05,
                3.5356242271040426e-05,
                4.006371126555232e-05,
                5.144220138599094e-05,
                0.00013982207356410913,
                0.0003799844388827615
            ],
            [
                3.120191508185304e-05,
                5.82912515784739e-05,
                8.939695237959376e-06,
                4.006371126336615e-05,
                8.481105142266346e-05,
                6.9622570784012604e-06,
                4.006369694755693e-05,
                4.785093353187292e-06,
                2.1444948411552198e-05,
                5.1442213646395314e-05
            ],
            [
                0.00010889689629856828,
                NaN,
                0.00013982212355325894,
                5.8291244672006574e-05,
                0.0001584361789554265,
                8.481107156496966e-05,
                5.144221974927673e-05,
                0.0001584362355707695,
                9.610238054937517e-05,
                5.144220137401424e-05
            ],
            [
                0.00048785723279543865,
                0.0001584362166913023,
                5.8291293252246584e-05,
                0.0004878572324264574,
                0.0001584361790591598,
                0.9999962733598274,
                0.0002959571349112548,
                0.0001398220736556569,
                0.00015843627348876844,
                8.481108171572136e-05
            ],
            [
                6.605217615887045e-05,
                NaN,
                1.4738978455325741e-05,
                4.006368259400487e-05,
                3.535626756559877e-05,
                2.144495863614743e-05,
                5.829127939137956e-05,
                8.939699499432793e-06,
                5.144221363067589e-05,
                4.222831933296096e-06
            ],
            [
                0.00023050663184326586,
                0.9992903294521301,
                0.9241418257242036,
                4.785096205930373e-06,
                0.9978172834004982,
                0.9796676472880741,
                0.9998204721048237,
                0.9996646497710006,
                0.9579122701319097,
                0.9902915229544276
            ],
            [
                1.9947290080125335e-06,
                6.962256249758443e-06,
                1.3007134665674251e-05,
                2.4300246523773334e-05,
                1.473898899908247e-05,
                5.829129330398681e-05,
                1.4738980214843206e-05,
                2.1444950968441685e-05,
                8.93969417167259e-06,
                2.753569761591508e-05
            ],
            [
                1.6701421837158667e-05,
                0.0004305570885518083,
                0.001032231182607643,
                0.00012339453055529076,
                7.4846236168209e-05,
                0.00013982202382113886,
                0.00013982207330370664,
                6.605215250517728e-05,
                3.53562633231704e-05,
                NaN
            ],
            [
                0.00013982210740626523,
                2.753568781423318e-05,
                4.539787945313924e-05,
                5.8291286322448804e-05,
                0.0001398221070929684,
                0.00023050668755227535,
                0.00010889687025437763,
                7.484625393972985e-05,
                1.8925145978942173e-05,
                4.006371128012683e-05
            ],
            [
                2.5612831264675113e-06,
                2.7535704222728874e-05,
                1.2098655392811161e-06,
                6.475947981975644e-07,
                1.0129993393945642e-05,
                4.222834954514924e-06,
                8.939699500327152e-06,
                7.889259763326495e-06,
                6.144175333926503e-06,
                3.9278634073625165e-07
            ],
            [
                3.535626755260807e-05,
                0.0001584362349852524,
                1.1478769493728398e-05,
                4.5397852394305204e-05,
                0.00026119024624545313,
                4.5397857795336036e-05,
                1.6701421840318107e-05,
                5.829124465589078e-05,
                8.481102113640367e-05,
                5.144220137401424e-05
            ],
            [
                NaN,
                0.0001233945453458395,
                0.006692852496922295,
                NaN,
                NaN,
                0.006692850054381233,
                0.0004305570823141267,
                0.0017007226490147159,
                NaN,
                0.00020342707016545293
            ],
            [
                0.00020342689913319638,
                0.0004878571169637165,
                8.481106148209239e-05,
                1.1478773597390071e-05,
                0.9579122699817196,
                4.539786863059458e-05,
                0.00010889687012128086,
                8.48110109893614e-05,
                0.00020342706955280511,
                8.481104128178784e-05
            ],
            [
                8.93969736955767e-06,
                3.5356242266024216e-05,
                2.4300237830711845e-05,
                5.1442195248304415e-05,
                6.96225375833433e-06,
                6.962257079376403e-06,
                6.144173136885882e-06,
                8.939698434966738e-06,
                1.892515049702235e-05,
                2.4300252316291068e-05
            ],
            [
                0.00023050671474278403,
                0.0004878571132171383,
                2.430024651882284e-05,
                0.0004878572280554485,
                5.1442219781089866e-05,
                2.1444940743225995e-05,
                6.605212892117389e-05,
                5.829124466818968e-05,
                8.481108166450792e-05,
                0.0002959572387247301
            ],
            [
                8.48110109893614e-05,
                3.1201903929204235e-05,
                0.0002611902436919703,
                1.8925143726890553e-05,
                8.481101103563856e-05,
                0.00020342699727517416,
                0.0004305571329921613,
                5.8291265503797524e-05,
                0.00020342694835512147,
                8.481103122174425e-05
            ],
            [
                3.2887490653408545e-06,
                2.561281293950654e-06,
                NaN,
                NaN,
                1.8925141473186853e-05,
                NaN,
                6.144175333401224e-06,
                8.93969417150998e-06,
                NaN,
                NaN
            ],
            [
                5.8291265499980624e-05,
                1.0129988564099116e-05,
                7.484621830139833e-05,
                5.8291286239325165e-05,
                2.9023123310290063e-06,
                5.422220908634683e-06,
                8.93969310647542e-06,
                6.605214463743442e-05,
                2.1444940741392653e-05,
                2.7535697658087296e-05
            ],
            [
                0.00015843621625101194,
                0.0003799844816206224,
                0.00048785711199666207,
                0.00048785723350501796,
                0.0003799845747462832,
                0.0005527785444045657,
                0.0009110512250241528,
                0.00037998448017244335,
                0.9999957771675623,
                0.0001795279659172125
            ],
            [
                0.00013982204046248067,
                4.785096776194573e-06,
                1.6701423834226767e-05,
                8.481105143068482e-05,
                9.610243780928898e-05,
                0.00013982210715806904,
                7.48462272100267e-05,
                1.8925152748558416e-05,
                4.0063677853357896e-05,
                4.539786862811735e-05
            ],
            [
                NaN,
                1.1478766756653273e-05,
                2.4300237832303074e-05,
                3.5356250701614645e-05,
                6.144172404380855e-06,
                2.430024941459533e-05,
                4.006367785875045e-05,
                2.7535681250497054e-05,
                6.962259567217739e-06,
                3.53562591336057e-05
            ],
            [
                1.6701425825492673e-05,
                1.4738978456049602e-05,
                1.4738978454172926e-05,
                8.481108176384966e-05,
                2.7535684526905577e-05,
                1.0129992185981682e-05,
                NaN,
                3.120191881094355e-05,
                1.8925148239290237e-05,
                3.726641061027928e-06
            ],
            [
                8.481107165567298e-05,
                0.0002034270458400805,
                2.144495863482118e-05,
                6.60521604272245e-05,
                7.48462093933156e-05,
                9.610244931343393e-05,
                6.605213676488686e-05,
                0.00020342692463945134,
                3.53562506982705e-05,
                3.535625070778844e-05
            ],
            [
                4.222833444283541e-06,
                1.4738976700661033e-05,
                3.2887498493325602e-06,
                1.3007125363057018e-05,
                8.315283250305684e-07,
                2.1444953514565465e-05,
                1.8925157261545463e-05,
                1.300712691308661e-05,
                6.9622579096593295e-06,
                NaN
            ],
            [
                1.670142381757896e-05,
                2.7535687801010546e-05,
                1.892515726099468e-05,
                8.939698434657777e-06,
                1.8925157259824262e-05,
                1.4738976695942536e-05,
                4.222833947728508e-06,
                3.288748673265808e-06,
                3.53562591237019e-05,
                1.300712536203966e-05
            ],
            [
                6.962253759752719e-06,
                1.7603440526806268e-06,
                8.939699500489763e-06,
                1.4738978457872657e-05,
                2.144494329769612e-05,
                2.7535691095550887e-05,
                3.2887486732358968e-06,
                3.7266392832104296e-06,
                3.53562591336057e-05,
                6.962253759271479e-06
            ],
            [
                3.120190393374457e-05,
                0.0001584362733320158,
                0.00012339457488744337,
                4.539787403691212e-05,
                0.00013982214014578718,
                1.8925152746768368e-05,
                5.8291279382897555e-05,
                0.0001233946042836264,
                2.7535694379773952e-05,
                4.0063696902084474e-05
            ],
            [
                4.006370651032745e-05,
                NaN,
                1.6701423834226767e-05,
                2.561281600049467e-06,
                4.539787403938935e-05,
                NaN,
                1.892515049571424e-05,
                2.4300246521474893e-05,
                7.889266347356409e-06,
                1.670141587174774e-05
            ],
            [
                6.96225956921868e-06,
                0.00017952804989847249,
                1.8925143725341476e-05,
                7.484623607019228e-05,
                1.8925141440966004e-05,
                3.535623806128476e-05,
                6.962257079465052e-06,
                4.539788486688977e-05,
                1.6701427813417103e-05,
                0.0002305067968039464
            ],
            [
                0.000179527987343505,
                0.00017952802954048367,
                2.1444948407573453e-05,
                1.670141587068447e-05,
                4.006368738143655e-05,
                6.962255419653012e-06,
                2.5612816000145246e-06,
                1.4738988994498018e-05,
                NaN,
                3.535625492217596e-05
            ],
            [
                8.939695237666677e-06,
                3.2887494572873306e-06,
                8.93969310584124e-06,
                4.7850950646797465e-06,
                1.4738987239295859e-05,
                2.430023783150746e-05,
                2.7535681224252135e-05,
                4.785096775998733e-06,
                6.962257079275089e-06,
                3.726638395527247e-06
            ],
            [
                4.0063711285810896e-05,
                4.222835458002318e-06,
                3.1201900207380036e-05,
                7.484621775141582e-05,
                6.9622579075254155e-06,
                2.5612834320214477e-06,
                1.670142781709299e-05,
                0.00010889696084103356,
                7.889261644760245e-06,
                2.7535691093547457e-05
            ],
            [
                3.5356246476937965e-05,
                0.00023050663178960924,
                4.0063682618927264e-05,
                0.00015843625450556338,
                4.539785239182798e-05,
                9.610242617999399e-05,
                0.00010889694801936731,
                3.120191508707442e-05,
                3.120190020068305e-05,
                0.00010889692216847163
            ],
            [
                5.144223197188398e-05,
                3.1201915085825835e-05,
                1.670141586907437e-05,
                6.144177531381426e-06,
                1.4738980213020151e-05,
                2.7535684529910724e-05,
                4.006368736948546e-05,
                6.605217613436184e-05,
                2.7535704227537108e-05,
                1.3007131564643372e-05
            ],
            [
                8.481103114029641e-05,
                0.0001398220738102709,
                NaN,
                NaN,
                0.00669285096452951,
                0.0003353500290163234,
                NaN,
                0.00026119021575565446,
                5.829127942361117e-05,
                3.120190392137216e-05
            ]
        ]
    },
    {
        "q_id": "8581_mmlu_math",
        "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,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            45,
            47,
            48,
            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,
            87,
            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": [
            [
                0.9999974387171787,
                0.9999970976887068,
                0.9999984465022455,
                0.999998790134028,
                0.9999938558232011,
                0.9999832985821381,
                0.9999993524050474,
                0.9999998144608538,
                0.9999996940977002,
                0.9999994956524114
            ],
            [
                0.9999984465028011,
                0.9999994956526519,
                0.9999810748449961,
                0.9999977396765105,
                0.999994577780384,
                0.9999997300421581,
                0.9999994284993486,
                0.9999990577554061,
                0.9999995549150542,
                0.9999987901338838
            ],
            [
                1.7603434231705793e-06,
                9.422445939002803e-07,
                3.2887478892504536e-06,
                2.5612816000331606e-06,
                1.6701429807630274e-05,
                1.7603430034743913e-06,
                1.0129988564430787e-05,
                1.1478768125201194e-05,
                1.9947290081286418e-06,
                4.785092783210732e-06
            ],
            [
                1.9947297215043796e-06,
                3.288749457383046e-06,
                6.1441731370702875e-06,
                6.14417533430649e-06,
                4.222835458117536e-06,
                4.785092783415276e-06,
                2.561282516042282e-06,
                2.2603242978665707e-06,
                1.553497199007048e-06,
                4.222833947897496e-06
            ],
            [
                8.939698434153684e-06,
                6.144173136885882e-06,
                4.222834954514924e-06,
                6.962257079275089e-06,
                1.3709578605617394e-06,
                1.5534975693601474e-06,
                1.7603430034655858e-06,
                8.939699500489763e-06,
                3.726638395527247e-06,
                2.2603251061232293e-06
            ],
            [
                0.9999998555019962,
                0.9999962733616046,
                0.9999998362622943,
                0.9999982396565767,
                0.9999994956525318,
                0.9999997897566338,
                0.9999987901344607,
                0.9999998362623137,
                0.9999997300420937,
                0.9999998724809723
            ],
            [
                1.0129992186939844e-05,
                1.553498310118888e-06,
                1.3709568799823232e-06,
                1.55349775456958e-06,
                9.422448185388577e-07,
                7.88925976359915e-06,
                2.260323489435463e-06,
                2.2603248367173307e-06,
                1.7603430033991435e-06,
                1.7603425837494853e-06
            ],
            [
                4.785095065093186e-06,
                2.260325375664839e-06,
                1.5534979397394734e-06,
                6.144177531599359e-06,
                2.5612834320214477e-06,
                2.561281905376098e-06,
                1.994730197071414e-06,
                6.144176066443055e-06,
                6.144172404520556e-06,
                3.288750633569722e-06
            ],
            [
                0.9999994284994848,
                0.9999997617631184,
                0.9999986290427931,
                0.9999997617631469,
                0.9999921107402385,
                0.999999814460876,
                0.9999982396567868,
                0.9999998724809571,
                0.9999986290421394,
                0.999999855502048
            ],
            [
                5.4222215550004564e-06,
                1.4738985484227961e-05,
                2.753568124348506e-05,
                7.889266347248781e-06,
                5.422219616026655e-06,
                1.0129993394811673e-05,
                8.93969310675186e-06,
                3.120190020613144e-05,
                8.93969630362837e-06,
                6.144176799166453e-06
            ],
            [
                0.9999974387184,
                0.9999980052705163,
                0.9999994284996893,
                0.9999885212264024,
                0.9999994284993486,
                0.9999984465026158,
                0.9999994284995529,
                0.9999996940978095,
                0.9999980052705163,
                0.9999987901340283
            ],
            [
                0.999999694097846,
                0.9999995549150542,
                0.9999994956524114,
                0.9999974387168733,
                0.9999930377412606,
                0.9999997300421581,
                0.9999970976890528,
                0.9999994284994849,
                0.9999991684722698,
                0.999997438717484
            ],
            [
                3.726640616670918e-06,
                8.31528424146183e-07,
                1.1478764019557924e-05,
                1.8925145979561802e-05,
                7.889266347356409e-06,
                4.785096776303374e-06,
                3.1201903930339314e-05,
                2.14449535222109e-05,
                3.1201900207380036e-05,
                1.0129990978220553e-05
            ],
            [
                6.144174601879434e-06,
                2.9023112931688987e-06,
                4.785093923982095e-06,
                1.994729008105057e-06,
                4.2228329408924035e-06,
                1.370956879949281e-06,
                4.785096205973894e-06,
                4.785094494716039e-06,
                1.1478773598329648e-05,
                3.2887506334560605e-06
            ],
            [
                0.9999962733616046,
                0.9999997897565838,
                0.9999986290429566,
                0.9999930377420909,
                0.9999992661790195,
                0.9999977396765105,
                0.9999967112513267,
                0.9999980052702786,
                0.999998005269803,
                0.9999991684715758
            ],
            [
                0.9999986290421394,
                0.9999996072138465,
                0.9999885212346113,
                0.9999994956524114,
                0.9999885212359796,
                0.9999980052709918,
                0.9999991684716749,
                0.9999995549150542,
                0.999999352404893,
                0.9999869928715355
            ],
            [
                5.422217676866151e-06,
                0.00010889693519770254,
                1.3709568799879344e-06,
                6.475949526003845e-07,
                9.422443692527585e-07,
                6.1441760667392215e-06,
                4.22283394786293e-06,
                1.6701421843720577e-05,
                2.260324028404236e-06,
                4.222833947960866e-06
            ],
            [
                0.9999970976880148,
                0.999986992868439,
                0.9999995549151072,
                0.9999999006880549,
                0.9999997300421903,
                0.9999898700102283,
                0.9999952149066464,
                0.9999998555020135,
                0.9999810748562741,
                0.999997097687323
            ],
            [
                0.9999921107392955,
                0.9999994956526519,
                0.9999994956525318,
                0.999999266179107,
                0.9999957771675627,
                0.9999997897565838,
                0.9999984465018751,
                0.999999352405279,
                0.999999495652712,
                0.9999996533673788
            ],
            [
                0.9999930377445803,
                0.9996646500101373,
                0.9999945777803838,
                0.9999810748495034,
                0.9998415637265112,
                0.9998415637266149,
                0.9999970976883608,
                0.9999962733616043,
                0.9999546021097148,
                0.9999885212277695
            ],
            [
                0.999999694097846,
                0.9999999123575359,
                0.9999952149072168,
                0.9999977396751633,
                0.9999999317440197,
                0.9999996533675028,
                0.9999996940978095,
                0.9999997300421903,
                0.9999987901341723,
                0.9999986290421394
            ],
            [
                0.9999962733593833,
                0.9999994956525918,
                0.999999057755743,
                0.9999998724809419,
                0.9999997897565587,
                0.9999967112517189,
                0.9999987901347491,
                0.9999980052707541,
                0.999998790134605,
                0.9999997617630616
            ],
            [
                0.9999980052707541,
                0.9999997617630899,
                0.9999986290426298,
                0.999999789756684,
                0.9999994956525918,
                0.9999996533672549,
                0.9999995549149481,
                0.9999992661790196,
                0.9999996940977366,
                0.9999974387187053
            ],
            [
                8.939695237666677e-06,
                1.3007125360478133e-05,
                4.785093353739995e-06,
                6.144175334367959e-06,
                6.962257079629686e-06,
                3.726638839806038e-06,
                2.9023109471188266e-06,
                1.4738983728784933e-05,
                6.1441746017453204e-06,
                1.3709572068272963e-06
            ],
            [
                1.1478768124992398e-05,
                5.422220262195015e-06,
                1.1478765388314311e-05,
                1.0129994602656007e-05,
                1.8925155003330605e-05,
                3.120190765307203e-05,
                3.7266401725681614e-06,
                6.144177531459659e-06,
                2.430023493564795e-05,
                1.1478766755985128e-05
            ],
            [
                0.9999994284995529,
                0.9999869928668853,
                0.9999756997679619,
                0.999999730042126,
                0.9999756997679643,
                0.999999352405279,
                0.9999989322970027,
                0.9997965730513342,
                0.9999885212346111,
                0.9999986290426297
            ],
            [
                0.9999993524054334,
                0.9999997897566089,
                0.9999996940978825,
                0.9999997617631468,
                0.9999987901337396,
                0.999998790134028,
                0.9999910603015656,
                0.9999997897565587,
                0.9999998362623332,
                0.9999977396751634
            ],
            [
                0.9999980052702786,
                0.9999999397642508,
                0.9999977396754327,
                0.9999995549150011,
                0.9999970976873229,
                0.9999986290424663,
                0.9999980052695652,
                0.9999997617631183,
                0.9999952149037941,
                0.9999997897566589
            ],
            [
                0.9999997617629764,
                0.9999995549147889,
                0.9999996940976271,
                0.9999993524054335,
                0.9999993524052018,
                0.9999599362935014,
                0.9999996072137998,
                0.9999785550566999,
                0.9999785550515897,
                0.9999998144609645
            ],
            [
                8.481103123717e-05,
                1.147877359872636e-05,
                4.0063696951637786e-05,
                6.962259568775433e-06,
                6.605217615887045e-05,
                1.670142781086525e-05,
                8.93969417167259e-06,
                6.962257079553702e-06,
                0.00023050671480314775,
                3.1201922517673344e-05
            ],
            [
                1.0129990979381404e-05,
                2.902311985079115e-06,
                1.9947306725868575e-06,
                3.7266383953679482e-06,
                8.31528325021115e-07,
                1.0677028700130727e-06,
                7.889265406681968e-06,
                1.3709568799368123e-06,
                3.2887486731641103e-06,
                4.785093924156175e-06
            ],
            [
                1.1478765388314311e-05,
                6.144177531381426e-06,
                2.5612831266608576e-06,
                1.1478773599102191e-05,
                2.1444956079842134e-05,
                6.1441760667392215e-06,
                4.222832941072913e-06,
                3.7266401725935817e-06,
                7.889265406904397e-06,
                3.726641061085547e-06
            ],
            [
                6.144173869312763e-06,
                1.1478769493916314e-05,
                3.72664061681327e-06,
                1.0129992187253088e-05,
                2.9023133690637e-06,
                6.962253759670401e-06,
                1.7603440527046419e-06,
                1.7603436330091044e-06,
                4.222832437677995e-06,
                1.3709576971379186e-06
            ],
            [
                0.9999852610197867,
                0.9999599362887237,
                0.9999898700102289,
                0.999820471970039,
                0.9999417087414969,
                0.9999994956524114,
                0.9999998874648379,
                0.9999938558268633,
                0.9999998362622942,
                0.9999996072137529
            ],
            [
                4.785096205882502e-06,
                4.785094494716039e-06,
                5.1442219789698126e-05,
                1.553498495338299e-06,
                5.144223205029401e-05,
                3.726639728184142e-06,
                6.144173869379821e-06,
                2.430023493936082e-05,
                1.0129990979381404e-05,
                4.53978524104898e-05
            ],
            [
                3.120190392534495e-05,
                7.88926634687567e-06,
                6.605216826661615e-05,
                4.539786323088365e-05,
                1.8925143727854426e-05,
                3.726640616748873e-06,
                2.4300232038197563e-05,
                1.9947299592407137e-06,
                6.144176066521288e-06,
                7.484620045964068e-05
            ],
            [
                0.999998790134605,
                0.9999986290427931,
                0.9999970976880149,
                0.9999986290421394,
                0.9999970976880148,
                0.9999938558239333,
                0.9999938558246659,
                0.9999974387180947,
                0.9999997617630333,
                0.999993855826131
            ],
            [
                1.892515049423401e-05,
                1.147877086073156e-05,
                0.9999938558232008,
                0.9999930377437503,
                0.00017952800835971484,
                2.4300234936443568e-05,
                6.605213675960068e-05,
                0.00010889692223185108,
                8.481103122976564e-05,
                2.4300234934056724e-05
            ],
            [
                1.2098661162023305e-06,
                1.7603436330179102e-06,
                5.422217677028889e-06,
                1.0129990979694647e-05,
                3.7266401725935817e-06,
                4.222834451327159e-06,
                3.288749457432399e-06,
                1.147877359872636e-05,
                9.422445939002803e-07,
                1.994730434847717e-06
            ],
            [
                0.9999986290421394,
                1.5534984953298217e-06,
                1.3007131564383116e-05,
                2.753569109925723e-05,
                3.288748281220719e-06,
                2.5612831266608576e-06,
                3.120192252686752e-05,
                1.3007133114886634e-05,
                1.3007133115667397e-05,
                6.144173869072478e-06
            ],
            [
                0.999820471948819,
                0.999820472078735,
                0.9999756997535132,
                0.9994472214574606,
                0.9999756997651453,
                0.9998204720983304,
                0.9998415637730321,
                0.9999724643156179,
                0.9999930377454187,
                0.9999485577986978
            ],
            [
                1.0129988564430787e-05,
                2.5612816000145246e-06,
                3.120191507912884e-05,
                2.7535694382378416e-05,
                8.939694172420599e-06,
                1.1478764019996392e-05,
                4.222831934202483e-06,
                1.6701415871049018e-05,
                1.1478768125577027e-05,
                8.939695238089467e-06
            ],
            [
                0.9999970976876689,
                0.999998005269803,
                0.9999938558239334,
                0.9999967112517189,
                0.9999957771675622,
                0.9999962733598274,
                0.9999930377454102,
                0.9999996533672549,
                0.999985261021543,
                0.99999303774624
            ],
            [
                0.9999962733602715,
                0.9999910603047618,
                0.9999898700126431,
                0.9996646498893982,
                0.9999910603047616,
                0.9999599363173673,
                0.9997388097221476,
                0.9999885212305066,
                0.9992903295373299,
                0.9999869928668851
            ],
            [
                1.7603438428740716e-06,
                2.1444945855248125e-05,
                2.9023116391477434e-06,
                8.939698434332555e-06,
                4.2228324377164004e-06,
                1.670141586907437e-05,
                1.3709573702778664e-06,
                0.0001795280088037561,
                4.006371127619171e-05,
                2.9023116391675407e-06
            ],
            [
                3.5356246490314526e-05,
                4.222833444229772e-06,
                5.422219616026655e-06,
                5.1442213657997754e-05,
                4.006370651557427e-05,
                6.1441746018123775e-06,
                8.939693106020111e-06,
                1.9947290080905435e-06,
                3.288749457409966e-06,
                3.726637951170554e-06
            ],
            [
                0.9999980052700407,
                0.9999970976866309,
                0.9999982396572065,
                0.9999970976880149,
                0.9999952149072177,
                0.9999986290421394,
                0.999999814460876,
                0.9999997897565838,
                0.9999994284996211,
                0.9999997300421581
            ],
            [
                0.9999994284996893,
                0.9999982396559473,
                0.9995694428590541,
                0.9999989322972572,
                0.9999995549147889,
                0.9999980052693274,
                0.9999938558268631,
                0.9999996072138465,
                0.9999898700078126,
                0.9999885212305066
            ],
            [
                1.3007123811229494e-05,
                1.6701425824733193e-05,
                3.5356238064371654e-05,
                6.962256249517824e-06,
                1.5534984953298217e-06,
                6.144177531660828e-06,
                1.2098658277335738e-06,
                2.4300232040584407e-05,
                5.14421952570998e-05,
                2.1444945853999886e-05
            ],
            [
                0.999997438717484,
                0.9999810748562717,
                0.9999980052705163,
                0.999999266178932,
                0.9999921107336527,
                0.9999989322972572,
                0.9999832985801471,
                0.9999945777790912,
                0.9999957771645418,
                0.9999996533674202
            ],
            [
                0.9999785550515954,
                0.9999930377429205,
                0.9999952149066468,
                0.9999930377454107,
                0.9999898700078128,
                0.9999869928746392,
                0.9999251537638889,
                0.9999417087066693,
                0.9999251537371064,
                0.9999832985761665
            ],
            [
                0.9999991684715759,
                0.999999554914895,
                0.9999970976876689,
                0.9999974387168732,
                0.9999996072137061,
                0.9999984465016899,
                0.9999986290429566,
                0.9999974387177893,
                0.9999977396754327,
                0.9999977396757022
            ],
            [
                2.56128159999123e-06,
                4.785095065045315e-06,
                1.670142781709299e-05,
                2.9023116391675407e-06,
                2.5612828213352452e-06,
                5.422220262555012e-06,
                1.4738976699427788e-05,
                6.144173869312763e-06,
                5.043475885674441e-07,
                4.222833444506298e-06
            ],
            [
                0.9999977396751634,
                0.9999993524052018,
                0.9999945777790912,
                0.9999977396759716,
                0.9999952149043646,
                0.9999986290424664,
                0.9999996072137529,
                0.9999980052702785,
                0.9999952149043645,
                0.9999984465024306
            ],
            [
                0.9740426429905804,
                0.9999945777810466,
                0.999998629043284,
                0.9999910603047856,
                0.999978555049282,
                0.9999921107374152,
                0.9999646437619418,
                0.9999687980737719,
                0.9999974387165679,
                0.9999982396561572
            ],
            [
                0.9999952149049349,
                0.9999957771655489,
                0.9999967112501505,
                0.999991060302631,
                0.9999962733620488,
                0.9999987901337396,
                0.9999810748585277,
                0.9999967112497586,
                0.9999994284997573,
                0.9999945777829694
            ],
            [
                0.9999339478317094,
                0.9999992661792819,
                0.9999832985841286,
                0.9999930377437504,
                0.9999989322972572,
                0.9999952149043645,
                0.9999986290426297,
                0.9999989322972572,
                0.999995214904935,
                0.9999986290421394
            ],
            [
                8.93969630362837e-06,
                5.422217030614265e-06,
                7.88926164518358e-06,
                1.0129995809929273e-05,
                5.422218969720291e-06,
                2.5612825160271407e-06,
                1.2098658277451275e-06,
                6.962253759752719e-06,
                5.422217677078203e-06,
                4.7850967763512445e-06
            ],
            [
                7.338212429537553e-07,
                1.6701423833436905e-05,
                8.93970056668775e-06,
                7.889259764079887e-06,
                1.1478770862067849e-05,
                8.93969736955767e-06,
                1.5534984953298217e-06,
                1.300712536203966e-05,
                8.93969950101825e-06,
                1.9947294835630703e-06
            ],
            [
                1.892514147046736e-05,
                0.9999485577863448,
                4.539786861523573e-05,
                5.829127924760961e-05,
                5.829127240857092e-05,
                7.889264466344872e-06,
                4.785093924047376e-06,
                1.473898021366358e-05,
                3.1201911358551906e-05,
                3.5356246483883486e-05
            ],
            [
                0.9999993524049703,
                0.9999991684715759,
                0.9999989322971299,
                0.999995214906076,
                0.9999974387168733,
                0.9999990577556308,
                0.9999997617630332,
                0.9999992661786695,
                0.9999810748585277,
                0.9999970976890529
            ],
            [
                1.370957533534567e-06,
                7.889264461924958e-06,
                1.3007133115667397e-05,
                6.1441738691562974e-06,
                2.4300234936443568e-05,
                1.6701419852090592e-05,
                5.422220908634683e-06,
                3.726638838711279e-06,
                2.4300237829827827e-05,
                6.144174601097106e-06
            ],
            [
                5.829126546053932e-05,
                2.144495863614743e-05,
                1.1478764020727177e-05,
                3.535625070778844e-05,
                8.939698435226916e-06,
                1.8925141471913163e-05,
                1.4738987242137685e-05,
                6.1441746018123775e-06,
                8.939700566289352e-06,
                4.222833444467892e-06
            ],
            [
                0.9999992661792819,
                0.9999998144608317,
                0.9999687980811974,
                0.9999980052700408,
                0.9999986290424663,
                0.9999982396561571,
                0.9999980052693274,
                0.9999852610127585,
                0.9999599362887278,
                0.9999996940978095
            ],
            [
                1.3007131564383116e-05,
                2.7535681236473055e-05,
                2.9023123309973302e-06,
                4.006367785146321e-05,
                3.7266388397382506e-06,
                6.605217609735863e-05,
                2.260323758939877e-06,
                2.1444950965906214e-05,
                1.473898197154587e-05,
                1.4738976699427788e-05
            ],
            [
                3.120191880379252e-05,
                2.1444940740066406e-05,
                8.481105139057794e-05,
                3.535625492359079e-05,
                1.8925157262578186e-05,
                1.0129987356706945e-05,
                3.5356267564055315e-05,
                2.7535691100158776e-05,
                1.670141985166528e-05,
                5.8291244683457274e-05
            ],
            [
                1.2098662604049616e-06,
                7.889260704531226e-06,
                3.726640616670918e-06,
                2.5612812946890944e-06,
                1.6701427815999337e-05,
                3.2887490653109436e-06,
                2.43002378338943e-05,
                1.994730434816876e-06,
                5.422218323231539e-06,
                8.939699500896292e-06
            ],
            [
                0.9999996072139402,
                0.9999996533674615,
                0.9999991684722698,
                0.9999993524049703,
                0.9999898700078128,
                0.9999990577549568,
                0.999999554914789,
                0.9999885212264013,
                0.9999982396567867,
                0.9999996072137998
            ],
            [
                1.4738988998117324e-05,
                1.5534975693792215e-06,
                2.2603251062147097e-06,
                6.962253759752719e-06,
                4.7850933538313875e-06,
                7.889262585642319e-06,
                1.2098655392871682e-06,
                6.962256249327861e-06,
                1.760344052714248e-06,
                6.144176066672166e-06
            ],
            [
                0.9999998144608319,
                0.9999994284994167,
                0.9999998144608317,
                0.9999995549151072,
                0.9999992661791944,
                0.9999996533674201,
                0.9999810748540172,
                0.9999991684719725,
                0.999999352405279,
                0.9999998555019274
            ],
            [
                0.9999945777790912,
                0.9999910603058275,
                0.9999970976880149,
                0.9999962733616046,
                0.9999952149060758,
                0.9999980052707541,
                0.9999910603036963,
                0.9999938558246662,
                0.9999869928684356,
                0.999999495652652
            ],
            [
                0.9999998874648245,
                0.9999970976869771,
                0.9999977396759716,
                0.9999986290429566,
                0.9999996072136125,
                0.9999999006879957,
                0.9999980052693275,
                0.9999997300421903,
                0.9999990577552939,
                0.9999991684719723
            ],
            [
                0.9999687980737526,
                0.999995777168066,
                0.9999945777810513,
                0.9999898700090206,
                0.9999852610233009,
                0.9999945777810303,
                0.9999967112509347,
                0.9999945777829696,
                0.9999485577679585,
                0.9999810748585286
            ],
            [
                4.006370171895837e-05,
                7.484621824966732e-05,
                0.0003353500072784023,
                0.00043055708340384213,
                0.0002611904326725625,
                0.9999151889182442,
                1.3007130009313495e-05,
                2.7535684528909006e-05,
                0.00012339460390659108,
                6.605215250517728e-05
            ],
            [
                0.9999957771680658,
                0.9999986290427931,
                0.9999996072138934,
                0.9999986290423029,
                0.9999993524049702,
                0.9999995549150542,
                0.9999994956526519,
                0.9999994284996211,
                0.9999996072137061,
                0.999999352405279
            ],
            [
                0.999988521233244,
                0.9999997897566089,
                0.9999996533674615,
                0.9999996072138934,
                0.9999984465020603,
                0.9999996533674614,
                0.999999554914895,
                0.9999995549150542,
                0.999999730042126,
                0.9999997897566089
            ],
            [
                5.422218969661113e-06,
                1.8925157262578186e-05,
                1.670141985245514e-05,
                1.994729721469003e-06,
                1.1478772229300848e-05,
                1.012999339449843e-05,
                8.481104132991612e-05,
                3.120190021453107e-05,
                6.144173137014406e-06,
                1.1478772229781076e-05
            ],
            [
                1.0677031245851707e-06,
                1.2098661161982042e-06,
                2.902310947208574e-06,
                2.902313023039776e-06,
                7.889264466639056e-06,
                1.9947290081286418e-06,
                1.5534975693601474e-06,
                7.889265407004852e-06,
                6.144176798590883e-06,
                6.144176066672166e-06
            ],
            [
                7.338207180864763e-07,
                1.2098658277451275e-06,
                4.222834954687752e-06,
                1.067703379154416e-06,
                3.7266406168403854e-06,
                4.785093353787868e-06,
                1.9947301970813926e-06,
                4.785093353874907e-06,
                3.7266388397721442e-06,
                1.9947299592933255e-06
            ],
            [
                0.9999970976866309,
                0.999999855502048,
                0.9999998144608319,
                0.9999999317439464,
                0.9999999123574628,
                0.9999994284996893,
                0.9999994284994849,
                0.9999984465022455,
                0.999998005269803,
                0.9999957771675623
            ],
            [
                0.9999957771670589,
                0.9999646437492907,
                0.9999251537549172,
                0.9999151889687937,
                0.9997965729295001,
                0.999998005270042,
                0.9999599363221447,
                0.9999546021205469,
                0.999989870006605,
                0.9999687980849082
            ],
            [
                0.9999945777829696,
                0.9999945777784449,
                0.9999987901344608,
                0.9999910603015656,
                0.9999910603058279,
                0.9999996533674202,
                0.9999970976890528,
                0.9999986290421395,
                0.9999997897566338,
                0.9999930377454113
            ],
            [
                1.3007130013856124e-05,
                1.3709567165386693e-06,
                4.450848927637999e-07,
                1.0677026154551157e-06,
                1.0677027427068966e-06,
                7.338207180714596e-07,
                6.475951069961737e-07,
                2.2603245672497918e-06,
                4.785092783454444e-06,
                4.222834954561012e-06
            ],
            [
                0.9999995549150542,
                0.999999814460854,
                0.9999998724810026,
                0.9999982396569966,
                0.9999999006881496,
                0.9999996533673375,
                0.9999999397643156,
                0.9999996533672135,
                0.9999998724809267,
                0.999999900688043
            ],
            [
                8.93970056668775e-06,
                1.2098655392871682e-06,
                5.043476486915964e-07,
                7.889260704308795e-06,
                4.785095065093186e-06,
                6.144172404520556e-06,
                7.88926540679677e-06,
                1.670141587068447e-05,
                8.939695238089467e-06,
                2.5612831267086116e-06
            ],
            [
                0.9999957771645419,
                0.9999980052705163,
                0.999999057755743,
                0.999994577782323,
                0.999999266179107,
                0.9999991684719723,
                0.9999977396765106,
                0.999998239656367,
                0.9999945777797377,
                0.9999986290423029
            ],
            [
                0.9999987901338838,
                0.9999998144609202,
                0.9999957771675623,
                0.9999989322970027,
                0.9999998144609645,
                0.9999984465026158,
                0.9999998362623332,
                0.9999994956523514,
                0.9999974387180947,
                0.9999996940977366
            ],
            [
                0.9999987901344607,
                0.9999952149032236,
                0.9999977396757023,
                0.9999984465022455,
                0.9999996533675028,
                0.9999989322973846,
                0.9999970976880149,
                0.9999986290426297,
                0.999999730042319,
                0.9999984465026158
            ],
            [
                0.9999999123574732,
                0.9999989322972572,
                0.9999974387180947,
                0.9999996533673375,
                0.9999986290423029,
                0.9999998362622552,
                0.9999992661790196,
                0.9999982396574163,
                0.9999996072139402,
                0.9999921107374156
            ],
            [
                0.9999869928668849,
                0.999991060303696,
                0.999999266178757,
                0.9999980052707541,
                0.999999168471675,
                0.9999962733607158,
                0.999997438716568,
                0.9999967112521109,
                0.9999930377420904,
                0.9999977396762411
            ],
            [
                0.9999984465022455,
                0.999998790134028,
                0.9999984465026158,
                0.9999989322968754,
                0.9999869928730862,
                0.9999151889283141,
                0.9999989322967481,
                0.9999869928684346,
                0.9999993524051246,
                0.999998790134028
            ],
            [
                0.999997438717484,
                0.9999984465018751,
                0.999985261021543,
                0.9999957771665554,
                0.9999952149055052,
                0.9999989322970027,
                0.9999986290426297,
                0.9999990577554061,
                0.9999970976890528,
                0.9999991684721706
            ],
            [
                0.9999921107364741,
                0.9999982396572065,
                0.9999957771655487,
                0.9999974387171787,
                0.9999980052693274,
                0.9999952149066462,
                0.9999994284996893,
                0.9999986290423029,
                0.9999957771680658,
                0.9999938558275955
            ],
            [
                7.889259764079887e-06,
                3.535624228313077e-05,
                1.5534979397677313e-06,
                3.7266388397382506e-06,
                5.829127941979426e-05,
                2.2603248367173307e-06,
                1.4738988999672284e-05,
                1.3007131565613412e-05,
                2.561283432005142e-06,
                2.7535687817839356e-05
            ],
            [
                0.9999974387168733,
                0.999999266179107,
                0.9999930377420904,
                0.9999967112501504,
                0.9999991684719723,
                0.9999987901347492,
                0.9999810748562726,
                0.9999990577552937,
                0.9999989322968754,
                0.9999687980811924
            ],
            [
                0.9999998724809267,
                0.9999995549149481,
                0.9999756997505882,
                0.9999992661792819,
                0.9999996940978095,
                0.9999984465020603,
                0.9999987901337396,
                0.999999495652652,
                0.999985261019786,
                0.9999994284996893
            ],
            [
                0.9999977396746245,
                0.9999998555019446,
                0.9999996940977002,
                0.9999990577554061,
                0.9999994956525918,
                0.9999997897566089,
                0.9999994284992805,
                0.9999885212332428,
                0.9999995549150011,
                0.9999992661786695
            ],
            [
                0.9999997617631468,
                0.9999996072138934,
                0.9999997300422869,
                0.9999980052707541,
                0.999999554914895,
                0.9999998362622943,
                0.9999962733611603,
                0.9999993524049702,
                0.9999986290432834,
                0.9999997300422547
            ],
            [
                2.9023123310290063e-06,
                5.8291272389486416e-05,
                5.422221555069497e-06,
                6.962254589104433e-06,
                1.994729008074216e-06,
                4.785093924047376e-06,
                1.3007133115903994e-05,
                2.7535691093547457e-05,
                6.144174601499446e-06,
                7.889264465986113e-06
            ],
            [
                1.1478768125577027e-05,
                8.939694172656384e-06,
                8.939694172656384e-06,
                3.120190393260949e-05,
                7.889263525261671e-06,
                1.1478764020372226e-05,
                1.209865827740176e-06,
                4.222834451292594e-06,
                1.0129987357020188e-05,
                3.535623806861614e-05
            ],
            [
                1.0129993394811673e-05,
                1.4738978457336465e-05,
                3.72664061671159e-06,
                3.726638395415398e-06,
                3.726641061058432e-06,
                1.670142781478417e-05,
                1.3709567165386693e-06,
                2.4300252319296727e-05,
                1.9947292458603553e-06,
                9.422447062150634e-07
            ],
            [
                0.9999910602994342,
                0.9999982396563669,
                0.9999756997534786,
                0.9998601778760724,
                0.999997438717484,
                0.9999996533672549,
                0.9999990577552937,
                0.9999945777816766,
                0.9999930377429207,
                0.999999266178757
            ],
            [
                0.9999997300421581,
                0.9999999397642796,
                0.9999997300420937,
                0.9999998874648647,
                0.9999994956525317,
                0.9999967112513266,
                0.9999997897567341,
                0.9999997617631752,
                0.9999980052709918,
                0.9999997617630616
            ],
            [
                0.9999989322971301,
                0.9999998362622747,
                0.9999993524053562,
                0.9999997617629764,
                0.9999997617631184,
                0.9999962733620487,
                0.9999990577556308,
                0.9999997300422868,
                0.9999996072139402,
                0.9999999006881259
            ],
            [
                0.9999785550567016,
                0.9999974387184,
                0.9999997897567091,
                0.9999998144609202,
                0.9999952149043646,
                0.999989870010228,
                0.9999957771650453,
                0.9999945777797374,
                0.9999998362622357,
                0.9999724643121898
            ],
            [
                1.5534983101602148e-06,
                1.9947304348595095e-06,
                2.5612825159677387e-06,
                6.1441746018123775e-06,
                1.670141786036971e-05,
                1.4738983728784933e-05,
                3.7266397278791014e-06,
                2.9023116391675407e-06,
                7.889259764079887e-06,
                3.726640172537657e-06
            ],
            [
                0.9999987901344607,
                0.9999994284997573,
                0.999997438716568,
                0.9999998555019446,
                0.9999974387168735,
                0.9999962733607161,
                0.9999998144608981,
                0.9999994284996893,
                0.9999962733593835,
                0.9999977396759716
            ],
            [
                0.9999756997476854,
                0.9999724643089034,
                0.9999869928653335,
                0.9998911030907103,
                0.9999952149049349,
                0.9999687980886347,
                0.9999957771645468,
                0.9997965729538639,
                0.9999546021112287,
                0.999915188958662
            ],
            [
                7.88926258532661e-06,
                1.6701425825128124e-05,
                5.422220261948442e-06,
                3.7266383954560706e-06,
                2.1444940741392653e-05,
                4.0063677853357896e-05,
                1.1478766756653273e-05,
                2.4300232040584407e-05,
                2.7535694375867267e-05,
                2.902312677084523e-06
            ],
            [
                1.1478766755233466e-05,
                3.7266379512518984e-06,
                2.75357009372024e-05,
                4.785096776251149e-06,
                1.5534975693488444e-06,
                4.5397852399094525e-05,
                1.9947301970587145e-06,
                9.42244256915735e-07,
                4.7850950646797465e-06,
                6.144176798479122e-06
            ],
            [
                0.9999997897567091,
                0.9999995549151073,
                0.9999991684721706,
                0.9999986290429566,
                0.9999984465018751,
                0.9999998555019274,
                0.9999982396567867,
                0.9999994956523514,
                0.9999982396565769,
                0.9999977396759717
            ],
            [
                4.2228349546493465e-06,
                1.5534973841705173e-06,
                7.889265406681968e-06,
                1.473897670007122e-05,
                4.785096776251149e-06,
                1.370956716519966e-06,
                7.889265406567165e-06,
                5.422217030495909e-06,
                2.5612828212909852e-06,
                4.222834451215781e-06
            ],
            [
                0.9999962733620487,
                0.9999996940977002,
                0.999996273358939,
                0.9999992661791945,
                0.9999974387187053,
                0.9999974387180947,
                0.9999852610197867,
                0.999999266179107,
                0.9999994956523514,
                0.9999785550490321
            ],
            [
                0.9999687980923566,
                0.9999930377412605,
                0.9999756997534754,
                0.9999974387187053,
                0.9999930377454103,
                0.9999962733611601,
                0.9999952149055054,
                0.9999967112497585,
                0.9999952149060757,
                0.9999957771655487
            ],
            [
                5.144222590043998e-05,
                3.53562591237019e-05,
                5.8291251573808804e-05,
                3.120190764058611e-05,
                1.3007126912258525e-05,
                2.4300246523773334e-05,
                2.753568452790729e-05,
                0.00015843615985927873,
                5.8291279378656556e-05,
                4.5397879429522924e-05
            ],
            [
                0.999998239656367,
                0.9999869928684351,
                0.9999957771675624,
                0.9999952149072165,
                0.999997097687669,
                0.999988521231875,
                0.9999962733598274,
                0.9999957771660523,
                0.9999989322966208,
                0.9999967112505427
            ],
            [
                0.9999962733598274,
                0.9999980052700408,
                0.9999994284994167,
                0.9999986290426297,
                0.9999967112517186,
                0.9999990577555185,
                0.9999982396572064,
                0.9999980052702785,
                0.9999989322968754,
                0.9999980052709919
            ],
            [
                2.4300246525983375e-05,
                4.5397863211726375e-05,
                3.535626335108113e-05,
                9.61024377673388e-05,
                0.9999982396563669,
                1.6701423834226767e-05,
                8.481106156230622e-05,
                6.60521210438226e-05,
                4.7850956352353935e-06,
                3.1201926246083686e-05
            ],
            [
                0.9999998555019446,
                0.99999893229713,
                0.9999998362623332,
                0.9999994284995529,
                0.9999999123574941,
                0.9999998144608319,
                0.9999995549149481,
                0.9999995549148419,
                0.9999993524051246,
                0.9999994956524115
            ],
            [
                0.9999998874648782,
                0.9999993524049703,
                0.9999945777790913,
                0.9999996940977001,
                0.9999996533672136,
                0.9999996533672549,
                0.9999898700090211,
                0.9999991684716749,
                0.9999994956524716,
                0.9999995549150011
            ],
            [
                5.144220138599094e-05,
                3.53562507106181e-05,
                1.473898372822193e-05,
                1.1478772230198667e-05,
                7.484621834387223e-05,
                5.1442201382996765e-05,
                3.726641061027928e-06,
                4.5397890289724144e-05,
                2.1444948412722418e-05,
                1.8925141472360678e-05
            ],
            [
                0.9999982396561572,
                0.9999980052693274,
                0.99999992265575,
                0.9999998724809875,
                0.9999993524052018,
                0.9999945777816769,
                0.9999986290421394,
                0.9999962733620488,
                0.9999980052707541,
                0.9999998874647574
            ]
        ]
    },
    {
        "q_id": "8645_mmlu_math",
        "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,
            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,
            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,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                3.2887494572873306e-06,
                1.5534977545243671e-06,
                1.7603438427467903e-06,
                8.315279285149107e-07,
                2.902313368583287e-06,
                2.260324836624822e-06,
                6.96225956921868e-06,
                2.9023112930659533e-06,
                4.222834954607099e-06,
                2.260324028404236e-06
            ],
            [
                0.9999952149055056,
                0.9999980052698031,
                0.999993855827596,
                0.9999987901340281,
                0.9999977396754328,
                0.9999980052695652,
                0.9999970976883608,
                0.9999993524054335,
                0.9999977396757022,
                0.9999977396746244
            ],
            [
                0.9999724642990779,
                0.9998204720346757,
                0.9999251537733073,
                0.9999417087345682,
                0.8175744739711883,
                0.9999599362982811,
                0.9998415638211505,
                0.9999546021313848,
                0.8933094010836642,
                0.5621765008857981
            ],
            [
                0.9999996072137061,
                0.9999992661791945,
                0.9999999006880668,
                0.9999998724809419,
                0.9999998874648647,
                0.9999999006879957,
                0.9999997617630616,
                0.9999998555019274,
                0.9999993524053562,
                0.9999993524051246
            ],
            [
                0.9999991684717741,
                0.9999996533672136,
                0.9999992661792819,
                0.9999998555019618,
                0.9999997897567341,
                0.9999995549148419,
                0.999999789756684,
                0.9999994284994849,
                0.9999995549150542,
                0.9999997897566589
            ],
            [
                2.5612828202776674e-06,
                1.7603432133136672e-06,
                8.93969630362837e-06,
                2.561281599881745e-06,
                1.1478766756214804e-05,
                8.315277302059155e-07,
                6.144174601208867e-06,
                1.7603425836678333e-06,
                5.422218969532895e-06,
                2.9023123304218908e-06
            ],
            [
                6.962259566204604e-06,
                1.5534983100228109e-06,
                2.260323489410794e-06,
                8.939699500766203e-06,
                1.4738983716586539e-05,
                2.56128159999123e-06,
                2.7535687811228037e-05,
                1.0129994600638342e-05,
                1.3007131547513873e-05,
                1.6701425822059825e-05
            ],
            [
                2.561282515988704e-06,
                1.3007128463352975e-05,
                6.1441767989541075e-06,
                1.5534981249496567e-06,
                3.7266383955611403e-06,
                7.889261644057078e-06,
                1.2098655392090423e-06,
                2.2603251061232293e-06,
                5.422218969217281e-06,
                1.6701415867221242e-05
            ],
            [
                2.5612831261041147e-06,
                6.144173868882483e-06,
                2.90231094702116e-06,
                5.422219615898437e-06,
                8.93970056529743e-06,
                4.7850933535006355e-06,
                9.422442569028803e-07,
                8.31528325021115e-07,
                3.2887506334560605e-06,
                6.14417313680765e-06
            ],
            [
                6.1441724019276964e-06,
                2.9023123309973302e-06,
                1.4738985482753428e-05,
                3.2887482811220126e-06,
                2.5612819052374947e-06,
                7.889265405333033e-06,
                1.0129993391808207e-05,
                1.3007130012673148e-05,
                2.4300243614475748e-05,
                6.962257909121104e-06
            ],
            [
                3.288749849209925e-06,
                1.670142383015595e-05,
                5.422219615750493e-06,
                1.9947294836483373e-06,
                6.475945665741875e-07,
                6.962253759271479e-06,
                1.5534973841154145e-06,
                7.889262585541864e-06,
                7.889263525261671e-06,
                1.7603434230921292e-06
            ],
            [
                0.999997438716568,
                0.9999994284996211,
                0.9999967112509347,
                0.9999970976880154,
                0.9999986290431201,
                0.9999930377412611,
                0.9999997617631184,
                0.9999980052695653,
                0.9999984465015047,
                0.9999945777790915
            ],
            [
                4.222831934156396e-06,
                2.2603251061232293e-06,
                6.144175333401224e-06,
                1.994729245722476e-06,
                3.7266379512518984e-06,
                1.0677032518093368e-06,
                1.9947301970587145e-06,
                7.889262583633267e-06,
                1.2098652507847127e-06,
                1.3007125359413455e-05
            ],
            [
                3.2887490648622804e-06,
                7.889260703906985e-06,
                1.0129990975567187e-05,
                6.475947209709154e-07,
                1.3709570433536782e-06,
                1.7603438427467903e-06,
                5.422218969384951e-06,
                5.422220908634683e-06,
                1.3709572065835317e-06,
                2.5612825154622447e-06
            ],
            [
                3.288748280293481e-06,
                7.889264464508026e-06,
                6.962257906765564e-06,
                5.422220908116881e-06,
                1.1478768124553928e-05,
                8.481102096116742e-05,
                3.726641060244989e-06,
                3.726637950973972e-06,
                2.753570422373059e-05,
                2.260325375615501e-06
            ],
            [
                1.6701425824733193e-05,
                1.0677024881140118e-06,
                2.4300232012472705e-05,
                3.726638395320497e-06,
                2.9023133690188264e-06,
                3.288748280891699e-06,
                3.726638395493353e-06,
                1.4738978451920916e-05,
                3.1201922517673344e-05,
                5.144220129392002e-05
            ],
            [
                0.2450850021044189,
                0.9465966735899122,
                0.9241418158002492,
                0.8519528038477825,
                0.5312093733737562,
                0.16451645880021026,
                0.26894141551050293,
                0.2018132150593341,
                0.9999599362935444,
                0.9996200155175502
            ],
            [
                0.9999974387184,
                0.9999910602994345,
                0.999995777165549,
                0.9999984465016899,
                0.9999967112513268,
                0.9999962733607161,
                0.9999962733607162,
                0.9999977396748939,
                0.9999832985721872,
                0.9999957771660523
            ],
            [
                3.726639727994339e-06,
                4.785093353687772e-06,
                1.300713311517055e-05,
                1.012999460108057e-05,
                2.5612828211442287e-06,
                4.785096205717126e-06,
                4.222832436955956e-06,
                1.370956716529941e-06,
                2.2603237589028734e-06,
                2.9023109469842055e-06
            ],
            [
                0.99999893229713,
                0.9999996533672962,
                0.9999993524052018,
                0.9999995549147359,
                0.999999168471675,
                0.9999996072137998,
                0.9999997617631752,
                0.999999814460876,
                0.9999996072136125,
                0.9999952149066462
            ],
            [
                1.5534981247426673e-06,
                8.939694171331106e-06,
                1.4738981962698681e-05,
                5.422218969601935e-06,
                6.1441753335241615e-06,
                6.1441746016670885e-06,
                2.902313023039776e-06,
                4.785096776303374e-06,
                2.9023123309973302e-06,
                6.962255418924822e-06
            ],
            [
                0.9999938558246677,
                0.9999957771660521,
                0.9999970976873391,
                0.9999832985781634,
                0.999997097686631,
                0.9999945777810305,
                0.9999810748427365,
                0.999992110735535,
                0.999992110736474,
                0.9999910603058306
            ],
            [
                1.4738985482351282e-05,
                1.892515500715167e-05,
                2.902310945682868e-06,
                2.260325375615501e-06,
                2.1444950958338794e-05,
                0.00010889687017515336,
                1.994730434778778e-06,
                1.6701423829669885e-05,
                1.0677028700053041e-06,
                2.561281294616881e-06
            ],
            [
                6.962256249327861e-06,
                8.939700566289352e-06,
                1.1478768124783601e-05,
                3.5356250651195314e-05,
                1.9947297214182054e-06,
                6.962257078553231e-06,
                4.222832938649476e-06,
                7.88926540679677e-06,
                5.422217676200406e-06,
                6.962259568509485e-06
            ],
            [
                0.999991060306894,
                3.120191137012976e-05,
                0.00029595712201207136,
                1.2098661161602417e-06,
                1.994729721482609e-06,
                6.144177531208195e-06,
                8.93969736942758e-06,
                2.9023109470871505e-06,
                2.561282515914161e-06,
                1.9947301970287804e-06
            ],
            [
                2.2603248366762157e-06,
                6.144175334094145e-06,
                1.2098656834723998e-06,
                1.0677033791204289e-06,
                4.7850956352353935e-06,
                1.2098652507120887e-06,
                2.561282515988704e-06,
                6.962259569117366e-06,
                6.47594720949123e-07,
                6.144172403592939e-06
            ],
            [
                0.9999998144609202,
                0.9999991684722698,
                0.9999997897566338,
                0.999999887464811,
                0.9999996940978825,
                0.9999996072137998,
                0.9999995549149481,
                0.9999998362622943,
                0.9999995549147359,
                0.9999996072137061
            ],
            [
                0.9999957771660523,
                0.9999957771645419,
                0.9999957771675624,
                0.9999991684718734,
                0.9999990577555183,
                0.9998415637462229,
                0.9999910603058304,
                0.999995214904935,
                0.9999970976883609,
                0.9999952149049353
            ],
            [
                5.422219615395428e-06,
                5.422217027576489e-06,
                5.422218967491273e-06,
                2.144494073569759e-05,
                6.962255419380732e-06,
                6.1441738691562974e-06,
                7.889260704179641e-06,
                7.889264465842609e-06,
                6.962259568078904e-06,
                1.994729721396435e-06
            ],
            [
                2.5612815999679353e-06,
                9.422444815679433e-07,
                4.222831934052698e-06,
                3.120192251631124e-05,
                3.726639282763036e-06,
                2.753568773760199e-05,
                7.338207180761315e-07,
                1.3709570433786157e-06,
                2.561281294616881e-06,
                1.760343632854606e-06
            ],
            [
                3.4663249713489575e-07,
                6.962254588977791e-06,
                4.785095634843714e-06,
                1.0677029972522599e-06,
                6.144175333635923e-06,
                9.422443692261927e-07,
                9.422442569208767e-07,
                5.4222202623972055e-06,
                1.0129990979215566e-05,
                1.760342793515064e-06
            ],
            [
                0.5,
                0.1329642281726931,
                0.7772998663336157,
                0.07585818263281054,
                0.9924227593554403,
                0.9968273174800379,
                0.9046505351008906,
                0.9982992772774582,
                0.8670357529306639,
                0.3208213138121609
            ],
            [
                3.28875024125221e-06,
                4.785096205347206e-06,
                1.4738985479214553e-05,
                1.0129994600398803e-05,
                1.3007130012010681e-05,
                4.222833947498071e-06,
                4.222833443553821e-06,
                4.222832436955956e-06,
                8.939694170940841e-06,
                4.785095062634308e-06
            ],
            [
                3.2887498494282754e-06,
                1.300713311112477e-05,
                2.4300252309307336e-05,
                4.222832940500659e-06,
                2.2603253755476615e-06,
                2.7535681224252135e-05,
                1.9947304346826253e-06,
                6.962253759271479e-06,
                1.8925157262061825e-05,
                7.889259763010786e-06
            ],
            [
                1.7603427933917854e-06,
                1.3709576970824327e-06,
                1.0677027427413698e-06,
                3.288748672413347e-06,
                2.561282515289864e-06,
                1.6701429805655623e-05,
                1.994729007936337e-06,
                3.288750633192845e-06,
                1.370957533676711e-06,
                4.785093923982095e-06
            ],
            [
                4.2228324372555256e-06,
                7.88925976418034e-06,
                1.1478764019996392e-05,
                6.1441731363550164e-06,
                6.144173868781898e-06,
                6.144174600325954e-06,
                1.4738980212296288e-05,
                2.9023123308072772e-06,
                1.1478773595009805e-05,
                1.9947299588742466e-06
            ],
            [
                0.46879062662624377,
                NaN,
                0.999876605469696,
                0.4073334000459302,
                0.9999930377464126,
                0.9999687980998082,
                0.9999957771657114,
                0.9999869928746383,
                0.8807970748488297,
                0.9999339478323073
            ],
            [
                0.9999992661788446,
                0.9999996072138934,
                0.999999352404893,
                0.9999992661788445,
                0.9999962733620489,
                0.9999952149043646,
                0.9999994956524716,
                0.9999974387187053,
                0.9999994956524114,
                0.9999984465015047
            ],
            [
                9.422447061782138e-07,
                1.3709572066782945e-06,
                3.288750633025344e-06,
                1.99472900790731e-06,
                1.994729008056074e-06,
                3.288747889178668e-06,
                4.78509563509613e-06,
                4.785093923768848e-06,
                4.222834450820197e-06,
                1.2098661161107252e-06
            ],
            [
                0.9999982396572067,
                7.88926352407059e-06,
                0.9999984465022456,
                0.9999977396765106,
                0.9999986290421394,
                0.9999810748450727,
                0.9999980052702787,
                0.9999970976890528,
                0.9999417087553925,
                0.9999984465016899
            ],
            [
                0.9999980052693275,
                0.9999938558253996,
                0.9999989322972572,
                0.9999987901337397,
                0.9999852610192528,
                0.9999970976876694,
                4.785096205717126e-06,
                0.999998932296621,
                0.9999986290429567,
                0.9999977396757023
            ],
            [
                0.9999852610145312,
                0.9999832985801506,
                0.9988304899613673,
                0.9999938558232011,
                0.9999921107345976,
                0.999991060302632,
                0.999983298584689,
                0.9999339478405785,
                0.9999945777797381,
                0.9999852610215451
            ],
            [
                0.0001233945446133141,
                5.422218322457301e-06,
                2.7535697619320912e-05,
                1.4738978456049602e-05,
                1.3007126910649678e-05,
                1.994729483535857e-06,
                8.939694167639847e-06,
                7.889260703619978e-06,
                2.260324027765926e-06,
                3.7266383950934104e-06
            ],
            [
                2.9023116391477434e-06,
                5.422218968931258e-06,
                4.785092782501357e-06,
                1.012999460108057e-05,
                1.994729245842213e-06,
                1.0129995806022926e-05,
                1.994729245722476e-06,
                1.0129994598777299e-05,
                4.785095634930755e-06,
                3.2887482811579057e-06
            ],
            [
                0.9999982396574163,
                0.9999977396762411,
                0.999999057755743,
                0.999997438716568,
                0.9999980052702785,
                0.9999994284992805,
                0.9999990577555185,
                0.9999982396559474,
                0.9999957771645418,
                0.999995214904935
            ],
            [
                3.726640616477725e-06,
                6.144173136243255e-06,
                2.1444950958338794e-05,
                1.3007133110320344e-05,
                1.8925143719695944e-05,
                4.785096775920397e-06,
                2.1444943291142893e-05,
                1.3007128458384476e-05,
                1.8925154999337424e-05,
                8.939697366029015e-06
            ],
            [
                5.42222090821551e-06,
                2.5612831264675113e-06,
                1.7603427934206038e-06,
                0.0001398221216917874,
                1.7603430033991435e-06,
                1.0129988563730593e-05,
                4.785096205778054e-06,
                6.144176798255599e-06,
                2.260323758835034e-06,
                1.067702742656401e-06
            ],
            [
                0.9999986290421395,
                0.9999967112505427,
                0.9999910603026304,
                0.9999952149072165,
                0.9999996072136125,
                0.9999962733607162,
                0.9999921107364745,
                0.9999989322970028,
                0.9999930377404305,
                0.999999352404893
            ],
            [
                2.902312677007974e-06,
                1.2098658277181688e-06,
                2.1444953520182517e-05,
                7.484625399146089e-05,
                1.2098661161789477e-06,
                2.14449535222109e-05,
                2.9023109470871505e-06,
                8.939700566289352e-06,
                1.1478772229050293e-05,
                8.93969417199781e-06
            ],
            [
                4.78509563509613e-06,
                1.8925157259824262e-05,
                4.222834954403545e-06,
                1.994729008074216e-06,
                2.902312676941983e-06,
                1.7603430034311638e-06,
                1.5534971987760398e-06,
                1.5534977545384963e-06,
                6.9622579086271995e-06,
                7.889259762666377e-06
            ],
            [
                1.0129990977262395e-05,
                5.422217676397663e-06,
                2.9023123690343993e-06,
                2.9023119843875324e-06,
                0.0002611903070882675,
                8.939696303010449e-06,
                2.561281294616881e-06,
                4.222835457664342e-06,
                1.0129993393540266e-05,
                1.0129992186589747e-05
            ],
            [
                0.9999921107355336,
                0.999993037740431,
                0.9999974387187053,
                0.9999938558261311,
                0.9999885212305064,
                0.9999952149066461,
                0.9999997897566589,
                0.9999967112501507,
                0.999995777167059,
                0.9999967112517187
            ],
            [
                0.9999996533673375,
                0.9999994956525317,
                0.9999994956525317,
                0.9999994956527721,
                0.9999994956523514,
                0.9999996533673375,
                0.9999998555020135,
                0.9999998144609202,
                0.9999992661786695,
                0.9999997300421903
            ],
            [
                2.260324028372372e-06,
                8.315279285149107e-07,
                4.2228319341064674e-06,
                4.785094493184135e-06,
                3.2887490652810324e-06,
                9.422442569208767e-07,
                2.902312330849511e-06,
                7.88925976316864e-06,
                3.7266410609160796e-06,
                2.561282210530385e-06
            ],
            [
                1.760344052632596e-06,
                9.422448185015797e-07,
                1.0677031245905116e-06,
                6.962257079553702e-06,
                9.422442568163268e-07,
                1.7603425836870455e-06,
                4.222835458044565e-06,
                1.5534975692866768e-06,
                1.7603434229832599e-06,
                4.7850944945245504e-06
            ],
            [
                0.9999970976890544,
                0.9999921107364778,
                0.9999994956527721,
                0.9999962733620487,
                0.9999785550490348,
                0.9999967112517187,
                0.9999984465015048,
                0.9999974387171787,
                0.999997438716568,
                0.9999957771670589
            ],
            [
                1.3709570432277435e-06,
                8.315281267037064e-07,
                7.338208055302923e-07,
                7.889261643727018e-06,
                3.726640172337686e-06,
                4.785092782501357e-06,
                2.56128282048266e-06,
                2.5612834317908303e-06,
                1.760344052650207e-06,
                2.26032537546132e-06
            ],
            [
                2.561282821352716e-06,
                8.939698434820389e-06,
                6.962259568889411e-06,
                1.760343213227212e-06,
                6.144176066353646e-06,
                1.9947294836483373e-06,
                7.889265406151004e-06,
                4.785093923982095e-06,
                3.7266410609940346e-06,
                4.7850933535659155e-06
            ],
            [
                0.9997965731058568,
                0.7772998560157665,
                0.9579122714836208,
                0.26894141551050293,
                0.7310585727705127,
                0.9465966743431868,
                0.9997388096621711,
                0.9992903297102886,
                0.7981867825403177,
                7.889261641904523e-06
            ],
            [
                0.9999898700078134,
                0.9999832985781628,
                0.9999852610197885,
                0.9999687980997913,
                0.9999885212318801,
                0.999978555054146,
                0.9999930377437515,
                0.9999885212359836,
                0.999985261023307,
                0.9999852610215451
            ],
            [
                0.9999989322966208,
                0.8933094124452288,
                0.9999952149060758,
                0.9999991684719723,
                0.9046505408849363,
                0.9999938558261305,
                0.9999967112509346,
                0.9999930377437505,
                0.999998005269803,
                0.9999990577551814
            ],
            [
                0.9999938558254037,
                2.7535681241281285e-05,
                0.9999724642959198,
                0.9999724643154743,
                0.0075772404274547355,
                1.67014178590634e-05,
                0.9999945777797399,
                0.9999785550413696,
                0.9999724643089247,
                0.9999910603069287
            ],
            [
                1.760344052402049e-06,
                9.422447061576466e-07,
                1.0677028699625768e-06,
                1.5534971988495103e-06,
                1.5534971989427613e-06,
                1.5534981247426673e-06,
                2.902311984952413e-06,
                6.1441753337365085e-06,
                1.2098653944483372e-06,
                8.315282257750556e-07
            ],
            [
                2.2603234894560207e-06,
                2.9023130230133794e-06,
                3.7266401724291984e-06,
                1.994730434778778e-06,
                6.962259568648793e-06,
                4.785093923982095e-06,
                6.9622570786798724e-06,
                7.889266347133978e-06,
                2.260325375572331e-06,
                9.422444815495185e-07
            ],
            [
                8.315280275900177e-07,
                3.726641060244989e-06,
                2.260324567087388e-06,
                1.9947299591826594e-06,
                8.939698434657777e-06,
                8.315281267706361e-07,
                4.222833443046859e-06,
                7.889261645090304e-06,
                2.902313022802209e-06,
                1.760344052693435e-06
            ],
            [
                1.209866260303728e-06,
                1.5534983101061718e-06,
                5.04347348070562e-07,
                1.4738987239698005e-05,
                1.9947292458603553e-06,
                1.5534981247426673e-06,
                8.31528424151477e-07,
                1.7603438428028262e-06,
                3.2887482811908074e-06,
                1.9947301970287804e-06
            ],
            [
                2.1444956072586775e-05,
                1.1478773595009805e-05,
                8.939693105662367e-06,
                1.7603438427852151e-06,
                1.0129994600159262e-05,
                6.9622545892184106e-06,
                1.3007134663521234e-05,
                3.1201911334034104e-05,
                3.2887486720783454e-06,
                2.753568124348506e-05
            ],
            [
                1.3709578604981489e-06,
                3.726638395215427e-06,
                6.475949525919915e-07,
                6.144174601309452e-06,
                4.785095634756674e-06,
                2.260324836696773e-06,
                4.785095064601411e-06,
                5.144220744957233e-05,
                1.5534971989427613e-06,
                3.1201918798457626e-05
            ],
            [
                2.260324028281919e-06,
                1.0677024881382882e-06,
                6.144172404218801e-06,
                1.3709578605118645e-06,
                6.962254585710433e-06,
                3.288748280837859e-06,
                1.3709578603435361e-06,
                4.785092783267308e-06,
                4.7850961899411305e-06,
                8.93969630317306e-06
            ],
            [
                3.288748281220719e-06,
                1.99472995920443e-06,
                5.422220908634683e-06,
                2.260324028281919e-06,
                7.338207180287456e-07,
                4.222832940834793e-06,
                3.288748673035494e-06,
                3.288749065125496e-06,
                2.260323489299784e-06,
                3.2887490653109436e-06
            ],
            [
                0.9999810748472503,
                0.9999982396561572,
                0.9999967112501507,
                0.9999992661788446,
                0.9999977396751633,
                0.9999974387177893,
                0.9999952149043644,
                0.9999982396561571,
                0.9999982396567868,
                0.9999938558224687
            ],
            [
                8.93969736929749e-06,
                6.962257077932685e-06,
                7.889264465986113e-06,
                7.889260703619978e-06,
                1.8925157258585e-05,
                2.4300243625614346e-05,
                8.93969736942758e-06,
                2.7535691080725503e-05,
                3.535625912717466e-05,
                2.4300240728162926e-05
            ],
            [
                6.962255419570695e-06,
                3.120191136899467e-05,
                2.4300252313904224e-05,
                1.0129993393945642e-05,
                2.430024072471526e-05,
                1.670142582254589e-05,
                3.2887506333812835e-06,
                2.1444953522913026e-05,
                3.2887502412970765e-06,
                1.8925150490826034e-05
            ],
            [
                0.999995214906076,
                0.9999921107402361,
                0.999995214906076,
                0.9999885212291413,
                0.9999970976876689,
                0.9999938558268633,
                0.9999977396754327,
                0.9999970976866309,
                0.99999862904312,
                0.9999987901338839
            ],
            [
                5.422217676397663e-06,
                6.962258738701267e-06,
                1.5534981243724885e-06,
                5.1442195197777694e-05,
                4.2228349543420954e-06,
                1.994729721396435e-06,
                1.7603425837366772e-06,
                1.4738987241494252e-05,
                3.726640172337686e-06,
                1.3007133113017532e-05
            ],
            [
                0.9999977396762411,
                2.9023119851266288e-06,
                4.222833947198501e-06,
                0.9999945777829696,
                7.889260700721204e-06,
                0.9999945777803839,
                0.9999962733589389,
                0.9999980052695652,
                0.9999952149037942,
                0.9999938558232009
            ],
            [
                3.726640171131078e-06,
                4.785095634843714e-06,
                5.422220908314139e-06,
                5.422219615286937e-06,
                1.0129987356375273e-05,
                1.5534983099790112e-06,
                1.0129990978847043e-05,
                2.2603240281606297e-06,
                1.994729245842213e-06,
                2.561281905293402e-06
            ],
            [
                1.5534975691778837e-06,
                0.9999646437492968,
                0.9999687980812059,
                5.4222202617511845e-06,
                0.9999687980886374,
                7.338211554641698e-07,
                0.9997965730999463,
                1.9947292457750883e-06,
                0.9999898700066073,
                0.99996879809608
            ],
            [
                0.9999970976876689,
                0.9999938558253986,
                0.9999962733602716,
                0.9999977396748938,
                0.9999980052702785,
                0.9999980052702786,
                0.9999945777784448,
                0.9999957771665554,
                0.99998987000419,
                0.9999898700090204
            ],
            [
                5.422220908634683e-06,
                1.1478769489719528e-05,
                3.7266410609160796e-06,
                1.994729008056074e-06,
                1.1478772229300848e-05,
                1.01299933928585e-05,
                1.4738976698006875e-05,
                6.962256248606003e-06,
                6.475946437928669e-07,
                1.1478773595657069e-05
            ],
            [
                1.9947306726049992e-06,
                1.994729721469003e-06,
                3.2887482810801374e-06,
                1.99472995920443e-06,
                2.260323758806253e-06,
                2.9023112930659533e-06,
                8.939699499432793e-06,
                2.2603251061458426e-06,
                1.9947304346535984e-06,
                1.9947292458004866e-06
            ],
            [
                0.9999991684715758,
                0.9999984465020603,
                0.9999986290424664,
                0.9999982396572065,
                0.9999977396765105,
                0.9999974387171787,
                0.9999989322967482,
                0.9999994284993485,
                0.9999986290426297,
                0.9999957771650455
            ],
            [
                1.012998856312253e-05,
                4.22283294098842e-06,
                2.4300240728162926e-05,
                1.6701427807888088e-05,
                3.2887498492518007e-06,
                2.902311984989368e-06,
                8.9396941702904e-06,
                1.3007131564903626e-05,
                2.9023112930949896e-06,
                2.1444958632714784e-05
            ],
            [
                4.450851049645897e-07,
                1.067702488159652e-06,
                3.288748280837859e-06,
                7.338213303475785e-07,
                5.043472879337165e-07,
                1.9947294834143063e-06,
                7.338210679622478e-07,
                7.33820980469346e-07,
                8.315277302059155e-07,
                6.144173868312501e-06
            ],
            [
                2.1444953517061932e-05,
                2.260324028351814e-06,
                5.422219616085833e-06,
                3.2887478891128633e-06,
                1.1478764015736973e-05,
                4.7850956352353935e-06,
                4.0063696945516495e-05,
                6.962255419380732e-06,
                5.422218969532895e-06,
                1.2098662603499435e-06
            ],
            [
                1.0129987355988324e-05,
                0.999994577782323,
                0.9999687980737768,
                1.8925152746768368e-05,
                6.144176798255599e-06,
                1.3007126911974612e-05,
                1.8925145977014425e-05,
                3.2887498492518007e-06,
                0.9999980052700408,
                1.3709578604981489e-06
            ],
            [
                1.2098662603202336e-06,
                1.300712536203966e-05,
                1.9947292458603553e-06,
                2.1444950965282096e-05,
                4.785093924103951e-06,
                1.0677031245623505e-06,
                3.726639283806955e-06,
                8.939700566435704e-06,
                4.785095634460739e-06,
                2.561282515820982e-06
            ],
            [
                2.9023130227124616e-06,
                7.88926258532661e-06,
                3.2887506326006084e-06,
                2.902310946944611e-06,
                2.260325375391425e-06,
                3.7266388396128453e-06,
                2.561282821106957e-06,
                6.962258738283349e-06,
                7.889261643899223e-06,
                2.2603240281935217e-06
            ],
            [
                0.9999810748562732,
                0.9999952149060758,
                0.9999945777797375,
                0.9999945777823229,
                0.9999869928684451,
                0.9999982396572065,
                0.9999982396559473,
                0.9999962733593833,
                0.9999785550515903,
                0.9999957771680661
            ],
            [
                1.553497384058899e-06,
                6.96225707894582e-06,
                1.0129987355988324e-05,
                1.4738976694012237e-05,
                5.422217029006611e-06,
                3.2887502413389517e-06,
                1.3007126909537681e-05,
                2.260325374750031e-06,
                5.422219614833243e-06,
                8.93969630348202e-06
            ],
            [
                1.994730672265745e-06,
                1.4738978451438343e-05,
                1.9947304347098384e-06,
                1.147877086073156e-05,
                1.8925148230890784e-05,
                1.76034363298589e-06,
                2.7535681233968765e-05,
                4.2228349543420954e-06,
                1.0129994596455602e-05,
                6.962259568230874e-06
            ],
            [
                2.260325375572331e-06,
                1.0129995809431767e-05,
                4.785096205260165e-06,
                3.7266379509129646e-06,
                1.553497754476329e-06,
                3.726637951126493e-06,
                2.260324028351814e-06,
                3.72664061671159e-06,
                1.067702487977091e-06,
                3.288749065167371e-06
            ],
            [
                1.7603430034151537e-06,
                4.785093352813021e-06,
                7.338208929524281e-07,
                1.0677029972745947e-06,
                5.043474681674453e-07,
                3.7266379512112265e-06,
                1.7603432132464244e-06,
                1.2098659719232413e-06,
                4.222832437443716e-06,
                3.288750633545794e-06
            ],
            [
                3.2887482811908074e-06,
                5.422217029943586e-06,
                1.067702615348298e-06,
                2.9023130227599746e-06,
                1.5534977545102382e-06,
                3.2887478887958082e-06,
                5.422218966643064e-06,
                1.147877222702498e-05,
                2.260324567227179e-06,
                1.5534973841592143e-06
            ],
            [
                3.726638395415398e-06,
                2.5612831265909735e-06,
                1.7603436329554703e-06,
                0.9999646437492953,
                1.3709572067181944e-06,
                6.1441753337365085e-06,
                5.8291258453558646e-05,
                2.902311984989368e-06,
                6.605212095972449e-05,
                1.994729008105057e-06
            ],
            [
                2.5612822106654943e-06,
                9.422448185388577e-07,
                6.47594643788744e-07,
                1.0677024880858507e-06,
                1.2098653950315304e-06,
                8.315279285205827e-07,
                2.5612831265630198e-06,
                5.715002426254813e-07,
                1.9947299591354906e-06,
                4.222834954403545e-06
            ],
            [
                0.9999952149037942,
                0.9999921107336532,
                0.999997097688707,
                0.9999957771650456,
                0.9999921107374147,
                0.9999986290432834,
                0.999993855826131,
                0.9999938558224685,
                0.999993855822469,
                0.9999852610215476
            ],
            [
                8.939694170518055e-06,
                2.561282821209454e-06,
                1.0129993393742954e-05,
                9.422449307649713e-07,
                6.96225541655662e-06,
                8.315283249280938e-07,
                2.5612828212909852e-06,
                1.7603440525925705e-06,
                1.4738987237124277e-05,
                2.9023119850210436e-06
            ],
            [
                5.82912515996789e-05,
                2.260323758835034e-06,
                6.475945665853783e-07,
                6.962257078249291e-06,
                4.785092783371756e-06,
                1.9947301970106386e-06,
                9.422446917520523e-07,
                2.4300232012472705e-05,
                7.889264462958184e-06,
                4.785096775920397e-06
            ],
            [
                0.9999991684722698,
                0.9999945777816771,
                0.9999977396746245,
                0.9999724643056201,
                0.9999910603004991,
                0.999989870005401,
                0.9999952149072169,
                0.999993855825398,
                0.9999930377462408,
                0.9999982396559474
            ],
            [
                0.9999832985701952,
                0.9999832985761654,
                0.9999785550516034,
                0.9999832985721862,
                0.9999832985841803,
                0.9999869928730917,
                0.9999724643023419,
                0.999959936322143,
                0.999925153737126,
                0.9999898700066091
            ],
            [
                0.9999930377404304,
                0.9999967112509348,
                0.9999756997477014,
                0.9525741236248059,
                0.9999957771680658,
                0.9999485577805591,
                0.9999756997687985,
                0.9999945777784449,
                0.9999910603004992,
                0.999986992874641
            ],
            [
                3.7266383952696564e-06,
                1.994729959224386e-06,
                6.144175334094145e-06,
                2.5612819052072116e-06,
                2.902311985079115e-06,
                3.726637950973972e-06,
                4.785093352813021e-06,
                2.9023133689317184e-06,
                1.2098655391617266e-06,
                2.2603245667050187e-06
            ],
            [
                1.0129995808418327e-05,
                3.2887478889513447e-06,
                6.962256249429175e-06,
                5.4222196154940574e-06,
                5.71500515151976e-07,
                2.5612828212676906e-06,
                1.0677033791107183e-06,
                6.144175333926503e-06,
                1.99472900796355e-06,
                1.4738980210687712e-05
            ],
            [
                1.553498495295912e-06,
                1.0129994602057158e-05,
                1.3709570433387154e-06,
                5.422220262037209e-06,
                0.999991060300501,
                4.22283344433731e-06,
                0.9999921107392986,
                7.889260702744606e-06,
                9.422450431569214e-07,
                3.7266401724291984e-06
            ],
            [
                1.1478768123823146e-05,
                4.785093924047376e-06,
                2.5612831265909735e-06,
                8.315283250260307e-07,
                8.31527829351332e-07,
                8.315282257901809e-07,
                1.2098658277181688e-06,
                2.902313368963394e-06,
                1.7603434230921292e-06,
                4.222834451012227e-06
            ],
            [
                1.5534981245957261e-06,
                8.939696302652706e-06,
                6.1441731363550164e-06,
                2.9023109471188266e-06,
                6.47594875389178e-07,
                1.3709567164326847e-06,
                2.9023119851055122e-06,
                2.7535684526905577e-05,
                1.5534973841592143e-06,
                1.7603430034151537e-06
            ],
            [
                0.9999986290431201,
                0.9999910603036961,
                0.9999910603036963,
                0.9999957771670592,
                0.9999970976876692,
                0.9999970976887068,
                0.9999945777797375,
                0.999998005269803,
                0.9999982396559474,
                0.9999952149032242
            ],
            [
                1.4738981970312625e-05,
                1.5534979396984994e-06,
                0.9999930377437505,
                0.9999974387174846,
                0.00020342699678979154,
                0.999933947824179,
                5.144221362768171e-05,
                1.3007126911643378e-05,
                1.5534979396024226e-06,
                1.0129990979381404e-05
            ],
            [
                0.9999785550516256,
                0.9999957771655487,
                0.999997438718708,
                0.999995214906076,
                0.9999986290424664,
                0.999991060303696,
                0.9999945777803839,
                0.9999898700053986,
                0.9999810748586622,
                0.9999980052693275
            ],
            [
                0.9999885212346207,
                0.9999957771670589,
                0.9999921107374146,
                0.999959936294083,
                0.9999832985825665,
                0.9525741286736911,
                0.9999970976876689,
                0.9999970976873229,
                0.9999810748427365,
                0.9999898700102291
            ],
            [
                7.338210679695891e-07,
                7.338211554464836e-07,
                7.889260690274135e-06,
                9.422444815628016e-07,
                4.222831933726245e-06,
                1.5534983100920427e-06,
                2.2603237587774727e-06,
                1.067702742726318e-06,
                1.2098653950205268e-06,
                9.422448185101494e-07
            ],
            [
                4.222834451065997e-06,
                2.561282821239737e-06,
                1.6701425805958843e-05,
                2.1444940698874713e-05,
                2.902311292960369e-06,
                2.4300249384892373e-05,
                1.5534984952492866e-06,
                1.1478773596283455e-05,
                2.260324566803695e-06,
                4.222833444467892e-06
            ],
            [
                3.726639728184142e-06,
                7.889261644501938e-06,
                3.7266410608245674e-06,
                1.8925143722381014e-05,
                2.1444950968441685e-05,
                5.043474081831035e-07,
                9.42244256886598e-07,
                6.9622537593854575e-06,
                1.0677031244429091e-06,
                4.785092782597101e-06
            ],
            [
                0.9999982396559473,
                0.9999990577554061,
                0.9999996533675028,
                0.9999990577554061,
                0.9999990577551815,
                0.9999994284995529,
                0.9999993524049702,
                0.9999997897567091,
                0.9999991684715759,
                0.9999984465015047
            ],
            [
                0.4073334000459302,
                0.0010322309060274914,
                0.000430556985154105,
                0.9999485577679615,
                0.32082131381216084,
                0.9993736659166544,
                0.012431648029001733,
                2.4300237829827827e-05,
                0.9999599363174215,
                0.9998601778603485
            ],
            [
                0.9999997617630332,
                0.9999970976890528,
                0.99999976176309,
                0.9999921107364742,
                0.9999990577555185,
                0.9999982396572064,
                0.9999982396567867,
                0.9999996072136592,
                0.9999977396757022,
                0.9999994284996891
            ],
            [
                0.9999952149037941,
                0.9999869928684346,
                0.9999962733598275,
                0.9999930377454106,
                0.999997097688707,
                0.9999974387180947,
                0.9999921107402359,
                0.9999962733593833,
                0.9999967112513269,
                0.8933094124452288
            ],
            [
                1.4738980210258757e-05,
                1.670142183983204e-05,
                1.0129993393945642e-05,
                0.9990889489852608,
                0.9999885212332438,
                3.2887478887958082e-06,
                0.9999810748585323,
                0.9999785550439201,
                2.902311984873224e-06,
                1.0129988562661878e-05
            ],
            [
                1.8925141466439755e-05,
                1.1478766756653273e-05,
                3.5356267564055315e-05,
                3.535626333461766e-05,
                0.9999938558239336,
                1.5534983101301911e-06,
                6.144173868670137e-06,
                0.999997438717484,
                4.785094494463623e-06,
                2.2603234893594005e-06
            ],
            [
                4.222834954687752e-06,
                7.484620044058188e-05,
                0.9999993524051246,
                6.962257909412379e-06,
                1.2098658276862581e-06,
                1.6701421833391647e-05,
                1.1478764017720528e-05,
                0.9999986290427931,
                0.9999989322972572,
                2.4300243625614346e-05
            ],
            [
                0.9999952149066464,
                0.9999990577551815,
                0.9999885212346129,
                0.9999962733593831,
                0.9999921107336528,
                0.9999952149037967,
                0.9999885212305081,
                0.9999885212305059,
                0.9999930377420905,
                0.9999977396748938
            ],
            [
                0.999999352404893,
                0.0002305066561363093,
                0.9999987901344612,
                0.9999974387165693,
                7.8892625849535e-06,
                5.144221976237626e-05,
                5.14422381473764e-05,
                0.00015843623423837232,
                0.00010889686979329236,
                0.0001398221072211353
            ],
            [
                0.9999984465015047,
                0.9999986290426298,
                0.999998790134028,
                0.9999995549147359,
                0.9999996940978095,
                0.9999997617630616,
                0.9999995549148419,
                0.9999992661786696,
                0.9999984465026158,
                0.9999996072138465
            ],
            [
                0.9999989322970029,
                0.9999957771655497,
                0.9999974387184,
                0.9999952149037942,
                0.9999921107364742,
                0.9999945777790913,
                0.9999921107355338,
                0.9999970976876689,
                0.9999938558268633,
                0.9999957771675626
            ]
        ]
    },
    {
        "q_id": "8038_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            18,
            19,
            20,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            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,
            74,
            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,
            124,
            125,
            126,
            127,
            21,
            46
        ],
        "rewards": [
            [
                0.9999980052707541,
                0.9999986290432835,
                0.9999984465016899,
                0.9999996072136592,
                0.9999977396754328,
                0.9999986290423029,
                0.99999976176309,
                0.9999996533675028,
                0.9999992661791944,
                0.9999996940977001
            ],
            [
                3.72664061681327e-06,
                2.2603237589542675e-06,
                1.2098655392871682e-06,
                2.2603242978377903e-06,
                1.067702615468225e-06,
                1.0677029973114952e-06,
                2.9023112932045342e-06,
                4.222835458002318e-06,
                2.5612828213352452e-06,
                4.4508505193932864e-07
            ],
            [
                0.9999957771670591,
                0.9999938558224692,
                0.9999970976880149,
                0.9999921107355341,
                0.9999957771670591,
                0.9999945777810306,
                0.9999945777797377,
                0.9999898700066067,
                0.9999982396559474,
                0.9999832985781592
            ],
            [
                0.9996200154270999,
                0.9996646499705251,
                0.9999724643058021,
                0.9999898700066077,
                0.9999832985741752,
                0.9999417087553165,
                0.9999546021367831,
                0.9999251537816986,
                0.9999938558246664,
                0.999985261023328
            ],
            [
                0.9999898700126442,
                0.9999970976887073,
                0.999997097688361,
                0.9999921107392958,
                0.9999921107364751,
                0.9999980052709919,
                0.9980732655518109,
                0.9999989322967482,
                0.9999869928730875,
                0.9999991684717742
            ],
            [
                0.999983298574178,
                0.9999687980923667,
                0.9999546021259933,
                0.9999646437450858,
                0.9999910603058282,
                0.999997097687669,
                0.9999417087484398,
                0.9997965730291426,
                0.999948557780265,
                0.9999987901337396
            ],
            [
                5.422218323290717e-06,
                1.0677024881382882e-06,
                8.315278293838516e-07,
                4.785096205512581e-06,
                4.222834954403545e-06,
                2.2603245673155757e-06,
                6.1441738691562974e-06,
                4.4508515805199415e-07,
                3.2887490653408545e-06,
                2.9023130224326608e-06
            ],
            [
                0.9998911030518365,
                0.9999756997592744,
                0.9999852610197855,
                0.9999756997621677,
                0.999997097688015,
                0.9996646497316323,
                0.9999724643056184,
                0.9999869928653358,
                0.9999546021367691,
                0.9999151889586936
            ],
            [
                0.40733340004593027,
                0.4687906266262437,
                0.9999724643121954,
                0.9998204720127244,
                0.999796572979015,
                0.9988304896060263,
                0.999738809691445,
                0.9669140183935203,
                0.9994472213863268,
                0.9933071491716832
            ],
            [
                3.288750633518874e-06,
                2.2603242977555607e-06,
                1.370957043323753e-06,
                1.147877086020957e-05,
                6.144175333926503e-06,
                2.5612828212909852e-06,
                1.6701415867221242e-05,
                1.7603434231097403e-06,
                1.3007125361448172e-05,
                1.9947290080905435e-06
            ],
            [
                0.999995777168066,
                0.9999599363221466,
                0.9999921107383557,
                0.9999785550439215,
                0.9999785550413645,
                0.9999417087484042,
                0.9999724643187554,
                0.9999921107345933,
                0.9999485577924977,
                0.9999885212359793
            ],
            [
                9.422447062240614e-07,
                3.4663253845007707e-07,
                6.47594952595231e-07,
                0.9995694429109848,
                1.5534971989992774e-06,
                5.422219616085833e-06,
                3.9278605978261504e-07,
                4.7850944943330625e-06,
                1.3709576971160984e-06,
                2.2603248367656408e-06
            ],
            [
                0.9999962733589393,
                0.9999724643023534,
                0.9999962733589389,
                0.999992110740238,
                0.999738809568209,
                0.9999994956525918,
                0.9999930377462414,
                0.9999756997621694,
                0.9999852610110026,
                0.9999785550439201
            ],
            [
                8.315281267834927e-07,
                2.9023109470871505e-06,
                8.939694172290508e-06,
                3.72664061671159e-06,
                1.994729483705484e-06,
                4.785092783210732e-06,
                3.7266410609940346e-06,
                7.88926352599354e-06,
                3.4663253846718004e-07,
                9.42244256915735e-07
            ],
            [
                0.9999646437324375,
                0.9997694933684385,
                0.999933947839654,
                0.9999599363078145,
                0.9999810748585273,
                0.9999485577925209,
                0.9999251537995278,
                0.9999599363221504,
                0.9999485577679469,
                0.9999724642957943
            ],
            [
                0.9999984465024306,
                0.9999992661791945,
                0.9999938558246664,
                0.9999967112493665,
                0.9999994956526519,
                0.9999980052707541,
                0.9999990577552937,
                0.9999977396748939,
                0.9999977396746246,
                0.9999945777823231
            ],
            [
                6.144176065582494e-06,
                9.422448185264317e-07,
                3.7266410604686857e-06,
                4.222834450820197e-06,
                1.5534979396815448e-06,
                5.422220908634683e-06,
                6.962253759043525e-06,
                1.994729008056074e-06,
                3.288747889038086e-06,
                1.4738978454172926e-05
            ],
            [
                6.475951069855719e-07,
                8.315279285088606e-07,
                1.0677032518413822e-06,
                1.9947292458603553e-06,
                1.9947299591354906e-06,
                1.9947290080343035e-06,
                2.5612819053586272e-06,
                1.994729959224386e-06,
                2.2603234895053587e-06,
                3.726637951170554e-06
            ],
            [
                0.9999967112505427,
                0.999983298578157,
                0.9999970976873229,
                0.9999546021313646,
                0.9999852610197877,
                0.9999756997592695,
                0.9999957771670591,
                0.999986992876188,
                0.9999977396757022,
                0.9999970976890529
            ],
            [
                0.9999952149066468,
                0.9999945777797377,
                0.9999885212305062,
                0.9999898700054001,
                0.9999417087205958,
                0.9999756997476879,
                0.9999982396567868,
                0.9999921107402365,
                0.9999989322973846,
                0.9999938558232017
            ],
            [
                0.9999974387184,
                0.9999945777803843,
                0.99998987001023,
                0.999985261011005,
                0.9999967112501513,
                0.9999885212332438,
                0.999988521229141,
                0.9999898700126436,
                0.9999938558232011,
                0.9999945777829693
            ],
            [
                0.9999938558246657,
                0.9626731085061155,
                0.1329642316084462,
                0.7549149868676283,
                0.9999910603005134,
                0.9998911031042987,
                0.7772998663336157,
                0.8354835391516132,
                0.9999938558261652,
                0.32082130731838393
            ],
            [
                1.1478772230407462e-05,
                0.9999417087136648,
                2.1444958637941764e-05,
                4.785096205973894e-06,
                1.0129988563914856e-05,
                0.9999898700126444,
                2.2603251061849014e-06,
                2.7535697661092444e-05,
                6.144173136729416e-06,
                5.422220908762902e-06
            ],
            [
                0.9999994284995529,
                0.9999996072137061,
                0.9999998144609645,
                0.9999990577549569,
                0.9999995549147359,
                0.9999998362623137,
                0.9999984465015047,
                0.9999990577552937,
                0.9999984465016899,
                0.9999996940978461
            ],
            [
                0.9999930377445803,
                0.9999957771645419,
                0.9999962733598275,
                0.9999930377462404,
                0.9999485577679644,
                0.9999910603047619,
                0.9999945777810304,
                0.9999869928653341,
                0.9998766054694448,
                0.9999724643187728
            ],
            [
                0.9999687980813792,
                0.9996200155162237,
                0.16451646494473965,
                0.9999485577924977,
                0.9465966696352197,
                0.8807970904940926,
                0.9999962733602719,
                0.999948557798623,
                0.9999832985801487,
                0.9999485577986293
            ],
            [
                0.9999832985761693,
                0.9999962733620487,
                0.9999987901347491,
                0.9999957771645421,
                0.999975699762166,
                0.9999977396765105,
                0.9999921107345933,
                0.9999852610215446,
                0.9999945777790911,
                0.9999945777793439
            ],
            [
                6.1441760657054305e-06,
                5.829125843744285e-05,
                2.7535684498857565e-05,
                1.300712381094558e-05,
                1.1478773597118638e-05,
                0.9890130583510434,
                4.539786860136322e-05,
                0.9984988175546303,
                4.0063687390327e-05,
                0.9997694933579754
            ],
            [
                0.9465966685053075,
                0.9999810748540204,
                0.9998911031297076,
                0.9999417087553398,
                0.996827317139106,
                0.9999832985849952,
                0.9999485577740902,
                0.999959936317373,
                0.9997388097534734,
                0.999769493257899
            ],
            [
                0.9999974387177893,
                0.9999599362982768,
                0.9999885212291383,
                0.9999869928684358,
                0.999991060299434,
                0.9999756997563768,
                0.9999945777823234,
                0.9999921107355342,
                0.9999756997650695,
                0.9999869928730878
            ],
            [
                0.9999970976866313,
                0.9999930377420918,
                0.9999852610162746,
                0.9999993524054335,
                0.999991060301566,
                0.9999945777784449,
                0.9999967112497589,
                0.9999980052709919,
                0.9999986290427932,
                0.9999974387168734
            ],
            [
                2.753568453191415e-05,
                1.9947301970287804e-06,
                1.5534981248528732e-06,
                8.939693106873817e-06,
                1.1478765388523107e-05,
                1.2098659719441482e-06,
                2.9023126769050284e-06,
                0.9982992772059076,
                2.2603251060985603e-06,
                9.422447062202052e-07
            ],
            [
                1.5534975692471157e-06,
                1.3709567165087443e-06,
                1.6701423834591316e-05,
                8.939695237341456e-06,
                1.2098662604049616e-06,
                1.012998977108606e-05,
                2.9023116390104826e-06,
                1.9947292458930106e-06,
                1.994730434816876e-06,
                4.7850927830845245e-06
            ],
            [
                0.9999921107345933,
                0.9998766054104872,
                0.9999485577740902,
                0.9999852610162717,
                0.9999687980886276,
                0.9999785550439243,
                0.9999485577986111,
                0.9999957771655492,
                0.9999869928668853,
                0.9999898700041906
            ],
            [
                0.9999974387171787,
                0.9999967112493665,
                0.9999970976866311,
                0.999978555056705,
                0.9999989322967482,
                0.8519528019683106,
                0.9978172836560737,
                0.9999910603037034,
                0.9999974387184005,
                0.9999980052702789
            ],
            [
                0.9999930377445814,
                0.9999898700090233,
                0.9999945777816771,
                0.9999991684715759,
                0.9999852610233009,
                0.9999869928653384,
                0.9999962733620489,
                0.9999832985721876,
                0.999998005269803,
                0.9999980052707541
            ],
            [
                0.9999921107374153,
                0.9999945777810304,
                0.9999724643187576,
                0.9999852610145185,
                0.9999967112505427,
                0.9999599363078342,
                0.9999910603015649,
                0.9999962733611605,
                0.9999885212264015,
                0.999995214904935
            ],
            [
                1.9947297214182054e-06,
                1.0677032518501217e-06,
                8.315284241174449e-07,
                7.338208055436404e-07,
                4.222833443968609e-06,
                4.450851049890802e-07,
                4.785095635017795e-06,
                1.7603438426491283e-06,
                9.422445938642879e-07,
                6.144176797864436e-06
            ],
            [
                0.8175744806385543,
                0.9999687980886335,
                0.9998415637834978,
                0.9997040427614646,
                0.9999251537461092,
                0.8519528000888386,
                0.6513548646660542,
                0.9997388097536861,
                0.9994472212417115,
                0.999948557761856
            ],
            [
                1.0677032518578904e-06,
                3.726639728224814e-06,
                2.260323758713745e-06,
                3.2887494572514376e-06,
                1.994729721436347e-06,
                1.3709576971061233e-06,
                2.1444958627955892e-05,
                1.012999460150437e-05,
                6.14417606659952e-06,
                1.7603440526662173e-06
            ],
            [
                0.9999910603068933,
                0.999995777167059,
                0.9999251537817307,
                0.9999810748517638,
                0.9999885212359807,
                0.9999898700066057,
                0.9999646437619418,
                0.9999810748427375,
                0.9999546021097218,
                0.9999417087414357
            ],
            [
                0.9999485577863724,
                0.9999151889890939,
                0.9999485577740902,
                0.5312093733737563,
                0.9999485577864112,
                0.9999599363173749,
                0.9999339478789513,
                0.9999898700055513,
                0.9999599362982811,
                0.9999687980886429
            ],
            [
                0.9999938558261305,
                0.9999832985822034,
                0.5926665999540697,
                0.2018132150593341,
                0.9999687980855241,
                0.9991959139843068,
                0.7772998663336158,
                0.9999546021259487,
                0.8519528057272543,
                0.9999957771675625
            ],
            [
                0.9999980052700407,
                0.9999930377429208,
                0.9999980052698031,
                0.9999980052707541,
                0.9999945777810305,
                0.9999921107374148,
                0.9999945777829694,
                0.9999852610145165,
                0.9999952149043648,
                0.9999967112497585
            ],
            [
                0.9999945777829694,
                0.999996711251327,
                0.999988521233246,
                0.9999987901337396,
                0.9999957771675625,
                0.9999930377404308,
                0.999989870012645,
                0.9999785550490401,
                0.9999910603037008,
                0.999997438716568
            ],
            [
                0.9999885212359809,
                0.9999785550592607,
                0.9999921107374148,
                0.9999962733616045,
                0.9999646437619467,
                0.9999810748427401,
                0.999996273360272,
                0.9999785550439207,
                0.9999957771675627,
                0.9999724643056319
            ],
            [
                0.9999485577679615,
                0.999993037742922,
                0.9998415637093907,
                0.9998601779438178,
                0.9998601779759694,
                0.9998204720769719,
                0.9999852610127603,
                0.9999546021314331,
                0.9992903295540065,
                0.14804720179063333
            ],
            [
                0.9999910603047619,
                0.9999938558261308,
                0.9999952149066464,
                0.9999957771665556,
                0.9999885212332477,
                0.9999646437492907,
                0.9997040428653471,
                0.9999967112509347,
                0.9999967112517187,
                0.9998766053662735
            ],
            [
                1.7603432132784448e-06,
                1.7603430034311638e-06,
                1.3007131564643372e-05,
                5.422219615582823e-06,
                0.9998204720141193,
                1.4738980212296288e-05,
                1.4738983727900215e-05,
                1.0129992185539456e-05,
                6.475946437966953e-07,
                0.9999785550439195
            ],
            [
                0.9999646437324458,
                0.9999952149066467,
                0.999975699747687,
                0.9999967112521109,
                0.9999485578047611,
                0.9999986290429566,
                0.9999910603005008,
                0.9999852610145168,
                0.9999930377429215,
                0.9999852610197889
            ],
            [
                0.9999952149037947,
                0.9999898700066073,
                0.9999938558232023,
                0.9999930377420911,
                0.9999982396561572,
                0.9999994956527721,
                0.9999994284996893,
                0.9999993524050474,
                0.9999980052693275,
                0.9999930377454104
            ],
            [
                0.9999756997563826,
                0.9999930377420908,
                0.9999646437324408,
                0.9999810748517634,
                0.9999756997621758,
                0.9999869928653348,
                0.9999832985741784,
                0.9999756997650734,
                0.9999898700090213,
                0.9999885212264029
            ],
            [
                2.9023130230133794e-06,
                1.5534975693601474e-06,
                1.9947297214182054e-06,
                1.7603430033799313e-06,
                2.260325375664839e-06,
                1.0677024881887838e-06,
                2.90231163910023e-06,
                1.3709572067955008e-06,
                4.222833947774596e-06,
                1.5534984953199313e-06
            ],
            [
                0.9999938558246658,
                0.9999785550490401,
                0.9999832985741774,
                0.9999687980886605,
                0.9999646437492937,
                0.9999724642957828,
                0.9999930377462405,
                0.9999991684721706,
                0.9999962733598274,
                0.9999869928684362
            ],
            [
                0.9999832985721839,
                0.9999938558246659,
                0.9999898700053989,
                0.999989870010228,
                0.9999938558268631,
                0.9999869928684358,
                0.9999810748472503,
                0.9999957771675624,
                0.9999910603005002,
                0.9999957771665555
            ],
            [
                0.9998766054355224,
                5.144220748924517e-05,
                1.6701421837158667e-05,
                NaN,
                0.9995121429398309,
                2.561281294558644e-06,
                0.9988304897212096,
                0.9998601778761151,
                0.2450850131323717,
                1.1478773597640625e-05
            ],
            [
                0.9999930377454113,
                0.9999832985801487,
                0.9999251537370873,
                0.9999785550515897,
                0.9999989322972572,
                0.9999832985721876,
                0.9999921107392958,
                0.9999785550490354,
                0.9999832985721862,
                0.9999938558232014
            ],
            [
                0.9999756997679643,
                0.9999339478711234,
                0.9999885212305086,
                0.9999898700114392,
                0.999948557798617,
                0.9999962733598274,
                0.9999151889183355,
                0.9998601779093998,
                0.9999832985821377,
                0.9999921107364742
            ],
            [
                0.9999756997592727,
                0.9999724642990885,
                0.9999898700126436,
                0.9999546021206008,
                0.9998766054253622,
                0.9994472212622927,
                0.9999785550439251,
                0.9999938558246666,
                0.9999687980775028,
                0.9999869928653341
            ],
            [
                0.9999599363221695,
                0.9999987901347492,
                0.9999646437324624,
                0.9999546021151331,
                0.9999485577803159,
                0.9770226313026177,
                0.9999910603036983,
                0.9999930377404306,
                0.9999930377462414,
                0.9999646437577489
            ],
            [
                0.999978555054146,
                0.9999952149060763,
                0.9999810748495074,
                0.999915188928401,
                0.9999832985841317,
                0.9999974387171787,
                0.9999852610233088,
                0.9999930377445808,
                0.9999785550413712,
                0.9999724643187715
            ],
            [
                0.9999599363126035,
                0.9998911031038805,
                0.7772998714925403,
                0.9999962733589396,
                0.9999967112509369,
                0.9999485577679742,
                0.999995777166052,
                0.9999869928761882,
                0.9999970976887069,
                0.9999599363221628
            ],
            [
                1.0677032518413822e-06,
                3.288748280658394e-06,
                2.5612825159677387e-06,
                1.2098662603499435e-06,
                1.7603438427660027e-06,
                8.315278293899016e-07,
                1.3709575336405514e-06,
                9.422443692261927e-07,
                1.3709568799368123e-06,
                3.2887494572095624e-06
            ],
            [
                0.9999957771650453,
                0.9999957771660533,
                0.9999957771670593,
                0.9999945777829696,
                0.999989870011436,
                0.9999938558239334,
                0.9999869928653368,
                0.9999852610110029,
                0.999986992876194,
                0.9999869928715396
            ],
            [
                0.9999724642990576,
                0.9999810748472532,
                0.999993855824666,
                0.9999724642957752,
                0.9999038975850683,
                0.9998601779761789,
                0.9999687980811937,
                0.9999599362887345,
                0.9999646437408619,
                0.999903897550639
            ],
            [
                0.9999938558275955,
                0.9999756997563752,
                0.9999339478238508,
                0.9999599363078128,
                0.9241418131886822,
                0.9999962733607158,
                0.9997388097558977,
                0.9999970976880199,
                0.9999957771680659,
                0.6513548646660542
            ],
            [
                1.7603434231505666e-06,
                6.475948753991907e-07,
                1.760343423160973e-06,
                8.315282259009745e-07,
                1.209865971934245e-06,
                1.3709572068478697e-06,
                6.47594875389178e-07,
                2.9023133690425823e-06,
                8.315277302747361e-07,
                1.0129987356706945e-05
            ],
            [
                5.043472278227948e-07,
                2.2603237588597026e-06,
                9.422443692446175e-07,
                1.4738978451438343e-05,
                1.9947301970451086e-06,
                1.5534971989907999e-06,
                8.315282259051341e-07,
                1.9947294836483373e-06,
                1.3709568799760888e-06,
                3.466327450744504e-07
            ],
            [
                9.422442568951678e-07,
                6.47594798194325e-07,
                1.9947292458603553e-06,
                2.1444953522913026e-05,
                5.422220908703723e-06,
                5.715002426202836e-07,
                5.043475284350422e-07,
                8.315282258900085e-07,
                1.3709576971061233e-06,
                9.422444815409489e-07
            ],
            [
                0.9999977396757023,
                0.9999962733620488,
                0.9999967112505428,
                0.9999967112517187,
                0.999998446502801,
                0.999999057755743,
                0.9999930377454109,
                0.9999945777784454,
                0.999996711252111,
                0.9999986290423029
            ],
            [
                0.5312093733737563,
                0.7057850154599562,
                0.26894141551050293,
                0.11920291419948607,
                0.9990889486948142,
                0.999954602115151,
                0.9996646498927155,
                0.9149009642742805,
                0.9999756997506015,
                0.1192029235866439
            ],
            [
                9.422450431912e-07,
                6.144172403928222e-06,
                5.715005832827105e-07,
                1.0677027427569065e-06,
                4.222834954461155e-06,
                3.7266388397721442e-06,
                1.5534981249291695e-06,
                3.288750241374845e-06,
                1.067703379136937e-06,
                2.561282210618905e-06
            ],
            [
                0.9999967112493665,
                0.9999485577802218,
                0.9999952149055056,
                0.9999952149060757,
                0.999986992876188,
                0.9999885212264013,
                0.9999921107345936,
                0.9999885212359807,
                0.999995214903224,
                0.9999945777790915
            ],
            [
                0.9999785550490341,
                0.9999724642957762,
                0.9999921107355334,
                0.9999952149055054,
                0.9999810748517645,
                0.9999990577557432,
                0.9999885212318752,
                0.9999852610127585,
                0.9999646437619467,
                0.9999967112497586
            ],
            [
                0.9999646437577273,
                0.9999885212291376,
                0.9999885212291378,
                0.9993736658292114,
                0.9999546021367736,
                0.6513548511303336,
                0.9999546021421944,
                0.9999910602994336,
                0.9998415637647842,
                0.9997694933133399
            ],
            [
                0.9988304896167695,
                0.9999921107336526,
                0.9999974387168733,
                0.9998601779594093,
                0.9999546021259682,
                0.9959298627258002,
                0.9999977396746244,
                0.9999982396565767,
                0.9999852610233023,
                0.9999952149049351
            ],
            [
                3.2887506334560605e-06,
                0.20181321745968234,
                0.20181322466072713,
                0.8933094124452287,
                0.9947798731844332,
                1.0677026153784014e-06,
                8.315277302588544e-07,
                2.260324028351814e-06,
                5.422220908762902e-06,
                1.7603430034439723e-06
            ],
            [
                0.9997388096301462,
                0.5312093733737562,
                0.999978555041362,
                0.9992903296318586,
                0.9525741268224333,
                0.9999852610110026,
                0.9999417087278926,
                0.9999417087345043,
                0.6791786926816161,
                0.9999785550541487
            ],
            [
                0.999876605469328,
                0.9999038975506481,
                0.9999962733598274,
                0.9998415638398986,
                0.999992110740236,
                0.9999921107374143,
                0.9999957771655487,
                0.999992110740236,
                0.9999910603015647,
                0.9999810748585273
            ],
            [
                0.9999921107336539,
                0.9999785550515891,
                0.9999810748562746,
                0.9999869928730871,
                0.9999952149032658,
                0.9999957771675662,
                0.9984988174450455,
                0.9999898700102395,
                0.9999938558224688,
                0.9999546021313848
            ],
            [
                0.9999724643056332,
                0.9999910603036969,
                0.9999984465016898,
                0.9999930377429216,
                0.9999910603026309,
                0.9999756997534794,
                0.9999785550490328,
                0.9999687980774782,
                0.9999938558224685,
                0.9999957771675625
            ],
            [
                0.9999910603004999,
                0.9999974387187054,
                0.9999885212277704,
                0.9999785550413688,
                0.9999938558239335,
                0.9999957771655489,
                0.9999967112501505,
                0.999997097686631,
                0.9999993524054334,
                0.9999898700041905
            ],
            [
                5.043474081957179e-07,
                7.889259764359722e-06,
                2.56128282131428e-06,
                2.9023119850527192e-06,
                1.0677024881829577e-06,
                5.422219616140078e-06,
                1.473898372822193e-05,
                2.902312331081799e-06,
                9.422450431732037e-07,
                2.902310946944611e-06
            ],
            [
                0.9999339478711562,
                0.9999957771665555,
                0.999983298578157,
                0.9999898700114355,
                0.9999724642957772,
                0.9999832985721872,
                0.9999810748562717,
                0.9999977396748938,
                0.999989870005398,
                0.9999785550464741
            ],
            [
                3.288749457432399e-06,
                1.5534975693601474e-06,
                1.0677029973056687e-06,
                2.699577452733192e-07,
                1.3709576970949014e-06,
                9.422448185264317e-07,
                2.2603242978377903e-06,
                1.2098655392811161e-06,
                2.2603234894745224e-06,
                1.7603434231705793e-06
            ],
            [
                8.3152792852928e-07,
                6.475948753930064e-07,
                3.4663262110803996e-07,
                5.7150044702099e-07,
                1.0677028700130727e-06,
                1.553498124964492e-06,
                6.475946437996402e-07,
                8.315277302788957e-07,
                1.3709575336947905e-06,
                1.3709578605542582e-06
            ],
            [
                0.9999898700041914,
                0.9998766053812974,
                0.9998911031036888,
                0.9999962733593831,
                0.999994577779738,
                0.9999930377462408,
                0.9999938558261307,
                0.9999832985721865,
                0.9998415637454691,
                0.9999921107345934
            ],
            [
                0.9999982396563669,
                0.9999810748472489,
                0.9999885212318756,
                0.9998766054696027,
                0.32082128783705344,
                0.9579122765900843,
                0.9999980052695652,
                0.9241418147556224,
                0.6224593382055109,
                0.9669140211345885
            ],
            [
                5.4222202529041566e-06,
                6.144176797115634e-06,
                1.892514823013346e-05,
                2.1444950959977102e-05,
                1.4738987240475486e-05,
                1.1478772224060087e-05,
                1.892515274546026e-05,
                0.9980732649771384,
                2.2603253755476615e-06,
                2.561281599138645e-06
            ],
            [
                0.9993736657565971,
                0.9998204720776067,
                0.9986749778894974,
                0.9999852610110034,
                0.9399133555065331,
                0.9999810748540244,
                0.9999417087564625,
                0.8519528038477825,
                0.9998601779760934,
                0.7310585903489891
            ],
            [
                0.99998329857418,
                0.9980732650698203,
                0.999704042831067,
                0.9998415638405949,
                0.9997965730996001,
                0.9996646497733519,
                0.9999599362935362,
                0.9999687980813127,
                0.9982992773709483,
                0.9999339478554053
            ],
            [
                0.9999038975965528,
                0.9971990732377282,
                0.9999417087553318,
                0.9999151889687629,
                0.817574478416099,
                0.5926665999540698,
                0.9999646437324492,
                0.9669140235181256,
                0.13296425050508953,
                0.8670357598021707
            ],
            [
                0.9999982396567867,
                0.9999980052705163,
                0.999995214906076,
                0.9999938558246664,
                0.9999995549149481,
                0.9999986290424663,
                0.9999938558239336,
                0.9999938558275955,
                0.9999984465015046,
                0.9999974387187053
            ],
            [
                1.5534981249397663e-06,
                5.043473480730849e-07,
                8.3152792852928e-07,
                1.2098652508056196e-06,
                5.715004470313855e-07,
                1.7603438428564603e-06,
                2.5612819051722694e-06,
                1.0677028699858827e-06,
                7.338211554688417e-07,
                1.994729008056074e-06
            ],
            [
                0.9998911030519537,
                0.9996646499698518,
                0.9999832985701924,
                0.999992110736474,
                0.9999546021151456,
                0.9999724643056231,
                0.9999546021367783,
                0.9999810748427375,
                0.9997965731000796,
                0.9999646437535068
            ],
            [
                0.9999930377429204,
                0.9999898700053986,
                0.9999995549151073,
                0.9999982396561572,
                0.9999952149049351,
                0.999998005269803,
                0.9999869928746379,
                0.9999885212291407,
                0.9999938558232011,
                0.9999852610162764
            ],
            [
                2.902312677060767e-06,
                2.9023130230846496e-06,
                1.3709567165530083e-06,
                1.9947301970587145e-06,
                1.76034300345598e-06,
                3.7266410609940346e-06,
                3.288750633545794e-06,
                1.2098661161789477e-06,
                2.5612828213690224e-06,
                1.3709568799679844e-06
            ],
            [
                1.2098655392354511e-06,
                6.475951069961737e-07,
                1.2098656834834034e-06,
                6.475949526003845e-07,
                3.288750633488963e-06,
                1.3709570434054234e-06,
                1.0677029973056687e-06,
                2.902311293147782e-06,
                1.3709578605355551e-06,
                3.059023727894942e-07
            ],
            [
                0.999915188939035,
                0.9998415637078668,
                0.9997694931751738,
                0.9999756997650686,
                0.24508501864634824,
                0.9993736658977084,
                0.9998601779428534,
                0.9999646437450808,
                0.9999339478397375,
                0.679178699175393
            ],
            [
                0.24508500761839522,
                0.9999852610233939,
                0.9999945777784448,
                0.9999724643056213,
                0.8519528019683106,
                0.9999810748585282,
                0.6791786861878392,
                0.08509903688588202,
                0.999986992876188,
                0.5621765008857982
            ],
            [
                0.9999921107402359,
                0.9999980052702786,
                0.9999832985761661,
                0.9999970976883624,
                0.9999910603036961,
                0.9999945777816832,
                0.9999930377437506,
                0.9999967112493665,
                0.999968798081195,
                0.999993855826131
            ],
            [
                8.315280276505193e-07,
                5.422218323290717e-06,
                1.2098662603961589e-06,
                1.5534977545497995e-06,
                3.2887478891487563e-06,
                7.889264466344872e-06,
                6.1441775312976045e-06,
                3.7266410604686857e-06,
                9.422447061953531e-07,
                4.78509563546605e-06
            ],
            [
                6.475945666033422e-07,
                1.2098653950315304e-06,
                9.422449308673789e-07,
                5.043472879525233e-07,
                4.450849458179853e-07,
                3.059021904580685e-07,
                7.889259763326495e-06,
                0.9998766054252095,
                3.05902263389638e-07,
                4.450849458125204e-07
            ],
            [
                1.1478772229551402e-05,
                4.222833444283541e-06,
                8.315277302701984e-07,
                8.315280276546789e-07,
                2.9023109471689794e-06,
                1.0677029972522599e-06,
                9.422447062202052e-07,
                1.5534975693601474e-06,
                1.553497384196656e-06,
                1.7603434231385591e-06
            ],
            [
                0.9999485577864516,
                0.9999898700090265,
                0.9999785550515939,
                0.999968798081212,
                0.9999930377454106,
                0.9999756997563787,
                0.9999687980998007,
                0.9999945777829697,
                0.9999852610127591,
                0.9999967112493665
            ],
            [
                0.9999546021368159,
                0.9999980052702786,
                0.9999852610110012,
                0.9999885212346309,
                0.9999984465018767,
                0.999995214904935,
                0.9999251537995529,
                0.9999910603026306,
                0.9999810748517617,
                0.9999970976883618
            ],
            [
                0.999903897539346,
                0.9999417087484351,
                0.9999910603068937,
                0.9999756997476957,
                0.9999930377445821,
                0.9999970976876689,
                0.9999869928761898,
                0.9999952149037953,
                0.9999952149066468,
                0.9999869928668843
            ],
            [
                1.760342793515064e-06,
                1.9947292458603553e-06,
                1.7603436326432711e-06,
                8.93969417167259e-06,
                8.315282258037938e-07,
                2.5612831263929686e-06,
                7.338212429167144e-07,
                4.785093923690512e-06,
                9.422448185101494e-07,
                2.2603251061458426e-06
            ],
            [
                0.9046505325302034,
                0.9999945777829697,
                0.9999910603058276,
                0.9999852610197867,
                0.2227001285074597,
                0.9999599363030465,
                0.9999724643187533,
                0.9999810748562717,
                0.9999810748449914,
                0.999860177892907
            ],
            [
                3.927863875520681e-07,
                5.04347528431602e-07,
                2.260324028281919e-06,
                1.553497198908852e-06,
                5.4222183231674305e-06,
                1.0677032518316716e-06,
                1.0677032518093368e-06,
                1.4738978456719842e-05,
                1.0677026154279257e-06,
                2.260325375615501e-06
            ],
            [
                0.1824255326961778,
                0.9999910602994342,
                0.9999251537818918,
                0.9998766053957809,
                0.5621765008857981,
                0.9999910603047895,
                0.5621765008857981,
                0.5926665999540698,
                0.9999485577802407,
                0.9998601779426847
            ],
            [
                0.9999962733593835,
                0.9999952149043646,
                0.9999910603068931,
                0.9999952149037941,
                0.9999984465026158,
                0.9999852610110009,
                0.9999785550515939,
                0.9999930377437504,
                0.9999957771675624,
                0.9999980052707541
            ],
            [
                0.9999832985701956,
                0.9999251537906448,
                0.9999910603015651,
                0.9999869928668851,
                0.9999832985701943,
                0.9999869928684344,
                0.9999785550592574,
                0.9999810748517612,
                0.9999038975621215,
                0.9999687980849061
            ],
            [
                0.9999785550541473,
                0.9999646437408634,
                0.9990889489023441,
                0.9999417087553356,
                0.9999962733598274,
                0.9999785550567005,
                0.9999832985841296,
                0.9999724643023399,
                0.9998415637457089,
                0.9999869928684348
            ],
            [
                0.9999930377420905,
                0.9999930377429205,
                0.9999938558253987,
                0.9999930377429205,
                0.9999974387184001,
                0.9999980052705163,
                0.9999967112509347,
                0.9999599363078145,
                0.9999852610110019,
                0.9999938558246657
            ],
            [
                5.043472278227948e-07,
                2.902311639126627e-06,
                9.422447062094932e-07,
                5.4222202621161125e-06,
                9.422448185435711e-07,
                1.2098656834834034e-06,
                1.0677029972920738e-06,
                5.043475284430694e-07,
                1.994729483630195e-06,
                6.9622545877746946e-06
            ],
            [
                0.622459324198198,
                0.9999885212332438,
                0.9999832985741745,
                0.9999930377445803,
                0.9999646437619537,
                0.9999646437613898,
                0.9999952149066461,
                0.9999756997679619,
                0.9999724643023473,
                0.7057850340255386
            ],
            [
                0.8354835391516133,
                0.9999869928761882,
                0.5312093733737563,
                0.9999785550490341,
                0.9999869928746377,
                0.9999546021476212,
                0.14804719427274568,
                0.9999756997592735,
                0.7057850154599562,
                0.9999974387180947
            ],
            [
                0.9999921107374159,
                0.999998790134028,
                0.9999989322967482,
                0.9999930377404308,
                0.9999952149037942,
                0.9999885212318762,
                0.9999994284993485,
                0.9999921107364743,
                0.9999957771680659,
                0.9999921107355342
            ],
            [
                0.9999646437324458,
                0.9933071502799589,
                0.9999832985721847,
                0.9996646500099129,
                0.9998911030388326,
                0.9997694933680964,
                0.9996200154729662,
                0.9997965729784409,
                0.9999599363185805,
                0.9999251537728232
            ],
            [
                0.9999869928653365,
                0.9999930377429213,
                0.9999952149049351,
                0.9999910603058282,
                0.9999885212277709,
                0.9999982396572065,
                0.9999832985781624,
                0.9999945777823234,
                0.9999994284997573,
                0.9999938558239336
            ],
            [
                0.9999898700102279,
                0.9999756997650636,
                0.999994577780384,
                0.9999984465026158,
                0.9999930377412607,
                0.9999898700126435,
                0.999983298582142,
                0.9999832985801479,
                0.9999869928746377,
                0.999994577778445
            ],
            [
                2.260324836696773e-06,
                2.2603251062270446e-06,
                1.5534971989568904e-06,
                9.422447062202052e-07,
                1.7603436329554703e-06,
                8.3152792852928e-07,
                4.785096205830278e-06,
                2.561283431986506e-06,
                2.9023133686835932e-06,
                4.785095635624897e-06
            ],
            [
                9.422448185435711e-07,
                1.2098658277335738e-06,
                4.222833947897496e-06,
                1.5534983101478522e-06,
                1.3709572068354007e-06,
                6.47594566597747e-07,
                1.553498310118888e-06,
                8.31527928532683e-07,
                6.475950297868629e-07,
                3.466327037539638e-07
            ]
        ]
    },
    {
        "q_id": "8702_mmlu_math",
        "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,
            28,
            29,
            30,
            31,
            32,
            33,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            61,
            62,
            63,
            64,
            65,
            66,
            68,
            69,
            70,
            71,
            73,
            74,
            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,
            113,
            114,
            115,
            116,
            117,
            118,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999984465020604,
                0.9999986290424663,
                0.9999994284995529,
                0.9999996533672549,
                0.99999893229713,
                0.9999991684717742,
                0.9999980052700409,
                0.9999986290426299,
                0.9999990577549568,
                0.9999994284994848
            ],
            [
                0.9999986290426298,
                0.9999993524051246,
                0.9999994956524716,
                0.9999996533672135,
                0.9999994284992805,
                0.9999982396559474,
                0.999999057755743,
                0.9999987901343165,
                0.9999986290431201,
                0.9999982396561573
            ],
            [
                0.9999994284994167,
                0.9999989322970028,
                0.9999987901347491,
                0.9999984465024307,
                0.9999990577551815,
                0.9999997300422547,
                0.999998790134028,
                0.9999991684715759,
                0.9999980052693275,
                0.9999990577555185
            ],
            [
                0.999998629042303,
                0.9999995549149481,
                0.9999990577550693,
                0.9999991684719723,
                0.9999991684722698,
                0.9999992661788446,
                0.9999991684720715,
                0.9999995549149481,
                0.999998932296621,
                0.9999995549150011
            ],
            [
                0.9999992661788445,
                0.9999995549150542,
                0.999999352404893,
                0.9999996940976271,
                0.9999995549150542,
                0.9999989322972573,
                0.999999554914895,
                0.9999996072138466,
                0.9999996533675028,
                0.999999266179107
            ],
            [
                0.9999974387180947,
                0.9999984465022455,
                0.9999987901337396,
                0.9999994284992805,
                0.9999980052693274,
                0.9999994956527121,
                0.9999417087415846,
                0.9999994284993486,
                0.999995777165549,
                0.9999986290429566
            ],
            [
                0.998830489873518,
                0.9999756997505845,
                0.9999599363030746,
                0.9999898700066059,
                0.9999852610233032,
                0.999978555056705,
                0.9999832985761693,
                0.9999785550464814,
                0.9999724643089143,
                0.999981074849511
            ],
            [
                0.9999989322975119,
                0.9999982396574163,
                0.9999996533672962,
                0.9999989322973846,
                0.9999990577552939,
                0.999998239656367,
                0.9999986290429567,
                0.9999990577550691,
                0.9999993524053562,
                0.9999980052693275
            ],
            [
                0.9999982396569966,
                0.9999977396751636,
                0.9999991684720715,
                0.9999970976876692,
                0.9999970976876692,
                0.9999970976883614,
                0.9999986290424666,
                0.9999986290431203,
                0.999996273361605,
                0.999999428499553
            ],
            [
                0.9999977396762411,
                0.999996273360272,
                0.9999977396746245,
                0.9999967112505428,
                0.999997438717484,
                0.9999987901344607,
                0.9999986290429566,
                0.9999987901338838,
                0.9999974387177895,
                0.9999957771680659
            ],
            [
                0.9999992661786695,
                0.9999991684717742,
                0.9999996940978825,
                0.9999987901337396,
                0.9999991684720715,
                0.9999990577554061,
                0.9999993524050474,
                0.9999994956525918,
                0.9999992661791071,
                0.9999993524049702
            ],
            [
                0.9999990577552939,
                0.9999996533674615,
                0.9999995549150541,
                0.9999990577554062,
                0.9999994284993486,
                0.9999994956523514,
                0.9999986290429567,
                0.9999994956524716,
                0.9999994284994849,
                0.9999987901341724
            ],
            [
                1.4738985479697128e-05,
                7.484624487808333e-05,
                8.939696301611998e-06,
                4.00636778083227e-05,
                1.300712846115264e-05,
                0.0001088969608251887,
                4.006367775556302e-05,
                3.5356267535501495e-05,
                3.535623803067304e-05,
                3.120192250053358e-05
            ],
            [
                0.999999266179107,
                0.9999992661790195,
                0.9999994956527721,
                0.9999990577556307,
                0.9999996072137061,
                0.9999996533673788,
                0.9999994284994849,
                0.999999814460876,
                0.9999993524050474,
                0.9999984465024307
            ],
            [
                0.9999996072137998,
                0.9999992661786696,
                0.9999990577555185,
                0.9999986290424663,
                0.9999995549149481,
                0.9999996940977002,
                0.9999992661791944,
                0.9999991684722698,
                0.9999992661788446,
                0.9999987901337396
            ],
            [
                0.9999970976883609,
                0.9999945777829702,
                0.9999930377429215,
                0.9999945777816773,
                0.9999962733607162,
                0.9999785550413659,
                0.9999957771670592,
                0.9999930377462409,
                0.9999921107374159,
                0.9999921107336535
            ],
            [
                0.9999994284995529,
                0.9999990577552939,
                0.9999997300421581,
                0.9999991684720715,
                0.9999987901347492,
                0.9999984465022456,
                0.9999990577550693,
                0.9999987901343165,
                0.9999984465018751,
                0.999999266179107
            ],
            [
                0.9999984465026158,
                0.9999989322975118,
                0.9999996072136592,
                0.9999994284994167,
                0.9999989322970028,
                0.9999991684715759,
                0.99999893229713,
                0.9999991684722698,
                0.9999993524053562,
                0.9999994284997573
            ],
            [
                0.9999982396559475,
                0.9999996072138465,
                0.9999993524051247,
                0.9999993524052018,
                0.9999991684718732,
                0.9999996072139402,
                0.999999352404893,
                0.999999554914895,
                0.9999992661792819,
                0.9999990577555186
            ],
            [
                0.9999992661786696,
                0.9999994284993486,
                0.9999993524052018,
                0.9999994284994849,
                0.9999993524053562,
                0.9999996940977366,
                0.9999997617631753,
                0.9999994284993486,
                0.9999997617631469,
                0.9999986290427934
            ],
            [
                0.9999994284996893,
                0.9999996072138934,
                0.9999996072138934,
                0.9999993524052019,
                0.9999996072137061,
                0.9999990577550693,
                0.9999991684720715,
                0.999999266178757,
                0.9999993524052018,
                0.9999997897566089
            ],
            [
                0.9999994284996891,
                0.9999993524049702,
                0.9999989322975119,
                0.9999996533673375,
                0.9999993524054335,
                0.9999989322968754,
                0.9999996072137998,
                0.9999987901338839,
                0.9999991684720715,
                0.9999986290424664
            ],
            [
                0.9999991684717741,
                0.9999997617631183,
                0.9999991684720715,
                0.9999996533674201,
                0.9999994284997574,
                0.9999993524052018,
                0.9999994284995529,
                0.999999554914895,
                0.9999996940978461,
                0.9999994956526519
            ],
            [
                0.999999266178757,
                0.9999993524054335,
                0.9999994284993485,
                0.9999994284994167,
                0.9999994956524716,
                0.9999996940977366,
                0.9999994284994167,
                0.9999994956525318,
                0.9999995549150011,
                0.9999974387165684
            ],
            [
                0.9999990577549569,
                0.9999986290427932,
                0.9999991684721706,
                0.9999986290427932,
                0.999999352404893,
                0.999999266179107,
                0.9999989322972573,
                0.9999987901346051,
                0.9999994284994167,
                0.9999986290432836
            ],
            [
                0.9999993524054335,
                0.9999987901344608,
                0.9999994956527722,
                0.9999996072138934,
                0.9999994284992804,
                0.9999991684715759,
                0.9999996533672962,
                0.9999990577552939,
                0.9999996533675028,
                0.9999987901344607
            ],
            [
                0.9999996072136125,
                0.9999994284992805,
                0.9999991684720715,
                0.9999994956525317,
                0.9999986290424664,
                0.9999994284997574,
                0.9999993524050474,
                0.9999996533672548,
                0.9999991684717741,
                0.9999990577554062
            ],
            [
                8.481103106933806e-05,
                2.7535687809124434e-05,
                1.1478773596847203e-05,
                8.939696302831578e-06,
                8.939700566289352e-06,
                1.8925145980181433e-05,
                3.120191878631223e-05,
                5.144223195579028e-05,
                2.144494073796001e-05,
                3.535626754900668e-05
            ],
            [
                0.9999980052693275,
                0.9999984465028011,
                0.9999996940978095,
                0.999999168471675,
                0.9999987901337396,
                0.9999984465028011,
                0.9999992661788446,
                0.9999986290429567,
                0.9999984465028012,
                0.9999987901337396
            ],
            [
                0.9999990577556308,
                0.9999986290421394,
                0.9999996533673375,
                0.9999994956526519,
                0.9999994956527722,
                0.9999984465022456,
                0.9999991684717742,
                0.999998629042303,
                0.9999987901341723,
                0.9999987901347491
            ],
            [
                0.9999996072136593,
                0.9999991684715759,
                0.9999993524050474,
                0.9999992661788445,
                0.9999996072139402,
                0.9999997617630332,
                0.9999997300421581,
                0.9999989322973846,
                0.9999996072136125,
                0.9999994284996211
            ],
            [
                0.9999994956524716,
                0.999999694097846,
                0.999998790134028,
                0.9999996940976271,
                0.9999989322967482,
                0.9999989322975119,
                0.9999990577550693,
                0.9999990577552939,
                0.9999994284994849,
                0.9999997897566589
            ],
            [
                0.9999996940976636,
                0.9999980052693275,
                0.9999991684720715,
                0.9999992661792819,
                0.9999996072137529,
                0.9999989322968754,
                0.9999987901340281,
                0.999998932296621,
                0.9999992661790195,
                0.9999990577552937
            ],
            [
                0.9999485577741227,
                0.99994855779869,
                0.9999869928684365,
                0.9999810748540223,
                0.9999785550464837,
                0.9999785550490482,
                0.9999687980774912,
                0.9999546021151456,
                0.9999687980737891,
                0.9999869928730878
            ],
            [
                0.999999694097846,
                0.9999996533672549,
                0.9999995549150011,
                0.999999428499553,
                0.999999266178757,
                0.999999428499553,
                0.9999986290432835,
                0.9999991684718732,
                0.9999982396569966,
                0.9999991684718732
            ],
            [
                0.9999962733602717,
                0.9999869928746383,
                0.9999980052702786,
                0.9999980052702786,
                0.9999986290431201,
                0.999998239656367,
                0.9999938558232012,
                0.9999952149055055,
                0.9999980052700408,
                0.9999967112521109
            ],
            [
                0.9999898700053983,
                0.9999785550413659,
                0.999993855823201,
                0.9999599362982748,
                0.999981074844995,
                0.9999910603058282,
                0.999992110733653,
                0.999995214904935,
                0.9999869928668853,
                0.9999962733598274
            ],
            [
                0.9999974387174841,
                0.9999921107355355,
                0.9999910602994362,
                0.9999952149055058,
                0.999998239656367,
                0.9999898700041923,
                0.9999986290426298,
                0.999992110740238,
                0.9999990577549569,
                0.9999970976880151
            ],
            [
                0.999998005269803,
                0.9999989322968754,
                0.9999991684719723,
                0.9999980052693275,
                0.9999992661792819,
                0.999999168471576,
                0.999999168471675,
                0.9999984465016901,
                0.9999993524050474,
                0.9999993524054335
            ],
            [
                0.999997739674894,
                0.9999987901337396,
                0.9999994284997573,
                0.9999982396572065,
                0.9999986290426297,
                0.9999989322966208,
                0.9999989322966208,
                0.9999989322973846,
                0.9999994284997573,
                0.9999980052702787
            ],
            [
                0.9999987901340281,
                0.9999994284992805,
                0.9999996940976271,
                0.9999996533675028,
                0.9999994284996891,
                0.9999989322970028,
                0.9999996533672136,
                0.9999997617630617,
                0.9999995549148419,
                0.9999994956527722
            ],
            [
                1.1478769492642663e-05,
                2.144494839142443e-05,
                2.260325375520937e-06,
                1.3007128457485415e-05,
                6.144172403827636e-06,
                1.012999580884213e-05,
                3.2887506334201674e-06,
                4.222831933726245e-06,
                2.1444948408275583e-05,
                6.1441767987808774e-06
            ],
            [
                0.9999986290429567,
                0.9999993524052018,
                0.9999987901344608,
                0.9999994284996211,
                0.9999990577555185,
                0.999999168471675,
                0.9999986290424664,
                0.9999991684717742,
                0.9999989322972572,
                0.99999844650169
            ],
            [
                0.9999974387177893,
                0.9999921107364762,
                0.9999980052693274,
                0.9999980052702786,
                0.9999986290427932,
                0.9999986290426298,
                0.9999977396754329,
                0.9999977396751634,
                0.999998239656367,
                0.9999980052693275
            ],
            [
                0.9999989322971301,
                0.999999168471675,
                0.9999987901347492,
                0.9999994956527121,
                0.9999989322967482,
                0.9999986290421395,
                0.9999992661789321,
                0.9999996533672549,
                0.9999989322970028,
                0.9999990577549568
            ],
            [
                0.9999997617630049,
                0.9999994284996211,
                0.9999993524053563,
                0.9999994956525918,
                0.9999993524053562,
                0.9999997300420937,
                0.999999266179282,
                0.999999168471675,
                0.9999996072137061,
                0.9999996940976272
            ],
            [
                0.9999785550490693,
                0.9999957771655501,
                0.999995214906076,
                0.9999930377445815,
                0.999988521234614,
                0.9999785550439309,
                0.9999546021368217,
                0.9999832985781592,
                0.9999852610233041,
                0.9998204719724264
            ],
            [
                0.9999991684717742,
                0.9999990577555185,
                0.9999991684721706,
                0.9999994956527722,
                0.9999986290423029,
                0.999999352405279,
                0.9999986290429567,
                0.9999990577554061,
                0.9999990577554061,
                0.9999986290432835
            ],
            [
                0.9999957771655489,
                0.9999869928668866,
                0.9999756997534762,
                0.9999921107355337,
                0.9999970976887068,
                0.9999938558275956,
                0.9999869928715361,
                0.9999852610215446,
                0.9999938558253983,
                0.999972464305641
            ],
            [
                0.9999996072138934,
                0.9999994284993485,
                0.9999995549148419,
                0.9999992661791944,
                0.9999987901341723,
                0.9999995549147889,
                0.9999990577556308,
                0.9999996940977001,
                0.9999987901340281,
                0.9999989322970029
            ],
            [
                0.9999996940977366,
                0.999999352405279,
                0.9999989322972572,
                0.9999994284993486,
                0.9999995549150011,
                0.9999980052695653,
                0.999999428499553,
                0.9999992661790195,
                0.9999995549151072,
                0.999999730042126
            ],
            [
                0.9999980052698032,
                0.9999990577551816,
                0.9999991684717741,
                0.9999994956524114,
                0.9999993524050474,
                0.9999991684722698,
                0.9999990577554062,
                0.9999992661789321,
                0.9999993524051246,
                0.9999992661788445
            ],
            [
                0.9999992661786696,
                0.9999989322970028,
                0.9999996533673788,
                0.9999992661791944,
                0.9999986290431201,
                0.9999980052707542,
                0.9999990577554062,
                0.9999987901343166,
                0.9999992661786696,
                0.9999986290429567
            ],
            [
                0.999999352405279,
                0.9999991684721706,
                0.999998932296621,
                0.9999990577555185,
                0.9999990577556308,
                0.9999996072137061,
                0.9999994284996893,
                0.9999995549147358,
                0.9999992661791945,
                0.9999996940978095
            ],
            [
                0.999999266179282,
                0.9999996533674614,
                0.9999991684718733,
                0.9999990577551816,
                0.9999991684719723,
                0.9999989322970028,
                0.9999994956524716,
                0.999999428499553,
                0.9999991684716749,
                0.9999991684717742
            ],
            [
                0.9999997300421581,
                0.999999352404893,
                0.999999352404893,
                0.9999994956524716,
                0.9999989322972573,
                0.9999993524050474,
                0.9999991684722698,
                0.9999997617630048,
                0.9999990577552939,
                0.9999995549150542
            ],
            [
                0.999998790134605,
                0.999998239656367,
                0.9999989322970027,
                0.9999986290431201,
                0.9999989322975118,
                0.9999980052700409,
                0.9999990577555185,
                0.9999982396574163,
                0.9999984465020603,
                0.9999982396567867
            ],
            [
                0.999999266178757,
                0.999998005270992,
                0.9999987901340281,
                0.9999984465018752,
                0.9999977396762412,
                0.9999970976880153,
                0.9999991684722698,
                0.9999980052700409,
                0.9999982396561572,
                0.9999986290431201
            ],
            [
                0.9999986290424664,
                0.9999992661788446,
                0.9999977396765106,
                0.9999982396563671,
                0.9999991684720716,
                0.9999991684715758,
                0.9999991684715759,
                0.9999991684721706,
                0.9999997300420937,
                0.9999994956523514
            ],
            [
                0.9999986290432835,
                0.99999893229713,
                0.9999986290421395,
                0.9999996072138934,
                0.9999996533674201,
                0.9999998362623332,
                0.999999653367379,
                0.999999554914895,
                0.999999694097846,
                0.999999730042319
            ],
            [
                0.9999977396746245,
                0.999998932296621,
                0.999999554914895,
                0.9999989322970028,
                0.9999992661790195,
                0.9999996072136592,
                0.999999266178757,
                0.9999994956525918,
                0.9999984465022455,
                0.9999980052707542
            ],
            [
                0.9999989322975119,
                0.9999989322968754,
                0.9999991684718733,
                0.9999987901341724,
                0.9999986290431201,
                0.999999352405279,
                0.9999986290427932,
                0.9999987901341724,
                0.9999990577552939,
                0.999999554914895
            ],
            [
                0.9999910603015654,
                0.9999938558253986,
                0.9999962733620488,
                0.9999962733589389,
                0.999993855822469,
                0.9999930377429207,
                0.9999869928746402,
                0.9999930377429207,
                0.9999832985701967,
                0.9999945777816768
            ],
            [
                0.999996711249367,
                0.9999986290421395,
                0.9999990577557432,
                0.9999995549149481,
                0.9999989322968754,
                0.9999997300422546,
                0.9999996533672962,
                0.9999990577550693,
                0.9999987901338838,
                0.999999352405279
            ],
            [
                0.9999996533672962,
                0.9999992661786696,
                0.999999168471675,
                0.9999996072139402,
                0.9999990577551815,
                0.9999995549147358,
                0.9999996533674202,
                0.9999996533674202,
                0.9999994284994849,
                0.9999984465020604
            ],
            [
                4.7850950648799385e-06,
                6.9622595694023114e-06,
                5.422217676866151e-06,
                0.9999898700114359,
                8.939698434657777e-06,
                1.9947306725868575e-06,
                8.939695237341456e-06,
                4.785096205882502e-06,
                7.889262585211807e-06,
                6.144174601588856e-06
            ],
            [
                0.999999694097773,
                0.99999893229713,
                0.9999994956523514,
                0.9999996533673375,
                0.9999993524053562,
                0.9999996533673375,
                0.999999266178757,
                0.9999996533672962,
                0.9999996940978095,
                0.9999986290424664
            ],
            [
                0.9999984465028011,
                0.999998239656367,
                0.9999991684721706,
                0.9999977396746247,
                0.9999991684720716,
                0.9999986290421395,
                0.9999991684720715,
                0.9999994284992805,
                0.9999986290427932,
                0.999998005270041
            ],
            [
                0.9999980052705165,
                0.9999994284997573,
                0.9999994956524716,
                0.9999991684719723,
                0.9999986290421394,
                0.9999990577555185,
                0.9999992661791944,
                0.999998790134028,
                0.9999996072136592,
                0.9999996072136125
            ],
            [
                0.9999995549147358,
                0.9999987901337396,
                0.9999994284996893,
                0.9999991684722697,
                0.9999991684717742,
                0.9999990577551815,
                0.9999994284995529,
                0.9999992661790195,
                0.9999991684719723,
                0.9999982396565769
            ],
            [
                0.9999996072137061,
                0.9999986290426298,
                0.9999994956525918,
                0.999999266178757,
                0.9999996072137529,
                0.9999994956524114,
                0.9999991684718733,
                0.9999991684722697,
                0.9999996940977731,
                0.9999989322967482
            ],
            [
                0.9999984465015047,
                0.9999852610180329,
                0.9999952149060772,
                0.9999990577549569,
                0.9999982396574164,
                0.9999990577549568,
                0.9999980052702792,
                0.9999982396574164,
                0.9999989322967482,
                0.9999986290431201
            ],
            [
                0.9999974387177893,
                0.9999898700066056,
                0.999975699762171,
                0.9999938558261318,
                0.9999957771665556,
                0.9999910603068946,
                0.9999885212264031,
                0.999975699759271,
                0.9999921107336528,
                0.9999869928715373
            ],
            [
                0.9999987901338838,
                0.9999989322972573,
                0.9999986290431201,
                0.9999984465015047,
                0.9999992661791944,
                0.9999984465028011,
                0.9999993524053562,
                0.9999984465024306,
                0.9999993524053563,
                0.9999984465028011
            ],
            [
                0.9999996940977731,
                0.9999991684721706,
                0.9999995549149481,
                0.9999987901347491,
                0.9999989322970028,
                0.9999997617630332,
                0.9999997300423191,
                0.9999994956524716,
                0.9999989322968754,
                0.9999993524051247
            ],
            [
                0.9999991684721706,
                0.9999987901346051,
                0.9999987901338838,
                0.9999986290429568,
                0.9999987901341724,
                0.9999990577554061,
                0.9999989322973846,
                0.9999991684721706,
                0.9999995549148419,
                0.9999994284994168
            ],
            [
                8.939698434966738e-06,
                1.760342583722268e-06,
                2.2603242977555607e-06,
                3.7266388392671313e-06,
                2.2603234894745224e-06,
                1.5534983101393749e-06,
                2.902312677007974e-06,
                6.962253758017727e-06,
                7.338209805200689e-07,
                4.222834451215781e-06
            ],
            [
                0.9999987901340281,
                0.9999995549151073,
                0.999999653367379,
                0.9999996533673375,
                0.9999987901341723,
                0.9999995549150541,
                0.9999991684722698,
                0.9999994284994168,
                0.9999986290426298,
                0.9999996533672136
            ],
            [
                1.994730672407252e-06,
                2.260324567054496e-06,
                2.260324836651547e-06,
                2.902312676941983e-06,
                4.222834450420771e-06,
                3.288749848749297e-06,
                3.288749849114211e-06,
                2.5612831266608576e-06,
                5.422219614833243e-06,
                5.4222183222304545e-06
            ],
            [
                0.9999987901343165,
                0.999998239656367,
                0.9999921107383563,
                0.9999974387168734,
                0.9999974387177893,
                0.999998239656367,
                0.9999986290427931,
                0.9999977396757022,
                0.9999952149037947,
                0.9999982396574163
            ],
            [
                0.9999992661792819,
                0.9999990577556308,
                0.99999893229713,
                0.9999986290431201,
                0.9999986290424665,
                0.9999990577549568,
                0.9999982396574163,
                0.999999266179107,
                0.9999980052702787,
                0.9999990577551815
            ],
            [
                0.9999994284996211,
                0.9999992661789321,
                0.999999554914895,
                0.9999992661786696,
                0.9999987901344608,
                0.9999991684722697,
                0.9999996072136125,
                0.9999994284993485,
                0.9999994284996211,
                0.999998790133884
            ],
            [
                0.9999994284994848,
                0.9999980052695654,
                0.9999995549149481,
                0.9999992661786696,
                0.9999996533674202,
                0.999999352405279,
                0.9999994956527121,
                0.999999352404893,
                0.9999994956523514,
                0.9999989322972573
            ],
            [
                0.9999986290429567,
                0.9999994956525317,
                0.9999996072137998,
                0.9999995549148419,
                0.9999984465015048,
                0.9999996072138465,
                0.9999987901338838,
                0.9999992661791071,
                0.9999984465020604,
                0.9999996533672135
            ],
            [
                0.9999991684717742,
                0.9999984465022456,
                0.9999993524054334,
                0.9999992661787571,
                0.9999994284993486,
                0.9999995549151073,
                0.999998790134028,
                0.9999996072138465,
                0.9999980052693275,
                0.9999986290432835
            ],
            [
                2.4300252297461515e-05,
                1.3007126907455643e-05,
                2.4300249412738893e-05,
                2.902311984989368e-06,
                8.939693106182721e-06,
                0.00033535010162567315,
                1.0129990978847043e-05,
                7.48462002984577e-05,
                3.5356267545276676e-05,
                1.3007126911643378e-05
            ],
            [
                0.9999995549150542,
                0.9999994956526519,
                0.9999994284996211,
                0.9999995549147889,
                0.9999995549149481,
                0.9999986290421395,
                0.9999992661790195,
                0.9999977396762413,
                0.9999993524054334,
                0.9999996533673788
            ],
            [
                0.9999991684720715,
                0.9999994284992805,
                0.9999994956527121,
                0.9999989322975119,
                0.9999990577552937,
                0.9999991684717741,
                0.9999993524051246,
                0.999997438718095,
                0.9999982396561572,
                0.999996711249367
            ],
            [
                0.9999996072138465,
                0.9999991684722698,
                0.9999991684718732,
                0.9999994284996211,
                0.9999997617631468,
                0.99999893229713,
                0.9999996940977731,
                0.9999995549151072,
                0.999999266179107,
                0.9999995549149481
            ],
            [
                0.9999984465020604,
                0.9999996940977366,
                0.9999994956527722,
                0.9999996940978095,
                0.999999730042319,
                0.9999998144608097,
                0.9999994956525918,
                0.9999986290429568,
                0.9999992661791944,
                0.9999982396572065
            ],
            [
                0.9999980052698031,
                0.9999992661789321,
                0.9999989322966208,
                0.9999990577552939,
                0.999998239656577,
                0.9999989322967482,
                0.999999266179107,
                0.9999989322966208,
                0.9999992661790195,
                0.9999992661786696
            ],
            [
                0.9999996533675028,
                0.9999992661787571,
                0.9999986290424664,
                0.9999984465022456,
                0.9999982396561572,
                0.999998790134605,
                0.9999991684720715,
                0.9999996533674615,
                0.9999986290427932,
                0.9999995549151073
            ],
            [
                0.9999967112501505,
                0.9999993524052019,
                0.9999994956524715,
                0.9999885212305066,
                0.9999991684720715,
                0.9999938558232009,
                0.9999967112497584,
                0.999997438717484,
                0.9999986290423029,
                0.9999993524053562
            ],
            [
                0.9999990577549568,
                0.9999987901340281,
                0.9999996533674201,
                0.9999982396574164,
                0.9999992661786695,
                0.9999992661790196,
                0.9999993524052019,
                0.9999990577556308,
                0.9999987901343165,
                0.9999987901341723
            ],
            [
                0.9999984465028011,
                0.9999982396567868,
                0.9999994284994849,
                0.9999991684716749,
                0.9999987901338838,
                0.9999993524049703,
                0.9999982396561572,
                0.9999982396565771,
                0.999999266179107,
                0.9999991684719723
            ],
            [
                0.9999998362622357,
                0.9999996940976636,
                0.9999997897566089,
                0.9999990577555185,
                0.9999996072138934,
                0.9999987901347491,
                0.9999989322971301,
                0.9999996072137529,
                0.9999997617631183,
                0.9999995549147358
            ],
            [
                0.9999992661789321,
                0.9999992661792819,
                0.9999977396762413,
                0.9999990577550693,
                0.9999993524053562,
                0.9999992661790195,
                0.9999990577552939,
                0.9999991684720716,
                0.9999990577556308,
                0.9999994956523514
            ],
            [
                0.9999990577550691,
                0.999999495652652,
                0.9999994956523514,
                0.9999998144609202,
                0.9999996072136125,
                0.9999997300422869,
                0.9999996940977366,
                0.9999994284995529,
                0.9999995549148419,
                0.9999994284994849
            ],
            [
                0.99999844650169,
                0.9999986290421395,
                0.9999996072137529,
                0.9999990577550693,
                0.9999994956525918,
                0.9999995549147889,
                0.999999428499553,
                0.9999996940977366,
                0.9999996072139402,
                0.9999990577551815
            ],
            [
                0.999999352404893,
                0.9999996533672135,
                0.9999992661790195,
                0.9999991684717741,
                0.9999987901341723,
                0.9999991684722698,
                0.9999994956524716,
                0.9999987901340281,
                0.9999987901343165,
                0.9999996072136125
            ],
            [
                0.9999994956524115,
                0.999999694097773,
                0.999999495652712,
                0.9999995549150011,
                0.9999987901344608,
                0.9999996940976636,
                0.9999997617630333,
                0.9999996533674614,
                0.9999993524052789,
                0.9999995549148419
            ],
            [
                0.9999993524052019,
                0.999999168471675,
                0.9999994284994167,
                0.9999984465020604,
                0.9999996072139402,
                0.9999996072136125,
                0.9999992661791945,
                0.9999996940977002,
                0.9999991684719723,
                0.999999266178932
            ],
            [
                0.9999996533675028,
                0.9999994956524115,
                0.9999996072136592,
                0.9999994956523512,
                0.9999994284996211,
                0.999999266179107,
                0.999999694097846,
                0.9999996533672136,
                0.9999992661791944,
                0.9999980052705166
            ],
            [
                1.3007130009739366e-05,
                7.88926540454376e-06,
                1.0129988563343644e-05,
                5.422218969306048e-06,
                1.3007126911643378e-05,
                1.4738985480608657e-05,
                1.012998856048759e-05,
                0.00010889689600702287,
                2.1444943290362748e-05,
                3.120190391410763e-05
            ],
            [
                0.9999980052705165,
                0.9999989322973846,
                0.999998790134605,
                0.9999986290427934,
                0.9999997617630616,
                0.9999995549147358,
                0.9999994284994167,
                0.999999352405279,
                0.9999992661788446,
                0.9999982396561572
            ],
            [
                0.9999994284997574,
                0.9999996940977002,
                0.9999991684718733,
                0.9999991684718732,
                0.9999987901347492,
                0.9999993524054335,
                0.9999996940976272,
                0.9999990577549568,
                0.9999989322975119,
                0.9999994956526519
            ],
            [
                0.9999997617630616,
                0.9999996072136125,
                0.999999789756684,
                0.9999991684720715,
                0.9999996940976636,
                0.9999996072137529,
                0.9999995549147889,
                0.9999993524054335,
                0.9999996940977001,
                0.9999996533675028
            ],
            [
                1.0129992184544441e-05,
                3.120191133766637e-05,
                1.8925141464512013e-05,
                1.4738988990369329e-05,
                8.93969843377968e-06,
                4.2228319341064674e-06,
                1.0129987354882753e-05,
                1.1478772229050293e-05,
                7.48462268811262e-05,
                1.6701415864001047e-05
            ],
            [
                0.9999994956527721,
                0.9999996533675028,
                0.9999995549149481,
                0.9999994284997574,
                0.9999994956524114,
                0.9999994284997574,
                0.9999995549147889,
                0.9999994956525317,
                0.9999991684720715,
                0.9999995549147359
            ],
            [
                0.9999990577549568,
                0.9999992661787571,
                0.999999266178757,
                0.9999993524049703,
                0.999999428499553,
                0.9999992661790195,
                0.9999990577551815,
                0.9999990577552939,
                0.9999990577552939,
                0.9999990577552939
            ],
            [
                0.9999989322973847,
                0.9999990577555185,
                0.9999989322973846,
                0.9999996072137998,
                0.9999991684716749,
                0.9999974387165682,
                0.9999994956524114,
                0.9999995549147889,
                0.999999266178932,
                0.9999995549148419
            ],
            [
                0.9999994284994849,
                0.9999993524051246,
                0.9999989322973846,
                0.999999653367379,
                0.9999987901346051,
                0.9999992661788445,
                0.9999991684721706,
                0.9999989322973846,
                0.9999994284992805,
                0.9999994956524716
            ],
            [
                0.9999990577551815,
                0.9999991684716749,
                0.9999992661788445,
                0.9999974387184002,
                0.9999990577552939,
                0.9999986290421395,
                0.9999990577549569,
                0.9999994284994849,
                0.999999266179282,
                0.9999994284992805
            ],
            [
                0.9999989322968754,
                0.9999994956527121,
                0.999998629042303,
                0.9999989322967482,
                0.9999991684722698,
                0.999998005270992,
                0.9999989322970028,
                0.9999986290431201,
                0.9999980052707543,
                0.9999994284994167
            ],
            [
                0.9999995549149481,
                0.9999992661788445,
                0.9999993524052019,
                0.9999982396569966,
                0.9999989322970027,
                0.9999986290431201,
                0.9999992661791944,
                0.9999994956525317,
                0.9999993524054335,
                0.999998239656367
            ],
            [
                0.9999993524053562,
                0.9999990577555185,
                0.999999653367379,
                0.9999991684716749,
                0.9999991684719723,
                0.9999991684718732,
                0.999999266178757,
                0.9999997300422547,
                0.9999994284995529,
                0.9999989322970027
            ],
            [
                0.9999997300421903,
                0.999999266179282,
                0.9999997897565587,
                0.9999998144608317,
                0.9999991684722698,
                0.9999994284997574,
                0.9999993524052018,
                0.9999992661792819,
                0.9999997617631469,
                0.9999998144608981
            ]
        ]
    },
    {
        "q_id": "8652_mmlu_math",
        "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,
            41,
            42,
            43,
            44,
            45,
            46,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            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,
            99,
            100,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            112,
            113,
            114,
            116,
            117,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                6.605212071415797e-05,
                5.829126542194621e-05,
                0.00013982205680883731,
                0.0004305570363456723,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                6.605212849539707e-05
            ],
            [
                0.9998204719484768,
                0.9991959139510092,
                0.9997388096289302,
                0.9986749776795293,
                0.9997040428298269,
                0.9902915222828819,
                0.994088931458429,
                0.9975273769249129,
                0.9999038976079864,
                0.9986749776770646
            ],
            [
                0.0002305067133611251,
                4.006370172507966e-05,
                0.00023050674112844595,
                4.785093353739995e-06,
                1.6701421841259862e-05,
                1.3007133115667397e-05,
                2.7535700934898458e-05,
                NaN,
                5.144223203551027e-05,
                6.9622562492265485e-06
            ],
            [
                6.605213659861282e-05,
                1.892515500388139e-05,
                1.300712536258383e-05,
                4.006369217003476e-05,
                2.144495351940237e-05,
                6.9622579096593295e-06,
                2.2603242976733308e-06,
                1.0129987355988324e-05,
                3.726640172337686e-06,
                6.144176066521288e-06
            ],
            [
                0.9999982396563669,
                9.610241469123354e-05,
                0.00013982208999184544,
                0.00023050673919009903,
                2.5612822106654943e-06,
                9.610240295496837e-05,
                0.9999869928761884,
                0.9999910603004994,
                7.4846209355198e-05,
                4.0063687408107886e-05
            ],
            [
                0.9997388096594276,
                0.9997388097221476,
                0.9975273771477331,
                0.9996646498906275,
                0.14804720179063335,
                0.9770226279155795,
                0.9999485577803794,
                0.9933071485030027,
                0.9902915222112503,
                0.9978172831530363
            ],
            [
                0.0001795279630831852,
                3.5356267550807374e-05,
                4.539787391916088e-05,
                2.7535697654881812e-05,
                0.9324533088603709,
                5.829125832548044e-05,
                1.209865539274514e-06,
                5.422217676925328e-06,
                1.147877222879974e-05,
                6.144173868983067e-06
            ],
            [
                3.12019039027568e-05,
                1.4738988948760721e-05,
                NaN,
                3.535624637944346e-05,
                NaN,
                7.484622697043032e-05,
                NaN,
                NaN,
                0.00015843623443200788,
                1.1478768123823146e-05
            ],
            [
                0.9991959141446217,
                0.3775406687981454,
                2.7535697646567574e-05,
                0.999290329548888,
                0.43782349911420193,
                0.9968273168482461,
                0.9971990732403295,
                2.9023126767360923e-06,
                0.9968273169594356,
                0.9986749776915451
            ],
            [
                1.892515500450102e-05,
                7.88926258381982e-06,
                2.7535697653779924e-05,
                1.3007126909916233e-05,
                3.5356246488642456e-05,
                7.484624488625138e-05,
                2.7535691069506297e-05,
                6.962259569117366e-06,
                2.7535700932494338e-05,
                8.481105125791664e-05
            ],
            [
                0.9992903294578266,
                NaN,
                0.9902915253630379,
                0.11920293297380238,
                0.37754067580180184,
                0.4073334000459302,
                0.4687906266262437,
                5.829127904404153e-05,
                0.9964063974577636,
                0.9669140239948332
            ],
            [
                6.144176798479122e-06,
                1.0129989769188164e-05,
                3.927861066170637e-07,
                2.5612819053166966e-06,
                1.2098652507583041e-06,
                2.2603245672497918e-06,
                2.7535681225754707e-05,
                3.726639283291774e-06,
                4.222833947820683e-06,
                4.2228319341064674e-06
            ],
            [
                0.13296423332632276,
                0.3208213138121609,
                0.5,
                0.9998766053707656,
                0.2018132270610754,
                0.9579122686300084,
                0.9975273763558024,
                0.9875683498442848,
                0.999769493333689,
                0.9964063970267437
            ],
            [
                1.0129989770662257e-05,
                8.315280276399315e-07,
                1.892514823364471e-05,
                1.0129992186939844e-05,
                1.670142781432848e-05,
                7.889266347133978e-06,
                6.1441753327418334e-06,
                3.2887478890769702e-06,
                1.3007131561804229e-05,
                1.994729245878497e-06
            ],
            [
                0.9975273762822946,
                0.9998415637267211,
                0.9996200154693735,
                0.9997694932300513,
                0.9998204719911963,
                0.9991959140549239,
                0.998299277250182,
                0.9999038975620929,
                0.9996646497696542,
                0.9997965730750646
            ],
            [
                2.9023116390421582e-06,
                6.962257907880012e-06,
                5.422219615898437e-06,
                4.7850944943330625e-06,
                1.4738976698757546e-05,
                4.222834451292594e-06,
                4.539785779797843e-05,
                3.726637951126493e-06,
                1.6701419848475466e-05,
                2.7535687797204028e-05
            ],
            [
                0.0002959572399905383,
                NaN,
                9.610242602198156e-05,
                0.999997097688707,
                NaN,
                9.610244874081359e-05,
                0.00029595723730392506,
                0.0007096705168281311,
                0.0002034269229820478,
                NaN
            ],
            [
                0.00015843621613344748,
                1.3007125357804606e-05,
                7.484624505832518e-05,
                3.5356267539488744e-05,
                4.006368258642613e-05,
                2.9023116389365734e-06,
                7.484624471254397e-05,
                5.1442213614207906e-05,
                5.1442213565178264e-05,
                1.892515724543503e-05
            ],
            [
                6.605213662504366e-05,
                1.8925145963175983e-05,
                3.120191508446373e-05,
                6.962253759271479e-06,
                5.42221702873045e-06,
                3.288750241473551e-06,
                8.93969417150998e-06,
                3.1201926246083686e-05,
                2.260324836651547e-06,
                3.2887490652451393e-06
            ],
            [
                4.785093924047376e-06,
                4.785096205651846e-06,
                1.7603430033799313e-06,
                2.9023130229209922e-06,
                9.422448185264317e-07,
                4.222833947498071e-06,
                1.0129987355785634e-05,
                8.939693105272102e-06,
                2.144495351862222e-05,
                8.315284241560147e-07
            ],
            [
                9.610239057407012e-05,
                3.535624646947797e-05,
                1.300712846115264e-05,
                9.610246067494954e-05,
                5.8291258543467846e-05,
                2.1444958636771547e-05,
                3.1201900209877224e-05,
                6.605212879670866e-05,
                4.222834448492775e-06,
                NaN
            ],
            [
                1.147877222702498e-05,
                2.753569109454917e-05,
                3.120190019784534e-05,
                1.0129990978644356e-05,
                5.144220135417782e-05,
                5.829129331162062e-05,
                2.4300249410794055e-05,
                5.144221356929526e-05,
                0.0001398220898168875,
                4.006367782114826e-05
            ],
            [
                2.9023112931213857e-06,
                3.288748281220719e-06,
                3.7266392838544054e-06,
                4.7850956352353935e-06,
                1.5534971989809095e-06,
                6.962254589528684e-06,
                5.422220261544064e-06,
                4.222833947728508e-06,
                2.9023109471689794e-06,
                2.9023112931213857e-06
            ],
            [
                1.1478773597870298e-05,
                1.6701423833011596e-05,
                1.3007133108948093e-05,
                3.120191878472311e-05,
                2.7535687813231466e-05,
                3.1201918766788786e-05,
                4.006367782114826e-05,
                3.120191878472311e-05,
                2.753570419988976e-05,
                3.120191135264947e-05
            ],
            [
                4.006369209133245e-05,
                7.889260703462123e-06,
                0.0002034269472748494,
                5.144223815748175e-05,
                3.120192623836512e-05,
                0.00015843621627867414,
                NaN,
                5.1442213498932095e-05,
                0.00010889688295561384,
                4.539786319306454e-05
            ],
            [
                5.1442238010018466e-05,
                7.484625364295695e-05,
                4.006368725697032e-05,
                1.8925150490206403e-05,
                0.0001584362149877705,
                8.481108161946477e-05,
                NaN,
                1.0677033791291683e-06,
                1.3007131562514014e-05,
                0.00012339460365882503
            ],
            [
                9.610246050644951e-05,
                NaN,
                NaN,
                6.60521288207367e-05,
                0.0003353502245601093,
                6.605213677978425e-05,
                2.144494329496561e-05,
                4.5397879408714157e-05,
                0.00012339458948050277,
                NaN
            ],
            [
                1.473898899846585e-05,
                0.00012339454457201975,
                3.1201903906162046e-05,
                7.48462182289749e-05,
                2.4300252317086683e-05,
                2.7535691069506297e-05,
                4.006371122007986e-05,
                2.1444943285915917e-05,
                7.889261643554814e-06,
                0.0002034270435226738
            ],
            [
                0.9992903297087612,
                0.9990889488833767,
                0.9997694932297292,
                0.994779873198942,
                0.9968273172075869,
                0.9997694933679286,
                0.9975273769484583,
                0.9968273175610368,
                0.9924227597371248,
                0.9995694429615251
            ],
            [
                0.996406396712441,
                0.9988304897205296,
                0.9999038975735655,
                0.9953904268719731,
                0.999195914240025,
                0.9914225128835125,
                0.9980732655607657,
                0.9984988176849806,
                0.989013058148644,
                0.9975273769157244
            ],
            [
                2.7535687811228037e-05,
                2.1444940742640888e-05,
                2.4300243577612267e-05,
                0.00010889690847534261,
                0.00017952794385881705,
                5.144222583232244e-05,
                5.829127239924071e-05,
                6.605217605122477e-05,
                0.00012339460332847028,
                7.889266346746518e-06
            ],
            [
                0.00012339460423515042,
                2.4300237824258528e-05,
                0.00010889686991846671,
                3.5356246493272806e-05,
                2.753569438157704e-05,
                3.535625070315809e-05,
                2.1444945853999886e-05,
                3.120192252175965e-05,
                1.300713311517055e-05,
                2.7535704202894907e-05
            ],
            [
                2.144494073483943e-05,
                2.90231094702116e-06,
                1.8925157261545463e-05,
                0.0001584361590709057,
                6.9622562487453084e-06,
                8.481106146543261e-05,
                0.00013982209027259192,
                1.670142582102693e-05,
                2.7535684524701807e-05,
                1.1478773598099973e-05
            ],
            [
                5.144220749598207e-05,
                7.484623573530184e-05,
                0.9902915255689785,
                0.00012339452973658598,
                8.481105125791664e-05,
                NaN,
                NaN,
                1.0129994600159262e-05,
                6.605213677497863e-05,
                0.9998766053811413
            ],
            [
                0.9995694429115358,
                0.9399133540338004,
                0.9947798731626701,
                NaN,
                0.9978172839075923,
                0.9988304898774617,
                0.9706877724285167,
                0.9984988176968465,
                0.9875683517194515,
                0.9980732657752324
            ],
            [
                2.1444948408977715e-05,
                5.829125836916275e-05,
                0.00010889694593735195,
                1.473898196763166e-05,
                1.0129995793198314e-05,
                9.610238008932154e-05,
                2.4300234906298624e-05,
                9.610241483875839e-05,
                5.422217676797111e-06,
                1.0129990975862006e-05
            ],
            [
                2.5612834318257725e-06,
                8.939698434495167e-06,
                4.785096775998733e-06,
                2.260323758939877e-06,
                2.902312330965655e-06,
                2.9023123307122503e-06,
                1.5534979397394734e-06,
                3.2887478891487563e-06,
                1.760342793583908e-06,
                2.144495863614743e-05
            ],
            [
                0.0005527785369438728,
                0.0002959569853479269,
                0.0005527786604955352,
                0.00029595709155518993,
                NaN,
                0.00048785716101439514,
                0.00043055713748880385,
                0.00010889690897128673,
                0.0015011824319332628,
                0.000911051365002205
            ],
            [
                NaN,
                4.785095065093186e-06,
                0.9999910603015648,
                4.006370646879011e-05,
                0.9996200155613383,
                4.0063706476368846e-05,
                1.6701427794095925e-05,
                4.539786859541785e-05,
                5.829125144488242e-05,
                NaN
            ],
            [
                8.481103115695619e-05,
                1.0129994596455602e-05,
                5.144223796922279e-05,
                0.00010889693501231766,
                6.605217592003159e-05,
                1.3709578605118645e-06,
                7.484621685292953e-05,
                5.829127228812649e-05,
                1.0129992185539456e-05,
                2.43002465110435e-05
            ],
            [
                1.1478773597118638e-05,
                7.889261644501938e-06,
                2.7535697662094155e-05,
                1.4738988998787566e-05,
                1.1478773598538445e-05,
                1.1478766756444477e-05,
                1.6701429800582296e-05,
                1.4738985485166298e-05,
                1.1478765386894505e-05,
                1.6701427811412077e-05
            ],
            [
                4.006371126555232e-05,
                7.889262584508638e-06,
                6.14417460073947e-06,
                7.889259763857458e-06,
                5.422220908018252e-06,
                1.6701419848475466e-05,
                1.1478764018576587e-05,
                3.7266406163624873e-06,
                2.43002436174814e-05,
                4.006368255581968e-05
            ],
            [
                0.9796676448764484,
                0.9988304899579675,
                0.9995121429623957,
                0.9968273174660471,
                0.9933071502459058,
                0.9902915256943335,
                0.9796676477703993,
                0.9914225149268431,
                0.9982992773144194,
                0.9669140193469353
            ],
            [
                3.5356246476937965e-05,
                1.147876949310201e-05,
                8.48110109893614e-05,
                2.430023493228869e-05,
                2.1444948403750736e-05,
                4.2228349539810764e-06,
                8.481106145679419e-05,
                5.144221976237626e-05,
                6.60521288918597e-05,
                9.610240329616323e-05
            ],
            [
                6.9622545892184106e-06,
                7.889265404959923e-06,
                1.0129990978644356e-05,
                1.0129988558423862e-05,
                3.120190389560577e-05,
                3.7266397280960194e-06,
                NaN,
                3.5356259106723956e-05,
                2.1444953515423628e-05,
                2.5612825153504304e-06
            ],
            [
                0.9933071499146614,
                0.9995121427647069,
                0.9971990732175684,
                0.9996200154243915,
                0.9820137920118696,
                0.9978172839233121,
                0.9796676442828174,
                0.9978172839623584,
                0.9995121428213029,
                0.9964063975669775
            ],
            [
                0.9984988180667828,
                0.9964063967066051,
                0.9975273772683316,
                0.9875683502902086,
                0.9991959142359097,
                0.9947798740404482,
                0.9982992774759022,
                0.9978172831393448,
                0.9890130554364933,
                0.9990889488732042
            ],
            [
                1.8925150494750372e-05,
                2.7535681248693975e-05,
                6.9622570786798724e-06,
                3.120190763922401e-05,
                3.120190763332158e-05,
                4.222833444168322e-06,
                1.6701425825857226e-05,
                6.605212085976786e-05,
                6.144176066353646e-06,
                2.1444956079218013e-05
            ],
            [
                NaN,
                7.484624474085991e-05,
                8.481106135683544e-05,
                1.14787667504103e-05,
                4.006367785700152e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                0.00017952792250305392
            ],
            [
                2.1444950958338794e-05,
                3.120191126048069e-05,
                6.605213675431452e-05,
                2.144494328950459e-05,
                NaN,
                2.4300249411766472e-05,
                5.8291272294063885e-05,
                0.00033535009579116693,
                7.484624480293717e-05,
                0.0001398220229890718
            ],
            [
                NaN,
                3.535625069312567e-05,
                7.48462449913471e-05,
                4.539786317192547e-05,
                9.610240338425864e-05,
                0.0001398220567376335,
                7.484621824258834e-05,
                NaN,
                5.1442207479139826e-05,
                NaN
            ],
            [
                4.539786857031521e-05,
                NaN,
                NaN,
                NaN,
                4.539789020847081e-05,
                3.5356263316996617e-05,
                NaN,
                NaN,
                0.00013982205599101085,
                4.539787932217606e-05
            ],
            [
                5.8291251536063904e-05,
                2.7535684528909006e-05,
                5.829128637885414e-05,
                3.288749849000549e-06,
                2.7535681216639104e-05,
                6.60521682560438e-05,
                NaN,
                2.4300243625614346e-05,
                8.939698435096828e-06,
                1.9947292458603553e-06
            ],
            [
                8.939697369151141e-06,
                1.4738983724575818e-05,
                3.726640616748873e-06,
                1.147876538789672e-05,
                1.3007130012673148e-05,
                8.939699499823059e-06,
                6.96225541916544e-06,
                1.8925157260443894e-05,
                5.8291251541153115e-05,
                3.5356254720498605e-05
            ],
            [
                0.9999967112505438,
                8.481107164765161e-05,
                3.1201922517673344e-05,
                2.4300243611116483e-05,
                0.00043055697915440867,
                0.0001584362541805322,
                0.00015843621158762253,
                0.00010889694783239789,
                0.00017952790125438557,
                3.535626333809042e-05
            ],
            [
                4.006370650464339e-05,
                0.0001233945451573219,
                3.5356254914330094e-05,
                1.670141786036971e-05,
                1.012998856312253e-05,
                0.0001584361786580577,
                1.4738981968462759e-05,
                7.484623558174233e-05,
                NaN,
                NaN
            ],
            [
                4.222834953520201e-06,
                5.144221974927673e-05,
                5.8291272333081096e-05,
                6.605214461148412e-05,
                1.147876401160283e-05,
                2.4300252317086683e-05,
                2.7535681249595513e-05,
                2.144495863411905e-05,
                5.82912445736154e-05,
                0.00010889687022902587
            ],
            [
                4.539786849599816e-05,
                1.3007126913583456e-05,
                1.8925145978942173e-05,
                0.9999417087066922,
                8.939699500327152e-06,
                2.7535684522397864e-05,
                5.829126548725762e-05,
                1.8925152732723376e-05,
                2.1444956079218013e-05,
                6.962254589104433e-06
            ],
            [
                NaN,
                3.5356242264223526e-05,
                1.1478773591543802e-05,
                4.5397890257685224e-05,
                4.785096205347206e-06,
                2.430024649256756e-05,
                7.484623613063591e-05,
                3.120190390934028e-05,
                2.4300252309307336e-05,
                4.006367782348017e-05
            ],
            [
                0.9997040428652609,
                0.9971990729229758,
                0.9997694932028607,
                0.9995694428590541,
                0.9968273174226022,
                0.9940889308290833,
                0.9968273171803418,
                0.16451646904109268,
                5.422218322763051e-06,
                0.999569443012441
            ],
            [
                NaN,
                4.0063687388140825e-05,
                0.00010889696049086198,
                NaN,
                4.00636778083227e-05,
                5.144221364340114e-05,
                0.0002305067941881835,
                0.957912271934191,
                0.00020342692415998816,
                4.006369693473136e-05
            ],
            [
                2.4300252304268445e-05,
                6.605213639389391e-05,
                3.1201922520397544e-05,
                6.9622545892184106e-06,
                NaN,
                3.5356250660713247e-05,
                5.144219523894761e-05,
                8.481103091322968e-05,
                0.00012339461824470617,
                8.481107160692766e-05
            ],
            [
                4.539785780557527e-05,
                2.753568124769226e-05,
                3.1201926219749737e-05,
                2.753569765908901e-05,
                8.481107155633124e-05,
                2.7535694382378416e-05,
                4.00636874062132e-05,
                3.5356238062828204e-05,
                NaN,
                7.484621826273621e-05
            ],
            [
                3.120191133017482e-05,
                1.4738988995838502e-05,
                3.120192251336002e-05,
                1.670141785651155e-05,
                4.006369693473136e-05,
                2.753568781022632e-05,
                4.006368262883792e-05,
                2.7535684524701807e-05,
                4.006367784140681e-05,
                2.1444953521586782e-05
            ],
            [
                0.9992903294489104,
                0.9982992774717516,
                0.999978555054151,
                0.9990889486511573,
                0.9994472213195986,
                0.999664649850791,
                0.9997965729538639,
                0.9990889486531707,
                0.9989677687955445,
                0.99986017797589
            ],
            [
                0.9995694429496133,
                0.9933071487382792,
                0.9953904268356508,
                0.9947798744805463,
                0.5,
                0.9986749776940099,
                0.9991959141567343,
                0.16451645880021026,
                0.7057850278370112,
                0.6513548714339145
            ],
            [
                0.00010889689533520087,
                9.610241451644106e-05,
                3.5356246471407274e-05,
                0.00020342706418695746,
                NaN,
                0.9997694933405772,
                0.00013982207240043553,
                2.4300246515109972e-05,
                NaN,
                NaN
            ],
            [
                6.962257079059797e-06,
                6.605212102892523e-05,
                1.3007130014376633e-05,
                4.539785777882115e-05,
                2.4300252313020203e-05,
                4.539789026032761e-05,
                4.5397879405741464e-05,
                6.144172404380855e-06,
                0.00020342702066233158,
                7.484626289355904e-05
            ],
            [
                4.006368260814213e-05,
                5.144223202577919e-05,
                5.144221340536407e-05,
                1.012999580884213e-05,
                2.1444953516281788e-05,
                4.539787943778038e-05,
                1.4738981970312625e-05,
                3.535626755260807e-05,
                2.1444940705896026e-05,
                1.6701421832054962e-05
            ],
            [
                1.3007130011655787e-05,
                3.120191133585023e-05,
                NaN,
                NaN,
                0.00015843622970176762,
                0.00017952800807500606,
                0.00013982209045161867,
                5.82912863042125e-05,
                5.14422380702763e-05,
                4.006370650464339e-05
            ],
            [
                6.144172404380855e-06,
                8.939698434153684e-06,
                1.012999339309804e-05,
                1.1478764019328247e-05,
                2.9023116391477434e-06,
                7.889263525534328e-06,
                2.2603234895053587e-06,
                2.902313022984344e-06,
                4.539789022795839e-05,
                4.5397874000744484e-05
            ],
            [
                4.539786863059458e-05,
                4.006370172712009e-05,
                0.00015843621641929045,
                0.0003353500944740125,
                2.7535684521195802e-05,
                0.00013982214009899607,
                5.8291265499980624e-05,
                0.00010889694799084654,
                0.00017952800661489394,
                5.8291272448012225e-05
            ],
            [
                0.9924227574084995,
                0.9796676442828174,
                0.9940889312750979,
                0.9990889489120399,
                0.995390427700976,
                0.9980732650870582,
                NaN,
                0.9975273767319551,
                0.9980732655518109,
                0.9902915248526633
            ],
            [
                NaN,
                6.605214462205646e-05,
                NaN,
                5.144219523894761e-05,
                0.00017952800715296746,
                0.00012339461836499843,
                7.48462003289518e-05,
                0.0002034270692805172,
                NaN,
                8.481104100042252e-05
            ],
            [
                0.0001795280295039156,
                0.00013982210693632,
                1.5534975693036317e-06,
                0.0001584361786580577,
                9.610240338425864e-05,
                0.00012339463292933644,
                4.539789026032761e-05,
                NaN,
                0.0003353501790841194,
                9.610240332972338e-05
            ],
            [
                2.430024072648329e-05,
                7.88926352599354e-06,
                1.6701417848187652e-05,
                2.430023493052066e-05,
                1.3007125361755747e-05,
                1.4738981961519057e-05,
                5.829128628512799e-05,
                2.1444945839255133e-05,
                5.829128591531261e-05,
                1.1478769493331685e-05
            ],
            [
                1.6701415854279704e-05,
                0.00013982205694717612,
                6.605216006055645e-05,
                4.539785238670836e-05,
                8.939699487025595e-06,
                3.535624648041073e-05,
                4.006370171458602e-05,
                4.539786857989385e-05,
                3.120191508185304e-05,
                9.610238050882334e-05
            ],
            [
                NaN,
                0.00012339454510166436,
                2.7535684532815695e-05,
                0.00010889687018941373,
                9.61024378393533e-05,
                6.605212890675706e-05,
                5.829127929680522e-05,
                5.829125857569945e-05,
                0.00026119040013843466,
                0.00013982204026107567
            ],
            [
                6.962256248871951e-06,
                6.962257079465052e-06,
                NaN,
                2.4300246516082393e-05,
                1.8925152747388e-05,
                4.006371128012683e-05,
                6.962255419653012e-06,
                1.3007123810638006e-05,
                1.1478764018305152e-05,
                2.144495863411905e-05
            ],
            [
                6.144173868882483e-06,
                1.300713311517055e-05,
                5.829127930231852e-05,
                6.605212085304002e-05,
                0.00029595706072804137,
                0.00012339455994966783,
                NaN,
                1.3007123811513407e-05,
                NaN,
                2.144495863045236e-05
            ],
            [
                0.00012339463335484782,
                NaN,
                6.605212891684883e-05,
                0.00010889690883660543,
                5.422220908703723e-06,
                7.484623598905621e-05,
                0.00026119030819781683,
                8.481101094863749e-05,
                0.0002305066303542942,
                4.006368738143655e-05
            ],
            [
                1.3007126911974612e-05,
                1.0129987356706945e-05,
                8.939698435226916e-06,
                2.1444950966608343e-05,
                8.939697369151141e-06,
                1.3007131564643372e-05,
                2.144494585583323e-05,
                2.753569437145972e-05,
                4.785095065132354e-06,
                7.484620933559467e-05
            ],
            [
                NaN,
                1.892514822620912e-05,
                4.539786862811735e-05,
                4.006370172318498e-05,
                5.8291258547708845e-05,
                0.00010889688324557471,
                4.006370647374544e-05,
                2.430025231213619e-05,
                1.30071315640992e-05,
                0.9999485577741969
            ],
            [
                6.605212093617702e-05,
                NaN,
                6.605215247346026e-05,
                1.8925150495232307e-05,
                0.00010889693408063965,
                1.4738985484871391e-05,
                1.0129988564099116e-05,
                5.8291265441454815e-05,
                5.144220135417782e-05,
                4.539789026032761e-05
            ],
            [
                2.144494583184375e-05,
                4.0063677758769415e-05,
                0.0002305067082637429,
                1.147876675341695e-05,
                1.3007130010543792e-05,
                3.120192619909121e-05,
                4.006370638746435e-05,
                8.939695237162584e-06,
                4.006371126117997e-05,
                9.610241455559457e-05
            ],
            [
                4.5397874031792504e-05,
                2.4300249419722622e-05,
                2.1444940743772097e-05,
                3.535625488822007e-05,
                1.0129992179495674e-05,
                3.5356250694926364e-05,
                3.2887506333812835e-06,
                8.4811031131658e-05,
                9.610238052909926e-05,
                2.9023126768680736e-06
            ],
            [
                7.484623609796368e-05,
                5.829124443026963e-05,
                3.7266388393349185e-06,
                6.605213649769506e-05,
                1.8925154985774363e-05,
                0.00020342692293469342,
                NaN,
                7.889265405146477e-06,
                1.892514145328979e-05,
                2.144494838580738e-05
            ],
            [
                6.962257908487893e-06,
                5.829125852607975e-05,
                NaN,
                3.5356242231939725e-05,
                2.1444945848226808e-05,
                4.0063692132141055e-05,
                2.1444950945466384e-05,
                1.4738985476533587e-05,
                3.5356259028265286e-05,
                4.5397884834850856e-05
            ],
            [
                7.484626287395567e-05,
                8.939695236593446e-06,
                6.962254589332388e-06,
                2.4300240729754152e-05,
                2.1444958633416914e-05,
                5.829127247939563e-05,
                5.144222569009901e-05,
                2.4300252282875242e-05,
                1.6701415871049018e-05,
                1.3007128461507534e-05
            ],
            [
                4.785096205973894e-06,
                5.422221555069497e-06,
                5.829125856424875e-05,
                1.670142781244497e-05,
                6.144175334094145e-06,
                2.4300246504236573e-05,
                2.1444958625381407e-05,
                0.9989677690556786,
                2.1444953504969666e-05,
                2.430023783309869e-05
            ],
            [
                1.473898371722997e-05,
                6.144174600605357e-06,
                1.300712380997554e-05,
                0.00010889693477781366,
                3.535624646150348e-05,
                NaN,
                0.00012339457442243326,
                2.144494072867628e-05,
                0.00013982203916250294,
                0.9996200155618469
            ],
            [
                0.5926665999540698,
                0.998073264926544,
                1.8925148224556773e-05,
                0.3775406687981454,
                0.9859363715362616,
                0.9820137872743625,
                0.994779875452631,
                0.996406396570713,
                0.9626731145299533,
                0.9971990732448817
            ],
            [
                3.2887502411026557e-06,
                1.76034300345598e-06,
                4.7850944942634305e-06,
                6.144173135483279e-06,
                7.889265404959923e-06,
                2.5612828212909852e-06,
                6.962257907702715e-06,
                1.0677029973114952e-06,
                6.962254588116627e-06,
                6.144173868781898e-06
            ],
            [
                2.260323758713745e-06,
                2.902311984783477e-06,
                8.939695237813028e-06,
                2.561282210618905e-06,
                5.422217029509618e-06,
                2.561282821239737e-06,
                6.962258739169842e-06,
                6.144173131236355e-06,
                4.7850967745625735e-06,
                2.561283126679493e-06
            ],
            [
                0.9940889324845359,
                0.9914225149268431,
                0.9986749778294185,
                0.9924227591768542,
                0.9525741269907294,
                0.9859363751133208,
                0.977022632264369,
                0.9933071490323747,
                0.9740426405416754,
                0.9924227591768542
            ],
            [
                6.9622587372828785e-06,
                NaN,
                8.939696302652706e-06,
                5.42222090882208e-06,
                3.1201922498830954e-05,
                3.288748281220719e-06,
                4.0063706481032684e-05,
                6.605216038349344e-05,
                1.4738978455701077e-05,
                2.561283432005142e-06
            ],
            [
                2.1444958578416598e-05,
                6.144174600985344e-06,
                2.43002378338943e-05,
                1.0129990976156825e-05,
                5.144223812641715e-05,
                4.7850933519861414e-06,
                3.120190016685757e-05,
                1.670141586907437e-05,
                8.939699500636112e-06,
                5.422218968822766e-06
            ],
            [
                5.422219616140078e-06,
                4.222833947897496e-06,
                2.26032348933062e-06,
                1.3709568799243436e-06,
                4.785095635296322e-06,
                2.2603237589676295e-06,
                2.9023116389761676e-06,
                2.260325375650449e-06,
                1.9947297214182054e-06,
                8.315278294001114e-07
            ],
            [
                0.9978172832291005,
                0.982013786221583,
                0.9990889489970757,
                3.5356246483883486e-05,
                0.9986749776906209,
                0.995929863197698,
                0.9968273174807742,
                0.9968273173592759,
                4.53978577543791e-05,
                4.0063711274151284e-05
            ],
            [
                6.96225458885115e-06,
                4.006367772466509e-05,
                1.14787681240737e-05,
                4.006369693910372e-05,
                1.5534977545102382e-06,
                1.4738976694977387e-05,
                2.43002523073625e-05,
                4.006369214729855e-05,
                0.00020342706999379315,
                4.006369212660275e-05
            ],
            [
                0.0002611902743337654,
                8.481105121966081e-05,
                4.006368260129212e-05,
                NaN,
                2.75357009146638e-05,
                8.481107163160885e-05,
                0.00010889689584382082,
                7.484623609088468e-05,
                2.7535704221626983e-05,
                7.889260704631679e-06
            ],
            [
                2.4300243623139103e-05,
                9.610241469123354e-05,
                9.610242608490687e-05,
                6.144176065828368e-06,
                2.7535691044062732e-05,
                0.9994472213268984,
                9.610241479471069e-05,
                4.5397873946245314e-05,
                3.535626334156318e-05,
                4.0063696869729076e-05
            ],
            [
                6.1441760667392215e-06,
                2.1444953513707305e-05,
                2.9023109465275493e-06,
                7.889265397024165e-06,
                6.144175334015912e-06,
                1.6701427813417103e-05,
                8.939694171135975e-06,
                1.0129992186589747e-05,
                1.1478770861441461e-05,
                4.785095635413826e-06
            ],
            [
                6.1441746016670885e-06,
                1.1478770861859053e-05,
                1.3007134663521234e-05,
                1.4738976691331275e-05,
                1.8925155006118952e-05,
                1.670142979997471e-05,
                2.7535694379773952e-05,
                5.1442201310013716e-05,
                NaN,
                2.753568122996191e-05
            ],
            [
                3.1201915085825835e-05,
                0.00013982212184843578,
                6.605216040319643e-05,
                4.00636778258121e-05,
                6.605217605747206e-05,
                5.8291265401165313e-05,
                0.00012339452927875765,
                0.00015843615952272183,
                NaN,
                1.4738985479697128e-05
            ],
            [
                5.1442201347440924e-05,
                2.753569108453202e-05,
                3.120190763922401e-05,
                6.605217598202397e-05,
                6.60521759752961e-05,
                7.484624466571374e-05,
                4.006370169593065e-05,
                1.0129987355785634e-05,
                2.430024648072174e-05,
                0.0002034269237042022
            ],
            [
                0.999841563783258,
                0.9991959142393704,
                0.9986749776727513,
                0.998498817853546,
                0.9953904283056351,
                0.9933071477785989,
                0.995929862399247,
                0.9940889301805838,
                0.9875683515708102,
                0.994779874811829
            ],
            [
                0.9940889305445096,
                0.9991959139504012,
                0.970687766174766,
                0.99640639659489,
                0.9991959140498733,
                0.982013788327142,
                0.9924227605180019,
                0.9990889487596111,
                0.9820137862873817,
                0.998830489582772
            ],
            [
                0.9902915226499935,
                0.9579122741870426,
                0.999738809659496,
                0.9968273167039207,
                0.9626731143960903,
                0.9991959140448224,
                0.998299277275284,
                0.9988304897364403,
                0.9890130597374783,
                0.9986749776635083
            ],
            [
                0.9994472212555717,
                0.9978172837884252,
                0.9999151889796861,
                0.0293122290024261,
                0.9984988174494078,
                0.9975273769599439,
                0.34864514210180597,
                0.9998601778762229,
                0.9996200155603212,
                0.9989677691842451
            ],
            [
                9.610246065397443e-05,
                NaN,
                5.82912931135658e-05,
                0.00013982204039738008,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.8925152744771773e-05
            ],
            [
                1.3007130008414434e-05,
                3.726637951126493e-06,
                1.892515500388139e-05,
                2.902313368963394e-06,
                NaN,
                1.760343632774555e-06,
                2.753569763394596e-05,
                1.9947306725868575e-06,
                4.222834451215781e-06,
                7.889265406438011e-06
            ],
            [
                5.829129325648758e-05,
                4.006370171677219e-05,
                5.829124463468578e-05,
                6.144173866379033e-06,
                3.535624648542694e-05,
                1.3007128462785148e-05,
                4.006370170554982e-05,
                8.481101090606248e-05,
                3.535623805498234e-05,
                3.5356242271040426e-05
            ],
            [
                NaN,
                0.0006263340810502211,
                0.00012339460315252047,
                0.9399133481428691,
                0.999998005270992,
                3.53562633231704e-05,
                0.9964063980355135,
                0.00012339457438472975,
                5.8291293252246584e-05,
                0.999915188979021
            ],
            [
                6.605217600797426e-05,
                8.481104126512805e-05,
                NaN,
                0.00012339457470790277,
                9.610246058755327e-05,
                3.535624636015035e-05,
                0.00012339454497239518,
                0.00010889692189118655,
                0.00012339461882462246,
                NaN
            ],
            [
                5.144223804819424e-05,
                4.006370169826257e-05,
                4.5397863134932104e-05,
                6.144173866937839e-06,
                9.610239181859224e-05,
                3.1201907597112416e-05,
                1.8925152752138513e-05,
                3.1201915058697335e-05,
                8.939696293806686e-06,
                1.670141785237998e-05
            ],
            [
                9.610241465487671e-05,
                4.539789022795839e-05,
                3.5356238042506135e-05,
                3.535625907765566e-05,
                NaN,
                2.7535694360340682e-05,
                0.00015843615834938306,
                5.1442207372098016e-05,
                0.9999993524052018,
                0.00012339452960372603
            ],
            [
                3.535626331056557e-05,
                6.605215248979934e-05,
                7.484624476808677e-05,
                9.422442568660309e-07,
                3.1201926209079954e-05,
                4.5397873731551607e-05,
                0.00010889693474612394,
                3.120191506550783e-05,
                7.484620890377677e-05,
                2.75357009146638e-05
            ],
            [
                0.9982992773922948,
                0.9990889487604059,
                0.24508501864634824,
                0.9968273173740029,
                NaN,
                0.9998911030947618,
                0.4378234991142019,
                0.9740426408242415,
                0.9993736658687429,
                0.10669059039516232
            ],
            [
                2.5612831264675113e-06,
                1.6701429772937207e-05,
                1.0129987354882753e-05,
                8.939698429893283e-06,
                4.222835457852533e-06,
                8.939699498099386e-06,
                2.753569104967234e-05,
                2.7535681241281285e-05,
                0.00015843625311784163,
                1.7603434231241496e-06
            ]
        ]
    },
    {
        "q_id": "8916_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            23,
            24,
            25,
            26,
            28,
            29,
            30,
            31,
            32,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            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,
            87,
            88,
            89,
            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": [
            [
                1.0129987356706945e-05,
                1.4738981969240237e-05,
                8.939693103158165e-06,
                1.0677032518316716e-06,
                1.0129990978847043e-05,
                8.315284241257637e-07,
                4.22283294098842e-06,
                6.9622579092224155e-06,
                5.422221555069497e-06,
                7.889261644501938e-06
            ],
            [
                2.260323489435463e-06,
                1.300712846361323e-05,
                6.144177531532303e-06,
                5.422218323231539e-06,
                1.2098655392222467e-06,
                4.785095065045315e-06,
                1.7603427935678977e-06,
                6.1441746016670885e-06,
                2.2603234894560207e-06,
                1.2098658276730537e-06
            ],
            [
                0.9999832985781574,
                0.9999417087206302,
                1.1478773597640625e-05,
                1.4738978450955768e-05,
                2.561282515783711e-06,
                8.939697368110433e-06,
                6.144174601410037e-06,
                3.7266392838544054e-06,
                2.9023123308072772e-06,
                8.939699500766203e-06
            ],
            [
                5.4222183231674305e-06,
                0.9999810748452506,
                0.9997965729393469,
                2.902311292960369e-06,
                0.017986210652978007,
                0.999769493349947,
                0.006692849961508967,
                0.4378234991142019,
                1.9947299591100915e-06,
                0.9933071493264704
            ],
            [
                2.902313368963394e-06,
                1.9947290079889487e-06,
                4.450852641656969e-07,
                5.043473480460215e-07,
                3.7266410608720178e-06,
                3.288748673265808e-06,
                3.2887490653408545e-06,
                7.889265405677441e-06,
                4.785093924047376e-06,
                2.2603242978377903e-06
            ],
            [
                0.43782349911420193,
                0.9989677690335906,
                0.37754066879814546,
                0.4378234991142019,
                0.0124316499499042,
                0.07585818628900447,
                0.9991959141690806,
                0.0040701385860758615,
                2.260324836624822e-06,
                0.11920292045759123
            ],
            [
                3.120190391558324e-05,
                8.939697367264857e-06,
                0.9997388097329619,
                0.9998911031054348,
                1.4738987238464762e-05,
                0.9997965729577737,
                3.2887482810382622e-06,
                0.9997965729610174,
                0.9993736657436628,
                0.26894141551050293
            ],
            [
                9.422444815495185e-07,
                3.7266392836984955e-06,
                2.2603245672497918e-06,
                1.7603425836870455e-06,
                3.927863407065117e-07,
                3.726640616670918e-06,
                1.7603430033158905e-06,
                9.422445938797133e-07,
                4.785094493836935e-06,
                1.0129988563343644e-05
            ],
            [
                1.7603434230088762e-06,
                1.3709568799243436e-06,
                3.726638395527247e-06,
                4.7850950647493785e-06,
                4.222835458044565e-06,
                1.370957370196196e-06,
                5.422217030663578e-06,
                1.5534977544565482e-06,
                9.422443691996268e-07,
                3.2887478892683997e-06
            ],
            [
                5.715003788933905e-07,
                3.7266388394569345e-06,
                1.067703379136937e-06,
                2.9023123310580418e-06,
                1.3709576971160984e-06,
                5.422220262333096e-06,
                8.31528126775552e-07,
                6.475949525781504e-07,
                5.422217030209884e-06,
                3.9278610660598936e-07
            ],
            [
                5.422217676654099e-06,
                0.029312232288295083,
                0.999948557780272,
                6.962259569117366e-06,
                0.9999151889588787,
                0.9999546021476535,
                0.9997694933078399,
                0.5,
                0.9999251537770113,
                0.9999852610164384
            ],
            [
                0.2942149783515162,
                0.9999756997506362,
                0.9999852610162943,
                0.24508500761839525,
                0.7549149813536516,
                0.053403331494692494,
                0.9997694933390145,
                0.9999417087345488,
                0.20181321745968234,
                0.9999832985805983
            ],
            [
                5.422218969128516e-06,
                6.144173868558375e-06,
                1.8925150491445666e-05,
                6.962254589528684e-06,
                1.473898196210887e-05,
                1.553497754476329e-06,
                3.2887494571676872e-06,
                8.939697367492512e-06,
                4.2228344511197656e-06,
                8.93969630317306e-06
            ],
            [
                1.1478770862067849e-05,
                3.7266379512857925e-06,
                7.889259764079887e-06,
                4.222831934202483e-06,
                1.7603438426491283e-06,
                2.260324567268294e-06,
                3.7266383951544193e-06,
                1.3007131559390956e-05,
                1.2098656834922064e-06,
                3.7266392836984955e-06
            ],
            [
                9.422450431912e-07,
                2.90231198483099e-06,
                6.1441767989541075e-06,
                7.88926258381982e-06,
                2.9023133689317184e-06,
                6.144176066051891e-06,
                4.785094493636744e-06,
                2.2603237589028734e-06,
                2.5612825159421147e-06,
                2.5612819050161955e-06
            ],
            [
                3.726640616630245e-06,
                3.288749065029781e-06,
                3.7266397278791014e-06,
                1.9947290080343035e-06,
                NaN,
                3.726639283752725e-06,
                5.422220908560712e-06,
                3.7266397283231055e-06,
                2.902313023063532e-06,
                3.726639283752725e-06
            ],
            [
                4.222833444229772e-06,
                1.01299933928585e-05,
                1.2098662603862553e-06,
                7.889264465067689e-06,
                2.902313022659669e-06,
                0.9990889489917776,
                0.320821300824607,
                0.9980732649538561,
                6.96225458885115e-06,
                0.5312093733737563
            ],
            [
                6.962256249682458e-06,
                6.144176798479122e-06,
                4.785093353626844e-06,
                4.785092782692845e-06,
                4.78509563509613e-06,
                2.9023126766832993e-06,
                6.962253759157502e-06,
                2.2603251061232293e-06,
                3.7266410609160796e-06,
                6.1441731363550164e-06
            ],
            [
                1.5534981249164537e-06,
                2.902313022554084e-06,
                2.9023126770343703e-06,
                1.553497384180408e-06,
                2.5612834318583854e-06,
                2.561283432005142e-06,
                1.553498495281783e-06,
                1.5534981249496567e-06,
                6.47594875389178e-07,
                3.2887478892504536e-06
            ],
            [
                2.260323489490968e-06,
                0.008577484043571925,
                0.2018132270610754,
                0.16451647108926923,
                0.9988304898044352,
                0.5926665999540698,
                0.16451646289656316,
                0.9947798734576809,
                0.43782349911420193,
                0.9982992773288482
            ],
            [
                1.2098653948994866e-06,
                1.1478765388105516e-05,
                1.994729483680993e-06,
                1.5534979396984994e-06,
                9.422450431800595e-07,
                1.7603440525205244e-06,
                5.422218969532895e-06,
                2.561281905293402e-06,
                1.2098656835076114e-06,
                2.260325375664839e-06
            ],
            [
                8.939695237504067e-06,
                1.0129995809044816e-05,
                1.5534977545603963e-06,
                4.2228319339950885e-06,
                2.4300231993112754e-05,
                4.222834954211514e-06,
                1.1478773595009805e-05,
                2.6995784182073116e-07,
                7.889262585082652e-06,
                3.7266410608245674e-06
            ],
            [
                8.939694172542558e-06,
                NaN,
                6.144176066443055e-06,
                4.785096205512581e-06,
                3.726640172337686e-06,
                1.3007130013856124e-05,
                3.726641055377885e-06,
                1.4738988999940381e-05,
                2.144495352533148e-05,
                1.8925150493717652e-05
            ],
            [
                0.9959298619518878,
                0.5,
                0.06754669207816587,
                0.998498817534563,
                0.08509904616718289,
                0.0850990490675896,
                0.029312228949428216,
                0.996827316825419,
                0.2942149659744614,
                0.04742586947505113
            ],
            [
                1.5534983101478522e-06,
                6.9622562472889285e-06,
                1.7603425837791042e-06,
                3.726640616748873e-06,
                9.422442569028803e-07,
                1.7603434231241496e-06,
                4.4508510498604413e-07,
                9.422443692390473e-07,
                5.04347588554027e-07,
                5.715004470243685e-07
            ],
            [
                4.222832437497486e-06,
                3.288750633545794e-06,
                1.892515724633005e-05,
                6.96225707894582e-06,
                0.1824255326961778,
                4.222834954211514e-06,
                2.902311984952413e-06,
                2.260324567268294e-06,
                0.13296423160844623,
                7.889264465699106e-06
            ],
            [
                0.9999785550464919,
                0.999978555056719,
                0.9999952149066466,
                0.999997097686631,
                0.9999785550465029,
                0.9999952149032255,
                0.999986992876194,
                0.9999977396762412,
                0.999995777165046,
                0.9997965730761567
            ],
            [
                7.338210679816025e-07,
                2.2603242978213447e-06,
                1.994730434778778e-06,
                1.994730434847717e-06,
                7.338207180454308e-07,
                7.889259763010786e-06,
                7.338208055579897e-07,
                7.338207180761315e-07,
                2.2603245673155757e-06,
                9.422444815679433e-07
            ],
            [
                4.785095635017795e-06,
                3.120190019636974e-05,
                1.4738987237124277e-05,
                1.9947292457750883e-06,
                3.7266383946527958e-06,
                4.222834954461155e-06,
                1.0677032518316716e-06,
                3.53562549292501e-05,
                1.5534983101061718e-06,
                4.222834954057889e-06
            ],
            [
                1.3709578603884238e-06,
                1.3709567164663505e-06,
                1.760343632774555e-06,
                2.260324028281919e-06,
                5.715002426202836e-07,
                4.785092783149804e-06,
                1.0677028699858827e-06,
                9.42244593835151e-07,
                1.0129987355343409e-05,
                1.1478766754377407e-05
            ],
            [
                1.3007128463352975e-05,
                4.222834953896582e-06,
                1.1478770860481005e-05,
                8.93969417167259e-06,
                3.726638839806038e-06,
                1.2098659719716573e-06,
                4.222834954561012e-06,
                4.785096775058701e-06,
                1.5534973841309562e-06,
                1.147877222702498e-05
            ],
            [
                8.93969736929749e-06,
                5.422221555133606e-06,
                1.3709573702566696e-06,
                4.222834954461155e-06,
                6.1441775312976045e-06,
                5.7150044702099e-07,
                3.726641061085547e-06,
                6.144172404302622e-06,
                1.0129994602057158e-05,
                2.902313023063532e-06
            ],
            [
                6.1441738691562974e-06,
                2.9023130224326608e-06,
                3.7266397272757976e-06,
                1.9947304344830644e-06,
                1.994729959019382e-06,
                1.7603440522963817e-06,
                6.144174601588856e-06,
                1.0129987356375273e-05,
                1.5534979396984994e-06,
                5.422220262333096e-06
            ],
            [
                1.8925157255280296e-05,
                4.222835458044565e-06,
                2.561282821352716e-06,
                4.785092783371756e-06,
                2.5612812946681295e-06,
                3.72664017246987e-06,
                1.5534981248712412e-06,
                4.785096205973894e-06,
                8.315279285149107e-07,
                1.2098656834723998e-06
            ],
            [
                1.3709576970387918e-06,
                6.962258739068529e-06,
                2.5612822106654943e-06,
                6.475946437928669e-07,
                3.7266406165319545e-06,
                5.715006513308086e-07,
                4.2228324375973415e-06,
                3.2887482811579057e-06,
                1.6701427812931038e-05,
                0.0017007224442457556
            ],
            [
                3.0590229984892605e-07,
                0.0758581847220642,
                4.4508489275469177e-07,
                3.2887494570181325e-06,
                4.785096776303374e-06,
                0.11920291263495983,
                0.09534945461636171,
                2.902313368583287e-06,
                1.2098658277181688e-06,
                0.9997040427704803
            ],
            [
                2.902313022554084e-06,
                2.1444943298944354e-05,
                1.3007128462785148e-05,
                7.88926164421493e-06,
                1.892514822276672e-05,
                3.726640172337686e-06,
                3.120190763332158e-05,
                3.535626334799422e-05,
                3.7266401724291984e-06,
                1.4738985483879434e-05
            ],
            [
                2.1444948410928083e-05,
                6.962257902991637e-06,
                1.300712536203966e-05,
                1.4738985484227961e-05,
                8.939695237959376e-06,
                8.93969736929749e-06,
                1.4738976700366126e-05,
                8.93969736929749e-06,
                6.9622587393661365e-06,
                NaN
            ],
            [
                1.370957533625589e-06,
                2.902311638654133e-06,
                3.2887482811579057e-06,
                1.7603432133032607e-06,
                6.962258739068529e-06,
                1.9947299591100915e-06,
                1.7603430034151537e-06,
                7.338211554725124e-07,
                2.260325375615501e-06,
                1.9947290081286418e-06
            ],
            [
                3.726641060773727e-06,
                1.760343842833246e-06,
                4.785093353626844e-06,
                4.7850933534310035e-06,
                3.927862938877536e-07,
                4.222833444429485e-06,
                7.338210679909462e-07,
                1.3709575336093795e-06,
                6.962259569484628e-06,
                4.7850950649408664e-06
            ],
            [
                0.1329642316084462,
                0.4073334000459302,
                0.9990889489091259,
                0.18242551936144574,
                0.9990889489124638,
                0.9986749778791761,
                0.020332353862085824,
                0.4073334000459303,
                0.3486451285660856,
                0.999860177870189
            ],
            [
                5.422220908560712e-06,
                0.9989677690501567,
                2.1444940722669156e-05,
                2.144495863614743e-05,
                0.9971990734991549,
                2.902312331081799e-06,
                6.962253759581752e-06,
                1.1478770126169087e-05,
                3.2887494570181325e-06,
                0.9988304898663105
            ],
            [
                0.05340333507274788,
                0.957912274637613,
                0.9999485577805853,
                0.2942149783515162,
                0.00460957151916335,
                0.14804719427274568,
                0.9770226304663119,
                0.9999151889629065,
                0.9997388097014462,
                0.880797071719777
            ],
            [
                2.5612828212909852e-06,
                5.715003107655392e-07,
                2.260325375650449e-06,
                8.315283250260307e-07,
                3.4663262110803996e-07,
                4.78509563546605e-06,
                4.450851049941403e-07,
                7.33821067986608e-07,
                5.71500242637956e-07,
                2.5612828213690224e-06
            ],
            [
                6.962257078819179e-06,
                5.422219615898437e-06,
                6.962255419380732e-06,
                1.0129995805027913e-05,
                3.7266379512518984e-06,
                1.3709572068079696e-06,
                1.2098655392464547e-06,
                4.222831933726245e-06,
                6.144173135762683e-06,
                4.222834954134701e-06
            ],
            [
                5.422221555133606e-06,
                7.88926258532661e-06,
                6.962258739271155e-06,
                5.4222183222304545e-06,
                5.422218968931258e-06,
                0.9999646437579299,
                2.902312677060767e-06,
                5.422220908634683e-06,
                6.1441724044534996e-06,
                7.889259763326495e-06
            ],
            [
                6.144173136729416e-06,
                1.7603432131119386e-06,
                6.144174601879434e-06,
                2.2603237588597026e-06,
                6.1441746016670885e-06,
                5.422220260360515e-06,
                8.93969310675186e-06,
                1.370956716529941e-06,
                4.78509563546605e-06,
                4.785092783210732e-06
            ],
            [
                1.670141786036971e-05,
                2.5612822106421996e-06,
                1.3709576970824327e-06,
                2.9023112931213857e-06,
                2.260323489192885e-06,
                1.1478764018827141e-05,
                5.422217676654099e-06,
                1.0129993393742954e-05,
                5.422220908018252e-06,
                1.370956716519966e-06
            ],
            [
                6.144176066521288e-06,
                5.71500310747347e-07,
                1.0677032518209896e-06,
                3.2887482811220126e-06,
                1.9947299592824403e-06,
                1.0129995809044816e-05,
                4.785096205882502e-06,
                7.338208930315157e-07,
                6.962254589433702e-06,
                4.222832437677995e-06
            ],
            [
                6.144173868044274e-06,
                2.561282515783711e-06,
                1.2098661160612089e-06,
                3.726640172337686e-06,
                3.726641060956752e-06,
                2.2603245672025095e-06,
                2.9023133689317184e-06,
                3.2887498493325602e-06,
                2.5612819051722694e-06,
                1.76034363298589e-06
            ],
            [
                6.144173136952939e-06,
                5.422218323019487e-06,
                8.939695235959266e-06,
                1.147877086073156e-05,
                1.3007133110320344e-05,
                1.2098652508056196e-06,
                8.939693106182721e-06,
                8.939696301839653e-06,
                0.9999546021422945,
                2.260323758939877e-06
            ],
            [
                1.370956716450141e-06,
                1.067702869935387e-06,
                6.962259568775433e-06,
                0.9997388097572731,
                8.939699500164542e-06,
                5.422218322457301e-06,
                3.2887486731641103e-06,
                5.422220261652556e-06,
                7.889265405677441e-06,
                0.9982992776970765
            ],
            [
                1.370957370146321e-06,
                2.9023123310290063e-06,
                9.422447061679302e-07,
                7.33821067986608e-07,
                3.7266410609940346e-06,
                1.0677029973056687e-06,
                1.7603432132624344e-06,
                1.994729959224386e-06,
                9.422444815409489e-07,
                6.144176798691468e-06
            ],
            [
                6.962257909722651e-06,
                3.535623803273096e-05,
                1.0677032518700286e-06,
                4.222832941111319e-06,
                7.889264466545779e-06,
                3.288749457409966e-06,
                2.5612834318583854e-06,
                2.902313022984344e-06,
                3.288750633518874e-06,
                6.47594875389178e-07
            ],
            [
                0.9999417087514776,
                0.40733340004593027,
                0.9999921107396127,
                0.9999417087557932,
                0.320821300824607,
                0.9999646437622814,
                0.5926665999540698,
                0.9999646437586347,
                0.9999832985792485,
                4.785093353274332e-06
            ],
            [
                3.726640616423495e-06,
                5.42221961567159e-06,
                1.2098656834834034e-06,
                3.726639283901856e-06,
                1.3709576970949014e-06,
                4.222832940715735e-06,
                1.7603425837062577e-06,
                7.8892625849535e-06,
                5.422220261948442e-06,
                5.422220908560712e-06
            ],
            [
                8.939693105467234e-06,
                2.9023116387069255e-06,
                1.7603427935678977e-06,
                1.3709578604831862e-06,
                1.6701425786941456e-05,
                1.0129990975862006e-05,
                3.288749065125496e-06,
                1.473898899908247e-05,
                4.785095635017795e-06,
                1.7603436328994344e-06
            ],
            [
                0.10669059394565118,
                1.7603434230921292e-06,
                1.7603436328770204e-06,
                1.0129994591922764e-05,
                2.2603253755949437e-06,
                4.7850933529174686e-06,
                9.422443692390473e-07,
                4.222834954561012e-06,
                6.962257908880483e-06,
                6.144173136243255e-06
            ],
            [
                2.2603237588597026e-06,
                9.422449307915373e-07,
                3.726639728224814e-06,
                6.144174601309452e-06,
                3.7266406163624873e-06,
                1.1478769492642663e-05,
                7.889263525261671e-06,
                7.889262584809997e-06,
                8.939698434495167e-06,
                4.222835457852533e-06
            ],
            [
                0.4073334000459302,
                0.9998415637302756,
                0.9998766054263477,
                0.03308597898458847,
                0.06754669583231304,
                0.14804719803168945,
                0.9994472214830585,
                0.9992903296811456,
                0.04208772686428807,
                0.9999417087074178
            ],
            [
                5.422217677028889e-06,
                2.43002523073625e-05,
                2.430024362932722e-05,
                7.889264465842609e-06,
                4.222834954514924e-06,
                2.430023494002383e-05,
                2.7535697661092444e-05,
                1.0129988563343644e-05,
                6.9622537593854575e-06,
                8.939699500489763e-06
            ],
            [
                8.315277302588544e-07,
                7.889260703619978e-06,
                8.31528424151477e-07,
                1.0677028700053041e-06,
                1.2098653950315304e-06,
                5.043474081831035e-07,
                1.0129990978220553e-05,
                3.2887478892055875e-06,
                6.962257079465052e-06,
                9.422447061876404e-07
            ],
            [
                1.9947294835866542e-06,
                0.05340332697504391,
                0.3208212943308302,
                0.14804719803168948,
                0.9999546021256825,
                0.0953494648991095,
                0.0040701379367443285,
                0.7981867777396212,
                0.0007096702811253912,
                0.006692850528029811
            ],
            [
                1.0129987355785634e-05,
                1.473897669838221e-05,
                7.889265405677441e-06,
                1.4738978454172926e-05,
                1.3007126912826352e-05,
                1.8925157255968775e-05,
                2.902312677060767e-06,
                0.9997694932043028,
                8.939698434820389e-06,
                2.5612815999679353e-06
            ],
            [
                1.0129988561648438e-05,
                1.6701415868193372e-05,
                1.670142780594382e-05,
                2.5612819051722694e-06,
                1.4738980213341866e-05,
                1.1478768124783601e-05,
                5.82912653104079e-05,
                5.422218969661113e-06,
                3.1201903888114227e-05,
                5.422219615750493e-06
            ],
            [
                0.9999910603016694,
                0.8519528019683105,
                0.7549149923816048,
                0.8175744695262777,
                0.9999945777792959,
                0.9999898700066152,
                8.939697368110433e-06,
                1.2098653949688097e-06,
                0.9999938558232018,
                0.9982992777806838
            ],
            [
                8.939693106329072e-06,
                7.889264465699106e-06,
                4.2228344508893285e-06,
                4.2228324372555256e-06,
                1.0677031245783732e-06,
                2.260323758676741e-06,
                1.2098653950403334e-06,
                5.422217030555087e-06,
                1.3709567164962755e-06,
                4.78509563546605e-06
            ],
            [
                7.33820805514942e-07,
                2.260324567302214e-06,
                2.5612831266608576e-06,
                1.2098661161107252e-06,
                3.2887486732358968e-06,
                4.450849458179853e-07,
                6.144175334094145e-06,
                5.043474081785165e-07,
                6.475947209768052e-07,
                5.04347588554027e-07
            ],
            [
                2.5612816000145246e-06,
                6.144177531599359e-06,
                9.422442568951678e-07,
                1.8925148238808306e-05,
                4.222832940942332e-06,
                6.962254589528684e-06,
                4.785095635413826e-06,
                1.3007133115903994e-05,
                2.2603251062147097e-06,
                NaN
            ],
            [
                2.1444958627955892e-05,
                4.222835457852533e-06,
                1.670142582102693e-05,
                0.9997694933680427,
                7.88926258532661e-06,
                2.902312330601386e-06,
                1.4738988997044936e-05,
                NaN,
                0.9996646498525276,
                0.999820471948819
            ],
            [
                4.450849988733914e-07,
                2.902311984915459e-06,
                4.785093353787868e-06,
                1.9947304348332037e-06,
                1.3709578605455302e-06,
                6.1441760667392215e-06,
                1.3007130014376633e-05,
                3.726638839656906e-06,
                1.7603430033799313e-06,
                3.7266397281434697e-06
            ],
            [
                0.22270013882530887,
                0.46879062662624377,
                0.9993736659158529,
                0.9890130569646082,
                0.9996200154833357,
                3.2887506334201674e-06,
                0.9988304896604222,
                0.06754669395523943,
                4.7850950649408664e-06,
                0.9999151889303275
            ],
            [
                1.0677028700203557e-06,
                1.473898899846585e-05,
                4.785093923916815e-06,
                2.56128159999123e-06,
                6.1441753337365085e-06,
                1.067702997240607e-06,
                1.300712381094558e-05,
                6.9622595694023114e-06,
                4.006368261266023e-05,
                3.2887498493325602e-06
            ],
            [
                4.78509563509613e-06,
                1.9947290079889487e-06,
                2.26032348933062e-06,
                0.9986749778790222,
                1.7603440526662173e-06,
                1.0129993394129904e-05,
                3.9278638750062605e-07,
                4.222832437677995e-06,
                2.9023119850527192e-06,
                9.422444814749625e-07
            ],
            [
                1.3007134666431358e-05,
                7.338208930265102e-07,
                1.0129995809431767e-05,
                5.422217030555087e-06,
                0.999978555046489,
                6.9622554187981796e-06,
                7.889261644875049e-06,
                6.1441760657054305e-06,
                8.315282259009745e-07,
                7.889264465699106e-06
            ],
            [
                0.9980732654906945,
                0.9241418173671895,
                2.2603253754284284e-06,
                0.999088948619951,
                0.9996200154827276,
                2.1444943298944354e-05,
                3.726640172537657e-06,
                0.5,
                0.999959936299236,
                0.03732688935207537
            ],
            [
                1.0677032518700286e-06,
                6.475951069896949e-07,
                1.994729483694599e-06,
                1.3709575336405514e-06,
                1.2098662604192665e-06,
                1.2098652508056196e-06,
                1.0677026154730804e-06,
                3.288749457409966e-06,
                8.315282259051341e-07,
                2.260324567302214e-06
            ],
            [
                1.994729245749689e-06,
                5.715007195353674e-07,
                6.962254589781966e-06,
                1.0677028700053041e-06,
                2.561281904969606e-06,
                8.315283250260307e-07,
                5.715002426410745e-07,
                8.315284240879503e-07,
                9.422442568763144e-07,
                1.0677029973056687e-06
            ],
            [
                3.2887498494551953e-06,
                1.0677032518316716e-06,
                5.8291251268880934e-05,
                2.260324567227179e-06,
                1.5534984953199313e-06,
                4.222833947674739e-06,
                1.5534983101061718e-06,
                1.3007131561804229e-05,
                5.715004470025379e-07,
                4.785092783371756e-06
            ],
            [
                6.144176799166453e-06,
                0.9995121429512127,
                0.9975273770874337,
                0.9982992773497993,
                0.022977371666267666,
                3.535626334323525e-05,
                0.1480471923932738,
                1.3709567163017629e-06,
                0.9991959141775453,
                0.4073334000459302
            ],
            [
                2.561281905376098e-06,
                1.5534973840786793e-06,
                4.450849458153541e-07,
                1.9947306726594253e-06,
                1.3709570433979422e-06,
                4.785093353626844e-06,
                2.5612812946681295e-06,
                3.2887478889034873e-06,
                1.0677033791291683e-06,
                1.209865250822125e-06
            ],
            [
                0.13296422989056964,
                1.3709570434054234e-06,
                0.05340332942318685,
                1.994730434778778e-06,
                3.7266383953679482e-06,
                0.18242552158390102,
                0.9996646499111752,
                3.7266388397382506e-06,
                1.2098655392662613e-06,
                0.9994472212731943
            ],
            [
                6.96225956921868e-06,
                0.9997040428814495,
                4.7850944942634305e-06,
                6.962257079275089e-06,
                6.962255418658875e-06,
                6.144173869312763e-06,
                4.222831933795376e-06,
                0.00010889694701797178,
                0.5926665999540698,
                3.726639728262097e-06
            ],
            [
                1.0677026154619133e-06,
                1.4449806935092113e-07,
                5.422220908314139e-06,
                1.2098655392662613e-06,
                6.144177531007026e-06,
                2.561282821352716e-06,
                2.2603248367173307e-06,
                5.422220262264056e-06,
                1.553498310118888e-06,
                1.3709568799760888e-06
            ],
            [
                3.7266383939817055e-06,
                8.93970056152486e-06,
                6.144172402285332e-06,
                1.4738976674655674e-05,
                4.785095634121282e-06,
                2.5612828208367393e-06,
                3.288749847798131e-06,
                4.222833947774596e-06,
                3.7266410594993323e-06,
                2.9023133685252154e-06
            ],
            [
                1.1478764016780948e-05,
                3.7266406161591266e-06,
                3.7266401704599874e-06,
                2.2603240279591663e-06,
                2.5612825154622447e-06,
                4.785095634121282e-06,
                7.889260703906985e-06,
                8.939698433974813e-06,
                2.902311984783477e-06,
                4.222832940715735e-06
            ],
            [
                0.9902915253809457,
                0.9933071500849271,
                1.7603434230088762e-06,
                1.0129987356541108e-05,
                0.998498817887922,
                3.288748280891699e-06,
                2.7535697651475977e-05,
                1.5534971987506078e-06,
                3.120191505506507e-05,
                3.120192251903545e-05
            ],
            [
                0.9998601778623403,
                0.2450850131323717,
                0.06008665606493927,
                0.11920293140927592,
                0.006692852162582021,
                3.2887498492518007e-06,
                0.0019267350349504938,
                0.09534946618445303,
                5.1442201310013716e-05,
                0.9998204720802082
            ],
            [
                4.222832437497486e-06,
                0.9999151889185779,
                0.9999785550413746,
                0.9999852610145218,
                0.9999869928684372,
                0.999941708706696,
                0.9999687980774881,
                7.889263525534328e-06,
                0.9999756997534958,
                0.9996200155629634
            ],
            [
                6.475949525663707e-07,
                7.889266347133978e-06,
                2.902311984915459e-06,
                6.1441767990323395e-06,
                1.994730672265745e-06,
                6.962254589433702e-06,
                1.7603430034151537e-06,
                1.370957533625589e-06,
                1.0129994600638342e-05,
                4.785096776194573e-06
            ],
            [
                5.043474683220276e-07,
                9.422445938917108e-07,
                1.0677026154730804e-06,
                3.288750241374845e-06,
                1.2098656835136636e-06,
                1.2098659718990333e-06,
                8.315277302788957e-07,
                6.144175333401224e-06,
                1.553498495308628e-06,
                5.422220908314139e-06
            ],
            [
                6.962256249606473e-06,
                1.0677032518316716e-06,
                1.3007125360809367e-05,
                8.939699499627926e-06,
                0.999820471995715,
                1.0129995808418327e-05,
                0.9996200154261381,
                1.0677028699742299e-06,
                2.561282515988704e-06,
                2.9023126768258393e-06
            ],
            [
                4.222832940834793e-06,
                1.3007125360146898e-05,
                1.6701427815999337e-05,
                6.962257078553231e-06,
                6.1441775309064404e-06,
                1.9947299592407137e-06,
                1.1478772230407462e-05,
                8.939695237504067e-06,
                8.939699498814873e-06,
                2.1444945829581326e-05
            ],
            [
                6.962259568230874e-06,
                1.0129987355343409e-05,
                2.5612822107167428e-06,
                4.00636969277356e-05,
                1.5534975693488444e-06,
                6.962254589617333e-06,
                0.11920292045759122,
                8.939699499026267e-06,
                1.5534981248881956e-06,
                2.902311984873224e-06
            ],
            [
                5.422218323231539e-06,
                1.994729959224386e-06,
                1.012999460108057e-05,
                1.7603430033607189e-06,
                8.93969950000193e-06,
                1.9947304347570075e-06,
                8.939698434966738e-06,
                1.3007123811229494e-05,
                4.785096776303374e-06,
                1.0677026154376365e-06
            ],
            [
                5.422218969217281e-06,
                9.422442569208767e-07,
                1.994729007809344e-06,
                6.144176066353646e-06,
                3.2887494573232236e-06,
                6.4759479808713e-07,
                9.422447061876404e-07,
                2.2603251060142746e-06,
                1.5534984953298217e-06,
                8.31528126775552e-07
            ],
            [
                0.999769493345091,
                0.9999599363175663,
                0.7772998611746912,
                0.40733340004593027,
                2.902313368897403e-06,
                1.892514371356847e-05,
                0.9999038975752016,
                1.892514596944115e-05,
                0.9999339478729972,
                2.144494839033223e-05
            ],
            [
                6.144173136952939e-06,
                2.2603251062013478e-06,
                1.0129987355988324e-05,
                0.9999038975736655,
                2.2603240283888175e-06,
                1.7603427936079236e-06,
                1.2098653950403334e-06,
                2.1444958635523312e-05,
                8.93969630388855e-06,
                2.430023202246208e-05
            ],
            [
                1.2098661161789477e-06,
                1.9947301969217434e-06,
                6.962255419475714e-06,
                1.3709567164962755e-06,
                1.0677027427413698e-06,
                1.9947299591826594e-06,
                6.475950297868629e-07,
                7.889264465555602e-06,
                7.338208055613267e-07,
                1.0677026154619133e-06
            ],
            [
                1.0129988563914856e-05,
                1.670142781520948e-05,
                1.6701421842140854e-05,
                1.147876949310201e-05,
                6.96225707894582e-06,
                3.7266401725681614e-06,
                1.7603432132464244e-06,
                3.726639284017094e-06,
                8.93969310675186e-06,
                1.3007128458384476e-05
            ],
            [
                6.144176798691468e-06,
                3.927861534370498e-07,
                1.5534973840984598e-06,
                4.222832437677995e-06,
                1.4738987232888351e-05,
                5.715003788933905e-07,
                6.475945665900901e-07,
                6.962256249112569e-06,
                2.9023112926779284e-06,
                6.962257909323729e-06
            ],
            [
                6.962255419570695e-06,
                6.144173869312763e-06,
                4.785094494576774e-06,
                1.5534973841450852e-06,
                1.3007123808153756e-05,
                1.1478765388314311e-05,
                3.2887494572873306e-06,
                6.475949525834513e-07,
                2.5612828209811664e-06,
                8.939693105662367e-06
            ],
            [
                4.222832940942332e-06,
                7.889260703619978e-06,
                3.288750241042834e-06,
                1.5534983100425914e-06,
                1.553497198908852e-06,
                4.222834954461155e-06,
                4.785096776303374e-06,
                1.9947306725868575e-06,
                3.7266397273639203e-06,
                6.9622579086271995e-06
            ],
            [
                6.144175334094145e-06,
                1.994729721323867e-06,
                1.3709570433661467e-06,
                3.46632703727876e-07,
                6.962253759486771e-06,
                4.785096776133645e-06,
                2.561281599734989e-06,
                5.422220261849814e-06,
                5.715006514105942e-07,
                4.785096205717126e-06
            ],
            [
                6.144173869240119e-06,
                2.561283126502453e-06,
                4.4508510497875774e-07,
                1.2098655392222467e-06,
                0.9999832985704638,
                1.994729959019382e-06,
                0.9995121429485162,
                1.067702615468225e-06,
                6.475949525663707e-07,
                3.2887494573232236e-06
            ],
            [
                1.3007133114602719e-05,
                4.222833946645451e-06,
                6.962256248871951e-06,
                1.8925141448401585e-05,
                1.5534971986601824e-06,
                4.7850950648799385e-06,
                1.670142383167491e-05,
                6.96225375833433e-06,
                3.7266388384265735e-06,
                7.88926070293116e-06
            ],
            [
                1.1478769492642663e-05,
                4.222832941111319e-06,
                1.0129992185539456e-05,
                1.2098653950606901e-06,
                1.5534971989992774e-06,
                3.2887482810801374e-06,
                1.7603430034439723e-06,
                4.222834450666572e-06,
                5.422219615582823e-06,
                4.785096776133645e-06
            ],
            [
                2.7535681231364308e-05,
                1.147877222879974e-05,
                3.120190019636974e-05,
                3.5356254903911806e-05,
                1.6701423832586287e-05,
                1.8925143725341476e-05,
                1.012998977088337e-05,
                1.3007125360478133e-05,
                2.1444940733201126e-05,
                7.889264464895484e-06
            ],
            [
                1.670142780910326e-05,
                0.9990889488764361,
                0.9975273765573743,
                0.9959298631278571,
                0.9986749773986988,
                3.726640172290235e-06,
                0.9993736658264423,
                0.0035936020787026234,
                4.222835457794923e-06,
                0.9940889317621566
            ],
            [
                1.0129994601872894e-05,
                5.4222215532202016e-06,
                3.726640616477725e-06,
                4.785095634930755e-06,
                4.222832437497486e-06,
                6.962256248606003e-06,
                5.422219614004759e-06,
                5.422221555069497e-06,
                4.785092783267308e-06,
                2.4300249421225448e-05
            ],
            [
                1.994729721482609e-06,
                1.2098656834481918e-06,
                5.043476486833397e-07,
                2.902311639073834e-06,
                1.3709573702566696e-06,
                3.7266392839832006e-06,
                2.699579061798195e-07,
                1.994729483694599e-06,
                7.338212429420757e-07,
                1.7603436329714805e-06
            ],
            [
                1.760343423160973e-06,
                2.9023133690188264e-06,
                3.7266392835086923e-06,
                3.726637950723161e-06,
                2.9023133682084594e-06,
                4.785095634460739e-06,
                8.939697366793286e-06,
                6.962254588433232e-06,
                1.0677026153784014e-06,
                1.2098656834922064e-06
            ],
            [
                2.5612828210277558e-06,
                8.93970056529743e-06,
                2.9023126768680736e-06,
                4.7850944937411915e-06,
                3.288750241374845e-06,
                3.7266388395620047e-06,
                3.7266383950256237e-06,
                2.561281905293402e-06,
                1.1478770858372173e-05,
                3.288750633139005e-06
            ],
            [
                6.144172404302622e-06,
                2.9023126770343703e-06,
                7.338207180838067e-07,
                4.222831934321543e-06,
                6.144177531532303e-06,
                8.939694172420599e-06,
                4.222833444383398e-06,
                4.785095065045315e-06,
                2.9023116388969785e-06,
                7.889262585441413e-06
            ],
            [
                4.222834450950777e-06,
                0.1066905854244781,
                0.9999785550415171,
                0.999820472018314,
                0.9999038976202603,
                0.4073334000459302,
                0.08509904848750825,
                0.9997040429137233,
                1.5534979396645902e-06,
                0.9999546021368376
            ],
            [
                2.90231163910023e-06,
                1.553498495230919e-06,
                1.3007134663876127e-05,
                7.338207180601138e-07,
                6.144176066672166e-06,
                1.670141585731762e-05,
                2.2603248365960415e-06,
                1.0677026154055912e-06,
                2.9023133690188264e-06,
                1.9947303400361714e-06
            ],
            [
                4.222833444467892e-06,
                6.144172404218801e-06,
                1.1478764019996392e-05,
                2.1444948410303962e-05,
                1.3007131564643372e-05,
                3.72664061681327e-06,
                1.300712691308661e-05,
                4.222834954607099e-06,
                2.260325375572331e-06,
                1.0129993394811673e-05
            ],
            [
                6.962259569003389e-06,
                8.939694171135975e-06,
                6.9622562492265485e-06,
                4.785093924103951e-06,
                2.9023130228840374e-06,
                2.9023130227124616e-06,
                2.561283126535066e-06,
                2.9023116389365734e-06,
                6.962257079173776e-06,
                2.2603245671202796e-06
            ],
            [
                3.2887506333812835e-06,
                1.2098662604049616e-06,
                3.2887506333394084e-06,
                2.561281294616881e-06,
                3.726639727940109e-06,
                7.8892654060075e-06,
                7.338211554591642e-07,
                1.7603430033399058e-06,
                1.2098662603752517e-06,
                2.260325375650449e-06
            ],
            [
                7.8892625849535e-06,
                1.2098652508056196e-06,
                1.1478773597870298e-05,
                8.93969630388855e-06,
                1.6701425824733193e-05,
                3.726638395215427e-06,
                1.0129989768322136e-05,
                1.4738985481520185e-05,
                6.962257908880483e-06,
                6.962257078819179e-06
            ]
        ]
    },
    {
        "q_id": "8455_mmlu_math",
        "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,
            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,
            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,
            34,
            74
        ],
        "rewards": [
            [
                0.9999994956526519,
                0.9999994956524715,
                0.9999994956523512,
                0.9999996533672549,
                0.9999994956525317,
                0.9999996533672549,
                0.999999352404893,
                0.9999991684720715,
                0.9999996533672549,
                0.999999266179107
            ],
            [
                0.999999266178932,
                0.9999994956525318,
                0.9999994956525318,
                0.9999994956526519,
                0.9999994284994849,
                0.9999994956523512,
                0.999999266179107,
                0.9999995549148419,
                0.9999995549151072,
                0.9999994284996212
            ],
            [
                0.9999995549147889,
                0.9999995549149481,
                0.9999994956524115,
                0.9999994956526519,
                0.9999993524050473,
                0.9999996072139402,
                0.9999994956527121,
                0.999999352404893,
                0.9999996072138934,
                0.9999995549151072
            ],
            [
                0.9999995549147358,
                0.9999994956525918,
                0.9999992661791944,
                0.999999554914895,
                0.9999994956523514,
                0.9999994284997574,
                0.9999994956525918,
                0.9999996072136125,
                0.9999992661791944,
                0.9999994956525318
            ],
            [
                0.9999996533672549,
                0.9999995549150542,
                0.999999730042126,
                0.9999987901341724,
                0.9999993524051246,
                0.9999995549150542,
                0.9999992661790195,
                0.9999994956525917,
                0.9999989322973846,
                0.9999990577549568
            ],
            [
                0.999999554914895,
                0.9999996533672136,
                0.9999995549147358,
                0.9999994956524716,
                0.9999993524049703,
                0.9999995549147889,
                0.9999994956525918,
                0.9999996072136592,
                0.999999428499553,
                0.9999994284994168
            ],
            [
                0.9999992661788445,
                0.9999991684722698,
                0.9999994284997573,
                0.9999993524052019,
                0.9999992661786696,
                0.9999991684719723,
                0.9999994956525918,
                0.9999993524053562,
                0.9999992661786696,
                0.9999994284995529
            ],
            [
                0.9999993524049702,
                0.9999994284992805,
                0.9999994284996211,
                0.9999996072137998,
                0.9999995549148419,
                0.9999994284992805,
                0.9999994956527121,
                0.9999996533675028,
                0.9999995549148419,
                0.9999994284997573
            ],
            [
                0.9999995549147358,
                0.9999994956524716,
                0.999999495652652,
                0.9999994284993485,
                0.9999995549147358,
                0.9999996072139402,
                0.9999992661790195,
                0.9999993524050474,
                0.9999993524049702,
                0.9999996072139402
            ],
            [
                0.9999987901343166,
                0.9999991684722698,
                0.9999986290429567,
                0.9999991684719723,
                0.9999993524053562,
                0.9999994284997574,
                0.9999990577552939,
                0.9999986290429567,
                0.9999989322970028,
                0.9999989322967481
            ],
            [
                0.9999993524049702,
                0.9999995549147358,
                0.999999266178757,
                0.9999993524050474,
                0.9999992661786696,
                0.9999991684721706,
                0.9999992661788445,
                0.9999993524053562,
                0.9999994284996893,
                0.9999989322975118
            ],
            [
                0.9999992661789321,
                0.9999995549150541,
                0.9999993524052018,
                0.9999994284994848,
                0.9999994284996893,
                0.9999996072138466,
                0.9999992661788445,
                0.9999994956524716,
                0.9999995549147889,
                0.999999266179107
            ],
            [
                0.9999994284997574,
                0.9999993524054335,
                0.9999996072138466,
                0.9999996072136125,
                0.999999266179107,
                0.9999994956524115,
                0.9999994284996211,
                0.9999994284993485,
                0.9999993524050474,
                0.9999996072137529
            ],
            [
                0.9999995549150011,
                0.9999995549150542,
                0.9999996533674202,
                0.9999996072138465,
                0.9999993524049702,
                0.9999994956527121,
                0.999999352404893,
                0.9999992661791944,
                0.9999995549147889,
                0.9999996072136592
            ],
            [
                0.9999994956527121,
                0.9999993524053562,
                0.9999995549147358,
                0.9999994956525318,
                0.9999994956523514,
                0.9999996533672548,
                0.9999994284996893,
                0.9999994284993486,
                0.999999352405279,
                0.9999993524053562
            ],
            [
                0.9999994284996893,
                0.9999996072136125,
                0.999999266179107,
                0.9999992661786695,
                0.9999993524051246,
                0.9999995549150011,
                0.9999990577555185,
                0.9999993524049703,
                0.9999993524052019,
                0.9999996533672136
            ],
            [
                0.9999995549149481,
                0.9999991684715759,
                0.9999995549151072,
                0.9999995549147359,
                0.9999992661790196,
                0.9999992661786695,
                0.9999995549150011,
                0.9999994284996891,
                0.9999996072136592,
                0.9999994284995529
            ],
            [
                0.9999994284996893,
                0.9999994284996211,
                0.9999995549147358,
                0.9999989322967482,
                0.9999991684722697,
                0.9999990577556307,
                0.9999994956524716,
                0.9999989322967482,
                0.9999994956525918,
                0.999999168471675
            ],
            [
                0.9999992661788445,
                0.9999994956525917,
                0.9999994284996893,
                0.9999996072136592,
                0.9999994956523512,
                0.9999995549151073,
                0.9999996072137998,
                0.9999995549150542,
                0.9999994956524715,
                0.9999993524052789
            ],
            [
                0.9999992661788446,
                0.9999994956525317,
                0.9999993524050474,
                0.9999994284996211,
                0.9999994284995529,
                0.9999996072136592,
                0.9999994284994167,
                0.9999992661787571,
                0.9999990577557432,
                0.999999168471675
            ],
            [
                0.9999996533674202,
                0.999999495652652,
                0.9999995549149481,
                0.999999554914895,
                0.9999996072137529,
                0.9999994284993486,
                0.9999995549151072,
                0.9999993524054334,
                0.9999994284992805,
                0.9999994956527121
            ],
            [
                0.9999994956526519,
                0.999999352404893,
                0.9999991684719723,
                0.9999994956527722,
                0.9999996072137529,
                0.9999990577554061,
                0.9999994284994167,
                0.999999428499553,
                0.9999991684722698,
                0.9999991684722698
            ],
            [
                0.999999814460876,
                0.9999996533673375,
                0.9999997300422225,
                0.9999996072136592,
                0.9999998362622943,
                0.99999976176309,
                0.999999730042126,
                0.9999994284992805,
                0.9999994284994849,
                0.999999352405279
            ],
            [
                0.9999994956525918,
                0.9999993524054335,
                0.9999996072136125,
                0.9999995549149481,
                0.9999992661788445,
                0.9999996072138465,
                0.9999993524052018,
                0.9999995549150011,
                0.9999994956525917,
                0.9999995549150542
            ],
            [
                0.9999995549150011,
                0.999999352404893,
                0.9999996072137998,
                0.9999992661791944,
                0.9999993524053562,
                0.9999996072137529,
                0.999999352404893,
                0.9999993524053562,
                0.9999996072137061,
                0.9999996072136592
            ],
            [
                0.9999991684721706,
                0.9999993524051246,
                0.9999993524050474,
                0.9999994956523514,
                0.9999993524054334,
                0.9999993524054334,
                0.9999991684717741,
                0.9999992661788446,
                0.999999352404893,
                0.9999994956527722
            ],
            [
                0.9999994956525918,
                0.9999994284993486,
                0.9999992661789321,
                0.9999990577550693,
                0.9999996072138934,
                0.9999995549151073,
                0.9999994284993486,
                0.9999994956525918,
                0.9999995549149481,
                0.9999994956527722
            ],
            [
                0.9999993524052019,
                0.9999995549150541,
                0.9999996072137529,
                0.9999995549147889,
                0.9999993524054334,
                0.9999994956527722,
                0.9999993524051246,
                0.9999996072138465,
                0.999999168471675,
                0.999999554914895
            ],
            [
                0.9999995549149481,
                0.9999994956524716,
                0.9999995549150542,
                0.9999995549147889,
                0.999999554914842,
                0.999999554914895,
                0.9999994956527121,
                0.9999994284993485,
                0.9999994956527121,
                0.9999991684719723
            ],
            [
                0.9999996533674615,
                0.9999994956526519,
                0.9999991684721706,
                0.9999994284994168,
                0.9999994284994168,
                0.9999991684720716,
                0.9999996072138934,
                0.9999995549151072,
                0.9999994284997574,
                0.9999993524054335
            ],
            [
                0.999999428499553,
                0.9999993524049703,
                0.9999993524052019,
                0.9999995549151072,
                0.9999992661789321,
                0.9999995549150011,
                0.999999554914895,
                0.9999994284994168,
                0.9999995549148419,
                0.9999991684721706
            ],
            [
                0.9999996072136125,
                0.9999996072139402,
                0.9999995549149481,
                0.9999995549148419,
                0.9999994956527722,
                0.9999996072138465,
                0.9999991684720715,
                0.9999994284994848,
                0.9999996072136125,
                0.999999352405279
            ],
            [
                0.9999994284996211,
                0.9999994956527121,
                0.9999990577550691,
                0.9999994956527721,
                0.9999995549147889,
                0.9999994956527721,
                0.999999428499553,
                0.9999994284995529,
                0.9999995549150011,
                0.999999428499553
            ],
            [
                0.9999994956524114,
                0.9999992661788445,
                0.9999991684719723,
                0.9999993524054335,
                0.9999993524053563,
                0.9999996072136125,
                0.9999992661792819,
                0.9999994956524114,
                0.9999994956524114,
                0.999999428499553
            ],
            [
                0.999999168471675,
                0.9999991684717741,
                0.9999995549147358,
                0.9999994956525918,
                0.9999994284997574,
                0.9999994284992804,
                0.9999991684718732,
                0.9999994284994848,
                0.999999428499553,
                0.9999996072138934
            ],
            [
                0.9999993524052019,
                0.9999993524050473,
                0.999999352404893,
                0.9999995549147359,
                0.9999996940978825,
                0.9999994284993485,
                0.9999991684718732,
                0.999999266179107,
                0.9999996072138934,
                0.9999994284997574
            ],
            [
                0.9999993524051246,
                0.9999994956525917,
                0.9999993524054334,
                0.999999428499553,
                0.9999995549149481,
                0.9999992661791944,
                0.9999993524052019,
                0.9999991684719723,
                0.9999995549150011,
                0.9999994284996211
            ],
            [
                0.9999994956523514,
                0.9999994956526519,
                0.999999554914895,
                0.9999994284993485,
                0.9999994956524115,
                0.9999996072139402,
                0.9999994956524716,
                0.9999995549150011,
                0.9999996072136125,
                0.9999996072136592
            ],
            [
                0.9999993524051246,
                0.9999995549147358,
                0.9999995549150011,
                0.999999266179107,
                0.9999996072138934,
                0.9999994284993485,
                0.9999992661786696,
                0.9999994956527721,
                0.9999994956524716,
                0.9999994284994168
            ],
            [
                0.9999995549149481,
                0.9999993524049703,
                0.9999995549147889,
                0.9999994956526519,
                0.9999990577550691,
                0.9999994956524716,
                0.9999995549151072,
                0.9999996940976272,
                0.9999994956525317,
                0.9999994956527121
            ],
            [
                0.9999995549149481,
                0.9999994284995529,
                0.9999996072138934,
                0.9999995549150542,
                0.9999989322968754,
                0.9999992661786695,
                0.9999994956523514,
                0.9999995549150542,
                0.9999993524052018,
                0.9999997617631183
            ],
            [
                0.9999991684717741,
                0.9999993524052789,
                0.9999994284994848,
                0.9999993524049703,
                0.9999992661786696,
                0.9999992661790195,
                0.9999993524050474,
                0.9999995549148419,
                0.9999993524049703,
                0.9999993524052019
            ],
            [
                0.9999996072139402,
                0.9999996072137529,
                0.9999996940977366,
                0.9999996072136125,
                0.999999495652652,
                0.9999996533672548,
                0.9999995549147358,
                0.9999994956527121,
                0.9999993524051246,
                0.9999994956526519
            ],
            [
                0.9999994956527722,
                0.999999495652652,
                0.9999994284994168,
                0.9999995549150542,
                0.9999991684719723,
                0.9999995549150011,
                0.9999994284996893,
                0.9999993524052018,
                0.9999994284996891,
                0.9999995549148419
            ],
            [
                0.9999994956527721,
                0.9999995549150541,
                0.9999994956526519,
                0.9999993524049702,
                0.9999991684721706,
                0.9999996072136125,
                0.9999994284996893,
                0.999999352405279,
                0.9999995549150011,
                0.9999995549147358
            ],
            [
                0.9999994956527121,
                0.9999994284992804,
                0.9999994284994849,
                0.9999995549147889,
                0.9999994956524114,
                0.9999996940976272,
                0.9999995549147889,
                0.9999994956527721,
                0.9999991684720715,
                0.9999994284994849
            ],
            [
                0.999999428499553,
                0.9999996072138466,
                0.9999996072138466,
                0.9999994284996211,
                0.9999994956527722,
                0.9999995549149481,
                0.9999994284993485,
                0.9999994956523514,
                0.9999994956525918,
                0.999999266179282
            ],
            [
                0.9999992661786695,
                0.9999995549150542,
                0.9999996072137998,
                0.9999995549149481,
                0.9999994284993485,
                0.9999993524054335,
                0.9999993524052018,
                0.9999993524050474,
                0.9999994284993485,
                0.999999352404893
            ],
            [
                0.9999990577550691,
                0.9999992661788446,
                0.9999994284994167,
                0.999999352405279,
                0.9999993524052018,
                0.9999994284997574,
                0.999999266179107,
                0.9999996072137529,
                0.9999994956527721,
                0.9999993524051246
            ],
            [
                0.9999995549147358,
                0.9999995549150542,
                0.9999995549147358,
                0.9999994956526519,
                0.9999996533672548,
                0.9999995549148419,
                0.999999428499553,
                0.9999995549150541,
                0.999999554915001,
                0.9999996533673375
            ],
            [
                0.9999996072139402,
                0.9999994956524716,
                0.9999995549147358,
                0.9999994956524716,
                0.9999994284996211,
                0.999999554914895,
                0.999999352405279,
                0.999999554914895,
                0.9999995549147358,
                0.999999554914895
            ],
            [
                0.9999992661788445,
                0.9999994956524716,
                0.9999994956524716,
                0.9999994956523514,
                0.9999995549151072,
                0.9999996072137998,
                0.9999994956524716,
                0.999999352404893,
                0.9999994956525317,
                0.9999994956523514
            ],
            [
                0.9999995549149481,
                0.9999993524051247,
                0.9999991684717742,
                0.9999990577555185,
                0.9999995549148419,
                0.9999990577554062,
                0.9999993524053562,
                0.9999989322968754,
                0.999999495652712,
                0.9999991684719723
            ],
            [
                0.9999996072139402,
                0.9999992661790195,
                0.9999995549148419,
                0.9999995549147889,
                0.9999994956525917,
                0.9999994284993485,
                0.9999994956527721,
                0.9999994956525918,
                0.9999993524050474,
                0.9999994284993485
            ],
            [
                0.9999994284996212,
                0.9999994956526519,
                0.9999994956524715,
                0.9999994956527721,
                0.9999993524053562,
                0.9999994956524716,
                0.9999994956525918,
                0.9999995549147358,
                0.9999993524051246,
                0.9999994956527121
            ],
            [
                0.9999994956524716,
                0.9999996072137998,
                0.9999996072138466,
                0.9999993524050474,
                0.9999994956527722,
                0.9999995549148419,
                0.9999995549150542,
                0.9999995549150011,
                0.9999992661786696,
                0.9999994956525918
            ],
            [
                0.9999994956526519,
                0.9999994956523514,
                0.9999994284996212,
                0.9999992661788445,
                0.999999653367503,
                0.9999996072139402,
                0.9999993524051247,
                0.9999996072137998,
                0.999999554914895,
                0.9999992661791944
            ],
            [
                0.9999995549148419,
                0.9999993524053563,
                0.9999994956527721,
                0.999999352404893,
                0.9999996533675028,
                0.9999994284993486,
                0.9999995549150011,
                0.9999994284996893,
                0.9999995549147889,
                0.9999996072136592
            ],
            [
                0.9999994956526519,
                0.9999992661786696,
                0.9999992661790195,
                0.9999994956524716,
                0.9999995549150011,
                0.9999995549150011,
                0.999999428499553,
                0.9999994956524716,
                0.9999993524054335,
                0.9999991684715759
            ],
            [
                0.9999996072137998,
                0.9999994956527121,
                0.9999994956527721,
                0.9999994284994167,
                0.9999994956525918,
                0.9999993524052019,
                0.9999993524052019,
                0.999999428499553,
                0.9999993524051246,
                0.9999996072138934
            ],
            [
                0.9999996072137529,
                0.999999266179107,
                0.9999994956524114,
                0.9999995549151072,
                0.9999994956527121,
                0.9999994956527721,
                0.999999168471675,
                0.9999996072139402,
                0.999999352405279,
                0.9999993524050473
            ],
            [
                0.9999996072137061,
                0.9999996533672962,
                0.9999994956526519,
                0.999999352404893,
                0.9999996072137529,
                0.9999993524054334,
                0.9999995549150011,
                0.9999996533672549,
                0.9999996072137998,
                0.9999992661792819
            ],
            [
                0.9999992661791944,
                0.9999994956525317,
                0.9999995549147358,
                0.9999993524052018,
                0.9999996072137998,
                0.9999994956523514,
                0.9999992661789321,
                0.9999990577552939,
                0.9999994956527121,
                0.9999994284997574
            ],
            [
                0.9999992661786695,
                0.9999995549147889,
                0.9999994956524114,
                0.9999991684717742,
                0.9999994284996211,
                0.9999994956525317,
                0.999999266178757,
                0.9999991684718732,
                0.9999993524050474,
                0.9999990577549568
            ],
            [
                0.9999995549147358,
                0.9999994284992805,
                0.9999990577552937,
                0.9999990577551815,
                0.9999994956527721,
                0.9999993524050474,
                0.9999993524054334,
                0.9999992661790195,
                0.9999994284996891,
                0.9999994956524114
            ],
            [
                0.999999428499553,
                0.9999995549147358,
                0.9999995549147358,
                0.9999991684720715,
                0.9999994284997574,
                0.9999993524050474,
                0.9999992661791944,
                0.9999994956523514,
                0.9999994284996893,
                0.999999554915001
            ],
            [
                0.9999994284993486,
                0.9999994956523514,
                0.9999996072138465,
                0.999999266179107,
                0.9999994284994168,
                0.999999554914895,
                0.9999995549150541,
                0.9999993524053562,
                0.9999996072136592,
                0.9999993524049702
            ],
            [
                0.999999428499553,
                0.9999991684719723,
                0.9999991684722697,
                0.999999554914895,
                0.9999994956524716,
                0.9999993524054335,
                0.9999992661790195,
                0.9999994956527121,
                0.9999990577551815,
                0.9999997617630048
            ],
            [
                0.999999554915001,
                0.9999996533674201,
                0.9999992661788445,
                0.999999554915001,
                0.9999995549149481,
                0.9999993524054334,
                0.9999994284994849,
                0.999999428499553,
                0.9999995549150541,
                0.9999992661792819
            ],
            [
                0.9999994956524716,
                0.9999994284993485,
                0.999999495652652,
                0.9999994956523514,
                0.9999994956524114,
                0.999999554914842,
                0.9999995549147889,
                0.9999994284997574,
                0.9999996072136592,
                0.9999993524054335
            ],
            [
                0.9999994956524115,
                0.999999352405279,
                0.9999996072137061,
                0.9999995549151072,
                0.9999994284996893,
                0.999999554914895,
                0.9999994284996893,
                0.9999994956525918,
                0.9999996072137998,
                0.9999994284996893
            ],
            [
                0.9999995549150542,
                0.9999994284994849,
                0.9999995549147358,
                0.9999995549151072,
                0.9999995549148419,
                0.9999996072137998,
                0.9999992661790195,
                0.9999991684718733,
                0.999999653367503,
                0.9999996533674615
            ],
            [
                0.999999554915001,
                0.9999993524052019,
                0.9999993524054335,
                0.9999994284994168,
                0.9999995549147358,
                0.9999994284996893,
                0.9999995549147889,
                0.9999996533673376,
                0.9999994284992804,
                0.9999994956527721
            ],
            [
                0.9999994284996893,
                0.999999352404893,
                0.9999994956525318,
                0.9999994956526519,
                0.9999994956525917,
                0.9999990577552939,
                0.9999995549149481,
                0.9999995549147359,
                0.9999995549150542,
                0.9999995549147359
            ],
            [
                0.9999994956527722,
                0.9999993524050474,
                0.9999994956527722,
                0.9999993524052789,
                0.999999554915001,
                0.9999993524050474,
                0.9999995549147889,
                0.999999168471675,
                0.9999993524050474,
                0.999999554915001
            ],
            [
                0.9999994284997574,
                0.9999993524051246,
                0.999999352404893,
                0.999999352405279,
                0.9999993524049703,
                0.9999994956524114,
                0.9999994956524114,
                0.9999993524052789,
                0.9999995549151072,
                0.999999352405279
            ],
            [
                0.9999995549151072,
                0.9999991684721706,
                0.9999990577552939,
                0.9999992661788445,
                0.9999994956525918,
                0.9999996533672549,
                0.9999993524054334,
                0.9999994956523514,
                0.9999995549147889,
                0.9999991684715759
            ],
            [
                0.9999995549151072,
                0.9999994956525918,
                0.9999995549151072,
                0.999999266178757,
                0.9999995549150011,
                0.9999992661786695,
                0.9999996072136592,
                0.9999993524049702,
                0.9999994284996212,
                0.9999995549150011
            ],
            [
                0.9999996533675028,
                0.999999554915001,
                0.9999996533674615,
                0.9999993524053562,
                0.9999996072138934,
                0.9999994284993485,
                0.999999554915001,
                0.9999992661786695,
                0.9999991684715758,
                0.9999992661787571
            ],
            [
                0.9999993524054334,
                0.9999996072137529,
                0.9999994956527721,
                0.9999996072139402,
                0.9999995549150011,
                0.9999994956527722,
                0.9999992661790195,
                0.9999994284997574,
                0.999999352404893,
                0.9999994956523514
            ],
            [
                0.9999994956523514,
                0.9999994956524114,
                0.9999995549151072,
                0.9999994956526519,
                0.999999352404893,
                0.9999994284996211,
                0.999999266178757,
                0.9999994956527721,
                0.9999991684721706,
                0.9999994284994849
            ],
            [
                0.9999994956523514,
                0.9999996072137998,
                0.9999994956525317,
                0.9999995549148419,
                0.9999994956527121,
                0.9999994284996893,
                0.9999995549150541,
                0.9999993524052018,
                0.9999996072138465,
                0.9999995549149481
            ],
            [
                0.999999266179107,
                0.9999995549148419,
                0.9999994956524114,
                0.9999994284993485,
                0.9999994284994848,
                0.9999996072137529,
                0.999999352404893,
                0.9999996072138934,
                0.9999994956525317,
                0.9999993524053563
            ],
            [
                0.9999991684717742,
                0.9999994284997574,
                0.9999991684720715,
                0.9999993524053562,
                0.9999990577556308,
                0.9999995549148419,
                0.9999987901337396,
                0.9999994284994849,
                0.9999994284994168,
                0.9999994956524716
            ],
            [
                0.9999995549150541,
                0.9999996072137061,
                0.9999995549149481,
                0.9999993524053563,
                0.9999991684715758,
                0.9999991684721706,
                0.999999352405279,
                0.9999994284994167,
                0.9999993524051246,
                0.9999994956524716
            ],
            [
                0.9999994284995529,
                0.9999996072136125,
                0.9999994956524716,
                0.9999995549149481,
                0.9999993524054334,
                0.999999266178757,
                0.9999995549151072,
                0.9999994284993486,
                0.9999993524050473,
                0.999999554915001
            ],
            [
                0.9999991684722697,
                0.9999994956527121,
                0.9999994284996211,
                0.999999653367379,
                0.999999266179282,
                0.999999428499553,
                0.9999994284994167,
                0.9999995549150011,
                0.9999996072138934,
                0.9999993524050474
            ],
            [
                0.9999996533673375,
                0.999999554914895,
                0.9999995549147358,
                0.999999352404893,
                0.9999994284997574,
                0.9999996940977366,
                0.999999495652652,
                0.9999996072138465,
                0.999999653367379,
                0.9999994956524716
            ],
            [
                0.9999995549148419,
                0.9999993524052019,
                0.9999991684717742,
                0.9999991684715758,
                0.9999992661789321,
                0.9999996072138465,
                0.9999995549150011,
                0.9999994956526519,
                0.9999994284993486,
                0.9999993524051247
            ],
            [
                0.9999993524050474,
                0.9999991684721706,
                0.9999992661786696,
                0.9999993524054334,
                0.9999994284993485,
                0.9999994284994848,
                0.9999993524054335,
                0.9999995549147889,
                0.9999995549147889,
                0.9999993524052019
            ],
            [
                0.9999994284992804,
                0.9999994956524716,
                0.9999994284993485,
                0.9999994956526519,
                0.999999352404893,
                0.9999994284996211,
                0.9999992661788446,
                0.9999993524054334,
                0.9999994284997573,
                0.9999996072136592
            ],
            [
                0.9999994956523514,
                0.9999995549147889,
                0.9999994284994849,
                0.999999352404893,
                0.9999996072136125,
                0.9999994956524716,
                0.9999994956525318,
                0.9999994956526519,
                0.9999996072136125,
                0.999999428499553
            ],
            [
                0.9999995549149481,
                0.999999352405279,
                0.999999352405279,
                0.9999996072137529,
                0.999999495652652,
                0.999999168471675,
                0.9999991684715759,
                0.9999994956524115,
                0.9999994956523512,
                0.9999994956526519
            ],
            [
                0.9999994956524115,
                0.9999992661788445,
                0.9999994956524716,
                0.9999992661792819,
                0.9999993524054334,
                0.9999990577557432,
                0.9999996533672135,
                0.999999266179107,
                0.9999996072138934,
                0.9999996072136125
            ],
            [
                0.9999992661790195,
                0.9999995549151072,
                0.9999994284994849,
                0.9999993524049703,
                0.9999994956527121,
                0.999999352405279,
                0.9999994284996893,
                0.9999995549147889,
                0.9999994284994848,
                0.9999996072138466
            ],
            [
                0.9999991684718733,
                0.9999995549147358,
                0.9999994956523514,
                0.9999993524050474,
                0.9999995549149481,
                0.9999994956524716,
                0.9999994956527721,
                0.999999428499553,
                0.9999992661790196,
                0.9999991684721706
            ],
            [
                0.999999352405279,
                0.9999995549147889,
                0.9999992661791944,
                0.9999993524054334,
                0.9999992661790195,
                0.9999994284995529,
                0.9999994284995529,
                0.9999991684716749,
                0.9999995549148419,
                0.999999495652712
            ],
            [
                0.999999428499553,
                0.9999994284994168,
                0.9999995549147358,
                0.9999994284992805,
                0.9999996072137998,
                0.9999993524052019,
                0.999999352404893,
                0.9999996072138934,
                0.9999994284993486,
                0.9999996072137061
            ],
            [
                0.9999994956527721,
                0.9999995549150541,
                0.9999992661788445,
                0.9999994956527121,
                0.9999995549150011,
                0.9999995549149481,
                0.9999994956525917,
                0.9999993524054334,
                0.999999428499553,
                0.9999995549148419
            ],
            [
                0.9999994956527721,
                0.9999995549147358,
                0.9999992661792819,
                0.999999352404893,
                0.9999994956524115,
                0.9999994956527721,
                0.9999994284996211,
                0.9999995549150541,
                0.9999995549150011,
                0.9999995549148419
            ],
            [
                0.999999554915001,
                0.9999996533672135,
                0.9999996940978825,
                0.9999994284994168,
                0.9999994956524716,
                0.999999554914895,
                0.9999994956525317,
                0.9999996072136125,
                0.9999996072138934,
                0.9999996533672962
            ],
            [
                0.9999994284996211,
                0.9999995549151072,
                0.9999994284997574,
                0.9999994956525318,
                0.9999994284993486,
                0.9999992661788445,
                0.9999994284996893,
                0.9999993524054335,
                0.9999994284994849,
                0.9999994284995529
            ],
            [
                0.9999993524051246,
                0.9999993524049703,
                0.9999994956524716,
                0.9999995549147358,
                0.9999992661792819,
                0.9999995549147889,
                0.9999994284994849,
                0.9999994284996212,
                0.9999990577555185,
                0.9999989322968754
            ],
            [
                0.9999993524049702,
                0.9999993524051246,
                0.9999994956527121,
                0.9999994956524716,
                0.9999994956523512,
                0.9999994956525317,
                0.9999995549147889,
                0.9999996072136125,
                0.9999996072136592,
                0.9999993524054335
            ],
            [
                0.9999992661791944,
                0.9999993524053562,
                0.9999992661791944,
                0.9999995549147889,
                0.9999994284994849,
                0.9999993524052019,
                0.9999996072138934,
                0.9999995549148419,
                0.9999994956524114,
                0.9999994956525318
            ],
            [
                0.9999996072137529,
                0.999999352405279,
                0.9999996072136593,
                0.9999996072136125,
                0.9999994956526519,
                0.9999996072137061,
                0.9999994956527721,
                0.9999994956524716,
                0.9999995549151073,
                0.9999993524049703
            ],
            [
                0.9999994284994167,
                0.9999990577550693,
                0.9999991684721706,
                0.9999994284994167,
                0.9999989322975118,
                0.9999996940977731,
                0.9999993524049703,
                0.9999987901346049,
                0.9999994284993485,
                0.999999352404893
            ],
            [
                0.9999994956527721,
                0.9999992661786695,
                0.9999994284994168,
                0.9999993524052019,
                0.9999990577550693,
                0.9999993524050474,
                0.9999991684722697,
                0.9999992661792819,
                0.9999995549147889,
                0.9999994956525318
            ],
            [
                0.9999996533674615,
                0.9999996533673375,
                0.9999992661788445,
                0.9999994284994849,
                0.9999994284994849,
                0.9999994284992805,
                0.9999993524052018,
                0.9999996072137529,
                0.9999994284997574,
                0.9999994956523514
            ],
            [
                0.9999994284992804,
                0.9999994284992805,
                0.9999996072137061,
                0.9999994284994849,
                0.9999994956524716,
                0.9999995549147889,
                0.9999994284996212,
                0.9999996072136592,
                0.9999991684717742,
                0.9999994956525317
            ],
            [
                0.9999994284996893,
                0.9999989322967482,
                0.9999994956527721,
                0.9999994284992804,
                0.9999994956527721,
                0.9999994284997574,
                0.9999996533672549,
                0.9999994956525317,
                0.9999993524054334,
                0.9999993524051246
            ],
            [
                0.999999694097846,
                0.9999993524049702,
                0.9999994284996893,
                0.9999995549147358,
                0.9999994956524114,
                0.9999992661792819,
                0.9999996072138465,
                0.9999996072136592,
                0.9999997617630616,
                0.9999991684716749
            ],
            [
                0.999999266178757,
                0.9999994284993485,
                0.9999996072137061,
                0.9999995549147359,
                0.9999994284996891,
                0.9999994284993485,
                0.9999989322973846,
                0.9999992661792819,
                0.999999266178757,
                0.9999993524054334
            ],
            [
                0.9999993524050474,
                0.9999994956525918,
                0.9999992661788445,
                0.999999266178757,
                0.9999995549147358,
                0.9999989322967482,
                0.9999994284995529,
                0.999999554914895,
                0.9999996072138934,
                0.9999996533675028
            ],
            [
                0.9999996072136592,
                0.9999992661791944,
                0.9999994284992804,
                0.9999994284992805,
                0.9999994956526519,
                0.9999993524049702,
                0.9999992661786696,
                0.999999554915001,
                0.9999996072137061,
                0.999999266178757
            ],
            [
                0.999998932296621,
                0.9999989322972572,
                0.999999352404893,
                0.9999992661790196,
                0.9999987901344608,
                0.9999990577556307,
                0.9999994284996891,
                0.999999057755743,
                0.99999893229713,
                0.9999991684721706
            ],
            [
                0.9999995549150011,
                0.9999995549148419,
                0.9999992661787571,
                0.9999994956527721,
                0.9999991684721706,
                0.9999994284996212,
                0.9999994956527722,
                0.999999352404893,
                0.9999994956523514,
                0.9999992661786696
            ],
            [
                0.999999168471675,
                0.999999266178757,
                0.9999993524053562,
                0.9999994284994168,
                0.9999992661786696,
                0.9999995549149481,
                0.9999996533672135,
                0.9999992661792819,
                0.9999994284996212,
                0.9999992661786696
            ],
            [
                0.9999993524054335,
                0.9999991684717742,
                0.9999993524053562,
                0.999999495652652,
                0.9999996072136125,
                0.9999991684721706,
                0.9999993524054334,
                0.9999991684722697,
                0.9999994284997574,
                0.9999993524049702
            ],
            [
                0.999999168471675,
                0.999999554915001,
                0.9999993524053562,
                0.999999554915001,
                0.9999994956527721,
                0.9999994956527721,
                0.9999994956524716,
                0.9999990577556308,
                0.9999994956527722,
                0.9999995549147358
            ],
            [
                0.9999992661786696,
                0.9999994956527121,
                0.9999992661791944,
                0.9999992661789321,
                0.9999990577549569,
                0.9999994956526519,
                0.9999990577554061,
                0.999999730042319,
                0.9999995549151073,
                0.9999994956525317
            ],
            [
                0.9999993524052019,
                0.9999992661791944,
                0.999999495652712,
                0.9999992661788446,
                0.9999991684719723,
                0.9999991684722698,
                0.9999994956525917,
                0.9999994284996212,
                0.9999991684721706,
                0.9999991684719723
            ],
            [
                0.9999991684719723,
                0.9999994284996893,
                0.9999994284996893,
                0.9999993524049702,
                0.999999352404893,
                0.9999993524050473,
                0.999999266179107,
                0.9999996072137529,
                0.999999653367379,
                0.9999996072138466
            ],
            [
                0.9999995549151072,
                0.9999995549149481,
                0.9999996072136125,
                0.9999995549151072,
                0.999999266178932,
                0.9999996533674202,
                0.9999994284993485,
                0.9999994284992805,
                0.9999996072139402,
                0.9999994956525918
            ],
            [
                0.9999994284994849,
                0.9999994956523514,
                0.9999994284993486,
                0.9999994956525318,
                0.9999994284994849,
                0.9999996533672963,
                0.9999992661791944,
                0.9999994284997574,
                0.9999994956523514,
                0.9999995549151073
            ],
            [
                0.9999994284994168,
                0.9999995549147358,
                0.9999995549147358,
                0.9999992661786696,
                0.999999352405279,
                0.9999992661791944,
                0.9999994956527121,
                0.9999992661786696,
                0.9999994284996211,
                0.9999995549151072
            ],
            [
                0.9999996072137529,
                0.999999266178757,
                0.9999992661786695,
                0.999999554914895,
                0.9999996072136125,
                0.999999266179107,
                0.9999992661788445,
                0.999999057755743,
                0.9999996533673375,
                0.9999995549150011
            ],
            [
                0.9999994956525318,
                0.9999994284992805,
                0.9999994284996893,
                0.9999994956524115,
                0.9999991684715759,
                0.9999995549147358,
                0.9999995549150541,
                0.9999996072137529,
                0.9999995549149481,
                0.9999996072137061
            ]
        ]
    },
    {
        "q_id": "8801_mmlu_math",
        "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": [
            [
                0.999999428499553,
                0.9999996072139402,
                0.9999996072137061,
                0.9999996940976272,
                0.9999994956525317,
                0.9999997300421581,
                0.9999992661792819,
                0.9999996940977366,
                0.9999993524049703,
                0.9999997300423191
            ],
            [
                0.9999994284993486,
                0.9999996940978095,
                0.999999352404893,
                0.9999996533672136,
                0.9999996072136592,
                0.9999998144608097,
                0.9999998362623723,
                0.9999996940976271,
                0.9999996072137061,
                0.9999997300421581
            ],
            [
                0.999999266178932,
                0.9999994284994849,
                0.9999996533674202,
                0.9999996072136592,
                0.9999996072136592,
                0.9999997617630616,
                0.9999997617630049,
                0.9999990577552939,
                0.9999994284997574,
                0.9999992661788446
            ],
            [
                0.9999993524050474,
                0.9999994956525317,
                0.999999352404893,
                0.999999266178932,
                0.9999992661789321,
                0.9999995549148419,
                0.9999996533673375,
                0.9999990577552937,
                0.9999992661786696,
                0.9999993524053563
            ],
            [
                0.9999997300422547,
                0.9999997300422547,
                0.9999998362622747,
                0.9999997617630616,
                0.9999998555019962,
                0.999999814460876,
                0.9999996072137998,
                0.9999997300422547,
                0.9999998144608981,
                0.9999993524051246
            ],
            [
                0.9999993524050474,
                0.9999996533674202,
                0.9999994956527121,
                0.9999997300422869,
                0.9999989322967482,
                0.9999995549149481,
                0.9999996072136125,
                0.9999996072138934,
                0.9999996940977366,
                0.9999996940978461
            ],
            [
                0.9999996072137061,
                0.999999789756684,
                0.9999995549147359,
                0.999999789756634,
                0.9999997300422225,
                0.9999997300423191,
                0.9999994956527121,
                0.9999996533672549,
                0.9999994284996211,
                0.999999694097846
            ],
            [
                0.9999995549150011,
                0.9999996940978825,
                0.9999997300420939,
                0.9999994956525317,
                0.9999996072137061,
                0.9999996533674201,
                0.999999352404893,
                0.9999997617630616,
                0.999999428499553,
                0.9999998144609645
            ],
            [
                0.9999991684715759,
                0.9999997897566338,
                0.9999992661791944,
                0.9999996072136592,
                0.9999993524054335,
                0.9999986290421394,
                0.9999993524050474,
                0.9999991684719725,
                0.9999986290424664,
                0.9999993524051246
            ],
            [
                0.9999994956525918,
                0.9999996072139402,
                0.9999996533672548,
                0.9999993524052018,
                0.9999996533672135,
                0.9999996072138466,
                0.9999997617631183,
                0.9999990577551815,
                0.9999996533672135,
                0.9999998362623137
            ],
            [
                5.04347348075149e-07,
                9.422449308420983e-07,
                9.422444815628016e-07,
                8.315282259009745e-07,
                1.8553910183607374e-07,
                3.059022269250683e-07,
                5.715004470272272e-07,
                1.2098662604247682e-06,
                3.059021904580685e-07,
                4.450852111135988e-07
            ],
            [
                0.9999996072139402,
                0.9999995549148419,
                0.9999995549148419,
                0.9999996940976636,
                0.9999997300423191,
                0.9999996940978095,
                0.9999996940978825,
                0.9999997617631183,
                0.9999994956526519,
                0.9999997897566089
            ],
            [
                0.9999998144609202,
                0.9999998724809571,
                0.999999694097773,
                0.9999996940976271,
                0.9999997300422869,
                0.9999996940978095,
                0.9999997617630616,
                0.9999996940976272,
                0.9999996533672549,
                0.999999789756684
            ],
            [
                0.9999996940977002,
                0.9999996533673375,
                0.9999997300423191,
                0.9999989322970028,
                0.9999995549147889,
                0.9999993524049703,
                0.9999994284996211,
                0.9999996940977731,
                0.9999997897567341,
                0.9999990577551816
            ],
            [
                0.999999694097846,
                0.9999996940977731,
                0.9999998144608981,
                0.9999996072138934,
                0.9999994284995529,
                0.9999996072137061,
                0.9999997897566589,
                0.9999996533674202,
                0.9999997897565587,
                0.9999998362623332
            ],
            [
                0.9999992661791944,
                0.9999995549150541,
                0.9999995549148419,
                0.999999730042126,
                0.9999994956525918,
                0.9999994956523514,
                0.9999998362622552,
                0.9999994956525317,
                0.9999991684721706,
                0.9999995549150541
            ],
            [
                0.999999057755743,
                0.9999997300422225,
                0.9999997617630616,
                0.9999994956523514,
                0.999999694097846,
                0.9999997897567091,
                0.9999997897565587,
                0.9999995549150542,
                0.9999996533672135,
                0.9999996533675028
            ],
            [
                0.9999997300422869,
                0.9999994284993486,
                0.9999995549147358,
                0.9999997300421581,
                0.99999976176309,
                0.9999996072136125,
                0.9999996533673375,
                0.9999996940977002,
                0.999999694097773,
                0.9999996533673375
            ],
            [
                0.9999996533672135,
                0.9999996533674615,
                0.9999996072136125,
                0.999999814460854,
                0.9999997897566089,
                0.999999653367379,
                0.999999554914895,
                0.9999994956526519,
                0.9999995549149481,
                0.9999994956527121
            ],
            [
                0.9999991684722697,
                0.999999495652652,
                0.9999996072136125,
                0.9999990577554062,
                0.9999996533673376,
                0.9999997300420939,
                0.9999995549148419,
                0.9999998362622943,
                0.9999996533672548,
                0.9999995549150011
            ],
            [
                0.9999991684717742,
                0.9999997897566589,
                0.9999994956527721,
                0.9999990577551815,
                0.9999991684718732,
                0.9999990577551815,
                0.9999997617631752,
                0.9999994956527721,
                0.9999994956524716,
                0.9999992661787571
            ],
            [
                0.9999996940978095,
                0.9999997617631184,
                0.99999976176309,
                0.9999996940978825,
                0.9999998555019618,
                0.9999997897566089,
                0.9999995549147889,
                0.9999997300423191,
                0.9999997300420937,
                0.999999730042126
            ],
            [
                0.9999995549147358,
                0.9999995549147358,
                0.9999996072137998,
                0.9999998144608983,
                0.9999994956526519,
                0.9999996533672549,
                0.9999996533674614,
                0.9999996072137529,
                0.9999996072137529,
                0.9999997617630616
            ],
            [
                0.9999997617631469,
                0.9999995549150542,
                0.9999998555019962,
                0.9999997300421581,
                0.9999997897567091,
                0.9999998144608981,
                0.9999996072137061,
                0.9999996533672962,
                0.9999993524054335,
                0.9999994956524115
            ],
            [
                0.9999995549149481,
                0.9999997897565587,
                0.9999997300421581,
                0.9999995549150542,
                0.9999995549148419,
                0.9999995549147889,
                0.9999996072136592,
                0.9999996072137529,
                0.9999996072137529,
                0.9999996072138465
            ],
            [
                0.9999994956525917,
                0.9999996940976271,
                0.9999996533674201,
                0.9999997617630616,
                0.9999996072136125,
                0.9999995549150011,
                0.999999653367379,
                0.9999995549147889,
                0.9999996072138465,
                0.9999995549147889
            ],
            [
                0.9999997617631468,
                0.9999993524051246,
                0.9999997897566089,
                0.9999997300422869,
                0.9999997897567091,
                0.9999994956525918,
                0.9999996940978095,
                0.9999989322972573,
                0.999999694097773,
                0.9999993524049702
            ],
            [
                0.999999352405279,
                0.9999997897565838,
                0.9999997897566589,
                0.9999997617631469,
                0.9999997617631753,
                0.9999996533674201,
                0.999999730042126,
                0.9999997897565838,
                0.9999997617630332,
                0.9999998144609424
            ],
            [
                0.99999976176309,
                0.999999730042126,
                0.9999997300422225,
                0.999999789756634,
                0.999999653367379,
                0.9999996940976271,
                0.9999996072137998,
                0.9999996072137061,
                0.999999266179282,
                0.9999994956527121
            ],
            [
                0.9999993524049703,
                0.9999998144609202,
                0.9999996072137061,
                0.9999998362623528,
                0.9999997897565587,
                0.9999997897567091,
                0.9999997897565587,
                0.999999730042126,
                0.9999997617630049,
                0.9999996940978825
            ],
            [
                0.9999998144608097,
                0.9999996940978461,
                0.999999730042126,
                0.9999994956524114,
                0.9999998144608317,
                0.999999554915001,
                0.9999994956525918,
                0.9999998724809115,
                0.9999993524049703,
                0.9999994956523514
            ],
            [
                0.9999996533672136,
                0.9999992661789321,
                0.9999992661789321,
                0.9999995549147889,
                0.9999984465024307,
                0.999999495652712,
                0.9999997300422547,
                0.9999996072138934,
                0.9999994956524715,
                0.999999495652652
            ],
            [
                0.9999997617630048,
                0.999999814460876,
                0.9999992661791071,
                0.9999996072138465,
                0.9999993524049702,
                0.9999994956524716,
                0.9999991684717742,
                0.999999653367379,
                0.9999997300421903,
                0.9999997897566089
            ],
            [
                0.9999998144609645,
                0.9999997617631468,
                0.999999694097846,
                0.9999998362622552,
                0.9999996533672962,
                0.9999997617630616,
                0.9999998874648514,
                0.9999997300421581,
                0.9999997897565838,
                0.9999996940977366
            ],
            [
                0.9999994956525317,
                0.999999730042126,
                0.999999789756634,
                0.9999997897567091,
                0.9999997897565838,
                0.9999997300422225,
                0.9999997617630332,
                0.9999997617630616,
                0.9999996072138934,
                0.9999997300420939
            ],
            [
                0.9999996072138466,
                0.9999994956527121,
                0.9999997617631184,
                0.9999996940978095,
                0.9999998362623722,
                0.9999996940977002,
                0.9999998362622747,
                0.9999996940978825,
                0.9999998362622357,
                0.9999998555019618
            ],
            [
                0.999999789756634,
                0.9999996940977366,
                0.9999996072137998,
                0.9999997300422547,
                0.9999997617630048,
                0.9999996533672136,
                0.9999996533675028,
                0.9999996533674615,
                0.999999653367379,
                0.9999998362623137
            ],
            [
                0.9999996072137061,
                0.9999996533673788,
                0.9999996533672548,
                0.999999789756634,
                0.9999993524053562,
                0.9999996072137998,
                0.9999994956526519,
                0.9999991684719723,
                0.9999994956525317,
                0.9999997300420937
            ],
            [
                0.9999994956524115,
                0.9999996940977002,
                0.9999996940977002,
                0.9999997300422225,
                0.9999997300422225,
                0.999999694097846,
                0.9999994284994849,
                0.9999994284996893,
                0.9999998144608097,
                0.999999694097846
            ],
            [
                0.9999997300422225,
                0.9999996072139402,
                0.9999998362623138,
                0.9999997897565587,
                0.9999996940977002,
                0.9999994284994849,
                0.9999996533672548,
                0.9999995549148419,
                0.9999994284992805,
                0.999999730042126
            ],
            [
                0.9999993524048931,
                0.9999997617631469,
                0.9999999006881259,
                0.9999993524053562,
                0.999999730042126,
                0.9999997300422869,
                0.9999996940978095,
                0.9999997300421581,
                0.999999855502048,
                0.9999993524052018
            ],
            [
                0.999999266179107,
                0.9999996533674615,
                0.9999996072138465,
                0.999999554914842,
                0.999999789756684,
                0.999999554914895,
                0.999999495652712,
                0.9999996533674202,
                0.9999991684721706,
                0.9999996072139402
            ],
            [
                0.9999997617631184,
                0.9999996940976272,
                0.9999998144608981,
                0.9999998874647976,
                0.9999997897566089,
                0.9999997300422225,
                0.999999730042126,
                0.9999994956527721,
                0.9999997897567091,
                0.9999996940977001
            ],
            [
                0.9999998144608098,
                0.9999997617630616,
                0.9999998362622357,
                0.999999730042319,
                0.9999998144608317,
                0.9999997300422869,
                0.9999998144609202,
                0.9999997300423191,
                0.9999997300423191,
                0.9999998362622942
            ],
            [
                0.9999997300421903,
                0.999999653367503,
                0.9999996533672136,
                0.9999997300421903,
                0.9999995549148419,
                0.9999998874648917,
                0.9999996072136125,
                0.9999997300422869,
                0.9999998724809116,
                0.9999996940978825
            ],
            [
                0.9999994956524716,
                0.9999996533674615,
                0.9999996533672549,
                0.9999996940977731,
                0.9999995549148419,
                0.9999997897565587,
                0.9999996533672136,
                0.9999996072138934,
                0.9999997300422225,
                0.9999993524054334
            ],
            [
                0.9999986290421394,
                0.9999995549150011,
                0.9999996072137061,
                0.9999996072139402,
                0.99999976176309,
                0.9999994284992805,
                0.9999994284997574,
                0.9999996072136592,
                0.9999994284994849,
                0.9999994284996893
            ],
            [
                0.9999996072137529,
                0.9999986290423029,
                0.9999994284996211,
                0.9999991684717741,
                0.9999990577552939,
                0.9999990577554061,
                0.9999994956524716,
                0.9999990577551815,
                0.9999996072138465,
                0.9999989322972572
            ],
            [
                0.9999994956523514,
                0.9999995549150542,
                0.999999730042319,
                0.999999789756684,
                0.9999994956523514,
                0.99999976176309,
                0.9999991684721706,
                0.9999997897567091,
                0.9999997300422547,
                0.9999996072137998
            ],
            [
                0.9999996533672962,
                0.9999997617629764,
                0.9999993524050474,
                0.9999996940978825,
                0.9999995549148419,
                0.9999994284993485,
                0.9999991684720715,
                0.999999266178757,
                0.9999994956524114,
                0.9999994956525317
            ],
            [
                0.9999993524054335,
                0.9999993524051246,
                0.9999987901340281,
                0.9999990577549569,
                0.9999990577551815,
                0.9999992661786696,
                0.9999991684720715,
                0.9999997617630049,
                0.9999991684722697,
                0.9999992661787571
            ],
            [
                0.9999994284997574,
                0.9999996533674202,
                0.9999996072137529,
                0.9999996533674201,
                0.9999996940978095,
                0.9999995549147889,
                0.9999994284996893,
                0.9999997617631184,
                0.9999995549150011,
                0.999999554915001
            ],
            [
                0.9999990577554062,
                0.9999996533675028,
                0.9999993524053562,
                0.9999996072139402,
                0.9999997300423191,
                0.9999994956523514,
                0.9999994956525918,
                0.9999992661786695,
                0.999999653367379,
                0.999999428499553
            ],
            [
                0.9999996940977002,
                0.9999996533674615,
                0.9999998724810027,
                0.999999789756684,
                0.9999996533674202,
                0.9999998144608981,
                0.9999997300421581,
                0.9999997300422547,
                0.9999996940977366,
                0.9999996940976272
            ],
            [
                0.9999996072136592,
                0.9999997300422869,
                0.999999789756684,
                0.9999997897565587,
                0.9999997617629763,
                0.9999998144608097,
                0.9999997897567091,
                0.999999789756684,
                0.9999995549151072,
                0.9999996533674614
            ],
            [
                0.999999057755743,
                0.9999957771675626,
                0.9999980052695652,
                0.9999987901347492,
                0.9999982396572065,
                0.9999984465026159,
                0.9999977396765106,
                0.9999980052700408,
                0.9999982396567867,
                0.9999982396574163
            ],
            [
                0.9999991684716749,
                0.9999996072136125,
                0.9999996533672136,
                0.9999992661791071,
                0.999999694097846,
                0.9999994956523512,
                0.9999990577550693,
                0.9999996072136592,
                0.9999996072137998,
                0.9999993524053562
            ],
            [
                0.9999994956526519,
                0.9999994284996211,
                0.9999996533672549,
                0.9999994956527721,
                0.9999997300422869,
                0.999999352405279,
                0.9999994284993485,
                0.9999991684722697,
                0.9999996072139402,
                0.9999991684718733
            ],
            [
                0.9999995549149481,
                0.9999996533674614,
                0.9999994956525318,
                0.9999991684717741,
                0.9999996072137061,
                0.9999996072136125,
                0.9999992661786696,
                0.9999994956523512,
                0.9999994284994848,
                0.999999352405279
            ],
            [
                0.9999995549150542,
                0.9999994956526519,
                0.9999994956527121,
                0.9999996072138465,
                0.9999990577555186,
                0.9999993524051246,
                0.9999994284997573,
                0.9999994284996211,
                0.999999789756634,
                0.999998932296621
            ],
            [
                0.9999996940976271,
                0.9999998144608981,
                0.9999996072137061,
                0.9999993524048931,
                0.9999995549148951,
                0.9999993524051246,
                0.9999996940977001,
                0.9999996940978825,
                0.9999996940978825,
                0.9999998144608317
            ],
            [
                0.9999997617630049,
                0.9999998144609202,
                0.9999998144608538,
                0.9999998362622357,
                0.9999996940977002,
                0.9999994956526519,
                0.9999997300420937,
                0.999999789756634,
                0.9999997300422225,
                0.9999997300421903
            ],
            [
                0.99999976176309,
                0.9999996072138465,
                0.9999998144608097,
                0.9999997897566089,
                0.9999989322972572,
                0.999999653367379,
                0.9999996533672962,
                0.9999996940976271,
                0.999999653367379,
                0.999999814460876
            ],
            [
                0.9999996533674615,
                0.9999996533672136,
                0.9999995549149481,
                0.999999554914895,
                0.9999994956527721,
                0.9999995549150541,
                0.999999789756684,
                0.9999997897565587,
                0.9999996940976272,
                0.9999994956525317
            ],
            [
                0.9999997897566589,
                0.9999994956525918,
                0.9999996533675028,
                0.9999997617630048,
                0.999999352404893,
                0.9999995549151073,
                0.99999976176309,
                0.9999997617631184,
                0.9999992661788446,
                0.9999997897565838
            ],
            [
                0.9999994956525918,
                0.9999995549151073,
                0.9999996072137998,
                0.9999994284992804,
                0.9999996940976272,
                0.9999997897566589,
                0.9999994284992805,
                0.9999997300422547,
                0.9999996533674614,
                0.9999994956524114
            ],
            [
                0.9999996072138465,
                0.999999814460876,
                0.9999996072137998,
                0.9999997300420937,
                0.9999996533675028,
                0.9999994284996893,
                0.9999998144609645,
                0.9999995549151072,
                0.9999994956527721,
                0.9999997617631468
            ],
            [
                0.999999730042319,
                0.9999995549150011,
                0.9999993524049702,
                0.99999976176309,
                0.9999995549149481,
                0.9999994284994167,
                0.9999994284992805,
                0.9999994956523514,
                0.999999554914895,
                0.999999554914895
            ],
            [
                0.9999997617629764,
                0.9999997897565587,
                0.9999998362623528,
                0.9999998144609423,
                0.9999993524050474,
                0.9999995549151073,
                0.999999814460876,
                0.999999694097846,
                0.9999997300423191,
                0.9999997300423191
            ],
            [
                0.9999998144609645,
                0.9999995549151072,
                0.9999997897567091,
                0.999999730042126,
                0.9999997897565587,
                0.9999995549151073,
                0.9999997300422869,
                0.9999996072139402,
                0.9999997617630048,
                0.9999994956525318
            ],
            [
                0.999999266179282,
                0.9999995549151073,
                0.9999992661792819,
                0.9999994284992805,
                0.9999997300421581,
                0.999999266179282,
                0.9999996533674202,
                0.9999997897566589,
                0.9999997617630049,
                0.999999653367503
            ],
            [
                0.999999730042126,
                0.9999998362622943,
                0.9999998144609423,
                0.9999997897567341,
                0.9999997897566089,
                0.9999999123575045,
                0.9999998555019446,
                0.9999997897565838,
                0.9999996940978825,
                0.9999996940976272
            ],
            [
                0.999999352404893,
                0.9999994284994167,
                0.9999996072137061,
                0.9999997897565838,
                0.999999730042126,
                0.9999996940978095,
                0.999999495652652,
                0.9999998874648514,
                0.9999994956527722,
                0.999999653367379
            ],
            [
                0.9999997300420937,
                0.9999996533672136,
                0.9999996072137061,
                0.9999996533675028,
                0.9999996940978825,
                0.9999996533673375,
                0.9999996940976636,
                0.9999996533674615,
                0.999999730042319,
                0.9999994284993486
            ],
            [
                0.9999991684721706,
                0.9999997300422225,
                0.9999998555020135,
                0.9999996072136592,
                0.9999997300420937,
                0.9999996940976271,
                0.999999653367379,
                0.9999998362623528,
                0.9999994956525918,
                0.999999814460854
            ],
            [
                0.999999789756684,
                0.9999997300422869,
                0.9999997897567342,
                0.9999997897565587,
                0.9999999006880668,
                0.99999976176309,
                0.9999998724808964,
                0.999999855501979,
                0.9999997617630049,
                0.9999997617629763
            ],
            [
                0.9999996533675028,
                0.9999997617630899,
                0.9999996940976272,
                0.9999993524050474,
                0.9999994956523514,
                0.9999996940978825,
                0.9999997897565587,
                0.9999997897566089,
                0.9999994284993486,
                0.9999998144608538
            ],
            [
                0.9999990577556308,
                0.9999990577555185,
                0.9999994284996891,
                0.9999994956524114,
                0.9999995549149481,
                0.9999994284996211,
                0.9999991684718732,
                0.999999653367379,
                0.9999996533673375,
                0.9999992661790195
            ],
            [
                0.999999554914895,
                0.9999997300422869,
                0.9999994956525318,
                0.999999352405279,
                0.999999554914789,
                0.9999994284996211,
                0.9999993524052018,
                0.9999993524053562,
                0.9999996072139402,
                0.9999994284996211
            ],
            [
                0.9999997617631183,
                0.9999996533672135,
                0.9999994284994168,
                0.9999996940976636,
                0.9999992661792819,
                0.999999789756634,
                0.9999995549148419,
                0.9999995549147889,
                0.9999996533672962,
                0.9999998144608319
            ],
            [
                0.9999996940977731,
                0.9999997300421581,
                0.999999789756684,
                0.9999996072137998,
                0.9999995549151072,
                0.9999997300421581,
                0.9999998144608538,
                0.9999996940976636,
                0.9999997617631753,
                0.9999996072137061
            ],
            [
                0.999999428499553,
                0.9999994956527121,
                0.9999997300422869,
                0.9999997300421903,
                0.9999997897567091,
                0.9999996072137998,
                0.9999992661790195,
                0.9999998144609424,
                0.9999994956527121,
                0.9999997897566589
            ],
            [
                0.9999996072139402,
                0.9999997617631183,
                0.9999995549148419,
                0.999999168471576,
                0.999999730042126,
                0.9999996940976272,
                0.9999996533672135,
                0.9999994956525317,
                0.9999995549149481,
                0.9999996072137529
            ],
            [
                0.9999996940977731,
                0.9999994956525918,
                0.999999352405279,
                0.999999814460876,
                0.99999976176309,
                0.9999996072138465,
                0.9999998362622943,
                0.999999789756634,
                0.9999998362623332,
                0.9999997300421581
            ],
            [
                0.9999995549149481,
                0.9999993524050474,
                0.9999995549147889,
                0.999999352405279,
                0.9999996533675028,
                0.9999996533672549,
                0.999999730042126,
                0.9999993524053562,
                0.9999996072138934,
                0.9999996533672549
            ],
            [
                0.9999996072138934,
                0.9999991684718733,
                0.9999991684715758,
                0.9999997300420937,
                0.9999994956525917,
                0.9999996072136592,
                0.9999993524052019,
                0.9999994956527721,
                0.9999994284995529,
                0.9999993524051246
            ],
            [
                0.9999996072138934,
                0.9999997897566338,
                0.9999996072137529,
                0.9999998362623332,
                0.9999994284997574,
                0.9999996533673375,
                0.9999995549147889,
                0.9999996940977731,
                0.9999994284996212,
                0.9999998724809723
            ],
            [
                0.9999994956527121,
                0.999999730042126,
                0.9999997300422225,
                0.999999266178757,
                0.999999694097846,
                0.9999992661788446,
                0.9999996072139402,
                0.9999998362623332,
                0.9999989322973846,
                0.999999554914842
            ],
            [
                0.9999998362623137,
                0.9999997300422869,
                0.9999996940978095,
                0.9999997897565587,
                0.9999995549149481,
                0.9999996072136125,
                0.9999996940977002,
                0.9999998874647842,
                0.999999730042126,
                0.999999694097773
            ],
            [
                0.9999996533675028,
                0.9999997300421903,
                0.999999554914895,
                0.9999997300422869,
                0.9999997617630332,
                0.9999996940978825,
                0.9999997617630049,
                0.9999997897566589,
                0.9999994284997574,
                0.999999730042126
            ],
            [
                0.9999998362622943,
                0.9999998555019618,
                0.9999998362623528,
                0.99999976176309,
                0.9999997617629763,
                0.9999997300422225,
                0.9999997617631752,
                0.9999997617630616,
                0.9999998144608097,
                0.9999997617630049
            ],
            [
                0.9999996072136592,
                0.9999996533673375,
                0.9999997617631468,
                0.9999994284997574,
                0.9999998144608981,
                0.9999997300421903,
                0.9999998555020135,
                0.999999653367379,
                0.999999789756684,
                0.999999814460876
            ],
            [
                0.9999997300422547,
                0.99999844650169,
                0.9999994284996893,
                0.9999995549147889,
                0.9999991684722698,
                0.9999990577555185,
                0.9999995549150541,
                0.9999996533672136,
                0.9999994956527121,
                0.9999996072137998
            ],
            [
                0.9999997300421903,
                0.9999996940976636,
                0.9999998362622357,
                0.9999996940976272,
                0.9999998144609424,
                0.999999814460854,
                0.9999998144608319,
                0.9999997897567342,
                0.999999814460876,
                0.9999996940977366
            ],
            [
                0.9999998144609645,
                0.9999994956526519,
                0.999999814460876,
                0.9999997617631753,
                0.9999997617631469,
                0.9999996072137529,
                0.9999996072137061,
                0.9999996940978825,
                0.9999996940977731,
                0.999999428499553
            ],
            [
                0.9999996940977366,
                0.9999996533672136,
                0.999999730042126,
                0.9999994956527722,
                0.9999987901344608,
                0.9999996533674202,
                0.9999991684718732,
                0.9999991684722698,
                0.9999990577552939,
                0.9999995549150542
            ],
            [
                0.9999998724809115,
                0.9999994284997574,
                0.999999730042319,
                0.9999997300422547,
                0.9999997617630332,
                0.9999997300422869,
                0.9999998144608981,
                0.9999995549149481,
                0.9999997300420937,
                0.9999998362623332
            ],
            [
                0.9999990577557432,
                0.9999994284992805,
                0.9999996072137529,
                0.9999998724809875,
                0.9999996940976636,
                0.9999989322967482,
                0.9999992661786696,
                0.9999993524049703,
                0.9999992661792819,
                0.9999993524052019
            ],
            [
                0.9999997617631752,
                0.9999994956524716,
                0.9999997617629764,
                0.9999991684715759,
                0.9999996940976271,
                0.999999789756634,
                0.999999554914895,
                0.9999996533674201,
                0.9999997617631752,
                0.9999994284993486
            ],
            [
                0.9999993524053563,
                0.9999997300421903,
                0.9999998555020134,
                0.9999997617630616,
                0.9999996533674615,
                0.9999997897566089,
                0.9999997300422869,
                0.9999997897566589,
                0.999999653367379,
                0.9999996072136125
            ],
            [
                0.9999996940978825,
                0.9999998874648245,
                0.9999994284994167,
                0.9999996072138465,
                0.9999996533672135,
                0.9999994956527721,
                0.9999995549147359,
                0.9999995549151073,
                0.9999994956524114,
                0.9999996940976271
            ],
            [
                0.9999997897567091,
                0.9999998555019791,
                0.9999997617629764,
                0.999999789756634,
                0.9999997617630049,
                0.9999998874647842,
                0.999999653367379,
                0.999999814460854,
                0.9999997300422869,
                0.9999998874648514
            ],
            [
                0.9999994956526519,
                0.9999994284996893,
                0.9999990577549569,
                0.9999993524052018,
                0.9999994284994849,
                0.999999168471675,
                0.9999994284996891,
                0.9999990577556308,
                0.9999995549150542,
                0.999999352405279
            ],
            [
                0.9999996940978095,
                0.9999997897566089,
                0.9999996940978095,
                0.9999997617631752,
                0.9999996072139402,
                0.9999993524052019,
                0.9999993524051247,
                0.9999997617630049,
                0.9999997617630616,
                0.9999997300422869
            ],
            [
                0.999999730042126,
                0.9999998144609202,
                0.9999996533675028,
                0.9999997897565838,
                0.9999994956524716,
                0.999999789756634,
                0.9999997300422547,
                0.9999996533672136,
                0.9999994956527121,
                0.9999996940977366
            ],
            [
                0.9999996533673375,
                0.999999855502048,
                0.9999992661790196,
                0.9999996533673375,
                0.9999996533672549,
                0.9999990577555186,
                0.9999996533672136,
                0.9999997897565587,
                0.9999995549150542,
                0.9999991684722698
            ],
            [
                0.9999996072137998,
                0.9999996940976636,
                0.9999998362623137,
                0.999999789756634,
                0.999999789756684,
                0.9999998362622357,
                0.9999995549149482,
                0.9999997617631752,
                0.999999554914895,
                0.9999996940977002
            ],
            [
                0.9999995549149481,
                0.9999989322967482,
                0.9999990577555186,
                0.9999997897567341,
                0.9999996940976271,
                0.9999996533672962,
                0.9999996533672962,
                0.9999996940977001,
                0.9999991684720715,
                0.9999995549147889
            ],
            [
                0.999999653367379,
                0.9999997617629763,
                0.9999997300421581,
                0.999999266178757,
                0.9999997300422225,
                0.9999997897566589,
                0.9999998144609424,
                0.9999998144608981,
                0.9999996940977002,
                0.999999694097846
            ],
            [
                0.9999994956523514,
                0.999999428499553,
                0.9999994284994168,
                0.9999998555020306,
                0.9999996940977002,
                0.9999997300422869,
                0.9999997300422225,
                0.9999998144608981,
                0.9999998362622357,
                0.9999996940977001
            ],
            [
                0.9999997897567091,
                0.9999996072139402,
                0.9999997300423191,
                0.9999996533674201,
                0.9999997300422547,
                0.9999999006881377,
                0.999999789756684,
                0.9999996940976272,
                0.9999996940976636,
                0.9999998144609202
            ],
            [
                0.9999995549148419,
                0.9999997617631184,
                0.9999998144608981,
                0.9999997300422225,
                0.9999996072136125,
                0.9999996533672548,
                0.9999996533673375,
                0.9999997897566589,
                0.9999995549149481,
                0.9999995549150542
            ],
            [
                0.9999992661788446,
                0.999999168471576,
                0.9999991684715759,
                0.9999990577557432,
                0.9999993524054335,
                0.999999266179282,
                0.9999994956524716,
                0.9999994956524716,
                0.999999789756634,
                0.9999995549148419
            ],
            [
                0.9999996940977366,
                0.9999997897565587,
                0.9999994284994167,
                0.9999998362622357,
                0.9999997617631184,
                0.9999997897566089,
                0.9999996940978095,
                0.999999495652652,
                0.9999996072137998,
                0.9999996940977731
            ],
            [
                0.9999993524051247,
                0.9999994956523512,
                0.9999994956527722,
                0.9999997617630616,
                0.9999996072138934,
                0.999999730042319,
                0.9999992661789321,
                0.9999996940976636,
                0.9999994956526519,
                0.999999352405279
            ],
            [
                0.9999997300422225,
                0.9999995549149481,
                0.9999996533672135,
                0.9999995549148419,
                0.9999994284995529,
                0.9999994284995529,
                0.9999997300422547,
                0.9999997300423191,
                0.9999997300422869,
                0.9999996072136125
            ],
            [
                0.999999814460854,
                0.9999996533674614,
                0.999999694097846,
                0.9999997617631184,
                0.999999554914895,
                0.99999976176309,
                0.9999996072138934,
                0.9999995549151073,
                0.9999998144608538,
                0.9999996940977366
            ],
            [
                0.9999996533675028,
                0.9999998144609202,
                0.9999998144608317,
                0.9999996940978095,
                0.9999997617631469,
                0.9999997300421581,
                0.9999998874648245,
                0.9999997897567342,
                0.999999789756684,
                0.999999554914895
            ],
            [
                0.9999998144608538,
                0.9999997897565838,
                0.9999996533672135,
                0.9999993524051246,
                0.9999997300422869,
                0.9999996072138465,
                0.9999996940978095,
                0.9999995549147358,
                0.9999996533672548,
                0.9999992661791944
            ],
            [
                0.9999998144609423,
                0.9999997897567091,
                0.999999730042126,
                0.9999998144609644,
                0.9999994956525918,
                0.9999997617630899,
                0.9999996940978095,
                0.999999814460854,
                0.9999996940977366,
                0.9999996940977366
            ],
            [
                0.9999992661786696,
                0.9999994956526519,
                0.9999990577550691,
                0.9999994284997573,
                0.9999996533672136,
                0.9999992661790196,
                0.9999990577557432,
                0.9999993524053562,
                0.9999994284993485,
                0.9999991684715759
            ],
            [
                0.9999997897565587,
                0.9999996940977002,
                0.9999999123575359,
                0.9999996533672136,
                0.9999997897566589,
                0.9999996940976272,
                0.9999995549151073,
                0.99999976176309,
                0.9999997300422869,
                0.9999997300421903
            ],
            [
                0.9999996533672135,
                0.9999994284994848,
                0.9999995549150011,
                0.9999997300422869,
                0.9999997300420937,
                0.999999428499553,
                0.999999789756684,
                0.9999996940978825,
                0.9999996072136592,
                0.9999995549150542
            ],
            [
                0.9999997300422869,
                0.9999995549149481,
                0.9999997897566589,
                0.999999554914895,
                0.9999996072137061,
                0.9999995549150011,
                0.999999730042126,
                0.999999789756684,
                0.9999994956527121,
                0.9999998555019962
            ],
            [
                0.9999996533672548,
                0.999999789756684,
                0.9999996072137529,
                0.9999996072139402,
                0.9999997300421903,
                0.9999996533674615,
                0.9999996940977731,
                0.9999994956527121,
                0.9999996533672549,
                0.9999997617631468
            ],
            [
                0.9999996940976271,
                0.9999996940977366,
                0.9999994284994849,
                0.9999996533672962,
                0.9999996940976636,
                0.9999994284996211,
                0.999999730042126,
                0.999999428499553,
                0.999999653367503,
                0.9999997617630616
            ],
            [
                0.9999997300422225,
                0.999999554914895,
                0.9999997617631183,
                0.9999997897565587,
                0.9999996533674614,
                0.999999653367379,
                0.9999990577551815,
                0.9999996072138934,
                0.9999995549150011,
                0.9999996533672962
            ],
            [
                0.9999996072137061,
                0.9999996072138465,
                0.999999554914895,
                0.9999994284996893,
                0.9999998144608317,
                0.9999996940977731,
                0.9999996072138934,
                0.999999352405279,
                0.9999996072139402,
                0.9999994284997574
            ]
        ]
    },
    {
        "q_id": "7844_mmlu_math",
        "cot_ids": [
            0,
            3,
            5,
            6,
            9,
            10,
            11,
            13,
            14,
            15,
            16,
            19,
            20,
            21,
            23,
            25,
            27,
            30,
            32,
            33,
            34,
            35,
            36,
            39,
            41,
            43,
            44,
            46,
            47,
            49,
            52,
            53,
            54,
            56,
            57,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            69,
            72,
            73,
            75,
            78,
            79,
            81,
            83,
            84,
            85,
            86,
            88,
            90,
            91,
            93,
            95,
            96,
            97,
            98,
            99,
            101,
            102,
            104,
            105,
            108,
            112,
            113,
            114,
            116,
            117,
            119,
            121,
            122,
            123,
            124,
            125,
            126
        ],
        "rewards": [
            [
                0.9999852610145789,
                0.9999921107402375,
                0.9999810748431075,
                0.999997438718095,
                0.9999852610180324,
                0.9999898700102287,
                0.9999832985722346,
                0.9999724643056793,
                0.9999974387171787,
                0.9999980052695652
            ],
            [
                1.0129988562661878e-05,
                3.2887506333812835e-06,
                9.422443691524936e-07,
                3.12019150894581e-05,
                7.889263524788109e-06,
                5.422217029844958e-06,
                3.2887490652451393e-06,
                2.902313022952668e-06,
                1.3709578604981489e-06,
                1.892514372479069e-05
            ],
            [
                0.9999869928701522,
                0.9999952149037951,
                0.9999724643024054,
                0.9998415637664116,
                0.9999984465018751,
                0.9999832985724662,
                0.24508500761839527,
                0.32082131381216084,
                0.9999785550542488,
                0.9999339478807592
            ],
            [
                0.9999980052695655,
                0.999820471948994,
                0.9999945777829847,
                0.9999869928768673,
                0.999997097688707,
                0.9999646437414669,
                0.9999938558276671,
                0.9999546021215405,
                0.999991060299476,
                0.9999810748450194
            ],
            [
                7.338208055489796e-07,
                6.475948753847607e-07,
                4.45084945805234e-07,
                7.338213303355652e-07,
                1.370957533676711e-06,
                1.7603436328994344e-06,
                9.422442568763144e-07,
                6.475950297821511e-07,
                2.9023119851055122e-06,
                3.7266392839425286e-06
            ],
            [
                1.5534971986912662e-06,
                1.5534973840786793e-06,
                4.222834451254188e-06,
                1.3709568799679844e-06,
                5.8291244607543396e-05,
                1.994729008105057e-06,
                6.605212008462348e-05,
                6.144173869312763e-06,
                3.120192246511896e-05,
                4.785093353739995e-06
            ],
            [
                0.9999852610234234,
                0.999995214906648,
                0.999983298574187,
                0.9999687980816807,
                0.9999910603058306,
                0.9999952149043645,
                0.9999945777790951,
                0.9999957771650457,
                0.9999957771670601,
                0.9999990577552939
            ],
            [
                2.2603245668530326e-06,
                1.0129988562164371e-05,
                6.962253759752719e-06,
                2.5612825159677387e-06,
                1.2098661161861e-06,
                1.994730434816876e-06,
                4.785092783371756e-06,
                0.0007096704608951621,
                2.902311984915459e-06,
                3.288749457383046e-06
            ],
            [
                1.994729245878497e-06,
                0.0013250225147258795,
                7.88926164299515e-06,
                2.5612815993296616e-06,
                1.0129992186202796e-05,
                1.0677027426088186e-06,
                6.144175333021237e-06,
                1.370956716450141e-06,
                4.78509563509613e-06,
                7.889262582800945e-06
            ],
            [
                1.553498495295912e-06,
                1.0677033790320615e-06,
                1.994729959270648e-06,
                9.422448184912962e-07,
                2.9023119850210436e-06,
                5.71500583272315e-07,
                1.067702615348298e-06,
                1.2098658276730537e-06,
                2.902311292783513e-06,
                1.0677028700130727e-06
            ],
            [
                5.715004470170917e-07,
                2.144494327998681e-05,
                2.1444943298944354e-05,
                3.288750241374845e-06,
                2.4300237828943813e-05,
                2.430024941804299e-05,
                6.144176797998549e-06,
                4.222832437324657e-06,
                5.422218969029887e-06,
                2.1444945841205498e-05
            ],
            [
                0.9999945777823244,
                0.9999970976890529,
                0.9999982396567874,
                0.9999989322967482,
                0.9999930377454121,
                0.9999977396751634,
                0.9999991684719725,
                0.9999993524054335,
                0.9999952149072182,
                0.9999885212305126
            ],
            [
                5.715005832762133e-07,
                3.2887502415243994e-06,
                5.043472879481655e-07,
                5.043474081902134e-07,
                4.785093353787868e-06,
                1.370957533676711e-06,
                1.5534975693347152e-06,
                6.475945665671197e-07,
                1.7603427935967163e-06,
                3.05902117518448e-07
            ],
            [
                2.9023130229209922e-06,
                2.1024326583176705e-07,
                4.222832437497486e-06,
                1.5534975693707442e-06,
                3.4663274507098256e-07,
                1.0677032518501217e-06,
                1.5534973841450852e-06,
                4.222834451292594e-06,
                1.7603438428564603e-06,
                1.2098656834922064e-06
            ],
            [
                1.0677024881140118e-06,
                0.00023050665325897188,
                6.962257075969737e-06,
                4.785095065045315e-06,
                2.9023130227599746e-06,
                3.927862002213179e-07,
                2.260325375650449e-06,
                2.5612822106654943e-06,
                1.5534973839896667e-06,
                2.7535681236473055e-05
            ],
            [
                8.315283250006957e-07,
                3.2887506334560605e-06,
                2.902313022984344e-06,
                8.315282258900085e-07,
                5.422217676397663e-06,
                2.5612825160096693e-06,
                8.315279285205827e-07,
                4.222832941072913e-06,
                7.338213304196583e-07,
                6.144172404520556e-06
            ],
            [
                6.475950297868629e-07,
                7.889262584666493e-06,
                5.715006514040971e-07,
                2.2603234895176927e-06,
                7.338211554641698e-07,
                3.726640172337686e-06,
                1.370957533625589e-06,
                7.338212429420757e-07,
                8.315282258900085e-07,
                7.338208930355202e-07
            ],
            [
                0.9579122708828602,
                0.9999945777829717,
                0.9999921107383711,
                0.9999546021459126,
                0.9999852610221538,
                0.9796676450248561,
                0.9999151889792813,
                0.9999810748519968,
                0.9999417087068805,
                0.9999810748427528
            ],
            [
                5.043475885606781e-07,
                5.715004470077356e-07,
                9.422443692489024e-07,
                1.2098659719122375e-06,
                9.422443692330485e-07,
                1.3709572067955008e-06,
                8.315277302747361e-07,
                4.785095064819011e-06,
                1.2098662603499435e-06,
                1.0677024881382882e-06
            ],
            [
                5.043476486764593e-07,
                7.338209804987119e-07,
                1.5534977545243671e-06,
                6.962254589528684e-06,
                9.610244823181772e-05,
                2.7535681242383173e-05,
                3.7266388395620047e-06,
                7.33820718019402e-07,
                3.7266388396128453e-06,
                3.7266392836374875e-06
            ],
            [
                0.9998204720360025,
                0.24508501313237172,
                0.9149009555730612,
                0.9999251537380899,
                0.8670357666736772,
                0.999968798077518,
                0.9999869928732015,
                0.6224593241981982,
                0.9999339478396271,
                0.9999687980737616
            ],
            [
                3.927861065988446e-07,
                1.2098661159797817e-06,
                7.889260704308795e-06,
                1.3709570433661467e-06,
                3.7266383954560706e-06,
                2.5612825156159896e-06,
                1.5534973841154145e-06,
                1.5534983101061718e-06,
                4.222835458044565e-06,
                4.222833444467892e-06
            ],
            [
                1.0677028699858827e-06,
                6.475947208372161e-07,
                8.48110306528434e-05,
                1.4738988997768797e-05,
                7.338208055613267e-07,
                6.475950297644816e-07,
                7.33820893021171e-07,
                1.5534973841309562e-06,
                4.785094494402695e-06,
                1.2098659719441482e-06
            ],
            [
                0.9999989322972572,
                0.9999987901337396,
                0.999998239656577,
                0.9999952149060757,
                0.9999986290427931,
                0.9999987901344608,
                0.9999989322970027,
                0.9999986290424663,
                0.9999989322972573,
                0.9999930377462418
            ],
            [
                0.9992903296615382,
                0.06754668879328725,
                0.9984988174267231,
                0.9986749773942314,
                0.9998766054550079,
                0.9997694932033637,
                0.9999251537906645,
                0.08509903862612586,
                0.2689414213699951,
                0.9999687980929743
            ],
            [
                1.994729245878497e-06,
                6.144176798870286e-06,
                1.1478768124992398e-05,
                1.3709578604831862e-06,
                1.9947306725451314e-06,
                1.0677033791437343e-06,
                5.82912931135658e-05,
                3.7266401716055872e-06,
                1.0129994599624903e-05,
                4.222833444168322e-06
            ],
            [
                1.2098655391947376e-06,
                1.3709570433661467e-06,
                1.5534983099309726e-06,
                4.450852641656969e-07,
                9.422444815563743e-07,
                7.33820805514942e-07,
                8.31527928417352e-07,
                1.0677029972745947e-06,
                1.2098652507957165e-06,
                6.475945665853783e-07
            ],
            [
                4.539787932217606e-05,
                5.422217676299034e-06,
                1.7603438427243761e-06,
                1.012998977198894e-05,
                1.5534975693347152e-06,
                1.760344052632596e-06,
                1.553498495230919e-06,
                1.0677033791107183e-06,
                2.5612831266165976e-06,
                1.2098653950315304e-06
            ],
            [
                2.5612834317116285e-06,
                1.1478769492893215e-05,
                1.370956716529941e-06,
                2.699578096373564e-07,
                3.7266392839425286e-06,
                9.422447062094932e-07,
                3.7266379512518984e-06,
                8.315278294001114e-07,
                3.927863875520681e-07,
                0.0005527787137816198
            ],
            [
                1.209865971934245e-06,
                1.370956716519966e-06,
                5.715006513952608e-07,
                1.9947304348332037e-06,
                8.315280276263186e-07,
                1.7603434231097403e-06,
                1.5534981249164537e-06,
                3.2887506333812835e-06,
                2.2603253755476615e-06,
                4.785094494402695e-06
            ],
            [
                0.9999984465024306,
                0.9999989322975118,
                0.9999945777803845,
                0.9999997617631184,
                0.9999970976876693,
                0.9999957771665557,
                0.9999646437408746,
                0.9999724642990675,
                0.9999910603026312,
                0.9999724643154776
            ],
            [
                2.2603242977802297e-06,
                1.147876675686207e-05,
                2.7535700943413033e-05,
                3.726638839806038e-06,
                6.962253759157502e-06,
                5.829128623423597e-05,
                7.889261644760245e-06,
                9.422447062030659e-07,
                1.3709570433786157e-06,
                1.147877359872636e-05
            ],
            [
                2.260325375677174e-06,
                5.715007195410849e-07,
                6.475948753794598e-07,
                1.9947290081177566e-06,
                2.5612816000331606e-06,
                1.9947299592824403e-06,
                5.422221554670048e-06,
                9.422443692390473e-07,
                5.04347528440776e-07,
                6.47594875389178e-07
            ],
            [
                0.9999339478400318,
                0.999925153764135,
                0.9997388097540433,
                0.9465966724600001,
                0.11920290950590741,
                0.999915188929481,
                0.9999417087459813,
                0.9997388096686233,
                0.9999251537925763,
                0.3775406687981454
            ],
            [
                0.9998415637374862,
                0.5,
                0.9999785550592586,
                0.9999546021325673,
                0.7981867801399695,
                0.9999921107402608,
                0.9999810748450708,
                0.5621765008857981,
                0.9999810748562864,
                0.9996646500020686
            ],
            [
                0.9999756997504039,
                0.9999962733593833,
                0.9999921107393861,
                0.9999921107402546,
                0.999954602145614,
                0.9999869928749889,
                0.9999910603058704,
                0.9999724643121954,
                0.9999921107404733,
                0.9999852610180429
            ],
            [
                4.450852641656969e-07,
                1.0677028698868336e-06,
                7.8892607025437e-06,
                1.2098655392662613e-06,
                2.9023126769050284e-06,
                5.4222202617511845e-06,
                6.475948753276293e-07,
                1.9947301970106386e-06,
                4.785094493932679e-06,
                1.2098653950403334e-06
            ],
            [
                5.043475885453117e-07,
                8.315277302747361e-07,
                5.715005832827105e-07,
                1.9947292458930106e-06,
                1.9947306725868575e-06,
                2.699577774560111e-07,
                1.0677031245783732e-06,
                3.4663257978039603e-07,
                3.9278638755671223e-07,
                3.466325384589045e-07
            ],
            [
                7.338209804987119e-07,
                1.9947294835866542e-06,
                1.5534979395006942e-06,
                2.2603240283888175e-06,
                1.147876538789672e-05,
                1.3709575336947905e-06,
                1.994729483666479e-06,
                1.3709578605542582e-06,
                1.5534983100920427e-06,
                2.2603240281606297e-06
            ],
            [
                2.9023123311055552e-06,
                1.9947297213746646e-06,
                4.785096205882502e-06,
                2.9023133684090715e-06,
                1.370957370236096e-06,
                3.2887486729876365e-06,
                1.7603425836870455e-06,
                7.338208055302923e-07,
                6.9622570786798724e-06,
                5.8291251608160896e-05
            ],
            [
                1.553498495281783e-06,
                5.043473480730849e-07,
                1.0677033791000363e-06,
                9.422442568163268e-07,
                1.0677031245783732e-06,
                5.829126548725762e-05,
                9.422447062030659e-07,
                1.994730434798734e-06,
                8.315282259009745e-07,
                7.338207180714596e-07
            ],
            [
                0.7981867873410141,
                0.16451646289656316,
                0.7549149813536518,
                0.5621765008857981,
                0.9999251537479155,
                0.16451646699291617,
                0.10669058897496682,
                NaN,
                0.9999151889792924,
                0.9998415638059179
            ],
            [
                1.3007134661628471e-05,
                1.4738987238893715e-05,
                1.2098652505118222e-06,
                2.2603251061232293e-06,
                1.9947299592407137e-06,
                7.338210679949506e-07,
                1.3709576970949014e-06,
                2.260324567054496e-06,
                5.043475885606781e-07,
                6.144174601499446e-06
            ],
            [
                3.2887478891487563e-06,
                1.0677028699858827e-06,
                9.422443692261927e-07,
                3.9278634073098236e-07,
                5.422218322940583e-06,
                2.2603248367173307e-06,
                1.5534973840150989e-06,
                4.7850939232204965e-06,
                6.962254588724508e-06,
                2.5612819052072116e-06
            ],
            [
                0.9999339478713373,
                0.9999852610163005,
                0.9999485577926672,
                0.9997965729459292,
                0.9999885212346237,
                0.9999980052700417,
                0.9999546021314772,
                0.9999417087139304,
                0.999995777168082,
                0.9999898700120775
            ],
            [
                0.9999930377413287,
                0.99998852123325,
                0.9999898700066883,
                0.9999910603015686,
                0.9999962733589431,
                0.999997097689075,
                0.9149009532527357,
                0.9999938558239384,
                0.99999893229713,
                0.9999038976172161
            ],
            [
                0.9995121428075087,
                0.9999921107346138,
                0.4378234991142019,
                0.9579122728353318,
                0.9999967112493742,
                0.9999980052702805,
                0.9579122680292479,
                0.9999832985781923,
                0.9999910603026994,
                0.9999869928700279
            ],
            [
                4.222833947728508e-06,
                0.00010889692132869394,
                6.144177531660828e-06,
                7.889264465067689e-06,
                1.8925148239290237e-05,
                8.93969630333567e-06,
                1.300712380997554e-05,
                7.338208055536515e-07,
                2.7535691093547457e-05,
                3.7266401725935817e-06
            ],
            [
                0.9997388097245566,
                0.3208213073183839,
                0.3208213138121609,
                0.01798620667215645,
                0.9998601778585359,
                0.9995694428883136,
                0.10669058755477132,
                0.3486451488696663,
                0.3208212878370535,
                0.22270014398423357
            ],
            [
                1.553497384180408e-06,
                7.338212429504183e-07,
                3.7266388395111645e-06,
                1.275190276853036e-07,
                7.338212429367364e-07,
                2.2603234894560207e-06,
                1.7603427935967163e-06,
                1.6373774480479287e-07,
                2.1024331596961412e-07,
                2.9023112931213857e-06
            ],
            [
                2.4300249418927004e-05,
                4.7850950649408664e-06,
                1.994729008056074e-06,
                1.2098662603862553e-06,
                5.422218969532895e-06,
                1.5534981249397663e-06,
                7.889260703619978e-06,
                1.5534979396448094e-06,
                2.4300232040584407e-05,
                2.5612834319655406e-06
            ],
            [
                1.012999580884213e-05,
                0.0028009267915359215,
                1.0677032518501217e-06,
                2.5612828211442287e-06,
                1.2098652507285942e-06,
                6.144175333837093e-06,
                3.726637950973972e-06,
                6.1441724029223715e-06,
                1.209866116170145e-06,
                8.939696302652706e-06
            ],
            [
                8.315284241401329e-07,
                4.785096205930373e-06,
                1.7603432132784448e-06,
                1.9947301968963442e-06,
                1.5534981249023245e-06,
                6.475949525919915e-07,
                5.422218321993744e-06,
                1.0129988563546333e-05,
                9.42244818532859e-07,
                1.7603425836870455e-06
            ],
            [
                6.962256247998122e-06,
                9.422448185264317e-07,
                9.422442569208767e-07,
                1.3709578605542582e-06,
                1.209865394997419e-06,
                4.785095064523075e-06,
                4.222834451215781e-06,
                9.422442569097361e-07,
                7.338211554464836e-07,
                2.260324567227179e-06
            ],
            [
                0.999995777165554,
                0.9046505254608135,
                0.9999724643030254,
                0.9999869928669538,
                0.966914022326357,
                0.9999785550519201,
                NaN,
                0.9999885212318844,
                0.9999910603050126,
                0.9999646437324707
            ],
            [
                0.9999599363046029,
                0.8933094096048376,
                0.9999952149038148,
                0.9999898700066662,
                0.9999967112498044,
                0.9399133502467731,
                0.9999832985782802,
                0.9999417087414243,
                0.9999852610110869,
                0.9999852610137497
            ],
            [
                0.9999962733602735,
                0.9999993524051246,
                0.9999977396759718,
                0.9999994284994851,
                0.9999987901341723,
                0.9999977396759717,
                0.9999986290421395,
                0.9999970976880158,
                0.9999980052698058,
                0.9999980052693275
            ],
            [
                3.2887486732358968e-06,
                2.561281599914358e-06,
                2.1024341621637506e-07,
                8.315278293762888e-07,
                3.288748280891699e-06,
                5.715007195384861e-07,
                2.260325106045111e-06,
                1.55349775456958e-06,
                1.9947294831748327e-06,
                2.561283431916622e-06
            ],
            [
                1.5534977545603963e-06,
                6.475948753741589e-07,
                8.315279285088606e-07,
                4.4508526415598164e-07,
                7.889263525663481e-06,
                1.994729721482609e-06,
                4.2228324375512536e-06,
                2.260324567268294e-06,
                2.260325106045111e-06,
                4.222834954607099e-06
            ],
            [
                0.9999974387177922,
                0.9999962733616048,
                0.9999930377437504,
                0.9996646497750594,
                0.9999687980849485,
                0.9999646437578442,
                0.9999938558275995,
                0.9999869928746704,
                0.99998699286544,
                0.9999852610233118
            ],
            [
                5.715003788749385e-07,
                3.7266383953679482e-06,
                1.7603432132079998e-06,
                5.422217030032353e-06,
                1.2098652508144226e-06,
                1.6701415867707307e-05,
                6.962255418924822e-06,
                8.9396941718352e-06,
                1.6701419850389357e-05,
                2.5612822103812995e-06
            ],
            [
                3.4663278639265633e-07,
                2.5612812946681295e-06,
                4.785096776251149e-06,
                5.715006513999389e-07,
                1.553497198908852e-06,
                1.7603438428028262e-06,
                1.2098658277181688e-06,
                3.288747889229516e-06,
                2.2603253754921562e-06,
                5.422219616085833e-06
            ],
            [
                0.9999646437326991,
                0.9999869928668931,
                0.9999984465026202,
                0.9999038975741235,
                0.3775406687981454,
                0.9999785550413773,
                0.9999417087390413,
                0.9999756997593423,
                0.9999962733598302,
                0.7772998611746912
            ],
            [
                9.422445938728576e-07,
                3.726638395493353e-06,
                1.2098656835076114e-06,
                7.889263525534328e-06,
                2.90231094702116e-06,
                2.5612819052374947e-06,
                7.33820718037422e-07,
                6.962257079465052e-06,
                1.7603436330091044e-06,
                1.9947294836483373e-06
            ],
            [
                0.9999967112505427,
                0.999996273360716,
                0.9999810748450262,
                0.9999994956524716,
                0.9999921107383551,
                0.9999980052700408,
                0.9999910603068948,
                0.9999945777784451,
                0.9999869928730875,
                0.9999869928668857
            ],
            [
                7.889265406681968e-06,
                7.8892625849535e-06,
                2.9023123310580418e-06,
                NaN,
                6.96225541916544e-06,
                6.962259568889411e-06,
                2.902312677007974e-06,
                7.889266347004826e-06,
                4.2228324375512536e-06,
                7.889261644631091e-06
            ],
            [
                3.2887482811579057e-06,
                2.5612822106421996e-06,
                1.2098652507957165e-06,
                1.0677026154551157e-06,
                1.1478769492392108e-05,
                2.561283126639892e-06,
                7.88926634687567e-06,
                1.9947306723419413e-06,
                3.2887502411026557e-06,
                1.2098653950315304e-06
            ],
            [
                0.9999910603047691,
                0.9999417087345043,
                0.9999910603036972,
                0.9999687980849181,
                0.9999869928731319,
                0.9999945777810322,
                0.9999952149037957,
                0.9999810748495105,
                0.9999930377462413,
                0.9999987901343166
            ],
            [
                1.553498310118888e-06,
                3.9278629390507954e-07,
                6.144173869446876e-06,
                2.9023130228840374e-06,
                2.90231163910023e-06,
                8.315279285088606e-07,
                5.422218969463855e-06,
                5.829125857951634e-05,
                1.0129992187400498e-05,
                1.7603425837366772e-06
            ],
            [
                1.2098653948576728e-06,
                8.315281266371544e-07,
                1.9947294834796172e-06,
                1.9947290078746543e-06,
                5.422217676797111e-06,
                3.2887490649221017e-06,
                1.5534975693347152e-06,
                2.260323489410794e-06,
                1.7603427935678977e-06,
                1.5534979396984994e-06
            ],
            [
                0.9999810748452506,
                NaN,
                0.9999930377445806,
                0.9999810748541316,
                0.9999869928765219,
                0.9999599363182504,
                0.9999810748456244,
                0.7310585727705126,
                0.999981074847388,
                0.9999945777797455
            ],
            [
                6.9622545892184106e-06,
                3.2887502409830123e-06,
                2.260324028351814e-06,
                4.0063687374440786e-05,
                2.2603248366762157e-06,
                7.889262585211807e-06,
                1.4738985483504099e-05,
                5.422218322851817e-06,
                2.902312676941983e-06,
                2.260324028004393e-06
            ],
            [
                1.2098662603752517e-06,
                5.4222183231674305e-06,
                6.475948753847607e-07,
                2.561283431942246e-06,
                2.9023116389365734e-06,
                1.7603434231241496e-06,
                7.338208930265102e-07,
                7.338208053968112e-07,
                7.889265403883644e-06,
                4.2228319341064674e-06
            ],
            [
                8.315283250150648e-07,
                2.260324028331257e-06,
                9.422448185187191e-07,
                1.9947294835866542e-06,
                4.222831933726245e-06,
                6.962257079465052e-06,
                6.9622545892184106e-06,
                3.726639283806955e-06,
                1.994729721469003e-06,
                6.962257909323729e-06
            ],
            [
                0.999998239656367,
                0.9999991684719723,
                0.9999832985781694,
                0.9999921107383558,
                0.9999785550567928,
                0.9999810748427401,
                0.9999967112493665,
                0.9999921107345939,
                0.9999885212305117,
                0.9999994284996893
            ],
            [
                6.962254589332388e-06,
                1.2098662604126641e-06,
                1.2098655392464547e-06,
                1.994729959160889e-06,
                2.9023116385379885e-06,
                6.962256249327861e-06,
                8.939697368663308e-06,
                8.939697368842181e-06,
                7.88925976359915e-06,
                4.785093353787868e-06
            ],
            [
                0.9998601778630889,
                0.9999885212264727,
                0.999925153737218,
                0.9999724643134172,
                0.651354857898194,
                0.9999832985742085,
                0.9999810748543746,
                0.9999756997680187,
                0.999995777166055,
                0.9999970976887077
            ],
            [
                NaN,
                NaN,
                0.966914022326357,
                0.9999339478728415,
                0.9999687981007732,
                NaN,
                0.9998415638532295,
                0.9999724642964386,
                0.6791787056691697,
                0.9999546021100192
            ],
            [
                6.475947209826952e-07,
                1.209865250822125e-06,
                8.315279284657531e-07,
                3.0590237278532086e-07,
                6.47594643788744e-07,
                3.059021175247079e-07,
                7.338212429464139e-07,
                2.9023109471188266e-06,
                4.78509563546605e-06,
                3.927862002641863e-07
            ],
            [
                0.9999957771680674,
                0.9999724642958451,
                0.9999898700066181,
                0.4378234991142019,
                0.9999599362887743,
                0.46879062662624377,
                0.9706877665987492,
                NaN,
                0.43782349911420193,
                0.9998415637923634
            ]
        ]
    },
    {
        "q_id": "8274_mmlu_math",
        "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,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            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,
            92,
            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": [
            [
                0.9999980052693274,
                0.9999984465020603,
                0.9999989322966208,
                0.9999977396748938,
                0.9999970976873231,
                0.9999984465015047,
                0.999998629042303,
                0.9999974387171787,
                0.9999989322968754,
                0.9999945777784449
            ],
            [
                0.9999977396748938,
                0.9999977396762411,
                0.9999967112497584,
                0.9999921107364745,
                0.9999952149055052,
                0.9999967112513267,
                0.9999898700102279,
                0.9999991684718732,
                0.999999554914842,
                0.9999974387168732
            ],
            [
                0.9999986290427931,
                0.9999982396572065,
                0.9999984465016899,
                0.9999967112517187,
                0.9999910602994343,
                0.9999991684717742,
                0.999999057755743,
                0.9999991684719723,
                0.9999993524051246,
                0.9999984465016899
            ],
            [
                0.2942149783515162,
                0.5926665999540698,
                0.0015011821148699063,
                0.9998415638022965,
                0.00026119030753664704,
                0.0009110512295276099,
                0.00012339455905914664,
                0.00023050663184326586,
                0.000430557183081505,
                0.9993736658262602
            ],
            [
                0.9999990577554061,
                0.9999990577551814,
                0.9999984465022455,
                0.9999992661792819,
                0.9999982396574162,
                0.9999993524049703,
                0.9999989322970027,
                0.9999898700126436,
                0.9999990577556308,
                0.9999984465015047
            ],
            [
                0.9999994956524716,
                0.9999993524050474,
                0.9999991684722698,
                0.999996273362049,
                0.999999352405279,
                0.9999987901347491,
                0.9999996072138465,
                0.9999994956524114,
                0.9999994956523512,
                0.9999996072138465
            ],
            [
                0.9999995549150542,
                0.9999996940976272,
                0.9999962733607158,
                0.9999994284992805,
                0.9999993524051246,
                0.9999996533674201,
                0.9999998144609203,
                0.999999352404893,
                0.999999352404893,
                0.9999990577549568
            ],
            [
                5.42222090821551e-06,
                1.0129988564264954e-05,
                1.8925152746768368e-05,
                2.902311984989368e-06,
                5.422220908314139e-06,
                3.7266410608720178e-06,
                1.209865250822125e-06,
                1.7603432132912532e-06,
                5.8291251623852595e-05,
                1.1478768122987964e-05
            ],
            [
                0.9999982396565769,
                0.9999998362623528,
                0.9999990577552937,
                0.9999997617630049,
                0.9999982396559473,
                0.9999996533675028,
                0.9999990577549568,
                0.9999997617631752,
                0.9999991684722698,
                0.9999996533672549
            ],
            [
                0.9999997897567091,
                0.9999974387165681,
                0.9999921107402363,
                0.9999984465022455,
                0.9999994956525317,
                0.9999921107355337,
                0.9999945777797379,
                0.9999982396569966,
                0.9999992661788445,
                0.9999994956524716
            ],
            [
                0.9999546021368129,
                0.9999962733602722,
                0.9999930377462408,
                0.9999987901337396,
                0.9999977396759717,
                0.999998790134028,
                0.9999990577555185,
                0.9999984465026158,
                0.9999989322967481,
                0.9999987901341724
            ],
            [
                0.9999989322967481,
                0.9999994956525317,
                0.999997097686631,
                0.9999989322970028,
                0.9999989322972572,
                0.9999986290426297,
                0.9999992661791944,
                0.9999994956527722,
                0.999999554914895,
                0.9999991684719723
            ],
            [
                0.9999990577549569,
                0.9999996940977002,
                0.9999987901344607,
                0.9999994956524716,
                0.999997438717484,
                0.9999996940976272,
                0.9999977396748944,
                0.9999997617630333,
                0.9999995549149481,
                0.9999992661791944
            ],
            [
                0.9999980052702785,
                0.9999995549147359,
                0.9999998362623528,
                0.9999984465015046,
                0.9999997300420939,
                0.9999982396567868,
                0.9999994956525317,
                0.9999990577554061,
                0.9999991684718732,
                0.9999974387180947
            ],
            [
                0.9999984465020603,
                0.9999990577555185,
                0.9999974387187053,
                0.9999989322968754,
                0.9999980052702785,
                0.9999980052693274,
                0.9999957771665555,
                0.999995214904935,
                0.9999986290432834,
                0.9999957771655487
            ],
            [
                0.999986992876188,
                0.9999832985721839,
                0.999738809691445,
                0.9999930377445803,
                0.999915188978871,
                0.9999599362934897,
                0.9997040429007811,
                0.9999599362982898,
                0.9999546021151307,
                0.999995777166052
            ],
            [
                0.9999997300422868,
                0.9999967112497585,
                0.9999989322970027,
                0.9999852610180308,
                0.9999921107364745,
                0.999998790134605,
                0.9999910603004993,
                0.999994577780384,
                0.9999724642957752,
                0.9999957771675624
            ],
            [
                0.9999974387177893,
                0.9999970976880151,
                0.9999987901341723,
                0.9997965729848427,
                0.9999994284994185,
                0.9999967112517189,
                0.9999982396561571,
                0.9999990577557432,
                0.9999992661790195,
                0.9999994284997573
            ],
            [
                6.1441767990323395e-06,
                1.47389854857293e-05,
                3.1201918809808464e-05,
                3.535625914093709e-05,
                3.120190021339598e-05,
                1.4738978455325741e-05,
                0.9999993524052019,
                6.962253759670401e-06,
                1.0129994601688632e-05,
                1.0129992187253088e-05
            ],
            [
                0.9999993524051246,
                0.9999994284995529,
                0.9999989322970027,
                0.9999977396754327,
                0.9999992661788445,
                0.9999957771655487,
                0.9999996072137061,
                0.9999987901343165,
                0.9999989322968753,
                0.999997097688015
            ],
            [
                0.9999977396762411,
                0.9999885212277709,
                0.9999945777810305,
                0.9999945777816766,
                0.9999952149043646,
                0.999986992869989,
                0.9999957771670589,
                0.9999967112517187,
                0.9999952149049351,
                0.999998790134028
            ],
            [
                0.9999989322967482,
                0.9999996940978825,
                0.9999998144608097,
                0.999999495652712,
                0.9999993524050474,
                0.9999996940976636,
                0.9999993524051246,
                0.9999996072136125,
                0.9999986290432835,
                0.9999990577556307
            ],
            [
                1.1478773598538445e-05,
                3.726639283901856e-06,
                4.785096776194573e-06,
                3.288748281220719e-06,
                2.1444956079842134e-05,
                1.147877223059538e-05,
                1.0129992187253088e-05,
                2.4300240719941574e-05,
                6.144175334094145e-06,
                6.962259569313662e-06
            ],
            [
                0.9999885212305076,
                0.9999930377462403,
                0.9999974387187053,
                0.9999994284996891,
                0.9999996072136125,
                0.9999984465022455,
                0.9999962733620488,
                0.9999938558253981,
                0.999999168471675,
                0.9999938558246657
            ],
            [
                0.9999992661788446,
                0.9999974387168733,
                0.9999993524054335,
                0.9999952149055056,
                0.9999938558232017,
                0.9999993524049703,
                0.9999996940978825,
                0.9999994284996211,
                0.999997438716568,
                0.9999991684715759
            ],
            [
                0.9999987901341724,
                0.9999993524053562,
                0.9999996072139402,
                0.9999984465022455,
                0.9999982396567868,
                0.9999997300421903,
                0.9999994956527721,
                0.999991060305474,
                0.9999997897565587,
                0.9999991684720715
            ],
            [
                2.260324836341129e-06,
                1.0129988563914856e-05,
                3.2887478888496478e-06,
                3.726638839395927e-06,
                3.2887490649759413e-06,
                6.962257906765564e-06,
                3.7266392835764795e-06,
                2.430024361951464e-05,
                4.006371124165013e-05,
                9.422445937837332e-07
            ],
            [
                0.9999996940977366,
                0.9999995549148419,
                0.9999994956523514,
                0.9999999006880312,
                0.9999990577556307,
                0.9999993524054335,
                0.9999997300421261,
                0.9999996940977731,
                0.9999995549148419,
                0.9999999123574419
            ],
            [
                2.753568780802255e-05,
                1.2098653950315304e-06,
                1.8925155007633607e-05,
                7.889262585642319e-06,
                4.539786318711917e-05,
                4.0063692137387875e-05,
                4.785096205778054e-06,
                1.3007123812057577e-05,
                8.939695237504067e-06,
                6.6052121039017e-05
            ],
            [
                0.9999994284993485,
                0.9999990577549568,
                0.9999999006880904,
                0.9999998144609203,
                0.9999989322972572,
                0.9999994284993485,
                0.9999987901343165,
                0.9999989322973846,
                0.9999993524049702,
                0.9999984465022455
            ],
            [
                0.9999993524054335,
                0.999999266179107,
                0.999999554914842,
                0.9999990577551815,
                0.9999994284996891,
                0.9999993524053563,
                0.9999995549150542,
                0.9999987901343166,
                0.9999962733602723,
                0.9999952149066478
            ],
            [
                0.999999352404893,
                0.9999992661786696,
                0.9999997617630049,
                0.999996273360272,
                0.9999996072137998,
                0.999999168471675,
                0.9999989322971299,
                0.9999992661791071,
                0.9999994284994849,
                0.999999168471675
            ],
            [
                0.9999970976873229,
                0.9999885212318762,
                0.9999977396754327,
                0.9999957771675625,
                0.9999991684720715,
                0.9999962733620487,
                0.9999982396563669,
                0.9999930377437506,
                0.9999938558253982,
                0.9999930377462414
            ],
            [
                2.2603234894745224e-06,
                0.9999984465016899,
                2.753570421481532e-05,
                1.3709575336947905e-06,
                1.0129994602057158e-05,
                1.3709568799368123e-06,
                6.962256249682458e-06,
                1.3007134665674251e-05,
                0.9999989322971299,
                2.1444958638526877e-05
            ],
            [
                1.3007126911004571e-05,
                1.473898197154587e-05,
                3.288750241374845e-06,
                3.2887506333812835e-06,
                1.5534977545384963e-06,
                4.222832437639588e-06,
                6.144177531599359e-06,
                4.785093924103951e-06,
                9.422450431654909e-07,
                8.939695237813028e-06
            ],
            [
                1.5534981249291695e-06,
                1.994729008056074e-06,
                9.422444815628016e-07,
                1.0677028700203557e-06,
                1.2098652508056196e-06,
                8.315280276546789e-07,
                1.7603427935967163e-06,
                1.0677029973056687e-06,
                8.315282258956806e-07,
                3.7266379513434106e-06
            ],
            [
                0.9999984465026158,
                0.9999970976880149,
                0.9999945777810304,
                0.9999938558246658,
                0.999999554914895,
                0.9999991684717742,
                0.999981074845,
                0.9999982396561571,
                0.9999991684718732,
                0.9999974387177893
            ],
            [
                0.9999967112493666,
                0.9999967112501505,
                0.9999967112501507,
                0.9999980052700407,
                0.9999945777790916,
                0.9999984465022455,
                0.9999984465020603,
                0.9999938558253989,
                0.9999984465015047,
                0.9999977396751633
            ],
            [
                4.7850956352353935e-06,
                1.2098652508287273e-06,
                1.892514147143123e-05,
                7.484621828887399e-05,
                2.1444943297072005e-05,
                9.610239190878512e-05,
                1.892515500808112e-05,
                4.539786321684599e-05,
                0.00017952800843023904,
                5.422217676654099e-06
            ],
            [
                1.8925152752999112e-05,
                1.994730434798734e-06,
                1.012998977022003e-05,
                1.3709578605542582e-06,
                3.2887486731641103e-06,
                4.222832437386106e-06,
                1.0129989771473008e-05,
                2.1444953504969666e-05,
                6.962254589433702e-06,
                4.78509563546605e-06
            ],
            [
                1.3709578605243332e-06,
                1.370957043323753e-06,
                2.4300240728162926e-05,
                5.4222202621161125e-06,
                9.422450431800595e-07,
                6.962255419728997e-06,
                1.1478772229989872e-05,
                2.4300252317882297e-05,
                3.288750633569722e-06,
                3.28874906467085e-06
            ],
            [
                0.999999554914895,
                0.9999998362623528,
                0.9999993524054335,
                0.9999994956527121,
                0.9999996940978825,
                0.9999996533672135,
                0.999999730042126,
                0.9999991684718732,
                0.9999984465024306,
                0.9999998874647842
            ],
            [
                0.9999962733598274,
                0.9999921107345932,
                0.9999992661789321,
                0.9999992661787571,
                0.9999994284994848,
                0.9999987901338838,
                0.9999990577551814,
                0.9999994284992805,
                0.9999987901341723,
                0.9999987901337397
            ],
            [
                4.222833444429485e-06,
                8.939695236983711e-06,
                1.209865250822125e-06,
                1.209866116149238e-06,
                6.1441746017453204e-06,
                8.315283250150648e-07,
                1.1478773598099973e-05,
                2.2603245670174926e-06,
                1.5534971989809095e-06,
                3.2887478891128633e-06
            ],
            [
                0.9999989322973845,
                0.9999990577549568,
                0.9999974387171787,
                0.9999970976873229,
                0.9999977396762411,
                0.9999996940978825,
                0.9999992661786696,
                0.9999996533672549,
                0.99999893229713,
                0.9999993524054335
            ],
            [
                0.999998629042303,
                0.9999980052709919,
                0.999995777164542,
                0.9999990577550691,
                0.9999987901347491,
                0.9999990577555185,
                0.9999992661788445,
                0.9999994956525918,
                0.9999982396565767,
                0.9999989322967481
            ],
            [
                0.9999995549151072,
                0.999999495652652,
                0.9999989322972572,
                0.9999980052695652,
                0.999998790134605,
                0.999998446502801,
                0.9999994284995529,
                0.999999789756634,
                0.9999986290426297,
                0.9999997300422869
            ],
            [
                0.9999982396561571,
                0.9999967112493665,
                0.9999970976873229,
                0.9999967112497584,
                0.9999952149037942,
                0.9999952149072171,
                0.9999945777784451,
                0.9999938558253983,
                0.9999885212277704,
                0.9999984465015047
            ],
            [
                0.9999990577552937,
                0.9999987901338838,
                0.9999997617631183,
                0.9999989322973846,
                0.9999994284997573,
                0.9999989322970027,
                0.9999990577555185,
                0.999999495652712,
                0.999999266179107,
                0.9999994284994167
            ],
            [
                0.9999996940978825,
                0.9999994284995529,
                0.9999977396751634,
                0.9999992661791945,
                0.9999995549147358,
                0.9999977396759717,
                0.9999992661787571,
                0.9999997897565838,
                0.9999986290427932,
                0.9999980052705164
            ],
            [
                0.9999756997650667,
                0.9999930377445811,
                0.9999921107392977,
                0.9999546021205622,
                0.9999599363174034,
                0.9999910603047633,
                0.9999910603036979,
                0.9999967112521109,
                0.9999952149066466,
                0.999997097687669
            ],
            [
                0.9999930377404309,
                0.9999910603026315,
                0.999996273358939,
                0.9999898700066077,
                0.9999957771680658,
                0.9999977396748938,
                0.9999952149032242,
                0.9999898700041931,
                0.9999910603004992,
                0.9999970976880149
            ],
            [
                2.9023133690637e-06,
                9.422450431372112e-07,
                3.059021539909339e-07,
                8.31528325021115e-07,
                2.260323758835034e-06,
                7.338213304243302e-07,
                4.785096776194573e-06,
                1.5534983101393749e-06,
                1.4738983726908257e-05,
                4.785093924330255e-06
            ],
            [
                0.9999921107336528,
                0.9999989322975118,
                0.9999990577554061,
                0.9999910603036967,
                0.9999992661792819,
                0.99999303774624,
                0.9999898700066056,
                0.9999992661786696,
                0.9999982396559474,
                0.9999974387187053
            ],
            [
                1.1478765384430723e-05,
                0.9999994284994167,
                6.96225956921868e-06,
                6.962255419653012e-06,
                0.9999992661788446,
                4.222833444429485e-06,
                1.0129990979547237e-05,
                0.9999977396751633,
                2.1444948401176257e-05,
                7.88925976316864e-06
            ],
            [
                0.9999970976887069,
                0.999996273361605,
                0.9999982396567867,
                0.9999987901337396,
                0.9999990577549569,
                0.9999970976876689,
                0.9999982396565767,
                0.9999987901337396,
                0.9999957771660526,
                0.9999962733620488
            ],
            [
                0.9999977396754327,
                0.9999992661790195,
                0.9999974387168733,
                0.9999930377420907,
                0.9999986290431201,
                0.9999938558253983,
                0.9999996072137061,
                0.9999945777823231,
                0.9999974387168733,
                0.999997438717484
            ],
            [
                0.9999997617630332,
                0.99999862904312,
                0.9999980052700408,
                0.9999998144608319,
                0.9999970976866309,
                0.9999984465016899,
                0.9999984465022455,
                0.9999991684719723,
                0.9999962733611605,
                0.9999984465016899
            ],
            [
                0.999999789756684,
                0.9999999317439302,
                0.9999938558268635,
                0.9999992661791944,
                0.9999997300422547,
                0.9999994956524716,
                0.9999984465018751,
                0.9999998555019963,
                0.9999994284996893,
                0.999999554914842
            ],
            [
                8.93970056565517e-06,
                8.481105137391814e-05,
                2.144494584573034e-05,
                4.539789027816371e-05,
                1.892515725665725e-05,
                2.902312330759764e-06,
                1.67014297980912e-05,
                1.0129989770441144e-05,
                1.4738976697631541e-05,
                0.00012339460401431546
            ],
            [
                3.2887494573232236e-06,
                7.889264465986113e-06,
                1.0677029973114952e-06,
                5.422217676397663e-06,
                5.043472278299047e-07,
                1.7603427935967163e-06,
                1.3007133114886634e-05,
                5.422217029844958e-06,
                1.0129987356191011e-05,
                5.422217030495909e-06
            ],
            [
                0.9999977396762411,
                0.9999945777829694,
                0.9999952149055059,
                0.9999980052702785,
                0.9999974387174841,
                0.9999785550515911,
                0.9999599363078321,
                0.9999339478239252,
                0.9999970976880148,
                0.999995214904935
            ],
            [
                0.9999997897567091,
                0.9999998724809116,
                0.9999994956523512,
                0.9999984465016898,
                0.9999984465020603,
                0.9999994284994167,
                0.9999982396565769,
                0.9999989322968754,
                0.999999554914895,
                0.9999962733607161
            ],
            [
                0.9999984465015047,
                0.9999989322973845,
                0.999999887464744,
                0.9999992661790196,
                0.9999994956525918,
                0.9999991684717742,
                0.9999992661787571,
                0.9999996533674614,
                0.999999814460854,
                0.9999986290423029
            ],
            [
                0.999999789756634,
                0.99999893229713,
                0.9999996533675028,
                0.9999994284996211,
                0.9999991684719723,
                0.9999997300420939,
                0.9999992661786695,
                0.999999352405279,
                0.9999998144608319,
                0.9999987901341724
            ],
            [
                0.9999957771655487,
                0.9999885212332436,
                0.9999967112493665,
                0.9999921107383551,
                0.9999994956526519,
                0.9999869928668843,
                0.9999945777810305,
                0.9999898700066052,
                0.999998005269803,
                0.9998204720341507
            ],
            [
                0.9999982396567868,
                0.9999832985701939,
                0.9999962733616046,
                0.999995214904935,
                0.9999599362887198,
                0.9999485577680016,
                0.9999852610233028,
                0.9999599363078259,
                0.9999832985701924,
                0.9999485578047876
            ],
            [
                0.9999885212264016,
                0.9999852610162737,
                0.999988521226404,
                0.9999885212318756,
                0.9999982396567867,
                0.99999893229713,
                0.9999987901344608,
                0.9999945777803843,
                0.9999921107364742,
                0.9999962733616045
            ],
            [
                0.9999957771655488,
                0.9999994956527121,
                0.9999996940976636,
                0.999999266178757,
                0.9999962733593833,
                0.9999990577554061,
                0.9999977396762411,
                0.9999990577550691,
                0.9999984465026158,
                0.9999945777816768
            ],
            [
                0.9999986290424663,
                0.9999997617630049,
                0.999997097688361,
                0.9999994956524114,
                0.9999974387184,
                0.999997097687669,
                0.9999962733607162,
                0.9999952149066464,
                0.9999980052695652,
                0.9999967112505427
            ],
            [
                2.260324567302214e-06,
                8.939695238211425e-06,
                4.785093353626844e-06,
                2.5612812947240366e-06,
                1.8925150496609267e-05,
                3.726638839833152e-06,
                1.012998856312253e-05,
                3.5356242271040426e-05,
                2.2603245672497918e-06,
                3.120191880504111e-05
            ],
            [
                3.535625912717466e-05,
                0.9999930377437506,
                1.7603434229832599e-06,
                3.5356238059741304e-05,
                0.9999974387184001,
                4.2228344508893285e-06,
                2.260323489435463e-06,
                6.144176798132662e-06,
                4.0063687394553603e-05,
                6.605216036763493e-05
            ],
            [
                0.9999930377437506,
                0.9999987901337396,
                0.9999967112497586,
                0.9999987901343165,
                0.9999984465016899,
                0.9999970976876689,
                0.9999990577552939,
                0.9999987901343166,
                0.9999986290427931,
                0.9999970976880149
            ],
            [
                0.9999989322975118,
                0.9999546021151431,
                0.9999974387168734,
                0.9999921107345932,
                0.9999930377404308,
                0.9999938558246659,
                0.9999852610233015,
                0.9999898700126431,
                0.9999982396567868,
                0.9999038975392522
            ],
            [
                1.2098662604049616e-06,
                1.3709572067680694e-06,
                8.31528424151477e-07,
                6.475951069896949e-07,
                1.0677032518700286e-06,
                5.043472278280699e-07,
                9.422445938917108e-07,
                5.715002426343175e-07,
                3.726640616670918e-06,
                1.2098655392574583e-06
            ],
            [
                0.9999977396765105,
                0.999999730042319,
                0.9999997617630616,
                0.9999997617631183,
                0.9999996072137529,
                0.9999938558268638,
                0.9999997300423191,
                0.9999967112497585,
                0.9999982396574162,
                0.9999986290423029
            ],
            [
                0.9999998555019618,
                0.99999893229713,
                0.9999992661788446,
                0.9999980052705163,
                0.9999990577550691,
                0.9999991684722697,
                0.9999984465016899,
                0.9999996072137529,
                0.9999996940976272,
                0.9999991684717741
            ],
            [
                0.9999991684720715,
                0.9999996533674614,
                0.9999996533673788,
                0.999999266178932,
                0.999999266178932,
                0.9999989322966208,
                0.9999994956525918,
                0.9999921107336524,
                0.9999996072138934,
                0.9999994284996893
            ],
            [
                1.3709570434122812e-06,
                1.5534973841450852e-06,
                4.7850927830148924e-06,
                1.4738980211116665e-05,
                6.1441738691562974e-06,
                7.338211554688417e-07,
                4.222834954687752e-06,
                3.120190021657421e-05,
                4.785096776133645e-06,
                1.3709576971061233e-06
            ],
            [
                0.9999785550541502,
                0.9999832985781624,
                0.999993855822469,
                0.999959936307828,
                0.9999898700114371,
                6.60521524840326e-05,
                0.9999810748517622,
                0.9999485577740995,
                0.999978555049031,
                0.9999417087483918
            ],
            [
                0.9999785550541487,
                0.9999852610233005,
                0.9999852610197867,
                0.9999885212264077,
                0.9999910603026312,
                0.9999832985741757,
                0.999981074856277,
                0.999954602142192,
                0.9999810748495156,
                0.9998911031038535
            ],
            [
                0.9999992661786696,
                0.9999982396572064,
                0.999998446502801,
                0.9999952149055054,
                0.9999974387187053,
                0.9999977396751633,
                0.9999984465020603,
                0.9999992661787571,
                0.9999945777790911,
                0.9999984465018751
            ],
            [
                0.9999991684716749,
                0.9999994956523514,
                0.9999967112513267,
                0.9999990577550691,
                0.9999885212332431,
                0.9999952149060761,
                0.9999984465026158,
                0.9999921107402363,
                0.9999993524053562,
                0.999996273358939
            ],
            [
                0.9999989322968754,
                0.9999967112513269,
                0.9999980052707542,
                0.999999266179107,
                0.9999982396567867,
                0.999999168471675,
                0.9999974387177895,
                0.9999945777816771,
                0.9999982396567868,
                0.9999980052693274
            ],
            [
                1.370957697068717e-06,
                2.260323758557508e-06,
                6.475947981695877e-07,
                1.0677027427413698e-06,
                4.2228324375512536e-06,
                3.726640616670918e-06,
                3.927862002582919e-07,
                1.2098655392662613e-06,
                9.42244256886598e-07,
                9.422449308335287e-07
            ],
            [
                0.9999952149072165,
                0.9999986290421394,
                0.9999977396762411,
                0.9999989322975118,
                0.9999986290424664,
                0.9999977396759717,
                0.9999996072137998,
                0.9999987901347491,
                0.999998629042303,
                0.99999862904312
            ],
            [
                0.9999990577554061,
                0.9999994284992805,
                0.9999997300420937,
                0.9999986290429566,
                0.999999730042319,
                0.9999991684718733,
                0.9999987901341723,
                0.9999996940978825,
                0.9999994956527121,
                0.9999997617630617
            ],
            [
                0.999991060301566,
                0.9999974387174841,
                0.9999994284992805,
                0.9999938558239339,
                0.9999990577555185,
                0.9999938558261311,
                0.9999987901346049,
                0.9999982396572065,
                0.9999967112513268,
                0.9999992661786696
            ],
            [
                0.9999996533675028,
                0.9999967112513268,
                0.9999987901338838,
                0.9999996072137529,
                0.9999982396567867,
                0.9999869928653352,
                0.9999938558224685,
                0.9999945777803839,
                0.9999810748540177,
                0.9999687980960844
            ],
            [
                6.962254589705982e-06,
                2.9023109471689794e-06,
                1.473898899846585e-05,
                8.939698434153684e-06,
                8.939699500636112e-06,
                1.0677028700130727e-06,
                6.144173868781898e-06,
                2.2603251061458426e-06,
                4.222834954607099e-06,
                1.6701417861949427e-05
            ],
            [
                0.999997438717484,
                0.999993855823201,
                0.9999546021421896,
                0.9999994956524716,
                0.999991060303696,
                0.9999967112517189,
                0.9999970976869769,
                0.9999869928746368,
                0.9999930377445811,
                0.9999952149066461
            ],
            [
                0.9999885212346119,
                0.9999989322967481,
                0.9999852610145359,
                0.9999687980811988,
                0.9999970976873247,
                0.999620015544745,
                0.9999852610232997,
                0.9999952149060766,
                0.9998415637649272,
                0.999989870011497
            ],
            [
                0.9999986290421395,
                1.1478772230407462e-05,
                7.889259764079887e-06,
                5.829127243528923e-05,
                1.4738978455325741e-05,
                2.4300249422639878e-05,
                8.93970056565517e-06,
                1.067703251864202e-06,
                3.53562591336057e-05,
                1.4738983725406915e-05
            ],
            [
                0.9999962733607161,
                0.9999987901346049,
                0.99999976176309,
                0.9999995549150542,
                0.9999994956523514,
                0.9999990577554061,
                0.9999993524053563,
                0.9999990577556308,
                0.9999984465018751,
                0.999999789756684
            ],
            [
                1.3709567165386693e-06,
                6.144173136556186e-06,
                1.4738985484549675e-05,
                6.605214464272057e-05,
                0.9999962733611603,
                0.999997097686977,
                6.962254589781966e-06,
                1.8925150495232307e-05,
                0.9999898700090208,
                6.962255419728997e-06
            ],
            [
                0.999997438716568,
                0.9999962733616047,
                0.999997438716568,
                0.9999996940977366,
                0.9999832985841314,
                0.9999967112517189,
                0.999989870007814,
                0.9999984465018751,
                0.9999151889890939,
                0.9999986290431201
            ],
            [
                7.889259764079887e-06,
                0.9999952149049351,
                1.9947292458930106e-06,
                1.670142781478417e-05,
                0.9999994284992805,
                5.422217030555087e-06,
                1.4738985485461206e-05,
                0.999998239656367,
                0.9999930377404319,
                4.222833947897496e-06
            ],
            [
                0.9999994956526519,
                0.9999994284995529,
                0.9999980052709919,
                0.9999992661790195,
                0.9999970976873231,
                0.9999970976873231,
                0.9999994284994848,
                0.9999967112509349,
                0.9999996072139402,
                0.9999945777803845
            ],
            [
                0.9999989322967481,
                0.9999990577554061,
                0.9999998144609645,
                0.9999987901347492,
                0.9999991684722698,
                0.9999982396569966,
                0.9999984465028012,
                0.99999862904312,
                0.9999996072137061,
                0.9999994284994167
            ],
            [
                0.9999980052700408,
                0.9999910603058276,
                0.9999945777803845,
                0.9999974387184,
                0.9999974387177893,
                0.9999993524052019,
                0.9999970976866309,
                0.9999997897567091,
                0.9999991684719725,
                0.9999989322970027
            ],
            [
                0.9999987901338838,
                0.999998790134028,
                0.9999977396759716,
                0.9999970976880149,
                0.9999987901347491,
                0.9999970976869771,
                0.9999986290429566,
                0.9999987901347492,
                0.9999991684716749,
                0.99999893229713
            ],
            [
                0.9999991684717741,
                0.9999992661791944,
                0.999999057755743,
                0.9999990577549569,
                0.9999995549150542,
                0.9999996940977731,
                0.9999994284993485,
                0.999999730042126,
                0.9999997617631468,
                0.9999993524054334
            ],
            [
                1.1478768124783601e-05,
                1.89251482372248e-05,
                5.422218969720291e-06,
                1.3007128462477575e-05,
                1.6701429807630274e-05,
                7.484626293113213e-05,
                3.72664017246987e-06,
                3.2887486732358968e-06,
                6.9622570786798724e-06,
                1.012998735687278e-05
            ],
            [
                0.999999730042126,
                0.9999957771680658,
                0.9999984465020603,
                0.9999994284993485,
                0.9999992661786695,
                0.9999993524049702,
                0.9999980052709919,
                0.9999991684719725,
                0.9999982396574163,
                0.9999989322975118
            ],
            [
                0.9999989322975118,
                0.9999992661786695,
                0.9999998144608317,
                0.999999730042319,
                0.9999998724809419,
                0.999999554914895,
                0.9999996533674615,
                0.9999996940978825,
                0.9999994956523514,
                0.9999982396574162
            ],
            [
                0.9999996072137998,
                0.9999996072137529,
                0.9999998555019963,
                0.999999352404893,
                0.9999994284994849,
                0.9999987901344608,
                0.9999997617629764,
                0.9999994956524716,
                0.9999996533674614,
                0.9999992661788446
            ],
            [
                0.9999997300422225,
                0.9999974387177893,
                0.9999980052702786,
                0.9999967112513267,
                0.9999974387171787,
                0.999999694097773,
                0.9999982396574163,
                0.999998446502801,
                0.999998629042303,
                0.9999982396561571
            ],
            [
                0.9999996940978825,
                0.9999991684717741,
                0.9999991684722697,
                0.9999991684722698,
                0.9999974387184,
                0.9999989322972572,
                0.9999994956525918,
                0.9999982396572065,
                0.9999974387168733,
                0.9999994284994167
            ],
            [
                0.9999991684722697,
                0.9999970976883609,
                0.9999997617631184,
                0.9999995549151073,
                0.9999996533673375,
                0.9999982396572065,
                0.9999986290426297,
                0.9999986290429566,
                0.9999930377437514,
                0.9999996072138934
            ],
            [
                0.9999962733616045,
                0.9999980052700408,
                0.9999984465016899,
                0.9999898700102282,
                0.999996273358939,
                0.9999980052695652,
                0.9999957771670591,
                0.9999970976869769,
                0.9999982396574163,
                0.999999168471675
            ],
            [
                0.9999994284996211,
                0.9999986290429566,
                0.9999977396757023,
                0.999998790134028,
                0.9999986290426298,
                0.9999974387180947,
                0.9999986290424663,
                0.9999994284995529,
                0.9999989322968754,
                0.9999977396762411
            ],
            [
                4.222833444283541e-06,
                2.2603237588597026e-06,
                2.430024362932722e-05,
                1.4738985485166298e-05,
                3.7266388397382506e-06,
                1.1478769493540482e-05,
                3.2887494572095624e-06,
                4.222833947774596e-06,
                7.889261645090304e-06,
                4.785096205651846e-06
            ],
            [
                0.9999898700102283,
                0.9999994284996893,
                0.9999994956525918,
                0.9999885212346119,
                0.9999970976890528,
                0.9999995549147359,
                0.9999993524052018,
                0.9999989322968754,
                0.9999994956527722,
                0.9999991684717741
            ],
            [
                1.3007133114602719e-05,
                1.5534981249496567e-06,
                1.0129987357158383e-05,
                2.902312677104321e-06,
                6.1441724046434924e-06,
                4.785096776251149e-06,
                1.0677028699955933e-06,
                5.422221555133606e-06,
                4.222835458044565e-06,
                8.939696303758459e-06
            ],
            [
                0.9999974387171787,
                0.999993037741261,
                0.9999967112501507,
                0.9999977396751633,
                0.9999977396757022,
                0.9999910603026306,
                0.9999991684716749,
                0.9999984465026159,
                0.9999952149060757,
                0.9999930377429206
            ],
            [
                0.9999997617630048,
                0.999991060303697,
                0.9999974387187053,
                0.9999785550413688,
                0.9999921107345929,
                0.9999977396757022,
                0.9999910603068933,
                0.9999952149072167,
                0.9999986290421394,
                0.9999756997679626
            ],
            [
                8.939698434495167e-06,
                1.2098655392662613e-06,
                1.1478772229781076e-05,
                3.726639283440905e-06,
                5.422220262555012e-06,
                3.7266392839832006e-06,
                6.144175334015912e-06,
                5.715007195353674e-07,
                1.670142980608093e-05,
                8.93969417214416e-06
            ],
            [
                2.9023119851055122e-06,
                1.4738980214280206e-05,
                2.9023133689924295e-06,
                1.670141786231398e-05,
                2.753570422373059e-05,
                2.9023112931213857e-06,
                2.144495096457996e-05,
                2.2603237587774727e-06,
                3.5356254907513187e-05,
                3.535624227875767e-05
            ],
            [
                0.9999998555019446,
                0.9999996940978461,
                0.9999998144609202,
                0.9999998144608981,
                0.9999980052705164,
                0.9999996533675028,
                0.9999993524054335,
                0.9999996940977731,
                0.9999998555019446,
                0.9999999226557776
            ]
        ]
    },
    {
        "q_id": "8509_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            14,
            15,
            16,
            18,
            19,
            21,
            22,
            23,
            24,
            25,
            27,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            39,
            42,
            45,
            47,
            48,
            52,
            53,
            54,
            55,
            56,
            57,
            59,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            75,
            78,
            80,
            82,
            83,
            84,
            87,
            88,
            89,
            90,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            102,
            104,
            105,
            106,
            107,
            109,
            110,
            111,
            112,
            113,
            114,
            116,
            119,
            120,
            121,
            122,
            123,
            125,
            126,
            127
        ],
        "rewards": [
            [
                7.484622697043032e-05,
                7.889264465067689e-06,
                6.144175331009535e-06,
                0.00010889690886829515,
                7.88926258532661e-06,
                1.0129988564430787e-05,
                1.9947297212331575e-06,
                6.60521757383795e-05,
                1.147876533949801e-05,
                6.144176796780352e-06
            ],
            [
                1.760342793266906e-06,
                5.422218323019487e-06,
                1.1478773598914277e-05,
                7.889261644501938e-06,
                7.889263524788109e-06,
                3.120190019636974e-05,
                5.829127245988703e-05,
                1.4738980214280206e-05,
                4.0063687367153544e-05,
                1.0129992186202796e-05
            ],
            [
                5.422220908634683e-06,
                2.902312677007974e-06,
                2.5612822106421996e-06,
                4.222831933726245e-06,
                3.288749849114211e-06,
                5.422220262195015e-06,
                1.5534983101393749e-06,
                3.726640172385136e-06,
                1.5534975693036317e-06,
                1.9947301969707264e-06
            ],
            [
                3.05902117518448e-07,
                5.4222202614355715e-06,
                1.3007131562845248e-05,
                1.300713311112477e-05,
                1.5534977544141614e-06,
                6.1441738691562974e-06,
                1.6701425823882575e-05,
                7.889265405505236e-06,
                2.699579061798195e-07,
                3.12019113570763e-05
            ],
            [
                2.260325375391425e-06,
                7.48462268811262e-05,
                1.3709567162743315e-06,
                1.4738985481091229e-05,
                3.53562591237019e-05,
                3.7266397276079535e-06,
                2.1444940743772097e-05,
                2.4300243618542217e-05,
                1.0129992187253088e-05,
                1.3709567164139816e-06
            ],
            [
                2.75357041747467e-05,
                1.3007123810306773e-05,
                5.829127930740772e-05,
                2.7535687702141286e-05,
                2.430023776874232e-05,
                2.5612815992038705e-06,
                4.006371120842025e-05,
                1.8925157255968775e-05,
                2.144494073796001e-05,
                1.994730434778778e-06
            ],
            [
                5.829127246412803e-05,
                5.829127240390582e-05,
                8.93969417150998e-06,
                6.1441753335241615e-06,
                2.4300237825230942e-05,
                3.53562633231704e-05,
                0.0003799844499707265,
                4.222832940834793e-06,
                2.260324836624822e-06,
                4.222831934052698e-06
            ],
            [
                1.8925150493166868e-05,
                7.889263525893087e-06,
                0.00012339453003282785,
                1.892514146884943e-05,
                1.6701417861189946e-05,
                4.222833947498071e-06,
                3.2887506334560605e-06,
                2.5612819050161955e-06,
                1.8925150491445666e-05,
                6.144176066264237e-06
            ],
            [
                1.0129992185981682e-05,
                5.144221364340114e-05,
                3.535626334645077e-05,
                2.7535697652678035e-05,
                1.012999218277553e-05,
                7.484626270351544e-05,
                1.670141786036971e-05,
                5.144220749598207e-05,
                1.0129993393945642e-05,
                7.484620910307734e-05
            ],
            [
                1.5534977545603963e-06,
                1.2098652508144226e-06,
                1.370956716529941e-06,
                4.7850950648799385e-06,
                0.0004878572093793201,
                6.144177531532303e-06,
                1.7603434231385591e-06,
                9.422447062094932e-07,
                4.222832941072913e-06,
                2.561283431942246e-06
            ],
            [
                2.144494585197151e-05,
                1.3007126911974612e-05,
                8.939699496489538e-06,
                2.1444940736477737e-05,
                5.1442225840182154e-05,
                2.1444940731484803e-05,
                3.2887486731641103e-06,
                1.6701429799367125e-05,
                8.939697368305565e-06,
                8.939699500164542e-06
            ],
            [
                1.9947290079889487e-06,
                3.72663839489005e-06,
                6.144173132689249e-06,
                0.00020342690014243665,
                2.9023109454928147e-06,
                2.5612828209811664e-06,
                7.889264463890957e-06,
                2.902310945682868e-06,
                6.96225541916544e-06,
                6.962256248314727e-06
            ],
            [
                8.939696302457574e-06,
                1.892515725920463e-05,
                3.535626334156318e-05,
                9.610246063230013e-05,
                1.6701425822059825e-05,
                3.120191879107958e-05,
                2.1444945852673643e-05,
                1.6701423830702777e-05,
                0.00015843615897639317,
                6.962259568509485e-06
            ],
            [
                1.5534983100765009e-06,
                1.0129992186939844e-05,
                1.2098653949688097e-06,
                1.855391681891831e-07,
                1.7603434230921292e-06,
                2.2603237589542675e-06,
                3.927863875520681e-07,
                1.7603436329394601e-06,
                8.939699500766203e-06,
                2.3823693839057394e-07
            ],
            [
                8.939693105272102e-06,
                2.2603242977802297e-06,
                2.7535700941409604e-05,
                5.422219616140078e-06,
                4.539786864232016e-05,
                3.2887506332945414e-06,
                8.939696302051047e-06,
                5.4222202617511845e-06,
                1.5534981249291695e-06,
                1.4738988996240646e-05
            ],
            [
                3.535625067794842e-05,
                1.0677026154619133e-06,
                3.2887506334560605e-06,
                4.222833947728508e-06,
                4.450851580321588e-07,
                5.043474081684252e-07,
                6.144175331009535e-06,
                9.422449307915373e-07,
                0.0002611902429776032,
                2.144495863614743e-05
            ],
            [
                7.338209804172883e-07,
                6.144176065940129e-06,
                1.4738978454950406e-05,
                1.2098652506548698e-06,
                1.067702615330819e-06,
                0.00015843627216098136,
                4.222833443968609e-06,
                1.473898371722997e-05,
                3.1201922520397544e-05,
                4.785095065045315e-06
            ],
            [
                7.889264465986113e-06,
                4.222833444168322e-06,
                5.4222170229803784e-06,
                4.0063696899461064e-05,
                6.144177531381426e-06,
                2.4300249406550775e-05,
                5.8291286290217195e-05,
                3.5356254898252494e-05,
                1.7603436328289897e-06,
                1.5534975692471157e-06
            ],
            [
                1.1478765384054893e-05,
                1.6701425821573757e-05,
                1.0129992185539456e-05,
                7.88926164421493e-06,
                0.0001398220568780067,
                4.539785234971499e-05,
                0.00033535022278438935,
                2.90231233035854e-06,
                5.8291265499980624e-05,
                2.9023109469842055e-06
            ],
            [
                7.889263524960312e-06,
                1.6701415868193372e-05,
                8.315278293407441e-07,
                1.7603436329714805e-06,
                6.47595029750346e-07,
                4.222834450820197e-06,
                1.3007133112662637e-05,
                5.422218968221128e-06,
                8.939695235243779e-06,
                1.1478765386894505e-05
            ],
            [
                0.00010889693515967489,
                5.422220261070644e-06,
                2.2603237587774727e-06,
                7.88926070328992e-06,
                8.315282258756395e-07,
                1.012999460108057e-05,
                1.892515273086448e-05,
                2.9023116390104826e-06,
                2.7535687803514833e-05,
                2.5612819051373276e-06
            ],
            [
                2.144495608105136e-05,
                1.3007123806876143e-05,
                4.450851049890802e-07,
                2.902311292371731e-06,
                1.6701421840318107e-05,
                4.539785239182798e-05,
                3.5356254903911806e-05,
                4.539787943778038e-05,
                1.8925145982350146e-05,
                2.5612819052654485e-06
            ],
            [
                0.952574130693245,
                0.9999945777785698,
                0.9999938558247796,
                0.9999967112509486,
                0.999995777165207,
                0.9999546021170129,
                0.9999810748605258,
                0.9999930377430226,
                0.9999038975943225,
                0.9999945777792973
            ],
            [
                3.4663253846316044e-07,
                5.422220262505697e-06,
                4.2228339475595195e-06,
                4.5397879448184774e-05,
                6.475951069896949e-07,
                3.0590211752039556e-07,
                1.6701429803316423e-05,
                3.059021539864825e-07,
                5.422218323093458e-06,
                2.56128129449109e-06
            ],
            [
                0.4378234991142019,
                0.9999599362937921,
                0.99995460213158,
                0.5926665999540697,
                0.9525741229516211,
                1.637377643221385e-07,
                3.927862939075802e-07,
                0.9999646437350297,
                3.4663249712890574e-07,
                0.9998601778760643
            ],
            [
                1.8925150492616083e-05,
                1.4738981970312625e-05,
                3.120191137012976e-05,
                1.3007130012980722e-05,
                0.00015843615960801365,
                4.222833444429485e-06,
                2.144495863482118e-05,
                0.0001088969092152976,
                1.892515725665725e-05,
                2.561282515988704e-06
            ],
            [
                0.9999921107346096,
                0.9999599363211221,
                0.6513548511303338,
                0.9999967112521398,
                0.8354835371034368,
                0.9999810748427972,
                0.9998766054605682,
                0.9999898700080054,
                0.9998415637235444,
                0.9840936061889035
            ],
            [
                1.67014238321306e-05,
                1.6373764720752638e-07,
                3.4663253845638233e-07,
                1.9947290079889487e-06,
                1.1478766755985128e-05,
                1.892514823364471e-05,
                0.0011695103813267023,
                2.9023133687786197e-06,
                2.5612815999679353e-06,
                5.715003107619008e-07
            ],
            [
                1.6701417859519093e-05,
                6.144177531381426e-06,
                2.5612834318583854e-06,
                4.222833947121688e-06,
                1.1478770856952364e-05,
                1.553498495308628e-06,
                1.4738985481520185e-05,
                1.067702742726318e-06,
                4.2228334445370225e-06,
                5.422217676486429e-06
            ],
            [
                4.78509449410676e-06,
                1.6701419848961534e-05,
                6.962257078249291e-06,
                1.670142382067764e-05,
                1.3709572068179446e-06,
                1.4738983726908257e-05,
                8.939700564890901e-06,
                2.2603237589028734e-06,
                7.88926634687567e-06,
                2.1444943285915917e-05
            ],
            [
                4.006367784956852e-05,
                1.300713466316634e-05,
                6.962258738827909e-06,
                1.3007130011655787e-05,
                1.6701429787579988e-05,
                5.422218322457301e-06,
                8.939700566143004e-06,
                2.144494328404357e-05,
                3.5356238010608196e-05,
                1.6701427805275476e-05
            ],
            [
                0.9999910603069031,
                0.9999339478321082,
                0.9999756997616174,
                0.9399133557169235,
                0.999933947880322,
                0.9999038975802887,
                5.715005151353432e-07,
                0.9999898700116968,
                0.9999756997706711,
                0.999998446502619
            ],
            [
                2.561283430914951e-06,
                1.4738978454172926e-05,
                1.3007130013288297e-05,
                2.5612825157045092e-06,
                9.42244481461251e-07,
                3.28875024125221e-06,
                2.7535681245588654e-05,
                6.9622570786798724e-06,
                8.939693102865466e-06,
                4.222835457280279e-06
            ],
            [
                0.18242552380635635,
                0.20181321505933408,
                5.04347528438253e-07,
                0.7981867801399695,
                2.26032537546132e-06,
                0.9999980052710027,
                1.20986611609532e-06,
                0.5926665999540698,
                0.7981867873410141,
                4.4508521106168286e-07
            ],
            [
                1.6701417859944398e-05,
                1.6701421825979123e-05,
                1.67014178576052e-05,
                3.5356250658398075e-05,
                8.939697368110433e-06,
                1.8925145980181433e-05,
                8.93969310367852e-06,
                4.2228349543420954e-06,
                2.430025231469984e-05,
                3.2887478891487563e-06
            ],
            [
                3.927862938956128e-07,
                2.102432658440048e-07,
                1.994729721469003e-06,
                4.4508526416286326e-07,
                2.6995774527184606e-07,
                1.0129995809763438e-05,
                2.1444950963097686e-05,
                8.939699500164542e-06,
                3.9278615343222713e-07,
                1.8553907971682908e-07
            ],
            [
                1.2098662603862553e-06,
                1.670141786036971e-05,
                3.7266388394569345e-06,
                2.9023123310580418e-06,
                2.1444945844014022e-05,
                2.1444950959196957e-05,
                2.1444945842219688e-05,
                6.962254588585202e-06,
                7.889259762666377e-06,
                2.4300246507772637e-05
            ],
            [
                1.1478764019787597e-05,
                1.1478768124324254e-05,
                2.430023493564795e-05,
                2.4300252285704095e-05,
                3.2887482811220126e-06,
                1.370957370247318e-06,
                6.144176799099397e-06,
                5.043475885453117e-07,
                6.144177531381426e-06,
                4.0063696945516495e-05
            ],
            [
                1.3007123806876143e-05,
                2.1444950966608343e-05,
                1.0129992186202796e-05,
                7.889263525893087e-06,
                3.2887486729876365e-06,
                1.3007130012980722e-05,
                1.0129989767032304e-05,
                1.012999097799944e-05,
                1.6701427806612162e-05,
                1.1478764018012839e-05
            ],
            [
                0.9999251537733824,
                0.817574478416099,
                1.553498495091042e-06,
                3.927862470816829e-07,
                0.9999646437578288,
                0.9525741239613982,
                5.42221767672807e-06,
                0.6791787056691698,
                0.24508500761839527,
                1.2098659719122375e-06
            ],
            [
                3.5356254902111115e-05,
                4.006369214992195e-05,
                1.4738983726184394e-05,
                0.00017952802886397372,
                5.422220908481809e-06,
                1.670142980112912e-05,
                1.8925150479534963e-05,
                4.5397873946245314e-05,
                4.785094493184135e-06,
                1.892514823426434e-05
            ],
            [
                2.144495096387783e-05,
                4.5397868612593344e-05,
                1.300713311112477e-05,
                2.144495352474637e-05,
                1.3007131563507714e-05,
                2.144495606626759e-05,
                7.889266344766165e-06,
                8.481103073675937e-05,
                9.422447061576466e-07,
                1.670142781025767e-05
            ],
            [
                1.4738981971813965e-05,
                5.422219615829396e-06,
                1.4738976690741464e-05,
                6.144174601309452e-06,
                8.939693095613033e-06,
                1.1478764013398468e-05,
                1.4738987239295859e-05,
                2.7535694354731078e-05,
                7.889259763469998e-06,
                7.484620890377677e-05
            ],
            [
                2.6995774527184606e-07,
                1.0129988562901417e-05,
                1.7603425834564988e-06,
                6.962257909121104e-06,
                1.8553907971682908e-07,
                6.14417753110761e-06,
                6.144175334015912e-06,
                5.422218969306048e-06,
                3.7266388392671313e-06,
                1.370956716529941e-06
            ],
            [
                0.9999869928734104,
                0.8933094067644466,
                0.9999970976885001,
                0.9999810748495913,
                9.422448185015797e-07,
                0.999978555045107,
                1.5534981248528732e-06,
                0.9999930377421744,
                0.9525741248028791,
                1.067703251797684e-06
            ],
            [
                3.2887478889513447e-06,
                1.4738988997768797e-05,
                2.430023493052066e-05,
                0.0001088969610644462,
                1.209866260246509e-06,
                5.82912863088776e-05,
                1.1478772230407462e-05,
                8.939694170940841e-06,
                8.481106143026193e-05,
                1.2098659718847284e-06
            ],
            [
                1.1478764019996392e-05,
                1.147877222879974e-05,
                2.1444948403750736e-05,
                2.1444940743225995e-05,
                1.3007126909159127e-05,
                6.962258739068529e-06,
                1.0129987355988324e-05,
                0.00010889692178502596,
                4.5397879206902045e-05,
                6.605214456631139e-05
            ],
            [
                1.3007125357804606e-05,
                3.535625492217596e-05,
                4.22283394762097e-06,
                4.22283394762097e-06,
                1.1478768124324254e-05,
                2.9023112931213857e-06,
                3.535623805163821e-05,
                1.6701425824733193e-05,
                1.7603432130222817e-06,
                6.605213678458984e-05
            ],
            [
                1.4738976694494812e-05,
                7.484620021677718e-05,
                0.00015843619557580807,
                1.9947301968056346e-06,
                4.5397890156614e-05,
                1.4738987238035806e-05,
                3.1201922511884416e-05,
                1.6701417853595148e-05,
                0.0002959571616309937,
                5.829125847900465e-05
            ],
            [
                1.2098658276290391e-06,
                1.1478766756214804e-05,
                1.3709578605355551e-06,
                2.2603242977308917e-06,
                8.93969417199781e-06,
                1.7603440525925705e-06,
                3.72664017246987e-06,
                2.4300234922476113e-05,
                1.0677033790475986e-06,
                3.2887490652810324e-06
            ],
            [
                3.059021539664509e-07,
                5.144223815074485e-05,
                2.2603248365343694e-06,
                1.7603432132784448e-06,
                7.889262584666493e-06,
                2.902313022305958e-06,
                1.4738981968060613e-05,
                1.892515499864894e-05,
                2.4300243618542217e-05,
                1.8925155002710973e-05
            ],
            [
                7.889265406294507e-06,
                2.7535684514885004e-05,
                1.994730672439908e-06,
                1.8925145963175983e-05,
                1.8925143719695944e-05,
                1.6701419850389357e-05,
                1.2098662603356388e-06,
                1.3007125358230479e-05,
                3.120192249167993e-05,
                5.422219615829396e-06
            ],
            [
                6.9622537587775775e-06,
                2.144494072680393e-05,
                6.962257077413455e-06,
                3.726638839656906e-06,
                1.1478773595009805e-05,
                2.7535684521195802e-05,
                4.785093922776592e-06,
                4.222832437186393e-06,
                0.00026119039848170977,
                2.902311292920774e-06
            ],
            [
                0.8807970670261976,
                0.029312229320413406,
                0.9999038975655558,
                0.9994472212840638,
                0.9997388097042048,
                0.9149009497722477,
                0.18242552602881168,
                0.9999485577812696,
                0.37754066879814546,
                0.2689414213699951
            ],
            [
                0.9999982396572067,
                0.9999756997593048,
                0.9999980052693286,
                0.9999992661791944,
                0.999992110740244,
                0.9999977396765138,
                0.9999962733602936,
                0.9999952149055099,
                0.9999977396751655,
                0.9999938558224919
            ],
            [
                8.93969417199781e-06,
                3.53562590871736e-05,
                3.1201900191715896e-05,
                8.315279284657531e-07,
                3.120191508321514e-05,
                4.785093353626844e-06,
                4.5397890204837524e-05,
                6.962258738574625e-06,
                3.5356254910985954e-05,
                4.2228324372555256e-06
            ],
            [
                3.120192622145237e-05,
                1.1478770853110533e-05,
                3.288748280837859e-06,
                3.2887486722518283e-06,
                1.9947301966568707e-06,
                2.902310946110488e-06,
                5.422220907909759e-06,
                1.5534984952662413e-06,
                2.2603234892298883e-06,
                1.994730671409446e-06
            ],
            [
                0.6513548511303338,
                0.9999994956527728,
                0.7772998611746912,
                0.9924227604409648,
                0.6791787056691697,
                0.9999921107366666,
                0.6513548782017745,
                0.9999251537919315,
                0.24508500761839527,
                0.999993037743801
            ],
            [
                0.8807970889295663,
                0.9999869928669676,
                0.9999869928716397,
                0.9999945777816845,
                0.9999957771665596,
                0.9999970976866818,
                0.9999977396746362,
                0.9999952149049457,
                0.9999974387172063,
                0.9999962733613176
            ],
            [
                2.26032348933062e-06,
                3.7266392835764795e-06,
                2.3823699517421218e-07,
                5.04347588540266e-07,
                6.9622579092224155e-06,
                8.939693106182721e-06,
                1.0129994599072117e-05,
                3.726640172290235e-06,
                2.3823682478845333e-07,
                1.7603427935678977e-06
            ],
            [
                2.9023119850527192e-06,
                2.9023123308072772e-06,
                0.0004878572136367961,
                2.2603234890695403e-06,
                6.605215251574962e-05,
                0.00026119033261550297,
                0.00013982203982978414,
                2.753569107391384e-05,
                1.8925152733687252e-05,
                0.002800927523790692
            ],
            [
                3.5356267539488744e-05,
                2.430024072648329e-05,
                3.2887490649221017e-06,
                1.0129992185299915e-05,
                4.53978848619353e-05,
                7.484622702869579e-05,
                2.144494072867628e-05,
                4.7850950646797465e-06,
                2.4300243611116483e-05,
                1.3007123809644304e-05
            ],
            [
                1.0129987356191011e-05,
                2.1444950968441685e-05,
                1.300712381094558e-05,
                1.760342793583908e-06,
                1.6701415866735174e-05,
                2.2603245672025095e-06,
                4.222833947897496e-06,
                2.7535687788789623e-05,
                1.1478765388105516e-05,
                6.144172404587612e-06
            ],
            [
                2.430025228977057e-05,
                2.7535691091443854e-05,
                3.1201926179794786e-05,
                7.484626266158608e-05,
                2.902311293034278e-06,
                6.962256249517824e-06,
                3.535625067794842e-05,
                4.539786314550164e-05,
                0.999995214903278,
                2.4300246504236573e-05
            ],
            [
                2.753570093009022e-05,
                1.300712380408432e-05,
                7.889262584666493e-06,
                1.0129990978847043e-05,
                8.939695237162584e-06,
                5.144220746454321e-05,
                7.8892625830162e-06,
                1.8925143723620274e-05,
                1.4738976688918406e-05,
                3.726638395215427e-06
            ],
            [
                1.473898547706978e-05,
                0.0001233946027539403,
                5.829129324249228e-05,
                2.1444940737257882e-05,
                5.4222215537823875e-06,
                9.610242625969935e-05,
                6.605214437024256e-05,
                1.3007123810306773e-05,
                3.120191877791261e-05,
                5.144220744957233e-05
            ],
            [
                0.00048785707319687344,
                2.4300243618542217e-05,
                8.481107134469015e-05,
                6.605216036234875e-05,
                1.1478769490053603e-05,
                4.006370645013473e-05,
                3.12019225022362e-05,
                1.3007123806876143e-05,
                5.829125151613121e-05,
                2.753569108573408e-05
            ],
            [
                1.0129990973134934e-05,
                1.1478770854906172e-05,
                1.1478769492642663e-05,
                0.00013982210728420155,
                1.0129989769464556e-05,
                1.1478768124324254e-05,
                1.3007128461838766e-05,
                0.00013982208917605316,
                0.0001233945892201689,
                7.889263523453522e-06
            ],
            [
                1.7603425836870455e-06,
                1.7603438426491283e-06,
                7.889262584508638e-06,
                6.144176064364297e-06,
                3.120191134459038e-05,
                4.53978523645784e-05,
                2.561281294644835e-06,
                6.962256249112569e-06,
                7.338208930355202e-07,
                1.994729483261914e-06
            ],
            [
                2.2603253755476615e-06,
                5.422220908634683e-06,
                5.422219615829396e-06,
                7.338211554231243e-07,
                5.144220137401424e-05,
                6.144174601097106e-06,
                1.6701419846288166e-05,
                1.2098659718539182e-06,
                3.1201922498830954e-05,
                1.5534975693036317e-06
            ],
            [
                2.753570421361326e-05,
                2.7535697645265342e-05,
                6.144176066353646e-06,
                1.3007130014873483e-05,
                8.481102076186704e-05,
                4.222834954514924e-06,
                9.422449307358345e-07,
                2.7535691068003722e-05,
                6.605216033495677e-05,
                2.4300232009732255e-05
            ],
            [
                3.7266397278180926e-06,
                7.88926446470893e-06,
                1.6701425805958843e-05,
                1.1478772221429265e-05,
                6.962256248871951e-06,
                1.994729245555571e-06,
                6.962253759043525e-06,
                4.5397873826016834e-05,
                1.4738981957765705e-05,
                2.4300240681044865e-05
            ],
            [
                1.5534975693707442e-06,
                5.043472278159142e-07,
                3.288749065167371e-06,
                4.7850944942634305e-06,
                1.7603430034439723e-06,
                5.422220908634683e-06,
                5.144223199845732e-05,
                1.3007128463069061e-05,
                1.0129990979031306e-05,
                NaN
            ],
            [
                3.5356242264223526e-05,
                1.0129989771823107e-05,
                2.430024940319151e-05,
                1.6701419850845044e-05,
                1.012999580884213e-05,
                4.222831934052698e-06,
                4.785095065093186e-06,
                1.147876949310201e-05,
                1.1478770861650256e-05,
                5.1442207514695673e-05
            ],
            [
                7.484625378235853e-05,
                1.0129995809929273e-05,
                1.7603434231097403e-06,
                4.4508526412562144e-07,
                3.120190392137216e-05,
                1.5534973841592143e-06,
                2.1444950968441685e-05,
                2.4300249418927004e-05,
                NaN,
                4.222834451215781e-06
            ],
            [
                0.999996273361079,
                0.999993037744916,
                0.7772998560157665,
                0.9999832985822779,
                0.9999832985702207,
                0.9999869928737553,
                0.43782349911420193,
                0.9999546021347433,
                0.7772998611746911,
                NaN
            ],
            [
                6.962256249327861e-06,
                8.93969736942758e-06,
                1.0129992186939844e-05,
                8.939696304002375e-06,
                2.1444940738662144e-05,
                1.4738988998787566e-05,
                1.8925143726890553e-05,
                1.5534984953298217e-06,
                1.473897670007122e-05,
                3.726639283901856e-06
            ],
            [
                1.7603438427852151e-06,
                2.4300252310279753e-05,
                4.785095633477187e-06,
                8.939697368110433e-06,
                1.1478773597870298e-05,
                3.535626755762428e-05,
                1.5534975692866768e-06,
                5.71500719531729e-07,
                5.422217676486429e-06,
                2.260324567177841e-06
            ],
            [
                5.829129330780371e-05,
                2.753569108573408e-05,
                2.430023781444595e-05,
                8.93969523573161e-06,
                5.422218968083048e-06,
                1.300712845966209e-05,
                3.726640172385136e-06,
                1.892514371356847e-05,
                1.670142183825232e-05,
                7.889266343575084e-06
            ],
            [
                4.222832940423847e-06,
                8.93969630362837e-06,
                2.4300240715698294e-05,
                1.3007134657984903e-05,
                2.1444958609544435e-05,
                4.222831932888989e-06,
                1.0129989768616954e-05,
                6.144176065012512e-06,
                2.260325106045111e-06,
                1.8925154992246077e-05
            ],
            [
                4.7850933535659155e-06,
                1.0129990975862006e-05,
                8.315283250006957e-07,
                3.059022269206168e-07,
                1.4738987240100149e-05,
                3.9278624706864377e-07,
                3.4663274506641133e-07,
                1.7603427936079236e-06,
                1.2098655392222467e-06,
                1.9947299591826594e-06
            ],
            [
                3.120192252686752e-05,
                0.0010322309629280896,
                1.0129992186774007e-05,
                3.535626755260807e-05,
                8.939700564890901e-06,
                4.785093923768848e-06,
                1.0129990977759901e-05,
                2.7535684505068197e-05,
                6.9622537587775775e-06,
                6.962259568230874e-06
            ],
            [
                1.4738988997768797e-05,
                7.889262585541864e-06,
                4.539786863059458e-05,
                2.1444950969026795e-05,
                1.8925148238291944e-05,
                4.006368261266023e-05,
                1.012998977108606e-05,
                2.1444956059090247e-05,
                1.9947304347570075e-06,
                6.962257909121104e-06
            ],
            [
                0.047425869306754964,
                0.9999910602994379,
                0.9999852610199829,
                0.9999910603026411,
                0.8519528000888387,
                9.42244593735743e-07,
                0.9999852610128105,
                0.9998204719755294,
                0.00043055701218405344,
                0.7549149868676283
            ],
            [
                2.7535684455583485e-05,
                1.0677026154279257e-06,
                1.892515048820981e-05,
                1.89251572498413e-05,
                2.4300246520590875e-05,
                8.939699500164542e-06,
                3.535626332111248e-05,
                4.539786862564012e-05,
                6.605213677497863e-05,
                7.484620926480483e-05
            ],
            [
                0.9997694932329554,
                0.999989870005441,
                0.5621765008857982,
                0.00037998456752749596,
                0.9999898700042266,
                1.99472900796355e-06,
                0.9999869928700051,
                0.9999898700078825,
                6.144176796221545e-06,
                0.5312093733737562
            ],
            [
                1.99472995920443e-06,
                6.144176797115634e-06,
                5.4222183231674305e-06,
                1.8925143714394646e-05,
                1.0129992184268048e-05,
                0.0001233945889939477,
                6.962254588977791e-06,
                3.7266410608245674e-06,
                1.670142980112912e-05,
                1.3007130012673148e-05
            ],
            [
                4.7850939230116e-06,
                1.6701425821573757e-05,
                3.1201915063805214e-05,
                2.430024072091399e-05,
                0.00010889690880650018,
                1.3007130012010681e-05,
                2.4300234925658572e-05,
                1.8925143714394646e-05,
                3.535625909386188e-05,
                4.006367783047594e-05
            ],
            [
                3.726639727940109e-06,
                6.962257079376403e-06,
                2.5612822106654943e-06,
                1.8925148238808306e-05,
                4.785094494019719e-06,
                1.8925148232267744e-05,
                1.5534975693488444e-06,
                2.4300252313904224e-05,
                2.4300249421225448e-05,
                1.3709578604831862e-06
            ],
            [
                1.8925143720384422e-05,
                3.12019187926687e-05,
                6.1441724019276964e-06,
                8.939694170729447e-06,
                NaN,
                6.9622537587775775e-06,
                1.9947301968382903e-06,
                1.670142383015595e-05,
                0.00020342689950907182,
                4.539785776395774e-05
            ],
            [
                0.9999982396559496,
                0.9999952149072279,
                0.9999982396565775,
                0.9999989322973851,
                0.9999485577987787,
                0.9999989322975131,
                0.9999984465015053,
                0.9999898700066382,
                0.9999992661789321,
                0.9999910603037147
            ],
            [
                3.5356254919217684e-05,
                5.144219521911119e-05,
                4.785092782779884e-06,
                7.484626282603639e-05,
                6.962257908348587e-06,
                4.539785234971499e-05,
                0.0015011822703478563,
                4.006370166911356e-05,
                5.829128633093081e-05,
                6.605215247346026e-05
            ],
            [
                0.9998911030844722,
                NaN,
                0.9999996940977367,
                0.9999945777797425,
                0.9999987901338846,
                0.9999967112493715,
                0.999999428499349,
                0.9999970976872034,
                0.9999898700126797,
                NaN
            ],
            [
                2.4300246515109972e-05,
                1.300712380455751e-05,
                0.3486451285660856,
                2.4300249420429837e-05,
                0.7549149868676284,
                0.0013250222109422052,
                4.0063706471413514e-05,
                1.3007125362820425e-05,
                1.4738981968864903e-05,
                3.535624645738762e-05
            ]
        ]
    },
    {
        "q_id": "8216_mmlu_math",
        "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": [
            [
                0.8670357683915538,
                6.605216032919004e-05,
                3.1201926219749737e-05,
                1.1478768117434013e-05,
                2.144495605448738e-05,
                2.7535694360340682e-05,
                4.006369214992195e-05,
                4.006371121133516e-05,
                7.484620024237041e-05,
                8.481103112301959e-05
            ],
            [
                3.120190388198478e-05,
                1.6701429796754513e-05,
                3.1201918798457626e-05,
                1.3007134659924986e-05,
                1.670141785651155e-05,
                7.484624477679936e-05,
                1.4738985454496043e-05,
                2.43002465110435e-05,
                7.889261643899223e-06,
                1.3007133110320344e-05
            ],
            [
                6.144177529855884e-06,
                1.3007125356006484e-05,
                8.939698433584547e-06,
                3.7266410607194972e-06,
                1.4738987229134998e-05,
                2.1444956070870452e-05,
                3.120191879107958e-05,
                3.1201922508819695e-05,
                3.1201900190126774e-05,
                2.7535684488840414e-05
            ],
            [
                1.3007128456065844e-05,
                3.120190763491069e-05,
                1.6701429803316423e-05,
                1.14787681240737e-05,
                1.1478765386330758e-05,
                1.0129988563546333e-05,
                3.120191128409043e-05,
                1.3007125360146898e-05,
                4.006370170788174e-05,
                8.939699499026267e-06
            ],
            [
                1.4738981957765705e-05,
                2.4300252304268445e-05,
                1.670142979608617e-05,
                7.889265405333033e-06,
                8.939696303010449e-06,
                6.96225956921868e-06,
                1.892514823488397e-05,
                1.4738976697631541e-05,
                4.22283545795623e-06,
                8.93969843377968e-06
            ],
            [
                1.4738976695459959e-05,
                5.422220262264056e-06,
                1.1478769490053603e-05,
                2.4300249381886717e-05,
                2.430024939965545e-05,
                4.7850944943330625e-06,
                1.3007130010117919e-05,
                7.88925976316864e-06,
                1.0677033791437343e-06,
                4.785096205651846e-06
            ],
            [
                6.144173136243255e-06,
                1.3007133113017532e-05,
                1.0129994600638342e-05,
                6.144174601410037e-06,
                1.0129989767363975e-05,
                1.9947294834469616e-06,
                1.8925141465820123e-05,
                0.0002611902426508182,
                1.3007126911643378e-05,
                8.939700564679507e-06
            ],
            [
                4.0063692129517645e-05,
                3.120192623836512e-05,
                1.0129994600638342e-05,
                4.539787933836066e-05,
                0.9046505331728752,
                3.5356263303877296e-05,
                4.0063692142343215e-05,
                1.0129995806612563e-05,
                1.8925148223661747e-05,
                2.7535687788789623e-05
            ],
            [
                4.5397857592863436e-05,
                1.3007125359413455e-05,
                4.0063687331300266e-05,
                2.4300234900640922e-05,
                1.8925152744771773e-05,
                2.9023130221686978e-06,
                3.120192247601577e-05,
                1.8925143711847272e-05,
                2.753570421601738e-05,
                3.535625068386498e-05
            ],
            [
                6.605214457784486e-05,
                4.006369215458579e-05,
                0.0003353500256990463,
                2.7535684522397864e-05,
                5.422218969128516e-06,
                0.9241418278134569,
                5.8291286115912004e-05,
                0.9399133534026292,
                3.53562591336057e-05,
                2.1444940733201126e-05
            ],
            [
                1.892515274194901e-05,
                7.889262582341733e-06,
                0.00017952800690743877,
                1.3007131561047124e-05,
                2.1444956071728615e-05,
                3.120191872978506e-05,
                4.006370172318498e-05,
                1.4738981964843453e-05,
                0.00026119033006201934,
                0.00010889688283360843
            ],
            [
                3.535626332509972e-05,
                1.3007125360146898e-05,
                4.539786315574087e-05,
                1.1478772225271098e-05,
                1.3007123810306773e-05,
                2.1444948406091176e-05,
                3.5356250701614645e-05,
                3.535625487510076e-05,
                1.4738987238035806e-05,
                1.473898196763166e-05
            ],
            [
                1.473898723508674e-05,
                4.785096775842062e-06,
                1.1478764018827141e-05,
                1.0129994600159262e-05,
                2.144495863201265e-05,
                8.939700566435704e-06,
                1.1478772229300848e-05,
                2.1444940737257882e-05,
                1.5534981249023245e-06,
                4.785092783210732e-06
            ],
            [
                9.610240313954919e-05,
                2.1444948403750736e-05,
                1.6701419838268058e-05,
                6.144172403470001e-06,
                1.8925143721761383e-05,
                6.60521444778882e-05,
                1.30071253513219e-05,
                5.829127935151415e-05,
                4.006370171239984e-05,
                6.9622554171645e-06
            ],
            [
                2.7535694330088887e-05,
                5.1442219658328595e-05,
                1.4738985475943776e-05,
                1.4738985467311063e-05,
                2.4300249391876106e-05,
                4.2228334417410455e-06,
                1.4738985476533587e-05,
                0.00012339458918246535,
                8.481102101484894e-05,
                3.5356250694926364e-05
            ],
            [
                3.535624224094318e-05,
                3.120191507629113e-05,
                0.9525741269907294,
                2.7535681225754707e-05,
                4.006370152599191e-05,
                1.3007133111929193e-05,
                1.0129995807165349e-05,
                4.006369172726139e-05,
                1.4738987222647056e-05,
                7.889260703117714e-06
            ],
            [
                0.999964643732444,
                0.9999869928746538,
                0.9999898700054292,
                0.9999546021478792,
                0.999933947847567,
                0.9999687980829679,
                0.9999339478240733,
                0.9999151889801118,
                0.9999546021423388,
                0.9999038976196115
            ],
            [
                1.0129990974572174e-05,
                8.939695235959266e-06,
                5.422218321993744e-06,
                1.670141586454787e-05,
                4.22283394762097e-06,
                1.6701429803316423e-05,
                6.962254589433702e-06,
                1.0129992180269573e-05,
                2.1444956067203762e-05,
                6.144177530671741e-06
            ],
            [
                2.4300252296223892e-05,
                7.889262583231455e-06,
                2.1444943278894603e-05,
                4.222832940423847e-06,
                6.144173867753695e-06,
                1.3007133107008012e-05,
                3.7266388395620047e-06,
                1.3007134660776729e-05,
                5.422219615750493e-06,
                3.288748280658394e-06
            ],
            [
                5.8291258404363053e-05,
                1.0129988559492579e-05,
                1.8925150458536325e-05,
                4.0063682470121634e-05,
                5.144219517045583e-05,
                1.4738981966291175e-05,
                1.6701423810652505e-05,
                6.144173136455602e-06,
                3.5356238000833036e-05,
                4.5397863104874985e-05
            ],
            [
                1.670141785596473e-05,
                6.605215235043667e-05,
                3.1201915058697335e-05,
                1.1478769492141554e-05,
                1.6701419846288166e-05,
                2.4300249406550775e-05,
                1.4738978452886064e-05,
                2.1444940740066406e-05,
                2.753569108924008e-05,
                1.0129990977520359e-05
            ],
            [
                0.9999546021422945,
                0.40733340004593027,
                0.9999687980812314,
                0.5312093733737563,
                0.9997040428343822,
                0.1824255304737224,
                0.6224593312018546,
                0.9999339478791008,
                0.99995460212094,
                0.9999646437451771
            ],
            [
                1.4738987237124277e-05,
                1.1478768123280277e-05,
                6.962254588724508e-06,
                3.5356246471407274e-05,
                1.892515500388139e-05,
                2.753570418897106e-05,
                1.0129992159632272e-05,
                1.6701421832723305e-05,
                7.88926070328992e-06,
                2.7535697653779924e-05
            ],
            [
                2.1444953507076064e-05,
                1.4738976698006875e-05,
                1.6701415863393463e-05,
                6.9622587372828785e-06,
                5.422219614152703e-06,
                1.4738988994498018e-05,
                1.0129993393319151e-05,
                1.1478764016446877e-05,
                6.962258739169842e-06,
                8.939696303758459e-06
            ],
            [
                4.006370169826257e-05,
                0.00020342692169164077,
                1.8925145981283003e-05,
                5.1442201281194775e-05,
                5.144221973505439e-05,
                8.481108129984348e-05,
                1.0129987354108855e-05,
                9.610238025712225e-05,
                8.481105067667505e-05,
                4.0063677627890424e-05
            ],
            [
                2.1444940738662144e-05,
                4.2228339475595195e-06,
                0.00017952805037124592,
                0.0005527785128252536,
                0.0003799845612373124,
                8.93969523264201e-06,
                1.147876401460948e-05,
                1.3007128462477575e-05,
                6.605217604545803e-05,
                5.829124445529153e-05
            ],
            [
                1.553497754476329e-06,
                2.144494583831896e-05,
                1.1478768121401121e-05,
                7.889264463890957e-06,
                4.539786319570692e-05,
                2.4300234910365097e-05,
                1.3007133103127848e-05,
                6.962257906562937e-06,
                2.5612812944538183e-06,
                6.962254587597396e-06
            ],
            [
                6.962253758017727e-06,
                1.892515725920463e-05,
                1.1478772226356834e-05,
                1.1478764015361142e-05,
                8.93969417150998e-06,
                3.120192623110058e-05,
                2.1444953520182517e-05,
                2.144494329496561e-05,
                2.4300234936443568e-05,
                0.00010889687018941373
            ],
            [
                1.4738987231708724e-05,
                2.430024072091399e-05,
                1.1478772226356834e-05,
                6.144174601309452e-06,
                7.889262584006375e-06,
                7.889266345584138e-06,
                1.6701429804744246e-05,
                2.1444958631232504e-05,
                2.4300249410794055e-05,
                1.3007134661628471e-05
            ],
            [
                2.9023126766305067e-06,
                4.5397868527706764e-05,
                3.535624213264453e-05,
                7.484620024237041e-05,
                4.006368732517898e-05,
                8.939696300376156e-06,
                2.43002523020584e-05,
                2.753569106169292e-05,
                3.535625490018181e-05,
                4.006367773195234e-05
            ],
            [
                4.222832437386106e-06,
                4.785095635017795e-06,
                7.889266345196678e-06,
                6.144175332596544e-06,
                1.8925145962212114e-05,
                4.78509449410676e-06,
                4.785095634121282e-06,
                2.561281599502042e-06,
                3.2887498493325602e-06,
                1.2098658277082653e-06
            ],
            [
                0.00017952804751893327,
                1.3007130012010681e-05,
                7.484620040083068e-05,
                6.605212090542114e-05,
                7.484626280425489e-05,
                4.539785770549502e-05,
                2.430024651882284e-05,
                1.89251527491092e-05,
                9.610246018063617e-05,
                5.829127933751884e-05
            ],
            [
                4.222833444037741e-06,
                2.1444950958338794e-05,
                1.1478764016112805e-05,
                1.3007123809644304e-05,
                3.7266401722360055e-06,
                1.8925145956015793e-05,
                1.7603440516111448e-06,
                4.7850956352353935e-06,
                1.3007126910649678e-05,
                2.4300249415479343e-05
            ],
            [
                6.605216020953037e-05,
                1.300713466316634e-05,
                1.670142781520948e-05,
                2.753569761771817e-05,
                2.902311638205396e-06,
                0.0010322312380677344,
                3.2887506330851655e-06,
                1.1478773596847203e-05,
                8.939693103158165e-06,
                8.939698432446272e-06
            ],
            [
                1.4738983715299675e-05,
                3.120192622644674e-05,
                3.120191877064807e-05,
                6.1441775248378034e-06,
                5.8291251531398806e-05,
                2.1444958625381407e-05,
                1.0129995807699706e-05,
                7.889262584809997e-06,
                3.5356259082286005e-05,
                2.753568451748946e-05
            ],
            [
                1.1478773596575768e-05,
                8.939700564890901e-06,
                1.892515274339482e-05,
                3.120190764058611e-05,
                8.939698433584547e-06,
                1.9947294834469616e-06,
                1.6701425819994037e-05,
                1.3007125361448172e-05,
                6.962257909121104e-06,
                6.144176796422715e-06
            ],
            [
                2.430023492663099e-05,
                3.5356267555952205e-05,
                6.9622570784012604e-06,
                5.144220133658703e-05,
                2.7535697636951104e-05,
                2.144495351940237e-05,
                8.939696301140427e-06,
                5.144223197188398e-05,
                2.753569437476538e-05,
                2.430024941804299e-05
            ],
            [
                3.535626332111248e-05,
                5.144220748250827e-05,
                4.5397863127665544e-05,
                1.4738988994498018e-05,
                1.4738980203985296e-05,
                6.605217594790412e-05,
                2.7535704187167975e-05,
                4.539787936115123e-05,
                0.00010889686936231232,
                2.7535684453379715e-05
            ],
            [
                3.1201918788014855e-05,
                1.1478769491014062e-05,
                6.605216035706259e-05,
                1.3007123808910861e-05,
                2.4300252304268445e-05,
                2.4300237821252875e-05,
                4.539787383097131e-05,
                3.535625911829982e-05,
                6.962253759157502e-06,
                1.1478766756444477e-05
            ],
            [
                1.0129989769722525e-05,
                1.6701429806475863e-05,
                0.00012339458712852086,
                3.5356250608493225e-05,
                1.6701425825492673e-05,
                8.93969630333567e-06,
                3.5356250648880135e-05,
                3.120190390445942e-05,
                8.939700565102295e-06,
                4.5397873994468824e-05
            ],
            [
                7.889263523668778e-06,
                1.670141984792864e-05,
                1.892515049199645e-05,
                8.939696302831578e-06,
                2.753569107391384e-05,
                1.67014178554179e-05,
                5.422217030362759e-06,
                6.9622537584863015e-06,
                6.144176064364297e-06,
                5.422220261948442e-06
            ],
            [
                6.962257908487893e-06,
                3.535626329667452e-05,
                1.1478773593548236e-05,
                4.5397857639435435e-05,
                1.1478769492141554e-05,
                3.535625908948878e-05,
                2.144494328864643e-05,
                8.939694169835089e-06,
                1.012998856048759e-05,
                0.00029595709712646536
            ],
            [
                1.6701427807280505e-05,
                6.962254581075343e-06,
                2.7535691058287085e-05,
                9.61024592339597e-05,
                5.82912863088776e-05,
                3.120192622315499e-05,
                1.670142781025767e-05,
                2.4300246513165137e-05,
                6.605217594790412e-05,
                2.4300240719941574e-05
            ],
            [
                2.7535700934898458e-05,
                4.5397868567012224e-05,
                2.144495607640949e-05,
                5.8291244542232006e-05,
                9.610245994431664e-05,
                2.7535684524701807e-05,
                2.9023130228444433e-06,
                0.0013250223247840507,
                2.43002319899303e-05,
                8.481103071331226e-05
            ],
            [
                6.96225541916544e-06,
                1.892514823426434e-05,
                4.006368253745581e-05,
                2.1444943275617995e-05,
                1.8925150469896243e-05,
                4.539785774116719e-05,
                8.939693091287588e-06,
                2.7535704143893865e-05,
                2.753569109254574e-05,
                1.473897669245728e-05
            ],
            [
                5.422217030362759e-06,
                6.962256249429175e-06,
                2.7535687809124434e-05,
                4.785096775842062e-06,
                1.0129987354108855e-05,
                7.889264465555602e-06,
                6.9622537576631295e-06,
                2.2603242972087315e-06,
                1.0129989768616954e-05,
                8.93969736547614e-06
            ],
            [
                9.610244816329906e-05,
                3.5356242264223526e-05,
                1.0129995806612563e-05,
                1.892514597494899e-05,
                4.006367749963485e-05,
                2.1444945854624007e-05,
                3.5356242258821454e-05,
                1.4738987238464762e-05,
                7.889262584508638e-06,
                1.670142780594382e-05
            ],
            [
                4.539786860697828e-05,
                4.222834953896582e-06,
                0.00013982212326844363,
                3.53562506877236e-05,
                3.120191863784327e-05,
                1.3007131563507714e-05,
                0.0001233945444212057,
                2.753569108453202e-05,
                7.484626281841286e-05,
                2.7535681233968765e-05
            ],
            [
                6.605215239608995e-05,
                6.605212091166841e-05,
                0.00012339458910885372,
                7.484620917931251e-05,
                0.0002611903672851254,
                1.670142183983204e-05,
                0.00015843628737751434,
                8.48110105660795e-05,
                1.4738978454950406e-05,
                2.4300249404340734e-05
            ],
            [
                0.0001795279823284515,
                3.1201918807538294e-05,
                4.5397852378781204e-05,
                4.539785778740889e-05,
                1.30071315640992e-05,
                6.60521523571645e-05,
                3.120190392137216e-05,
                1.8925157242612258e-05,
                5.8291286069685086e-05,
                2.144495861531752e-05
            ],
            [
                4.0063696893922756e-05,
                3.535625068000635e-05,
                2.1444943287710254e-05,
                1.4738985457284248e-05,
                6.1441738684354385e-06,
                0.8354835411997897,
                7.889266347004826e-06,
                1.670141984792864e-05,
                5.829127228812649e-05,
                1.994729245722476e-06
            ],
            [
                4.539786860136322e-05,
                4.539785779269366e-05,
                0.00015843629147844053,
                7.484623611811155e-05,
                1.0129995807441742e-05,
                1.3007134665413997e-05,
                0.9996200155174729,
                7.484622716319649e-05,
                2.430024941371131e-05,
                1.4738976694494812e-05
            ],
            [
                2.144495351097679e-05,
                1.8925148224556773e-05,
                2.4300246493981982e-05,
                1.670142781478417e-05,
                1.670141785651155e-05,
                1.8925145974191664e-05,
                8.939694168517944e-06,
                3.1201903906162046e-05,
                3.535623804623613e-05,
                1.1478765386894505e-05
            ],
            [
                8.939698433584547e-06,
                2.1444945847446664e-05,
                7.88925976359915e-06,
                1.8925145968614975e-05,
                6.144173136556186e-06,
                9.610239189829757e-05,
                0.10669059749614015,
                1.892515500388139e-05,
                1.012999460150437e-05,
                6.962259569003389e-06
            ],
            [
                1.4738987237553233e-05,
                5.144220745705777e-05,
                8.481104117750991e-05,
                2.7535681225754707e-05,
                2.43002465110435e-05,
                1.3007131555983986e-05,
                8.481101050931285e-05,
                1.1478764015361142e-05,
                3.535625488616215e-05,
                3.5356246471407274e-05
            ],
            [
                1.3007126910294786e-05,
                1.892515274194901e-05,
                6.144177530548804e-06,
                5.422219615188307e-06,
                1.0129995809247506e-05,
                6.144172403715875e-06,
                1.7603436327425345e-06,
                3.1201922495312196e-05,
                2.4300252311252174e-05,
                1.3007134657984903e-05
            ],
            [
                5.1442201272586515e-05,
                3.120191135560069e-05,
                1.6701423826206655e-05,
                0.00026119020520734006,
                5.1442207381454816e-05,
                1.4738988961200408e-05,
                8.939694170518055e-06,
                2.4300232030064617e-05,
                3.535625487278559e-05,
                1.8925150487521332e-05
            ],
            [
                3.535626755762428e-05,
                1.473898899664279e-05,
                2.753569108453202e-05,
                1.8925143715220825e-05,
                1.8925143719695944e-05,
                8.93969629982328e-06,
                1.3007133107008012e-05,
                2.1444956061196638e-05,
                3.535625067589049e-05,
                2.144495605448738e-05
            ],
            [
                2.4300252315495453e-05,
                3.1201915071864306e-05,
                1.670142382681424e-05,
                1.012998856078241e-05,
                1.0129994600859455e-05,
                8.939693103938694e-06,
                1.0129993392600532e-05,
                1.0129988562164371e-05,
                1.1478773595343877e-05,
                4.785096204868486e-06
            ],
            [
                0.9999599363128631,
                0.5926665999540698,
                0.9999756997592866,
                0.24508501313237172,
                0.9998415637846757,
                0.9999962733598297,
                0.9999151889196294,
                0.9999251537911169,
                0.9999151889392695,
                0.9999832985762005
            ],
            [
                7.889261641904523e-06,
                6.9622579075254155e-06,
                1.6701415860173268e-05,
                2.7535691075316245e-05,
                2.4300240707388545e-05,
                6.14417460073947e-06,
                6.144172404028807e-06,
                4.006370157117288e-05,
                2.1444945806957093e-05,
                1.9947301968673173e-06
            ],
            [
                2.1444945853375776e-05,
                7.889266345957247e-06,
                1.473898899256772e-05,
                4.539785230908836e-05,
                3.1201907631845964e-05,
                1.4738978451438343e-05,
                1.300713311155064e-05,
                2.753569764256071e-05,
                1.8925145972677006e-05,
                3.1201900183543295e-05
            ],
            [
                1.1478769489343698e-05,
                6.144174601309452e-06,
                8.93969843377968e-06,
                1.0129992178648069e-05,
                1.3007131563176482e-05,
                5.422219614951598e-06,
                6.962254587951994e-06,
                1.8925157257345735e-05,
                2.430024359741423e-05,
                1.1478769492141554e-05
            ],
            [
                1.6701427809710842e-05,
                1.6701429802769596e-05,
                0.00017952794256326186,
                1.8925157255280296e-05,
                1.892515499637696e-05,
                1.147876812069122e-05,
                7.484623589103951e-05,
                6.605212022110271e-05,
                2.1444948396573396e-05,
                2.430025230320762e-05
            ],
            [
                7.889263524443698e-06,
                1.8925145962212114e-05,
                1.67014158650947e-05,
                1.6701429785817993e-05,
                2.144494074076854e-05,
                2.4300234912928744e-05,
                8.939698434332555e-06,
                5.829124465207388e-05,
                1.1478766755233466e-05,
                2.2603251060738913e-06
            ],
            [
                2.4300246504236573e-05,
                2.1444948402034417e-05,
                4.006369209745375e-05,
                1.4738983717819781e-05,
                4.006371125185228e-05,
                1.892514597832254e-05,
                1.6701415858775822e-05,
                0.0011695099943000806,
                4.5397879411686836e-05,
                3.120191504553037e-05
            ],
            [
                1.670142581883963e-05,
                1.473897666811412e-05,
                7.889263523238269e-06,
                5.422220908116881e-06,
                4.785093353013212e-06,
                6.144176064185479e-06,
                4.785095635017795e-06,
                7.889264466115267e-06,
                5.422217676299034e-06,
                1.670141983085553e-05
            ],
            [
                1.3007131563507714e-05,
                0.00012339461718362097,
                2.4300246520590875e-05,
                2.1444940732342966e-05,
                2.7535700934898458e-05,
                5.829125851250855e-05,
                9.610243705208781e-05,
                2.7535684479824982e-05,
                7.484621821481694e-05,
                3.53562422342549e-05
            ],
            [
                0.0001233945446133141,
                7.889261642578988e-06,
                1.67014178554179e-05,
                2.1444945851269378e-05,
                4.785093351255006e-06,
                5.422220908314139e-06,
                3.726639727750306e-06,
                2.7535697643963113e-05,
                6.144176797585032e-06,
                4.5397879378987325e-05
            ],
            [
                1.6701427812931038e-05,
                1.4738978453743973e-05,
                0.0002305067917669261,
                4.006368737677271e-05,
                2.75356878022126e-05,
                3.5356246473207964e-05,
                1.6701419850389357e-05,
                2.4300237810821485e-05,
                7.889265406294507e-06,
                2.7535704217219437e-05
            ],
            [
                4.539786316564981e-05,
                3.5356242266024216e-05,
                1.3007134657464394e-05,
                4.222831933864508e-06,
                1.8925152742706337e-05,
                1.4738987237124277e-05,
                1.3007130012673148e-05,
                1.0129990977004428e-05,
                1.0129993391236997e-05,
                1.1478764013398468e-05
            ],
            [
                1.1478769489719528e-05,
                4.5397890190965e-05,
                3.120192238248485e-05,
                2.4300249415479343e-05,
                1.3007128456539035e-05,
                1.0129992185299915e-05,
                2.430023492353693e-05,
                3.120191133017482e-05,
                6.144174598794825e-06,
                5.144223195167328e-05
            ],
            [
                1.892515499637696e-05,
                6.144173868670137e-06,
                4.785096775171854e-06,
                1.3709570433387154e-06,
                3.288750241410738e-06,
                6.9622562481627565e-06,
                7.889259762666377e-06,
                1.0129994601688632e-05,
                1.3007133112662637e-05,
                1.3007133111929193e-05
            ],
            [
                2.144494328201519e-05,
                1.670142781432848e-05,
                1.1478772226690907e-05,
                1.8925141461620395e-05,
                4.539786858616951e-05,
                2.144495349943063e-05,
                2.430023782010365e-05,
                6.605216026911993e-05,
                3.120192247601577e-05,
                1.6701421834728333e-05
            ],
            [
                4.222832437186393e-06,
                6.9622587372828785e-06,
                7.889259762494174e-06,
                7.889260703619978e-06,
                1.3007131563815288e-05,
                3.7266379509129646e-06,
                3.2887494571676872e-06,
                1.4738981963234875e-05,
                5.8291258338203444e-05,
                1.3007130010922344e-05
            ],
            [
                1.3007128453983806e-05,
                1.89251437091622e-05,
                3.726639727994339e-06,
                1.8925157249015125e-05,
                1.6701427806612162e-05,
                5.422218321855664e-06,
                2.753570420970657e-05,
                7.889266345584138e-06,
                2.9023130227124616e-06,
                8.939697369004791e-06
            ],
            [
                8.939697369785323e-06,
                4.785093353274332e-06,
                1.3007130010922344e-05,
                1.473898722977843e-05,
                1.3007130009739366e-05,
                5.144221971259806e-05,
                4.785095633616451e-06,
                1.994729245878497e-06,
                3.5356267547205986e-05,
                1.892515724633005e-05
            ],
            [
                6.605215219569605e-05,
                1.4738980210258757e-05,
                1.147876675162131e-05,
                3.535625486326765e-05,
                7.889263521487523e-06,
                1.4738980204575109e-05,
                0.0005527786171463282,
                6.962257069029765e-06,
                8.939696297286554e-06,
                1.3007125358230479e-05
            ],
            [
                1.0129995808418327e-05,
                6.144173135896795e-06,
                7.88926446470893e-06,
                4.7850939232204965e-06,
                6.9622554187981796e-06,
                7.88926540679677e-06,
                2.7535684501962883e-05,
                3.7266388386231563e-06,
                1.3709576968081196e-06,
                1.892514597770291e-05
            ],
            [
                8.93969949923766e-06,
                0.0011695101952928077,
                8.481107159026786e-05,
                0.00010889689484559475,
                1.7603440525205244e-06,
                4.006370168310508e-05,
                6.605215986833208e-05,
                1.4738983722270186e-05,
                3.535624646356141e-05,
                7.484623515046881e-05
            ],
            [
                2.9023112925670636e-06,
                1.8925157255968775e-05,
                1.0129995804364571e-05,
                1.6701421837705495e-05,
                4.222832436379863e-06,
                1.760344052632596e-06,
                4.539785235863304e-05,
                1.6701415865641523e-05,
                3.2887486728201357e-06,
                4.5397879417962496e-05
            ],
            [
                6.144175333155351e-06,
                1.1478768123551712e-05,
                6.144173136243255e-06,
                5.422217029006611e-06,
                1.670141585731762e-05,
                3.535626755428014e-05,
                7.88926164421493e-06,
                8.939694169835089e-06,
                2.1444950953735936e-05,
                7.33820980469346e-07
            ],
            [
                6.1441767990323395e-06,
                2.561281293950654e-06,
                4.006367780569929e-05,
                3.120192250564146e-05,
                2.144495607336692e-05,
                6.144172403470001e-06,
                2.4300249408672413e-05,
                1.4738976678033687e-05,
                1.1478769489719528e-05,
                1.6701429795417824e-05
            ],
            [
                1.892515274614874e-05,
                4.222832436687113e-06,
                2.7535704212311033e-05,
                1.0129990977262395e-05,
                1.0129995807939249e-05,
                1.1478764015361142e-05,
                1.4738978454950406e-05,
                4.2228339475595195e-06,
                1.0129987355785634e-05,
                6.144172401547709e-06
            ],
            [
                1.6701427815999337e-05,
                3.1201900203407254e-05,
                2.144494329769612e-05,
                1.4738987235622935e-05,
                7.889266345397582e-06,
                6.605216794848473e-05,
                2.430023492353693e-05,
                2.1444953515423628e-05,
                6.144176066353646e-06,
                1.6701415855859424e-05
            ],
            [
                3.120191504371423e-05,
                2.4300237808257835e-05,
                1.1478769487464542e-05,
                1.1478764011143482e-05,
                5.829125136472753e-05,
                3.5356242264223526e-05,
                1.0129992185539456e-05,
                2.4300240711101413e-05,
                4.5397868592445174e-05,
                2.144495351862222e-05
            ],
            [
                1.553497569203316e-06,
                6.605213671058347e-05,
                3.535625070778844e-05,
                2.1444943294263477e-05,
                0.00029595705315041876,
                7.484620928658632e-05,
                4.0063711256516126e-05,
                7.484623591663277e-05,
                6.605215240858454e-05,
                4.785095634460739e-06
            ],
            [
                3.1201926235527406e-05,
                1.4738983722270186e-05,
                5.422220261948442e-06,
                8.939698433373153e-06,
                1.892514596503488e-05,
                2.1444950958338794e-05,
                2.1444953502863275e-05,
                1.1478768121735194e-05,
                1.1478768123280277e-05,
                1.670142781560441e-05
            ],
            [
                8.939699498587217e-06,
                4.2228329408924035e-06,
                1.4738980212296288e-05,
                6.962257076830902e-06,
                1.0129987351289655e-05,
                6.9622545877746946e-06,
                1.8925143724239906e-05,
                1.4738981968060613e-05,
                4.785095064601411e-06,
                1.0129994597855991e-05
            ],
            [
                3.726640172290235e-06,
                3.120190763025685e-05,
                2.753569436164291e-05,
                3.535624646947797e-05,
                1.8925157218446604e-05,
                4.006369199251733e-05,
                1.4738987228491566e-05,
                2.1444940713541454e-05,
                2.4300246506623417e-05,
                8.93969949421299e-06
            ],
            [
                1.4738988997768797e-05,
                8.939695237341456e-06,
                0.00017952798623340198,
                0.0008040860917820167,
                4.539787931821248e-05,
                4.006367783922064e-05,
                5.144221351278017e-05,
                6.962257904916592e-06,
                4.006368257301759e-05,
                5.8291286317783706e-05
            ],
            [
                1.1478772227964558e-05,
                1.3007126909159127e-05,
                1.3007126909916233e-05,
                6.60521682190406e-05,
                8.939693101987369e-06,
                1.6701421834059987e-05,
                1.6701419848475466e-05,
                2.430023491169112e-05,
                2.7535700934898458e-05,
                7.889266340676307e-06
            ],
            [
                2.753568446399789e-05,
                6.144174600471243e-06,
                1.4738976686988113e-05,
                5.422220908314139e-06,
                7.889264462958184e-06,
                1.1478770859917257e-05,
                1.8925143725892257e-05,
                1.0129987355564522e-05,
                8.939695237504067e-06,
                3.2887490652451393e-06
            ],
            [
                1.1478772223224906e-05,
                1.4738978454950406e-05,
                8.93969310584124e-06,
                6.962258736902953e-06,
                8.939700564468113e-06,
                2.753569108573408e-05,
                6.144172403827636e-06,
                2.144495607640949e-05,
                1.4738978402805636e-05,
                6.9622562487453084e-06
            ],
            [
                3.5356267511063545e-05,
                3.5356246493272806e-05,
                1.8925143720384422e-05,
                2.430023782222529e-05,
                4.5397863211726375e-05,
                5.1442201350809364e-05,
                4.0063677816192936e-05,
                1.4738987223451347e-05,
                0.000179528005914876,
                4.006368257593249e-05
            ],
            [
                1.4738981969240237e-05,
                7.889261643727018e-06,
                4.785092782188013e-06,
                1.670142582254589e-05,
                4.0063711246896956e-05,
                4.785092783415276e-06,
                5.422218969463855e-06,
                1.473898899664279e-05,
                2.4300234909039074e-05,
                1.1478772228528306e-05
            ],
            [
                5.422218323349895e-06,
                7.889265404959923e-06,
                1.8925141450398177e-05,
                1.3007125351889727e-05,
                5.144220733803926e-05,
                1.1478766748656418e-05,
                3.2887478882574116e-06,
                1.6701427808495672e-05,
                1.8925157255968775e-05,
                1.300712535865635e-05
            ],
            [
                2.430024941459533e-05,
                5.8291258442956145e-05,
                1.4738988994980593e-05,
                6.962255417544426e-06,
                4.7850933535659155e-06,
                6.962255418367598e-06,
                2.1444958614225316e-05,
                1.3007125360478133e-05,
                2.14449458053968e-05,
                7.8892625810789e-06
            ],
            [
                1.4738988994015443e-05,
                4.7850950646797465e-06,
                1.3007131557971383e-05,
                2.430023781683279e-05,
                3.1201900191715896e-05,
                2.5612825151640725e-06,
                7.889259763857458e-06,
                4.785096204868486e-06,
                1.473898371722997e-05,
                3.120191135412508e-05
            ],
            [
                4.7850944943330625e-06,
                3.5356267428231745e-05,
                5.422218968714274e-06,
                2.753568778728705e-05,
                5.422218969661113e-06,
                1.6701419847381817e-05,
                2.4300249415479343e-05,
                1.47389819699641e-05,
                1.670142780381727e-05,
                3.5356259096177054e-05
            ],
            [
                3.1201922523121745e-05,
                0.0001584362151237764,
                0.00033535022393568027,
                0.0001398220209261966,
                5.144219521911119e-05,
                6.605214445722408e-05,
                5.422217030032353e-06,
                1.3007133113703658e-05,
                0.00017952798406282417,
                3.120191871729913e-05
            ],
            [
                1.147877222485351e-05,
                8.939699491546175e-06,
                7.889262582800945e-06,
                1.4738981959696002e-05,
                7.484620900288251e-05,
                2.7535694343912553e-05,
                0.000261190304800772,
                2.1444948397509574e-05,
                1.4738987237553233e-05,
                4.222833947198501e-06
            ],
            [
                2.4300249398417826e-05,
                8.939699496489538e-06,
                7.889261644358435e-06,
                1.0129994600638342e-05,
                7.88926258343236e-06,
                6.1441738659766924e-06,
                1.2098659718187066e-06,
                5.422219614833243e-06,
                6.962259568889411e-06,
                5.422220907426478e-06
            ],
            [
                2.4300234929636645e-05,
                1.1478768107662397e-05,
                2.1444945848226808e-05,
                3.535625487047041e-05,
                2.753569107391384e-05,
                3.535625486558282e-05,
                3.120190762197074e-05,
                8.481104105225297e-05,
                1.3007125357804606e-05,
                2.1444956077189637e-05
            ],
            [
                6.962258735104638e-06,
                1.3007123810638006e-05,
                3.120191136649749e-05,
                5.144221351764571e-05,
                4.2228319329965265e-06,
                6.962254587420098e-06,
                1.209866116137134e-06,
                4.222832436871463e-06,
                1.8925141465200488e-05,
                5.422218967491273e-06
            ],
            [
                1.8925143723620274e-05,
                2.4300232030064617e-05,
                1.89251437091622e-05,
                7.889265405505236e-06,
                3.120191871729913e-05,
                2.144494328404357e-05,
                6.962258738131379e-06,
                4.7850944943330625e-06,
                4.006367765820538e-05,
                2.753568778107642e-05
            ],
            [
                3.2887498493325602e-06,
                1.670141586949968e-05,
                4.22283394762097e-06,
                3.288749849209925e-06,
                1.1478769489719528e-05,
                6.962257077033528e-06,
                1.0129995809044816e-05,
                5.422217030288788e-06,
                5.422218969306048e-06,
                1.0129993391531815e-05
            ],
            [
                1.012999339309804e-05,
                5.829124444893003e-05,
                3.535625487947387e-05,
                7.484621805799024e-05,
                1.6701425744167532e-05,
                1.2378189626143658e-10,
                0.00010889686957621787,
                0.0004878572035607696,
                2.1444943278894603e-05,
                4.539789016057757e-05
            ],
            [
                1.0129995807165349e-05,
                2.9023123308072772e-06,
                3.7266406165319545e-06,
                2.7535687767453096e-05,
                3.5356242207501795e-05,
                4.0063706481032684e-05,
                1.14787667504103e-05,
                1.6701423806824726e-05,
                1.3007131558917768e-05,
                1.0129989769962063e-05
            ],
            [
                0.9998766053670096,
                0.9820137909590902,
                0.999569442940545,
                0.9999546021315612,
                0.3486451285660856,
                0.9770226308426495,
                0.9999339478791605,
                0.9999485577988978,
                0.9996200154781288,
                3.288750240486491e-06
            ],
            [
                1.892515048889829e-05,
                1.473897845457507e-05,
                4.2228329408924035e-06,
                3.5356254894393866e-05,
                1.012999097276641e-05,
                1.4738985482351282e-05,
                1.1478765386623071e-05,
                8.939699500489763e-06,
                6.14417753110761e-06,
                1.1478765386623071e-05
            ],
            [
                7.889261641416608e-06,
                1.6701429804288556e-05,
                1.473898723610551e-05,
                1.5534973839896667e-06,
                4.785093923324944e-06,
                2.7535694350223355e-05,
                2.561283431669698e-06,
                1.473898899256772e-05,
                4.22283294025486e-06,
                1.6701427807888088e-05
            ],
            [
                2.4300246516082393e-05,
                1.3007126910294786e-05,
                5.8291265401165313e-05,
                2.430023200831783e-05,
                7.484625370612328e-05,
                2.144495093719684e-05,
                1.473898196763166e-05,
                1.473898021151881e-05,
                1.8925150493717652e-05,
                5.8291272311027895e-05
            ],
            [
                5.422217676397663e-06,
                1.4738981966291175e-05,
                2.753569754859982e-05,
                8.939700566143004e-06,
                5.422217676486429e-06,
                2.1444956074147067e-05,
                1.8925141462377723e-05,
                1.6701425821573757e-05,
                4.006368738595465e-05,
                4.006368257301759e-05
            ],
            [
                1.7603436328033735e-06,
                6.144173867608406e-06,
                8.93969736547614e-06,
                1.994729245749689e-06,
                3.2887482807182155e-06,
                6.605215244462661e-05,
                2.4300249383301144e-05,
                2.144494323481637e-05,
                1.8925154992246077e-05,
                8.939699495546396e-06
            ],
            [
                4.785096200855943e-06,
                1.3007125361755747e-05,
                2.753568449224625e-05,
                6.962256247998122e-06,
                3.120192249167993e-05,
                1.4738976681250846e-05,
                2.753569107251144e-05,
                8.9396941702904e-06,
                6.144177530146464e-06,
                8.939693105076969e-06
            ],
            [
                4.006369215458579e-05,
                2.4300243601392304e-05,
                3.1201903920010065e-05,
                0.00010889688040934541,
                1.1478770856158943e-05,
                0.00023050665660580492,
                6.144173867451939e-06,
                1.670142777653674e-05,
                3.1201915067096954e-05,
                3.2887494569044713e-06
            ],
            [
                6.605214450431904e-05,
                7.484621812387922e-05,
                1.4738978452886064e-05,
                4.539785223278955e-05,
                7.484622714958306e-05,
                3.5356246476937965e-05,
                8.939700563248534e-06,
                8.4811050928423e-05,
                1.300712380555121e-05,
                3.1201922517673344e-05
            ],
            [
                1.0129988562901417e-05,
                1.0129995802042874e-05,
                8.939699499026267e-06,
                1.892514823364471e-05,
                1.0129993391808207e-05,
                1.3007128460040644e-05,
                6.605212875874436e-05,
                1.892515725225098e-05,
                7.889260702744606e-06,
                1.8925152747938785e-05
            ],
            [
                1.4738983725809062e-05,
                1.1478768119563723e-05,
                1.670142382067764e-05,
                1.6701415865641523e-05,
                2.144494840531103e-05,
                1.0129995799905438e-05,
                4.539786315904385e-05,
                3.535624222267904e-05,
                2.2603251060142746e-06,
                1.670142183934597e-05
            ],
            [
                7.889261644358435e-06,
                2.144495351862222e-05,
                4.539785232329117e-05,
                4.539785756809109e-05,
                6.9622570786798724e-06,
                1.892514597770291e-05,
                1.1478773595970265e-05,
                3.1201907628667734e-05,
                1.3007134632243331e-05,
                1.1478773590165753e-05
            ],
            [
                5.1442213588757405e-05,
                3.5356267417942084e-05,
                4.53978523335304e-05,
                6.605214441493472e-05,
                8.939694170729447e-06,
                3.1201900194894126e-05,
                5.144222587386666e-05,
                1.6701427811412077e-05,
                6.9622537593854575e-06,
                1.3007128455545335e-05
            ],
            [
                8.939694170940841e-06,
                6.962255419051463e-06,
                1.0129990976728036e-05,
                4.222831933649433e-06,
                3.5356246382273116e-05,
                6.144176797998549e-06,
                4.222834451065997e-06,
                1.4738987239295859e-05,
                4.539785764835348e-05,
                1.0129987350147233e-05
            ],
            [
                4.785095634121282e-06,
                5.144223194755629e-05,
                8.939697368305565e-06,
                7.484620916297642e-05,
                2.1444950957402623e-05,
                1.8925150469896243e-05,
                6.962257077932685e-06,
                1.0129990976451642e-05,
                4.539788454749151e-05,
                0.0001233945450837103
            ],
            [
                5.144220104091213e-05,
                0.9992903296545208,
                1.1478772227964558e-05,
                1.892514370434284e-05,
                3.1201922453768124e-05,
                5.829129287819015e-05,
                8.481105080748527e-05,
                4.222834953197588e-06,
                4.785092782936557e-06,
                0.9989677690253076
            ],
            [
                0.9999810748540289,
                0.9999945777784462,
                0.9999910603015791,
                0.9999646437578743,
                0.22270013366638425,
                0.9999756997563973,
                0.9999810748472603,
                0.9999599363031034,
                0.9999852610233124,
                0.9999832985781861
            ],
            [
                8.93969630333567e-06,
                7.889261643554814e-06,
                1.4738985478142165e-05,
                4.2228349543420954e-06,
                5.422217029272909e-06,
                2.260323758882316e-06,
                8.939696301140427e-06,
                1.1478770855741353e-05,
                8.939699497042417e-06,
                4.785095634843714e-06
            ],
            [
                1.1478769491598686e-05,
                2.753570091316123e-05,
                1.0129989766700635e-05,
                1.3007123808153756e-05,
                5.829127856820116e-05,
                1.6701417860795016e-05,
                1.8925155000714377e-05,
                2.753568451618723e-05,
                1.4738976694494812e-05,
                4.785093922776592e-06
            ]
        ]
    },
    {
        "q_id": "7781_mmlu_math",
        "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,
            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,
            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,
            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,
            115,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            126,
            127
        ],
        "rewards": [
            [
                0.9947798741009013,
                0.9999646437324408,
                0.9975273762817204,
                0.9997965729295829,
                0.9997388095978097,
                0.9947798750584772,
                0.9989677688131908,
                0.9984988180105943,
                0.9999852610127579,
                0.9999251537371668
            ],
            [
                6.475947981813674e-07,
                9.42244256915735e-07,
                8.939694172290508e-06,
                2.3823699518905442e-07,
                1.2098655392574583e-06,
                2.753568781222975e-05,
                0.0005527786365698597,
                1.473898021151881e-05,
                NaN,
                2.902311639073834e-06
            ],
            [
                0.9999869928699849,
                0.999978555041362,
                0.9999869928761874,
                0.9999756997505781,
                0.9999898700114356,
                0.9999724642957742,
                0.9999832985821377,
                0.9999251537549232,
                0.9999810748449939,
                0.9940889324599094
            ],
            [
                0.9999646437366535,
                0.9999898700114355,
                0.9999687980960746,
                0.9999687980811913,
                0.9999952149055054,
                0.9999930377437503,
                0.9999852610180282,
                0.9999599363030504,
                0.999995214904935,
                0.9978172832453275
            ],
            [
                0.9999996940977366,
                0.9999984465018751,
                0.9999997300422868,
                0.9999996072138465,
                0.9999996940977001,
                0.9999994284997573,
                0.9999980052702785,
                0.9999994284997573,
                0.9999990577550691,
                0.9999992661792819
            ],
            [
                0.9999756997476821,
                0.9992903294482086,
                0.9999599363173639,
                0.9999832985721844,
                0.9999485577618238,
                0.9999339478317045,
                0.9999930377404321,
                0.9988304898702542,
                0.9999599362887323,
                0.9999810748472474
            ],
            [
                0.9990889488829529,
                0.9999151889892623,
                0.9999724643023399,
                0.999948557798702,
                0.9999977396751727,
                0.9982992772835855,
                0.9999921107364999,
                0.04208772851637929,
                0.9999852610215454,
                0.0019267348285430012
            ],
            [
                3.726638839806038e-06,
                0.999997097687323,
                0.9999869928699856,
                0.999993037740431,
                0.9999980052700407,
                0.00020342702042555955,
                0.9999977396754327,
                0.9999996940976636,
                0.9999994284994167,
                0.9999945777816766
            ],
            [
                0.9999952149060758,
                0.997817283900493,
                0.9999974387187053,
                0.9999885212332436,
                0.9999967112497585,
                0.9999977396754327,
                0.999988521229138,
                0.9999930377462402,
                0.9999987901337396,
                0.99956944285824
            ],
            [
                7.48462094287105e-05,
                7.889265407004852e-06,
                4.22283545808297e-06,
                2.902310947208574e-06,
                0.00012339463356491042,
                5.144220752349106e-05,
                0.9975273772447861,
                1.473898197154587e-05,
                2.5612825160096693e-06,
                2.902310947190096e-06
            ],
            [
                0.9669140183935203,
                0.11920291107043361,
                NaN,
                0.9999952149038032,
                0.9324533116759811,
                0.9999785550440025,
                5.422220261849814e-06,
                6.962254589851619e-06,
                NaN,
                NaN
            ],
            [
                0.9999485577681213,
                0.9999151889687783,
                0.9999339478789374,
                0.9999930377420919,
                0.999903897619545,
                0.9999962733611605,
                0.9999599363221412,
                0.9999869928762076,
                0.9999785550567073,
                0.9999151889889569
            ],
            [
                4.785095064819011e-06,
                4.006371128945452e-05,
                3.466324971415162e-07,
                4.785093353626844e-06,
                4.5397879405741464e-05,
                0.999664649855201,
                1.2098662603499435e-06,
                1.3709572068079696e-06,
                2.902312677060767e-06,
                2.144495096387783e-05
            ],
            [
                0.9999970976866309,
                1.6701421842566163e-05,
                0.9999986290421394,
                0.9998911030647897,
                4.006369219073056e-05,
                0.9999921107374143,
                0.9914225158138701,
                0.9999151889384766,
                0.9999417087275358,
                0.9999952149072167
            ],
            [
                5.422218323231539e-06,
                0.9997040428300853,
                0.9999038975736144,
                9.422447062240614e-07,
                2.5612825160096693e-06,
                1.4738976698757546e-05,
                6.144172403928222e-06,
                4.22283394786293e-06,
                0.9999938558268666,
                1.5534973841895917e-06
            ],
            [
                0.9914225150773209,
                1.1478766757049986e-05,
                0.9995694429094316,
                0.9149009468718409,
                7.338209805200689e-07,
                2.9023133690821773e-06,
                3.2887478892055875e-06,
                5.422219616085833e-06,
                4.785093924251918e-06,
                0.9947798734504266
            ],
            [
                0.9999921107355347,
                0.9999869928668839,
                0.9999984465016899,
                0.9999991684718732,
                0.9999996940977002,
                0.9999997300420937,
                0.9999945777810303,
                0.9999962733589389,
                0.9999994284995529,
                0.9999990577556308
            ],
            [
                0.9999832985841286,
                0.9999417087344762,
                0.9986749776804537,
                0.996406397045085,
                3.927862470840049e-07,
                0.9999599362982634,
                0.9959298631712717,
                0.00023050674181927547,
                1.5534981249397663e-06,
                1.892514823013346e-05
            ],
            [
                0.9999986290424663,
                0.9999998724809267,
                0.9999992661789321,
                0.9999980052702785,
                0.999999554914895,
                0.9999967112509346,
                0.9999997300422868,
                0.999997438716568,
                0.9999998874648915,
                0.9999994284993485
            ],
            [
                5.043472278227948e-07,
                8.315282258956806e-07,
                5.715002425495939e-07,
                5.715006513843456e-07,
                6.475946437722523e-07,
                2.5612819053166966e-06,
                7.889259763010786e-06,
                7.338212429167144e-07,
                1.5534981249164537e-06,
                3.288748673295719e-06
            ],
            [
                9.422444815323792e-07,
                6.962253759271479e-06,
                0.5312093733737563,
                0.9999038975621809,
                1.6701429805199933e-05,
                1.3709573702248741e-06,
                1.7603440527046419e-06,
                0.9989677691738014,
                1.2098655392222467e-06,
                1.3709570433786157e-06
            ],
            [
                0.9999996533673375,
                0.9999992661791944,
                0.9999990577551815,
                0.9999982396569965,
                0.9999989322967481,
                0.9999832985701935,
                0.9999999317439059,
                0.9999994284994167,
                0.9999996533674614,
                0.9999974387168733
            ],
            [
                0.9999991684720715,
                0.999964643732433,
                0.9999945777784447,
                0.9998601778774985,
                0.9999984465022455,
                0.9999417087067125,
                0.9999967112505427,
                0.9999996072139402,
                0.9999987901338838,
                0.999999352405279
            ],
            [
                1.7603440525925705e-06,
                6.14417606659952e-06,
                6.962254589705982e-06,
                2.902312330965655e-06,
                2.902311984783477e-06,
                2.4300240723831244e-05,
                1.7603436328033735e-06,
                1.2098658277181688e-06,
                5.043475885634304e-07,
                8.315282259009745e-07
            ],
            [
                3.726640172503764e-06,
                1.7603438428460541e-06,
                3.7266383955611403e-06,
                7.338212429504183e-07,
                1.1478772228528306e-05,
                1.9947299591826594e-06,
                1.0677031245710902e-06,
                6.962254589617333e-06,
                2.9023116390421582e-06,
                2.902312331125353e-06
            ],
            [
                0.9998766053662896,
                0.999704042936749,
                0.999991060304762,
                0.9999417087553242,
                0.9999251537906132,
                0.9999869928746379,
                0.9999339478475102,
                0.9999938558232009,
                0.9990889488841714,
                0.9997965730510766
            ],
            [
                0.9999885212359799,
                0.9999485577986293,
                0.9999921107374145,
                0.9999785550541448,
                0.9998204719482784,
                0.9999930377420903,
                0.9999485577986424,
                0.9997965730756625,
                0.9986749773004159,
                0.9999869928730869
            ],
            [
                0.9999986290432834,
                0.999997438717484,
                0.9999984465022455,
                0.9999910603047628,
                0.9999984465024306,
                0.9999832985761679,
                0.999998239656367,
                0.9999687980811924,
                0.9999921107364742,
                0.9999810748562722
            ],
            [
                1.9947297214544894e-06,
                1.7603438428460541e-06,
                1.994729245822257e-06,
                8.315282258900085e-07,
                1.9947290080125335e-06,
                1.5534977545603963e-06,
                3.92786340734912e-07,
                3.2887486729876365e-06,
                1.76034363298589e-06,
                1.0677027427340866e-06
            ],
            [
                0.9999994284993486,
                0.9999990577552937,
                0.9999993524052789,
                0.9999994284993486,
                0.9999995549148419,
                0.9999992661789321,
                0.9999997300422225,
                0.9999485577802131,
                0.9999989322967481,
                0.9999646437450891
            ],
            [
                0.9999982396559473,
                0.9999994284997573,
                0.9999989322968753,
                0.9999982396569966,
                0.9999991684722698,
                0.999999266178757,
                0.9999994284994167,
                0.9999987901341723,
                0.9999832985741745,
                0.9999945777790921
            ],
            [
                2.4300232036606334e-05,
                0.9982992779107397,
                0.9999910603036961,
                4.006368256456438e-05,
                4.0063711274151284e-05,
                0.00013982214061166373,
                0.9999869928746368,
                2.753568778728705e-05,
                0.9975273769455869,
                NaN
            ],
            [
                0.9999687980849329,
                0.9996646499738131,
                0.9999339478633947,
                0.9998911031170887,
                0.9999989322972572,
                0.9999687980998051,
                0.9998415637642725,
                0.9999987901340281,
                0.9996646498102713,
                0.9999869928761876
            ],
            [
                0.9999485577863421,
                0.999985261014514,
                0.999968798077472,
                0.9986749778472881,
                0.9999151889788488,
                0.999975699762164,
                0.9999921107355335,
                0.9999724643187476,
                0.9999756997650613,
                0.9982992776737534
            ],
            [
                0.9999998362623723,
                0.9999994956527121,
                0.9999995549149481,
                0.9999996072136125,
                0.9999997300421581,
                0.9999999006880904,
                0.9995694428576889,
                0.9999997897567091,
                0.9999998724809723,
                0.9999977396751633
            ],
            [
                0.9840936075884247,
                0.9995694430140066,
                0.9990889489905589,
                0.9999785550464785,
                0.9999756997621719,
                0.9999151889790031,
                0.9999546021367987,
                0.9770226325570761,
                0.9999756997621694,
                0.0031726821473669624
            ],
            [
                0.9999687980774685,
                0.9999938558275986,
                0.9999485578047742,
                0.9999970976887069,
                0.9999930377462405,
                0.9999546021333454,
                0.9995121428865275,
                0.9999151889387845,
                0.9999724643024095,
                0.9149009607937928
            ],
            [
                0.9999991684718733,
                0.9995694430186661,
                0.9999995549147889,
                0.9999957771665562,
                0.9999810748449939,
                0.9999991684715758,
                0.9999756997679633,
                0.999998239656367,
                0.9999974387187055,
                0.9999980052693274
            ],
            [
                0.9999977396751634,
                0.9999967112493667,
                0.9999957771660523,
                0.9999251537549951,
                0.9999038975509362,
                0.9999980052702785,
                0.9992903294513871,
                0.9999982396569966,
                0.9999994284994167,
                0.9999910603058275
            ],
            [
                1.8925157262061825e-05,
                1.1478768125577027e-05,
                3.7266379512857925e-06,
                8.939695237959376e-06,
                6.1441746016670885e-06,
                1.3007125362820425e-05,
                5.715005151550947e-07,
                8.315278294038928e-07,
                2.5612828213352452e-06,
                8.315278294001114e-07
            ],
            [
                0.9995121427903653,
                5.422218969858371e-06,
                0.9999980052705163,
                0.9999974387180947,
                4.5397890240179425e-05,
                0.9999810748562722,
                0.9999810748495053,
                0.9999952149032235,
                0.9947798735664964,
                0.9999970976866309
            ],
            [
                0.9999546021476057,
                0.9999869928761871,
                0.9995121429411367,
                0.999995777167059,
                0.9999980052693275,
                0.9999151889384605,
                0.9999995549151073,
                0.9999724643023546,
                0.9999991684719723,
                0.9999546021259581
            ],
            [
                0.6513548782017745,
                0.999997097689056,
                0.9999989322973888,
                0.9999038975749192,
                0.9999869928700299,
                0.9999967112521109,
                0.9999910603036983,
                0.9999989322967482,
                0.9999984465026238,
                0.9984988177256386
            ],
            [
                9.610246043233746e-05,
                0.9902915256943335,
                0.9999967112517189,
                0.9999869928761871,
                0.9995121427685102,
                2.4300246525276163e-05,
                0.9999810748540167,
                0.9999785550515903,
                6.962254589781966e-06,
                0.9999852610197855
            ],
            [
                0.9999977396765106,
                0.999999694097773,
                0.9999938558232008,
                0.9999977396757023,
                0.9999869928761874,
                0.999978555056705,
                0.9999724643056453,
                0.9999938558232024,
                0.999998446502801,
                0.9999992661786696
            ],
            [
                0.9999962733616045,
                0.9999992661792819,
                0.9999989322973845,
                0.999994577780384,
                0.9999997300421261,
                0.9999997617630333,
                0.9999996940977002,
                0.9999485577863757,
                0.9999996940978095,
                0.9999977396757022
            ],
            [
                0.9998766054252095,
                8.48110412132976e-05,
                0.9999930377412604,
                0.9999546021476109,
                0.9982992773144194,
                0.9999869928699864,
                0.9998911031297583,
                0.9999970976876693,
                0.9999832985841317,
                1.0677028700203557e-06
            ],
            [
                0.9999957771650506,
                0.5926665999540698,
                NaN,
                0.817574471748733,
                2.9023109467070445e-06,
                0.9997694932865181,
                0.995390428397509,
                NaN,
                0.5,
                0.9999957771650602
            ],
            [
                0.999088949005341,
                0.9999994284997573,
                0.9999485578047708,
                0.999993855826864,
                0.9999885212264021,
                0.999996711250543,
                0.9999982396561571,
                0.9740426406829585,
                0.9996646498528886,
                0.9999852610162727
            ],
            [
                0.9999898700126436,
                0.9999990577551814,
                0.9999921107402363,
                0.9997040428333057,
                0.9999991684719723,
                0.9999980052702786,
                0.9999980052709919,
                0.9999970976880149,
                0.9999994284996891,
                0.9984988173926959
            ],
            [
                NaN,
                0.9924227600732872,
                0.9996646500107031,
                0.9902915255510706,
                0.9999898700131545,
                0.9998204720983982,
                1.0129990978441666e-05,
                0.9995694428666071,
                0.9998911030780502,
                4.539785778179383e-05
            ],
            [
                7.338210679949506e-07,
                3.2887498494551953e-06,
                0.9998601779330029,
                0.9999970976873322,
                1.994729245749689e-06,
                5.4222183231674305e-06,
                NaN,
                5.422219615898437e-06,
                1.9947292458930106e-06,
                0.9999869928655393
            ],
            [
                0.7772998508568416,
                0.9995121428832917,
                0.017986210850374135,
                0.9984988175999999,
                0.9999417087137246,
                0.9999546021097193,
                0.9984988177570484,
                0.9997965730303205,
                0.9993736657557956,
                0.9999417087278256
            ],
            [
                0.9999930377404305,
                0.9998415637077862,
                0.9999898700126435,
                0.9999993524049702,
                0.9999993524051246,
                0.9999885212291382,
                0.9999996940976636,
                0.9996646498914276,
                0.9999910603036967,
                0.9999945777829694
            ],
            [
                0.9980732654544278,
                NaN,
                NaN,
                0.9997388095661343,
                0.8807970842359876,
                0.9998911030388833,
                0.9999810748585687,
                0.9999832985781602,
                0.9999756997505892,
                0.9999485577803114
            ],
            [
                0.9999992661791944,
                0.9999980052709919,
                0.9999994956525318,
                0.9999756997563707,
                0.9999991684721705,
                0.9999967112497586,
                0.9999986290431201,
                0.999999428499485,
                0.9999967112513268,
                0.9999869928715366
            ],
            [
                8.939700566801578e-06,
                1.209865250822125e-06,
                1.0129993393319151e-05,
                3.2887498494282754e-06,
                6.962256249606473e-06,
                0.9999910603070309,
                1.7603430033799313e-06,
                1.5534983101393749e-06,
                5.422221555192784e-06,
                3.288750633518874e-06
            ],
            [
                5.043473480678099e-07,
                7.338212429420757e-07,
                2.699576809107705e-07,
                2.699577452733192e-07,
                2.102434412837375e-07,
                3.9278634073312583e-07,
                6.475951069932288e-07,
                1.0677024881829577e-06,
                4.4508499887035535e-07,
                2.699578096373564e-07
            ],
            [
                9.422449308420983e-07,
                1.3709575336860625e-06,
                1.9947292458603553e-06,
                4.222832435127818e-06,
                1.9947301970106386e-06,
                1.7603436329394601e-06,
                2.260323489435463e-06,
                2.699578096393206e-07,
                5.043475885292571e-07,
                1.2098653949842147e-06
            ],
            [
                0.9999687980774782,
                0.9999038976079275,
                0.9999898700053976,
                6.60521210438226e-05,
                0.9997694932028004,
                0.9999967112521106,
                0.9999977396746244,
                0.9995121428241128,
                0.999996273358939,
                0.994779873160252
            ],
            [
                0.9999982396561571,
                0.9999996940977731,
                0.9999945777797375,
                0.9999977396765105,
                0.9999832985781587,
                0.9999984465022455,
                0.9999810748562713,
                0.9999994284994167,
                0.9999810748540182,
                0.9999832985741738
            ],
            [
                1.209865827740176e-06,
                4.222834451254188e-06,
                1.4738981970956057e-05,
                0.00023050671458181403,
                2.5612825159677387e-06,
                1.4738981970956057e-05,
                3.535623803067304e-05,
                1.0129990974572174e-05,
                4.222832941111319e-06,
                3.288748673265808e-06
            ],
            [
                0.9999987901344607,
                0.9999832985721844,
                0.999995777166052,
                0.9998766054398672,
                0.9999910603036978,
                1.5534983101393749e-06,
                1.5534971989907999e-06,
                0.9999910603058273,
                0.999996273358939,
                0.9999910603068933
            ],
            [
                0.9999869928715357,
                0.9999810748495063,
                0.9999546021205543,
                0.9999930377454103,
                0.9999832985801475,
                0.9998204720129621,
                0.9999687980960685,
                0.9875683499357564,
                0.9999038975735949,
                0.9999038975850585
            ],
            [
                0.9999852610197857,
                4.785096776251149e-06,
                0.9999970976883608,
                0.9999646437366654,
                4.0063692178050736e-05,
                0.999968798092358,
                0.9999546021476009,
                0.999975699756372,
                0.9999952149072167,
                0.9999687980774685
            ],
            [
                0.9999921107364742,
                0.9999990577554061,
                0.9999885212318756,
                0.9999974387180947,
                0.9998766053668714,
                0.999999694097773,
                0.9999962733620487,
                0.9999852610215433,
                0.9997040427601902,
                0.9999852610110015
            ],
            [
                7.889260703117714e-06,
                2.5612822103393692e-06,
                0.009708474431021574,
                0.00023050674082662724,
                1.0129988561648438e-05,
                3.2887486733420804e-06,
                2.7535691069506297e-05,
                3.7266401724291984e-06,
                0.9940889324708545,
                9.422450431569214e-07
            ],
            [
                4.785092783210732e-06,
                NaN,
                5.422217030663578e-06,
                0.999876605426583,
                3.72664061681327e-06,
                7.338208055613267e-07,
                1.1478770861650256e-05,
                0.010986943541390072,
                4.785096205930373e-06,
                8.481107156496966e-05
            ],
            [
                0.9998204719642194,
                2.2603237589542675e-06,
                0.9999646437366535,
                0.9978172840500856,
                0.9669140253057785,
                0.8354835432479661,
                0.4378234991142019,
                0.9999599363126077,
                0.02033235501224582,
                0.9998766053814608
            ],
            [
                0.9999810748517634,
                NaN,
                0.9997040429016766,
                0.9999785550413917,
                0.9999251537549356,
                0.9998415637454691,
                0.999972464308945,
                0.9999756997563787,
                0.9998415637845766,
                0.9999810748562803
            ],
            [
                0.9999980052707541,
                0.998830489898948,
                0.9999869928668857,
                0.9999251537907504,
                0.9997388096641623,
                0.9999957771665554,
                0.999993855826131,
                0.999995777166052,
                0.9999930377429203,
                0.9999852610197857
            ],
            [
                0.9940889307606763,
                0.9998911030517992,
                0.9999646437324317,
                0.9997694933404095,
                0.999664649850108,
                0.9988304900092357,
                0.9999869928653338,
                0.9999921107383551,
                0.9999910602994336,
                0.9999646437408712
            ],
            [
                0.9940889300711323,
                0.9989677691816041,
                0.9579122674284875,
                0.9999151889384766,
                0.9999339478711028,
                0.9890130584826029,
                0.9997965730511181,
                0.9999785550567105,
                0.9999546021367691,
                0.992422759859684
            ],
            [
                0.9999957771665556,
                0.9999984465026158,
                0.9999945777784448,
                0.9999898700102285,
                0.9999832985761654,
                0.9999945777829694,
                0.9999967112513267,
                0.9999967112497584,
                0.9999977396757022,
                0.9999987901343165
            ],
            [
                0.999993037740431,
                0.9999339478397065,
                0.9992903295708897,
                0.9999962733598274,
                0.9999852610127575,
                0.9999417087067969,
                0.999954602120557,
                0.9982992778955204,
                0.999999554914895,
                0.9999970976876691
            ],
            [
                0.8354835309589073,
                1.7603432132464244e-06,
                0.13296424363358259,
                0.06754669536304464,
                1.994729245842213e-06,
                0.18242551491653522,
                0.9149009462917594,
                0.9999869928746676,
                0.9999852610131482,
                0.8354835330070839
            ],
            [
                0.9999546021259487,
                0.9999832985821396,
                0.9999921107374143,
                0.9998766053812794,
                0.9999885212291385,
                0.9999756997621654,
                0.9999646437366474,
                0.9999952149043644,
                0.9999930377420904,
                0.9999977396746242
            ],
            [
                0.9999417087068924,
                0.9999996940976636,
                0.9999646437535129,
                0.9999982396569966,
                0.9999417087205764,
                0.9999996072136125,
                0.9999967112493665,
                0.9999977396748939,
                0.9999996072136125,
                0.9999546021313986
            ],
            [
                4.4508521110762794e-07,
                1.7603438427660027e-06,
                1.209865971934245e-06,
                8.939694170940841e-06,
                3.726641060773727e-06,
                4.785092782779884e-06,
                2.5612819052072116e-06,
                0.9999957771660538,
                3.535625911829982e-05,
                0.9982992779840693
            ],
            [
                2.4300252285704095e-05,
                0.9998601779159465,
                1.0129995810076682e-05,
                8.31528424162821e-07,
                3.726639283901856e-06,
                0.9999785550464785,
                1.1478772229300848e-05,
                8.939693106873817e-06,
                4.2228324375512536e-06,
                1.1478769493916314e-05
            ],
            [
                0.9999977396751633,
                0.9999756997476967,
                0.9999986290421395,
                0.9995121427654164,
                0.9999977396751633,
                0.9999995549150011,
                0.9999546021097268,
                0.9999599362935213,
                0.9999967112513267,
                0.9999984465022455
            ],
            [
                0.9999991684720715,
                0.9999996533672962,
                0.9999997897567341,
                0.9999921107364742,
                0.9999982396572064,
                0.9999996940976272,
                0.9999997617629764,
                0.999994577780384,
                0.9999982396567867,
                0.9999957771665555
            ],
            [
                0.9999970976876689,
                0.9999980052695652,
                0.9999982396563669,
                0.9999970976873229,
                0.9999998555019963,
                0.9999986290424663,
                0.9999885212360063,
                0.9999885212264576,
                2.7535681252300143e-05,
                0.9999417087275321
            ],
            [
                0.9999984465018751,
                0.9999991684718733,
                0.9999997300422225,
                0.9999994956524114,
                0.9999997617630333,
                0.9999995549147889,
                0.9999994956527721,
                0.9999997897565838,
                0.9999952149055061,
                0.9999996940977366
            ],
            [
                0.9924227600627821,
                0.999447221325194,
                0.9999485577740962,
                0.99995993629351,
                0.9988304897504473,
                0.9959298613856103,
                0.9933071487909069,
                0.9964063975419666,
                0.9953904281795755,
                0.9999546021259464
            ],
            [
                0.9999921107374169,
                0.9999930377437503,
                0.9999977396751633,
                0.9999984465024306,
                0.9999980052700407,
                0.9999869928684368,
                0.9999921107392964,
                2.4300232043987867e-05,
                0.9999938558268636,
                0.9999885212264011
            ],
            [
                3.7266379504926854e-06,
                5.715003107655392e-07,
                8.3152792852928e-07,
                2.9023119851055122e-06,
                3.7266406160032166e-06,
                2.9023116391477434e-06,
                8.315279285088606e-07,
                2.1444945853375776e-05,
                5.043474683126242e-07,
                8.31528424146183e-07
            ],
            [
                0.9997694932023711,
                0.9998415637460476,
                0.9999251537460537,
                0.9999977396757023,
                0.9999485578047457,
                0.9999992661786696,
                0.9999938558261308,
                0.9999038975623424,
                0.9999945777810304,
                0.9999724643089064
            ],
            [
                0.9875683464941387,
                0.9992903294872173,
                0.9999724642957742,
                0.9999339478474896,
                0.9740426404003926,
                0.9984988178894925,
                0.9982992773045367,
                0.9999938558224686,
                0.9996200154320635,
                0.9999990577552939
            ],
            [
                0.9999546021367857,
                0.9990889488732042,
                0.9999251537818146,
                0.9995121429386673,
                0.9999957771665676,
                0.9999687980923566,
                0.9999810748495038,
                0.9999417087344838,
                7.338209805170655e-07,
                0.7549149978955811
            ],
            [
                8.315277302165032e-07,
                1.5534983101301911e-06,
                2.9023112931213857e-06,
                3.288748280658394e-06,
                6.962257078819179e-06,
                2.260324836624822e-06,
                0.6791787056691697,
                2.2603248367173307e-06,
                2.2603245669804887e-06,
                1.5534973841592143e-06
            ],
            [
                0.9999989322971299,
                0.9947798747852297,
                3.120191880118183e-05,
                0.9999967112505427,
                0.9999898700078133,
                0.9859363747130001,
                0.9999987901346049,
                0.9999485577618208,
                0.9999898700090206,
                0.9999910603058275
            ],
            [
                0.9999993524050474,
                0.9999996533672962,
                0.9999995549147358,
                0.9999962733611603,
                0.9999996940977731,
                0.9999987901344607,
                0.9999996940978825,
                0.9999957771670589,
                0.9999998555019618,
                0.999999730042319
            ],
            [
                0.999999057755743,
                0.9999986290424663,
                0.9999967112509346,
                0.9999986290429566,
                0.9999994284992805,
                0.9999986290432834,
                0.9999990577551814,
                0.9999990577556307,
                0.9992903294662062,
                0.9999546021313904
            ],
            [
                0.9999994284996211,
                0.9999687980849082,
                0.9997388097845256,
                0.9999938558253989,
                0.999860177926322,
                0.9999970976869769,
                0.9999810748449911,
                0.9999996072138465,
                0.9999952149043645,
                0.9999957771670589
            ],
            [
                0.9999970976866309,
                0.9999994956524716,
                0.9999984465026158,
                0.999999057755743,
                0.9999957771655487,
                0.999954602131396,
                0.999915188938579,
                0.9999962733620487,
                0.9999996072138934,
                0.9999989322972572
            ],
            [
                1.9947304348332037e-06,
                2.5612816000331606e-06,
                0.8175744673038222,
                4.2228324375973415e-06,
                2.561281599502042e-06,
                0.6224593241981982,
                8.315278293951957e-07,
                5.829127240390582e-05,
                8.481103095395362e-05,
                4.22283394786293e-06
            ],
            [
                0.9999832985721885,
                0.9820137929659507,
                0.9999546021476294,
                1.3007128460419196e-05,
                3.535623804983752e-05,
                0.9947798731578338,
                0.9999982396567869,
                0.00020342706932787165,
                0.9999852610215426,
                0.9999756997563805
            ],
            [
                0.9953904280171935,
                0.9740426444034102,
                0.9626731150654055,
                4.785093924156175e-06,
                8.939698434966738e-06,
                0.9902915226320856,
                2.9023133689924295e-06,
                6.962257079465052e-06,
                1.670141786036971e-05,
                0.7310585786300049
            ],
            [
                0.9982992777087379,
                0.9999832985741741,
                0.9999938558239336,
                0.9999869928684346,
                0.9999810748585268,
                0.9996200154244688,
                0.9997694931747982,
                0.9998601778592275,
                0.9999974387187053,
                0.9999339478474506
            ],
            [
                0.9999938558224684,
                0.9999997300422546,
                0.9999998144608319,
                0.9999885212291378,
                0.9999997300422868,
                0.9999957771675623,
                0.9999998144608319,
                0.9999995549147358,
                0.999999730042126,
                0.9999994956523512
            ],
            [
                0.9999546021259655,
                0.9999687980893697,
                0.9999687980737564,
                0.9999251537370814,
                0.9999251537995856,
                0.9999885212318746,
                0.9999251537459781,
                0.9999962733593831,
                0.9999785550413609,
                0.9998415637264605
            ],
            [
                0.9999885212318741,
                0.9999910603004989,
                0.9999687980960641,
                0.9968273168048011,
                0.9990889486527997,
                0.9999038975391943,
                8.31527928532683e-07,
                0.9999485578047371,
                0.9996200154233965,
                0.999891103064765
            ],
            [
                0.999989870009023,
                1.4738976698006875e-05,
                2.5612834318583854e-06,
                1.5534977545102382e-06,
                0.46879062662624377,
                NaN,
                0.9998204720773193,
                1.76034363298589e-06,
                9.422450431800595e-07,
                0.9995694429146548
            ],
            [
                0.9999970976880148,
                0.9999990577550691,
                0.99999992265575,
                0.9999994956525918,
                0.9999898700066053,
                0.00020342704544940658,
                0.9999996072138465,
                0.9999417087068513,
                0.9999994284997573,
                0.9999974387180947
            ],
            [
                0.999999057755069,
                0.9999996072139402,
                0.9999996533672136,
                0.9999974387168733,
                0.9999987901341723,
                0.999999554914895,
                0.9999930377404305,
                0.999997438716568,
                0.9999984465016899,
                0.9999996072138465
            ],
            [
                0.9997388096283071,
                0.999995214903794,
                0.9999417087275172,
                0.9998766054692472,
                0.9999546021259442,
                0.9999957771645418,
                0.9999869928715355,
                0.9999687980886264,
                0.999991060303696,
                0.9999038975735753
            ],
            [
                0.9999724642990556,
                0.9999898700102282,
                0.9999962733602719,
                0.9998415638412494,
                0.9999974387168733,
                0.9996200154262819,
                0.9999885212318746,
                0.999972464302344,
                0.9999962733620488,
                0.9999952149032248
            ],
            [
                6.475945665671197e-07,
                3.4663257978465195e-07,
                2.9023112930659533e-06,
                3.0590215398968196e-07,
                7.338211554688417e-07,
                8.315282258680767e-07,
                5.04347528440776e-07,
                1.637377643221385e-07,
                8.315281267513512e-07,
                0.00013982212355325894
            ],
            [
                0.9999995549151073,
                0.9999995549150542,
                0.9999994284996211,
                0.999998790134028,
                0.9999993524053562,
                0.9999994956524716,
                0.999998629042303,
                0.9999996533672962,
                0.9999999006880668,
                0.9999982396563669
            ],
            [
                0.999959936317381,
                0.999999266179107,
                0.999999554914895,
                0.9999977396762411,
                0.9999998555020135,
                0.9999982396569966,
                0.9999995549151072,
                0.9999995549151072,
                0.9999987901338838,
                0.99999862904312
            ],
            [
                4.222835457664342e-06,
                2.9023123309287002e-06,
                2.2603242978665707e-06,
                0.999991060306894,
                1.3709572068272963e-06,
                1.5534971989809095e-06,
                1.4738981970956057e-05,
                0.9999785550515897,
                0.999993855826131,
                1.9947301968963442e-06
            ],
            [
                9.422444815563743e-07,
                0.9999339478475265,
                4.4508526416286326e-07,
                7.88926352599354e-06,
                1.994729483694599e-06,
                0.9996646499300152,
                1.5534984953453635e-06,
                1.5534979397677313e-06,
                1.0677031245851707e-06,
                2.9023112931213857e-06
            ],
            [
                0.9999962733602774,
                0.957912274787803,
                0.9999921107345979,
                0.9999599363125974,
                0.97702262871007,
                0.9999756997507692,
                0.6791787056691697,
                0.9999810748427369,
                0.9998766054546542,
                0.9998766053811413
            ],
            [
                0.9999785550592561,
                0.9998204719482784,
                0.9999938558224684,
                0.9999898700114355,
                0.9999885212277693,
                0.9999599362934934,
                0.9999646437492907,
                0.9999599363125995,
                0.9999898700066059,
                0.9999885212318742
            ],
            [
                0.9999910603026495,
                0.999903897607966,
                0.9940889303146617,
                0.9998766053817553,
                0.9986749776838426,
                0.9991959140476753,
                0.00015843629221379494,
                0.9993736659717071,
                0.9940889313462413,
                0.9988304895986828
            ],
            [
                0.9999982396561571,
                0.9999869928668851,
                0.9999977396757022,
                0.9999938558275958,
                0.9999952149043646,
                0.9999982396567867,
                0.9999910603036964,
                0.9999485577679709,
                0.9999921107345929,
                0.9999646437450841
            ],
            [
                0.9996646498524105,
                0.9999945777797375,
                0.999968798081189,
                7.889265407004852e-06,
                0.9994472214516722,
                0.9999957771645419,
                1.892514597770291e-05,
                0.9770226305917578,
                6.144172404587612e-06,
                2.4300252315495453e-05
            ],
            [
                0.9999990577552939,
                0.9999898700090208,
                0.9999869928761874,
                0.9999885212264016,
                0.9999945777797374,
                0.9999930377454107,
                0.999876605395702,
                0.9999898700053974,
                0.9995694428624236,
                0.9999957771655488
            ],
            [
                0.9997694933673787,
                0.9999986290426297,
                0.9999930377420904,
                0.9999910603004997,
                0.9998601779258989,
                0.9999952149043645,
                0.9999810748495044,
                0.9999869928668836,
                0.9997388097529946,
                0.9998911030648799
            ]
        ]
    },
    {
        "q_id": "8542_mmlu_math",
        "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,
            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,
            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,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.3007126911004571e-05,
                5.144222579863794e-05,
                0.0002034269692236113,
                0.000261190307757037,
                2.7535684488840414e-05,
                1.8925152736303473e-05,
                0.9992903297460362,
                0.9995121429330758,
                6.962257077223492e-06,
                2.753569764115831e-05
            ],
            [
                0.9959298617159389,
                0.9998766054574515,
                0.999876605441896,
                6.144174624745775e-06,
                4.006368736190672e-05,
                0.9996646498959059,
                0.00010889692214311985,
                0.9989677689804114,
                0.998073264916246,
                0.9994472213725308
            ],
            [
                2.4300234884728635e-05,
                0.9999151889847173,
                1.1478770854906172e-05,
                0.9999339478478696,
                0.999933947831781,
                0.9998766054406392,
                0.9999599362937484,
                3.120192622962497e-05,
                0.9998601778765628,
                1.670142979997471e-05
            ],
            [
                0.999981074849528,
                1.4738987239295859e-05,
                0.9999151889799723,
                0.9997694932643244,
                0.9999898700090634,
                0.9999687980886947,
                0.9999756997563826,
                0.999988521227772,
                0.9999921107336538,
                0.9999724643057024
            ],
            [
                0.9999756997622258,
                7.48462360195503e-05,
                0.9999885212305714,
                3.120191504553037e-05,
                0.9999038975755861,
                0.9999810748495466,
                0.9998415637670757,
                0.9995694428337527,
                0.9999724643157055,
                3.5356267503860776e-05
            ],
            [
                0.09534946939781196,
                0.9997388096359903,
                0.5926665999540698,
                0.9995694429711821,
                0.999860177911772,
                0.8354835350552603,
                0.9998601778607799,
                0.0017007228150436203,
                0.8175744828610095,
                0.9998601778955253
            ],
            [
                0.9996646498917788,
                0.9998766054585358,
                2.7535694366751658e-05,
                0.9999687980849362,
                0.37754066879814546,
                0.9999885212346271,
                0.9999885212346176,
                2.4300252229480643e-05,
                0.9998415638418604,
                0.9999687980812371
            ],
            [
                0.9999417087523444,
                0.9999417087070107,
                0.9995121429266044,
                0.06754669724011829,
                0.9999810748474064,
                0.00012339456070373816,
                0.7310585727705126,
                0.5312093733737563,
                0.320821300824607,
                0.10669058471438035
            ],
            [
                0.9994472212965412,
                0.9999251537740621,
                0.3208212878370535,
                0.999447221460805,
                0.9993736659726543,
                0.999447221372145,
                0.9994472214003155,
                0.14804719239327382,
                0.9902915233125852,
                0.9997040428808209
            ],
            [
                0.9999339478556682,
                0.9999251537998262,
                0.9999339478663059,
                0.9999485577986784,
                1.1478768119146135e-05,
                0.8933094003735664,
                0.9999885212346283,
                0.9999546021423473,
                0.9999885212360319,
                0.9997965729641783
            ],
            [
                0.9995121429338706,
                0.9999251537805595,
                0.9990889486862843,
                0.9998415637693023,
                0.9991959139366052,
                0.9978172837914677,
                0.9998766053733869,
                0.9999756997565559,
                0.9995121429570029,
                0.9997388096409301
            ],
            [
                0.001169510266279422,
                2.7535697650273915e-05,
                0.9998204720631569,
                9.422448146683713e-07,
                5.1442238103586536e-05,
                1.4738988993050295e-05,
                1.4738983725809062e-05,
                1.0129992185539456e-05,
                7.484626284672882e-05,
                2.4300246497960055e-05
            ],
            [
                0.9999885212359807,
                1.4738988990369329e-05,
                0.9999938558268693,
                0.9999417087207821,
                1.4738983715299675e-05,
                0.9999810748518236,
                0.9999832985721927,
                0.9999810748562776,
                0.9999724643122014,
                0.9999810748495415
            ],
            [
                9.61023917962188e-05,
                0.00015843615894412056,
                0.00043055703123528316,
                0.00017952804989847249,
                0.0021827168880382973,
                0.0001795279857188366,
                0.0005527786551572795,
                0.000552778671236363,
                0.11920290950590741,
                0.000626334295905137
            ],
            [
                0.3775406687981454,
                0.015906389991570128,
                0.0420877286665694,
                0.002472622729945554,
                0.9995694428308969,
                0.9999038976088065,
                0.9996646499513727,
                5.8291258338203444e-05,
                0.16451646494473965,
                3.535626330593522e-05
            ],
            [
                0.00037998443528995137,
                6.605213641023297e-05,
                0.00048785705622374085,
                0.0008040859543357665,
                0.0002611902912885895,
                0.00017952804716892418,
                0.04208773257151254,
                0.00012339460093160299,
                0.015906390341450367,
                0.00048785708315936466
            ],
            [
                0.9999869928699874,
                1.3007123807302014e-05,
                0.9999810748562947,
                0.9999885212346207,
                0.9999921107346111,
                0.9999945777803911,
                0.9999898700114658,
                0.999978555051619,
                0.9999646437366874,
                0.9999898700126468
            ],
            [
                2.43002465110435e-05,
                0.6513548714339145,
                0.9998601779457503,
                0.9998601778617421,
                0.5,
                0.9999852610145418,
                0.5,
                0.9999832985842664,
                0.9999485577743844,
                0.9984988173890315
            ],
            [
                0.9999485577989157,
                0.9998601779770903,
                0.9999417087279112,
                0.999769493178353,
                2.4300249404340734e-05,
                0.9997965730558327,
                0.9999785550516748,
                0.9990889489338155,
                0.9924227598246671,
                0.9998766054120491
            ],
            [
                0.999995214907222,
                0.999991060306899,
                0.9999974387171843,
                0.9999785550464881,
                0.9999957771645461,
                0.9999970976890556,
                0.9999756997653914,
                0.9999930377445811,
                0.9999962733611607,
                0.9999957771680671
            ],
            [
                2.1444948401176257e-05,
                2.1444943281001e-05,
                0.9998204719500232,
                0.9997040428035464,
                0.9995694429782966,
                0.9995694430204448,
                4.222831933104063e-06,
                0.999915188960631,
                4.785096205830278e-06,
                NaN
            ],
            [
                0.9997040428782291,
                1.3007130012010681e-05,
                0.999841563823714,
                0.06008665227791172,
                0.7549149978955811,
                0.6224593312018546,
                2.4300237809495462e-05,
                0.998674977316899,
                0.2942149597859341,
                0.34864514210180597
            ],
            [
                0.7772998663336158,
                0.999738809726069,
                0.9997388097369214,
                0.9992903295440996,
                8.939697365736316e-06,
                6.962259561240242e-06,
                0.1329642316084462,
                1.892514822937613e-05,
                0.9999339478397699,
                0.4073334000459302
            ],
            [
                0.01798620756043887,
                0.2942149597859341,
                0.0001233945869597527,
                0.999769493314775,
                0.2942149783515163,
                0.9999151889297203,
                0.2942149783515162,
                0.9996200155246253,
                0.9993736657908457,
                0.022977369742764476
            ],
            [
                2.7535691063295662e-05,
                7.88926258381982e-06,
                0.9999832985821797,
                1.4738988982594524e-05,
                0.9999910602994351,
                0.9999962733611636,
                0.9999785550465277,
                0.9999898700126556,
                0.9999646437578956,
                4.222833946315156e-06
            ],
            [
                5.144223201604811e-05,
                2.4300249415479343e-05,
                2.144494329496561e-05,
                4.539785775768208e-05,
                4.785093922889744e-06,
                1.1478769489719528e-05,
                1.3007134664514934e-05,
                2.7535687799708318e-05,
                6.9622579086271995e-06,
                5.144221357303798e-05
            ],
            [
                0.9924227585710613,
                0.43782349911420193,
                0.9924227589877627,
                0.9994472213720164,
                0.0002034269472748494,
                0.966914021492119,
                0.9968273171582511,
                0.2227001285074597,
                0.06008664554541885,
                0.24508500761839525
            ],
            [
                0.2018132150593341,
                0.9989677689540019,
                0.0015011825202293993,
                0.16451646494473962,
                0.09534947068315557,
                0.9999251537647613,
                0.7549149923816048,
                0.40733340004593027,
                0.3775406687981454,
                0.02595735545530691
            ],
            [
                0.9999417087415362,
                0.9999832985781947,
                0.9998766053667009,
                0.9999930377445814,
                0.9999898700066107,
                0.9999646437452049,
                0.9998204720996102,
                0.9999546021423473,
                0.9999910603015711,
                0.9999687980886459
            ],
            [
                0.9992903294603859,
                0.99973880966303,
                0.9998204719926328,
                0.9999151889388376,
                0.9992903297452932,
                0.5312093733737562,
                0.9996200154405204,
                0.9999151889695113,
                0.16451646904109268,
                0.1329642316084462
            ],
            [
                0.9999832985702237,
                0.9999898700126459,
                0.999978555056757,
                0.9999832985702152,
                4.006368736948546e-05,
                0.9999898700066125,
                0.9999921107336551,
                0.9999756997505934,
                0.999989870005401,
                0.9999810748495223
            ],
            [
                0.9996646498994476,
                0.9998766053942818,
                0.18242552380635635,
                0.9999756997593585,
                0.9999546021422423,
                0.9999724643154964,
                0.9998415637116912,
                0.8175744828610095,
                0.9999646437578475,
                0.9999038976094259
            ],
            [
                0.9999967112521111,
                0.9999989322972572,
                0.999994577780394,
                0.9999982396563679,
                0.9999987901346051,
                0.9999957771662511,
                0.9999986290426303,
                0.9999921107355412,
                0.999997739675972,
                3.120191878131786e-05
            ],
            [
                0.9999974387174858,
                0.999996711251328,
                0.9999945777784455,
                0.9999945777784484,
                0.9999980052698031,
                0.9999984465020618,
                0.9999957771665569,
                0.9999982396572068,
                0.9999982396559476,
                0.9999038975483003
            ],
            [
                8.93969310662177e-06,
                5.422221554482653e-06,
                3.53562633231704e-05,
                1.3007134657984903e-05,
                1.1478768123551712e-05,
                6.605212876547221e-05,
                2.1444943285915917e-05,
                2.430024941459533e-05,
                8.93970056350871e-06,
                3.1201899950964765e-05
            ],
            [
                0.9999885212359978,
                0.9999687980816488,
                0.3775406687981454,
                0.005911069578623181,
                0.9999485577938361,
                0.9999251537818991,
                0.9999724642959467,
                0.20181321505933414,
                0.9999869928653624,
                0.4073334000459302
            ],
            [
                0.9996646499559193,
                0.9999724643156452,
                0.9998766054121999,
                0.9999852610180436,
                2.753569108693614e-05,
                0.9999724643025462,
                NaN,
                1.3007123806876143e-05,
                0.999704042800412,
                0.9998415637648695
            ],
            [
                0.0021827159468718244,
                0.11920291419948607,
                0.0009110510875362688,
                0.0005527787118521296,
                0.00043055697905420497,
                0.07585817845430338,
                0.0006263342124698633,
                0.9993736659042666,
                0.00043055712088003534,
                0.008577485619629007
            ],
            [
                2.1444958632714784e-05,
                3.535624222267904e-05,
                8.4811010852998e-05,
                0.00010889693460193567,
                0.0001795279227538065,
                3.535625908948878e-05,
                0.9997694933171561,
                4.539785778179383e-05,
                8.48110816287202e-05,
                4.539787400371717e-05
            ],
            [
                0.22270013366638422,
                0.9996646499346009,
                0.09534946939781194,
                0.9997694933235145,
                0.18242552602881165,
                0.9998766053817967,
                0.37754066879814546,
                3.120190384588913e-05,
                0.5312093733737563,
                0.9994472213089863
            ],
            [
                0.13296424191570594,
                0.9999485577992607,
                0.00020342705668720146,
                0.9999485577689566,
                0.9992903294431313,
                3.535626330593522e-05,
                3.535625066508635e-05,
                0.9996200154036194,
                0.9999852610216742,
                0.18242551713899047
            ],
            [
                0.9997965730210924,
                0.3208213138121609,
                0.9999810748450443,
                0.047425868970162655,
                0.007577239727116411,
                0.9999251537551382,
                0.9999785550461973,
                0.9998911030525384,
                2.1444940709796752e-05,
                0.3775406617944891
            ],
            [
                0.9998204719739726,
                4.0063696631873165e-05,
                0.9999687980812632,
                0.999964643758464,
                0.9999151889496812,
                1.1478770859019436e-05,
                0.042087725362387016,
                0.5312093733737563,
                0.999941708734858,
                0.9999646437620586
            ],
            [
                4.006368735928331e-05,
                0.1824255304737224,
                3.1201915067096954e-05,
                5.144220747202866e-05,
                0.9992903297232503,
                3.535626333281696e-05,
                0.09534945718704857,
                4.5397890237206746e-05,
                6.605212082564807e-05,
                2.144494583831896e-05
            ],
            [
                0.9994472212341865,
                0.9999417087069047,
                0.9992903295965239,
                2.7535694333695055e-05,
                0.9999038975514032,
                0.9998911030912727,
                0.999891103104332,
                0.8933094081846421,
                0.9999038975741934,
                0.9999546021320116
            ],
            [
                0.0002959570468816584,
                0.00020342692317738462,
                0.017986214074511276,
                0.004070137725334084,
                0.6791786926816161,
                0.0005527787233325964,
                0.00026119024416314875,
                0.015906393898566563,
                0.017986207494640173,
                0.0007096704436405644
            ],
            [
                0.9999038975489715,
                0.9998204719725622,
                0.08509904964767095,
                0.9998415637677072,
                0.5,
                0.9996200154558644,
                0.06754669630158146,
                0.7057850216484838,
                0.9998911031236659,
                0.05340332396194506
            ],
            [
                0.9999756997651432,
                1.6701425821573757e-05,
                0.9999485577741635,
                0.3775406758018019,
                0.9999417087210485,
                0.9997965730809247,
                0.020332355160653563,
                0.9997388096949561,
                0.14804719803168948,
                0.9999485577621038
            ],
            [
                0.03308597791199667,
                7.484625387601897e-05,
                4.5397884676638064e-05,
                0.08509905312815914,
                0.09534946232842245,
                0.9999151889898213,
                1.4738988992031526e-05,
                0.4378234991142019,
                0.999704042977358,
                0.9998204720155245
            ],
            [
                0.999978555059284,
                0.9999724643155078,
                0.9046505248181418,
                0.999991060304766,
                0.9999945777823279,
                0.9998911030652222,
                0.9999599363174658,
                0.9998601778763999,
                0.9999885212291495,
                2.753570092478113e-05
            ],
            [
                2.4300246522270504e-05,
                0.9998601779802863,
                0.999989870004224,
                0.9999599362986757,
                0.9999898700054964,
                0.9997965730776749,
                1.6701421843720577e-05,
                2.144495607492721e-05,
                0.9999339478649546,
                2.4300243612265703e-05
            ],
            [
                0.10669058968506458,
                0.9999417087486285,
                0.00017952796077939538,
                0.9998204720570658,
                0.9994472213887707,
                1.4738988989779516e-05,
                2.43002523020584e-05,
                0.9999151889792813,
                0.43782349911420193,
                3.120190372352716e-05
            ],
            [
                1.473898547154699e-05,
                1.6701429792440666e-05,
                0.9999852610162868,
                1.1478765386894505e-05,
                2.430024069518912e-05,
                2.902312330759764e-06,
                0.9999938558261364,
                0.9999151889185681,
                2.144494840289258e-05,
                3.726640171842841e-06
            ],
            [
                0.9999724643192167,
                0.9999852610110103,
                1.892515270807579e-05,
                0.999995777165047,
                0.9999921107346014,
                0.9999967112501509,
                0.99999844650169,
                6.605212848674697e-05,
                0.9999038975971876,
                0.9999967112513286
            ],
            [
                0.9986749775381127,
                0.00522012540822009,
                0.060086643862295744,
                0.01798620765913692,
                0.6224593312018546,
                0.022977370871777196,
                2.144495862623957e-05,
                0.06008664975322681,
                0.1329642384799526,
                0.0758581847220642
            ],
            [
                0.9999646437536178,
                0.9999546021314502,
                0.9999756997477951,
                0.9999485577619474,
                0.999954602109956,
                0.9999646437504046,
                0.9999038976196576,
                0.9999151889794553,
                0.9999832985821762,
                0.851952809486198
            ],
            [
                0.9999546021371604,
                0.9999810748495709,
                0.9999417087208847,
                0.9997388097906812,
                2.1444950954750122e-05,
                0.999925153755917,
                0.9999646437324821,
                0.9997040427738042,
                0.9996200154816995,
                0.99997246431879
            ],
            [
                1.8925152744083297e-05,
                4.006371126555232e-05,
                0.9999151889591551,
                0.9993736658325634,
                0.9999832985782594,
                0.9999151889907087,
                0.9998204720149081,
                2.144495606626759e-05,
                0.6791786926816161,
                0.9999038975408233
            ],
            [
                0.0003799845196491421,
                0.00043055712361058697,
                0.0005527787273845258,
                0.00023050676571661254,
                0.00023050676749398965,
                0.00015843629132399303,
                0.00048785711199666207,
                0.9986749778348102,
                0.00037998443351012855,
                0.000261190400374024
            ],
            [
                0.00020342694798812497,
                0.060086652698692546,
                7.484620924247882e-05,
                0.0001398220399782949,
                0.00010889692189118655,
                0.0001398220400027076,
                1.1478770856158943e-05,
                0.0001584362350152198,
                3.5356267545276676e-05,
                1.147876401064237e-05
            ],
            [
                9.610244921065592e-05,
                0.24508501864634824,
                0.00010889694774049766,
                0.000139822073104336,
                4.539786315574087e-05,
                0.00010889689591987614,
                3.120192617275726e-05,
                1.3007126906509262e-05,
                0.9933071477476414,
                9.610244895475965e-05
            ],
            [
                0.9999810748540323,
                0.9999646437538994,
                0.9999982396567888,
                0.9999921107383583,
                0.9999967112505443,
                0.9999910603036991,
                0.999986992866892,
                0.9999957771665577,
                0.9999945777797387,
                0.9999785550439387
            ],
            [
                2.1444953506061874e-05,
                0.06754668785475053,
                0.24508501864634827,
                2.7535694357535878e-05,
                0.012431650681676646,
                0.37754066879814546,
                0.04208772476162661,
                5.14422128978511e-05,
                0.033085980772241536,
                0.999860177910938
            ],
            [
                0.99994855779883,
                0.9997694932887381,
                0.053403334131154334,
                0.9996200155337567,
                0.9999599362889149,
                0.16451645675203386,
                0.9999898700066423,
                0.9999417087278052,
                0.3208212943308302,
                0.9989677687656536
            ],
            [
                0.0001584362539523188,
                5.144220743759563e-05,
                4.006367783499403e-05,
                0.0002034269222776513,
                0.0002611903974861549,
                0.00043055717957437396,
                0.0001233946178568984,
                5.829127244377123e-05,
                5.144222581997146e-05,
                1.89251549826762e-05
            ],
            [
                0.9993736659279856,
                0.8670357494949105,
                0.014063625584012009,
                0.04208772881675952,
                0.03308597552845946,
                0.9999485577864112,
                0.22270013882530887,
                0.9994472214084837,
                0.10669060175672705,
                0.053403332436286
            ],
            [
                0.9999869928653401,
                0.9999938558268671,
                0.9999898700126495,
                0.9999485577869179,
                0.9999869928763211,
                0.999995777165047,
                8.481103982313081e-05,
                6.9622545835828505e-06,
                0.9999785550567687,
                0.9999938558246705
            ],
            [
                8.481105038050101e-05,
                0.9998415638170612,
                0.9997388096521472,
                4.0063706444596424e-05,
                0.9968273169056817,
                0.99979657300865,
                5.829124452017881e-05,
                1.6701427800050252e-05,
                0.9890130582599638,
                0.9997388096029394
            ],
            [
                0.042087725963147436,
                0.00048785708151314103,
                0.00026119022659275596,
                0.025957359552513166,
                0.0015011822181728747,
                0.9995121429531995,
                0.010986943146711408,
                0.16451646699291617,
                0.014063627030331902,
                7.889262580504884e-06
            ],
            [
                0.5,
                0.14804720179063335,
                0.9953904289017478,
                0.9989677690301094,
                0.999841563762917,
                4.539787932646994e-05,
                0.40733340004593027,
                0.14804719427274565,
                2.4300243524748098e-05,
                0.9995121428103185
            ],
            [
                6.60521752924188e-05,
                4.5397852246001465e-05,
                8.481103106933806e-05,
                0.9999687981034747,
                3.5356250543668364e-05,
                0.22270013882530884,
                3.5356267503860776e-05,
                1.4738987221038477e-05,
                0.00026119026782846336,
                0.00010889688169753223
            ],
            [
                0.9990889487885393,
                0.9998601778928643,
                0.9996200154884098,
                1.6701427797619914e-05,
                0.9996200155322089,
                0.9997040429445763,
                0.999704042881837,
                1.3007134662054344e-05,
                0.9999910603037002,
                0.9975273772717773
            ],
            [
                1.147876675162131e-05,
                5.829126492235635e-05,
                0.9998911030392508,
                5.829124445529153e-05,
                0.9997694932152689,
                0.05340333488442917,
                1.8925154985774363e-05,
                0.010986941223918127,
                0.00010889688278765834,
                4.53978631524379e-05
            ],
            [
                0.0006263342984555604,
                7.484622719695779e-05,
                4.5397852378781204e-05,
                0.0002611903958446293,
                0.00026119033805685504,
                0.00017952800796530176,
                0.0008040859630343036,
                9.610241456817964e-05,
                0.14804720179063335,
                0.0002959571951017109
            ],
            [
                2.1444956069076118e-05,
                2.7535694356133476e-05,
                2.561282210460501e-06,
                0.00012339458912680775,
                7.889264465067689e-06,
                0.000158436272776466,
                8.939693102280066e-06,
                2.7535691082027735e-05,
                0.0006263341476162521,
                2.1444950958338794e-05
            ],
            [
                0.9999852610198006,
                0.999933947847677,
                0.9999339478641242,
                0.9999151889900953,
                0.9998766053837213,
                0.9999869928730956,
                3.7266383951544193e-06,
                2.753568122134716e-05,
                0.9999646437535832,
                0.9999485577926327
            ],
            [
                0.9997965730809247,
                0.025957356491381995,
                3.535625482571039e-05,
                0.03308597898458846,
                0.009708475845744208,
                1.670142581075876e-05,
                1.4738980191009424e-05,
                0.08509904268669496,
                0.9988304899812218,
                0.9998415637875088
            ],
            [
                0.9999995549147889,
                0.9999980052693276,
                0.9999982396569974,
                0.9999984465015049,
                0.9999977396751634,
                0.9999992661791944,
                0.9999980052709927,
                0.9999991684718736,
                0.9999938558276443,
                0.9999989322971303
            ],
            [
                0.00023050665836976702,
                0.00015843629177119916,
                0.00037998450537739194,
                1.473897903701474e-05,
                0.0002959571647050985,
                0.000261190307012271,
                0.00037998448124475914,
                0.0002305068189373258,
                0.0004878571636256468,
                0.00043055716669819315
            ],
            [
                0.9975273763316826,
                0.2689414272294874,
                0.01590639171181471,
                1.4738980210687712e-05,
                0.20181322706107543,
                0.10669059607594457,
                0.9994472214399988,
                0.1645164567520338,
                0.29421497216298875,
                0.8519528019683105
            ],
            [
                0.99998107485183,
                1.0129995803996048e-05,
                0.9997965729835996,
                1.012998856312253e-05,
                0.9999832985821617,
                6.962257907880012e-06,
                0.9999898700054185,
                0.9996200155473098,
                0.9999151889493628,
                0.22270013366638422
            ],
            [
                0.999995214903796,
                0.9999970976873244,
                0.9999945777823247,
                0.9999974387187077,
                0.999994577782324,
                0.9999977396757025,
                0.9999945777816835,
                0.9999952149066464,
                0.9999930377462425,
                0.999997097689057
            ],
            [
                5.093702764129364e-06,
                0.000123394632379942,
                0.00029595709388014255,
                0.008577486570015325,
                0.0001584361970764834,
                0.008577486617534644,
                0.00048785715459979864,
                0.0003353500145764115,
                8.481103079352604e-05,
                0.00010889687006423939
            ],
            [
                0.9999982396561573,
                0.9999980052693276,
                0.9999869928685312,
                0.9999251537819083,
                0.9999962733620494,
                0.9999974387184011,
                0.9999986290427935,
                0.9999982396569969,
                0.9999984465020608,
                0.9999974387165692
            ],
            [
                0.9999832985742033,
                0.9999756997679764,
                0.9999832985841441,
                0.9998911030400035,
                0.9999852610162828,
                0.9999952149049389,
                0.2942149659744614,
                0.9999832985722189,
                0.0001233945596211086,
                0.9999869928761935
            ],
            [
                0.4378234991142019,
                3.7266392829528392e-06,
                0.9999485577622661,
                0.22270013882530887,
                7.484620008227652e-05,
                0.9999974387181362,
                0.06008664807010359,
                0.348645142101806,
                0.9959298631297447,
                0.9990889486834231
            ],
            [
                2.1444948395559206e-05,
                0.9999970976873231,
                2.7535691001590016e-05,
                0.999915188939188,
                0.9999921107364751,
                0.99998987000661,
                1.6701415856588526e-05,
                0.9999938558232021,
                0.9999898700102525,
                0.9999687980775741
            ],
            [
                0.00017952794264684607,
                0.029312233560244455,
                7.484626278955236e-05,
                1.6701415865641523e-05,
                1.6701415854279704e-05,
                1.670141785237998e-05,
                1.892515725376564e-05,
                3.5356267555952205e-05,
                7.889262584508638e-06,
                3.5356267541418054e-05
            ],
            [
                0.1480471923932738,
                0.9859363734603839,
                0.999860177877938,
                0.9993736658380284,
                0.005220126776876857,
                0.9994472212336397,
                0.00010889686905333766,
                3.1201922508819695e-05,
                0.9999151889505031,
                2.4300252285704095e-05
            ],
            [
                0.00020342696973267105,
                0.0001584362134133291,
                0.0001795280387425869,
                0.0004878571708349722,
                0.0002611902764236697,
                0.000230506621038161,
                0.00015843625380709215,
                0.0004878571055252999,
                0.0002611902733534103,
                0.0005527786460243604
            ],
            [
                0.14804720554957726,
                2.4300243595999808e-05,
                1.670142780381727e-05,
                0.18242551936144574,
                2.2603242977802297e-06,
                0.9978172837509002,
                0.5621765008857981,
                0.9990889486221761,
                1.6701417843448496e-05,
                0.40733340004593027
            ],
            [
                0.9999970976866314,
                3.53562380286151e-05,
                0.9999977396759726,
                0.9999986290424673,
                0.9999987901338839,
                0.9999984465024309,
                0.9999980052693277,
                0.9999989322967486,
                0.9999987901343176,
                0.9999984465018754
            ],
            [
                0.9999339478716401,
                0.9997040428411934,
                0.5,
                0.26894141551050293,
                0.9999339478241943,
                0.9998766054123543,
                0.9998601779459254,
                0.9998415638240643,
                0.9997694932890064,
                0.9998415637687169
            ],
            [
                2.4300243598740258e-05,
                3.535625486069523e-05,
                2.4300243570893748e-05,
                0.9999151889598967,
                2.4300240711101413e-05,
                6.60521287717195e-05,
                0.9997965730270088,
                0.11920291263495984,
                5.144222585927004e-05,
                0.9999646437537157
            ],
            [
                0.00010889696085529394,
                1.4738987234550548e-05,
                2.4300234921326896e-05,
                0.3486451285660856,
                0.00017952790121781749,
                7.484622686261196e-05,
                8.939699491123385e-06,
                8.481104034637157e-05,
                2.75357041747467e-05,
                1.892515724633005e-05
            ],
            [
                6.96225956921868e-06,
                7.889264464895484e-06,
                0.999512142978205,
                2.4300246516082393e-05,
                1.670142979875954e-05,
                1.1478769493728398e-05,
                0.9999599363176244,
                3.535625487510076e-05,
                8.939696303010449e-06,
                0.22270012850745968
            ],
            [
                0.9999832985702517,
                0.9999756997507011,
                0.999995214904374,
                0.9999785550516269,
                0.9999251537641896,
                0.9999599362889685,
                0.9999785550592784,
                0.9999251537470008,
                0.9999724642991519,
                0.9999832985841411
            ],
            [
                0.09534946040040722,
                0.0675466977093867,
                0.16451647108926923,
                1.4738988990369329e-05,
                0.9994472213719521,
                0.09534946489910949,
                1.8925145965998754e-05,
                0.16451646699291617,
                3.5356267531385634e-05,
                0.9991959140592732
            ],
            [
                4.0063692054313215e-05,
                1.8925141463066202e-05,
                1.1478768117434013e-05,
                0.9999994284996916,
                0.9999930377445827,
                0.9999921107374196,
                0.9999885212346179,
                0.999995214904935,
                0.9999898700102356,
                0.9999962733616061
            ],
            [
                0.002182716127904353,
                0.10669058471438037,
                3.5356259091803945e-05,
                0.012431650578771143,
                9.610240288505138e-05,
                8.939699490700597e-06,
                0.022977368404675392,
                0.004070137568664,
                4.222834450236421e-06,
                0.03308597922294221
            ],
            [
                0.9999687980849847,
                0.9998601779777901,
                0.9999251537999178,
                0.9999852610127956,
                0.9999038976094637,
                0.9999151889817975,
                0.9999485577683908,
                0.9999869928700182,
                0.9999546021261455,
                0.6513548646660542
            ],
            [
                2.753568780461672e-05,
                0.9999546021426214,
                4.2228324372555256e-06,
                6.144175333289463e-06,
                0.9999687980924229,
                4.0063696902084474e-05,
                0.9997965729319299,
                1.1478766753082876e-05,
                7.889260699630574e-06,
                0.9999251537552232
            ],
            [
                0.9999417087139372,
                0.9999339478636148,
                0.9999599363176832,
                0.9999810748563587,
                0.11920291889306492,
                0.9999038975699802,
                0.9997040429086601,
                0.32082129433083023,
                0.9999251537997172,
                0.8807970826714614
            ],
            [
                2.4300232018837615e-05,
                0.00017952800438946373,
                7.88926147391909e-06,
                0.00017952800792612165,
                6.96225894750838e-06,
                8.939694939389958e-06,
                5.829129308896798e-05,
                0.00013982210630158876,
                0.0002959570199466565,
                8.481103455616976e-05
            ],
            [
                0.999925153800851,
                0.9999417087278891,
                0.999975699747731,
                9.61024593654037e-05,
                0.9999646437493326,
                0.9999546021260888,
                0.9999852610215536,
                0.9999151889386246,
                0.00015843619092394522,
                8.481107094608913e-05
            ],
            [
                0.0004878570948532292,
                0.0006263341237880168,
                0.0002959570576883814,
                0.9324533079218342,
                0.06754669395523943,
                0.00048785722479138344,
                0.004609573061792105,
                0.0002034269225321811,
                0.00023050663004576857,
                0.0001795279210873466
            ],
            [
                0.32082131381216084,
                0.9997965729977704,
                0.999876605425933,
                0.9998601778811665,
                0.9999251537732343,
                0.9999962733598443,
                0.9988304896889799,
                0.22270013882530884,
                0.9998911030661191,
                0.9998911031183468
            ],
            [
                0.9046505299595162,
                0.9986749778511393,
                0.9890130581284042,
                0.9964063973101996,
                0.9984988177294777,
                0.9859363708518423,
                0.9890130572176073,
                0.9975273767239151,
                0.9986749775880245,
                0.9796676444683271
            ],
            [
                0.9998601779612769,
                0.7549149813536518,
                0.9998766054709439,
                0.22270013366638422,
                0.4378234991142019,
                0.9994472212812339,
                0.9997965729797165,
                0.09534947453918644,
                0.9579122735862822,
                0.22270014914315833
            ],
            [
                0.0006263340789734484,
                0.002472622870069597,
                0.014063627249862615,
                0.006692851397933494,
                0.0015011819302507678,
                0.0008040861095064585,
                0.0005527785700024617,
                0.007577241260857426,
                0.00013982202203087238,
                0.000295957235013415
            ],
            [
                6.605216818444021e-05,
                0.9914225141506944,
                3.1201907628667734e-05,
                3.535624224094318e-05,
                0.994088930508938,
                5.8291279258636216e-05,
                7.484625362444268e-05,
                2.430024359458538e-05,
                0.00017952802536910748,
                8.48110105660795e-05
            ],
            [
                0.004609573125890264,
                0.9995121428827525,
                0.9975273765154519,
                0.9996646497751862,
                0.9991959142098608,
                0.5926665999540697,
                0.03732688640708807,
                0.9999339478407382,
                0.9998415637285814,
                0.20181322226037884
            ],
            [
                0.0006263342361523634,
                0.00012339461794666872,
                0.00043055713309236507,
                8.481106138460176e-05,
                0.0007096705054764212,
                0.0007096703829605232,
                0.0003799845159789476,
                0.0004305571740130662,
                0.0534033331895608,
                0.00048785708372702793
            ],
            [
                0.00218271631958587,
                0.002800927458759177,
                0.9998204720806992,
                0.04742587317756678,
                0.000626334234112025,
                0.0004305570757633085,
                7.484620911178992e-05,
                8.481103099344347e-05,
                0.00015843621452903868,
                0.0002959571635684547
            ],
            [
                0.9999756997622797,
                0.9999417087352558,
                0.9999339478582786,
                1.0129988563730593e-05,
                0.9999151889395126,
                6.605212851269727e-05,
                4.006367768706288e-05,
                0.999959936322961,
                8.481103091322968e-05,
                9.610242518717262e-05
            ],
            [
                0.9975273773062341,
                0.9997694931904324,
                0.22270013882530887,
                0.9998415637285467,
                0.9998766054415584,
                0.03732689055684297,
                0.9959298622482397,
                0.9999251537862945,
                1.0129995801232122e-05,
                0.22270013366638422
            ],
            [
                0.999968798073847,
                0.9998415637652844,
                0.9999687980812332,
                0.9999151889502983,
                0.9999785550439528,
                0.9999251537552504,
                0.9999546021314878,
                0.9999687980886947,
                0.9996200155673632,
                0.9999038975855101
            ],
            [
                0.9999984465026162,
                0.9999977396746274,
                2.4300252309307336e-05,
                0.9999952149037948,
                0.999999057755294,
                0.9999957771670596,
                0.9999986290429567,
                0.9999974387187058,
                0.9999869928653489,
                0.99999926617867
            ],
            [
                0.99989110304094,
                0.9999599363126687,
                0.9999546021422361,
                0.9998415638074302,
                0.32082130082460697,
                0.9999646437537568,
                0.7057850154599562,
                0.9999930377420918,
                0.9999646437622624,
                0.9999038976207496
            ],
            [
                0.9998601778602448,
                0.9996200154555549,
                NaN,
                0.9999785550465053,
                6.96225707894582e-06,
                0.9998911031170887,
                0.9626731099786093,
                0.9998911031169144,
                0.9998204719710603,
                0.9999885212305316
            ],
            [
                0.9999485577680401,
                0.8670357666736772,
                0.9996200154503371,
                0.4073334000459302,
                0.9999485578003603,
                0.9997694933185981,
                0.9999599363222861,
                0.9998204721016423,
                0.03308597981882656,
                0.7057850216484838
            ],
            [
                4.00636969128696e-05,
                0.06754669489377624,
                0.07585818002124356,
                0.0002611903325471061,
                0.9999921107405318,
                0.20181322946142374,
                0.22270013882530887,
                0.5621765008857981,
                0.9997694933479013,
                0.003172682801249358
            ],
            [
                0.9998911031061954,
                0.999903897553642,
                0.5621765008857981,
                0.999933947863906,
                0.24508500761839527,
                0.9998911030932185,
                0.9999038975894926,
                0.999941708758331,
                0.9999251537467121,
                0.0009110511618697926
            ],
            [
                0.37754066879814546,
                0.9999810748472774,
                0.4687906266262437,
                0.9999756997507111,
                0.9999885212277801,
                0.0600866476493228,
                0.9999151889400839,
                0.015906395123147725,
                0.9999646437536301,
                0.13296425050508953
            ],
            [
                0.9999952149049366,
                0.9999832985761922,
                0.9999832985821729,
                0.9999885212264085,
                0.9999885212318816,
                0.999981074845087,
                3.5356246471407274e-05,
                0.9999852610127815,
                0.9999974387184003,
                0.9999832985722032
            ]
        ]
    },
    {
        "q_id": "7819_mmlu_math",
        "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,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            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": [
            [
                0.999964643732439,
                0.9999151889284097,
                0.9999599363078321,
                0.9999724643187504,
                0.9999930377429205,
                0.9998415638099566,
                0.9999599363221524,
                0.9999151889183269,
                0.9999810748562736,
                0.9999417087414566
            ],
            [
                1.209865683518615e-06,
                7.889265407090955e-06,
                2.7535687811228037e-05,
                4.78509563550957e-06,
                4.22283394786293e-06,
                2.9023112931213857e-06,
                0.9991959140073625,
                2.5612816000145246e-06,
                3.726641061027928e-06,
                2.902313023039776e-06
            ],
            [
                1.6701417861189946e-05,
                1.3709573702647743e-06,
                1.8925148238808306e-05,
                1.2098661161861e-06,
                2.9023130230846496e-06,
                1.1478764019787597e-05,
                1.209865827740176e-06,
                4.785092783371756e-06,
                1.5534973841895917e-06,
                1.5534971989907999e-06
            ],
            [
                1.4738987242137685e-05,
                0.9999485577863896,
                6.14417606659952e-06,
                0.9999687980998037,
                1.5534971989992774e-06,
                3.120191880118183e-05,
                3.2887498494551953e-06,
                1.0677027427068966e-06,
                1.3007126912542439e-05,
                4.78509563550957e-06
            ],
            [
                5.144222589407736e-05,
                4.222832437639588e-06,
                2.7535697660090726e-05,
                0.0002611904328853529,
                0.9465966745315055,
                1.0129993394811673e-05,
                3.1201907650801864e-05,
                6.60521445946645e-05,
                6.962257079553702e-06,
                0.9993736658260779
            ],
            [
                2.430024941804299e-05,
                5.829125856424875e-05,
                4.222835458117536e-06,
                9.610239202344896e-05,
                2.7535694377870696e-05,
                4.006367784344724e-05,
                5.144223203214182e-05,
                0.99944722139025,
                1.473898197063434e-05,
                0.00020342699705616006
            ],
            [
                1.7603436330091044e-06,
                1.473898021151881e-05,
                2.5612812946681295e-06,
                1.067703251864202e-06,
                4.78509506499309e-06,
                4.785093353787868e-06,
                1.3709567165461505e-06,
                1.553497754577351e-06,
                4.78509563546605e-06,
                2.5612822106841303e-06
            ],
            [
                6.9622562492265485e-06,
                3.726638839806038e-06,
                6.144172404380855e-06,
                3.726639284103523e-06,
                2.2603248367656408e-06,
                1.9947290081286418e-06,
                8.939700566143004e-06,
                4.2228324375973415e-06,
                7.889263525893087e-06,
                1.0129987356375273e-05
            ],
            [
                4.785096205582214e-06,
                1.994729959270648e-06,
                4.0063692172075196e-05,
                8.939700566565793e-06,
                5.422218323399208e-06,
                7.889264465986113e-06,
                1.147876812538911e-05,
                5.422218323290717e-06,
                8.93969310675186e-06,
                1.6701421842140854e-05
            ],
            [
                6.144173136952939e-06,
                4.539789028295303e-05,
                2.260325375664839e-06,
                3.2887490653647836e-06,
                1.1478770862589836e-05,
                4.222833947774596e-06,
                2.260324567268294e-06,
                5.4222215552470286e-06,
                1.5534983101478522e-06,
                1.5534984953199313e-06
            ],
            [
                1.147876949310201e-05,
                6.962257079465052e-06,
                1.7603432132784448e-06,
                1.8925152750176348e-05,
                3.726641061058432e-06,
                7.889265405333033e-06,
                2.9023112929973233e-06,
                1.5534977545603963e-06,
                2.5612828212676906e-06,
                1.2098659719661556e-06
            ],
            [
                3.120190020613144e-05,
                7.484623611811155e-05,
                NaN,
                0.000261190246663434,
                0.99998107485853,
                0.0003799844364396507,
                8.481108145286679e-05,
                4.539786864000808e-05,
                0.00015843627330665874,
                0.9999785550567065
            ],
            [
                5.422221554670048e-06,
                6.144174601879434e-06,
                7.889265406567165e-06,
                2.144494074076854e-05,
                2.2603248367512505e-06,
                1.4738988997044936e-05,
                0.9993736659065255,
                6.144173136885882e-06,
                7.484622719695779e-05,
                0.9993736657476342
            ],
            [
                7.889261644760245e-06,
                4.222832437497486e-06,
                8.315284241333265e-07,
                6.962255419570695e-06,
                6.144175333926503e-06,
                1.994729483694599e-06,
                2.5612828212676906e-06,
                9.422450431732037e-07,
                6.475947982002148e-07,
                5.715007195410849e-07
            ],
            [
                0.999769493257463,
                0.679178686187839,
                0.9999852610233104,
                0.13296425394084313,
                0.9996646498895055,
                0.34864514210180597,
                0.8519528076067262,
                0.5621765008857981,
                0.43782349911420193,
                0.9998911030647532
            ],
            [
                0.9999832985721862,
                2.1444948408977715e-05,
                5.422221555192784e-06,
                0.9875683490210408,
                4.785096205830278e-06,
                0.9999646437577213,
                0.9968273175013921,
                1.8925145980181433e-05,
                0.00023050674259059,
                0.9999832985821401
            ],
            [
                1.5534971989992774e-06,
                7.889260704818233e-06,
                6.962257079173776e-06,
                2.1444945853375776e-05,
                6.962255419653012e-06,
                7.889264466445326e-06,
                6.144172404380855e-06,
                6.1441767989541075e-06,
                1.012999460251781e-05,
                7.889259764079887e-06
            ],
            [
                1.6701423833436905e-05,
                5.422218969720291e-06,
                8.93969417214416e-06,
                3.726640616748873e-06,
                5.8291251608160896e-05,
                1.3007123812057577e-05,
                2.4300234936443568e-05,
                6.14417313680765e-06,
                3.1201903922734266e-05,
                5.4222202624563834e-06
            ],
            [
                4.222831934202483e-06,
                4.5397874048967995e-05,
                5.144221365238367e-05,
                4.785094494576774e-06,
                1.8925143725892257e-05,
                1.300712846411008e-05,
                0.9999810748449934,
                7.889259764079887e-06,
                2.7535687811228037e-05,
                1.3007134665934505e-05
            ],
            [
                5.715003789017068e-07,
                1.3709576971160984e-06,
                4.78509563546605e-06,
                1.55349775456958e-06,
                5.715003789017068e-07,
                8.3152792852928e-07,
                4.222833947674739e-06,
                8.939693106987645e-06,
                2.5612828213352452e-06,
                2.2603251062147097e-06
            ],
            [
                6.962256248871951e-06,
                3.1201907648418184e-05,
                5.422218969601935e-06,
                4.222832940777184e-06,
                5.715005832827105e-07,
                4.2228349546493465e-06,
                8.315278294038928e-07,
                4.785094494672519e-06,
                5.422218323231539e-06,
                8.93969310662177e-06
            ],
            [
                9.4224425692559e-07,
                2.260324028404236e-06,
                3.288748673265808e-06,
                1.5534984953199313e-06,
                1.7603440527046419e-06,
                9.422445938964242e-07,
                2.2603248367656408e-06,
                1.9947290081177566e-06,
                8.939699500896292e-06,
                2.2603248367512505e-06
            ],
            [
                0.9999151889181905,
                0.9997965729781864,
                0.9993736658990929,
                0.9999646437492865,
                0.9999724643121822,
                0.9996200154692297,
                0.9999756997505767,
                0.9999251537727529,
                0.9999546021421803,
                0.9999885212264054
            ],
            [
                0.9999938558239382,
                0.9933071495679382,
                0.9999977396759748,
                0.9999785550413738,
                0.9999251537460472,
                0.9999930377454103,
                0.9999938558275957,
                0.9999962733611621,
                0.9999910602994442,
                0.9999885212292275
            ],
            [
                1.0129988564430787e-05,
                5.422221555192784e-06,
                1.8925148238291944e-05,
                1.4738985484227961e-05,
                0.9999546021097317,
                7.889260704308795e-06,
                0.9999687980998022,
                1.5534984953199313e-06,
                0.9999599362934992,
                1.553498495308628e-06
            ],
            [
                2.4300252317882297e-05,
                1.1478770862255766e-05,
                2.902311985079115e-06,
                8.93969310647542e-06,
                1.6701417861949427e-05,
                5.8291244694483874e-05,
                2.9023130230133794e-06,
                3.726639728224814e-06,
                2.2603248367173307e-06,
                1.8925145983348442e-05
            ],
            [
                0.9998415637265112,
                2.9023116391477434e-06,
                0.9999151889788636,
                6.144173137014406e-06,
                3.7266379512857925e-06,
                4.2228324375512536e-06,
                2.4300246525276163e-05,
                1.4738980213341866e-05,
                3.7266379513162962e-06,
                1.8925157264471508e-05
            ],
            [
                0.9999417087553356,
                0.9999930377404308,
                1.5534984953298217e-06,
                6.144176066443055e-06,
                0.9999945777803839,
                5.829125858715015e-05,
                6.144176798255599e-06,
                2.1444940740066406e-05,
                0.9999546021259631,
                NaN
            ],
            [
                0.9999869928715365,
                0.9999852610233009,
                0.9999852610233009,
                0.9999885212318748,
                0.9999930377454104,
                0.9999898700114365,
                0.9999921107336538,
                0.9999945777816767,
                0.9999869928653341,
                0.9999869928730887
            ],
            [
                1.9947304348595095e-06,
                1.1478769493728398e-05,
                1.0129995810076682e-05,
                4.7850967763512445e-06,
                1.3007133115667397e-05,
                6.475946438022905e-07,
                7.889265406438011e-06,
                1.4738987242968784e-05,
                1.99473067264854e-06,
                8.93969630348202e-06
            ],
            [
                5.4222202624563834e-06,
                3.726639284017094e-06,
                4.222831934286977e-06,
                1.3007123810306773e-05,
                1.553497384196656e-06,
                6.962257079376403e-06,
                8.939699500489763e-06,
                0.9999832985801475,
                3.120190020068305e-05,
                1.5534975693869924e-06
            ],
            [
                5.422217676866151e-06,
                2.9023126771227976e-06,
                3.7266392840781026e-06,
                3.2887482812745586e-06,
                1.2098653950480359e-06,
                5.043472278312808e-07,
                2.753568780461672e-05,
                2.561281600049467e-06,
                5.422218969601935e-06,
                0.9995694429713825
            ],
            [
                1.2098655392921197e-06,
                1.0129988564430787e-05,
                2.1444950959196957e-05,
                6.144175334094145e-06,
                2.699577774579753e-07,
                7.338210679979539e-07,
                5.422218323349895e-06,
                4.222834954403545e-06,
                3.059022998569248e-07,
                1.3007128463352975e-05
            ],
            [
                0.00012339457475817416,
                3.2887494573561262e-06,
                0.00026119027812599176,
                0.00013982209062250782,
                3.535625911829982e-05,
                0.00043055703643335056,
                0.0011695102642395767,
                0.16451646494473965,
                0.00023050663267494372,
                4.006370171458602e-05
            ],
            [
                6.9622595694023114e-06,
                1.6701415868649062e-05,
                1.0129992187253088e-05,
                6.962257079629686e-06,
                6.605216041280767e-05,
                4.785093924047376e-06,
                7.889259764079887e-06,
                0.9999546021151239,
                1.012998977198894e-05,
                0.999985261021543
            ],
            [
                0.00012339456008432324,
                0.9998911030907974,
                0.9999852610145146,
                2.4300237830711845e-05,
                0.9999151889385265,
                0.00012339457485512604,
                0.00010889687025437763,
                2.7535681242383173e-05,
                4.5397868635383903e-05,
                0.99992515377279
            ],
            [
                2.9023119851055122e-06,
                4.222835457852533e-06,
                0.9999945777797374,
                7.889261644982674e-06,
                4.539787945561647e-05,
                4.2228334445370225e-06,
                5.422218323290717e-06,
                1.370956716519966e-06,
                4.222831934202483e-06,
                4.22283294098842e-06
            ],
            [
                0.9998911031297203,
                0.9996200155615594,
                0.999985261011,
                0.9999687980737526,
                0.9999962733616045,
                0.9999339478710932,
                0.9999785550592561,
                0.9999038976194401,
                0.9999599363221485,
                0.9999756997476807
            ],
            [
                0.9999952149032243,
                0.9999251537906008,
                0.9999756997505811,
                0.9999785550515903,
                0.9999938558253982,
                0.9999599363030408,
                0.9998415638021121,
                0.999994577780384,
                0.999995777164542,
                0.9999546021476133
            ],
            [
                1.1478768124992398e-05,
                7.889261644760245e-06,
                1.0129992185299915e-05,
                1.994729483680993e-06,
                1.012999339449843e-05,
                1.1478768124992398e-05,
                4.785093353787868e-06,
                4.5397852378781204e-05,
                7.88926258532661e-06,
                3.726638839806038e-06
            ],
            [
                0.9999785550490341,
                1.6701425824307884e-05,
                0.9999756997650606,
                2.902313022984344e-06,
                7.889264466344872e-06,
                3.535625492063251e-05,
                0.0001398220907445715,
                0.9999756997505781,
                0.9999251537370814,
                7.484621833788234e-05
            ],
            [
                5.422220262333096e-06,
                1.553498495338299e-06,
                4.222833444506298e-06,
                1.3709572068422585e-06,
                2.5612825160271407e-06,
                2.9023119851055122e-06,
                6.144177531660828e-06,
                1.3709572068354007e-06,
                2.2603240283888175e-06,
                5.422219616140078e-06
            ],
            [
                3.726639284017094e-06,
                6.962253759752719e-06,
                2.260323758882316e-06,
                4.222831934202483e-06,
                1.1478765388711023e-05,
                7.889260704732132e-06,
                3.726639728224814e-06,
                1.3709567165386693e-06,
                8.939695238211425e-06,
                8.315278293951957e-07
            ],
            [
                4.222833444506298e-06,
                1.3007133115430804e-05,
                1.4738987240824012e-05,
                3.2887482811908074e-06,
                1.55349775456958e-06,
                5.422217030555087e-06,
                1.892515726357648e-05,
                6.962258739530771e-06,
                2.561283126679493e-06,
                2.5612812947077304e-06
            ],
            [
                1.3709568799823232e-06,
                1.9947306726594253e-06,
                6.962254589617333e-06,
                7.889264466230069e-06,
                5.422217676397663e-06,
                6.144175334172377e-06,
                1.9947297215043796e-06,
                2.5612819053586272e-06,
                1.2098653950606901e-06,
                2.902312677084523e-06
            ],
            [
                1.670142781636389e-05,
                1.7603427936183298e-06,
                4.222834954687752e-06,
                3.726638839806038e-06,
                4.785095065132354e-06,
                1.3709572068478697e-06,
                1.1478768125201194e-05,
                8.93969417214416e-06,
                1.892515726357648e-05,
                1.0129989771823107e-05
            ],
            [
                4.785096776194573e-06,
                5.422219616026655e-06,
                3.2887498493983645e-06,
                6.962254589528684e-06,
                1.3007126913346863e-05,
                6.962255419728997e-06,
                2.260323758939877e-06,
                6.144173869446876e-06,
                6.144177531208195e-06,
                1.2098662603961589e-06
            ],
            [
                1.994730197071414e-06,
                1.6701415867707307e-05,
                1.5534971989992774e-06,
                6.962254589433702e-06,
                4.5397868604005595e-05,
                2.902312677104321e-06,
                2.561282516042282e-06,
                7.889263525534328e-06,
                2.1444945853375776e-05,
                1.6701425823882575e-05
            ],
            [
                3.7266379513434106e-06,
                4.0063682625048554e-05,
                2.7535694379773952e-05,
                5.8291272451829125e-05,
                0.9997965730510352,
                1.4738980213985297e-05,
                1.4738985482753428e-05,
                7.484626291261785e-05,
                0.9998911031296585,
                8.939700566565793e-06
            ],
            [
                3.726637951170554e-06,
                1.7603434231385591e-06,
                6.475945666009864e-07,
                2.9023133690425823e-06,
                1.76034300345598e-06,
                1.7603438428460541e-06,
                1.553498495338299e-06,
                3.726638839806038e-06,
                5.422220262264056e-06,
                7.338211554783522e-07
            ],
            [
                0.9999339478789658,
                0.9999546021205649,
                0.9998911030777563,
                0.9999970976880543,
                0.9999251537385788,
                0.9999852610197855,
                0.9999832985821381,
                0.6224593241981982,
                0.9999756997563707,
                0.9999151889182682
            ],
            [
                8.93969417150998e-06,
                5.422217676979575e-06,
                1.3007126913346863e-05,
                4.006370650653807e-05,
                7.889264466445326e-06,
                1.012998977108606e-05,
                1.6701417860795016e-05,
                2.1444945854624007e-05,
                6.9622587393661365e-06,
                2.561283432005142e-06
            ],
            [
                1.8925150494750372e-05,
                3.726640172385136e-06,
                2.561281294644835e-06,
                1.8925150492616083e-05,
                7.484625386839543e-05,
                7.8892625849535e-06,
                8.939698434657777e-06,
                6.962253759486771e-06,
                1.4738985484549675e-05,
                3.120191507912884e-05
            ],
            [
                2.902312677104321e-06,
                5.8291244679640374e-05,
                2.90231163910023e-06,
                7.889265406294507e-06,
                1.0129992187105678e-05,
                6.96225956921868e-06,
                2.7535704221626983e-05,
                2.144494329348333e-05,
                8.481103114893482e-05,
                8.939700566565793e-06
            ],
            [
                2.9023123310580418e-06,
                1.1478772229551402e-05,
                1.0129995809929273e-05,
                4.2228349546493465e-06,
                6.144176799283803e-06,
                1.4738985485461206e-05,
                2.561282210562998e-06,
                4.78509392429544e-06,
                2.561281600049467e-06,
                3.7266397280485686e-06
            ],
            [
                3.1201918807538294e-05,
                5.422217676866151e-06,
                5.422217676979575e-06,
                7.889265406294507e-06,
                1.0129990979215566e-05,
                0.00015843623535638724,
                1.1478769492893215e-05,
                1.8925148238808306e-05,
                5.4222183234485234e-06,
                5.829126548301662e-05
            ],
            [
                3.120190392670705e-05,
                2.902310947190096e-06,
                6.962259569003389e-06,
                5.422218969720291e-06,
                3.7266379512857925e-06,
                5.422220908925639e-06,
                1.2098662604291696e-06,
                1.9947290080905435e-06,
                6.144177531532303e-06,
                6.14417533430649e-06
            ],
            [
                1.3709572068354007e-06,
                1.3709567165386693e-06,
                5.42222090882208e-06,
                6.60521524840326e-05,
                1.3007130014376633e-05,
                2.7535681248693975e-05,
                1.994729721482609e-06,
                0.999915188968877,
                1.1478772230198667e-05,
                1.994730434847717e-06
            ],
            [
                2.7535704212311033e-05,
                1.0129992187253088e-05,
                1.3007123811229494e-05,
                4.222833444467892e-06,
                7.484626286034225e-05,
                1.7603425837702984e-06,
                1.3007131564643372e-05,
                4.7850967763512445e-06,
                4.222831934202483e-06,
                1.6701423832586287e-05
            ],
            [
                0.9998911030777563,
                0.999704042865614,
                0.9999852610145151,
                0.9999038976194303,
                0.9992903294521301,
                0.9997965730751475,
                0.9997040427953574,
                0.9998766053663058,
                0.9993736657520793,
                0.999876605454525
            ],
            [
                2.1444958633416914e-05,
                6.962257079173776e-06,
                3.7266406168403854e-06,
                5.422217676797111e-06,
                9.4224425692559e-07,
                5.422219615829396e-06,
                1.994730434847717e-06,
                1.3007123812317831e-05,
                2.5612816000331606e-06,
                1.3007126913583456e-05
            ],
            [
                1.4738978454950406e-05,
                0.9999151889789851,
                2.902312677084523e-06,
                2.2603234894745224e-06,
                5.422219616085833e-06,
                4.785093923982095e-06,
                4.78509563555309e-06,
                9.422450431912e-07,
                2.2603242978778778e-06,
                2.902311639126627e-06
            ],
            [
                0.9999785550464829,
                0.9999485577679806,
                0.9999852610215436,
                0.9999952149055054,
                0.9999885212318759,
                0.9999756997563761,
                0.9999970976890528,
                0.9999898700114365,
                0.9999852610162727,
                0.9999687980737689
            ],
            [
                2.561283432005142e-06,
                1.067703251864202e-06,
                1.553498310118888e-06,
                0.9998766054400844,
                1.067703379154416e-06,
                0.9999546021367831,
                0.999985261016273,
                1.670141984118446e-05,
                0.9999646437492937,
                4.5397890254712545e-05
            ],
            [
                6.144176066353646e-06,
                4.2228349546493465e-06,
                0.996827316600831,
                7.484620930074429e-05,
                1.1478773597870298e-05,
                0.9465966681286702,
                0.9998415638022435,
                1.012999460108057e-05,
                0.9971990726621994,
                0.9999546021097218
            ],
            [
                0.00012339453070430936,
                0.999992110739307,
                3.5356246487099006e-05,
                6.605216827622735e-05,
                0.9999921107374373,
                1.1478773598099973e-05,
                7.484625393265086e-05,
                0.9998601779428534,
                9.610244930364555e-05,
                0.00017952805159105365
            ],
            [
                8.93969736929749e-06,
                0.9997388095676922,
                1.0129992186387057e-05,
                1.670141586949968e-05,
                4.222834954514924e-06,
                5.422218969720291e-06,
                6.1441775312976045e-06,
                6.962255418924822e-06,
                6.962255419475714e-06,
                3.4663249714451116e-07
            ],
            [
                1.5534984953298217e-06,
                4.785093924047376e-06,
                1.0129994601688632e-05,
                1.3007128462785148e-05,
                3.7266379512112265e-06,
                2.4300246523066122e-05,
                4.006367784548767e-05,
                3.2887482812506295e-06,
                8.939695237813028e-06,
                0.9999646437450763
            ],
            [
                1.7603427935967163e-06,
                2.561282821352716e-06,
                5.422219616026655e-06,
                8.93969736942758e-06,
                1.8925143721761383e-05,
                3.288750633569722e-06,
                8.939697369151141e-06,
                6.1441767990323395e-06,
                1.3007123811229494e-05,
                1.3007131564643372e-05
            ],
            [
                3.726640172503764e-06,
                3.7266401725681614e-06,
                7.889263526093993e-06,
                1.3709572068354007e-06,
                3.927861534406222e-07,
                1.1478769493331685e-05,
                7.889259763857458e-06,
                8.315282259051341e-07,
                9.422444815726566e-07,
                6.144173869502757e-06
            ],
            [
                0.9999251537816681,
                0.9999546021421827,
                0.8354835391516133,
                0.9999485577863536,
                0.26894141551050293,
                0.9997694932575704,
                0.9046505286741726,
                0.8519528076067262,
                0.7549149813536518,
                0.9999852610232993
            ],
            [
                1.0129992186387057e-05,
                3.726640172503764e-06,
                0.00012339456008432324,
                6.144173136885882e-06,
                1.0129990979215566e-05,
                0.9999952149043645,
                1.4738981969240237e-05,
                6.144172404218801e-06,
                7.889266347356409e-06,
                4.539787402650773e-05
            ],
            [
                0.9998601778760948,
                0.02931223350724656,
                0.4073334000459302,
                0.6791787056691698,
                0.9999417087067253,
                0.9796676465089335,
                0.999841563802165,
                0.9998911030649053,
                0.9525741246345829,
                0.9999038975735851
            ],
            [
                1.473898724181597e-05,
                3.288750633569722e-06,
                1.994729721482609e-06,
                1.0129987355785634e-05,
                6.475951069961737e-07,
                1.5534984953298217e-06,
                6.1441767990323395e-06,
                1.4738988999377379e-05,
                2.1444945853999886e-05,
                5.715003107715166e-07
            ],
            [
                1.5534971989809095e-06,
                3.288748673295719e-06,
                1.553497384180408e-06,
                2.7535681250497054e-05,
                2.2603234895053587e-06,
                4.222835458044565e-06,
                1.8925157263094544e-05,
                2.56128282131428e-06,
                3.288749457409966e-06,
                4.2228324375512536e-06
            ],
            [
                7.338210679909462e-07,
                1.6701425823457267e-05,
                1.5534977545603963e-06,
                1.5534983101549167e-06,
                4.785095635592258e-06,
                2.561283431942246e-06,
                8.939697369671496e-06,
                2.902312331125353e-06,
                0.9999599363221628,
                4.2228324377164004e-06
            ],
            [
                6.144177531599359e-06,
                1.6701423834591316e-05,
                1.1478772230198667e-05,
                8.939694172290508e-06,
                2.144495608222158e-05,
                5.422220262333096e-06,
                1.1478766756444477e-05,
                6.144172404380855e-06,
                1.8925143725892257e-05,
                8.9396941718352e-06
            ],
            [
                2.2603234895176927e-06,
                1.1478773597118638e-05,
                7.889261644982674e-06,
                4.006370172712009e-05,
                0.9999339478474795,
                0.9999810748472532,
                3.288750633569722e-06,
                4.7850950649408664e-06,
                4.785093924103951e-06,
                0.999968798092358
            ],
            [
                1.2098658277181688e-06,
                5.422218322763051e-06,
                5.043475885657239e-07,
                4.785092783371756e-06,
                1.2098659719716573e-06,
                4.222832940834793e-06,
                2.2603248367656408e-06,
                9.422444815679433e-07,
                7.338212429504183e-07,
                7.8892625849535e-06
            ],
            [
                0.9998204720980665,
                0.9999852610216202,
                0.00010889687018941373,
                0.9999599363125995,
                0.999954602115151,
                0.00010889693515967489,
                0.9999869928668845,
                0.00023050677027072224,
                0.00017952798717633654,
                6.605215252536083e-05
            ],
            [
                1.8925145982866508e-05,
                0.9998204719487146,
                4.222832941072913e-06,
                2.902313023039776e-06,
                1.994729721482609e-06,
                1.147876402018431e-05,
                1.8925141470949294e-05,
                6.1441767990323395e-06,
                1.5534975693792215e-06,
                4.785092783319532e-06
            ],
            [
                1.370957860567974e-06,
                3.726640616748873e-06,
                6.962254589528684e-06,
                2.561281905376098e-06,
                2.9023133690425823e-06,
                7.889263525663481e-06,
                3.7266388396128453e-06,
                4.222832437639588e-06,
                6.96225956921868e-06,
                3.5356254914330094e-05
            ],
            [
                0.9997388096606132,
                0.9999785550567011,
                0.9999832985701939,
                0.9999417087205692,
                0.9998204720342186,
                0.999933947823871,
                0.9997694933400741,
                0.9999599363173711,
                0.9984988179278821,
                0.999964643732436
            ],
            [
                2.753569437145972e-05,
                2.2603248367656408e-06,
                6.144173136729416e-06,
                1.8925145982866508e-05,
                4.22283545808297e-06,
                1.3709576971379186e-06,
                6.1441767989541075e-06,
                5.1442238144007945e-05,
                6.1441775312976045e-06,
                1.3007133115903994e-05
            ],
            [
                3.120190020862863e-05,
                1.4738976700366126e-05,
                7.889264466230069e-06,
                7.889260704531226e-06,
                1.0129988563343644e-05,
                1.5534981249496567e-06,
                7.484625397893652e-05,
                1.670142781636389e-05,
                4.006367785525258e-05,
                3.7266388397721442e-06
            ],
            [
                3.726641060956752e-06,
                9.610240337377108e-05,
                1.3007125361755747e-05,
                1.0129987356191011e-05,
                0.9999810748585568,
                2.2603251061849014e-06,
                0.0008040859811796393,
                2.7535697654881812e-05,
                1.8925143725892257e-05,
                1.3007134665934505e-05
            ],
            [
                7.889260704531226e-06,
                0.9999852610233015,
                0.00010889692208924732,
                1.300712536258383e-05,
                1.012998977088337e-05,
                1.6701415869924985e-05,
                1.0129989771823107e-05,
                2.1444958633416914e-05,
                0.999876605410638,
                0.999915188928393
            ],
            [
                2.5612825159421147e-06,
                0.00013982214046315286,
                1.0129995809247506e-05,
                7.88925976397226e-06,
                8.939697368663308e-06,
                2.9023116391477434e-06,
                0.9914225159168286,
                0.9999151889688184,
                1.147876538789672e-05,
                0.999954602147594
            ],
            [
                3.5356238059741304e-05,
                2.1444943298320236e-05,
                0.9999599362934879,
                2.4300234933172706e-05,
                0.9999852610162715,
                0.9999687980811924,
                0.00033535026743106535,
                0.9989677690687634,
                2.561281600049467e-06,
                3.72664061681327e-06
            ],
            [
                0.9999970976876689,
                6.962256249606473e-06,
                1.4738985485461206e-05,
                8.939698434966738e-06,
                3.2887482812506295e-06,
                0.9999599363030484,
                1.1478770861211786e-05,
                7.889261644760245e-06,
                3.535625492063251e-05,
                1.1478773598538445e-05
            ],
            [
                1.8925141469950998e-05,
                0.0002034270458400805,
                3.1201922520397544e-05,
                3.120191508321514e-05,
                4.53978794604058e-05,
                6.144174601410037e-06,
                8.939695238333382e-06,
                0.9999869928746368,
                0.9999485577863448,
                0.9999785550413645
            ],
            [
                1.8925152751174644e-05,
                0.9997965730031658,
                8.93969630317306e-06,
                1.553498310118888e-06,
                1.76034300345598e-06,
                8.93970056565517e-06,
                7.889261644501938e-06,
                2.561282515988704e-06,
                3.7266397283231055e-06,
                1.2098662604049616e-06
            ],
            [
                6.144173137014406e-06,
                2.9023133690637e-06,
                7.889263525778283e-06,
                1.2098652508347793e-06,
                2.2603234894745224e-06,
                3.7266401725935817e-06,
                1.9947299592824403e-06,
                4.222834451169694e-06,
                2.2603234894560207e-06,
                4.222833444467892e-06
            ],
            [
                0.9999977396757022,
                0.9999974387180947,
                0.9999910603047634,
                0.9999967112501504,
                0.9999957771655488,
                0.999996273360716,
                0.9999485577679644,
                0.9999810748517602,
                0.999995777166052,
                0.9999921107364743
            ],
            [
                1.1478772229989872e-05,
                0.9999151889283684,
                1.3007126913346863e-05,
                1.994729245917502e-06,
                2.1444953524161264e-05,
                7.889266346746518e-06,
                6.144176799166453e-06,
                2.7535681250497054e-05,
                2.1444945856418342e-05,
                7.88926540679677e-06
            ],
            [
                5.144220135754627e-05,
                1.4738978456049602e-05,
                2.753568124769226e-05,
                8.93969310675186e-06,
                5.422218969463855e-06,
                2.561282210701601e-06,
                9.610240330734994e-05,
                5.422218323290717e-06,
                5.422217676925328e-06,
                1.7603434231505666e-06
            ],
            [
                4.7850944945245504e-06,
                0.5,
                0.06008664638698042,
                0.5,
                0.005911067499046399,
                0.9995121428242264,
                0.9998415637831035,
                0.6224593312018546,
                0.40733340004593027,
                3.2887506334560605e-06
            ],
            [
                6.144173136885882e-06,
                4.785096776303374e-06,
                1.0129993393945642e-05,
                4.785096205830278e-06,
                1.670141587031992e-05,
                0.9999687980849142,
                6.962254589528684e-06,
                6.144177531599359e-06,
                6.962259569484628e-06,
                3.726640172503764e-06
            ],
            [
                5.829124465589078e-05,
                1.3709568799592562e-06,
                3.288750241410738e-06,
                3.5356254903911806e-05,
                3.726638395527247e-06,
                4.78509506499309e-06,
                2.2603248367512505e-06,
                1.2098652508144226e-06,
                1.3007134665934505e-05,
                2.753570421361326e-05
            ],
            [
                1.5534983101478522e-06,
                1.4738985485461206e-05,
                2.2603234895053587e-06,
                2.144495352474637e-05,
                9.422445938964242e-07,
                1.2098661161982042e-06,
                2.9023112931688987e-06,
                1.0677033791437343e-06,
                2.561283432005142e-06,
                1.553497384180408e-06
            ],
            [
                1.1478768124324254e-05,
                6.144177531459659e-06,
                4.22283344433731e-06,
                1.6701417861949427e-05,
                1.300712691308661e-05,
                6.962256249758443e-06,
                2.4300249411766472e-05,
                1.300712846411008e-05,
                1.4738985484871391e-05,
                4.0063682616886836e-05
            ],
            [
                4.785093353787868e-06,
                5.422221555133606e-06,
                1.147876949310201e-05,
                6.962259568889411e-06,
                2.2603248367358324e-06,
                3.7266379512518984e-06,
                2.1444943296369872e-05,
                3.535626756251187e-05,
                4.785095065093186e-06,
                2.7535684529910724e-05
            ],
            [
                0.9999910603015644,
                0.9999339478553236,
                0.9998911030648022,
                0.99995460213136,
                0.9999151889789686,
                0.9999952149049351,
                0.9999885212265734,
                0.999876605410638,
                0.9999417087344762,
                0.9992903294538638
            ],
            [
                5.4222202624563834e-06,
                7.889265406904397e-06,
                1.67014238321306e-05,
                1.3007131564903626e-05,
                2.1444943292703185e-05,
                1.8925157262578186e-05,
                4.785093353687772e-06,
                5.4222202624563834e-06,
                4.785093923916815e-06,
                1.3007123810306773e-05
            ],
            [
                4.785094494628999e-06,
                4.785093924156175e-06,
                4.2228349546493465e-06,
                1.670142781520948e-05,
                1.5534979397740895e-06,
                3.2887506333812835e-06,
                1.9947299592933255e-06,
                4.222833444467892e-06,
                8.939694172290508e-06,
                6.9622570786798724e-06
            ],
            [
                1.1478773598329648e-05,
                7.48462272160166e-05,
                1.0129988563730593e-05,
                0.9999151889789345,
                5.422219616026655e-06,
                4.7850944943330625e-06,
                1.300713001414004e-05,
                6.962257909412379e-06,
                4.006370172318498e-05,
                3.120192251631124e-05
            ],
            [
                2.2603251062013478e-06,
                0.9999724642990576,
                1.0129994601301684e-05,
                6.96225707894582e-06,
                2.260324567268294e-06,
                1.0129992186387057e-05,
                6.144173869446876e-06,
                0.9999852610110056,
                3.288747889178668e-06,
                1.9947306726213275e-06
            ],
            [
                2.9023112931688987e-06,
                3.288750633569722e-06,
                3.2887490653647836e-06,
                3.7266383954560706e-06,
                6.962253759752719e-06,
                4.2228349546493465e-06,
                4.785094494576774e-06,
                3.288750241374845e-06,
                2.9023109471452223e-06,
                8.315280276263186e-07
            ],
            [
                2.902310947190096e-06,
                4.785095065132354e-06,
                1.2098662604192665e-06,
                2.9023119851635836e-06,
                1.5534979397677313e-06,
                6.475949525981759e-07,
                4.222834954687752e-06,
                1.553497384180408e-06,
                1.0677031245953668e-06,
                3.466325797888292e-07
            ],
            [
                4.785093924330255e-06,
                4.2228349546493465e-06,
                1.1478773597390071e-05,
                1.1478766755734576e-05,
                4.539785238406597e-05,
                1.670142781432848e-05,
                7.889265407090955e-06,
                7.889265406904397e-06,
                8.939698434657777e-06,
                6.144174601410037e-06
            ],
            [
                1.5534979397592542e-06,
                2.5612819053399912e-06,
                1.012999460108057e-05,
                4.2228324375512536e-06,
                8.315277302819205e-07,
                2.2603237589542675e-06,
                5.422218969463855e-06,
                1.147876402018431e-05,
                0.9995121427772238,
                2.2603237589542675e-06
            ],
            [
                1.4738978457336465e-05,
                1.7603425837702984e-06,
                5.715007195431641e-07,
                1.9947306726213275e-06,
                1.3709578605455302e-06,
                3.0590215399183813e-07,
                2.9023123311055552e-06,
                4.222833947728508e-06,
                7.889260703906985e-06,
                5.422218969720291e-06
            ],
            [
                1.5534971989907999e-06,
                1.3007134665934505e-05,
                1.3007123812057577e-05,
                2.7535691096552598e-05,
                1.892514147046736e-05,
                4.785094494402695e-06,
                0.00010889696121576468,
                4.785095065132354e-06,
                6.144173869446876e-06,
                8.93969310675186e-06
            ],
            [
                4.5397879429522924e-05,
                4.0063692185483734e-05,
                2.430023783309869e-05,
                6.962257909323729e-06,
                6.9622562492265485e-06,
                8.939696304002375e-06,
                1.300713311517055e-05,
                1.0129987355988324e-05,
                4.222832941111319e-06,
                3.1201907650801864e-05
            ],
            [
                5.422220908634683e-06,
                1.3709572068422585e-06,
                1.7603440527046419e-06,
                1.2098653950551882e-06,
                1.209865539274514e-06,
                4.222831934321543e-06,
                9.422444815726566e-07,
                2.5612831266165976e-06,
                1.553497199007048e-06,
                1.5534979397677313e-06
            ],
            [
                8.315283250343497e-07,
                1.1478772229781076e-05,
                5.422219615967477e-06,
                5.043475284430694e-07,
                1.0677026154774503e-06,
                1.2098662604192665e-06,
                1.0129990979031306e-05,
                2.144495096723246e-05,
                2.26032402841657e-06,
                7.88925976397226e-06
            ],
            [
                4.785094494628999e-06,
                3.72664061681327e-06,
                1.0677027427340866e-06,
                2.9023116391477434e-06,
                9.422447062240614e-07,
                1.0677031245953668e-06,
                2.902313023063532e-06,
                6.144176799166453e-06,
                2.260324567268294e-06,
                0.9998911030783433
            ],
            [
                3.2887486732358968e-06,
                1.9947301970451086e-06,
                8.315279285088606e-07,
                4.785092783371756e-06,
                1.2098659719524008e-06,
                1.3007131565376817e-05,
                2.2603248367173307e-06,
                3.466327863961242e-07,
                2.5612828212909852e-06,
                4.785093924251918e-06
            ],
            [
                3.120192251903545e-05,
                0.9999756997592703,
                4.539786861523573e-05,
                5.422218323290717e-06,
                1.670141985166528e-05,
                7.889260704179641e-06,
                2.9023112931213857e-06,
                3.288750241473551e-06,
                3.535626334323525e-05,
                3.12019225291377e-05
            ],
            [
                0.9999832985721839,
                1.8925152751174644e-05,
                2.561281905376098e-06,
                6.962254589528684e-06,
                7.889265406681968e-06,
                1.147877359872636e-05,
                1.3007128463352975e-05,
                2.9023130230846496e-06,
                4.785092783319532e-06,
                1.0129990979381404e-05
            ],
            [
                1.3007123811513407e-05,
                1.012999460251781e-05,
                8.939699500636112e-06,
                4.006370650464339e-05,
                9.422449308716635e-07,
                6.962255419728997e-06,
                4.785093353739995e-06,
                0.9999339478710692,
                2.5612831266946347e-06,
                2.9023112931873767e-06
            ],
            [
                3.288747889178668e-06,
                0.0004305571407579507,
                7.889264466445326e-06,
                1.0129990979215566e-05,
                3.120190764058611e-05,
                4.222835458044565e-06,
                6.144173869446876e-06,
                2.260324567302214e-06,
                1.3709572068422585e-06,
                0.999992110740236
            ],
            [
                0.9999151889687863,
                0.9999546021367668,
                0.9999869928653338,
                0.999915188948531,
                0.9999485577679555,
                0.9999151889889724,
                0.9999546021206244,
                0.9999756997679594,
                0.9399133510883348,
                0.867035763237924
            ],
            [
                2.902312677104321e-06,
                3.7266379512112265e-06,
                1.5534971989907999e-06,
                5.422217030555087e-06,
                3.726638839833152e-06,
                1.3007126912826352e-05,
                6.144173869240119e-06,
                6.962254589332388e-06,
                1.2098656835136636e-06,
                1.3709578605617394e-06
            ],
            [
                7.889266347356409e-06,
                2.144494329952946e-05,
                4.785093353787868e-06,
                2.1444945853999886e-05,
                8.939698435340743e-06,
                0.9999724643121858,
                9.610242643449187e-05,
                0.9999687980737504,
                1.5534971989907999e-06,
                2.1444958632714784e-05
            ]
        ]
    },
    {
        "q_id": "8597_mmlu_math",
        "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": [
            [
                0.9999910603015649,
                0.9999852610180333,
                0.9999546021205649,
                0.9999599363173896,
                0.9999646437408679,
                0.9999417087136441,
                0.9999885212291383,
                0.9998415637269378,
                0.9999599362934953,
                0.9999898700066057
            ],
            [
                0.9999898700114365,
                0.9999785550541495,
                0.9999869928746395,
                0.9999930377420908,
                0.9999852610110034,
                0.9999785550464791,
                0.999988521229139,
                0.9999938558246659,
                0.9999810748517638,
                0.99998329858015
            ],
            [
                0.9999832985781584,
                0.9998911031039645,
                0.9999810748495086,
                0.9999151889890767,
                0.9999599362982855,
                0.9999417087275647,
                0.9999599363221628,
                0.9999756997621728,
                0.9999724642957828,
                0.9999910603068939
            ],
            [
                0.9999980052693275,
                0.9999974387177893,
                0.9999967112497586,
                0.9999910603026315,
                0.9999938558224688,
                0.9999938558253988,
                0.9999945777823234,
                0.9999898700078143,
                0.9999962733616047,
                0.9999962733620493
            ],
            [
                0.9999687980849267,
                0.999933947823931,
                0.9999885212291413,
                0.9999599363030609,
                0.999988521229139,
                0.9999339478238921,
                0.9999785550592668,
                0.9999921107392965,
                0.9999646437619519,
                0.9999832985721872
            ],
            [
                0.9999724643154743,
                0.9999910603047628,
                0.9999852610215454,
                0.9999546021313848,
                0.9999921107402365,
                0.9999785550567036,
                0.9999869928730883,
                0.9999921107374152,
                0.9999921107355343,
                0.9999339478711735
            ],
            [
                0.999983298580152,
                0.9999852610197885,
                0.9999910603068942,
                0.9999852610127615,
                0.9999756997592744,
                0.9999756997650695,
                0.9999930377454131,
                0.9999869928715396,
                0.9999957771645421,
                0.9999785550592636
            ],
            [
                0.9999910602994342,
                0.9999852610127599,
                0.999991060306894,
                0.9999852610197894,
                0.9999898700053989,
                0.9999930377462407,
                0.9999910603068937,
                0.9999852610162746,
                0.9999921107402365,
                0.9999852610110026
            ],
            [
                0.9999885212291387,
                0.999986992869987,
                0.9999898700126442,
                0.9999832985741766,
                0.9999485578047708,
                0.9999852610127608,
                0.9999869928668877,
                0.9999869928730863,
                0.9999885212346123,
                0.999991060303697
            ],
            [
                0.9999756997505854,
                0.9999962733593832,
                0.9999852610215443,
                0.9999910603004999,
                0.9999930377445811,
                0.9999938558246662,
                0.9999930377437508,
                0.9999921107383557,
                0.9999910603015656,
                0.9999898700066062
            ],
            [
                0.9999910603036969,
                0.999964643732451,
                0.9999687980923682,
                0.9999885212291387,
                0.9999945777829695,
                0.99997569976797,
                0.9999898700041907,
                0.9998766053813334,
                0.9999646437366584,
                0.9999546021097568
            ],
            [
                0.9999910602994339,
                0.9999938558253988,
                0.9999724643089131,
                0.999986992866886,
                0.9999930377454112,
                0.9999810748449967,
                0.9999852610233045,
                0.9999852610215467,
                0.9999724642990628,
                0.9999151889487236
            ],
            [
                0.9999756997476879,
                0.9999869928730883,
                0.9999832985701967,
                0.9999724643154788,
                0.9999921107383557,
                0.9999898700066062,
                0.9999756997476957,
                0.9999898700126446,
                0.9999898700053986,
                0.9999687980923763
            ],
            [
                0.9999251537460603,
                0.9999724643056297,
                0.9999785550464798,
                0.999959936312614,
                0.9999687980923682,
                0.9999910603047624,
                0.9999977396751633,
                0.9999852610127603,
                0.999993855822469,
                0.9999957771665557
            ],
            [
                0.9999898700126435,
                0.9999832985701952,
                0.9999785550413638,
                0.9999687980923541,
                0.9999898700114365,
                0.9999485577679806,
                0.9999930377437508,
                0.999972464315473,
                0.9999967112517189,
                0.9999885212318754
            ],
            [
                0.9999599362935014,
                0.9999930377462406,
                0.9999869928653348,
                0.9999646437619555,
                0.9999687980960844,
                0.9999810748495086,
                0.9999869928761901,
                0.9999930377462407,
                0.9999869928715386,
                0.9999785550490354
            ],
            [
                0.9999785550567057,
                0.9999852610197881,
                0.9999646437450891,
                0.9999785550413696,
                0.9999832985821409,
                0.9999885212264026,
                0.9999810748427455,
                0.9999724642990628,
                0.9999724643121954,
                0.9999646437450943
            ],
            [
                0.9999832985701952,
                0.9999832985701952,
                0.9999885212346126,
                0.9999417087345441,
                0.9999832985821409,
                0.9999785550413659,
                0.999978555056705,
                0.9999687980774836,
                0.9999785550490375,
                0.9999756997592744
            ],
            [
                0.9999151889891026,
                0.9999785550515939,
                0.9999832985741811,
                0.999988521234613,
                0.9999945777823233,
                0.999993855822469,
                0.9999852610197885,
                0.9999646437366636,
                0.9999599362982944,
                0.9999785550541535
            ],
            [
                0.9999599363221608,
                0.9999885212277707,
                0.9999724643023452,
                0.9999756997592771,
                0.9999251537460472,
                0.9999546021205734,
                0.9999869928699864,
                0.999876605381538,
                0.9999417087275482,
                0.999986992873088
            ],
            [
                0.9999832985781602,
                0.9999687980812059,
                0.9999417087345305,
                0.9999646437535324,
                0.999975699767967,
                0.9999785550490391,
                0.9999852610233032,
                0.9999810748427408,
                0.9999646437493034,
                0.999991060299434
            ],
            [
                0.9999910603047624,
                0.9999810748495125,
                0.9999957771680656,
                0.9999910602994345,
                0.9999417087553831,
                0.9999938558261312,
                0.9999832985781592,
                0.9999885212318756,
                0.9999898700126439,
                0.9999898700102289
            ],
            [
                0.9999938558239337,
                0.9999756997650704,
                0.9999967112521111,
                0.9999921107345937,
                0.9999339478790235,
                0.9999952149049351,
                0.9999910603058285,
                0.9999945777790915,
                0.9999898700126454,
                0.9999910603015656
            ],
            [
                0.9999952149049351,
                0.9999852610145271,
                0.9999910603058291,
                0.9999885212346126,
                0.9999869928668857,
                0.9999898700090213,
                0.9999938558253986,
                0.9999921107345939,
                0.9999724642957795,
                0.999978555056703
            ],
            [
                0.9999810748427401,
                0.9999339478553727,
                0.9999832985761689,
                0.9999756997534811,
                0.9999417087345169,
                0.9999852610110034,
                0.9999885212264018,
                0.9999810748449955,
                0.9999756997650667,
                0.9999832985701956
            ],
            [
                0.9999910602994342,
                0.9999898700114365,
                0.9999869928699874,
                0.9999910603037008,
                0.9999339478238973,
                0.9999832985781574,
                0.9999869928730897,
                0.9999810748517622,
                0.9999852610180304,
                0.9999646437577374
            ],
            [
                0.9999921107383558,
                0.9999869928653365,
                0.9999852610162758,
                0.9999945777810311,
                0.9999546021097508,
                0.9999885212359813,
                0.9999599363173919,
                0.9999898700114368,
                0.999988521234612,
                0.9999852610197898
            ],
            [
                0.9999724643056332,
                0.9999852610127615,
                0.9999869928653352,
                0.9999885212277715,
                0.9999724643089074,
                0.9999339478240049,
                0.999975699753483,
                0.9999869928730887,
                0.9999852610197864,
                0.9999785550515924
            ],
            [
                0.9999724643056253,
                0.999925153790678,
                0.999959936317381,
                0.9999930377445807,
                0.999991060306894,
                0.9999785550592659,
                0.9999885212346129,
                0.9999921107345938,
                0.999986992873088,
                0.9999687980849237
            ],
            [
                0.9999724643154743,
                0.9999810748540244,
                0.9999832985701949,
                0.9999417087553654,
                0.9999832985721853,
                0.9999810748449992,
                0.999986992873088,
                0.9999485577618885,
                0.9999724643056253,
                0.9999832985821404
            ],
            [
                0.9999832985721872,
                0.9999910603047626,
                0.9999938558275958,
                0.9999869928653352,
                0.9998911030909859,
                0.9999251537371887,
                0.9999869928730875,
                0.9999832985781607,
                0.9999151889486958,
                0.9999599363030722
            ],
            [
                0.999993037740431,
                0.9999921107383564,
                0.9999945777829696,
                0.9999869928715381,
                0.9999599363173941,
                0.9999930377454109,
                0.9999921107336531,
                0.9999952149066467,
                0.9999930377429213,
                0.9999810748472558
            ],
            [
                0.9999832985801483,
                0.9999910603036969,
                0.999994577779092,
                0.9999898700066062,
                0.9999885212277707,
                0.9999832985801511,
                0.9999930377412609,
                0.9999921107364745,
                0.999986992866886,
                0.9999785550541495
            ],
            [
                0.9999785550464837,
                0.9999832985721862,
                0.9999852610145168,
                0.9999038975967038,
                0.9999785550439235,
                0.9999810748585355,
                0.9999785550490391,
                0.999991060302631,
                0.9999417087553831,
                0.999993855823202
            ],
            [
                0.999993037742922,
                0.9999885212264021,
                0.9999921107345937,
                0.9999724643056309,
                0.9999785550592593,
                0.9999898700041923,
                0.9999852610180336,
                0.9999251537996199,
                0.9999930377437507,
                0.99998329858015
            ],
            [
                0.999991060304763,
                0.9999756997505873,
                0.9999957771665557,
                0.9999952149037943,
                0.9999938558253986,
                0.9999910603036973,
                0.9999852610197881,
                0.9999251537550087,
                0.9999938558261312,
                0.999992110733653
            ],
            [
                0.9999885212264021,
                0.999988521234614,
                0.9999485577925141,
                0.9999945777790913,
                0.999993037746241,
                0.9999898700102291,
                0.9999852610197898,
                0.9999687980812073,
                0.9999910603026312,
                0.9999810748427421
            ],
            [
                0.9999339478239545,
                0.9999869928684368,
                0.9999485577680091,
                0.9999921107374158,
                0.9999930377412616,
                0.9999852610215463,
                0.9999869928699887,
                0.9999910603026312,
                0.9999970976887068,
                0.9999869928684358
            ],
            [
                0.9999724643121898,
                0.9999687980812059,
                0.9999485578047809,
                0.9999869928730878,
                0.9999885212318754,
                0.999891103130129,
                0.9999852610180308,
                0.9999687980774836,
                0.9999785550515924,
                0.9999417087206391
            ],
            [
                0.9999151889183892,
                0.9999898700114366,
                0.999925153763988,
                0.9999921107392958,
                0.9999930377462407,
                0.9999869928746379,
                0.9999852610233015,
                0.9999756997650695,
                0.9999810748495105,
                0.9999687980812002
            ],
            [
                0.9999810748585347,
                0.999981074854021,
                0.9999599362887388,
                0.9999898700126446,
                0.9999910603036964,
                0.9999852610197894,
                0.9999885212264026,
                0.9999832985781587,
                0.9999546021313874,
                0.9999785550413696
            ],
            [
                0.9999938558239337,
                0.9999921107336532,
                0.9999921107345938,
                0.9999417087067435,
                0.9999945777784452,
                0.999993037740431,
                0.9999832985841344,
                0.9999921107383557,
                0.9999546021476324,
                0.9999687980886429
            ],
            [
                0.9999910602994342,
                0.9999910603047626,
                0.9999785550464837,
                0.9999869928699859,
                0.9999852610127603,
                0.99995993630786,
                0.9999952149055057,
                0.9999921107374153,
                0.9999546021422047,
                0.9999921107402364
            ],
            [
                0.9999930377445808,
                0.9999852610197881,
                0.9999785550515897,
                0.9999785550464814,
                0.9999910603026313,
                0.9999898700053991,
                0.9999938558246659,
                0.9999869928715386,
                0.9999724643089097,
                0.9999930377420913
            ],
            [
                0.999993855826131,
                0.9999945777823234,
                0.9999417087206214,
                0.9999930377462403,
                0.9999756997621777,
                0.9999982396572065,
                0.9999646437450961,
                0.9999930377445811,
                0.9999921107364742,
                0.99998329858015
            ],
            [
                0.9999599362887301,
                0.9999885212346126,
                0.9999546021259818,
                0.9999339478317487,
                0.9999417087206125,
                0.9999417087484309,
                0.9999885212277709,
                0.9999599362887301,
                0.9999869928653345,
                0.9999646437493017
            ],
            [
                0.9999599362935121,
                0.9999756997563777,
                0.9999869928699864,
                0.9999910603058282,
                0.9998766053960197,
                0.9998766053960377,
                0.9999599363030746,
                0.9999785550464806,
                0.9999832985821424,
                0.9999869928746383
            ],
            [
                0.9999898700078149,
                0.9999832985701956,
                0.999994577781677,
                0.9999938558261309,
                0.9999810748449992,
                0.999997097688015,
                0.9999952149055052,
                0.9999930377445806,
                0.9999898700066067,
                0.999994577782323
            ],
            [
                0.999993855826131,
                0.99996879809608,
                0.999975699750582,
                0.9999756997563796,
                0.9999832985761699,
                0.999991060303697,
                0.9999832985821414,
                0.9999724642957795,
                0.999992110737415,
                0.9999869928761903
            ],
            [
                0.9998766054695308,
                0.999964643732439,
                0.9998601779096806,
                0.9999251537728575,
                0.9999251537460739,
                0.9998204720772121,
                0.9999546021259791,
                0.9999646437408746,
                0.9999921107392962,
                0.9999646437577197
            ],
            [
                0.9999251537460674,
                0.9999546021367987,
                0.9999898700114392,
                0.9999930377429206,
                0.9999832985841317,
                0.9999852610197889,
                0.9999832985701952,
                0.9999921107402361,
                0.9999339478711234,
                0.9999756997505845
            ],
            [
                0.9999546021313904,
                0.9999885212277707,
                0.9999832985841398,
                0.9999485577618665,
                0.9999967112497585,
                0.9999646437619502,
                0.9999724643023546,
                0.9999869928668853,
                0.9999785550567036,
                0.9999785550515924
            ],
            [
                0.9999852610145168,
                0.9999910603015666,
                0.9999869928653341,
                0.9999885212332451,
                0.9999885212359813,
                0.9999339478396766,
                0.9999546021422182,
                0.9999417087414739,
                0.9999910603047625,
                0.9999930377429209
            ],
            [
                0.9999339478632779,
                0.9999869928653352,
                0.9999687980960786,
                0.9999898700102285,
                0.9999785550464829,
                0.999981074856277,
                0.9999869928668851,
                0.9999852610127603,
                0.9999869928668857,
                0.999983298576167
            ],
            [
                0.9999869928761901,
                0.9999832985701943,
                0.9999546021476212,
                0.9999910603036986,
                0.9999038976195779,
                0.9999251537995719,
                0.9999756997650677,
                0.9998204720349343,
                0.9999417087345169,
                0.999959936317381
            ],
            [
                0.9999417087345128,
                0.9999546021313848,
                0.9999898700114366,
                0.999941708706721,
                0.9999977396751634,
                0.9999885212318762,
                0.9999417087136733,
                0.9999852610162754,
                0.9999885212346129,
                0.9999852610110037
            ],
            [
                0.9999810748427385,
                0.999993855827596,
                0.9999599362887259,
                0.9999785550439235,
                0.9999910603068939,
                0.9999687980960889,
                0.9999646437493611,
                0.9999785550439235,
                0.9999546021314016,
                0.999933947831781
            ],
            [
                0.9999957771665557,
                0.9999885212332442,
                0.99998329858015,
                0.999933947831754,
                0.9999756997592727,
                0.9999832985721862,
                0.9999898700078136,
                0.9999599362982898,
                0.999925153781771,
                0.9999832985741784
            ],
            [
                0.9999945777790913,
                0.9999898700078138,
                0.9999756997505957,
                0.9999785550413712,
                0.9999910603036969,
                0.9999832985781587,
                0.999992110737415,
                0.9999910603005,
                0.9999980052709919,
                0.9999869928761908
            ],
            [
                0.9999898700102289,
                0.9999832985841314,
                0.9999938558239335,
                0.9999599363078431,
                0.9999485578048097,
                0.9999832985761679,
                0.9999869928653368,
                0.9999646437408817,
                0.9999785550490369,
                0.9999756997476907
            ],
            [
                0.9999785550413696,
                0.9999785550592659,
                0.999954602109754,
                0.9999546021259734,
                0.9999898700126439,
                0.9999810748585377,
                0.9999687980997979,
                0.9999785550515972,
                0.9999785550439235,
                0.9999724643154754
            ],
            [
                0.9999485577925504,
                0.9999546021422182,
                0.9999724643187544,
                0.9999546021422242,
                0.9999810748449961,
                0.9999251537371533,
                0.9999910603068937,
                0.9999898700114368,
                0.9999724643154788,
                0.9999945777816774
            ],
            [
                0.9999938558224687,
                0.9999869928684365,
                0.9999910603047624,
                0.9999151889688855,
                0.9999151889284615,
                0.9999885212332448,
                0.9999546021097749,
                0.9999852610145172,
                0.9999869928730883,
                0.9999898700102295
            ],
            [
                0.999981074849511,
                0.9999687980960773,
                0.9999646437324492,
                0.9999810748585329,
                0.9999898700053982,
                0.9999756997592781,
                0.9999957771645421,
                0.9999756997679626,
                0.9999599363126119,
                0.9999898700126444
            ],
            [
                0.9999945777810305,
                0.9999898700041909,
                0.9999687980774823,
                0.9999756997650714,
                0.9999646437366602,
                0.999992110733653,
                0.9999785550490348,
                0.999975699762171,
                0.9999810748540237,
                0.9999756997679764
            ],
            [
                0.9999945777816772,
                0.9999687980737645,
                0.9999810748562741,
                0.9999910603068946,
                0.9999724642957807,
                0.9999962733611603,
                0.999993855826131,
                0.9999756997505903,
                0.9999885212305079,
                0.9999852610110037
            ],
            [
                0.9999898700078138,
                0.9999885212318759,
                0.9999869928761901,
                0.9999832985801516,
                0.999989870006606,
                0.9999785550413652,
                0.9999921107392962,
                0.9999687980811974,
                0.9999962733607161,
                0.9999832985801506
            ],
            [
                0.9998911030780216,
                0.9999832985821424,
                0.9999885212291393,
                0.9999546021260025,
                0.999986992873088,
                0.9999785550592614,
                0.9999687980812002,
                0.9998601778931797,
                0.9999417087414781,
                0.9999038975967038
            ],
            [
                0.9999785550490354,
                0.9999599362887458,
                0.9999869928653358,
                0.9999756997563787,
                0.9999885212305079,
                0.999948557780265,
                0.9999810748585323,
                0.9999952149043647,
                0.9999930377462405,
                0.9999810748427433
            ],
            [
                0.9999785550490348,
                0.9999852610110034,
                0.999954602131393,
                0.9999687980812089,
                0.9999038975394235,
                0.9999599363030609,
                0.9999832985701977,
                0.9999599362982876,
                0.9999832985801511,
                0.9999869928653352
            ],
            [
                0.999925153790678,
                0.9999485577680239,
                0.9999810748585323,
                0.999975699767967,
                0.9999885212305076,
                0.9999151889587774,
                0.9999724643089085,
                0.9999930377462408,
                0.9999832985761693,
                0.9999038975852054
            ],
            [
                0.9999832985701943,
                0.9999724643187624,
                0.99990389756239,
                0.9999852610127595,
                0.9999885212291385,
                0.9999885212346137,
                0.9999885212359814,
                0.9999852610197894,
                0.999933947863301,
                0.9999885212318764
            ],
            [
                0.9999938558268634,
                0.9999756997476845,
                0.9999785550592627,
                0.9999810748562746,
                0.999975699747687,
                0.9999546021151678,
                0.9999921107336531,
                0.9999417087484639,
                0.9999810748540182,
                0.9999785550541495
            ],
            [
                0.9999898700090213,
                0.9999810748540204,
                0.9999921107336535,
                0.9999962733607162,
                0.9999785550464785,
                0.9999898700053983,
                0.9999957771660523,
                0.9999945777829696,
                0.9999945777810305,
                0.9999910603036969
            ],
            [
                0.9999921107402363,
                0.9999869928746405,
                0.9999485577863929,
                0.9999869928746377,
                0.9999930377454107,
                0.9999869928715366,
                0.9999251537372105,
                0.999964643732444,
                0.9999921107336528,
                0.9999930377429209
            ],
            [
                0.9999646437450891,
                0.9999898700114366,
                0.9999485577986323,
                0.9999898700102295,
                0.9999974387177893,
                0.999964643753523,
                0.9999599362982855,
                0.9999810748472526,
                0.999996273360716,
                0.9999852610145165
            ],
            [
                0.9999832985781584,
                0.9999885212318756,
                0.9999756997476897,
                0.9999910603047625,
                0.9999832985821414,
                0.9999646437408728,
                0.9999646437577393,
                0.9998911030519949,
                0.9999869928746392,
                0.9999417087484351
            ],
            [
                0.999933947863301,
                0.9999038975509362,
                0.9999898700053991,
                0.9998766053667189,
                0.9999724642990687,
                0.9999546021097849,
                0.9999339478633182,
                0.9999810748562803,
                0.9999687980997952,
                0.9999756997476907
            ],
            [
                0.9999785550490354,
                0.9999910603047638,
                0.9999869928684368,
                0.9999810748427396,
                0.9999898700126454,
                0.9999910603026313,
                0.999994577780384,
                0.9999921107336528,
                0.9999852610215463,
                0.9999885212332446
            ],
            [
                0.9999785550515917,
                0.9999832985841324,
                0.9999687980886429,
                0.999991060303697,
                0.9999930377445808,
                0.9999869928668857,
                0.9999885212305073,
                0.9999038976195121,
                0.9999785550464798,
                0.999860177893019
            ],
            [
                0.9999938558232014,
                0.9999417087275871,
                0.9999756997621728,
                0.9999546021422047,
                0.9999546021313986,
                0.9999485578047951,
                0.99997569975928,
                0.9999785550515979,
                0.9999785550439235,
                0.9999869928761898
            ],
            [
                0.9999724643056241,
                0.9999869928684368,
                0.9999646437408712,
                0.9999785550490354,
                0.9999251537639157,
                0.9999417087206043,
                0.9999885212359807,
                0.999989870005398,
                0.9999756997592687,
                0.9999724643089118
            ],
            [
                0.9999952149066464,
                0.9999832985841317,
                0.9999151889588317,
                0.9999930377445807,
                0.9999251537907204,
                0.9999869928715376,
                0.9999885212318762,
                0.9999967112517189,
                0.9999898700114362,
                0.999986992869987
            ],
            [
                0.9999546021151592,
                0.9999339478317756,
                0.9999852610145165,
                0.9999898700053989,
                0.999983298574177,
                0.999959936298279,
                0.9998766054695488,
                0.9999687980997993,
                0.9999921107336532,
                0.999981074847252
            ],
            [
                0.999988521233244,
                0.9999785550464806,
                0.9999687980997979,
                0.9999885212291397,
                0.9999885212332442,
                0.9999417087275961,
                0.9999646437535306,
                0.9999339478238862,
                0.99996879808864,
                0.9999945777797377
            ],
            [
                0.9999852610197889,
                0.9999832985761689,
                0.9999832985721857,
                0.9999646437408746,
                0.9999785550541495,
                0.9999038976196226,
                0.99995460213681,
                0.9999930377454104,
                0.99990389759675,
                0.9999785550439251
            ],
            [
                0.9999785550567073,
                0.9999852610127599,
                0.9999869928684368,
                0.9999852610110019,
                0.9999810748449955,
                0.9999869928699864,
                0.9999938558224687,
                0.9999724642957807,
                0.9999546021368159,
                0.9999756997505828
            ],
            [
                0.9999957771675625,
                0.9999869928668851,
                0.9999485577618628,
                0.9999852610110034,
                0.999985261018032,
                0.9999885212305103,
                0.9999756997476854,
                0.999993855827596,
                0.9999756997679619,
                0.999933947855428
            ],
            [
                0.9998766054547905,
                0.9999869928715381,
                0.9999898700126442,
                0.999975699759281,
                0.9999945777784449,
                0.9999687980811988,
                0.9999810748540182,
                0.9999646437366654,
                0.9999151889890853,
                0.9999485577925318
            ],
            [
                0.9999852610215451,
                0.9999869928668863,
                0.9999810748472628,
                0.9999832985761714,
                0.9999724643187647,
                0.9999921107383557,
                0.9999785550490369,
                0.9999810748517645,
                0.9999898700114368,
                0.9999485577618699
            ],
            [
                0.9999938558275958,
                0.9999852610127611,
                0.999986992876195,
                0.9999938558239336,
                0.9999952149037944,
                0.9999852610162758,
                0.9999952149043646,
                0.9999945777790913,
                0.9999885212305079,
                0.9999974387168734
            ],
            [
                0.9999785550439266,
                0.9999785550541502,
                0.9999687980998067,
                0.999841563840392,
                0.9999546021422125,
                0.9999756997534849,
                0.9997965729791986,
                0.9999417087206302,
                0.99995993629351,
                0.9999417087484261
            ],
            [
                0.9999485577680091,
                0.9999869928715388,
                0.9999898700114362,
                0.9999756997592727,
                0.9999687980849298,
                0.9999724643121964,
                0.9999869928699877,
                0.999975699767967,
                0.9999687980997979,
                0.999975699767967
            ],
            [
                0.9999898700102293,
                0.9999910603068942,
                0.9999945777797378,
                0.9999724642990687,
                0.9999898700090213,
                0.9999910603015656,
                0.9999945777823231,
                0.999992110739296,
                0.9999785550464785,
                0.9999921107392964
            ],
            [
                0.9999832985721865,
                0.9999921107402365,
                0.9999687980886474,
                0.999989870009021,
                0.9999910603036972,
                0.9999546021259847,
                0.9999785550541526,
                0.9999646437619575,
                0.9999756997534945,
                0.9999910603047634
            ],
            [
                0.9999485577925318,
                0.9999962733616046,
                0.9999885212318759,
                0.9999724643023485,
                0.9999832985801526,
                0.9999810748427408,
                0.9999885212305076,
                0.9999687980849252,
                0.999891103129893,
                0.9999687980997979
            ],
            [
                0.9999687980849181,
                0.9999810748472509,
                0.9999810748540188,
                0.9999832985721853,
                0.9999921107383554,
                0.9999910603047628,
                0.9998911030909304,
                0.999981074856277,
                0.9999921107383555,
                0.9999832985841314
            ],
            [
                0.9999687980775102,
                0.999991060305829,
                0.9999832985721862,
                0.9999930377437508,
                0.9999930377412614,
                0.9999921107345934,
                0.9999945777829701,
                0.9999599363030871,
                0.999993037740431,
                0.9999869928761898
            ],
            [
                0.99997569975928,
                0.9999417087066922,
                0.9999785550464814,
                0.9999687980886445,
                0.9999885212264024,
                0.9999945777810305,
                0.9999810748585323,
                0.9999756997534811,
                0.9999687980923566,
                0.9999756997505845
            ],
            [
                0.9999898700066062,
                0.9999832985801526,
                0.999975699765066,
                0.9999869928668863,
                0.9999885212264037,
                0.9999852610197921,
                0.9999898700078138,
                0.9999687980849329,
                0.999978555054151,
                0.9999885212264029
            ],
            [
                0.9999921107336528,
                0.9999546021421969,
                0.9999151889182929,
                0.9999724642957762,
                0.9999810748495047,
                0.9998911031039645,
                0.9999546021151431,
                0.9999938558224686,
                0.9999599363126381,
                0.9999687980960746
            ],
            [
                0.9999945777784452,
                0.9999957771650457,
                0.9999485577925209,
                0.9999945777829696,
                0.9999869928761882,
                0.9999957771665559,
                0.9999938558224688,
                0.9999910603068937,
                0.9999938558246662,
                0.9999646437493034
            ],
            [
                0.9999832985761693,
                0.9999885212277704,
                0.9999938558246662,
                0.9999921107336532,
                0.9999339478238973,
                0.999981074847252,
                0.9999938558232012,
                0.9999921107364748,
                0.9999785550592685,
                0.9999938558224692
            ],
            [
                0.9999756997650787,
                0.9999724643187565,
                0.999991060304763,
                0.9999724643121942,
                0.9999869928746383,
                0.9999646437535324,
                0.9999724643089085,
                0.9999485577802578,
                0.9999687980849181,
                0.9999869928684368
            ],
            [
                0.9999485577618298,
                0.9999898700066067,
                0.9998766054695308,
                0.999876605440246,
                0.9999546021367987,
                0.9999417087136733,
                0.9999339478318213,
                0.9999832985781584,
                0.9999485578047775,
                0.9999852610162749
            ],
            [
                0.9999910603036979,
                0.9999945777829702,
                0.9999869928699867,
                0.999988521229139,
                0.9999852610233023,
                0.9999832985701983,
                0.9999852610180346,
                0.9999756997679643,
                0.9999945777790914,
                0.999964643749322
            ],
            [
                0.9999251537460739,
                0.9999339478632615,
                0.9999785550567065,
                0.9999756997592744,
                0.999989870005401,
                0.9999869928684362,
                0.999972464299064,
                0.9999785550413688,
                0.9999921107383561,
                0.9999910603026316
            ],
            [
                0.999975699753477,
                0.9999599363126097,
                0.999983298582142,
                0.9999251537639369,
                0.9999921107402365,
                0.9999687980923623,
                0.9999417087553654,
                0.999954602109754,
                0.9999921107364751,
                0.9998911031039502
            ],
            [
                0.9999898700090227,
                0.999985261018032,
                0.9999832985821414,
                0.9999724642990628,
                0.9999910603004997,
                0.9999980052693274,
                0.9999687980923636,
                0.9999967112517189,
                0.9999687980774912,
                0.9999724642957828
            ],
            [
                0.9999921107345939,
                0.9999967112513267,
                0.9999938558239335,
                0.999997097686631,
                0.9999869928684368,
                0.9999910603036978,
                0.9999938558246662,
                0.9999885212305106,
                0.9999756997505903,
                0.9999724643154838
            ],
            [
                0.9999938558239336,
                0.999978555041372,
                0.9999945777797378,
                0.9999687980849267,
                0.9999599363078385,
                0.999975699762171,
                0.9999339478397001,
                0.999989870009022,
                0.9999810748495068,
                0.9999945777784449
            ],
            [
                0.9999724643023429,
                0.999948557780265,
                0.9999810748540204,
                0.9999785550490427,
                0.9999885212346123,
                0.9999417087275736,
                0.999991060302632,
                0.9999945777823235,
                0.9999910603058282,
                0.9999938558224688
            ],
            [
                0.9999417087414438,
                0.9999151889183269,
                0.9999832985701977,
                0.9999785550413659,
                0.9999687980960875,
                0.9999646437493034,
                0.9998911030780803,
                0.9999810748495068,
                0.999975699765066,
                0.9999724643121942
            ],
            [
                0.9999687980774881,
                0.9999869928715373,
                0.9999898700041912,
                0.9999885212291407,
                0.9999910603015651,
                0.9999945777823233,
                0.999985261012762,
                0.9999869928761898,
                0.9999898700066067,
                0.999992110737415
            ],
            [
                0.999993037740431,
                0.999998239656367,
                0.9999724643154788,
                0.9999952149055057,
                0.9999977396765105,
                0.9999952149072169,
                0.9999970976873229,
                0.9999977396754328,
                0.999983298582142,
                0.9999945777803841
            ],
            [
                0.9999785550515954,
                0.9999646437324375,
                0.9999251537996199,
                0.9999756997592735,
                0.9999832985821409,
                0.9999485577802507,
                0.9999599363221765,
                0.9999756997563768,
                0.9999687980923594,
                0.9999785550592795
            ],
            [
                0.9999599362983042,
                0.9999885212305086,
                0.9999810748562741,
                0.9999546021314398,
                0.9999724642957851,
                0.9998911030650289,
                0.9999151889790031,
                0.9999417087275825,
                0.9999417087345043,
                0.9999832985761699
            ],
            [
                0.9999756997592744,
                0.9999785550541473,
                0.9999898700066057,
                0.999985261016273,
                0.9999832985781592,
                0.9999898700053989,
                0.9999756997621798,
                0.9999930377454107,
                0.9999885212264029,
                0.9999885212318759
            ],
            [
                0.9999785550413652,
                0.9999724643122028,
                0.9999756997505903,
                0.9999832985701949,
                0.9999898700066062,
                0.9999852610197874,
                0.9999885212359807,
                0.9999832985841324,
                0.9999646437324492,
                0.999978555059262
            ],
            [
                0.9999885212332457,
                0.9999485577925141,
                0.9999910603058326,
                0.9999885212277707,
                0.9999339478790071,
                0.999968798092365,
                0.9999898700114366,
                0.99998987000419,
                0.9999646437408781,
                0.9999910603068937
            ],
            [
                0.999981074844998,
                0.999981074854021,
                0.9999724643121909,
                0.9999810748540188,
                0.999972464299064,
                0.9999756997563815,
                0.999993855822469,
                0.9999930377420909,
                0.999996273358939,
                0.9999756997592754
            ],
            [
                0.9999938558239339,
                0.9999785550567065,
                0.9999910603068943,
                0.9999921107364752,
                0.999992110737415,
                0.9999885212318762,
                0.9999885212359817,
                0.999988521231878,
                0.9999910603058285,
                0.9999885212346129
            ],
            [
                0.9999810748540198,
                0.9999151889587689,
                0.9999852610233012,
                0.999968798077481,
                0.9999832985761689,
                0.9999852610110029,
                0.9999869928715381,
                0.9999957771675627,
                0.9999785550464821,
                0.9999785550541467
            ],
            [
                0.9999921107355337,
                0.999981074844995,
                0.9999485577802507,
                0.9999810748495074,
                0.9999810748472515,
                0.9999251537638956,
                0.9999832985741774,
                0.9999646437450999,
                0.9999724642990652,
                0.999985261014518
            ],
            [
                0.9999810748562803,
                0.9999832985821396,
                0.9999687980997993,
                0.9999832985801511,
                0.9999921107336528,
                0.9999921107364762,
                0.9999869928715369,
                0.9999898700041907,
                0.9999832985701983,
                0.9999852610180304
            ],
            [
                0.9999151889486958,
                0.9999724643056345,
                0.9999938558246664,
                0.9999832985721857,
                0.9999485577863858,
                0.9999546021314647,
                0.999986992869987,
                0.9999756997621719,
                0.9999945777803841,
                0.9999832985841324
            ],
            [
                0.9999485577680127,
                0.9999724643121964,
                0.9999546021368069,
                0.9999869928746389,
                0.999968798081203,
                0.9999869928746385,
                0.9999869928653345,
                0.9999885212305076,
                0.9999810748585312,
                0.9999832985841359
            ],
            [
                0.9999646437450925,
                0.9999785550515917,
                0.9999546021422242,
                0.9999852610215454,
                0.9999687980774852,
                0.9999832985721862,
                0.9999646437408728,
                0.9999852610162746,
                0.9999785550515924,
                0.9999810748562752
            ]
        ]
    },
    {
        "q_id": "8454_mmlu_math",
        "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": [
            [
                0.9999898700078136,
                0.9999945777803917,
                0.9924227588511967,
                0.9999977396748938,
                0.9999945777816769,
                0.999954602115224,
                0.9999852610127585,
                0.9999938558232009,
                0.9999756997592744,
                0.9999970976887068
            ],
            [
                0.7549149923816048,
                0.9999810748472479,
                0.9890130583712834,
                0.9669140248290712,
                0.9999724643190243,
                0.9999646437577469,
                0.9999869928653696,
                0.9999646437368962,
                0.9999810748427369,
                0.9994472212585944
            ],
            [
                0.9999974387187053,
                0.9999687980962159,
                0.9999994956526519,
                0.9999910603036973,
                0.9999982396559474,
                0.999989870009069,
                0.9669140204195271,
                0.952574129683468,
                0.9796676470283606,
                0.9999945777810352
            ],
            [
                0.9999724643121954,
                0.9999869928746379,
                0.9999417087553356,
                0.9999151889182596,
                0.9998415638211253,
                0.9992903297112792,
                0.9999832985781574,
                0.9999810748517607,
                0.9999898700041906,
                0.999991060303696
            ],
            [
                0.9706877685596711,
                0.9999546021152748,
                0.9999687980886588,
                0.9997965730578335,
                0.9525741290102834,
                0.9999785550439195,
                0.8670357666736772,
                0.999948557780244,
                0.9999810748585282,
                0.9999938558224746
            ],
            [
                5.715007195447234e-07,
                7.338207180884785e-07,
                5.715004470295662e-07,
                7.338210680002898e-07,
                2.260323489490968e-06,
                7.338211554758494e-07,
                3.2887478891128633e-06,
                4.450851580555361e-07,
                8.315277302819205e-07,
                1.855391460719133e-07
            ],
            [
                0.999978555043919,
                0.9975273766079109,
                0.9999485578049561,
                0.9997388096288542,
                0.9993736657489823,
                0.9999724643154654,
                0.9998204720553105,
                0.9999485577618125,
                0.9999151889889798,
                0.999841563839772
            ],
            [
                0.9999930377445804,
                0.9999869928700299,
                0.9999945777816768,
                0.9996646498528886,
                0.9999417087206345,
                0.9999756997621694,
                0.9999038975966046,
                0.9999417087553203,
                0.9998204720344955,
                0.9999756997679652
            ],
            [
                3.726637951367137e-06,
                1.0677031245953668e-06,
                1.300712536203966e-05,
                8.315281267800897e-07,
                1.1478766756214804e-05,
                1.5534971989992774e-06,
                3.288747889178668e-06,
                8.939700567004841e-06,
                1.3007134665130082e-05,
                3.7266379513434106e-06
            ],
            [
                0.9998911030967138,
                0.999876605454541,
                0.9997040428653471,
                0.9998911031296703,
                0.9999945777790911,
                0.9991959140508085,
                0.9999151889890513,
                0.8807970811069351,
                0.9999417087553165,
                0.8807970732843033
            ],
            [
                0.7549149868676284,
                0.880797068590724,
                0.9999151889893784,
                0.9999599363037028,
                0.999948557780254,
                0.9399133552961427,
                0.999941708724274,
                0.904650538956921,
                0.9997040428662339,
                0.999983298582147
            ],
            [
                1.7603440527222532e-06,
                1.2098662604126641e-06,
                1.5534973841895917e-06,
                4.222834954561012e-06,
                2.260323758923431e-06,
                2.260325375615501e-06,
                1.3709570434122812e-06,
                1.553498495338299e-06,
                7.338208055664991e-07,
                2.1024326584639497e-07
            ],
            [
                2.2603251062147097e-06,
                9.422442569315887e-07,
                1.760343003481596e-06,
                7.889265407090955e-06,
                7.889264466725156e-06,
                5.422219616140078e-06,
                1.1478766757049986e-05,
                2.5612822107167428e-06,
                1.2098652508287273e-06,
                4.785093924251918e-06
            ],
            [
                0.9999852610233037,
                0.9998415637078946,
                0.9999251537657307,
                0.9999339478553327,
                0.970687769142648,
                0.999998932297258,
                0.990291524440782,
                0.9999646437324528,
                0.9999785550567089,
                0.9998601778598297
            ],
            [
                0.9999646437368137,
                0.9999546021421849,
                0.9999832985761654,
                0.9999832985801549,
                0.9999885212332433,
                0.9999599363030427,
                0.99999800527028,
                0.9999251537828115,
                0.9999599363093028,
                0.952574131703022
            ],
            [
                0.9999990577556307,
                0.9999989322972572,
                0.9999994284996211,
                0.9999938558239335,
                0.9999974387171787,
                0.9999982396565769,
                0.9999986290431201,
                0.9999977396757022,
                0.9999921107392954,
                0.999997438717484
            ],
            [
                5.715007195447234e-07,
                1.994729483705484e-06,
                1.2098653950656417e-06,
                1.6373776432481905e-07,
                2.5612831267086116e-06,
                1.5534983101549167e-06,
                2.260324028404236e-06,
                1.2098659719757836e-06,
                2.2603251062270446e-06,
                1.2098659719716573e-06
            ],
            [
                0.999860177926147,
                0.9999756997534821,
                0.9579122756889438,
                0.9999599363125902,
                0.9999869928653405,
                0.9999785550413627,
                0.9999546021313986,
                0.9964063977503902,
                0.9999756997563835,
                0.999968798077481
            ],
            [
                2.561281905390075e-06,
                4.22283545808297e-06,
                0.9999832985761657,
                6.144173136885882e-06,
                3.726639284050988e-06,
                6.962257079629686e-06,
                1.0677028700363782e-06,
                3.2887486733420804e-06,
                2.260324567302214e-06,
                4.785095065093186e-06
            ],
            [
                2.7535691091443854e-05,
                6.144176799166453e-06,
                1.553498495338299e-06,
                1.3709568799879344e-06,
                6.144174601879434e-06,
                1.2098653950656417e-06,
                4.222834451169694e-06,
                2.9023119851266288e-06,
                2.260324028427877e-06,
                7.889265406904397e-06
            ],
            [
                0.9999987901346049,
                0.9999993524049702,
                0.9999977396765105,
                0.9999938558268634,
                0.9999993524052018,
                0.9999982396559473,
                0.9999994956525318,
                0.9999977396751633,
                0.99999893229713,
                0.9999967112501507
            ],
            [
                7.338212429562581e-07,
                1.0677024881887838e-06,
                1.2098652508347793e-06,
                1.9947297214944016e-06,
                1.7603432133296774e-06,
                1.2098661161927025e-06,
                2.6995790618252024e-07,
                3.0590226338838606e-07,
                1.0677024881980089e-06,
                4.450849988798682e-07
            ],
            [
                0.9999646437577306,
                0.9999898700126436,
                0.9999810748517607,
                0.9998911030777436,
                0.9999938558246656,
                0.9997965730998575,
                0.9999852610162713,
                0.999769493367486,
                0.9999930377454102,
                0.999959936298279
            ],
            [
                0.9999982396565769,
                0.9626731126558705,
                0.9999756997535474,
                0.9999930377437609,
                0.9999810748449934,
                0.999981074844992,
                0.9241418147556224,
                0.9999852610127595,
                0.9999646437621025,
                0.9999756997505863
            ],
            [
                1.76034300345598e-06,
                1.5534983101393749e-06,
                2.6995784182140636e-07,
                7.338213304196583e-07,
                1.209865683518615e-06,
                2.1024334103505245e-07,
                6.475945666033422e-07,
                1.7603427936263351e-06,
                1.0677031245953668e-06,
                3.0590222692437275e-07
            ],
            [
                0.9997965730993486,
                0.9940889320877746,
                0.9978172838913651,
                0.9997965729780206,
                0.9984988175326436,
                0.9914225147922051,
                0.06008664807010359,
                0.9902915214949348,
                0.008577483615898194,
                0.9940889310917668
            ],
            [
                4.2228324377164004e-06,
                5.043473480730849e-07,
                6.475950297993789e-07,
                1.553497384196656e-06,
                5.043475284430694e-07,
                4.450851049959619e-07,
                3.288749849477628e-06,
                1.012998735687278e-05,
                1.760343213322473e-06,
                1.5534973841895917e-06
            ],
            [
                6.962253759904688e-06,
                6.962254589851619e-06,
                7.889261645090304e-06,
                1.0129993395088066e-05,
                2.9023133690637e-06,
                4.785094494716039e-06,
                2.9023109471452223e-06,
                2.5612834320214477e-06,
                3.288748673319648e-06,
                1.300713311614059e-05
            ],
            [
                0.9999485578048216,
                0.9999417087553318,
                0.9999930377454105,
                0.9999986290421394,
                0.9998766054692795,
                0.9999921107374148,
                0.9999921107336526,
                0.9999687980960696,
                0.9999646437450979,
                0.9999974387171787
            ],
            [
                1.5534971989907999e-06,
                8.939697369671496e-06,
                2.9023123311055552e-06,
                6.144173137014406e-06,
                7.338208930443633e-07,
                1.9947306726594253e-06,
                6.9622579092224155e-06,
                1.994729721469003e-06,
                1.3709568799760888e-06,
                3.7266379513434106e-06
            ],
            [
                0.999972464299064,
                0.9999339478330097,
                0.999915188928393,
                0.9706877678177007,
                0.8175744739711883,
                0.8175744695262777,
                0.9999646437408798,
                0.9999038976006821,
                0.9999485577863506,
                0.9998911031038139
            ],
            [
                0.9999151889687863,
                0.9999810748495058,
                0.9999952149072168,
                0.9999810748449929,
                0.9999646437535052,
                0.9999962733598278,
                0.9999945777790914,
                0.9999984465018751,
                0.999992110733654,
                0.9999921107383553
            ],
            [
                1.7603434231385591e-06,
                1.2098659719441482e-06,
                3.288747889229516e-06,
                1.0677024881941248e-06,
                2.260323489490968e-06,
                1.2098659719661556e-06,
                1.2098662604291696e-06,
                1.7603432133032607e-06,
                2.561283126679493e-06,
                1.067703379154416e-06
            ],
            [
                0.9999952149055052,
                0.9999991684722698,
                0.9999977396754329,
                0.9999938558268632,
                0.9999945777816768,
                0.9999982396574162,
                0.9999993524049702,
                0.999996711251719,
                0.9999957771665557,
                0.9999869928699856
            ],
            [
                0.999948557798617,
                0.9999980052705163,
                0.9999974387168733,
                0.9999945777810304,
                0.9999756997506054,
                0.9999930377462422,
                0.9999957771650453,
                0.9999952149072169,
                0.9999977396751634,
                0.9820137938542332
            ],
            [
                6.475951069961737e-07,
                1.5534983101478522e-06,
                9.4224425692559e-07,
                6.144172404587612e-06,
                7.338212429562581e-07,
                2.2603245673279107e-06,
                7.889262585814522e-06,
                4.450852111120808e-07,
                1.9947297215043796e-06,
                9.422449308716635e-07
            ],
            [
                0.9999995549148419,
                0.9999930377445806,
                0.9999952149066466,
                0.9999687980849222,
                0.9999987901337396,
                0.999978555046477,
                0.9999986290429567,
                0.9999990577552939,
                0.9999982396567867,
                0.9999910603004992
            ],
            [
                0.9999646437624985,
                0.9999869928685642,
                0.9999869928746374,
                0.9999599363126381,
                0.999964643753547,
                0.9999938558268634,
                0.8519527944504227,
                0.9999546021313743,
                0.7310585786300049,
                0.999769493176703
            ],
            [
                0.9999599363034165,
                0.9999687980998007,
                0.9324533018213449,
                0.9999957771660524,
                0.9998204720398266,
                0.9999910603047621,
                0.9465966698235384,
                0.9999546021313743,
                0.9999910603004997,
                0.9999930377429205
            ],
            [
                2.561281905390075e-06,
                1.067703379154416e-06,
                8.939693106873817e-06,
                4.785094494463623e-06,
                2.9023130229209922e-06,
                4.222834954514924e-06,
                2.902312331125353e-06,
                2.5612828213690224e-06,
                1.5534977545603963e-06,
                5.422219616184461e-06
            ],
            [
                5.043474081993875e-07,
                2.2603234895289998e-06,
                3.726638839833152e-06,
                2.561283432035425e-06,
                2.2603237589542675e-06,
                2.6995784182073116e-07,
                8.939696304002375e-06,
                4.4508494582314646e-07,
                2.2603234895176927e-06,
                3.7266401725935817e-06
            ],
            [
                0.9999898700126436,
                0.9999930377445809,
                0.9999417087351141,
                0.999985261014514,
                0.999994577780384,
                0.9999974387180948,
                0.9999982396567868,
                0.9902915246914923,
                0.99999303774624,
                0.9999756997476862
            ],
            [
                0.9998204719911963,
                0.9999546021165822,
                0.9986749775570607,
                0.9997694933402955,
                0.9998766053956392,
                0.9998415637458196,
                0.9999251537906513,
                0.999195914240025,
                0.999948557798614,
                0.9997965729540741
            ],
            [
                0.7057850278370111,
                0.9999852610162897,
                0.99997569975068,
                0.7772998663336158,
                0.9999785550541817,
                0.9999038975850983,
                0.9999810748475063,
                0.9999832985722586,
                0.9998601778988169,
                0.9669140213729421
            ],
            [
                4.222832437747125e-06,
                1.012998977198894e-05,
                1.3709575337016483e-06,
                3.726641060956752e-06,
                6.962253759904688e-06,
                7.889266347456862e-06,
                2.561281905376098e-06,
                8.939698435340743e-06,
                3.2887502415243994e-06,
                4.222834954753043e-06
            ],
            [
                0.9999962733616199,
                0.9999930377445804,
                0.9999957771660549,
                0.9999930377421404,
                0.9999810748472489,
                0.9999930377454153,
                0.9999938558224687,
                0.9999921107336763,
                0.999948557761846,
                0.9999952149055314
            ],
            [
                0.9998911030521233,
                0.9999151889587515,
                0.9999910603005003,
                0.9999898700066052,
                0.9999898700102298,
                0.9999546021476239,
                0.9999646437577273,
                0.9999687980923541,
                0.8175744695262777,
                0.9999599363125974
            ],
            [
                3.2887490652451393e-06,
                3.726639284050988e-06,
                2.561283432035425e-06,
                1.9947306726594253e-06,
                8.939693106987645e-06,
                1.7603425837791042e-06,
                4.222833947932061e-06,
                5.422220908876325e-06,
                4.785096206013061e-06,
                3.726638839833152e-06
            ],
            [
                1.760343213322473e-06,
                1.0129994601872894e-05,
                5.422218323349895e-06,
                1.7603440527046419e-06,
                2.9023133690188264e-06,
                1.0129995809929273e-05,
                8.939697369671496e-06,
                1.370957860567974e-06,
                3.2887490653872164e-06,
                8.315284241560147e-07
            ],
            [
                0.9999339478238608,
                0.9999898700090208,
                0.9999869928715365,
                0.9999930377404305,
                0.9999952149055052,
                0.999993855824666,
                0.9999921107345938,
                0.9999987901344607,
                0.9999930377454106,
                0.9999982396569966
            ],
            [
                4.22283545808297e-06,
                1.370957860567974e-06,
                2.902311985079115e-06,
                4.222834954687752e-06,
                2.902310947208574e-06,
                5.422219615829396e-06,
                1.9947297215043796e-06,
                2.902313023039776e-06,
                7.338213304316717e-07,
                1.067703379154416e-06
            ],
            [
                1.7603438428740716e-06,
                6.475946438042047e-07,
                1.2098655392921197e-06,
                5.715007195431641e-07,
                1.0677029973114952e-06,
                1.209865827740176e-06,
                3.7266410605974813e-06,
                2.9023123311583482e-06,
                3.7266392839425286e-06,
                1.553497199007048e-06
            ],
            [
                0.9999910603058279,
                0.7981867777396212,
                0.9999930377404338,
                0.9999898700066059,
                0.9999869928761882,
                0.9740426425196372,
                0.9999724643023389,
                0.9999485577802278,
                0.9999485577618238,
                0.9999910603068958
            ],
            [
                5.422219616085833e-06,
                8.939698435226916e-06,
                1.2098652508347793e-06,
                5.422218969769604e-06,
                8.939699500766203e-06,
                6.144175334367959e-06,
                4.450849458200093e-07,
                7.88926352599354e-06,
                2.4300246523773334e-05,
                2.260324836776948e-06
            ],
            [
                2.4300249421225448e-05,
                3.7266392840781026e-06,
                2.561283432005142e-06,
                1.1478764019996392e-05,
                3.288748673360027e-06,
                1.9947292459265734e-06,
                3.288749065406658e-06,
                1.9947294837154625e-06,
                4.785093353739995e-06,
                7.889266347004826e-06
            ],
            [
                1.7603430034743913e-06,
                3.288749849477628e-06,
                1.7603427936263351e-06,
                1.553498124964492e-06,
                7.889264466344872e-06,
                1.2098655392871682e-06,
                2.9023112932177327e-06,
                1.7603430034743913e-06,
                2.5612825160562587e-06,
                7.338208055579897e-07
            ],
            [
                0.9999724643154672,
                0.9999810748472532,
                0.9999151889384075,
                0.9999687980849118,
                0.999876605381012,
                0.9999756997534733,
                0.9984988175479994,
                0.999915188978834,
                0.9980732653068979,
                0.9999546021421969
            ],
            [
                3.059021175247079e-07,
                5.043474683220276e-07,
                1.0677029973192638e-06,
                1.2098656835224664e-06,
                1.2098653950656417e-06,
                1.2098658277451275e-06,
                5.04347348075149e-07,
                5.043472278312808e-07,
                3.466326211105621e-07,
                5.715004470313855e-07
            ],
            [
                0.9999852610110009,
                0.9999910603058276,
                0.9999921107374145,
                0.9999687980960674,
                0.9999938558239333,
                0.999998790134028,
                0.9999957771660523,
                0.9999921107345937,
                0.9999970976869773,
                0.9999989322975118
            ],
            [
                0.9940889318716081,
                0.9998766053811593,
                0.2689414213699951,
                0.9999251537638819,
                0.9994472214509325,
                0.999373665745521,
                0.9998766054693604,
                0.32082129433083023,
                0.9999599363221718,
                0.999903897552354
            ],
            [
                4.222832941034507e-06,
                2.26032402841657e-06,
                4.785094494672519e-06,
                1.99472900813862e-06,
                6.144173869502757e-06,
                1.7603438428564603e-06,
                2.902313023039776e-06,
                7.889263525778283e-06,
                4.785094494716039e-06,
                3.726639284017094e-06
            ],
            [
                1.9947306725868575e-06,
                2.561281905376098e-06,
                4.78509563555309e-06,
                1.9947290080905435e-06,
                2.902310947190096e-06,
                2.9023133690188264e-06,
                1.5534979397500702e-06,
                1.9947297215043796e-06,
                2.2603242978377903e-06,
                2.2603248367358324e-06
            ],
            [
                0.7772998508568416,
                0.7549149758396752,
                0.8670357529306639,
                0.9998911030649876,
                0.999841563839772,
                0.9997040429011341,
                0.9998601779593259,
                0.9975273763293855,
                0.9947798745240725,
                0.9998204719911963
            ],
            [
                1.9947301970587145e-06,
                1.760344052714248e-06,
                7.889260704308795e-06,
                8.93969630333567e-06,
                1.1478766757049986e-05,
                3.7266397283231055e-06,
                1.5534981249574276e-06,
                3.7266406167827664e-06,
                2.561282210701601e-06,
                4.222834954753043e-06
            ],
            [
                0.9999251537770723,
                0.9999921107355337,
                0.9999938558246657,
                0.9998911030649195,
                0.9999910603058276,
                0.99999303774624,
                0.9999921107364741,
                0.9998204720554438,
                0.9999687980774697,
                0.9999852610145155
            ],
            [
                0.9046505447409666,
                0.9999785550598221,
                0.9626731122542814,
                0.9149009555730611,
                0.7549149868676283,
                0.9999785550439251,
                0.9999599363030465,
                0.9998601779311923,
                0.9999724643187485,
                0.9999724643023353
            ],
            [
                3.466325384661554e-07,
                9.422448185478557e-07,
                2.5612825160562587e-06,
                1.3709576971425944e-06,
                7.338211554783522e-07,
                1.0677031245851707e-06,
                1.3709567165579959e-06,
                1.0677032518785256e-06,
                1.3709578605542582e-06,
                1.3709570433979422e-06
            ],
            [
                1.994730434879465e-06,
                1.553497384180408e-06,
                8.31528424162821e-07,
                3.059021175255426e-07,
                9.422449308673789e-07,
                7.338209805224048e-07,
                4.450849458218309e-07,
                9.422447062202052e-07,
                3.9278624708775595e-07,
                5.71500651413193e-07
            ],
            [
                0.9999986290427931,
                0.9999599362887142,
                0.651354857898194,
                0.9999921107383547,
                0.9999952149066462,
                0.9999977396762411,
                0.9999962733620487,
                0.9999952149037975,
                0.9999962733602716,
                0.9999957771660566
            ],
            [
                0.9999945777829706,
                0.9669140233989487,
                0.9999546021369361,
                0.9998766053973197,
                0.9046505254608136,
                0.9997965730757956,
                0.9999687980774782,
                0.9999785550592695,
                0.2942149721629888,
                0.9324533036984185
            ],
            [
                1.370956716529941e-06,
                2.260325375634003e-06,
                3.9278605979208185e-07,
                6.962257079059797e-06,
                3.288749457432399e-06,
                4.4508505193386385e-07,
                1.012998977198894e-05,
                2.9023112931688987e-06,
                1.7603425837791042e-06,
                7.338213304343413e-07
            ],
            [
                0.9999417087277178,
                0.9996646500105861,
                0.9978172836733148,
                0.9982992774606829,
                0.9991959140498733,
                0.8933094159957173,
                0.9995121427647069,
                0.9995121428248224,
                0.8519528019683106,
                0.4378234991142019
            ],
            [
                0.9984988177306992,
                0.9999646437492881,
                0.9999938558246656,
                0.99995460213136,
                0.9999930377454105,
                0.999925153745984,
                0.9999957771650453,
                0.9982992773312199,
                0.9999546021097171,
                0.9999646437324344
            ],
            [
                6.962256249606473e-06,
                5.422218323290717e-06,
                1.7603432133032607e-06,
                1.9947292459265734e-06,
                4.2228324375973415e-06,
                4.222833444506298e-06,
                2.2603237589779086e-06,
                4.785095635592258e-06,
                1.5534979397677313e-06,
                1.553497754583709e-06
            ],
            [
                0.999915188958662,
                0.9999921107392978,
                0.9999785550517438,
                0.9999869928746385,
                0.9669140233989488,
                0.6224593312018546,
                0.5621765008857981,
                0.8670357683915538,
                0.999981074854021,
                0.9999898700126433
            ],
            [
                8.31528424162821e-07,
                7.338208055664991e-07,
                1.0677031245953668e-06,
                1.5534971989992774e-06,
                1.3709568799879344e-06,
                9.422449308748773e-07,
                7.338208055613267e-07,
                1.5534979397394734e-06,
                1.7603427936335396e-06,
                2.1024334103553052e-07
            ],
            [
                0.9999687980849129,
                0.9999485577710863,
                0.9999869928715386,
                0.9999687980950823,
                0.9999339478558393,
                0.9999952149060769,
                0.9999810748585601,
                0.9999785550464791,
                0.9998601779596922,
                0.9999898700114431
            ],
            [
                0.9999970976880149,
                0.9999785550596214,
                0.9999646437450749,
                0.9999724643095421,
                0.9999986290429566,
                0.9999974387168733,
                0.9999885212318759,
                0.9999938558253982,
                0.9999885212277698,
                0.9999952149072167
            ],
            [
                2.5612812947380135e-06,
                1.2098662604247682e-06,
                5.422217030614265e-06,
                4.785092783371756e-06,
                1.5534971990126997e-06,
                3.288749457409966e-06,
                3.726639728348526e-06,
                3.288748281220719e-06,
                1.5534975693933505e-06,
                4.785095065045315e-06
            ],
            [
                6.475951069961737e-07,
                2.699578096393206e-07,
                3.059021539909339e-07,
                2.382369383923073e-07,
                1.7603438428740716e-06,
                3.9278634073625165e-07,
                2.2603251062270446e-06,
                1.5534983101549167e-06,
                3.2887506336086064e-06,
                6.144175333926503e-06
            ],
            [
                0.9999724643121868,
                0.8933093975331752,
                0.999985261016272,
                0.9999967112505433,
                0.9999885212264225,
                0.9999945777784449,
                0.9999898700114355,
                0.9999832985781578,
                0.9999038975736144,
                0.999860177961875
            ],
            [
                2.5612825160562587e-06,
                1.55349775456958e-06,
                1.7603436330259153e-06,
                7.88925976418034e-06,
                6.962257909412379e-06,
                1.553497384196656e-06,
                1.0129993394314164e-05,
                4.785096776394765e-06,
                1.9947290081286418e-06,
                1.3007131564903626e-05
            ],
            [
                0.9998204720772462,
                0.9999938558232008,
                0.999975699753477,
                0.9999852610162717,
                0.9998415637647267,
                0.9999957771655488,
                0.9999646437619403,
                0.9999756997505803,
                0.9999957771665555,
                0.9999251537906192
            ],
            [
                0.9999832985781555,
                0.9998911031215143,
                0.9999251537553342,
                0.9999967112497671,
                0.9999810748563622,
                0.9999885212264173,
                0.999981074845158,
                0.9999151889614973,
                0.9999810748585277,
                0.9999785550491147
            ],
            [
                0.9999785550490304,
                0.9999546021102582,
                0.4378234991142019,
                0.004070137213796842,
                0.9997965730027693,
                0.7057850216484838,
                0.34864514210180597,
                0.2018132150593341,
                0.9999151889788562,
                0.7057850154599562
            ],
            [
                0.9149009590535488,
                0.37754066879814546,
                0.9999646437451443,
                0.9241418199787564,
                0.9999921107374147,
                0.9999898700126433,
                0.99979657307687,
                NaN,
                0.9998204720368228,
                0.9999852610215426
            ],
            [
                0.9998766054534943,
                0.9999724643089007,
                0.9999546021097292,
                0.9999869928668845,
                0.9999930377412608,
                0.6513548714339145,
                0.9999921107383698,
                0.904650536386234,
                0.9706877690366521,
                0.9999785550439729
            ],
            [
                1.2098655392921197e-06,
                1.553497384196656e-06,
                9.422443692527585e-07,
                1.6373766672973748e-07,
                3.9278610661822475e-07,
                6.475945666009864e-07,
                6.144173869446876e-06,
                1.3709572067955008e-06,
                1.0677028700266676e-06,
                7.338209805224048e-07
            ],
            [
                0.9999646437451443,
                0.924141814233309,
                0.9997388096363627,
                0.8670357718273068,
                0.9241418121440552,
                0.9999921107392962,
                0.9999910603070592,
                0.9046505383142492,
                0.7549149813536518,
                0.9241418126663686
            ],
            [
                1.6701423835624208e-05,
                3.53562591336057e-05,
                1.4738988999940381e-05,
                7.889259764273619e-06,
                6.144172404587612e-06,
                2.1444940745371397e-05,
                2.430023493936082e-05,
                1.0129995810076682e-05,
                7.88926164518358e-06,
                3.120191880504111e-05
            ],
            [
                2.699578096399958e-07,
                3.4663257978780455e-07,
                2.382369667929001e-07,
                1.0677031245953668e-06,
                6.475951070002966e-07,
                2.382369383923073e-07,
                9.422449308748773e-07,
                2.699577130944368e-07,
                2.6995771309523475e-07,
                1.6373766672973748e-07
            ],
            [
                1.0129988564578197e-05,
                5.422219616026655e-06,
                2.26032402841657e-06,
                1.0129994601688632e-05,
                7.889262585541864e-06,
                1.9947304348703948e-06,
                1.0129994602222992e-05,
                4.78509563546605e-06,
                2.9023133690980155e-06,
                5.422217030495909e-06
            ],
            [
                9.422449308673789e-07,
                1.7603436330091044e-06,
                1.0677028700363782e-06,
                1.9947299592933255e-06,
                3.9278610661822475e-07,
                3.466327450765785e-07,
                4.785096205930373e-06,
                6.475951069961737e-07,
                1.994729483705484e-06,
                1.7603425837702984e-06
            ],
            [
                2.902310947208574e-06,
                2.9023119851635836e-06,
                4.785096205882502e-06,
                2.561281905376098e-06,
                2.902312331125353e-06,
                2.9023123310290063e-06,
                7.889259764273619e-06,
                3.288748673360027e-06,
                6.475947982022763e-07,
                1.9947304348595095e-06
            ],
            [
                0.9999546021151307,
                0.9999810748562746,
                0.9999938558246658,
                0.9999980052693274,
                0.9999869928730869,
                0.9999930377412606,
                0.9999910603068943,
                0.999995777164542,
                0.9999921107392955,
                0.9999967112501504
            ],
            [
                0.9999646437408634,
                0.9999910603026305,
                0.999997097689053,
                0.9999646437535248,
                0.9999339478396881,
                0.9999869928746377,
                0.9999938558224688,
                0.9999910603036963,
                0.9999970976876689,
                0.9999885212332448
            ],
            [
                6.144176065828368e-06,
                1.9947301970813926e-06,
                9.422447062270609e-07,
                9.422444815563743e-07,
                1.0677032518748838e-06,
                1.209865683518615e-06,
                5.715007195447234e-07,
                5.715005151485975e-07,
                4.222832941072913e-06,
                2.2603248367173307e-06
            ],
            [
                7.338208930443633e-07,
                1.0677031245905116e-06,
                1.2098661161789477e-06,
                6.475946438022905e-07,
                3.927860597945825e-07,
                1.8553907971813685e-07,
                5.715003107755449e-07,
                9.422443692489024e-07,
                1.7603436330179102e-06,
                3.2887494574518405e-06
            ],
            [
                4.785096776394765e-06,
                9.422450431954847e-07,
                4.2228324377164004e-06,
                1.3709578605617394e-06,
                6.1441767990323395e-06,
                9.422449308716635e-07,
                5.4222183231674305e-06,
                2.902313023101807e-06,
                2.561283126679493e-06,
                1.553497754577351e-06
            ],
            [
                3.927862470899887e-07,
                1.760343213322473e-06,
                1.9947306726358406e-06,
                4.222834451292594e-06,
                1.0129995809431767e-05,
                2.3823690999160957e-07,
                3.726639284017094e-06,
                8.315278294072958e-07,
                1.3709575337016483e-06,
                1.2098652508347793e-06
            ],
            [
                0.9999852610215626,
                0.9998204720124919,
                0.9999646437450841,
                0.999959936307828,
                0.946596666245483,
                0.9999930377412649,
                0.9999852610203732,
                0.999964643732433,
                0.999975699753477,
                0.9996646497708933
            ],
            [
                0.9999921107336551,
                0.9999646437366584,
                0.9999986290421394,
                0.9999967112505428,
                0.9999910603004991,
                0.9999974387184,
                0.9999962733602717,
                0.9999898700114362,
                0.9999921107392957,
                0.9999977396757022
            ],
            [
                1.3709568799823232e-06,
                2.561282210701601e-06,
                6.475946438042047e-07,
                5.422218969661113e-06,
                1.2098658277082653e-06,
                1.3709578605542582e-06,
                3.2887478892683997e-06,
                3.7266388397382506e-06,
                1.994729245917502e-06,
                3.726639284103523e-06
            ],
            [
                0.9999885212318748,
                0.999992110740236,
                0.9999852610215424,
                0.9999945777829693,
                0.9999930377454102,
                0.9999962733598278,
                0.999992110734593,
                0.9999938558261307,
                0.9999930377412605,
                0.9999974387184
            ],
            [
                2.9023133690821773e-06,
                3.288748673360027e-06,
                1.7603434231705793e-06,
                1.553497754577351e-06,
                2.2603245673155757e-06,
                6.475947210031623e-07,
                2.5612812947240366e-06,
                1.7603427936183298e-06,
                9.422448185478557e-07,
                5.715006514151423e-07
            ],
            [
                9.422447062270609e-07,
                5.715002426460124e-07,
                4.78509563546605e-06,
                5.71500515159253e-07,
                1.2098661161927025e-06,
                2.902311985146426e-06,
                1.3709572068354007e-06,
                3.2887502415243994e-06,
                1.9947297215043796e-06,
                9.42244930862237e-07
            ],
            [
                5.715007195431641e-07,
                3.2887482812745586e-06,
                4.222831934202483e-06,
                7.889266347456862e-06,
                4.222834451327159e-06,
                5.043475885657239e-07,
                1.994729721469003e-06,
                3.7266401725935817e-06,
                4.785096205973894e-06,
                6.14417533430649e-06
            ],
            [
                0.9999930377404306,
                0.9998415638021374,
                0.9999756997534747,
                0.9999832985841286,
                0.9999869928699856,
                0.9999885212277692,
                0.999989870011436,
                0.9999952149060758,
                0.9999546021205351,
                0.9999921107392953
            ],
            [
                1.275190276859705e-07,
                1.1253518888531272e-07,
                1.5534981249697903e-06,
                1.55349775456958e-06,
                2.2603251062270446e-06,
                1.0677028700363782e-06,
                2.9023133690637e-06,
                1.2098655392871682e-06,
                1.855391239539711e-07,
                4.2228349547223175e-06
            ],
            [
                0.9999990577549569,
                0.9999724643089045,
                0.9999810748562736,
                0.9999869928746379,
                0.9999980052709919,
                0.9999930377454106,
                0.999999168471675,
                0.9999785550592574,
                0.9999957771655488,
                0.9999910603047621
            ],
            [
                1.0677024881887838e-06,
                3.466327450765785e-07,
                1.0677031245990084e-06,
                9.4224425692559e-07,
                3.927861534406222e-07,
                1.0677027427569065e-06,
                1.5534983101393749e-06,
                1.4449807263287805e-07,
                6.475950297971703e-07,
                9.422449308748773e-07
            ],
            [
                4.2228349547223175e-06,
                2.9023133690637e-06,
                2.2603234895176927e-06,
                1.1478766757404937e-05,
                7.889265406904397e-06,
                2.2603251061849014e-06,
                6.962259569560613e-06,
                3.2887482812745586e-06,
                1.5534971989992774e-06,
                3.7266379513434106e-06
            ],
            [
                0.9999724642990605,
                0.9999898700102279,
                0.9999898700102285,
                0.9999485577863476,
                0.9999910603058276,
                0.999959936322143,
                0.9999962733593835,
                0.9999417087554116,
                0.9999974387180947,
                0.9999810748517607
            ],
            [
                0.9999038976195017,
                0.9999785550490348,
                0.999996273358939,
                0.9999832985702107,
                0.9999898700078138,
                0.999941708741432,
                0.9999885212264024,
                0.9995121427681696,
                0.9999967112501505,
                0.9999546021476239
            ],
            [
                1.1478764020727177e-05,
                3.2887478892504536e-06,
                2.7535697662094155e-05,
                6.962254589433702e-06,
                1.0129990979381404e-05,
                4.222833444506298e-06,
                4.222835458002318e-06,
                1.30071315640992e-05,
                4.222835457906302e-06,
                4.222833444383398e-06
            ],
            [
                5.715005832798517e-07,
                5.043472278312808e-07,
                5.043475885657239e-07,
                2.260323489490968e-06,
                2.260325106045111e-06,
                1.76034363298589e-06,
                9.422442569290178e-07,
                6.475947981975644e-07,
                1.0677026154551157e-06,
                1.5534984953298217e-06
            ],
            [
                0.9999852610162709,
                0.9999952149072167,
                0.9999898700066053,
                0.9999852610110006,
                0.9999938558253982,
                0.9999885212305056,
                0.9998204720125233,
                0.9999151889283289,
                0.9999952149066461,
                0.9999646437450763
            ],
            [
                0.999972464305766,
                0.8670357649558007,
                0.9999151889688598,
                0.9796676482898262,
                0.9999417087496837,
                0.9997965730282903,
                0.9999930377429204,
                0.999860177882025,
                0.9997965729334276,
                0.9999810748562796
            ],
            [
                0.9998911030400035,
                0.9999785550439195,
                0.9999151889904854,
                0.9999970976866311,
                0.8807970670261976,
                0.9999810748427858,
                0.9999251537370814,
                0.9999885212277699,
                0.8807970732843033,
                0.9999921107384129
            ],
            [
                2.102434412871794e-07,
                1.3709576971316842e-06,
                2.902312677137316e-06,
                1.2098653950480359e-06,
                3.927862939113312e-07,
                7.338212429582604e-07,
                8.3152792852928e-07,
                1.2098662604126641e-06,
                8.315278294097538e-07,
                7.338210679979539e-07
            ],
            [
                0.46879062662624377,
                0.1066905889749668,
                0.3486451488696663,
                0.9997965730998575,
                0.9999151889610037,
                0.9997040429713907,
                0.5926665999540697,
                0.9999724642991746,
                0.26894141551050293,
                0.8354835432479661
            ],
            [
                0.9999151889891938,
                0.9999945777823231,
                0.999997097686977,
                0.9999991684717742,
                0.9999945777823254,
                0.9999938558268633,
                0.9999994284997573,
                0.9999984465015047,
                0.9999970976876689,
                0.9999980052695652
            ],
            [
                2.902312677137316e-06,
                1.760344052714248e-06,
                3.288747889229516e-06,
                5.422217677028889e-06,
                6.962259569484628e-06,
                2.90231233114251e-06,
                1.5534971989992774e-06,
                2.902310947190096e-06,
                1.7603440527286572e-06,
                8.939694172770212e-06
            ],
            [
                1.4738983729053029e-05,
                3.535626335686906e-05,
                1.9947299593014888e-06,
                6.962254589914941e-06,
                6.962254589705982e-06,
                2.561283432005142e-06,
                8.939693106987645e-06,
                2.1444948414321717e-05,
                3.535624649610246e-05,
                2.1444956081636468e-05
            ],
            [
                0.9890130578146853,
                0.9999756997652819,
                0.8807970904940926,
                0.9999832985721823,
                0.999978555056851,
                0.9998415637266933,
                0.9999485578047517,
                0.9046505383142494,
                0.9992903296205894,
                0.1480472036701053
            ],
            [
                0.9999599363174471,
                0.9988304894682687,
                0.9940889321534454,
                0.5312093733737562,
                0.9996646497307152,
                0.13296425050508953,
                0.9995694429607985,
                0.9984988178774522,
                0.10669058542447808,
                0.9989677687955445
            ],
            [
                1.99472924590571e-06,
                5.4222202624563834e-06,
                6.144173869446876e-06,
                1.55349775456958e-06,
                3.7266401725681614e-06,
                1.0677024881683915e-06,
                1.994729721469003e-06,
                8.31528126775552e-07,
                7.889266347456862e-06,
                1.5534975693869924e-06
            ],
            [
                0.7549149868676283,
                0.9999417087275282,
                0.015906387979758903,
                0.9999687980811974,
                0.9999546021429446,
                0.9669140216112958,
                0.999941708706696,
                0.9999546021422518,
                0.9999832985761657,
                0.8933094081846421
            ]
        ]
    },
    {
        "q_id": "8900_mmlu_math",
        "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,
            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": [
            [
                2.2603248365014775e-06,
                4.2228324356808684e-06,
                1.7603436329714805e-06,
                3.2887506333394084e-06,
                4.222832940646604e-06,
                1.473898020682712e-05,
                5.422217675628357e-06,
                1.0677027427068966e-06,
                1.7603436328994344e-06,
                2.5612815999423112e-06
            ],
            [
                6.9622554187981796e-06,
                1.9947292458930106e-06,
                3.2887482811908074e-06,
                3.7266379512112265e-06,
                0.00043055703053385716,
                1.994729245917502e-06,
                3.2887494573232236e-06,
                1.2098653950205268e-06,
                1.760343842833246e-06,
                6.9622537584863015e-06
            ],
            [
                1.5534977544932838e-06,
                6.144173134700951e-06,
                2.90231198483099e-06,
                1.3709578602637359e-06,
                1.7603438428028262e-06,
                1.2098655392222467e-06,
                2.5612834317908303e-06,
                3.726641060658489e-06,
                2.9023116383479355e-06,
                5.422217676397663e-06
            ],
            [
                1.5534981248330927e-06,
                2.2603234894745224e-06,
                2.561281599914358e-06,
                2.260324567268294e-06,
                1.553497754476329e-06,
                2.902311293034278e-06,
                1.7603430033991435e-06,
                2.2603237588597026e-06,
                3.288749065125496e-06,
                3.2887490652810324e-06
            ],
            [
                0.999999653367379,
                0.9999982396565771,
                0.9999991684717743,
                0.9999996072139402,
                0.999998005269803,
                0.9999997300421903,
                0.9999997897565587,
                0.9999995549147359,
                0.9999993524053562,
                0.9999994284993485
            ],
            [
                4.222834954561012e-06,
                1.9947299591826594e-06,
                1.5534971989568904e-06,
                1.0677029972993568e-06,
                9.422445938231535e-07,
                1.209866116137134e-06,
                1.994729245878497e-06,
                2.9023126768680736e-06,
                1.209865971934245e-06,
                1.2098652508056196e-06
            ],
            [
                1.1478770859332632e-05,
                3.2887502408573863e-06,
                2.9023109465909e-06,
                2.4300237794201987e-05,
                8.315278293687262e-07,
                1.7603432131119386e-06,
                2.902311983859607e-06,
                4.785096205077381e-06,
                2.260324836651547e-06,
                1.370956879799656e-06
            ],
            [
                5.422217026412668e-06,
                9.422449308241022e-07,
                7.889266346746518e-06,
                1.994729958830706e-06,
                2.561281599776919e-06,
                6.962253756232077e-06,
                4.785093922889744e-06,
                1.8925141446404996e-05,
                7.889263523869684e-06,
                4.2228334433617906e-06
            ],
            [
                2.9023126767836054e-06,
                3.7266410607194972e-06,
                1.9947299589105305e-06,
                6.9622562487453084e-06,
                2.2603240281606297e-06,
                2.561282515988704e-06,
                2.561281905100056e-06,
                4.222832437386106e-06,
                3.726637951126493e-06,
                1.0129989768616954e-05
            ],
            [
                0.9999485577619518,
                0.9999852610127759,
                0.9999967112517191,
                0.9999930377420916,
                0.9999974387180947,
                0.9999952149049377,
                0.999999168471675,
                0.9999989322975119,
                0.9999945777784454,
                0.9999546021422945
            ],
            [
                1.7603432132079998e-06,
                4.7850967757637256e-06,
                1.2098655392090423e-06,
                1.067703251864202e-06,
                9.422447061876404e-07,
                1.9947306725868575e-06,
                9.422450431474948e-07,
                6.1441753317695124e-06,
                2.5612819048205203e-06,
                3.288750241042834e-06
            ],
            [
                1.3709576970213355e-06,
                2.260325375520937e-06,
                1.5534977544932838e-06,
                7.338211554531576e-07,
                2.260324028306588e-06,
                8.939698433974813e-06,
                1.0129994596824126e-05,
                1.3709572067356507e-06,
                6.1441767949698196e-06,
                1.9947304347570075e-06
            ],
            [
                2.260323758713745e-06,
                2.260324567177841e-06,
                1.994730434816876e-06,
                1.7603440525701563e-06,
                9.422449308241022e-07,
                2.5612834318583854e-06,
                1.370956879777212e-06,
                3.2887494571676872e-06,
                3.2887490652810324e-06,
                1.370957370106421e-06
            ],
            [
                5.422217676797111e-06,
                6.144176798479122e-06,
                1.3007133106487501e-05,
                6.9622562487453084e-06,
                6.144174599532449e-06,
                1.4738978446451746e-05,
                2.430025228428967e-05,
                2.9023130228444433e-06,
                7.889263524257144e-06,
                4.785093923768848e-06
            ],
            [
                0.9999974387165681,
                0.999999814460876,
                0.9999986290424663,
                0.9999994284996211,
                0.9999994956526519,
                0.999997097686631,
                0.999999266179282,
                0.9999997617631469,
                0.999999730042126,
                0.9999997897566089
            ],
            [
                1.3709578604308174e-06,
                2.561281294558644e-06,
                2.2603242978007868e-06,
                1.2098662603356388e-06,
                3.288749065077638e-06,
                1.3709570432501875e-06,
                1.3709578605118645e-06,
                1.994729483508644e-06,
                1.7603432132784448e-06,
                6.962257906562937e-06
            ],
            [
                1.1478768120315386e-05,
                3.2887498493325602e-06,
                0.999796573058751,
                3.7266410608245674e-06,
                3.2887486725569194e-06,
                2.2603251057881422e-06,
                4.78509449280116e-06,
                1.300712690556288e-05,
                2.902312330965655e-06,
                1.9947294834796172e-06
            ],
            [
                1.2098652508056196e-06,
                8.315282258956806e-07,
                1.7603434230921292e-06,
                1.994729483508644e-06,
                1.5534984952662413e-06,
                4.450848927437622e-07,
                7.889265406438011e-06,
                6.47594566597747e-07,
                2.699578739999358e-07,
                5.422220262037209e-06
            ],
            [
                4.7850927830148924e-06,
                5.715006513999389e-07,
                2.5612834317116285e-06,
                3.7266383952696564e-06,
                1.5534983101301911e-06,
                2.260324567054496e-06,
                1.9947301970451086e-06,
                1.7603434231241496e-06,
                2.9023130229209922e-06,
                1.994729721265813e-06
            ],
            [
                0.999998790133884,
                0.00020342702013551378,
                6.962257079173776e-06,
                0.000552778595664675,
                3.535626333809042e-05,
                1.0129988562661878e-05,
                5.8291286335171815e-05,
                1.0129987356706945e-05,
                1.0129988559160908e-05,
                7.889262580504884e-06
            ],
            [
                1.0677027426709671e-06,
                4.2228334438149845e-06,
                1.2098661159335663e-06,
                1.7603425837062577e-06,
                4.785096775580942e-06,
                3.28874945711983e-06,
                3.288747889178668e-06,
                2.2603237588597026e-06,
                2.2603234891147668e-06,
                1.99472995920443e-06
            ],
            [
                7.889260702342794e-06,
                9.422444815563743e-07,
                2.902311984952413e-06,
                2.9023126769050284e-06,
                2.9023116388072315e-06,
                2.902313368897403e-06,
                6.962256246896338e-06,
                7.889260703619978e-06,
                5.422220908116881e-06,
                3.7266388394569345e-06
            ],
            [
                0.9999417087414438,
                0.9999417087138222,
                0.9999546021477804,
                0.9999599363078385,
                0.9999251537758438,
                0.9997040429724672,
                0.999985261021544,
                0.798186768138228,
                0.9996646500101373,
                0.9997694932582344
            ],
            [
                4.785092782692845e-06,
                8.939693105272102e-06,
                2.260325375634003e-06,
                3.7266392836374875e-06,
                2.9023116388072315e-06,
                6.144173867284299e-06,
                4.7850967749455485e-06,
                1.7603438428188364e-06,
                4.785093923768848e-06,
                2.2603242977308917e-06
            ],
            [
                0.8670357666736772,
                0.9999885212346389,
                0.999994577779757,
                0.9999921107364745,
                0.9999982396569966,
                0.9999810748495044,
                0.999995214904935,
                0.999983298574177,
                0.9999885212318752,
                0.999994577780384
            ],
            [
                3.7266388392671313e-06,
                5.422217674464535e-06,
                1.7603436329554703e-06,
                2.5612825159421147e-06,
                1.5534983100425914e-06,
                1.5534975693347152e-06,
                2.260324297702111e-06,
                5.715006514151423e-07,
                9.422449308035348e-07,
                4.222835457595211e-06
            ],
            [
                0.9999989322966208,
                0.9999989322967482,
                0.9999991684722697,
                0.9999977396759718,
                0.9999977396754327,
                0.9999977396751634,
                0.9999992661792819,
                0.9999996072137998,
                0.9999986290427932,
                0.9999992661792819
            ],
            [
                0.9999992661791945,
                0.9999996533674615,
                0.9999994284997573,
                0.9999996533672962,
                0.9999997897566089,
                0.9999998555020307,
                0.9999996533672549,
                0.9999996533674201,
                0.9999996072137529,
                0.9999997300421581
            ],
            [
                4.785093923690512e-06,
                4.222831934052698e-06,
                1.0129992183991656e-05,
                1.3007131564643372e-05,
                6.144176798255599e-06,
                5.422220261652556e-06,
                2.144495863045236e-05,
                2.14449535222109e-05,
                2.4300243607668818e-05,
                1.1478769491306371e-05
            ],
            [
                6.96225541788636e-06,
                7.338210679949506e-07,
                5.422217676101776e-06,
                2.9023126768258393e-06,
                1.8925150494750372e-05,
                4.222833947674739e-06,
                2.7535704221626983e-05,
                1.3007131553807308e-05,
                4.7850939242083995e-06,
                3.2887478891487563e-06
            ],
            [
                0.999999168471675,
                0.9999984465018751,
                0.9999997300421581,
                0.9999995549151073,
                0.9999984465028011,
                0.999999352404893,
                0.9999994284992805,
                0.9999994956524716,
                0.9999995549149481,
                0.9999997300422547
            ],
            [
                2.2603240281236263e-06,
                2.561282821069686e-06,
                1.3709567164962755e-06,
                1.5534979395006942e-06,
                2.5612819051373276e-06,
                8.315281267800897e-07,
                6.96225956837018e-06,
                2.5612825159677387e-06,
                7.889264465555602e-06,
                1.1478768117434013e-05
            ],
            [
                1.9947294834469616e-06,
                2.2603251061849014e-06,
                1.3007131558444574e-05,
                1.0129994598777299e-05,
                1.0677031245710902e-06,
                1.7603438427852151e-06,
                4.785096775058701e-06,
                1.2098658277264215e-06,
                1.7603440525701563e-06,
                6.144176797998549e-06
            ],
            [
                1.5534975693707442e-06,
                9.422449308335287e-07,
                2.2603245672497918e-06,
                1.3709578604981489e-06,
                3.288748672760313e-06,
                1.0677033791437343e-06,
                1.0677032518316716e-06,
                6.144174600985344e-06,
                3.7266383950256237e-06,
                3.2887482807780376e-06
            ],
            [
                1.7603436328994344e-06,
                3.7266379506485954e-06,
                2.260325105981383e-06,
                1.3709575336654889e-06,
                1.0129994599624903e-05,
                1.9947294835866542e-06,
                4.7850950646797465e-06,
                1.3709576970824327e-06,
                2.5612825157464395e-06,
                1.7603434231097403e-06
            ],
            [
                0.9999997617630332,
                0.9999994956527722,
                0.9999996533672549,
                0.9999995549151073,
                0.9999993524054334,
                0.9999998555019446,
                0.9999995549151073,
                0.9999996533673375,
                0.9999997617629763,
                0.9999921107392962
            ],
            [
                1.5534977545102382e-06,
                1.0677026154551157e-06,
                4.785093923916815e-06,
                3.2887478884069663e-06,
                1.9947290080125335e-06,
                1.9947290081177566e-06,
                3.2887498494282754e-06,
                1.8553919030776337e-07,
                1.5534979397394734e-06,
                2.56128159959988e-06
            ],
            [
                2.561281294558644e-06,
                3.2887482811579057e-06,
                2.561282515783711e-06,
                3.9278610661366994e-07,
                2.699576809107705e-07,
                3.726638395320497e-06,
                3.7266410607194972e-06,
                1.3007125358230479e-05,
                2.699578739999358e-07,
                7.338207180661203e-07
            ],
            [
                4.222833946845163e-06,
                1.3709570432888404e-06,
                0.0024726225926929137,
                7.88926258381982e-06,
                0.006692849580732689,
                5.422220908402905e-06,
                1.4738980210258757e-05,
                1.3007126896099073e-05,
                0.0011695104757035578,
                1.3007130006521673e-05
            ],
            [
                1.3709573701812335e-06,
                6.962258737814774e-06,
                2.260325105981383e-06,
                1.5534981248330927e-06,
                2.1444958621558693e-05,
                3.7266379512112265e-06,
                3.1201907620154606e-05,
                5.422217030288788e-06,
                3.288750240486491e-06,
                2.561283126535066e-06
            ],
            [
                5.422218322348809e-06,
                6.9622545877746946e-06,
                2.26032429753354e-06,
                1.1478764018576587e-05,
                2.902311984683171e-06,
                5.422221553910605e-06,
                5.422217674780147e-06,
                7.889263524257144e-06,
                1.7603436329394601e-06,
                2.260324836624822e-06
            ],
            [
                0.999941708748449,
                0.9999646437366894,
                0.9999151889385179,
                0.9999945777823239,
                0.9999151889183441,
                0.9999869928684365,
                0.9998601779606706,
                0.9999756997650695,
                0.9999038976090344,
                0.0002959570249754418
            ],
            [
                2.5612825157464395e-06,
                1.8553903548231313e-07,
                7.338207180534397e-07,
                7.338208930315157e-07,
                3.726640616630245e-06,
                2.2603242977555607e-06,
                5.4222202617511845e-06,
                3.7266410603195545e-06,
                6.144173133560988e-06,
                3.7266379509129646e-06
            ],
            [
                1.5534975691778837e-06,
                1.994730672468935e-06,
                4.222834450505264e-06,
                1.2098659718363124e-06,
                1.7603438427852151e-06,
                2.5612828206131103e-06,
                5.7150044702099e-07,
                4.2228319339950885e-06,
                9.422450431912e-07,
                3.2887506332466845e-06
            ],
            [
                4.222834450743383e-06,
                6.144175332115971e-06,
                1.0129993382982077e-05,
                1.1478769487840372e-05,
                1.994729721436347e-06,
                4.7850967757637256e-06,
                1.0129989762757436e-05,
                3.726638395415398e-06,
                2.4300232005488976e-05,
                3.288748279952497e-06
            ],
            [
                3.7266410609160796e-06,
                3.288747889178668e-06,
                2.9023130221686978e-06,
                1.9947301966967833e-06,
                1.3709573702647743e-06,
                3.2887506332466845e-06,
                4.222831932781451e-06,
                1.5534975692259223e-06,
                2.561282821106957e-06,
                1.994729721323867e-06
            ],
            [
                1.5534983100228109e-06,
                7.338213304083124e-07,
                4.785094494019719e-06,
                9.422449308035348e-07,
                1.5534973840984598e-06,
                1.9947304347570075e-06,
                2.902311984989368e-06,
                1.067702488159652e-06,
                1.7603436329554703e-06,
                1.7603438428188364e-06
            ],
            [
                0.9999995549150011,
                0.9999980052698031,
                0.9999995549148419,
                0.999998239656577,
                0.9999980052700408,
                0.9999898700114427,
                0.9999930377412624,
                0.9999970976890529,
                0.9999989322966208,
                0.9999938558246665
            ],
            [
                2.260323489192885e-06,
                1.7603434230729168e-06,
                1.3007133114011233e-05,
                1.553498495230919e-06,
                6.962254588433232e-06,
                4.7850927818311495e-06,
                7.338212429087055e-07,
                4.222833444106873e-06,
                3.726639727940109e-06,
                1.7603440525461408e-06
            ],
            [
                1.0677031245953668e-06,
                1.5534973841592143e-06,
                4.7850944937411915e-06,
                1.0129987347678128e-05,
                4.222831933864508e-06,
                1.3709572068179446e-06,
                6.144173867608406e-06,
                1.553497754476329e-06,
                1.067703251864202e-06,
                8.93969950000193e-06
            ],
            [
                1.7603427933309468e-06,
                2.2603242977308917e-06,
                3.2887486732000038e-06,
                5.71500515151976e-07,
                3.7266406165319545e-06,
                5.71500719531729e-07,
                1.5534973841450852e-06,
                2.5612834318583854e-06,
                9.42244818532859e-07,
                9.422443692261927e-07
            ],
            [
                1.4738987237553233e-05,
                4.785095634756674e-06,
                1.76034258364702e-06,
                6.962259565748692e-06,
                1.3007133106487501e-05,
                1.9947306726358406e-06,
                3.726637951170554e-06,
                2.260325105870372e-06,
                2.56128221029278e-06,
                2.260324297492425e-06
            ],
            [
                6.144177530794679e-06,
                3.2887494572514376e-06,
                2.9023119850210436e-06,
                5.422217030209884e-06,
                1.1478768122987964e-05,
                3.2887482807182155e-06,
                2.9023123310290063e-06,
                4.222832437324657e-06,
                1.5534977545102382e-06,
                6.962257908348587e-06
            ],
            [
                2.2603234894745224e-06,
                3.726638395493353e-06,
                2.5612819051373276e-06,
                3.726639728184142e-06,
                3.7266388396975786e-06,
                7.889264465842609e-06,
                1.1478769490053603e-05,
                7.889260700462896e-06,
                1.994729008074216e-06,
                5.42222090882208e-06
            ],
            [
                4.22283394762097e-06,
                4.7850967757637256e-06,
                2.26032348933062e-06,
                4.222832436687113e-06,
                1.8925143723000643e-05,
                1.7603436329394601e-06,
                4.78509563509613e-06,
                4.222833444383398e-06,
                2.902313368897403e-06,
                3.2887478889034873e-06
            ],
            [
                4.2228349547223175e-06,
                8.93969736929749e-06,
                1.0677032518700286e-06,
                8.315282258756395e-07,
                2.2603251058292572e-06,
                1.4738981964843453e-05,
                2.9023109470554753e-06,
                2.5612831265630198e-06,
                3.2887506332945414e-06,
                2.382368247909451e-07
            ],
            [
                7.889259762307618e-06,
                8.939693103418341e-06,
                6.9622570777680525e-06,
                5.422218968931258e-06,
                2.561281599914358e-06,
                4.2228319341064674e-06,
                8.9396994983433e-06,
                6.144177530425867e-06,
                6.144175332115971e-06,
                1.7603440527046419e-06
            ],
            [
                5.1442213448779634e-05,
                1.0129994601688632e-05,
                6.962259567914269e-06,
                6.605216034072351e-05,
                1.89251482355036e-05,
                2.4300246497960055e-05,
                1.67014238321306e-05,
                4.00637017209988e-05,
                4.0063706481032684e-05,
                2.7535697658087296e-05
            ],
            [
                1.3709578604831862e-06,
                1.3709578604981489e-06,
                1.3709576970213355e-06,
                2.382369099894428e-07,
                1.553497384058899e-06,
                6.9622545872301346e-06,
                2.2603248364233586e-06,
                2.2603242978007868e-06,
                1.553498495281783e-06,
                6.1441760651689774e-06
            ],
            [
                4.222835457906302e-06,
                1.994730434798734e-06,
                1.370956716519966e-06,
                4.222833946845163e-06,
                4.222835457906302e-06,
                1.4738980205164923e-05,
                2.260324836696773e-06,
                5.144221970062134e-05,
                3.2887478889513447e-06,
                1.7603436328770204e-06
            ],
            [
                1.994729483666479e-06,
                2.561282515853595e-06,
                2.260324028281919e-06,
                1.5534979397267575e-06,
                3.2887490652451393e-06,
                3.2887494571676872e-06,
                1.7603440526806268e-06,
                2.561281905058126e-06,
                1.9947290079889487e-06,
                5.4222202617511845e-06
            ],
            [
                1.994729245917502e-06,
                8.315283249923769e-07,
                1.5534983100228109e-06,
                1.14787708580381e-05,
                9.422445938728576e-07,
                2.9023130227124616e-06,
                1.994729245842213e-06,
                1.5534975692259223e-06,
                1.0677033791437343e-06,
                7.889259756352216e-06
            ],
            [
                7.88926352407059e-06,
                3.726640171842841e-06,
                6.144174601208867e-06,
                1.7603440525925705e-06,
                1.5534977544565482e-06,
                7.889265405677441e-06,
                4.2228349539810764e-06,
                6.9622579086271995e-06,
                1.3007128460040644e-05,
                1.7603425835749741e-06
            ],
            [
                2.902313368860448e-06,
                6.475947981975644e-07,
                2.260324297702111e-06,
                1.3709572067680694e-06,
                1.067703379136937e-06,
                1.5534984952492866e-06,
                1.1478772225271098e-05,
                2.5612828210277558e-06,
                3.7266383950256237e-06,
                2.5612822101436936e-06
            ],
            [
                2.561283126535066e-06,
                2.561282821209454e-06,
                1.7603427935342762e-06,
                2.2603234893594005e-06,
                1.2098652507583041e-06,
                1.3709578605455302e-06,
                2.561281294558644e-06,
                2.5612815999679353e-06,
                2.260323758746637e-06,
                1.994730434847717e-06
            ],
            [
                0.0008040859769706697,
                0.00048785716115631097,
                1.6701415862785876e-05,
                7.338209805133949e-07,
                6.144173135762683e-06,
                1.5534981249496567e-06,
                4.222832436164788e-06,
                1.0129992185760567e-05,
                1.5534975693347152e-06,
                1.3709572067955008e-06
            ],
            [
                1.670141983978702e-05,
                1.012998856312253e-05,
                2.5612812941789413e-06,
                1.7603425837494853e-06,
                1.8925155001402863e-05,
                1.8925152738024674e-05,
                1.9947292458004866e-06,
                6.144174601588856e-06,
                1.994730434735237e-06,
                1.3007128456065844e-05
            ],
            [
                6.962254589104433e-06,
                2.5612831262112703e-06,
                1.9947304347098384e-06,
                1.2098656835076114e-06,
                2.2603245668941476e-06,
                1.0677033791437343e-06,
                1.7603436328289897e-06,
                1.7603430034439723e-06,
                6.144172403067661e-06,
                4.222832940500659e-06
            ],
            [
                1.4738988991495334e-05,
                4.222834954057889e-06,
                2.260324567054496e-06,
                2.5612819047646128e-06,
                1.994729245842213e-06,
                3.726639283806955e-06,
                2.561282515988704e-06,
                3.726640616630245e-06,
                3.28874906467085e-06,
                2.9023112929973233e-06
            ],
            [
                1.14787681240737e-05,
                1.370956879949281e-06,
                4.222832437443716e-06,
                3.7266379513434106e-06,
                7.88926446470893e-06,
                5.422220260656402e-06,
                4.222835457526079e-06,
                3.7266392835086923e-06,
                4.785096205651846e-06,
                8.939700560874416e-06
            ],
            [
                1.3709573701812335e-06,
                3.2887506326006084e-06,
                1.370957533676711e-06,
                1.5534979397267575e-06,
                1.3709576970949014e-06,
                1.670142181188317e-05,
                5.715007195275709e-07,
                1.0677029971978802e-06,
                2.5612812945889277e-06,
                1.3709575334871855e-06
            ],
            [
                9.422442568951678e-07,
                1.3709578604831862e-06,
                2.6995768090929735e-07,
                1.3709575336947905e-06,
                3.7266388395620047e-06,
                8.315277302788957e-07,
                6.475950297868629e-07,
                6.475947981860793e-07,
                1.9947292458603553e-06,
                3.059022998558814e-07
            ],
            [
                1.1478769490700865e-05,
                4.7850967757637256e-06,
                1.0129993389652346e-05,
                1.0677026154619133e-06,
                3.288749065167371e-06,
                6.962256248871951e-06,
                4.785096205173126e-06,
                2.5612825159421147e-06,
                1.1478769487464542e-05,
                4.785096776068365e-06
            ],
            [
                2.561283126160022e-06,
                1.0677033790475986e-06,
                1.9947306725215466e-06,
                1.9947290078746543e-06,
                3.7266397276757403e-06,
                2.5612819052072116e-06,
                7.889265403654039e-06,
                3.726637950329997e-06,
                2.5612828209811664e-06,
                6.962259568078904e-06
            ],
            [
                2.2603242977555607e-06,
                5.7150044702099e-07,
                1.0677032518413822e-06,
                2.9023130227599746e-06,
                3.288749065167371e-06,
                1.994729959224386e-06,
                4.222833946645451e-06,
                5.422219615069953e-06,
                1.9947297213492663e-06,
                7.338210679622478e-07
            ],
            [
                1.0129992172346323e-05,
                1.99472972104811e-06,
                2.2603240283888175e-06,
                4.222831934156396e-06,
                1.5534983101061718e-06,
                1.6701423809741124e-05,
                5.04347648667744e-07,
                6.144172402452975e-06,
                7.889265406681968e-06,
                3.7266410609160796e-06
            ],
            [
                1.0677032518093368e-06,
                4.222833947198501e-06,
                3.726640172385136e-06,
                4.222833443968609e-06,
                1.3709572065835317e-06,
                2.2603234894745224e-06,
                1.2098653950205268e-06,
                1.2098662604192665e-06,
                7.338207180761315e-07,
                2.260323758835034e-06
            ],
            [
                0.5621765008857982,
                0.7549149923816048,
                0.9997965729783551,
                0.4378234991142019,
                0.9999952149072171,
                0.9999810748518118,
                0.9999962733616046,
                0.9999885212360199,
                0.9999921107383568,
                0.9999952149060758
            ],
            [
                6.962258736067116e-06,
                1.6373776432303203e-07,
                1.994729245842213e-06,
                4.4508521110762794e-07,
                1.99472972129484e-06,
                3.927862002625787e-07,
                3.726637951079042e-06,
                1.994729245722476e-06,
                1.9947294836483373e-06,
                1.760344052650207e-06
            ],
            [
                2.1444943264773968e-05,
                2.56128159959988e-06,
                0.0017007225960435925,
                4.785095634121282e-06,
                1.3007128460419196e-05,
                0.0013250222919717182,
                0.003172682258556414,
                2.4300243616508983e-05,
                1.0129990976451642e-05,
                3.7266383950934104e-06
            ],
            [
                1.3709575334373105e-06,
                5.422219615286937e-06,
                6.14417459774427e-06,
                4.222834450505264e-06,
                6.14417679836736e-06,
                3.726641060658489e-06,
                7.88926352407059e-06,
                1.5534977543661227e-06,
                1.760343632854606e-06,
                4.785095064436034e-06
            ],
            [
                3.726638839395927e-06,
                3.2887486729876365e-06,
                1.7603430032374404e-06,
                6.962258738435319e-06,
                6.14417313680765e-06,
                7.889261643181705e-06,
                4.222833443461647e-06,
                3.7266410609940346e-06,
                2.561281599881745e-06,
                1.3007133113017532e-05
            ],
            [
                6.962255416961874e-06,
                5.422220908703723e-06,
                2.902312676941983e-06,
                1.209865827698362e-06,
                3.288750633025344e-06,
                4.785096205077381e-06,
                6.962257077223492e-06,
                6.962259567914269e-06,
                1.760342583722268e-06,
                2.2603251060142746e-06
            ],
            [
                2.902311984873224e-06,
                1.5534975693792215e-06,
                4.222832940715735e-06,
                4.222833444283541e-06,
                5.422218969128516e-06,
                5.422218321855664e-06,
                1.3007123806450271e-05,
                6.962258738827909e-06,
                6.144176063626673e-06,
                0.9999546021112061
            ],
            [
                0.9999996533673375,
                0.9999990577550691,
                0.999999554914895,
                0.9999984465028011,
                0.9999992661791944,
                0.9999967112493687,
                0.9999996940976272,
                0.9999991684719723,
                0.9999997617630332,
                0.9999995549150542
            ],
            [
                1.209865827698362e-06,
                8.315278293899016e-07,
                1.9947304346535984e-06,
                2.56128129449109e-06,
                4.222832436779288e-06,
                7.889265406681968e-06,
                6.14417606400666e-06,
                1.2098655391947376e-06,
                7.338211554688417e-07,
                3.2887506333394084e-06
            ],
            [
                0.9999945777823233,
                0.9999724643023409,
                0.9999785550439207,
                0.9999938558246657,
                0.9999038975737187,
                0.999995777167059,
                0.9999756997534802,
                0.9999952149043647,
                0.999989870009023,
                0.999738809598448
            ],
            [
                1.2098655392464547e-06,
                1.370956716529941e-06,
                1.1478766751997141e-05,
                3.2887490648622804e-06,
                4.222831934156396e-06,
                6.144175333155351e-06,
                5.422218322940583e-06,
                2.902313023063532e-06,
                8.93969629829474e-06,
                3.288748673295719e-06
            ],
            [
                6.1441724029223715e-06,
                1.0129990969818226e-05,
                7.88926446470893e-06,
                8.939694170518055e-06,
                4.222832437109582e-06,
                4.222831933480445e-06,
                4.785092782936557e-06,
                5.422217029509618e-06,
                2.5612819052374947e-06,
                6.9622554187981796e-06
            ],
            [
                2.9023123309973302e-06,
                3.288748280658394e-06,
                1.0129992182112188e-05,
                1.1478772227651366e-05,
                9.422448185264317e-07,
                4.222833443968609e-06,
                1.553497198801472e-06,
                4.222832940577472e-06,
                6.144172402609439e-06,
                3.7266379512518984e-06
            ],
            [
                1.7603434230729168e-06,
                1.0129989771288745e-05,
                6.962258738574625e-06,
                5.422217675756574e-06,
                1.0677027427413698e-06,
                3.7266406163624873e-06,
                4.222834450743383e-06,
                5.422220908018252e-06,
                4.78509563509613e-06,
                2.9023133689317184e-06
            ],
            [
                1.0677029972270124e-06,
                7.889266344321303e-06,
                1.760342583229154e-06,
                2.561281294558644e-06,
                1.5534973840377051e-06,
                1.994729483508644e-06,
                1.6701415862117537e-05,
                4.222833443891798e-06,
                3.288749065209246e-06,
                2.902312330849511e-06
            ],
            [
                4.222833443645997e-06,
                9.422444815563743e-07,
                1.5534975693792215e-06,
                1.3709572068272963e-06,
                1.7603427935967163e-06,
                1.7603440526662173e-06,
                1.5534981248133121e-06,
                3.4663266242780743e-07,
                4.22283294007051e-06,
                1.370957860466977e-06
            ],
            [
                2.5612819052654485e-06,
                1.9947304346535984e-06,
                2.2603253754284284e-06,
                2.561281294123034e-06,
                1.9947306726213275e-06,
                2.5612815996464693e-06,
                3.2887490649221017e-06,
                3.2887506334201674e-06,
                3.7266388392671313e-06,
                4.222833444283541e-06
            ],
            [
                6.96225375863827e-06,
                4.222832940577472e-06,
                6.962253756004122e-06,
                0.0031726821252763436,
                4.222834954403545e-06,
                0.00017952800758656067,
                1.1478765386038447e-05,
                3.7266401719174067e-06,
                1.994730434816876e-06,
                2.561282210530385e-06
            ],
            [
                2.9023116390104826e-06,
                1.1478765381674627e-05,
                2.9023123310580418e-06,
                4.785094494185095e-06,
                1.994729245878497e-06,
                3.288747889038086e-06,
                3.2887502411026557e-06,
                1.7603430033799313e-06,
                5.422218969217281e-06,
                4.785092782597101e-06
            ],
            [
                2.5612831265909735e-06,
                3.7266388395111645e-06,
                5.422218968822766e-06,
                4.222835456227946e-06,
                1.7603432132624344e-06,
                2.2603240281236263e-06,
                1.9947301970587145e-06,
                3.2887478887958082e-06,
                1.5534977545603963e-06,
                1.7603438427243761e-06
            ],
            [
                6.144174600862407e-06,
                1.3007134654199377e-05,
                0.0009110510303688656,
                2.561282515820982e-06,
                2.5612822106654943e-06,
                4.2228324364874005e-06,
                2.902311638759718e-06,
                8.939696298945184e-06,
                4.785095062930243e-06,
                1.760344052402049e-06
            ],
            [
                8.31528424146183e-07,
                2.561282515564741e-06,
                6.144173864143809e-06,
                8.315283250006957e-07,
                1.3709576969402887e-06,
                1.994729245749689e-06,
                1.553497198826904e-06,
                2.260323489192885e-06,
                1.3709573702647743e-06,
                1.7603430033799313e-06
            ],
            [
                9.422442569097361e-07,
                3.7266397280485686e-06,
                2.5612825159677387e-06,
                1.760343423160973e-06,
                6.144176063425502e-06,
                4.222832940500659e-06,
                5.422218322565793e-06,
                5.42221702873045e-06,
                1.1478766752748805e-05,
                2.902313368963394e-06
            ],
            [
                1.7603430034151537e-06,
                6.1441760654483806e-06,
                1.6701417854810315e-05,
                4.222833947282995e-06,
                4.785093923847183e-06,
                0.998967768816672,
                2.9023130227124616e-06,
                4.22283344244772e-06,
                1.1478764014985311e-05,
                8.93969523678858e-06
            ],
            [
                3.2887502396310385e-06,
                8.315277302588544e-07,
                3.7266397280485686e-06,
                1.994729245749689e-06,
                2.902311984989368e-06,
                1.0677031245312763e-06,
                7.889259760542522e-06,
                2.2603234890695403e-06,
                1.9947306720008733e-06,
                2.9023130226068764e-06
            ],
            [
                4.78509506499309e-06,
                6.962258738827909e-06,
                1.9947294836483373e-06,
                1.5534979396984994e-06,
                6.144176798870286e-06,
                1.3007131560621253e-05,
                2.5612831265909735e-06,
                3.2887490648622804e-06,
                4.222833444283541e-06,
                2.144494585197151e-05
            ],
            [
                2.5612822106421996e-06,
                1.7603440524340693e-06,
                1.760343423160973e-06,
                1.2098652507120887e-06,
                2.561282210618905e-06,
                1.5534973841592143e-06,
                5.043472278255469e-07,
                1.9947297214182054e-06,
                1.0677024881829577e-06,
                1.3709575336530204e-06
            ],
            [
                1.1478768121401121e-05,
                1.209866260303728e-06,
                2.5612819052654485e-06,
                1.994729245842213e-06,
                1.2098658276730537e-06,
                2.5612819051722694e-06,
                1.5534979396448094e-06,
                3.7266379499571688e-06,
                1.9947301970287804e-06,
                1.994729483608425e-06
            ],
            [
                0.003593602523061508,
                1.3007126906509262e-05,
                2.7535697650273915e-05,
                3.288748673035494e-06,
                6.9622545877746946e-06,
                6.144176797998549e-06,
                1.9947294835866542e-06,
                1.9947301969707264e-06,
                6.962253756687988e-06,
                7.889261642134126e-06
            ],
            [
                4.785096205347206e-06,
                5.422217676101776e-06,
                2.26032537546132e-06,
                7.889259762106714e-06,
                3.288749064114508e-06,
                1.0129993385746e-05,
                1.4738983717819781e-05,
                7.889263524788109e-06,
                6.9622562478334885e-06,
                0.01243165054446931
            ],
            [
                0.9999485577741157,
                0.9997388097221476,
                0.9999687980774881,
                0.9999687980961062,
                0.9999990577555185,
                0.9999485578047914,
                0.9999832985701977,
                0.7549149813536518,
                0.9999646437408679,
                0.9999724642957817
            ],
            [
                1.6701419847381817e-05,
                6.962257077932685e-06,
                0.9992903294872173,
                3.726637951079042e-06,
                7.484623604187633e-05,
                1.7603427932989266e-06,
                8.9396973679153e-06,
                8.939698430218506e-06,
                3.2887494570181325e-06,
                6.144172403928222e-06
            ],
            [
                1.9947290076496946e-06,
                1.7603438427660027e-06,
                1.3007128457958606e-05,
                2.2603234894560207e-06,
                1.0677027427068966e-06,
                2.7535691071008866e-05,
                1.473897669015165e-05,
                0.0011695103111560195,
                1.7603427934206038e-06,
                1.01299933920846e-05
            ],
            [
                3.2887486728201357e-06,
                7.889262584006375e-06,
                7.8892607025437e-06,
                1.1478773595009805e-05,
                5.42222155351609e-06,
                2.2603242977555607e-06,
                4.785092782779884e-06,
                6.144173866379033e-06,
                6.144176066051891e-06,
                1.1478773592378984e-05
            ],
            [
                3.9278638755456876e-07,
                9.422447062094932e-07,
                1.5534977545102382e-06,
                2.2603248365960415e-06,
                7.889264463890957e-06,
                1.2098655391947376e-06,
                4.4508489275145346e-07,
                4.222831934156396e-06,
                1.5534979397267575e-06,
                1.0677027427340866e-06
            ],
            [
                7.889265403395731e-06,
                1.147876675162131e-05,
                6.962259568509485e-06,
                6.144177530548804e-06,
                2.1444940713541454e-05,
                0.0004878570130813328,
                3.726638838711279e-06,
                2.1444958627955892e-05,
                0.00020342699472987498,
                3.2887506334201674e-06
            ],
            [
                1.3709573702111586e-06,
                2.902311984318902e-06,
                1.370956716519966e-06,
                0.000295957154811131,
                2.9023112924403614e-06,
                2.260324836696773e-06,
                9.422449308138184e-07,
                1.760342793515064e-06,
                3.2887482810801374e-06,
                3.726639283440905e-06
            ],
            [
                1.5534981249397663e-06,
                3.288748280891699e-06,
                1.1478770857328198e-05,
                8.939696301839653e-06,
                1.0677024881829577e-06,
                1.2098655392354511e-06,
                2.260323758835034e-06,
                6.144175333401224e-06,
                1.3709578604981489e-06,
                1.0129989768616954e-05
            ],
            [
                0.9999996940977731,
                0.9999994284994849,
                0.9999984465026159,
                0.9999990577555185,
                0.9999995549150011,
                0.999997097688015,
                0.9999962733593837,
                0.9999986290431201,
                0.9999996072137529,
                0.9999994284993485
            ],
            [
                5.422217030121119e-06,
                4.222833444283541e-06,
                4.785095064523075e-06,
                1.3709568798220997e-06,
                3.7266397278791014e-06,
                5.422217676486429e-06,
                7.889259763469998e-06,
                7.889265405849647e-06,
                6.962254588281262e-06,
                1.3007133107528522e-05
            ],
            [
                0.9999989322972572,
                0.9999994284997573,
                0.9999992661789321,
                0.999999352404893,
                0.9999992661789321,
                0.9999990577554061,
                0.9999982396574163,
                0.9999987901347491,
                0.9999989322966208,
                0.9999990577554062
            ],
            [
                5.4222176755001384e-06,
                4.222835457595211e-06,
                1.4738985459965214e-05,
                6.1441760661636525e-06,
                2.260325105594902e-06,
                1.0129987347678128e-05,
                3.288748672760313e-06,
                0.00037998456597982343,
                1.1478764019077695e-05,
                4.785094492661896e-06
            ],
            [
                3.288748673265808e-06,
                3.288750241042834e-06,
                1.0129994602222992e-05,
                1.7603432133032607e-06,
                3.726638394957837e-06,
                4.222834450743383e-06,
                4.785094493932679e-06,
                2.5612828212909852e-06,
                7.889266345770692e-06,
                5.422219615395428e-06
            ],
            [
                2.9023130219364104e-06,
                7.338212429006964e-07,
                1.5534979396984994e-06,
                1.5534973841592143e-06,
                2.561283126502453e-06,
                3.7266392836984955e-06,
                6.475946437966953e-07,
                1.994729958743625e-06,
                7.338212429240558e-07,
                4.785096205582214e-06
            ],
            [
                2.260324028351814e-06,
                3.288750633025344e-06,
                3.7266406165827946e-06,
                4.785095064523075e-06,
                4.222832437639588e-06,
                6.144175333926503e-06,
                2.2603242977802297e-06,
                3.288748280658394e-06,
                1.892515047684989e-05,
                6.1441724029223715e-06
            ],
            [
                0.9999991684718733,
                0.9999970976876691,
                0.999999352404893,
                0.9999989322966208,
                0.9999992661789321,
                0.9999977396754328,
                0.999997438717484,
                0.9999977396748939,
                0.9999987901337396,
                0.9999992661786696
            ],
            [
                1.0129993389984017e-05,
                5.422218322565793e-06,
                2.2603251057881422e-06,
                1.2098656832369217e-06,
                2.9023112925037123e-06,
                1.5534984952111384e-06,
                1.3007123795850811e-05,
                7.889262582112126e-06,
                5.422220908018252e-06,
                1.0129989757340145e-05
            ],
            [
                8.93970055911822e-06,
                1.7603427935678977e-06,
                6.962255418658875e-06,
                1.147876675082789e-05,
                1.4738988981093183e-05,
                2.561281905293402e-06,
                4.785095633999427e-06,
                2.2603253754921562e-06,
                6.144173135483279e-06,
                6.1441738667590205e-06
            ],
            [
                3.2887482809455384e-06,
                5.422218322664422e-06,
                4.22283193393364e-06,
                3.2887498492518007e-06,
                1.1478773595343877e-05,
                8.93969949923766e-06,
                1.670142780381727e-05,
                1.3007128462477575e-05,
                1.8925145971093502e-05,
                5.829127238482131e-05
            ],
            [
                1.7603434231241496e-06,
                1.0129994600638342e-05,
                2.561283431478682e-06,
                2.5612815996930587e-06,
                2.260323758806253e-06,
                1.994729959224386e-06,
                1.9947294836483373e-06,
                5.715005151550947e-07,
                1.7603432132912532e-06,
                2.260323758835034e-06
            ]
        ]
    },
    {
        "q_id": "9026_mmlu_math",
        "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,
            38,
            39,
            40,
            41,
            43,
            44,
            45,
            47,
            48,
            49,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            74,
            75,
            76,
            77,
            78,
            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,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126
        ],
        "rewards": [
            [
                4.222834450505264e-06,
                2.4300237828943813e-05,
                2.2603237586397375e-06,
                7.889263523008662e-06,
                3.7266388395111645e-06,
                1.1478769483372156e-05,
                1.300712535865635e-05,
                6.144175332283612e-06,
                8.939700564890901e-06,
                4.222835457794923e-06
            ],
            [
                2.5612831266608576e-06,
                6.1441760661636525e-06,
                8.93970056529743e-06,
                6.475949525781504e-07,
                1.4738983726559732e-05,
                1.0677032518501217e-06,
                1.0129995807699706e-05,
                2.9023116388547446e-06,
                6.1441746017453204e-06,
                NaN
            ],
            [
                6.9622579092224155e-06,
                1.3709568796749682e-06,
                2.902313368583287e-06,
                5.4222196154940574e-06,
                1.9947297214182054e-06,
                1.4738987238464762e-05,
                1.2098662602663157e-06,
                2.561281294281438e-06,
                1.370956716450141e-06,
                5.42221702914469e-06
            ],
            [
                7.889259763326495e-06,
                2.9023119850210436e-06,
                4.006370647870077e-05,
                5.422220907909759e-06,
                1.8925143715220825e-05,
                1.067702488159652e-06,
                5.422217030362759e-06,
                1.6701429802769596e-05,
                1.1478770859332632e-05,
                1.0129987355343409e-05
            ],
            [
                3.0590222690893177e-07,
                1.5534979395006942e-06,
                5.043475885576967e-07,
                4.539787398158721e-05,
                6.962257077223492e-06,
                2.902313022984344e-06,
                5.715005151485975e-07,
                7.338210679816025e-07,
                5.71500378868701e-07,
                7.338208930078229e-07
            ],
            [
                1.1478768123280277e-05,
                1.9947294833417385e-06,
                4.785096205260165e-06,
                1.4738985474174337e-05,
                3.726638395415398e-06,
                1.8925150489517924e-05,
                NaN,
                1.012999212631777e-05,
                1.0129987353537646e-05,
                1.4738987238464762e-05
            ],
            [
                0.0007096702765021507,
                0.025957359929267797,
                0.00017952796546794733,
                0.02033235126495059,
                0.3775406617944891,
                0.005220125478345604,
                0.00317268329460666,
                0.16451646494473965,
                0.0017007220299642286,
                0.060086647228542005
            ],
            [
                0.9998415638419664,
                0.6513548511303338,
                0.9999852610111337,
                0.9998911031303049,
                0.9999724642991211,
                0.9978172840186458,
                0.9998601779543438,
                0.9465966707651319,
                2.7535681185986635e-05,
                0.9999417087487243
            ],
            [
                6.962257079059797e-06,
                1.4738983711117369e-05,
                8.93969949678224e-06,
                1.8925145982866508e-05,
                2.753568777787093e-05,
                2.144495351862222e-05,
                7.889259761030436e-06,
                2.430023492663099e-05,
                1.892515724357613e-05,
                2.430023782717578e-05
            ],
            [
                0.9997040428398157,
                0.9997965730598994,
                0.08509903746596331,
                NaN,
                0.9997388098031978,
                0.9998204719710603,
                4.222835456581284e-06,
                0.18242551491653522,
                0.8519527982093666,
                0.0005527786437411306
            ],
            [
                1.670142382796865e-05,
                2.9023123292710123e-06,
                4.222835456903897e-06,
                8.315281266053911e-07,
                NaN,
                6.962258738701267e-06,
                3.2887478873062457e-06,
                7.889261644982674e-06,
                1.6701421832723305e-05,
                1.9947306726049992e-06
            ],
            [
                0.0013250225805046048,
                0.003593602065363521,
                0.0007096703666140641,
                NaN,
                0.0003799845716951572,
                0.007577242836619065,
                0.005911068133864498,
                6.605217594790412e-05,
                0.029312228790434568,
                0.004070138116065526
            ],
            [
                2.4300240727367308e-05,
                1.1478768122695653e-05,
                2.144495351097679e-05,
                1.0129992185539456e-05,
                4.006371118306061e-05,
                1.892515047863994e-05,
                NaN,
                2.2603253749309368e-06,
                1.6701427808495672e-05,
                3.1201922523121745e-05
            ],
            [
                4.222833946937338e-06,
                8.939698433584547e-06,
                7.338212428813419e-07,
                5.043472277838052e-07,
                7.338208054114941e-07,
                6.144173134343315e-06,
                1.994729245822257e-06,
                6.962257908044647e-06,
                6.9622570761976915e-06,
                5.422220260794484e-06
            ],
            [
                1.1478764018576587e-05,
                7.33820805514942e-07,
                8.31528325021115e-07,
                8.939695235487695e-06,
                1.5534979396984994e-06,
                6.144174601097106e-06,
                8.315282258680767e-07,
                4.222832437109582e-06,
                6.962254588977791e-06,
                9.422449308241022e-07
            ],
            [
                1.3007125354586914e-05,
                6.605214450431904e-05,
                6.962257909121104e-06,
                6.144173136019732e-06,
                1.6701419844465412e-05,
                0.00010889693419472267,
                2.1444950939693305e-05,
                4.222833946845163e-06,
                1.7603438426747447e-06,
                5.422220907426478e-06
            ],
            [
                NaN,
                NaN,
                0.9992903297612269,
                NaN,
                0.32082128783705344,
                0.999664650017289,
                0.998674977456313,
                NaN,
                0.9998204720573114,
                0.9992903296408574
            ],
            [
                1.4738987232298539e-05,
                0.9999339478239984,
                8.48110614123681e-05,
                0.9999646437450979,
                0.9999599363031271,
                4.006370171895837e-05,
                1.8925155000025902e-05,
                0.9999151889284886,
                1.3007123807302014e-05,
                0.9999986290424663
            ],
            [
                0.9999957771680659,
                0.9999810748495156,
                0.9999599362935699,
                0.9999687980849222,
                0.9999967112509347,
                0.9999485577680203,
                0.9999967112501507,
                0.9999810748585323,
                0.9999962733607162,
                0.9999599362935362
            ],
            [
                1.1478764019996392e-05,
                2.7535700947019215e-05,
                6.1441738684354385e-06,
                5.8291251569143705e-05,
                6.605214464752619e-05,
                4.5397868635383903e-05,
                6.605214455429738e-05,
                5.144222586301276e-05,
                9.610240292700156e-05,
                4.222832437186393e-06
            ],
            [
                2.9023109470871505e-06,
                1.5534971988904843e-06,
                1.0677024881382882e-06,
                4.785093923603471e-06,
                4.222832940577472e-06,
                1.3709573702566696e-06,
                3.288748280891699e-06,
                5.043472879337165e-07,
                2.561282821209454e-06,
                1.5534977544932838e-06
            ],
            [
                0.999986992869995,
                0.9998601778598297,
                0.9999810748472532,
                0.9999967112501508,
                0.999925153737615,
                0.9999957771645439,
                0.9999417087414969,
                0.9999852610145409,
                0.99996879809982,
                0.9999885212305424
            ],
            [
                1.0129989769188164e-05,
                1.1478772212492829e-05,
                0.9999724643155111,
                9.610237962786958e-05,
                NaN,
                3.1201915003305256e-05,
                NaN,
                NaN,
                NaN,
                0.9999724643187674
            ],
            [
                1.4738976694977387e-05,
                2.5612828204174347e-06,
                1.012999097799944e-05,
                1.9947306723419413e-06,
                NaN,
                4.222832437324657e-06,
                1.6701419846834993e-05,
                6.144173868178388e-06,
                2.1444948379722244e-05,
                1.9947301969217434e-06
            ],
            [
                3.9278610661366994e-07,
                4.222833947121688e-06,
                8.315277302444853e-07,
                1.9947297214544894e-06,
                5.043474081931949e-07,
                2.561281294616881e-06,
                1.2098662603499435e-06,
                1.2098659718990333e-06,
                NaN,
                4.785094493836935e-06
            ],
            [
                4.785093922889744e-06,
                3.535624646947797e-05,
                6.962259567749634e-06,
                3.1201918794144304e-05,
                1.473898547706978e-05,
                1.6701425817016872e-05,
                1.892515048889829e-05,
                5.422221554374162e-06,
                8.939695235487695e-06,
                7.889261642578988e-06
            ],
            [
                1.6701429789281226e-05,
                4.222834450328596e-06,
                4.785095635296322e-06,
                2.260324028045508e-06,
                1.9947290080125335e-06,
                8.939694171331106e-06,
                1.3709567164139816e-06,
                2.260325105594902e-06,
                1.670142383015595e-05,
                2.144494840531103e-05
            ],
            [
                0.9999724643089107,
                0.9999687980923714,
                0.9999810748495079,
                0.9999898700102287,
                0.9999832985781659,
                0.9999832985821476,
                0.9999485577925392,
                0.9999756997592822,
                0.9999646437577393,
                0.999978555051593
            ],
            [
                2.753569108693614e-05,
                2.2603253755949437e-06,
                3.2887498491620677e-06,
                4.7850933527085725e-06,
                6.144177531381426e-06,
                3.927862470816829e-07,
                4.785093353352668e-06,
                1.9947306726049992e-06,
                5.422218323019487e-06,
                3.726639727994339e-06
            ],
            [
                8.939696302831578e-06,
                4.0063701685728496e-05,
                2.2603251061232293e-06,
                2.4300246460212557e-05,
                2.4300232012472705e-05,
                3.2887486729337966e-06,
                2.902311984915459e-06,
                1.3007133113703658e-05,
                4.785094494463623e-06,
                7.889266347248781e-06
            ],
            [
                0.9988304896536226,
                0.995390428489383,
                0.8354835411997897,
                0.9998911030525907,
                0.3775406617944891,
                0.6224593312018545,
                0.996827317457211,
                0.9995694429694661,
                0.9999417087162993,
                0.9986749775567526
            ],
            [
                7.889264463446097e-06,
                1.3007123811229494e-05,
                4.5397884829235786e-05,
                1.8925145982866508e-05,
                1.3007128461838766e-05,
                1.0129992185981682e-05,
                2.1444945850567248e-05,
                1.7603440526133836e-06,
                2.7535694369155778e-05,
                6.144173868781898e-06
            ],
            [
                4.2228354571957855e-06,
                2.260324027765926e-06,
                2.260325105693578e-06,
                6.144173136556186e-06,
                4.222834451065997e-06,
                8.315280276263186e-07,
                1.5534973840786793e-06,
                2.5612834318257725e-06,
                2.5612815998141903e-06,
                6.475951069855719e-07
            ],
            [
                0.00010889689526073005,
                5.144222586301276e-05,
                5.829126539607611e-05,
                5.8291265048738174e-05,
                4.0063692112611227e-05,
                1.4738987232298539e-05,
                7.484624464611041e-05,
                3.535625066740153e-05,
                1.8925145981283003e-05,
                1.670142779591868e-05
            ],
            [
                4.7850950648799385e-06,
                1.553498495308628e-06,
                4.222834450950777e-06,
                8.315282258590015e-07,
                9.422448184912962e-07,
                1.370956879799656e-06,
                5.422219615395428e-06,
                6.1441753337365085e-06,
                5.422219614576807e-06,
                9.42244481511812e-07
            ],
            [
                0.060086656064939264,
                0.7057850402140659,
                0.22270014398423357,
                0.008577483687177147,
                0.9998766054313246,
                0.24508500761839527,
                0.012431653734540278,
                0.03732689015525376,
                0.1645164628965632,
                0.4378234991142019
            ],
            [
                NaN,
                0.2689414272294874,
                0.9993736657656694,
                0.24508502416032485,
                NaN,
                0.9999724643000366,
                NaN,
                0.9999599363029426,
                0.26894141551050293,
                0.02595735465470346
            ],
            [
                0.999373665975387,
                1.4738981970312625e-05,
                1.1478766753751021e-05,
                1.30071315640992e-05,
                2.144495096083526e-05,
                1.0129989762757436e-05,
                6.144172402765906e-06,
                6.9622595668378125e-06,
                2.2603251051796405e-06,
                3.7266388393349185e-06
            ],
            [
                0.9997965729566846,
                8.48110614210065e-05,
                0.9997965730371101,
                0.9997965730243126,
                0.8933094003735664,
                0.053403324903538434,
                0.9997040428320744,
                3.7266397271876744e-06,
                0.9999756997535008,
                0.00015843617016806318
            ],
            [
                NaN,
                7.484622694429252e-05,
                1.1478770849561016e-05,
                4.539786320396437e-05,
                5.144221973168594e-05,
                7.484624498426811e-05,
                3.5356238024242e-05,
                3.12019076269651e-05,
                1.3007126912542439e-05,
                1.3007128456065844e-05
            ],
            [
                5.422218968822766e-06,
                1.3709567162469001e-06,
                6.475949525834513e-07,
                1.0677024881499412e-06,
                9.422445938454347e-07,
                8.315281267037064e-07,
                7.338208930078229e-07,
                4.785096205077381e-06,
                1.067703251784089e-06,
                1.5534984951673385e-06
            ],
            [
                1.3007133112307748e-05,
                6.144177530001174e-06,
                7.889264465986113e-06,
                3.7266410608720178e-06,
                4.7850933529174686e-06,
                5.422220261652556e-06,
                8.939695236398313e-06,
                7.889263525534328e-06,
                4.222834954134701e-06,
                7.889263519736775e-06
            ],
            [
                1.1478765385098868e-05,
                2.7535704219423216e-05,
                5.043474081867732e-07,
                1.5534977543661227e-06,
                6.962256244287517e-06,
                8.3152822584917e-07,
                1.7603427933917854e-06,
                1.012999097799944e-05,
                3.7266383950934104e-06,
                1.553497939625029e-06
            ],
            [
                1.3007134654767206e-05,
                8.939699497335115e-06,
                5.422218969029887e-06,
                6.1441753308083655e-06,
                1.3007125358230479e-05,
                2.9023126766832993e-06,
                6.1441775264248145e-06,
                1.5534981248330927e-06,
                3.2887482794499933e-06,
                2.9023133686360798e-06
            ],
            [
                4.7850950646797465e-06,
                4.785095635296322e-06,
                1.4738987240475486e-05,
                2.7535697650273915e-05,
                1.3007133112662637e-05,
                8.939698433373153e-06,
                6.96225375833433e-06,
                4.785094493305991e-06,
                3.1201900191715896e-05,
                1.1478772227964558e-05
            ],
            [
                3.288747889178668e-06,
                1.670142980380249e-05,
                5.422220908402905e-06,
                8.3152792848466e-07,
                7.88925976397226e-06,
                2.4300243598740258e-05,
                5.422217676299034e-06,
                3.288747889178668e-06,
                8.939697368842181e-06,
                1.7603434231385591e-06
            ],
            [
                0.9999938558276544,
                0.4073334000459302,
                0.8519528057272543,
                0.9999038975510578,
                0.9999251537822377,
                0.8807970858005139,
                0.9999869928671691,
                0.9465966651155708,
                0.999954602126061,
                0.9999852610163279
            ],
            [
                6.144176066264237e-06,
                5.422221554038823e-06,
                2.4300243620398656e-05,
                1.473898899908247e-05,
                2.5612831263929686e-06,
                5.42221767672807e-06,
                1.4738985479697128e-05,
                2.4300237828059798e-05,
                NaN,
                3.288748672879957e-06
            ],
            [
                NaN,
                NaN,
                3.1201903900940664e-05,
                2.1444943242929886e-05,
                2.144495863614743e-05,
                1.4738988995838502e-05,
                NaN,
                NaN,
                NaN,
                3.120191507629113e-05
            ],
            [
                0.9999962733611603,
                0.999988521233243,
                0.9999910603004992,
                0.9999952149043646,
                0.9999885212291395,
                0.9999898700078131,
                0.9999898700066064,
                0.999997097689053,
                0.9999832985721862,
                0.9999967112509347
            ],
            [
                0.8807970873650401,
                NaN,
                NaN,
                0.9997040427681813,
                NaN,
                0.9995121428380489,
                0.9994472214932526,
                0.9997388096668374,
                NaN,
                0.9999546021206316
            ],
            [
                1.2098661161239298e-06,
                2.260324567177841e-06,
                5.422218322348809e-06,
                6.144173868312501e-06,
                4.785096204972935e-06,
                1.670142781025767e-05,
                4.785093923982095e-06,
                4.7850944942634305e-06,
                7.889266346129453e-06,
                3.7266388396975786e-06
            ],
            [
                0.9999785550465936,
                0.9999151889287737,
                0.9998766054258307,
                0.999954602142233,
                0.9993736659081287,
                0.9999151889595673,
                0.9999417087416249,
                0.8933094010836642,
                0.24508500761839527,
                0.999941708720878
            ],
            [
                0.9997965731019145,
                6.962258739068529e-06,
                0.7310585727705126,
                0.11920291263495983,
                0.46879062662624377,
                0.9998601779764698,
                0.22270013882530884,
                0.26894141551050293,
                0.9999151889227207,
                0.5621765008857982
            ],
            [
                0.9998911031039217,
                0.9999485577680282,
                0.9999599363126164,
                NaN,
                0.9984988180022184,
                0.9999832985702228,
                1.670142183934597e-05,
                0.9998415638218952,
                4.539785237613882e-05,
                4.0063677816192936e-05
            ],
            [
                0.9999756997651809,
                0.9999885212319432,
                0.999975699762511,
                NaN,
                NaN,
                0.999988521228141,
                0.9997040427581323,
                0.9999756997651039,
                0.9999546021370362,
                0.9999339478555221
            ],
            [
                NaN,
                1.1478768123551712e-05,
                1.012998977088337e-05,
                1.1478765385098868e-05,
                4.5397884797196873e-05,
                6.144176066521288e-06,
                5.42221961567159e-06,
                1.4738985483504099e-05,
                6.962257908753841e-06,
                1.4738988995409548e-05
            ],
            [
                1.1478773590625104e-05,
                0.0003799845252760368,
                0.0006263342221979056,
                2.144495093719684e-05,
                1.4738981960339432e-05,
                7.484623577341946e-05,
                6.605216018886624e-05,
                0.00010889694747905738,
                1.670142581883963e-05,
                1.0129993384861544e-05
            ],
            [
                1.4738983724146862e-05,
                5.829125152122041e-05,
                NaN,
                1.4738978449883382e-05,
                2.1444958627955892e-05,
                1.670142183825232e-05,
                6.9622562481627565e-06,
                4.006370650070828e-05,
                6.144172385364693e-06,
                4.539787938262061e-05
            ],
            [
                0.9999785550464864,
                0.9999785550567211,
                0.9999930377420909,
                0.9999687980774978,
                0.9999974387168798,
                NaN,
                0.9999852610145252,
                0.9999869928746866,
                0.9875683489295692,
                0.9999980052695655
            ],
            [
                7.889264465397747e-06,
                6.144173865775523e-06,
                3.535626333461766e-05,
                0.00013982210686715055,
                2.7535687811228037e-05,
                5.144223199471459e-05,
                4.539789019426799e-05,
                NaN,
                6.144172404028807e-06,
                2.430024071781994e-05
            ],
            [
                3.726637951079042e-06,
                4.785093924047376e-06,
                1.3007126907881513e-05,
                1.9947294829825283e-06,
                1.3709567163940317e-06,
                8.93969736929749e-06,
                1.1478773598099973e-05,
                2.753568121974442e-05,
                1.0129990977004428e-05,
                2.2603242976404388e-06
            ],
            [
                1.8925145981283003e-05,
                2.430023492663099e-05,
                4.006371122561817e-05,
                3.5356250689524286e-05,
                5.42221767672807e-06,
                3.120190388198478e-05,
                1.892515048820981e-05,
                2.753569108693614e-05,
                1.3007131562514014e-05,
                4.222833443645997e-06
            ],
            [
                0.8933094025038599,
                0.9999852610162737,
                0.9999852610127649,
                0.9999339478449074,
                0.9999038975453917,
                NaN,
                4.222834450666572e-06,
                0.9999546021478227,
                0.9999756997651039,
                0.999959936315093
            ],
            [
                NaN,
                0.95791227058248,
                0.9998204720928608,
                0.9999810748518563,
                0.9999785550616043,
                0.9995694428885141,
                NaN,
                0.9999756997477486,
                NaN,
                0.9998766054001744
            ],
            [
                4.785092782188013e-06,
                2.561281905058126e-06,
                8.315283250150648e-07,
                2.561282515853595e-06,
                5.422218968822766e-06,
                4.7850956351657615e-06,
                2.2603248365343694e-06,
                8.939693105467234e-06,
                1.7603427931932593e-06,
                7.338212428913528e-07
            ],
            [
                4.222833945815874e-06,
                4.785096205077381e-06,
                2.5612815998491325e-06,
                2.2603234893861252e-06,
                5.422220257026851e-06,
                2.2603253750378357e-06,
                3.2887498489407274e-06,
                1.4738978452886064e-05,
                5.422218967797024e-06,
                6.962253755548213e-06
            ],
            [
                0.9999646437366552,
                0.9998766054106738,
                0.9999251537460537,
                0.9999546021422393,
                0.9998204720356317,
                0.9999417087206256,
                0.9999977396762411,
                0.9998766053662896,
                0.9998415638026884,
                0.9998415637649272
            ],
            [
                0.9999977396751636,
                0.9999898700066072,
                0.0017007220619840759,
                0.9999785550567073,
                NaN,
                0.999992110733654,
                0.0002305067088606732,
                0.9999938558232018,
                5.829127932267533e-05,
                7.484620028266614e-05
            ],
            [
                3.2887482811220126e-06,
                7.88926258532661e-06,
                2.1444958633416914e-05,
                1.300713466316634e-05,
                4.5397852378781204e-05,
                1.4738976699106073e-05,
                5.8291272364888606e-05,
                2.7535687799708318e-05,
                2.4300232034838305e-05,
                2.7535694358938284e-05
            ],
            [
                1.3007134663521234e-05,
                9.610241466746177e-05,
                1.1478766752748805e-05,
                4.785095634756674e-06,
                1.6701415868649062e-05,
                7.889261644358435e-06,
                2.1444958618516124e-05,
                8.939693100686484e-06,
                1.300713001414004e-05,
                2.561282820785491e-06
            ],
            [
                4.7850950646797465e-06,
                1.892514823013346e-05,
                7.889259763010786e-06,
                6.144173867608406e-06,
                5.422217028582506e-06,
                5.8291251560237615e-05,
                3.7266410609940346e-06,
                7.88926352599354e-06,
                3.2887478889962107e-06,
                1.3007126913346863e-05
            ],
            [
                NaN,
                7.4846218765344e-05,
                4.222833945815874e-06,
                1.1478764017428212e-05,
                NaN,
                4.22283293977094e-06,
                4.222835457449267e-06,
                4.222834450820197e-06,
                3.2887502408573863e-06,
                1.1478772210530154e-05
            ],
            [
                6.9622545752751505e-06,
                2.430023493228869e-05,
                9.422448185015797e-07,
                3.1201907620154606e-05,
                1.0129993389984017e-05,
                NaN,
                6.962253759157502e-06,
                1.0129990979381404e-05,
                6.144174601208867e-06,
                6.962257077223492e-06
            ],
            [
                7.889264463675704e-06,
                7.338212429087055e-07,
                6.144175327053188e-06,
                0.0006263342494874331,
                NaN,
                1.8925152736303473e-05,
                4.539785764835348e-05,
                NaN,
                3.2887506317631033e-06,
                1.7603432131855856e-06
            ],
            [
                1.2098661161602417e-06,
                4.785096776068365e-06,
                6.475951069219618e-07,
                7.338213304143191e-07,
                4.222832940500659e-06,
                1.2098658276862581e-06,
                2.2603242976733308e-06,
                2.5612819051373276e-06,
                2.2603234894560207e-06,
                3.726639283440905e-06
            ],
            [
                8.939699498099386e-06,
                1.0677028699858827e-06,
                6.144173868558375e-06,
                1.6701415862117537e-05,
                8.939698432446272e-06,
                1.6701423827421826e-05,
                6.9622554187981796e-06,
                3.7266383950256237e-06,
                6.962253756460032e-06,
                1.0129992183070348e-05
            ],
            [
                0.9999974387177893,
                0.9999977396759716,
                0.9999970976869769,
                0.9999930377445811,
                0.9999970976866309,
                0.9999974387184001,
                0.9999921107392955,
                0.9999869928746395,
                0.9999967112501509,
                0.9999832985701956
            ],
            [
                8.315283249636384e-07,
                6.9622537584863015e-06,
                1.1478768116974664e-05,
                5.422220261652556e-06,
                6.47594875389178e-07,
                3.2887502412970765e-06,
                2.144495863411905e-05,
                3.726638839656906e-06,
                1.553498111662075e-06,
                1.1478769491598686e-05
            ],
            [
                0.9991959139061602,
                0.7057850154599563,
                NaN,
                0.9997965729807702,
                0.0007096704317935083,
                0.02931222751848539,
                NaN,
                0.004609571709321161,
                0.9999646437577411,
                0.9996646497415743
            ],
            [
                1.209866116137134e-06,
                1.0677031245312763e-06,
                8.939694171331106e-06,
                1.0677029972920738e-06,
                1.7603432133136672e-06,
                3.28875024040274e-06,
                1.3007131557498195e-05,
                4.785093923916815e-06,
                4.222834450820197e-06,
                9.422444815323792e-07
            ],
            [
                0.999841563802746,
                0.9993736659093311,
                0.9995694428627994,
                0.9924227593099183,
                0.9998601778929741,
                0.9940889317019584,
                0.999915188990141,
                0.9988304897504473,
                0.9997965731008668,
                0.999988521231883
            ],
            [
                0.999968798084945,
                NaN,
                NaN,
                0.9999687980774995,
                NaN,
                0.9999810748495223,
                0.9999952149066464,
                0.9999957771675633,
                NaN,
                0.9999938558253993
            ],
            [
                2.260324567227179e-06,
                1.3709572068079696e-06,
                1.0677029972920738e-06,
                7.88926164064169e-06,
                2.5612819052374947e-06,
                3.726638838968869e-06,
                7.88926446470893e-06,
                1.5534977544565482e-06,
                1.3007126896099073e-05,
                5.144220704199006e-05
            ],
            [
                1.0129992186774007e-05,
                5.422219615286937e-06,
                1.4738987241172537e-05,
                1.012998977088337e-05,
                1.8925152746768368e-05,
                2.4300237830711845e-05,
                2.4300234931404677e-05,
                3.5356254910985954e-05,
                2.4300232018837615e-05,
                2.144495096457996e-05
            ],
            [
                2.2603240282243575e-06,
                2.2603251060142746e-06,
                4.785094493532295e-06,
                1.0677033791000363e-06,
                1.0129993394664264e-05,
                1.3709575334373105e-06,
                1.760344052491706e-06,
                4.785096204972935e-06,
                3.2887502411564953e-06,
                1.3007133104263505e-05
            ],
            [
                1.3007130004439633e-05,
                6.962259567407701e-06,
                NaN,
                5.422217029736466e-06,
                2.260324566540559e-06,
                6.962253759043525e-06,
                5.422220261544064e-06,
                3.7266397252896404e-06,
                7.889262578323629e-06,
                6.144173868670137e-06
            ],
            [
                5.144220121644571e-05,
                1.670141587031992e-05,
                4.006367781094611e-05,
                4.5397890187331725e-05,
                6.962254588116627e-06,
                2.4300252310279753e-05,
                5.144223816384438e-05,
                2.7535697653779924e-05,
                6.96225375833433e-06,
                4.006368739659403e-05
            ],
            [
                6.96225873895455e-06,
                1.012998855982425e-05,
                3.726638395415398e-06,
                1.2098652507715085e-06,
                0.9994472213879668,
                1.7603438427467903e-06,
                3.53562506982705e-05,
                1.994729721004569e-06,
                4.7850967763512445e-06,
                0.9988304896167695
            ],
            [
                4.450849458179853e-07,
                8.315283249742262e-07,
                7.338209805133949e-07,
                6.475951069808602e-07,
                1.2098662603752517e-06,
                2.5612812945260317e-06,
                3.2887482807182155e-06,
                1.067702742656401e-06,
                1.0677027427166074e-06,
                1.209865971934245e-06
            ],
            [
                4.222832436687113e-06,
                3.288748280293481e-06,
                4.222832940715735e-06,
                1.1478772229551402e-05,
                4.222833947728508e-06,
                5.422219613176275e-06,
                1.3007128455545335e-05,
                2.144494073569759e-05,
                1.8925141461620395e-05,
                2.902311637804172e-06
            ],
            [
                3.535625482571039e-05,
                NaN,
                7.889263524960312e-06,
                1.892514597632595e-05,
                1.1478769489009626e-05,
                6.1441738671166565e-06,
                1.8925143723620274e-05,
                2.2603234894745224e-06,
                2.5612815998491325e-06,
                1.9947299592407137e-06
            ],
            [
                2.9023123309287002e-06,
                2.260323489435463e-06,
                1.760343842700361e-06,
                4.7850950648799385e-06,
                3.7266401721817755e-06,
                3.7266388395620047e-06,
                1.7603434230088762e-06,
                4.450851049959619e-07,
                5.422217676925328e-06,
                4.222834450820197e-06
            ],
            [
                6.605217607477225e-05,
                7.889266343316778e-06,
                3.535623776597164e-05,
                2.144494838221871e-05,
                1.0129990974240505e-05,
                3.120191878949046e-05,
                NaN,
                1.6701415867221242e-05,
                0.00010889694758046453,
                2.561283126048207e-06
            ],
            [
                2.4300237808257835e-05,
                4.785093352813021e-06,
                7.889259758016858e-06,
                5.715004470129334e-07,
                5.42222090821551e-06,
                1.8925152747388e-05,
                6.96225707894582e-06,
                7.88925976359915e-06,
                4.785093351846877e-06,
                1.1478764015361142e-05
            ],
            [
                4.0063677765182186e-05,
                0.9999885212321165,
                0.9997694931702106,
                0.9933071501901825,
                NaN,
                0.5621765008857981,
                0.9997694932987049,
                0.9999832985823228,
                0.9465966653038895,
                4.785092782779884e-06
            ],
            [
                0.348645142101806,
                0.9324533140223229,
                0.6513548511303338,
                0.9999599362888202,
                0.9999885212278635,
                0.9740426406358641,
                0.9999832985742624,
                0.6513548646660542,
                0.014063629445169909,
                0.9999756997477003
            ],
            [
                3.2887502412970765e-06,
                8.31528027618756e-07,
                5.043474081831035e-07,
                3.2887502412970765e-06,
                1.370956716450141e-06,
                1.760344052650207e-06,
                1.0129987356541108e-05,
                5.043475284182996e-07,
                2.1444958631232504e-05,
                7.338207180534397e-07
            ],
            [
                1.0677026154055912e-06,
                4.006368729632147e-05,
                2.2603248359834287e-06,
                NaN,
                1.1478765381257036e-05,
                1.6701427809710842e-05,
                NaN,
                1.3709568798956654e-06,
                NaN,
                NaN
            ],
            [
                5.422217029272909e-06,
                4.222834953712232e-06,
                2.260323489435463e-06,
                1.6701427813417103e-05,
                4.785096775920397e-06,
                3.7266388390502134e-06,
                6.144173868983067e-06,
                1.670141784666869e-05,
                4.222831933726245e-06,
                1.892514597832254e-05
            ],
            [
                0.999964643736669,
                0.9999921107355368,
                0.9999810748540237,
                0.9999724643188183,
                0.9999938558224708,
                0.9999930377445808,
                0.9999885212359809,
                0.9999945777810313,
                0.9999885212346129,
                0.999975699767969
            ],
            [
                0.9999967112493666,
                0.9999962733593835,
                0.9999810748472499,
                0.9999984465018751,
                0.9999599363078364,
                0.999996273361161,
                0.9999599362887481,
                0.9999910603068946,
                0.9999832985821424,
                0.999998239656577
            ],
            [
                1.99472972129484e-06,
                1.1478769490700865e-05,
                4.7850933521167006e-06,
                2.9023116385379885e-06,
                5.422217676299034e-06,
                1.3007125357378736e-05,
                0.9993736658244748,
                9.422442561564636e-07,
                2.2603251059484907e-06,
                3.288750633025344e-06
            ],
            [
                5.829125112977616e-05,
                2.902313022802209e-06,
                4.7850956352353935e-06,
                4.2228324372555256e-06,
                6.144173134522134e-06,
                1.4738985477605971e-05,
                1.6701429804744246e-05,
                4.006368254998988e-05,
                3.7266388393349185e-06,
                5.422220908402905e-06
            ],
            [
                3.535623802218407e-05,
                NaN,
                NaN,
                0.00023050680799136336,
                6.605212083958431e-05,
                1.30071253611406e-05,
                9.610246066446198e-05,
                5.422217674780147e-06,
                5.14422258772351e-05,
                2.430023477228181e-05
            ],
            [
                0.999941708727552,
                0.99998526101803,
                0.9999810748449987,
                0.9999810748517645,
                0.9999546021313874,
                0.999983298580164,
                0.9999646437577528,
                0.9999938558268632,
                0.9999952149066462,
                0.9999910603015656
            ],
            [
                1.9947299589504427e-06,
                1.1478766748656418e-05,
                3.288748278098022e-06,
                3.726640172337686e-06,
                6.962256247656188e-06,
                2.2603240279591663e-06,
                7.889261643382609e-06,
                9.42244593835151e-07,
                1.5534977545102382e-06,
                5.422220908634683e-06
            ],
            [
                NaN,
                7.484624465591207e-05,
                1.8925148232956223e-05,
                8.481101091470089e-05,
                4.539789019426799e-05,
                2.4300246515109972e-05,
                5.144220135754627e-05,
                3.120191136774608e-05,
                4.5397890240179425e-05,
                1.4738988994015443e-05
            ],
            [
                NaN,
                1.012999460108057e-05,
                1.7603430031093589e-06,
                4.222832940646604e-06,
                NaN,
                3.726639728184142e-06,
                6.962254589528684e-06,
                1.2098655392354511e-06,
                1.4738988991495334e-05,
                1.9947299591354906e-06
            ],
            [
                0.999995777164542,
                0.9999930377454106,
                0.9999646437619778,
                0.9999977396765105,
                0.9999974387184005,
                0.9999984465022455,
                0.9999984465015047,
                0.9999945777803841,
                0.9999984465022455,
                0.9999957771660523
            ],
            [
                0.0021827159453505426,
                0.1066906045971184,
                0.00017952792228103338,
                0.22270013882530884,
                0.9997694933700213,
                0.7310585786300048,
                0.003593603383433838,
                0.07585818211049714,
                0.5312093733737563,
                0.9999687980821278
            ],
            [
                0.9999982396572065,
                2.144494329769612e-05,
                0.9999980052705163,
                0.999998005269803,
                0.9999967112497586,
                3.535626754900668e-05,
                6.605216816665945e-05,
                0.9999945777829699,
                7.889265405677441e-06,
                0.9999994284994167
            ],
            [
                4.7850933535006355e-06,
                5.8291265401165313e-05,
                1.4738981962698681e-05,
                6.144177528838857e-06,
                4.785092782396909e-06,
                2.2603240281606297e-06,
                1.3007131563815288e-05,
                6.962258738701267e-06,
                1.892514597343433e-05,
                1.7603427932989266e-06
            ],
            [
                6.1441760654483806e-06,
                6.1441738691562974e-06,
                3.7266410608245674e-06,
                4.7850967757637256e-06,
                8.939697368110433e-06,
                6.962258739454786e-06,
                4.785092783319532e-06,
                NaN,
                NaN,
                1.9947292458004866e-06
            ],
            [
                0.9999970976866311,
                0.9999967112521109,
                0.9999980052698029,
                0.9999910603004993,
                0.9999987901338838,
                0.9999938558246659,
                0.9999967112497586,
                0.9999646437408763,
                0.9999945777790913,
                0.9999785550541487
            ],
            [
                0.9999970976890531,
                0.9999038976196939,
                0.9999852610215443,
                0.939913352771458,
                0.9999957771671855,
                0.9999898700090285,
                0.9999980052700413,
                0.999981074856281,
                0.9999984465020604,
                0.9999962733589393
            ],
            [
                1.670141785237998e-05,
                0.9999251537728232,
                8.939696299530582e-06,
                8.939696301839653e-06,
                2.4300234900640922e-05,
                1.89251482286188e-05,
                1.3007133110320344e-05,
                0.9998911030778569,
                5.144219515810486e-05,
                5.422217676486429e-06
            ],
            [
                2.7535694357535878e-05,
                4.0063682618927264e-05,
                4.785094493184135e-06,
                3.2887494563241995e-06,
                1.4738978448274803e-05,
                4.006369216362198e-05,
                3.726638839395927e-06,
                3.535626325448691e-05,
                1.4738985484227961e-05,
                1.6701423833831836e-05
            ]
        ]
    },
    {
        "q_id": "8893_mmlu_math",
        "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": [
            [
                0.9999997300421903,
                0.9999997617631752,
                0.9999997617629763,
                0.999999814460876,
                0.9999996533674615,
                0.9999996533674202,
                0.9999997617630332,
                0.9999997300422869,
                0.9999996533675028,
                0.9999998555020135
            ],
            [
                0.9999998555020134,
                0.9999995549148419,
                0.9999994284992805,
                0.9999997897565587,
                0.9999998144608097,
                0.9999998555019963,
                0.9999997897566338,
                0.999999653367503,
                0.9999997617631469,
                0.9999992661790195
            ],
            [
                0.9999996940976271,
                0.9999996940977002,
                0.9999998362623723,
                0.9999996940978095,
                0.9999998555019618,
                0.9999996533672962,
                0.9999998144608981,
                0.9999999006880785,
                0.9999996072136593,
                0.9999998144609645
            ],
            [
                0.999999789756684,
                0.9999996940976636,
                0.999999789756634,
                0.9999997897567091,
                0.9999999006880549,
                0.9999997617631752,
                0.9999997617631184,
                0.9999997300422547,
                0.9999996940976271,
                0.9999998724809419
            ],
            [
                0.9999996940978095,
                0.9999998555019618,
                0.999999694097846,
                0.9999996533672135,
                0.9999997300422225,
                0.9999995549149481,
                0.9999994956524114,
                0.9999997300422547,
                0.9999993524052018,
                0.9999996072137061
            ],
            [
                0.9999999006880194,
                0.99999976176309,
                0.9999997617631752,
                0.9999996533674201,
                0.9999998874647306,
                0.999999900688043,
                0.9999998874647976,
                0.9999998144608981,
                0.9999998724809115,
                0.9999997897565838
            ],
            [
                0.999999855502048,
                0.9999994956527121,
                0.9999998555020135,
                0.9999999006880075,
                0.9999994956527121,
                0.9999996072136125,
                0.9999998724810027,
                0.9999996072138934,
                0.9999994284996211,
                0.999999855502048
            ],
            [
                0.9999998555019962,
                0.999999730042126,
                0.999999694097846,
                0.9999997897566589,
                0.9999996940977001,
                0.9999997300421581,
                0.9999996533672962,
                0.9999998555020307,
                0.9999999226558238,
                0.9999998724809875
            ],
            [
                0.9999996533674615,
                0.9999996533675028,
                0.9999996940976272,
                0.9999996533674201,
                0.9999998362623723,
                0.9999997897566338,
                0.999999352404893,
                0.9999997300422225,
                0.9999998144609423,
                0.9999997300421903
            ],
            [
                0.9999997897567091,
                0.9999999006880312,
                0.9999998144608317,
                0.9999998362622552,
                0.9999998362623332,
                0.9999997897565587,
                0.9999998555019618,
                0.9999997617629764,
                0.9999998362622552,
                0.9999996940977366
            ],
            [
                0.9999998144609645,
                0.9999998724809723,
                0.9999998724809571,
                0.9999998724809267,
                0.9999998874647976,
                0.9999998724809267,
                0.99999976176309,
                0.9999996533672549,
                0.9999996940977366,
                0.9999998555020306
            ],
            [
                0.9999998144609202,
                0.9999997897567091,
                0.9999997897567341,
                0.9999998362623332,
                0.9999997897565587,
                0.999999814460854,
                0.9999999006879957,
                0.9999998555019274,
                0.9999997897566338,
                0.9999998724810027
            ],
            [
                0.9999998144609202,
                0.9999996533672962,
                0.999999428499553,
                0.9999997617630899,
                0.9999998144609202,
                0.9999998724810027,
                0.9999997617630049,
                0.999999495652652,
                0.99999976176309,
                0.9999998555020306
            ],
            [
                0.9999995549151072,
                0.9999997617629763,
                0.9999992661791944,
                0.9999997300423191,
                0.999999495652652,
                0.9999998144609202,
                0.9999998144609202,
                0.9999989322968755,
                0.9999998874648647,
                0.9999997897566589
            ],
            [
                0.9999998555019274,
                0.9999998724809115,
                0.9999997897566338,
                0.9999998874649318,
                0.9999998144609645,
                0.9999997617631468,
                0.9999997617631752,
                0.9999997300422225,
                0.9999998144608538,
                0.9999999006880312
            ],
            [
                0.9999998362622942,
                0.9999997300422869,
                0.9999997897565587,
                0.9999997897566089,
                0.9999998874647842,
                0.9999998362622747,
                0.9999998144608097,
                0.9999999006879838,
                0.9999995549147359,
                0.9999999006880904
            ],
            [
                0.9999997617630048,
                0.9999998555019963,
                0.9999997897566589,
                0.9999997300422869,
                0.9999998555019274,
                0.9999998724809419,
                0.999999789756684,
                0.9999995549149481,
                0.9999998362623137,
                0.999999887464744
            ],
            [
                0.999999428499553,
                0.9999998144609423,
                0.9999996533673375,
                0.9999996072138934,
                0.9999996533672962,
                0.9999991684718733,
                0.9999996533672136,
                0.9999998144609645,
                0.9999996072138934,
                0.9999996533674201
            ],
            [
                0.9999998362622357,
                0.9999998362622942,
                0.9999998724809571,
                0.9999998144609423,
                0.999999694097773,
                0.9999998144608097,
                0.9999998362622746,
                0.9999996072136592,
                0.9999998874647976,
                0.9999997300422547
            ],
            [
                0.9999998362622357,
                0.9999997617631184,
                0.9999998362623722,
                0.9999998724809419,
                0.9999998144609644,
                0.9999996072137998,
                0.9999998144609423,
                0.9999996940976636,
                0.9999998724809267,
                0.9999997897565838
            ],
            [
                0.9999998144609202,
                0.9999997897565838,
                0.9999996940977001,
                0.99999976176309,
                0.999999855501979,
                0.9999997300421581,
                0.9999997617631752,
                0.9999998555019446,
                0.9999996940978825,
                0.9999998144609424
            ],
            [
                0.9999998555019962,
                0.9999997617631183,
                0.9999998874647976,
                0.9999997617631468,
                0.9999991684719723,
                0.9999999317439627,
                0.9999996533672549,
                0.9999997617631183,
                0.9999996940977731,
                0.9999996072136592
            ],
            [
                0.9999998144608538,
                0.9999997897565587,
                0.9999998144609645,
                0.9999997897566089,
                0.999999814460854,
                0.9999997897567341,
                0.9999998555020135,
                0.9999998362623528,
                0.9999997897566089,
                0.9999996940978825
            ],
            [
                0.9999998362623137,
                0.9999998874647976,
                0.9999998724809267,
                0.999999730042319,
                0.9999996533674615,
                0.9999997300421581,
                0.9999996533672549,
                0.999999730042319,
                0.9999998555019618,
                0.9999998724809571
            ],
            [
                0.9999997897565838,
                0.9999997897565838,
                0.9999998555019618,
                0.9999998555020307,
                0.9999999006880312,
                0.9999998144609645,
                0.9999996533674615,
                0.999999789756684,
                0.999999653367379,
                0.9999996940976636
            ],
            [
                0.999999554914842,
                0.9999996533672136,
                0.9999994956523514,
                0.9999998144608319,
                0.9999995549150011,
                0.9999996940978095,
                0.9999996533674615,
                0.9999996940978095,
                0.9999997897567091,
                0.9999994956524114
            ],
            [
                0.9999996072139402,
                0.9999997617629764,
                0.9999995549147359,
                0.9999999006881377,
                0.9999998362623528,
                0.999999789756684,
                0.999999694097846,
                0.9999998362622942,
                0.9999996940977001,
                0.9999996072138934
            ],
            [
                0.9999994956527121,
                0.9999997617630048,
                0.9999997897567341,
                0.9999997300421581,
                0.9999997300422547,
                0.9999998144609202,
                0.9999996940977731,
                0.9999997300421581,
                0.9999993524052019,
                0.9999998724809419
            ],
            [
                0.9999998724809419,
                0.9999998724809723,
                0.9999999226558053,
                0.9999996940977731,
                0.999999814460854,
                0.9999996072136592,
                0.9999998144609645,
                0.99999976176309,
                0.9999998555019962,
                0.9999995549149481
            ],
            [
                0.9999998874648379,
                0.9999993524054335,
                0.999999855502048,
                0.999999554914842,
                0.9999997300422547,
                0.9999995549151073,
                0.9999998144609202,
                0.99999976176309,
                0.9999995549148419,
                0.9999999006880075
            ],
            [
                0.999999814460876,
                0.9999998362623723,
                0.9999996072136593,
                0.9999999123574523,
                0.9999996072136593,
                0.999999730042319,
                0.9999998874648245,
                0.999999855501979,
                0.999999887464811,
                0.999999694097773
            ],
            [
                0.9999997617630332,
                0.9999998724808963,
                0.9999997300422225,
                0.9999996940977366,
                0.9999997300422547,
                0.9999998555020307,
                0.9999998362623137,
                0.9999997300422869,
                0.9999998362622552,
                0.9999998144609645
            ],
            [
                0.999998629042303,
                0.9999993524051246,
                0.9999977396751633,
                0.9999980052695652,
                0.9999995549151072,
                0.9999974387187053,
                0.9999994284993486,
                0.9999992661792819,
                0.9999993524052018,
                0.9999987901343165
            ],
            [
                0.9999996533672549,
                0.9999997617630332,
                0.9999996533673375,
                0.9999997897567091,
                0.9999998144608319,
                0.9999998724809267,
                0.9999996940978825,
                0.9999995549148419,
                0.9999997300420937,
                0.9999996533675028
            ],
            [
                0.9999997300422869,
                0.9999993524049703,
                0.9999996072137061,
                0.9999998555020306,
                0.9999997300423191,
                0.9999996072136125,
                0.99999976176309,
                0.9999997300421903,
                0.9999996940976272,
                0.9999997617630332
            ],
            [
                0.9999998362623528,
                0.9999998555019963,
                0.9999998724809267,
                0.999999855502048,
                0.9999998144608981,
                0.9999998555019446,
                0.9999998724808963,
                0.9999996533675028,
                0.9999998555020135,
                0.999999855501979
            ],
            [
                0.9999998874647709,
                0.9999998724809875,
                0.9999997300422869,
                0.99999976176309,
                0.9999997617630616,
                0.9999996072138465,
                0.9999996940978825,
                0.9999996533674615,
                0.9999996533673375,
                0.9999998724809419
            ],
            [
                0.9999998362623528,
                0.9999998362623137,
                0.9999997617630332,
                0.9999997617631469,
                0.9999999006881259,
                0.9999997897565587,
                0.9999996940976271,
                0.9999998555019274,
                0.9999998144609644,
                0.9999997300422547
            ],
            [
                0.9999957771645421,
                0.999986992865341,
                0.9999967112501509,
                0.9999832985841355,
                0.9999957771680661,
                0.9999599362983018,
                0.9999977396759717,
                0.9999832985761725,
                0.9999962733611605,
                0.9999930377445823
            ],
            [
                0.9999998555019618,
                0.9999999123574836,
                0.9999996940978825,
                0.9999997897567342,
                0.9999998362622552,
                0.9999998362622747,
                0.9999997300422869,
                0.9999997617631469,
                0.9999998362622746,
                0.9999997300421903
            ],
            [
                0.9999997300421903,
                0.9999997300420937,
                0.9999997300421903,
                0.9999996940978095,
                0.9999998724809875,
                0.999999855501979,
                0.9999997897567091,
                0.9999998362623137,
                0.9999998555019618,
                0.9999998724810027
            ],
            [
                0.9999999317439627,
                0.9999996940976636,
                0.9999997300422869,
                0.9999997300422869,
                0.9999997300420937,
                0.9999996940978461,
                0.9999998144608319,
                0.9999997617630048,
                0.9999996940976271,
                0.9999993524050474
            ],
            [
                0.9999998724809267,
                0.9999996533672136,
                0.9999990577557432,
                0.999999730042126,
                0.9999995549147359,
                0.999999495652652,
                0.9999997617629764,
                0.999999814460876,
                0.9999998362622747,
                0.9999997617631752
            ],
            [
                0.9999997300422225,
                0.9999998362623138,
                0.9999990577551815,
                0.9999997617631184,
                0.9999996940977731,
                0.9999994284997574,
                0.9999998724809723,
                0.9999997617630616,
                0.9999996940978095,
                0.9999994956527121
            ],
            [
                0.9999995549147889,
                0.9999998362622357,
                0.9999998362623332,
                0.9999993524053562,
                0.9999997300422547,
                0.9999998724808963,
                0.999999855501979,
                0.9999996533673375,
                0.9999997897567342,
                0.9999998724810026
            ],
            [
                0.9999996533673788,
                0.999999653367379,
                0.999999730042126,
                0.9999996533675028,
                0.9999996072138934,
                0.9999996533672136,
                0.99999976176309,
                0.9999997617631468,
                0.9999998362622357,
                0.999999554914842
            ],
            [
                0.9999998555020307,
                0.999999887464811,
                0.9999998362622552,
                0.9999998362622552,
                0.9999997897566338,
                0.9999999123575359,
                0.999999814460854,
                0.9999998555019446,
                0.9999998144608317,
                0.999999814460854
            ],
            [
                0.9999997897566089,
                0.9999996940978461,
                0.9999998144609645,
                0.9999997617631752,
                0.9999998555020306,
                0.9999998724809267,
                0.9999998144609645,
                0.9999997617631752,
                0.9999995549149481,
                0.9999997617631468
            ],
            [
                0.999999730042126,
                0.9999996533675028,
                0.9999999123574523,
                0.9999998555020135,
                0.9999998555019446,
                0.9999996072139402,
                0.9999997897565587,
                0.9999997897567091,
                0.9999998144609645,
                0.9999997617630048
            ],
            [
                0.9999995549150011,
                0.9999998144608098,
                0.9999997617630616,
                0.999999730042319,
                0.9999998362623528,
                0.9999997897566589,
                0.9999994956524716,
                0.9999996533672549,
                0.9999994284994849,
                0.9999998144609423
            ],
            [
                0.9999998362622747,
                0.999999887464811,
                0.9999998362622357,
                0.9999997300420939,
                0.9999998555019963,
                0.9999997617631184,
                0.9999998362622746,
                0.9999998362623528,
                0.9999997300422869,
                0.999999814460876
            ],
            [
                0.9999998144608319,
                0.999999814460854,
                0.9999997897565838,
                0.999999814460876,
                0.9999998724809115,
                0.9999998144608317,
                0.9999998362622747,
                0.9999997617630048,
                0.9999998555020135,
                0.9999997300421903
            ],
            [
                0.9999998144608317,
                0.999999855502048,
                0.9999997617630332,
                0.9999998555019962,
                0.999999887464811,
                0.9999998144608097,
                0.9999998362623722,
                0.9999998724810027,
                0.9999996940977731,
                0.9999997617630616
            ],
            [
                0.0013250224273803634,
                5.144222585927004e-05,
                1.6701427811412077e-05,
                4.006369694347607e-05,
                5.422217676486429e-06,
                1.760342583722268e-06,
                3.1201918798457626e-05,
                1.0129995807939249e-05,
                1.7603434231385591e-06,
                5.715006514105942e-07
            ],
            [
                0.9999996072137998,
                0.9999996072136125,
                0.9999997897565587,
                0.9999996940977366,
                0.9999997617630049,
                0.9999993524050474,
                0.9999997897565587,
                0.9999995549151073,
                0.999999266179107,
                0.9999997897566589
            ],
            [
                0.9999997617630899,
                0.9999995549150011,
                0.9999997300421903,
                0.9999998724809115,
                0.9999998362623722,
                0.9999995549149481,
                0.9999996940977366,
                0.9999997617631184,
                0.9999997617630332,
                0.9999998724809419
            ],
            [
                0.9999996940977002,
                0.9999997617631184,
                0.9999997897566589,
                0.9999998144608981,
                0.9999998362622747,
                0.9999996940978825,
                0.9999997300420937,
                0.999999789756684,
                0.9999997300421903,
                0.9999997617629764
            ],
            [
                0.9999998555019618,
                0.9999997300422547,
                0.9999996940976271,
                0.9999998144609202,
                0.9999995549148419,
                0.9999997897565838,
                0.9999998362622357,
                0.999999730042126,
                0.9999997617631752,
                0.9999998144608098
            ],
            [
                0.9999998724809723,
                0.9999998144608317,
                0.9999998362623723,
                0.9999996940977002,
                0.9999998362622943,
                0.9999998555019963,
                0.9999995549147889,
                0.9999998144609644,
                0.9999997617629764,
                0.9999996940977731
            ],
            [
                0.9999996533673375,
                0.9999998555020135,
                0.9999998724810027,
                0.9999997617630332,
                0.9999998362623722,
                0.999999789756634,
                0.999999814460876,
                0.9999998724810027,
                0.9999997617630048,
                0.9999998555019274
            ],
            [
                0.9999997300422547,
                0.9999996940978095,
                0.9999994956524114,
                0.9999998362623722,
                0.9999996940978095,
                0.999999789756634,
                0.9999996940978825,
                0.9999998724808964,
                0.9999996533674201,
                0.9999996072138934
            ],
            [
                0.9999998362622357,
                0.9999997617631184,
                0.9999998362623332,
                0.9999997897566589,
                0.9999997617630332,
                0.9999996940978461,
                0.9999997897565587,
                0.9999996533674201,
                0.999999814460876,
                0.9999989322970028
            ],
            [
                0.9999996940978095,
                0.9999998724810027,
                0.9999997300421903,
                0.9999996533673375,
                0.9999997897567341,
                0.9999996940977002,
                0.9999999006880785,
                0.9999997897567091,
                0.9999998555019446,
                0.9999998144609202
            ],
            [
                0.999999495652652,
                0.9999998555019446,
                0.9999995549151073,
                0.9999999123575464,
                0.9999997897565838,
                0.9999996072136125,
                0.999999789756634,
                0.9999997617630332,
                0.9999996940978095,
                0.9999997300422547
            ],
            [
                0.9999997300421581,
                0.9999998144609423,
                0.9999996533674614,
                0.9999997617629763,
                0.999999855502048,
                0.9999998724809267,
                0.9999996533674615,
                0.9999997300422869,
                0.9999996940977366,
                0.9999997617630332
            ],
            [
                0.9999998144608538,
                0.9999997897566589,
                0.9999998362622942,
                0.9999998555019446,
                0.9999997897565838,
                0.999999694097773,
                0.9999998362623332,
                0.9999997300422225,
                0.9999996533673788,
                0.999999814460876
            ],
            [
                0.9999997617630332,
                0.9999997300421581,
                0.9999998874648379,
                0.9999998362623528,
                0.999999730042126,
                0.9999998362623332,
                0.9999997897567091,
                0.9999997897566089,
                0.9999997617631752,
                0.9999997300421903
            ],
            [
                0.9999997897567091,
                0.9999998555019274,
                0.9999998724810027,
                0.999999789756684,
                0.9999996940976636,
                0.9999998874648245,
                0.9999997897567342,
                0.9999997897565838,
                0.9999996940977366,
                0.9999998362622552
            ],
            [
                0.9999998144609202,
                0.9999998555020135,
                0.9999998874649318,
                0.9999996940976636,
                0.9999996072137061,
                0.9999996533672136,
                0.9999997300422225,
                0.9999998362623137,
                0.9999998362622943,
                0.999999814460876
            ],
            [
                0.9999997897566589,
                0.9999996940978825,
                0.9999999123575359,
                0.999999554914895,
                0.9999998874647574,
                0.9999998724810026,
                0.9999997617631752,
                0.9999997300422547,
                0.999999855502048,
                0.9999999123574628
            ],
            [
                0.9999997300422547,
                0.9999994956523514,
                0.9999997300422225,
                0.999999694097773,
                0.9999997897566589,
                0.999999352404893,
                0.9999995549150011,
                0.9999996533672135,
                0.9999995549149481,
                0.9999998144608098
            ],
            [
                0.9999999123575359,
                0.9999996533672962,
                0.9999996533675028,
                0.9999997617629764,
                0.9999999123574941,
                0.9999998362623137,
                0.9999997897567342,
                0.999999694097846,
                0.9999997897567341,
                0.9999998144608097
            ],
            [
                0.9999996072138466,
                0.9999998555019274,
                0.9999994956527121,
                0.9999996072137529,
                0.9999998724809723,
                0.9999996940976636,
                0.9999996072136593,
                0.9999997300421581,
                0.999999789756684,
                0.9999998362623723
            ],
            [
                0.9999996533673375,
                0.9999997300421581,
                0.9999997300421581,
                0.9999998144609202,
                0.9999997300421581,
                0.9999994956525918,
                0.999999730042126,
                0.999999855502048,
                0.9999993524054335,
                0.9999995549148419
            ],
            [
                0.9999994284996212,
                0.9999997300421903,
                0.9999993524051247,
                0.999999495652652,
                0.9999994284994849,
                0.9999994956523514,
                0.999999814460876,
                0.999999855502048,
                0.9999998362623723,
                0.9999997617630049
            ],
            [
                0.9999998362623332,
                0.999999887464744,
                0.999999855501979,
                0.9999998362622552,
                0.9999996940977002,
                0.9999997897565587,
                0.9999997897567091,
                0.999999814460876,
                0.9999997300422869,
                0.9999997617631184
            ],
            [
                0.9999997897567342,
                0.9999997617630616,
                0.9999996533672549,
                0.9999997300421581,
                0.9999996940976272,
                0.999999887464811,
                0.999999789756684,
                0.9999996940978095,
                0.9999998724809571,
                0.9999998724809419
            ],
            [
                0.9999997617630332,
                0.9999998144609423,
                0.9999998144609202,
                0.9999997300422225,
                0.9999999006881496,
                0.9999998362623137,
                0.9999998724809571,
                0.9999998362623332,
                0.9999998362623137,
                0.9999998555019446
            ],
            [
                0.9999990577552939,
                0.9999997300421581,
                0.9999996533672962,
                0.9999998144609645,
                0.9999997897566589,
                0.999999554914842,
                0.9999994956524716,
                0.9999996940977366,
                0.9999996940977731,
                0.999998790134605
            ],
            [
                0.9999998144609423,
                0.9999998724810027,
                0.999999814460854,
                0.9999998724809116,
                0.9999997617631752,
                0.999999855501979,
                0.9999999006880549,
                0.9999998874648245,
                0.999999814460876,
                0.9999999226557592
            ],
            [
                0.9999994956524716,
                0.9999996940978825,
                0.9999994956525918,
                0.9999998555019274,
                0.9999998362623332,
                0.9999998144608317,
                0.9999997897567091,
                0.9999998144608317,
                0.999999855502048,
                0.99999992265575
            ],
            [
                0.9999998362622552,
                0.9999997617629763,
                0.9999998724809419,
                0.9999997897567342,
                0.9999998144608538,
                0.9999998144608098,
                0.999999855501979,
                0.9999998724809723,
                0.9999997617631752,
                0.9999997897565587
            ],
            [
                0.9999997300422225,
                0.9999998724809874,
                0.9999998874647574,
                0.9999997617630049,
                0.9999997897566589,
                0.9999998362623138,
                0.9999998555020135,
                0.999999814460876,
                0.9999998555019962,
                0.9999998362622552
            ],
            [
                0.9999997617630048,
                0.999999789756634,
                0.999999428499553,
                0.999999814460876,
                0.9999996533674615,
                0.9999996940978095,
                0.9999995549148419,
                0.999999730042319,
                0.9999998362623528,
                0.9999996072137061
            ],
            [
                0.9999997897567091,
                0.9999996533674615,
                0.9999996533672549,
                0.9999999006880668,
                0.9999997617631752,
                0.9999997617631752,
                0.9999996533673788,
                0.9999998144608097,
                0.9999996940977731,
                0.9999997617631469
            ],
            [
                0.9999997300422547,
                0.9999997617630616,
                0.9999998144609645,
                0.9999994284994849,
                0.9999992661790195,
                0.999999730042319,
                0.9999998874648782,
                0.9999995549148951,
                0.9999998362623137,
                0.9999996940978461
            ],
            [
                0.9999996072137529,
                0.9999997300421581,
                0.9999996940977731,
                0.9999996940977731,
                0.9999994284996211,
                0.9999994284996891,
                0.9999996940977001,
                0.9999997897566089,
                0.999999352405279,
                0.9999998362623528
            ],
            [
                0.9999996533675028,
                0.9999997300421581,
                0.9999997617630616,
                0.9999997897566089,
                0.999999694097773,
                0.999999730042126,
                0.9999997617629764,
                0.9999998144609645,
                0.9999996533672135,
                0.9999997617630049
            ],
            [
                0.9999995549150542,
                0.9999996940977366,
                0.9999998362622357,
                0.9999997617630616,
                0.9999996072138466,
                0.9999996072138466,
                0.9999998362623723,
                0.9999995549147358,
                0.9999994284995529,
                0.9999998874648782
            ],
            [
                0.9999997617630048,
                0.9999998555019446,
                0.9999996940977366,
                0.9999998362622943,
                0.9999998144608981,
                0.9999997300422225,
                0.9999998724809571,
                0.9999998362623137,
                0.999999789756684,
                0.9999998362622357
            ],
            [
                0.9999998144609424,
                0.9999998362622552,
                0.9999998874649184,
                0.9999998724809419,
                0.999999789756634,
                0.9999998144608097,
                0.9999998144609645,
                0.9999998362622552,
                0.9999998362622552,
                0.9999996533672136
            ],
            [
                0.9999998555019963,
                0.9999997617630048,
                0.9999997617631752,
                0.9999998144608098,
                0.9999998724809419,
                0.9999998874647842,
                0.9999998362622943,
                0.9999996533672962,
                0.9999996533673375,
                0.9999996072138465
            ],
            [
                0.999999653367379,
                0.9999998555019618,
                0.999999730042319,
                0.9999997897565838,
                0.9999997300422869,
                0.9999996533674615,
                0.9999997300422869,
                0.9999996072139402,
                0.999999814460876,
                0.9999996072138466
            ],
            [
                0.9999994956527121,
                0.999999814460876,
                0.9999997300422547,
                0.9999998144609202,
                0.9999996072137061,
                0.9999998874648514,
                0.9999996072137061,
                0.9999998724808964,
                0.9999997897565838,
                0.9999996940977002
            ],
            [
                0.9999998362622746,
                0.9999996533674615,
                0.9999996533674614,
                0.999999554914842,
                0.9999996940978825,
                0.9999996940977366,
                0.9999997897567341,
                0.9999998144609423,
                0.9999997897567091,
                0.9999998874647709
            ],
            [
                0.9999996533672548,
                0.9999998362623332,
                0.999999730042319,
                0.9999998724810027,
                0.9999998724809419,
                0.9999996533674615,
                0.9999997300421581,
                0.9999997617631184,
                0.9999997300422869,
                0.9999998724809115
            ],
            [
                0.9999991684719723,
                0.9999994956525918,
                0.9999997300422869,
                0.9999997300420937,
                0.9999998144608097,
                0.999999352405279,
                0.9999996533672136,
                0.9999997300421903,
                0.9999994284993486,
                0.9999998144608981
            ],
            [
                0.9999997897567091,
                0.9999997617630616,
                0.999999814460876,
                0.9999997300420937,
                0.9999996533673788,
                0.9999997897566589,
                0.9999996940977366,
                0.9999998362622552,
                0.9999997897565838,
                0.9999996533672548
            ],
            [
                0.9999997897566589,
                0.9999998724809571,
                0.9999993524054334,
                0.9999998555019963,
                0.9999998555019446,
                0.9999998144608097,
                0.9999998874647709,
                0.9999998874648514,
                0.9999998362622552,
                0.9999998144608981
            ],
            [
                0.9999998362623723,
                0.9999996940976636,
                0.9999997300422225,
                0.9999997617630332,
                0.9999998362622747,
                0.9999996940976271,
                0.9999998362623137,
                0.9999997897566589,
                0.9999997617630899,
                0.999999814460854
            ],
            [
                0.9999998724809419,
                0.9999998362623528,
                0.9999997617629764,
                0.9999997617631469,
                0.9999998874647842,
                0.9999996072136593,
                0.9999995549149481,
                0.9999998144608981,
                0.9999998144609424,
                0.9999996533673376
            ],
            [
                0.999999266179107,
                0.9999998144608981,
                0.9999997617629764,
                0.9999996940978461,
                0.9999996072137529,
                0.9999993524049702,
                0.9999996072138465,
                0.9999994956525317,
                0.9999997617631469,
                0.9999996072137998
            ],
            [
                0.9999998362623332,
                0.9999998362622357,
                0.9999996533673376,
                0.999999814460876,
                0.9999998362623528,
                0.9999996940978825,
                0.9999997617630332,
                0.9999998555019446,
                0.9999997617631468,
                0.9999997300420937
            ],
            [
                0.999999814460876,
                0.9999998555020135,
                0.9999997300422547,
                0.9999999006880075,
                0.9999994284997574,
                0.9999997897566589,
                0.9999998362623137,
                0.9999998362622357,
                0.9999998144609645,
                0.999999814460876
            ],
            [
                0.999999855502048,
                0.9999996940976636,
                0.9999996940976636,
                0.9999993524049702,
                0.9999999006880075,
                0.9999998874648379,
                0.999999814460854,
                0.9999998144609202,
                0.9999998362622357,
                0.9999997300421903
            ],
            [
                0.9999998555020307,
                0.9999996940978825,
                0.9999998724809115,
                0.9999996072137061,
                0.9999997300422869,
                0.9999997617629763,
                0.9999996072136592,
                0.9999996072137061,
                0.9999994956525918,
                0.9999998874647976
            ],
            [
                0.9999997300422869,
                0.9999997617631184,
                0.9999998362622552,
                0.9999995549151072,
                0.999999900688043,
                0.9999997897567091,
                0.9999998555020135,
                0.9999998555020134,
                0.9999997300422547,
                0.9999998362623138
            ],
            [
                0.999999789756634,
                0.9999998362623528,
                0.9999996072138934,
                0.9999998144608097,
                0.9999996533672962,
                0.9999999006880668,
                0.999999653367503,
                0.999999789756684,
                0.9999994284994849,
                0.9999998144609424
            ],
            [
                0.9999997897567091,
                0.9999996533672549,
                0.9999996533672549,
                0.9999997617630332,
                0.9999998144609645,
                0.9999998874647977,
                0.9999995549148419,
                0.9999998874648379,
                0.9999998362623722,
                0.9999997897567341
            ],
            [
                0.9999997897565838,
                0.9999996533674614,
                0.9999998724809571,
                0.9999998144609645,
                0.9999997617630616,
                0.9999994956525918,
                0.9999998362622943,
                0.9999997617630616,
                0.9999997617629763,
                0.9999994956525318
            ],
            [
                0.9999998362622943,
                0.9999998555019962,
                0.999999694097846,
                0.9999999006880549,
                0.999999789756684,
                0.9999997300422225,
                0.9999997617631752,
                0.999999653367379,
                0.9999996072138465,
                0.9999998555020307
            ],
            [
                0.9999996072137529,
                0.999999855501979,
                0.9999994284996211,
                0.9999996533672962,
                0.9999998362622942,
                0.9999998144609202,
                0.9999994284993486,
                0.9999998362622552,
                0.9999996072137529,
                0.9999997897566589
            ],
            [
                0.9999998362622747,
                0.9999998724809875,
                0.9999996533673375,
                0.9999997897565838,
                0.9999997897567091,
                0.9999996533672962,
                0.9999997300421903,
                0.9999997300421581,
                0.9999998144609645,
                0.9999996072137061
            ],
            [
                0.999999855502048,
                0.9999996533675028,
                0.9999998362623528,
                0.9999998724809723,
                0.9999998144609423,
                0.9999997617631752,
                0.9999991684720716,
                0.9999997897566338,
                0.9999998144609645,
                0.9999996940976636
            ],
            [
                0.999999789756684,
                0.9999997300421903,
                0.9999998362622746,
                0.9999994284993486,
                0.9999997300422225,
                0.9999998724810027,
                0.9999997617631469,
                0.9999997300421581,
                0.999999814460854,
                0.9999994956526519
            ],
            [
                0.9999998555019446,
                0.999999730042319,
                0.9999998144608983,
                0.9999993524053562,
                0.9999998874648379,
                0.9999998555019618,
                0.9999997617631183,
                0.999999789756684,
                0.9999997617630049,
                0.9999998144609202
            ],
            [
                0.9999998724809419,
                0.9999998555019618,
                0.9999997617631752,
                0.9999998724808963,
                0.999999653367503,
                0.9999999006880904,
                0.9999997300422547,
                0.9999997617631469,
                0.9999997617629764,
                0.999999730042319
            ],
            [
                0.999999855501979,
                0.9999997617631752,
                0.9999998362622746,
                0.9999998144608981,
                0.9999997897565587,
                0.9999998144609423,
                0.9999997300420937,
                0.9999996940976636,
                0.9999998362623137,
                0.9999998555019274
            ],
            [
                0.9999997300421581,
                0.999999694097846,
                0.9999996940977366,
                0.9999998144608981,
                0.9999996072137998,
                0.9999996533672962,
                0.9999998144609423,
                0.9999997897566589,
                0.9999998362623332,
                0.9999996533674615
            ],
            [
                0.9999997300421581,
                0.9999997897565587,
                0.9999997617631469,
                0.9999998362623332,
                0.9999998144609202,
                0.9999994956527721,
                0.9999998724809571,
                0.9999998144608317,
                0.9999996940978825,
                0.9999996940977002
            ],
            [
                0.9999996533675028,
                0.9999990577551816,
                0.9999998362623528,
                0.9999996940977366,
                0.9999996940977366,
                0.9999994284993485,
                0.9999998724809419,
                0.9999998724810027,
                0.9999998555020307,
                0.9999998144609645
            ],
            [
                0.9997388097854526,
                0.9999251537549172,
                0.9998766053813334,
                0.9995694429160199,
                0.9999339478475049,
                0.999876605410638,
                0.9999724643154826,
                0.9997694933401882,
                0.999954602142202,
                0.9999417087205725
            ],
            [
                0.9999997300421581,
                0.9999996533675028,
                0.9999997300422547,
                0.999999554914789,
                0.9999997617630049,
                0.9999998362623722,
                0.999999653367379,
                0.999999554914895,
                0.9999996533674615,
                0.9999997617631469
            ],
            [
                0.9999997617630616,
                0.9999998362623723,
                0.9999995549150542,
                0.9999998362623528,
                0.9999997300421903,
                0.9999998362623138,
                0.9999996940978461,
                0.9999998144608538,
                0.9999996940977731,
                0.9999999006880785
            ],
            [
                0.9999995549148419,
                0.999999352405279,
                0.9999996072136125,
                0.9999997617630048,
                0.9999998362622357,
                0.9999996533672135,
                0.9999998362623332,
                0.9999998362622357,
                0.9999998362622943,
                0.9999996533673375
            ],
            [
                0.9999998144608538,
                0.999999694097846,
                0.9999995549148419,
                0.9999998874648647,
                0.9999997617631752,
                0.9999997897565838,
                0.9999997300420937,
                0.9999996940977731,
                0.9999997897567091,
                0.9999997617629764
            ],
            [
                0.9999997617630049,
                0.9999998362623137,
                0.9999998724809571,
                0.9999991684717741,
                0.9999993524049702,
                0.9999994956527121,
                0.9999996072139402,
                0.999999653367379,
                0.9999998724808963,
                0.9999997617630616
            ],
            [
                0.9999994284994168,
                0.9999998362622746,
                0.99999976176309,
                0.9999998362623528,
                0.9999998144609202,
                0.9999998724809115,
                0.9999997617630616,
                0.9999998555019274,
                0.9999997617631183,
                0.9999998555019618
            ]
        ]
    },
    {
        "q_id": "8429_mmlu_math",
        "cot_ids": [
            0,
            3,
            4,
            6,
            7,
            9,
            10,
            13,
            19,
            25,
            26,
            29,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            43,
            45,
            46,
            47,
            48,
            50,
            51,
            55,
            58,
            59,
            60,
            63,
            64,
            65,
            67,
            69,
            72,
            74,
            75,
            77,
            79,
            85,
            88,
            89,
            90,
            92,
            94,
            97,
            100,
            101,
            102,
            104,
            106,
            107,
            108,
            109,
            111,
            112,
            115,
            116,
            117,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.260323488925638e-06,
                1.5534983091284474e-06,
                0.00020342701875631665,
                6.144174597520747e-06,
                2.9023112926779284e-06,
                1.3007133112662637e-05,
                3.535626334490732e-05,
                1.7603432131631714e-06,
                8.939700563752626e-06,
                0.0001584362350152198
            ],
            [
                2.260324836651547e-06,
                7.889260683615565e-06,
                9.422442567152048e-07,
                1.0129990976728036e-05,
                NaN,
                4.006368258380272e-05,
                4.222834450589758e-06,
                0.00017952798707185626,
                6.144173869072478e-06,
                1.0129988563343644e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                1.0129993383461157e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                3.1201926201134365e-05,
                NaN,
                2.260323489192885e-06,
                2.9023119839440746e-06,
                7.889259761905808e-06,
                NaN,
                1.1478765382509808e-05,
                3.726641060658489e-06,
                2.561282821209454e-06,
                2.1444943278894603e-05
            ],
            [
                2.2603253754284284e-06,
                1.3709576970387918e-06,
                3.4663278638193755e-07,
                1.3007126909537681e-05,
                3.927862938877536e-07,
                2.6995780963588326e-07,
                8.939696301384342e-06,
                1.7603436327425345e-06,
                4.222835457906302e-06,
                1.0129989770662257e-05
            ],
            [
                0.00023050676523370253,
                3.535625064630772e-05,
                2.430023491664161e-05,
                0.9859363745192965,
                0.00080408610501689,
                8.481103013453893e-05,
                0.0001795279635742425,
                NaN,
                2.4300232012472705e-05,
                0.001501182216427892
            ],
            [
                NaN,
                NaN,
                1.5534975692259223e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                3.726640157309322e-06
            ],
            [
                4.222833444037741e-06,
                NaN,
                NaN,
                NaN,
                1.3007129998382795e-05,
                0.0,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                1.1478769469800468e-05,
                4.006369684349497e-05,
                1.67014238214675e-05,
                4.006369200067905e-05,
                4.785096205347206e-06,
                4.539786857361818e-05,
                0.00010889688253730961,
                1.4738983710366698e-05,
                3.120190020204515e-05
            ],
            [
                5.4222176755001384e-06,
                1.3709568798607528e-06,
                1.2098659717086699e-06,
                NaN,
                1.0677033790883835e-06,
                1.1478764019328247e-05,
                6.144174600862407e-06,
                6.475949525663707e-07,
                2.144495096785658e-05,
                1.4738988989189704e-05
            ],
            [
                1.7603427935678977e-06,
                NaN,
                NaN,
                1.0129989764010414e-05,
                6.144177528235347e-06,
                NaN,
                NaN,
                7.889264463890957e-06,
                1.4738985469509454e-05,
                6.144176797283277e-06
            ],
            [
                3.1201914648024076e-05,
                NaN,
                3.726638394957837e-06,
                1.99472948120462e-06,
                NaN,
                1.4738985393155534e-05,
                3.726639726997871e-06,
                2.9023119847359636e-06,
                NaN,
                2.4300249412738893e-05
            ],
            [
                1.4738980168060362e-05,
                3.120190763332158e-05,
                4.539786858319682e-05,
                5.8291279317586125e-05,
                3.535625912190121e-05,
                2.260323758676741e-06,
                7.484624465591207e-05,
                NaN,
                2.1444948406091176e-05,
                0.0011695102162352184
            ],
            [
                6.962258737814774e-06,
                5.422219615286937e-06,
                4.222833946315156e-06,
                5.422220893204163e-06,
                1.473898899664279e-05,
                4.785096775842062e-06,
                1.553497568999859e-06,
                NaN,
                3.7266379505740294e-06,
                1.473898021366358e-05
            ],
            [
                2.2603248363822436e-06,
                NaN,
                4.222831932666232e-06,
                NaN,
                5.715002425937749e-07,
                1.370957533574467e-06,
                7.338212428813419e-07,
                1.3709575336947905e-06,
                4.785096205260165e-06,
                1.067702869849933e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                1.0677026152939181e-06,
                5.422220260360515e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.3007130008887624e-05,
                3.7266406153660187e-06,
                6.962258735839161e-06,
                6.962254588116627e-06,
                5.422217029272909e-06,
                5.422220260202708e-06,
                1.6701419845680582e-05,
                2.4300234933172706e-05,
                0.9324533022906133,
                0.9998766054690282
            ],
            [
                NaN,
                NaN,
                1.3007128457958606e-05,
                2.9023133677438847e-06,
                NaN,
                NaN,
                1.370956716216975e-06,
                4.006368727883207e-05,
                NaN,
                NaN
            ],
            [
                2.561282515564741e-06,
                3.72664017246987e-06,
                1.14787708580381e-05,
                1.6701425825492673e-05,
                1.012999339031569e-05,
                1.3709567164663505e-06,
                1.7603425835173373e-06,
                7.889260703906985e-06,
                2.260324566014287e-06,
                3.7266392835764795e-06
            ],
            [
                NaN,
                1.37095785892459e-06,
                1.3007131557971383e-05,
                3.5356259075083244e-05,
                6.962257075260544e-06,
                1.8925157237517507e-05,
                2.9023109445214314e-06,
                NaN,
                1.1478773595009805e-05,
                NaN
            ],
            [
                3.466326623177815e-07,
                6.475951069113601e-07,
                1.9947292451963607e-06,
                1.067702615161853e-06,
                7.338207179493245e-07,
                8.315283247375139e-07,
                9.422448183241877e-07,
                8.315284235774681e-07,
                2.2603242966454563e-06,
                1.2098656832853378e-06
            ],
            [
                2.2603242974060834e-06,
                NaN,
                6.475947208643094e-07,
                NaN,
                3.4663278636144555e-07,
                NaN,
                NaN,
                NaN,
                NaN,
                6.4759479808713e-07
            ],
            [
                NaN,
                8.315282258037938e-07,
                4.222834953420345e-06,
                NaN,
                5.829127218125326e-05,
                1.2098652507583041e-06,
                0.0010322308186358617,
                6.9622537587775775e-06,
                1.6701425823457267e-05,
                1.0129994600398803e-05
            ],
            [
                4.53978631524379e-05,
                2.7535697622726747e-05,
                NaN,
                NaN,
                4.006368041103649e-05,
                NaN,
                9.610242603456664e-05,
                1.6701427809710842e-05,
                NaN,
                6.605216814791757e-05
            ],
            [
                3.288748672168078e-06,
                6.9622595602271066e-06,
                3.288749848677511e-06,
                3.2887482789953484e-06,
                6.96225541098438e-06,
                3.2887498485279564e-06,
                4.785092780690926e-06,
                2.9023126764615702e-06,
                6.14417460073947e-06,
                1.0129994589969591e-05
            ],
            [
                6.475951069113601e-07,
                NaN,
                7.338209804853638e-07,
                2.1444940733201126e-05,
                3.059022633714149e-07,
                9.422449308138184e-07,
                8.315278293604072e-07,
                1.1478768123551712e-05,
                6.47595029750346e-07,
                1.0129993393540266e-05
            ],
            [
                5.422219353801565e-06,
                3.5356267488169044e-05,
                1.3007123807302014e-05,
                1.473898190747079e-05,
                4.006369198814498e-05,
                3.288749455331158e-06,
                5.1442206219340066e-05,
                6.9622570786798724e-06,
                1.8925152721432305e-05,
                7.889261626205216e-06
            ],
            [
                7.889264464106214e-06,
                9.422447059811116e-07,
                2.753570091616638e-05,
                2.144495093470037e-05,
                6.962255417721724e-06,
                1.7603438423321262e-06,
                NaN,
                0.005220125439655665,
                2.5612828208879873e-06,
                NaN
            ],
            [
                1.0129988561906404e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                3.2887502406420278e-06,
                NaN,
                NaN,
                2.1444940717130123e-05,
                NaN
            ],
            [
                6.1441753335241615e-06,
                2.4300249408672413e-05,
                6.6052120892446e-05,
                1.300712380997554e-05,
                7.48462091951041e-05,
                4.539785775768208e-05,
                1.147876401460948e-05,
                5.8291258415389654e-05,
                2.430023201636237e-05,
                1.4738976683502859e-05
            ],
            [
                1.4738976695942536e-05,
                2.753569107391384e-05,
                6.605213643522215e-05,
                4.006368259662828e-05,
                NaN,
                3.2887478877249985e-06,
                7.48462181396708e-05,
                1.8925145980181433e-05,
                NaN,
                3.726639726103083e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                4.0063711272110856e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                0.0017007226049379975,
                6.605216023019448e-05,
                4.222835456581284e-06,
                4.78509563466093e-06,
                3.288747887820713e-06,
                4.222834449921489e-06,
                1.6701419844465412e-05,
                1.3007126898133793e-05,
                7.889261642794245e-06,
                1.473898371722997e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                7.889263517699022e-06,
                NaN,
                NaN,
                NaN,
                0.9465966702001758,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                9.610239191997185e-05,
                NaN,
                5.4222183217274465e-06,
                NaN,
                1.6701423829123058e-05,
                6.962258732597129e-06,
                NaN
            ],
            [
                2.1444945755155414e-05,
                NaN,
                8.939697350515956e-06,
                0.00026119036910144283,
                1.012998976633211e-05,
                3.12019261368886e-05,
                NaN,
                1.3709575329460411e-06,
                2.4300243595999808e-05,
                1.0129989768322136e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                3.2887494543261513e-06,
                6.144176798132662e-06,
                4.785093353352668e-06,
                6.962253756232077e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                1.3007129991190302e-05,
                8.939694165298253e-06,
                8.939694170940841e-06,
                NaN,
                NaN,
                5.42221961567159e-06,
                1.2098655392222467e-06,
                NaN,
                7.88926258381982e-06,
                1.6701419846834993e-05
            ],
            [
                0.9997388097930598,
                0.0004878572179226553,
                0.007577241453450499,
                0.9669140238756562,
                NaN,
                0.9978172831966464,
                0.09534945461636171,
                0.017986210652978007,
                0.18242552158390102,
                NaN
            ],
            [
                0.00013982205588115355,
                0.00048785715335093917,
                7.889263525261671e-06,
                5.144221948429205e-05,
                0.00013982210586622825,
                9.610238038856615e-05,
                1.6701417859944398e-05,
                0.0005527786006813485,
                0.0001795279416490596,
                1.892515725665725e-05
            ],
            [
                1.3007134654767206e-05,
                3.120190385315366e-05,
                1.8925150486764003e-05,
                1.012998974816392e-05,
                1.6701415819647427e-05,
                7.889263524257144e-06,
                1.1478765385432939e-05,
                1.8925141400896494e-05,
                3.726638838968869e-06,
                4.0063687010952744e-05
            ],
            [
                3.1201900194894126e-05,
                NaN,
                1.670142781478417e-05,
                3.5356259098234985e-05,
                2.144494583831896e-05,
                NaN,
                4.222834954134701e-06,
                0.000487857154315967,
                NaN,
                NaN
            ],
            [
                0.0001795280261265897,
                1.3007123801387135e-05,
                2.7535684459790688e-05,
                NaN,
                8.481106119455672e-05,
                NaN,
                1.1478765381257036e-05,
                NaN,
                1.7603425829954052e-06,
                1.3007130003871806e-05
            ],
            [
                3.2887498485279564e-06,
                4.785095063069508e-06,
                NaN,
                NaN,
                6.605216027536722e-05,
                1.1478769489009626e-05,
                1.3007130013572209e-05,
                8.939699499823059e-06,
                0.00012339458879286226,
                NaN
            ],
            [
                1.1478766745733287e-05,
                NaN,
                8.939693102572767e-06,
                NaN,
                4.006368688328012e-05,
                NaN,
                1.6701419846834993e-05,
                0.00037998456614564543,
                0.7549149978955811,
                1.670142780235907e-05
            ],
            [
                1.3007134664514934e-05,
                5.42221767672807e-06,
                NaN,
                0.0003353500616817478,
                5.422220260360515e-06,
                1.4738987227794512e-05,
                6.144172404129392e-06,
                3.2887486726945097e-06,
                6.605217579700796e-05,
                2.561281599914358e-06
            ],
            [
                2.7535687809124434e-05,
                2.7535697652678035e-05,
                1.6701429797422853e-05,
                NaN,
                0.00012339453003282785,
                1.147876538716594e-05,
                NaN,
                6.605212887648175e-05,
                6.605217598875182e-05,
                NaN
            ],
            [
                5.4222176755001384e-06,
                8.939696296571067e-06,
                1.3007126901209531e-05,
                5.422221553072258e-06,
                NaN,
                5.422218320820059e-06,
                1.0129987353242826e-05,
                3.2887494567788457e-06,
                NaN,
                1.3007134658978603e-05
            ],
            [
                1.0129993393319151e-05,
                NaN,
                NaN,
                1.3007131561804229e-05,
                NaN,
                NaN,
                NaN,
                4.785095632554564e-06,
                NaN,
                7.48462002744981e-05
            ],
            [
                1.0129993393319151e-05,
                1.4738980207899506e-05,
                1.670142581762446e-05,
                NaN,
                1.8925150474922147e-05,
                7.889263522520747e-06,
                NaN,
                1.7603436326080487e-06,
                NaN,
                1.3709572062967502e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                6.9622537584863015e-06,
                NaN
            ],
            [
                1.8925148203902373e-05,
                4.222834953082369e-06,
                NaN,
                3.2887490644495094e-06,
                NaN,
                NaN,
                1.3709578603435361e-06,
                4.222832436871463e-06,
                1.012999459535003e-05,
                6.144176797864436e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                4.222831931298969e-06,
                1.5534979394696104e-06,
                3.288749456060984e-06,
                NaN,
                NaN,
                6.144172402765906e-06
            ],
            [
                5.422217670144583e-06,
                1.8925143723000643e-05,
                2.5612819038468034e-06,
                2.2603237572089375e-06,
                3.120190362409386e-05,
                5.422217669316099e-06,
                NaN,
                5.42222025793424e-06,
                1.1478764012939119e-05,
                3.726638394564673e-06
            ],
            [
                NaN,
                NaN,
                1.6701425815072606e-05,
                NaN,
                NaN,
                NaN,
                2.561281294281438e-06,
                NaN,
                9.422444815006715e-07,
                2.2603234892298883e-06
            ],
            [
                0.9820137868466708,
                0.022977368864643504,
                NaN,
                0.94659666812867,
                0.020332353491066487,
                0.7549149923816048,
                0.18242551713899047,
                NaN,
                NaN,
                0.9875683502330389
            ],
            [
                2.260324566359653e-06,
                0.5,
                3.7266410584011837e-06,
                3.2887482767221207e-06,
                5.422217021836282e-06,
                8.939698428559877e-06,
                2.2603234888763e-06,
                2.9023133683457202e-06,
                3.7266383940901643e-06,
                6.962253756004122e-06
            ],
            [
                NaN,
                2.1444950958338794e-05,
                2.260324564871291e-06,
                1.5534984948621528e-06,
                8.939699498587217e-06,
                2.9023126753476465e-06,
                1.1478765385098868e-05,
                5.829127225207798e-05,
                1.5534981245279071e-06,
                1.1478768123823146e-05
            ],
            [
                NaN,
                4.4508526415598164e-07,
                1.067702615348298e-06,
                2.9023123307122503e-06,
                NaN,
                3.7266410608720178e-06,
                5.8291293252246584e-05,
                NaN,
                1.0129988563343644e-05,
                1.3709570431554246e-06
            ],
            [
                3.120191878631223e-05,
                6.144173132912773e-06,
                2.9023119835956434e-06,
                2.9023119844508833e-06,
                8.93969416907082e-06,
                2.7535681204818868e-05,
                7.88926634644516e-06,
                1.3007129999707728e-05,
                7.889265403654039e-06,
                0.00010889694762958362
            ],
            [
                1.9947301969471416e-06,
                1.7603434226438436e-06,
                8.481102074088805e-05,
                NaN,
                3.120192249712832e-05,
                NaN,
                4.222833946537913e-06,
                3.2887482807780376e-06,
                NaN,
                2.5612822093330395e-06
            ],
            [
                NaN,
                NaN,
                2.561281294558644e-06,
                8.939697368500698e-06,
                2.5612812938854287e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                2.1444943270937118e-05
            ],
            [
                0.7772998508568416,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                4.785095631475268e-06,
                1.0129990975567187e-05,
                8.315279283568503e-07,
                NaN
            ],
            [
                2.4300231966238675e-05,
                0.7981867777396211,
                NaN,
                NaN,
                NaN,
                0.9149009567332238,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                1.3007131557025005e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                8.93969309928803e-06,
                NaN,
                7.88926258343236e-06
            ],
            [
                NaN,
                7.484624426057797e-05,
                1.0677029971473845e-06,
                1.3709578602637359e-06,
                3.12019076269651e-05,
                1.3007123806876143e-05,
                0.0013250222066288474,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                7.338208052740085e-07,
                6.475945665353147e-07,
                6.47594798049435e-07,
                2.56128251495908e-06,
                4.222835457526079e-06,
                1.0677028696071658e-06,
                1.5534977543661227e-06,
                2.902312676118419e-06,
                2.6995768087197756e-07
            ],
            [
                6.144174601097106e-06,
                1.5534979396024226e-06,
                1.2098653949192932e-06,
                6.144172400519507e-06,
                2.9023112929973233e-06,
                NaN,
                6.475945665152892e-07,
                4.222832436272325e-06,
                NaN,
                7.3382115488653e-07
            ],
            [
                2.4300234921326896e-05,
                5.1442238133528324e-05,
                6.605212077518918e-05,
                NaN,
                NaN,
                3.1201900143474856e-05,
                2.753569753277272e-05,
                8.481107116821975e-05,
                3.535625909386188e-05,
                6.605212885485651e-05
            ]
        ]
    },
    {
        "q_id": "7970_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            8,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            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,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            100,
            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": [
            [
                0.9999910603058279,
                0.9999869928746365,
                0.9999987901343167,
                0.9999687980997993,
                0.999995214903224,
                0.9999982396565767,
                0.9999885212277699,
                0.9999962733602717,
                0.9999977396759716,
                0.9999921107355337
            ],
            [
                0.9999993524050473,
                0.9999995549151073,
                0.9999970976883609,
                0.9999999123575359,
                0.9999982396567867,
                0.9999970976887068,
                0.9999970976887068,
                0.9999982396569965,
                0.9999982396574162,
                0.9999996072139402
            ],
            [
                0.9999992661791944,
                0.9999990577552939,
                0.9999885212359813,
                0.9999980052700407,
                0.9999993524052789,
                0.9999986290429566,
                0.9999957771665555,
                0.9999938558239334,
                0.9999989322972572,
                0.9999970976890528
            ],
            [
                0.9999980052705163,
                0.9999994284997573,
                0.9999997617630333,
                0.999999266179107,
                0.9999852610233009,
                0.9999952149049349,
                0.9999967112497586,
                0.9999980052709918,
                0.9999996072137529,
                0.999997438716568
            ],
            [
                0.9999991684716749,
                0.9999967112497584,
                0.9999957771650453,
                0.9999980052700408,
                0.9999962733598274,
                0.9999982396569966,
                0.9999898700041906,
                0.9999977396762411,
                0.9999962733589389,
                0.9999945777784449
            ],
            [
                0.9999910603036963,
                0.999997438716568,
                0.9999967112521109,
                0.9999995549147358,
                0.9999993524049702,
                0.9999974387177893,
                0.9999957771660521,
                0.9999993524053562,
                0.9999980052705163,
                0.9999994284994849
            ],
            [
                0.9999938558224682,
                0.9999952149049349,
                0.9999957771645419,
                0.9999977396751633,
                0.9999986290427931,
                0.9999952149072165,
                0.9999980052700407,
                0.9999982396559473,
                0.9999987901341723,
                0.9999977396751633
            ],
            [
                0.9999967112501505,
                0.999999554914895,
                0.9999952149037941,
                0.9999977396765105,
                0.9999980052705163,
                0.9999984465024306,
                0.9999921107364742,
                0.9999984465015046,
                0.9999930377404305,
                0.9999974387180947
            ],
            [
                1.9947290081177566e-06,
                2.1444945856418342e-05,
                1.147876402018431e-05,
                1.7603432132912532e-06,
                4.539789028295303e-05,
                5.422217676797111e-06,
                2.902310947190096e-06,
                4.785092783267308e-06,
                1.994729721469003e-06,
                1.1478765388898939e-05
            ],
            [
                0.9999970976880149,
                0.9999962733616043,
                0.9999962733611601,
                0.9999984465020603,
                0.9999852610162717,
                0.9999992661786696,
                0.9999945777790911,
                0.9999967112509347,
                0.9999987901337396,
                0.9999930377445804
            ],
            [
                0.9999986290426297,
                0.9999994284996211,
                0.9999930377462405,
                0.9999982396567867,
                0.9999987901341723,
                0.9999910603047617,
                0.9999977396759716,
                0.999999730042126,
                0.9999980052707541,
                0.9999980052693274
            ],
            [
                0.9999991684715758,
                0.9999991684718732,
                0.9999974387177893,
                0.9999962733611603,
                0.9999957771645419,
                0.9999980052693274,
                0.9999962733598274,
                0.9999962733602716,
                0.9999992661790195,
                0.9999991684715758
            ],
            [
                0.9999967112509346,
                0.9999992661791944,
                0.9999970976883608,
                0.9999967112509347,
                0.9999974387187053,
                0.9999957771655488,
                0.9999990577556308,
                0.9999986290426297,
                0.9999987901344607,
                0.9999810748472503
            ],
            [
                8.939700566435704e-06,
                1.4738976693529666e-05,
                7.8892654060075e-06,
                5.8291272439530227e-05,
                2.4300232038993178e-05,
                2.4300246525983375e-05,
                6.605213680381227e-05,
                2.753568781423318e-05,
                1.147877359872636e-05,
                1.6701423833011596e-05
            ],
            [
                0.9999957771675623,
                0.9999987901338838,
                0.9999967112509346,
                0.9999967112493664,
                0.9999945777797377,
                0.9999980052702785,
                0.9999986290426298,
                0.9999952149043645,
                0.999992110736474,
                0.9999991684716749
            ],
            [
                0.9999977396748938,
                0.9999910603026305,
                0.9999989322968753,
                0.9999977396748938,
                0.9999994284995529,
                0.9999962733593831,
                0.9999967112493665,
                0.9999974387177893,
                0.9999962733593832,
                0.9999977396765105
            ],
            [
                1.892514372640862e-05,
                6.962254589104433e-06,
                1.6701425814404263e-05,
                3.726638395320497e-06,
                1.670142183934597e-05,
                1.4738981966291175e-05,
                1.6701417858577338e-05,
                1.3007126910649678e-05,
                1.670142781086525e-05,
                6.9622562487453084e-06
            ],
            [
                0.999997438716568,
                0.9999998144608538,
                0.9999885212332433,
                0.9999984465016898,
                0.9999982396572064,
                0.9999980052693274,
                0.9999986290431201,
                0.9999977396765105,
                0.9999990577549568,
                0.9999938558232011
            ],
            [
                0.9999967112493665,
                0.9999982396569966,
                0.9999984465016899,
                0.9999967112505427,
                0.9999967112497584,
                0.9999980052702786,
                0.9999980052693274,
                0.9999977396754327,
                0.9999945777803839,
                0.9999938558253982
            ],
            [
                0.9999977396754327,
                0.9999980052693274,
                0.9999977396765105,
                0.9999986290429566,
                0.9999970976866309,
                0.9999970976873229,
                0.9999970976883608,
                0.9999970976876689,
                0.9999952149043645,
                0.9999986290427931
            ],
            [
                0.999999554914895,
                0.9999974387168733,
                0.999998446502801,
                0.9999986290431201,
                0.9999970976873229,
                0.999998446502801,
                0.9999967112497585,
                0.9999977396748938,
                0.9999996533672962,
                0.9999974387168734
            ],
            [
                0.9999930377404306,
                0.9999982396559473,
                0.9999993524049702,
                0.9999974387187053,
                0.9999977396759716,
                0.9999989322968753,
                0.9999977396754327,
                0.9999974387168734,
                0.9999967112505427,
                0.9999977396748938
            ],
            [
                0.9999986290423029,
                0.9999980052705163,
                0.9999980052695652,
                0.9999986290427931,
                0.9999974387184,
                0.9999967112513267,
                0.9999982396574162,
                0.9999984465024306,
                0.9999986290423029,
                0.9999974387171787
            ],
            [
                0.9999938558275955,
                0.9999982396563669,
                0.9999970976866309,
                0.9999977396751633,
                0.9999957771680656,
                0.9999910603004999,
                0.9999977396757022,
                0.9999986290426297,
                0.9999957771680656,
                0.9999967112513267
            ],
            [
                0.9999992661788446,
                0.9999990577556307,
                0.999998629042303,
                0.9999945777823231,
                0.9999962733607158,
                0.9999967112497585,
                0.9999995549148419,
                0.9999982396569965,
                0.9999990577550691,
                0.9999992661790195
            ],
            [
                0.9999982396565769,
                0.9999974387168733,
                0.9999984465026158,
                0.9999962733611601,
                0.9999996072139402,
                0.9999930377437506,
                0.9999962733589389,
                0.9999996072137998,
                0.999995214906076,
                0.9999970976883609
            ],
            [
                0.9999952149072165,
                0.9999962733602716,
                0.9999810748472494,
                0.9999970976890529,
                0.9999485577802218,
                0.9999898700102279,
                0.9999869928746383,
                0.9999930377437507,
                0.9999967112493664,
                0.9999977396765111
            ],
            [
                0.9999977396746244,
                0.9999921107402356,
                0.9999977396748938,
                0.999998446502801,
                0.9999977396746244,
                0.9999974387187053,
                0.9999977396765105,
                0.9999970976869769,
                0.9999987901340279,
                0.9999952149049348
            ],
            [
                0.9999869928746369,
                0.9999982396563669,
                0.9999952149037941,
                0.9999974387171787,
                0.9999898700066056,
                0.999995777166052,
                0.9999952149072167,
                0.9999967112517189,
                0.9999952149055054,
                0.9999885212359809
            ],
            [
                0.9999996533675028,
                0.9999991684718733,
                0.9999990577555183,
                0.9999994956524115,
                0.9999992661788446,
                0.9999996940978095,
                0.9999994284992805,
                0.9999996533673375,
                0.9999970976880149,
                0.9999987901338838
            ],
            [
                0.9999987901341723,
                0.9999938558261312,
                0.9999921107383698,
                0.9999995549150011,
                0.9999957771670589,
                0.9999977396757022,
                0.9999982396567867,
                0.9999938558224744,
                0.9999984465016937,
                0.9999970976890528
            ],
            [
                0.9999982396574163,
                0.9999962733593846,
                0.9999994284994167,
                0.9999993524051246,
                0.9999992661786696,
                0.9999974387165679,
                0.999995214904935,
                0.9999885212359799,
                0.9999977396757022,
                0.9999962733593832
            ],
            [
                0.9999980052693274,
                0.9999990577549568,
                0.9999994956525918,
                0.9999996940977002,
                0.999998790134028,
                0.9999957771670589,
                0.9999980052693274,
                0.9999982396563669,
                0.9999995549149481,
                0.9999989322973846
            ],
            [
                0.9999996940977002,
                0.9999989322972572,
                0.99999976176309,
                0.9999989322972572,
                0.9999984465024306,
                0.999999554914895,
                0.9999993524050473,
                0.9999986290427931,
                0.9999991684718732,
                0.9999974387177893
            ],
            [
                1.6701425824733193e-05,
                3.535625913952226e-05,
                2.1444940744864302e-05,
                1.6701423832586287e-05,
                1.6701423834591316e-05,
                2.9023116391675407e-06,
                7.889263525893087e-06,
                8.939695237666677e-06,
                1.892515500388139e-05,
                6.144175333926503e-06
            ],
            [
                1.5534971989809095e-06,
                1.1478764016780948e-05,
                7.338211554591642e-07,
                5.422217677028889e-06,
                1.553497384180408e-06,
                7.338209805170655e-07,
                1.3709576971242028e-06,
                7.338212429504183e-07,
                4.222834451169694e-06,
                1.209865827740176e-06
            ],
            [
                0.9999945777784449,
                0.9999977396762411,
                0.9999957771650454,
                0.9999990577549568,
                0.9999962733611603,
                0.9999938558224682,
                0.9999982396569965,
                0.9999987901343165,
                0.9999977396748938,
                0.9999989322975118
            ],
            [
                0.9999930377429208,
                0.9999982396567867,
                0.9999986290426297,
                0.9999930377462403,
                0.9999989322966208,
                0.9999987901340279,
                0.9999974387171786,
                0.9999938558261305,
                0.9999977396765105,
                0.9999998874649318
            ],
            [
                0.9999980052693274,
                0.9999980052698029,
                0.9999991684718732,
                0.9999957771655487,
                0.9999997897567341,
                0.9999962733616045,
                0.9999982396559473,
                0.9999982396559473,
                0.9999957771665555,
                0.9999987901337395
            ],
            [
                0.9999974387187053,
                0.9999980052707541,
                0.9999987901337396,
                0.9999987901346049,
                0.9999980052709918,
                0.9999996533673375,
                0.999998629042303,
                0.9999984465015047,
                0.9999977396757022,
                0.9999986290424664
            ],
            [
                0.9999982396572064,
                0.9999990577555185,
                0.9999974387184,
                0.9999993524054334,
                0.999999057755743,
                0.9999993524054334,
                0.9999991684722697,
                0.9999977396759716,
                0.9999938558275958,
                0.9999970976866309
            ],
            [
                0.9999945777810303,
                0.9999885212277695,
                0.9999982396569965,
                0.9999957771675623,
                0.9999945777823231,
                0.9999967112497585,
                0.9999993524049702,
                0.9999967112501505,
                0.9999977396746244,
                0.9999898700126431
            ],
            [
                0.9999810748562713,
                0.9999810748495038,
                0.9999852610233005,
                0.9999898700066053,
                0.9999785550592574,
                0.999991060306893,
                0.9999885212359795,
                0.9999898700053974,
                0.99997246431547,
                0.9999898700090202
            ],
            [
                0.9999930377429234,
                0.9999930377454138,
                0.9999810748472637,
                0.9999921107345937,
                0.9999910603005017,
                0.9999869928715396,
                0.9999910603036979,
                0.9999945777829701,
                0.9999869928699899,
                NaN
            ],
            [
                0.9999910603026304,
                0.9999967112497584,
                0.9999977396757022,
                0.9999993524050473,
                0.9999984465016899,
                0.9999980052698029,
                0.9999962733611603,
                0.999997097689053,
                0.9999982396574162,
                0.9999992661786695
            ],
            [
                3.288747889038086e-06,
                1.892515500808112e-05,
                4.00636778604994e-05,
                8.939697368500698e-06,
                8.939694170729447e-06,
                2.5612812945260317e-06,
                7.889261643899223e-06,
                1.0129992186939844e-05,
                1.9947301970451086e-06,
                1.1478773598538445e-05
            ],
            [
                0.9999952149037942,
                0.9999957771665554,
                0.999994577782323,
                0.9999957771650453,
                0.9999990577556307,
                0.9999952149072165,
                0.9999996533675028,
                0.999999352405279,
                0.9999970976873229,
                0.9999980052702785
            ],
            [
                0.9999869928699877,
                0.9999974387184,
                0.9999980052693274,
                0.999995214904935,
                0.9999952149055054,
                0.9999989322971299,
                0.9999982396574163,
                0.9999970976873228,
                0.9999910603036959,
                0.9999996533675028
            ],
            [
                0.9999996940977366,
                0.9999962733611603,
                0.9999994284993486,
                0.9999997300421581,
                0.9999991684720715,
                0.9999989322972572,
                0.9999987901338837,
                0.9999974387165679,
                0.9999970976883609,
                0.9999996940976636
            ],
            [
                0.9999962733589389,
                0.9999970976890528,
                0.999999266179107,
                0.9999945777803839,
                0.9999967112493664,
                0.999999352405279,
                0.9999974387180947,
                0.9999962733620487,
                0.9999970976866309,
                0.9999938558239332
            ],
            [
                0.9999930377412604,
                0.9999980052700407,
                0.9999982396572064,
                0.9999962733589389,
                0.9999990577555183,
                0.9999724643089074,
                0.9999967112493665,
                0.9999970976883609,
                0.999997438717484,
                0.9999967112501504
            ],
            [
                0.9999990577549568,
                0.999999266179107,
                0.9999996533673788,
                0.999998239656367,
                0.9999952149032237,
                0.9999994956527121,
                0.9999991684721706,
                0.9999952149060758,
                0.9999989322966208,
                0.999997438716568
            ],
            [
                0.9999957771655487,
                0.9999962733611603,
                0.9999989322967481,
                0.9999987901346049,
                0.9999989322971299,
                0.999995777166052,
                0.9999994956523512,
                0.9999921107345932,
                0.9999984465018751,
                0.9999810748517607
            ],
            [
                0.9999962733589389,
                0.9999989322973846,
                0.9999982396563669,
                0.9999945777803838,
                0.9999996533672962,
                0.9999930377420905,
                0.9999967112517187,
                0.9999996940978461,
                0.9999974387168733,
                0.9999984465015046
            ],
            [
                0.9999989322966208,
                0.9999957771650453,
                0.9999982396567867,
                0.9999994284993486,
                0.9999974387177892,
                0.9999992661788445,
                0.9999993524050474,
                0.9999980052693274,
                0.9999982396561571,
                0.9999982396567867
            ],
            [
                0.9999991684720715,
                0.9999962733593832,
                0.9999991684719723,
                0.9999957771660521,
                0.9999921107345929,
                0.9999987901340279,
                0.9999994284994849,
                0.9999962733616046,
                0.9999990577555183,
                0.9999885212318759
            ],
            [
                0.9999921107402359,
                0.9999930377454105,
                0.9999852610162717,
                0.9999980052709919,
                0.999978555043919,
                0.9999930377412609,
                0.9999952149066464,
                0.9999930377420907,
                0.9999962733602719,
                0.9999898700090203
            ],
            [
                0.9999974387168733,
                0.9999992661792819,
                0.9999995549147358,
                0.9999898700090208,
                0.9999993524054334,
                0.9999852610232997,
                0.9999910603047617,
                0.999999266179107,
                0.9999989322968753,
                0.9999974387180945
            ],
            [
                0.9999990577556307,
                0.9999986290427932,
                0.9999967112501504,
                0.999998446502801,
                0.9999990577554061,
                0.9999994956524114,
                0.999999266179107,
                0.9999987901344607,
                0.999998629042303,
                0.9999974387171787
            ],
            [
                1.3709573702566696e-06,
                1.5534981249291695e-06,
                4.7850933535659155e-06,
                4.222835458044565e-06,
                4.785093353787868e-06,
                6.144176798132662e-06,
                5.422218969463855e-06,
                1.0677026154376365e-06,
                2.561282821352716e-06,
                1.3709576970949014e-06
            ],
            [
                0.9999997300422546,
                0.9999998144608983,
                0.9999984465026158,
                0.9999989322970027,
                0.9999996072136125,
                0.9999989322972572,
                0.9999984465020603,
                0.9999982396559473,
                0.9999980052705163,
                0.9999977396757022
            ],
            [
                0.9999980052693274,
                0.999997438717484,
                0.9999970976880149,
                0.9999910603026305,
                0.999992110740236,
                0.9999957771675624,
                0.9999984465020603,
                0.9999938558224684,
                0.999999057755743,
                0.9999945777784447
            ],
            [
                0.9999945777810302,
                0.9999992661790195,
                0.999998446502801,
                0.9999967112521109,
                0.9999970976880149,
                0.9999952149032237,
                0.9999984465026158,
                0.9999994284995529,
                0.9999974387171787,
                0.9999987901337395
            ],
            [
                0.9999756997512316,
                0.9999785550474106,
                1.0,
                0.9998766054154173,
                0.8175744784160989,
                0.9998766054550456,
                0.9999852610146434,
                0.9706877672877218,
                0.9149009526726545,
                0.9999869928749551
            ],
            [
                0.9999982396574162,
                0.9999982396567867,
                0.9999986290423029,
                0.9999982396572064,
                0.9999967112497584,
                0.9999984465024306,
                0.9999970976876689,
                0.9999996940976271,
                0.9999957771650453,
                0.9999977396746244
            ],
            [
                0.9999986290424663,
                0.9999977396762411,
                0.9999952149043644,
                0.9999994284997573,
                0.9999982396559473,
                0.999999057755743,
                0.999995777166052,
                0.9999996533672962,
                0.9999967112509346,
                0.9999977396757022
            ],
            [
                0.9999957771660528,
                0.9999832985701939,
                0.9999038975966703,
                0.999983298578219,
                0.9999967112501538,
                0.9999885212264085,
                0.9999151889283604,
                0.9996200154243915,
                0.9999810748450022,
                0.9999910603068946
            ],
            [
                0.9999810748427385,
                0.999998790134028,
                0.9999990577549568,
                0.9999646437535039,
                0.9999952149060757,
                0.9999982396569965,
                0.9999832985721853,
                0.9999962733602716,
                0.9999984465024306,
                0.9999993524052018
            ],
            [
                0.9999952149060757,
                0.9999977396765105,
                0.9999957771660523,
                0.9999957771660521,
                0.9999952149055052,
                0.9999991684722697,
                0.9999967112501507,
                0.9999957771650454,
                0.9999952149066462,
                0.9999930377454104
            ],
            [
                0.9999993524048946,
                0.9999785550593633,
                0.7057850278370112,
                0.9525741303566527,
                0.5,
                0.9999599363078626,
                0.9241418252018903,
                0.9999832985801506,
                0.9626731135929119,
                0.2689414272294874
            ],
            [
                0.9999038975392522,
                0.9999984465024306,
                0.9999852610162724,
                0.9999982396574162,
                0.9999982396569965,
                0.9999967112509346,
                0.999996273360716,
                0.9999980052707541,
                0.999997438716568,
                0.9999921107336526
            ],
            [
                0.9999898700126431,
                0.9999957771650453,
                0.9999974387184,
                0.9999938558232012,
                0.999972464315472,
                0.9999991684719723,
                0.9999980052693275,
                0.9999957771680659,
                0.9999930377404308,
                0.999991060303696
            ],
            [
                0.9999869928746379,
                0.9999885212264021,
                0.9999885212318762,
                0.9999910603004993,
                0.9999967112517187,
                0.9999910603058283,
                0.9999938558239337,
                0.9999930377445805,
                0.999992110739296,
                0.999992110738355
            ],
            [
                0.9999852610233002,
                0.9999962733598274,
                0.9999945777784448,
                0.9999970976880148,
                0.9999987901347492,
                0.9999945777803838,
                0.9999910603047619,
                0.9999987901343165,
                0.9999982396569965,
                0.999995777166052
            ],
            [
                0.00013982212373432013,
                4.006370650070828e-05,
                0.9995694429123752,
                2.753570422573402e-05,
                0.9999646437577681,
                3.5356263316996617e-05,
                NaN,
                3.12019002122609e-05,
                NaN,
                2.430023491169112e-05
            ],
            [
                0.7981867729389246,
                0.9999599363144809,
                0.9820137941832265,
                0.8807970795424087,
                0.9999756997595721,
                0.9999687980813213,
                0.9999945777810685,
                0.8933094039240554,
                0.9999810748452018,
                0.9999339478715565
            ],
            [
                0.9999986290431201,
                0.9999977396748938,
                0.9999987901343165,
                0.9999991684719723,
                0.9999977396759716,
                0.9999989322972572,
                0.9999986290423029,
                0.9999921107374145,
                0.9999970976869769,
                0.9999967112517187
            ],
            [
                0.9999832985721836,
                0.9999967112517187,
                0.9999974387187053,
                0.9999974387184,
                0.9999952149072167,
                0.9999957771675623,
                0.9999945777797375,
                0.9999967112513268,
                0.9999982396561572,
                0.9999945777810303
            ],
            [
                0.9999989322972572,
                0.9999910603068933,
                0.9999938558239335,
                0.9999962733593832,
                0.9999921107402364,
                0.999992110740236,
                0.9999910603004994,
                0.9999852610110019,
                0.9999962733620487,
                0.9999970976890528
            ],
            [
                0.9999977396746244,
                0.9999980052693274,
                0.9999962733620488,
                0.9999994284995529,
                0.9999984465016899,
                0.9999980052705163,
                0.9999962733611604,
                0.9999974387184,
                0.9999990577552939,
                0.9999977396746244
            ],
            [
                0.9999952149072165,
                0.9999832985841289,
                0.9999785550490304,
                0.9999938558239342,
                0.9999910603026305,
                0.9999970976890528,
                0.9999724642957707,
                0.9999938558268631,
                0.9999984465022455,
                0.9999869928715366
            ],
            [
                0.9999991684716749,
                0.9999910603058275,
                0.9999967112521109,
                0.9999930377445804,
                0.999999694097846,
                0.9999993524054335,
                0.9999984465015047,
                0.9999977396757022,
                0.9999957771655487,
                0.9999977396748938
            ],
            [
                0.9998204719492866,
                2.1444940734059286e-05,
                0.9998204719924526,
                0.9997040427971915,
                0.9997965730529265,
                4.006370171895837e-05,
                0.9999646437577393,
                0.9999417087414828,
                0.9998766054255039,
                0.999704042833986
            ],
            [
                0.9999987901337396,
                0.999997097686977,
                0.9999967112493664,
                0.9999970976883608,
                0.9999962733602717,
                0.9999997617631469,
                0.99999862904312,
                0.9999938558232011,
                0.9999986290421394,
                0.9999945777816766
            ],
            [
                0.9999921107392958,
                0.9999930377429206,
                0.9999957771675624,
                0.999997438717484,
                0.9999980052705163,
                0.9999970976880148,
                0.9999910603036963,
                0.9999980052705163,
                0.9999930377437506,
                0.9999938558246659
            ],
            [
                0.9999785550413652,
                0.9999417087068805,
                0.9999756997505845,
                0.9999885212305096,
                0.9999151889890433,
                0.9997694933410333,
                0.9999151889485385,
                0.9999910603047628,
                0.9999151889386623,
                0.9999646437451225
            ],
            [
                0.9999990577552937,
                0.9999930377437504,
                0.9999957771680656,
                0.9999982396569966,
                0.9999970976880148,
                0.9999974387180947,
                0.9999967112517187,
                0.9999970976887068,
                0.9999930377445805,
                0.9999977396754327
            ],
            [
                0.9999984465018751,
                0.9999945777810304,
                0.9999921107364741,
                0.9999910603015654,
                0.9999977396757022,
                0.9999967112521109,
                0.9999962733589389,
                0.9999952149037944,
                0.9999938558268634,
                0.9999938558275958
            ],
            [
                0.9999952149032239,
                0.9999982396565769,
                0.9999962733607161,
                0.9999980052705163,
                0.9999977396765105,
                0.9999993524051246,
                0.9999957771665557,
                0.999998790134028,
                0.9999991684716749,
                0.9999957771660523
            ],
            [
                0.9999957771675624,
                0.9999986290427931,
                0.9999945777829693,
                0.9999785550592557,
                0.9999967112509346,
                0.9999921107374145,
                0.9999952149032235,
                0.999997438716568,
                0.9999938558239332,
                0.9999910602994334
            ],
            [
                0.999998446502801,
                0.9999977396754327,
                0.9999974387168732,
                0.9999930377420906,
                0.9999952149049349,
                0.9999869928746372,
                0.9999967112501504,
                0.9999986290424663,
                0.9999977396765104,
                0.9999885212346115
            ],
            [
                0.999996273358939,
                0.9999970976883609,
                0.9999921107355343,
                0.9999984465024306,
                0.9999977396746244,
                0.9999910603047619,
                0.9999997300420937,
                0.9999957771675624,
                0.9999977396765105,
                0.9999910603015651
            ],
            [
                0.9999991684721706,
                0.9999898700090204,
                0.9999898700090213,
                0.9999967112493664,
                0.9999970976887068,
                0.9999967112493664,
                0.9999980052693274,
                0.9999970976866309,
                0.999999057755743,
                0.9999974387184
            ],
            [
                0.9999991684718733,
                0.9999993524051246,
                0.9999991684715758,
                0.9999977396762411,
                0.9999980052700407,
                0.9999970976873229,
                0.9999994284996893,
                0.9999991684717741,
                0.9999993524053562,
                0.9999962733598274
            ],
            [
                1.4738981969615573e-05,
                2.9023126769050284e-06,
                5.422217676979575e-06,
                8.939697367703906e-06,
                1.8925148238291944e-05,
                3.7266410609940346e-06,
                1.0129987357020188e-05,
                1.0129988564716393e-05,
                7.889262585441413e-06,
                3.726638839656906e-06
            ],
            [
                0.9999962733598274,
                0.9999957771680656,
                0.9999977396754327,
                0.9999910602994334,
                0.9999967112501505,
                0.9999910602994336,
                0.9999921107345932,
                0.9999957771660523,
                0.9999945777784449,
                0.9999938558275955
            ],
            [
                0.9999852610145148,
                0.9999599363221412,
                0.9999151889889724,
                0.9999921107364745,
                0.9999687980812239,
                0.9999724643187504,
                0.9999898700090203,
                0.9999151889283684,
                0.999954602147616,
                0.9999546021368129
            ],
            [
                0.999998790134028,
                0.9999982396572065,
                0.9999967112509347,
                0.9999994284997574,
                0.9999993524051246,
                0.999995214903794,
                0.9999967112513266,
                0.9999984465016898,
                0.9999952149037942,
                0.999998629042303
            ],
            [
                0.9999938558261304,
                0.9999970976880148,
                0.9999987901347492,
                0.9999982396563669,
                0.999995777166052,
                0.9999996940977731,
                0.9999957771645418,
                0.9999989322967481,
                0.9999921107355335,
                0.9999986290421394
            ],
            [
                0.9999756997592695,
                0.9999962733620487,
                0.9999646437619418,
                0.9999898700041914,
                0.9999832985801506,
                0.9999898700041909,
                0.9999339478238459,
                0.999964643732444,
                0.999983298580152,
                0.9999977396762411
            ],
            [
                5.422218969720291e-06,
                4.450850519360903e-07,
                1.7603438428188364e-06,
                4.785095065045315e-06,
                1.0677033791437343e-06,
                6.962255419279419e-06,
                6.144173869312763e-06,
                5.043472278255469e-07,
                3.927862938991851e-07,
                1.994729959224386e-06
            ],
            [
                6.475950297971703e-07,
                1.9947301970287804e-06,
                1.3709576970949014e-06,
                1.5534977545384963e-06,
                2.5612822106654943e-06,
                1.994730434778778e-06,
                2.9023130230133794e-06,
                1.7603425837606927e-06,
                1.7603436329714805e-06,
                2.26032348933062e-06
            ],
            [
                0.999998005269803,
                0.9999962733620487,
                0.9999994284997573,
                0.9999997897565587,
                0.9999980052709918,
                0.9999989322971299,
                0.9999957771655487,
                0.9999984465020603,
                0.9999993524050474,
                0.999999352404893
            ],
            [
                0.999997097686977,
                0.9999992661791944,
                0.9999962733602716,
                0.9999980052705163,
                0.9999986290421394,
                0.9999984465016899,
                0.9999957771645419,
                0.9999994284996211,
                0.9999992661790195,
                0.9999970976883608
            ],
            [
                0.9999967112493665,
                0.9999957771680656,
                0.9999991684720715,
                0.999999789756684,
                0.9999980052707541,
                0.9999982396569965,
                0.9999984465026158,
                0.9999898700041898,
                0.9999989322975118,
                0.9999952149037942
            ],
            [
                0.9999974387183999,
                0.9999974387177893,
                0.9999994956527121,
                0.999998790134605,
                0.999999266178932,
                0.9999967112509346,
                0.9999986290432834,
                0.9999997617631184,
                0.9999996533672136,
                0.9999967112509347
            ],
            [
                0.9999989322971299,
                0.9999970976876689,
                0.9999986290427932,
                0.999996273358939,
                0.9999992661790195,
                0.9999967112509347,
                0.9999980052702785,
                0.9999974387168733,
                0.9999996940978095,
                0.9999982396569965
            ],
            [
                0.9999962733616046,
                0.9999970976890529,
                0.9999974387187053,
                0.9999974387171787,
                0.9999982396561572,
                0.9999921107392955,
                0.9999938558232009,
                0.9999974387184,
                0.9999962733593832,
                0.9999962733602719
            ],
            [
                1.0129988563546333e-05,
                1.14787708624228e-05,
                5.422220231521372e-06,
                7.889260704179641e-06,
                1.760343213227212e-06,
                3.726638395527247e-06,
                1.8925141472773765e-05,
                3.7266392839832006e-06,
                6.144172404302622e-06,
                6.144175333926503e-06
            ],
            [
                0.9999982396559473,
                0.9999987901343165,
                0.9999974387180947,
                0.9999785550592568,
                0.9999885212359804,
                0.9999977396765105,
                0.9999885212305062,
                0.9999957771655487,
                0.9999980052707541,
                0.9999989322966208
            ],
            [
                0.9999952149072167,
                0.9999982396561572,
                0.9999987901343165,
                0.9999945777816768,
                0.999997438717484,
                0.9999987901346049,
                0.999997097686977,
                0.9999898700102289,
                0.999996273360716,
                0.9999970976887068
            ],
            [
                0.9999967112509346,
                0.999998446502801,
                0.9999990577551814,
                0.999998790134028,
                0.999998239656367,
                0.9999987901338838,
                0.9999962733593831,
                0.9999982396563669,
                0.9999957771645419,
                0.999985261021544
            ],
            [
                0.9999997300421581,
                0.9999967112493665,
                0.999999495652652,
                0.9999986290432834,
                0.9999986290431201,
                0.9999910602994331,
                0.9999994284992805,
                0.9999977396751633,
                0.9999974387180947,
                0.9999945777829693
            ],
            [
                0.9999991684721706,
                0.9999952149032236,
                0.9999974387171787,
                0.9999997300422547,
                0.9999997300421581,
                0.9999980052700408,
                0.9999986290432834,
                0.9999984465022455,
                0.9999995549147358,
                0.9999995549150542
            ],
            [
                0.9999687980849252,
                0.9999485578048419,
                0.9999910603068937,
                0.9999885212359879,
                0.9999957771675629,
                0.9999921107355337,
                0.9999945777823243,
                0.9999852610127683,
                0.9999869928699912,
                0.999986992869988
            ],
            [
                0.9999987901338837,
                0.9999989322967482,
                0.9999989322968754,
                0.9999989322972572,
                0.999998005269803,
                0.9999952149037941,
                0.9999984465015046,
                0.9999980052695652,
                0.9999982396561571,
                0.9999994284992805
            ],
            [
                0.9999962733593831,
                0.9999990577549568,
                0.9999945777797375,
                0.9999945777810304,
                0.9999995549147358,
                0.9999991684717741,
                0.9999998144608981,
                0.9999982396565769,
                0.9999977396762411,
                0.9999987901341723
            ],
            [
                0.9999967112493666,
                0.9999991684722697,
                0.9999984465020603,
                0.9999962733611601,
                0.9999962733620487,
                0.999998239656367,
                0.9999994956525317,
                0.9999921107374146,
                0.9999993524052018,
                0.9999990577556308
            ],
            [
                0.9999967112505425,
                0.9999938558275954,
                0.9999898700053974,
                0.9999957771670588,
                0.9999974387177893,
                0.9999970976876689,
                0.9999957771665554,
                0.9999992661791944,
                0.9999962733602717,
                0.9999952149072167
            ],
            [
                0.9999996072139402,
                0.999997438717484,
                0.9999967112501505,
                0.9999938558246657,
                0.9999980052695652,
                0.9999957771670591,
                0.9999938558268633,
                0.9999982396569966,
                0.9999962733616043,
                0.9999986290432835
            ]
        ]
    },
    {
        "q_id": "8637_mmlu_math",
        "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,
            31,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            50,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            75,
            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,
            110,
            111,
            112,
            114,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126
        ],
        "rewards": [
            [
                7.889261641674914e-06,
                2.260324836567261e-06,
                3.7266397282926013e-06,
                6.962255419570695e-06,
                8.93969630362837e-06,
                8.9396941718352e-06,
                3.2887486731641103e-06,
                6.962257909501028e-06,
                4.785093923916815e-06,
                2.2603234890695403e-06
            ],
            [
                5.422217674780147e-06,
                1.5534973839359769e-06,
                2.561281294644835e-06,
                1.067702615468225e-06,
                1.4738987238893715e-05,
                8.939699500766203e-06,
                1.1478769491598686e-05,
                1.99472900777306e-06,
                2.2603234893861252e-06,
                7.889263525663481e-06
            ],
            [
                1.3007126911004571e-05,
                2.561283431986506e-06,
                4.006369692540368e-05,
                2.7535694366751658e-05,
                7.48462531561405e-05,
                6.144173136455602e-06,
                2.5612819053166966e-06,
                1.3007131560621253e-05,
                5.422219616184461e-06,
                5.82912515784739e-05
            ],
            [
                7.484620932198124e-05,
                5.829128633093081e-05,
                2.7535694375867267e-05,
                1.1478766754064213e-05,
                4.0063682618927264e-05,
                1.4738987234014356e-05,
                2.4300237824258528e-05,
                2.144494074076854e-05,
                3.535624646947797e-05,
                NaN
            ],
            [
                3.535625491265802e-05,
                6.962258739530771e-06,
                4.222834954514924e-06,
                2.753568453191415e-05,
                3.120190764716959e-05,
                7.484621823550934e-05,
                1.4738980207363312e-05,
                2.5612816000145246e-06,
                2.4300246515109972e-05,
                2.5612812945889277e-06
            ],
            [
                1.8925148232267744e-05,
                1.4738976698757546e-05,
                2.1444956061196638e-05,
                2.753569108573408e-05,
                1.8925145978942173e-05,
                8.939697369151141e-06,
                6.962258738131379e-06,
                1.3007126911643378e-05,
                1.8925152747388e-05,
                1.4738981970312625e-05
            ],
            [
                1.0129990954929888e-05,
                1.0129994597155795e-05,
                2.260324028351814e-06,
                NaN,
                2.1444956079842134e-05,
                1.670142183825232e-05,
                1.0129990979547237e-05,
                8.939697368663308e-06,
                NaN,
                1.7603434228007435e-06
            ],
            [
                3.535625910055016e-05,
                4.222833947359807e-06,
                1.5534975692259223e-06,
                4.22283193393364e-06,
                9.42244481461251e-07,
                1.4738988994015443e-05,
                1.370957370236096e-06,
                6.144177530548804e-06,
                6.144175334015912e-06,
                2.9023109468548636e-06
            ],
            [
                7.889260704050487e-06,
                2.7535704220525098e-05,
                6.962257079376403e-06,
                1.6701425818232042e-05,
                1.670141786036971e-05,
                7.889263524443698e-06,
                8.939696302831578e-06,
                1.3007125357804606e-05,
                1.6701419852090592e-05,
                4.222834954561012e-06
            ],
            [
                5.422218969029887e-06,
                4.2228324375512536e-06,
                8.481106129821764e-05,
                3.1201907614819715e-05,
                2.2603245672867952e-06,
                2.1444956075707356e-05,
                4.785096205830278e-06,
                5.1442219756013625e-05,
                4.006368258117931e-05,
                4.222832437324657e-06
            ],
            [
                1.8925152751174644e-05,
                1.0129987355785634e-05,
                1.4738987240475486e-05,
                3.535624649172935e-05,
                3.535625912717466e-05,
                2.1444948410303962e-05,
                4.539786320660675e-05,
                2.4300246515109972e-05,
                3.1201918806289706e-05,
                6.144173867608406e-06
            ],
            [
                4.539787941498982e-05,
                1.0129993393742954e-05,
                1.3007126912542439e-05,
                9.610242603456664e-05,
                1.8925145979561802e-05,
                3.1201911358551906e-05,
                6.144172403715875e-06,
                2.7535681210027785e-05,
                6.962259563418482e-06,
                9.610240306264051e-05
            ],
            [
                0.9999852610127603,
                0.9999756997679626,
                0.9999869928715365,
                0.9999967112509347,
                0.9999977396759716,
                0.9999869928761898,
                0.9999910603015663,
                0.9999957771680661,
                0.9999945777816767,
                0.9999810748540229
            ],
            [
                7.889259764273619e-06,
                2.5612834318257725e-06,
                1.4738981968462759e-05,
                0.9997965731023288,
                1.892514147046736e-05,
                4.2228319339950885e-06,
                2.561282515820982e-06,
                0.9999687980886276,
                2.5612834317535587e-06,
                NaN
            ],
            [
                3.1201918798457626e-05,
                3.1201922520397544e-05,
                4.006368261266023e-05,
                5.1442232005568484e-05,
                3.288749457383046e-06,
                1.4738987236641703e-05,
                3.120190391705884e-05,
                1.0129995807165349e-05,
                2.4300231977554073e-05,
                1.012999459535003e-05
            ],
            [
                6.144173868044274e-06,
                1.147876812538911e-05,
                2.2603242978007868e-06,
                4.785096775676685e-06,
                4.7850967763512445e-06,
                1.7603438428564603e-06,
                6.962257909412379e-06,
                6.144173136645595e-06,
                7.889264465699106e-06,
                4.222834451012227e-06
            ],
            [
                5.422218969029887e-06,
                4.006371119588617e-05,
                5.8291258507843456e-05,
                6.962253759043525e-06,
                7.889265406681968e-06,
                2.1444943291142893e-05,
                5.422218322457301e-06,
                2.1444956064317223e-05,
                4.006369207500901e-05,
                3.120191134118513e-05
            ],
            [
                8.9397005654763e-06,
                2.4300240718880753e-05,
                3.535625911829982e-05,
                8.939698434966738e-06,
                6.144174600985344e-06,
                3.1201918794144304e-05,
                4.222834954514924e-06,
                3.120190019932095e-05,
                2.1444945849006956e-05,
                2.7535681240079227e-05
            ],
            [
                2.5612828211442287e-06,
                1.0677024881004167e-06,
                1.7603425834564988e-06,
                4.7850950649408664e-06,
                2.9023133690188264e-06,
                6.475946437928669e-07,
                8.315278293407441e-07,
                1.2098658276730537e-06,
                8.315278292794863e-07,
                2.4300243577612267e-05
            ],
            [
                7.889261644501938e-06,
                2.4300249417247375e-05,
                3.2887494573232236e-06,
                1.8925157261545463e-05,
                1.3007133111929193e-05,
                1.3007123812057577e-05,
                4.5397874044343825e-05,
                6.962256249429175e-06,
                7.889259762666377e-06,
                6.144173136556186e-06
            ],
            [
                0.9994472213203381,
                0.40733340004593027,
                0.9999646437535097,
                0.9994472213219783,
                0.9998204719918885,
                0.999876605454541,
                0.9998204719538916,
                0.9840936048768523,
                0.9999251537729164,
                0.9999756997534762
            ],
            [
                1.0129992177800467e-05,
                3.726640172337686e-06,
                4.785096775998733e-06,
                6.144176799099397e-06,
                6.9622537593854575e-06,
                8.315279284430651e-07,
                6.144172403715875e-06,
                1.0129990976728036e-05,
                2.90231094702116e-06,
                7.889261644760245e-06
            ],
            [
                4.78509563546605e-06,
                1.9947306725451314e-06,
                1.9947301968963442e-06,
                1.5534975688557435e-06,
                3.927862002606139e-07,
                6.14417460073947e-06,
                2.260323489435463e-06,
                NaN,
                1.0129994598482479e-05,
                6.475951069696694e-07
            ],
            [
                NaN,
                3.535626333461766e-05,
                2.144494328685209e-05,
                6.962257908487893e-06,
                1.670142979608617e-05,
                4.785093353352668e-06,
                2.144494328950459e-05,
                NaN,
                1.8925141470949294e-05,
                8.939699499823059e-06
            ],
            [
                1.3007128445182463e-05,
                4.539786305929388e-05,
                4.222833444467892e-06,
                0.9999967112497584,
                2.4300252313904224e-05,
                0.999996273358939,
                2.430023781444595e-05,
                1.0129987356191011e-05,
                0.9999989322966208,
                0.9999996072136125
            ],
            [
                1.6701423833831836e-05,
                1.0129988561077228e-05,
                1.6701423832586287e-05,
                1.3007123811797321e-05,
                3.5356259128846735e-05,
                6.144175333837093e-06,
                7.484625386131644e-05,
                1.3007123812057577e-05,
                1.4738985483128763e-05,
                5.144223200893693e-05
            ],
            [
                4.222835458044565e-06,
                1.5534977544565482e-06,
                3.288748281220719e-06,
                6.144177530291754e-06,
                6.962257079059797e-06,
                3.7266388397721442e-06,
                2.260323489490968e-06,
                2.5612819053399912e-06,
                2.5612828211442287e-06,
                1.4738983726908257e-05
            ],
            [
                4.7850956342431385e-06,
                1.300713466420736e-05,
                0.9999977396751633,
                1.6701417850314193e-05,
                0.9999980052707541,
                1.300712846115264e-05,
                1.6701419849447602e-05,
                1.6701421844085127e-05,
                0.9999967112517187,
                2.430024072091399e-05
            ],
            [
                3.120192623257619e-05,
                2.430024362393472e-05,
                0.0001233946332632821,
                1.6701423833831836e-05,
                0.00010889689604980399,
                3.5356267564055315e-05,
                3.12019262448351e-05,
                3.1201915067096954e-05,
                1.473897670007122e-05,
                5.144223200893693e-05
            ],
            [
                5.1442225836439433e-05,
                5.829128617783064e-05,
                3.120192252686752e-05,
                4.006368733713007e-05,
                5.1442195242316055e-05,
                2.1444958633416914e-05,
                3.5356242267696286e-05,
                5.829126545587422e-05,
                1.4738987240100149e-05,
                1.670142780084011e-05
            ],
            [
                5.829125847900465e-05,
                3.120192250564146e-05,
                5.829125154581821e-05,
                1.8925150482908516e-05,
                7.889266345196678e-06,
                1.8925143722381014e-05,
                5.82912723385944e-05,
                2.4300249409733237e-05,
                3.120190020068305e-05,
                1.6701417861584877e-05
            ],
            [
                0.9999952149066462,
                0.9999987901344607,
                0.9999986290432835,
                0.9999930377412684,
                0.9999974387184,
                0.999999554914842,
                0.9999970976880149,
                0.999989870007814,
                0.9999991684717742,
                0.9999417087483837
            ],
            [
                0.00023050668547308019,
                4.785093923916815e-06,
                0.00012339455938231966,
                5.14422072852669e-05,
                1.6701415863393463e-05,
                6.144175328707254e-06,
                6.60521682560438e-05,
                2.144495608046625e-05,
                6.605212882650343e-05,
                1.4738981969240237e-05
            ],
            [
                0.9999832985761689,
                0.9999251537549417,
                0.9999910603059669,
                0.9999869928715365,
                0.017986211705757406,
                0.9999599363221447,
                0.9999646437577469,
                0.99984156372691,
                0.9999756997476794,
                0.7981867705385762
            ],
            [
                6.962254589528684e-06,
                5.04347528438253e-07,
                4.22283394762097e-06,
                5.71500583272315e-07,
                7.338210679622478e-07,
                1.9947306726594253e-06,
                2.1024331597066579e-07,
                1.2098661161107252e-06,
                6.962255419051463e-06,
                5.715004470025379e-07
            ],
            [
                0.9999952149060757,
                0.9999921107364742,
                0.9999810748428698,
                0.999998446502801,
                0.9999339478239194,
                0.9999910603015648,
                0.9999599363030566,
                0.9999852610110015,
                0.9999982396569965,
                0.9999756997477076
            ],
            [
                0.9991959139614848,
                0.9998415637268017,
                0.9995694430176015,
                0.9995694428642522,
                0.9997040429718298,
                0.9997965730518255,
                0.9999038975507893,
                0.9995121427683967,
                8.481107147426634e-05,
                0.9999724643089107
            ],
            [
                1.892515274546026e-05,
                0.999998790134605,
                5.829129326115268e-05,
                0.9999962733620489,
                0.00010889693488397425,
                0.00026119039592822544,
                6.605216816041215e-05,
                2.430023491549239e-05,
                0.9999980052707542,
                2.430023493564795e-05
            ],
            [
                0.9999832985781584,
                0.9986749778448234,
                0.9999832985701935,
                0.9999038975851613,
                0.9999957771680658,
                0.9997040429053018,
                0.9998601779592853,
                0.9999921107355336,
                0.9999038976193724,
                0.9999967112521109
            ],
            [
                2.4300243613326524e-05,
                2.753568780461672e-05,
                6.144174599353632e-06,
                9.610240313954919e-05,
                7.88925976397226e-06,
                2.753569434711804e-05,
                7.889265405333033e-06,
                4.785095064436034e-06,
                1.1478764020560142e-05,
                3.120190391104291e-05
            ],
            [
                5.144221363404434e-05,
                3.1201922523121745e-05,
                1.4738978455701077e-05,
                5.829125152630961e-05,
                7.484625391903742e-05,
                1.4738976699106073e-05,
                3.535624225509145e-05,
                2.4300243626409964e-05,
                4.785095635413826e-06,
                4.5397852394305204e-05
            ],
            [
                1.473898548194914e-05,
                1.209865971934245e-06,
                7.889261644982674e-06,
                5.715003107525447e-07,
                1.0129990979031306e-05,
                5.043472879291295e-07,
                1.2098656833491588e-06,
                1.3709572068079696e-06,
                6.144177531007026e-06,
                2.902310946944611e-06
            ],
            [
                0.00013982205620869103,
                3.12019225291377e-05,
                8.939693105662367e-06,
                3.535624645738762e-05,
                1.3007129966868308e-05,
                1.1478770859624945e-05,
                2.4300249408672413e-05,
                2.1444945850567248e-05,
                1.6701423830702777e-05,
                7.484625372354849e-05
            ],
            [
                3.726639727526609e-06,
                1.1478770859624945e-05,
                2.7535704187167975e-05,
                7.484623609088468e-05,
                1.1478764017720528e-05,
                8.48110715470758e-05,
                3.120191869868376e-05,
                7.889260704179641e-06,
                3.1201911365248895e-05,
                1.670142781432848e-05
            ],
            [
                4.006371126555232e-05,
                3.535625066508635e-05,
                5.422220908481809e-06,
                3.120190019330501e-05,
                8.93969310647542e-06,
                6.144173868781898e-06,
                8.939698434332555e-06,
                6.962257906562937e-06,
                1.012998977213635e-05,
                1.4738983727900215e-05
            ],
            [
                2.1444943287710254e-05,
                5.144222587049821e-05,
                4.006371127619171e-05,
                3.7266383941918447e-06,
                6.60521288207367e-05,
                3.5356238040705445e-05,
                1.147876675548402e-05,
                3.53562633126235e-05,
                4.006369215458579e-05,
                4.785096205582214e-06
            ],
            [
                3.53562591107112e-05,
                2.1444950965282096e-05,
                7.484625395279873e-05,
                2.1444956075707356e-05,
                3.535626329924694e-05,
                4.00636777619758e-05,
                2.4300246521474893e-05,
                2.753569108573408e-05,
                1.012998977108606e-05,
                2.1444940740066406e-05
            ],
            [
                NaN,
                1.1478768116515313e-05,
                4.539785778179383e-05,
                1.0129988563546333e-05,
                5.8291293278964903e-05,
                8.48110613938572e-05,
                5.829127940791947e-05,
                1.6701421843356024e-05,
                3.535626754900668e-05,
                1.012998856015592e-05
            ],
            [
                7.338208054635517e-07,
                2.5612828206736765e-06,
                1.2098653950315304e-06,
                6.962257078819179e-06,
                8.93969950000193e-06,
                1.760343842833246e-06,
                8.315277302588544e-07,
                1.8925155006118952e-05,
                2.144495607336692e-05,
                1.3709578604831862e-06
            ],
            [
                1.1478765382509808e-05,
                1.1478773596847203e-05,
                1.0129989769464556e-05,
                2.1444940734059286e-05,
                1.8925150489517924e-05,
                1.892515274614874e-05,
                5.422220908402905e-06,
                2.144494329348333e-05,
                2.7535687798506256e-05,
                2.144495096785658e-05
            ],
            [
                1.670141784666869e-05,
                4.785096776068365e-06,
                2.1444940737257882e-05,
                1.1478768124553928e-05,
                3.120190391853445e-05,
                1.4738983724146862e-05,
                1.3007130011655787e-05,
                2.7535681218241846e-05,
                3.535624226936835e-05,
                1.670141584644187e-05
            ],
            [
                0.9999987901337396,
                0.9999599362887345,
                0.99999862904312,
                0.9999977396759716,
                0.9999996072137061,
                0.9999989322967481,
                0.9999984465020604,
                0.9999995549150542,
                0.9999977396751636,
                0.999738809568133
            ],
            [
                1.0677031245783732e-06,
                6.14417460073947e-06,
                5.715004469963006e-07,
                6.475945665523951e-07,
                4.785094494019719e-06,
                1.553497198908852e-06,
                3.288749065077638e-06,
                1.553497384180408e-06,
                9.422443691524936e-07,
                4.7850933529174686e-06
            ],
            [
                0.9996200155404558,
                0.9999599362935554,
                0.9999251537732343,
                0.9999724642957929,
                0.9999251537729087,
                0.9996200155163675,
                0.9986749778472881,
                0.40733340004593027,
                0.9999546021107577,
                0.999860177893202
            ],
            [
                9.422444815495185e-07,
                9.42244256886598e-07,
                2.561283126502453e-06,
                9.42244481511812e-07,
                1.553497569095936e-06,
                8.315284240985381e-07,
                7.338211554641698e-07,
                5.04347588554027e-07,
                3.7266388394569345e-06,
                3.288749064371741e-06
            ],
            [
                0.9999986290424664,
                0.9999977396751634,
                0.9997694932311779,
                NaN,
                0.9999967112509347,
                NaN,
                0.9999687980924115,
                0.9999339478475049,
                0.9999993524054334,
                0.9999938558275958
            ],
            [
                2.561282820128581e-06,
                3.2887502412970765e-06,
                8.939697354808876e-06,
                1.7603440525925705e-06,
                1.760343632774555e-06,
                2.260325375572331e-06,
                5.422217673754406e-06,
                6.962259565520738e-06,
                1.3709567164326847e-06,
                7.889264462470271e-06
            ],
            [
                0.1480472036701053,
                1.8925150493166868e-05,
                4.539788485433845e-05,
                0.9998601779872562,
                0.9997388096640026,
                1.8925141467059383e-05,
                0.05340332415026374,
                0.9964063981122133,
                0.9993736658998581,
                0.04208772626352764
            ],
            [
                3.726637950723161e-06,
                8.939700565102295e-06,
                6.475950297906914e-07,
                1.209865971934245e-06,
                1.2098659719441482e-06,
                1.0129992186589747e-05,
                8.939700565834043e-06,
                6.962253759670401e-06,
                9.422444815679433e-07,
                6.14417753110761e-06
            ],
            [
                1.3007125357804606e-05,
                2.753568780461672e-05,
                1.3007126912258525e-05,
                8.939699498587217e-06,
                3.5356267564055315e-05,
                1.892515274614874e-05,
                4.7850933535006355e-06,
                2.144494329769612e-05,
                1.147876949310201e-05,
                3.5356242238628006e-05
            ],
            [
                4.5397857734561226e-05,
                3.120191507481552e-05,
                2.1444953516281788e-05,
                4.0063711282021514e-05,
                1.8925143721072897e-05,
                6.605214442935156e-05,
                0.00020342694803547934,
                4.539788474963394e-05,
                2.7535700933696396e-05,
                1.8925148223661747e-05
            ],
            [
                1.147876812069122e-05,
                2.7535704219423216e-05,
                3.7266410604686857e-06,
                6.962254586824882e-06,
                6.605216824066585e-05,
                1.6701419848961534e-05,
                7.484622689092787e-05,
                NaN,
                8.93969309375927e-06,
                1.1478769491598686e-05
            ],
            [
                1.30071346612026e-05,
                7.8892625849535e-06,
                1.4738987240475486e-05,
                8.939695234723424e-06,
                3.726639283901856e-06,
                4.006369211844103e-05,
                7.889260703763482e-06,
                4.006371119297127e-05,
                1.147877222879974e-05,
                2.4300249418927004e-05
            ],
            [
                1.994729008074216e-06,
                3.288749065167371e-06,
                6.144174600180663e-06,
                5.422220262264056e-06,
                1.2098653949534047e-06,
                1.1478769490387674e-05,
                4.222832940777184e-06,
                1.300712691308661e-05,
                1.2098652507583041e-06,
                2.2603245672497918e-06
            ],
            [
                2.9023116390104826e-06,
                7.338213303475785e-07,
                2.9023130229209922e-06,
                4.006368730943852e-05,
                1.9947297212331575e-06,
                1.2098658276598493e-06,
                7.338208055229508e-07,
                4.222834954607099e-06,
                5.715007195228928e-07,
                5.043473480276735e-07
            ],
            [
                6.144176797730321e-06,
                1.8925152728867892e-05,
                2.260325105981383e-06,
                1.1478773598914277e-05,
                1.5534975692866768e-06,
                1.0129994601688632e-05,
                3.28874867308036e-06,
                1.3007131563507714e-05,
                2.1444950959196957e-05,
                1.4738978456398127e-05
            ],
            [
                0.9964063966724237,
                0.9995121428809076,
                0.9998204720767055,
                0.9998415637642979,
                0.9984988177956124,
                0.867035758084294,
                0.9991959140760156,
                0.9999251537549613,
                0.9999832985704725,
                0.9999646437535052
            ],
            [
                4.5397857701531434e-05,
                0.9999989322973845,
                4.5397863181173815e-05,
                4.0063692172075196e-05,
                1.1478773596575768e-05,
                6.144174601410037e-06,
                7.484621826273621e-05,
                2.7535681245588654e-05,
                1.3007133110320344e-05,
                1.670141785809127e-05
            ],
            [
                0.9999785550592607,
                0.9997694931764213,
                0.9998204720771783,
                0.005911069882350904,
                0.9994472214946998,
                0.9999974387187056,
                NaN,
                0.9999898700078147,
                0.34864513533394575,
                0.9992903297135496
            ],
            [
                7.88926352599354e-06,
                2.7535700944314574e-05,
                5.1442195201520414e-05,
                4.222832940715735e-06,
                3.7266410607194972e-06,
                6.962258738435319e-06,
                3.7266406165319545e-06,
                1.7603427935678977e-06,
                2.561282515914161e-06,
                6.144175333289463e-06
            ],
            [
                8.31528325021115e-07,
                0.9999687980923457,
                1.1478764018305152e-05,
                1.6701423832586287e-05,
                0.9999038975391943,
                1.0129995808418327e-05,
                4.222832437386106e-06,
                5.422217029943586e-06,
                0.999903897596522,
                2.902310947190096e-06
            ],
            [
                1.0129988563546333e-05,
                1.209865683500459e-06,
                6.962254589433702e-06,
                2.902312331125353e-06,
                7.88926634755014e-06,
                NaN,
                1.3007126913346863e-05,
                4.785093923982095e-06,
                6.144172403592939e-06,
                1.012998977022003e-05
            ],
            [
                0.999995777164665,
                0.9999938558224692,
                0.9997965730526305,
                0.999994577779739,
                0.8519527982093666,
                0.9999485577803114,
                0.999995777166556,
                0.9999852610127611,
                0.9999952149049358,
                0.9999546021259487
            ],
            [
                1.0129990979215566e-05,
                5.422220261544064e-06,
                2.902311639073834e-06,
                7.889259763857458e-06,
                1.6701415862785876e-05,
                1.5534975692471157e-06,
                5.144223817619536e-05,
                2.561282515662579e-06,
                1.1478765388314311e-05,
                1.473898372822193e-05
            ],
            [
                1.147876675162131e-05,
                1.8925157259824262e-05,
                2.7535691088138193e-05,
                6.962255418658875e-06,
                2.753568780802255e-05,
                1.4738985482753428e-05,
                0.9999945777823231,
                2.144494328864643e-05,
                0.00013982210691394165,
                1.4738985484549675e-05
            ],
            [
                2.144494838924002e-05,
                3.1201922487820644e-05,
                8.939699501132077e-06,
                6.605215217166799e-05,
                8.481101093197769e-05,
                1.47389819699641e-05,
                2.4300234925658572e-05,
                7.889265406681968e-06,
                6.605216031188985e-05,
                5.829127939137956e-05
            ],
            [
                3.120191506210258e-05,
                1.892515726099468e-05,
                0.00010889689603554361,
                5.1442207485876726e-05,
                0.0003799844740480833,
                0.0003353500998792239,
                2.430024939585418e-05,
                4.5397884864412536e-05,
                3.1201903906162046e-05,
                7.484623597326465e-05
            ],
            [
                2.4300243623139103e-05,
                9.610240335209681e-05,
                4.222831934052698e-06,
                1.4738978453743973e-05,
                3.1201907650801864e-05,
                1.8925150494750372e-05,
                1.1478765389065974e-05,
                5.422217030209884e-06,
                2.1444956075707356e-05,
                1.3007134662054344e-05
            ],
            [
                1.8925155006118952e-05,
                2.144494840531103e-05,
                NaN,
                4.0063692134764465e-05,
                4.006368736453013e-05,
                1.3007131561047124e-05,
                1.4738988981093183e-05,
                1.3007130014376633e-05,
                2.1444940725789744e-05,
                1.2098652508287273e-06
            ],
            [
                3.1201922487820644e-05,
                1.1478769491014062e-05,
                1.1478770859332632e-05,
                4.222833947282995e-06,
                1.4738976697631541e-05,
                7.889264465067689e-06,
                1.1478772229551402e-05,
                1.8925145980732218e-05,
                NaN,
                0.0
            ],
            [
                7.338212429087055e-07,
                4.450851049743049e-07,
                8.31527829351332e-07,
                6.47594952559303e-07,
                1.3709575335121232e-06,
                5.043474081785165e-07,
                3.4663274507098256e-07,
                1.2098659718990333e-06,
                1.0677032518501217e-06,
                7.338208055369664e-07
            ],
            [
                3.535623805163821e-05,
                1.8925150496161756e-05,
                2.1444956075707356e-05,
                4.5397879429522924e-05,
                4.0063701703217896e-05,
                0.0002305068215866244,
                4.539787403443489e-05,
                6.605212095395777e-05,
                1.1478772230198667e-05,
                9.610242620376576e-05
            ],
            [
                2.5612825160271407e-06,
                3.7266406163624873e-06,
                1.4738976697631541e-05,
                6.962253758916883e-06,
                1.0129994602057158e-05,
                1.1478766757049986e-05,
                4.785096776251149e-06,
                1.1478769493540482e-05,
                1.0129995804696242e-05,
                6.962258735839161e-06
            ],
            [
                3.535624648542694e-05,
                8.939695235959266e-06,
                4.5397868612593344e-05,
                1.0129994598482479e-05,
                5.8291258551949844e-05,
                3.535625904575771e-05,
                0.00010889692110211241,
                4.222835458044565e-06,
                1.6701415865641523e-05,
                2.753570418015596e-05
            ],
            [
                1.3007123811229494e-05,
                2.430023493485234e-05,
                5.42222155426567e-06,
                1.8925148239290237e-05,
                2.5612825159421147e-06,
                7.889262585642319e-06,
                2.561282210618905e-06,
                8.93969736942758e-06,
                7.889261644631091e-06,
                1.670142780381727e-05
            ],
            [
                1.76034300345598e-06,
                2.902310946944611e-06,
                2.5612831264675113e-06,
                4.78509563546605e-06,
                2.561282515853595e-06,
                1.7603430032662588e-06,
                6.144172403335888e-06,
                2.2603245671490605e-06,
                6.144174601309452e-06,
                3.2887494572873306e-06
            ],
            [
                6.962257908753841e-06,
                3.7266388394569345e-06,
                1.1478773595657069e-05,
                1.3007128460797749e-05,
                1.3007133114011233e-05,
                4.222832436955956e-06,
                1.670142183983204e-05,
                3.120190390775116e-05,
                1.6701423830702777e-05,
                6.144172404380855e-06
            ],
            [
                6.605216032919004e-05,
                8.939695237813028e-06,
                4.785093924103951e-06,
                1.3007126912542439e-05,
                2.4300252296223892e-05,
                2.1444956078515887e-05,
                3.7266392839832006e-06,
                6.144176799099397e-06,
                1.670142184171555e-05,
                6.144173868044274e-06
            ],
            [
                4.222831934202483e-06,
                5.829127242214212e-05,
                5.4222215541571775e-06,
                5.829125150043951e-05,
                1.8925152751174644e-05,
                7.88926634455091e-06,
                1.6701425823882575e-05,
                1.8925152749659986e-05,
                1.8925145957048516e-05,
                4.7850933534310035e-06
            ],
            [
                1.3007126910294786e-05,
                NaN,
                8.939694169330997e-06,
                4.7850950643402904e-06,
                6.144174600471243e-06,
                2.430024648072174e-05,
                6.144177531007026e-06,
                5.422218969601935e-06,
                NaN,
                2.430024072648329e-05
            ],
            [
                4.7850944945245504e-06,
                1.2098662603631479e-06,
                0.9924227581368514,
                6.144176799099397e-06,
                1.8925150457297062e-05,
                5.422220261198862e-06,
                0.9997040427600956,
                1.9947292457750883e-06,
                6.962259569117366e-06,
                5.422217030614265e-06
            ],
            [
                3.1201911339482505e-05,
                2.144494329496561e-05,
                1.4738978453743973e-05,
                5.1442195212374294e-05,
                8.481101089742407e-05,
                7.889262584350785e-06,
                6.144173868983067e-06,
                7.88925976397226e-06,
                1.6701425820540864e-05,
                1.4738985483128763e-05
            ],
            [
                4.006370649866785e-05,
                1.300712846115264e-05,
                3.5356267550807374e-05,
                1.3007128462785148e-05,
                4.5397890240179425e-05,
                4.5397868612593344e-05,
                7.889264466344872e-06,
                2.753569109925723e-05,
                2.1444956079218013e-05,
                4.0063682616886836e-05
            ],
            [
                3.2887506321698918e-06,
                5.715005151296257e-07,
                8.939698434966738e-06,
                1.2098652507583041e-06,
                3.2887506333394084e-06,
                5.422220908762902e-06,
                1.2098662603862553e-06,
                2.5612822106654943e-06,
                1.2098658276862581e-06,
                6.144175334015912e-06
            ],
            [
                1.6701421833391647e-05,
                2.1444943297072005e-05,
                1.6701429785817993e-05,
                4.006370648788271e-05,
                1.6701427813417103e-05,
                6.1441760667392215e-06,
                4.0063711282021514e-05,
                5.144221357715497e-05,
                2.7535684510878145e-05,
                6.962259569117366e-06
            ],
            [
                1.4738976699427788e-05,
                1.6701423833436905e-05,
                6.962259567914269e-06,
                3.535625906222117e-05,
                3.1201915071864306e-05,
                2.4300246517938825e-05,
                1.012999581021488e-05,
                1.4738978456049602e-05,
                2.4300234931404677e-05,
                6.605214452978877e-05
            ],
            [
                1.5534973841895917e-06,
                1.9947306726358406e-06,
                6.47594566597747e-07,
                1.1478770860982112e-05,
                1.1478765387416494e-05,
                8.93969630348202e-06,
                1.370957697068717e-06,
                5.4222183234485234e-06,
                2.9023133690425823e-06,
                3.2887506334560605e-06
            ],
            [
                2.2603242978377903e-06,
                8.939696303758459e-06,
                7.338208930355202e-07,
                1.147877222879974e-05,
                1.067702742726318e-06,
                9.422443692261927e-07,
                7.889264466115267e-06,
                4.0063701672028456e-05,
                1.7603425836870455e-06,
                8.939696303010449e-06
            ],
            [
                3.120192621804711e-05,
                2.430024072471526e-05,
                1.3007131564383116e-05,
                6.144174601208867e-06,
                4.539789022498571e-05,
                1.4738978457041559e-05,
                2.4300234929636645e-05,
                4.0063682616886836e-05,
                4.00636969128696e-05,
                2.1444943291142893e-05
            ],
            [
                3.288749065125496e-06,
                3.1201918788014855e-05,
                1.1478765385432939e-05,
                1.1478766756214804e-05,
                NaN,
                6.962257062216434e-06,
                4.222833444283541e-06,
                2.1444953522913026e-05,
                6.144174601588856e-06,
                5.422217030663578e-06
            ],
            [
                3.9278615343222713e-07,
                5.715007195057402e-07,
                3.927862938991851e-07,
                1.0677026154055912e-06,
                6.475946437587058e-07,
                1.3709572068422585e-06,
                2.699578096253257e-07,
                5.043474683156057e-07,
                4.785095635413826e-06,
                1.5534983101478522e-06
            ],
            [
                4.5397874023865346e-05,
                3.5356267550807374e-05,
                4.7850939230116e-06,
                5.422220908116881e-06,
                1.473897669245728e-05,
                4.006371126117997e-05,
                2.4300232038197563e-05,
                0.00026119040067041054,
                8.939699498814873e-06,
                2.4300252306390083e-05
            ],
            [
                0.9999910603026313,
                0.11920292045759122,
                0.9998204720174626,
                0.9999945777829762,
                0.9999687980960991,
                0.4378234991142019,
                0.9999646437408953,
                0.6513548646660542,
                NaN,
                0.9999991684715759
            ],
            [
                4.006368735141308e-05,
                1.6701419838997157e-05,
                4.539785238670836e-05,
                3.7266410609160796e-06,
                6.605214456006411e-05,
                2.430024072648329e-05,
                5.829126546520442e-05,
                0.00015843619704651598,
                7.88925976316864e-06,
                4.5397884871679096e-05
            ],
            [
                2.260323758835034e-06,
                1.3007130013856124e-05,
                3.288750633139005e-06,
                1.370956879949281e-06,
                3.2887478891128633e-06,
                6.9622587393661365e-06,
                2.144495096083526e-05,
                2.1444956079842134e-05,
                6.144173867753695e-06,
                1.3007126908733257e-05
            ],
            [
                1.2098656834922064e-06,
                4.7850950648799385e-06,
                4.785095635296322e-06,
                4.222832940777184e-06,
                1.1478765386623071e-05,
                1.1478764019328247e-05,
                3.2887494572514376e-06,
                1.147877359872636e-05,
                3.2887498492936755e-06,
                2.902312677084523e-06
            ],
            [
                2.561282515914161e-06,
                1.0129994598777299e-05,
                1.0677026154376365e-06,
                2.2603234893594005e-06,
                1.0129995809431767e-05,
                7.889263525663481e-06,
                7.338208930078229e-07,
                3.726638839833152e-06,
                7.88926634687567e-06,
                1.5534981248133121e-06
            ],
            [
                2.430024650998268e-05,
                1.6701421842566163e-05,
                5.144220747202866e-05,
                4.78509563550957e-06,
                1.8925141459279565e-05,
                1.6701423824262386e-05,
                5.144223809946954e-05,
                2.4300232036606334e-05,
                2.7535681231364308e-05,
                3.5356259112640515e-05
            ],
            [
                5.422218323231539e-06,
                1.760343003208622e-06,
                2.56128282131428e-06,
                8.939700564679507e-06,
                3.7266410604686857e-06,
                2.5612812945889277e-06,
                2.2603242976733308e-06,
                3.288750241204353e-06,
                1.0677031244429091e-06,
                1.012999460108057e-05
            ],
            [
                5.144220748924517e-05,
                4.539786314550164e-05,
                3.120192623700302e-05,
                3.120192619704807e-05,
                6.605215242684585e-05,
                3.120191134788212e-05,
                0.0006263341684204154,
                1.8925148239772175e-05,
                3.120190760119872e-05,
                1.6701425824733193e-05
            ],
            [
                0.9999952149060758,
                0.9999996072138465,
                0.9999852610162746,
                0.999998239656367,
                0.999997097689053,
                0.9999986290423029,
                0.9999994956524114,
                0.9999945777829697,
                0.999999814460854,
                0.9999989322967481
            ],
            [
                0.9999921107383782,
                0.999569442962264,
                0.7772998611746912,
                0.5312093733737563,
                0.9991959141512626,
                0.40733340004593027,
                0.9998911030910144,
                0.9996646499294592,
                0.4378234991142019,
                0.9991959140559061
            ],
            [
                1.8925143726890553e-05,
                1.3007126912258525e-05,
                8.939695236398313e-06,
                5.422217675628357e-06,
                4.785092783210732e-06,
                6.962258738283349e-06,
                4.785096205930373e-06,
                3.726638839833152e-06,
                1.209866116149238e-06,
                2.9023130229209922e-06
            ]
        ]
    },
    {
        "q_id": "8723_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            5,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            25,
            26,
            27,
            28,
            30,
            31,
            33,
            34,
            35,
            36,
            37,
            38,
            40,
            42,
            43,
            44,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            57,
            58,
            60,
            63,
            65,
            67,
            68,
            69,
            71,
            72,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            91,
            92,
            94,
            95,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                4.222833947674739e-06,
                4.222835457852533e-06,
                1.2098652508056196e-06,
                2.5612822106841303e-06,
                4.78509506425325e-06,
                2.9023133689924295e-06,
                4.785094493836935e-06,
                4.222834954403545e-06,
                1.5534979397140412e-06,
                4.785095634460739e-06
            ],
            [
                3.288748673265808e-06,
                0.00010889693508045057,
                0.9999991684719723,
                4.222832941142044e-06,
                1.0129992185760567e-05,
                3.120192624846737e-05,
                0.0001233946189413239,
                8.93969630388855e-06,
                4.785094494672519e-06,
                3.5356250701614645e-05
            ],
            [
                0.9999885212277696,
                5.829129329168791e-05,
                1.0129994601872894e-05,
                0.9998204720768361,
                7.889263525405172e-06,
                0.9999417087275172,
                0.9999756997476837,
                1.4738985484549675e-05,
                9.61024378393533e-05,
                0.999964643736649
            ],
            [
                3.7266383955882547e-06,
                1.3007131564643372e-05,
                5.829127247557873e-05,
                2.1444956082767684e-05,
                1.1478770862067849e-05,
                0.0001795280299270608,
                1.147876949187012e-05,
                0.9999991684720715,
                NaN,
                2.75356976629957e-05
            ],
            [
                1.0129992182112188e-05,
                1.892515726357648e-05,
                2.144495352474637e-05,
                1.8925152746768368e-05,
                5.715002426439334e-07,
                1.5534979397394734e-06,
                1.4738983727900215e-05,
                3.5356246441695886e-05,
                1.892514147046736e-05,
                8.939693105467234e-06
            ],
            [
                0.9999038975509362,
                0.9995694428624236,
                0.9998766054548983,
                0.8807970889295664,
                0.9740426454865795,
                0.9997388097857415,
                0.9999869928762726,
                0.9998766053828415,
                0.999941708707076,
                0.9999417087346366
            ],
            [
                1.1478772230407462e-05,
                9.422450431912e-07,
                3.2887478891487563e-06,
                3.726640616630245e-06,
                5.715003789017068e-07,
                5.71500583272315e-07,
                1.0677031245851707e-06,
                8.315278293899016e-07,
                2.561283432005142e-06,
                2.2603248367358324e-06
            ],
            [
                2.4300240712250633e-05,
                1.0677026154376365e-06,
                2.1444953523537147e-05,
                2.260323758746637e-06,
                1.9947290080125335e-06,
                6.144173137014406e-06,
                1.9947306725215466e-06,
                1.994729483666479e-06,
                1.5534973841592143e-06,
                1.3709568799592562e-06
            ],
            [
                1.7603427935342762e-06,
                1.7603438427852151e-06,
                1.2098656834723998e-06,
                1.3709578605542582e-06,
                1.3709573702248741e-06,
                1.3709576971061233e-06,
                4.222834953312807e-06,
                3.288749064802458e-06,
                1.553498495295912e-06,
                2.2603251061232293e-06
            ],
            [
                0.999999855501979,
                0.9999996940978825,
                0.999999814460854,
                0.9999996940976636,
                0.9999997300422868,
                0.9999997897565838,
                0.9999997617631469,
                0.9999998362622943,
                0.999999789756684,
                0.9999998144609424
            ],
            [
                1.553498495308628e-06,
                2.9023133689317184e-06,
                5.04347348070562e-07,
                9.422447062150634e-07,
                1.2098655392811161e-06,
                3.288747889038086e-06,
                5.422220908560712e-06,
                1.209866116137134e-06,
                2.9023130230133794e-06,
                1.2098658277082653e-06
            ],
            [
                3.4663249714451116e-07,
                1.0677028699742299e-06,
                1.2098652507957165e-06,
                8.315284241597959e-07,
                1.5534975693792215e-06,
                1.2098653950606901e-06,
                1.0677024881683915e-06,
                3.726639728224814e-06,
                1.5534979397677313e-06,
                1.0677026154730804e-06
            ],
            [
                0.9999970976873229,
                0.9999921107392965,
                0.9999957771660524,
                0.000295957237019764,
                0.999985261023306,
                0.9999957771665557,
                0.9999885212359826,
                0.9999910603026321,
                0.9999957771660528,
                0.00015843615937519005
            ],
            [
                1.3709570433536782e-06,
                1.3709573702647743e-06,
                2.9023116391477434e-06,
                1.0677027426952437e-06,
                9.42244818532859e-07,
                8.315277302747361e-07,
                9.422443692489024e-07,
                2.9023133690425823e-06,
                1.0677032518578904e-06,
                2.561282821352716e-06
            ],
            [
                5.422220908925639e-06,
                2.4300234937239182e-05,
                5.144219519403497e-05,
                6.962254589433702e-06,
                3.120192251336002e-05,
                1.9947299592824403e-06,
                1.473898899908247e-05,
                8.939695235959266e-06,
                2.1444948410303962e-05,
                3.726640172503764e-06
            ],
            [
                1.2098653950606901e-06,
                4.4508515805199415e-07,
                2.2603245672867952e-06,
                1.209865539274514e-06,
                1.2098661161927025e-06,
                1.553498495338299e-06,
                1.3709575336947905e-06,
                8.315283250305684e-07,
                4.450849988780466e-07,
                5.043472879481655e-07
            ],
            [
                5.043473480678099e-07,
                5.04347227811786e-07,
                3.9278634073098236e-07,
                5.043474683156057e-07,
                5.043472879525233e-07,
                9.422447062150634e-07,
                1.0677027427166074e-06,
                5.715003107619008e-07,
                5.043474683204221e-07,
                4.450850519360903e-07
            ],
            [
                1.0129989771823107e-05,
                2.4300232043369055e-05,
                1.0129992187105678e-05,
                1.8925155003330605e-05,
                4.7850933535006355e-06,
                2.1444948410928083e-05,
                NaN,
                8.481106151541198e-05,
                6.605214464752619e-05,
                4.0063692174115624e-05
            ],
            [
                6.475948753847607e-07,
                1.209865827740176e-06,
                3.927862939126708e-07,
                3.927862470816829e-07,
                5.715007195410849e-07,
                6.475945666009864e-07,
                5.04347348075149e-07,
                7.338208055579897e-07,
                1.2098653950551882e-06,
                7.338212429504183e-07
            ],
            [
                6.605214461148412e-05,
                1.8925141467059383e-05,
                5.8291286359769625e-05,
                1.0129993394129904e-05,
                4.5397857817300854e-05,
                4.78509563535725e-06,
                4.222834451254188e-06,
                0.00010889687022902587,
                3.535625070920327e-05,
                2.9023123310580418e-06
            ],
            [
                1.6701427804546374e-05,
                8.939695237504067e-06,
                4.785096205973894e-06,
                5.144223201267966e-05,
                1.4738978457041559e-05,
                1.6701429805199933e-05,
                1.3007130011655787e-05,
                1.892515726099468e-05,
                1.1478764017428212e-05,
                2.4300234931404677e-05
            ],
            [
                0.9999996533672135,
                0.9999998144609202,
                0.9999996533672962,
                0.9999999006881141,
                0.9999998362622357,
                0.9999997897566089,
                0.9999996072136125,
                0.9999997300422868,
                0.9999995549147359,
                0.9999997897567342
            ],
            [
                5.715002426439334e-07,
                1.0677029972745947e-06,
                5.043472278280699e-07,
                9.422449308566668e-07,
                5.715005151574337e-07,
                9.422448185187191e-07,
                1.2098652508287273e-06,
                8.315282259051341e-07,
                1.5534977545497995e-06,
                5.715003107689177e-07
            ],
            [
                1.3709576971316842e-06,
                2.699576809121209e-07,
                6.475951069932288e-07,
                2.260324297853209e-06,
                4.450848927621807e-07,
                3.9278615343901467e-07,
                3.059021904571643e-07,
                8.315280276456036e-07,
                1.0677026154730804e-06,
                3.466327863961242e-07
            ],
            [
                1.1478772228528306e-05,
                1.14787681240737e-05,
                6.1441767990323395e-06,
                1.0129990979381404e-05,
                2.260323489410794e-06,
                1.1478773597640625e-05,
                3.2887506334201674e-06,
                1.1478769493540482e-05,
                1.8925157257345735e-05,
                2.5612828211442287e-06
            ],
            [
                1.2098659719601033e-06,
                3.05902263389638e-07,
                6.475951069855719e-07,
                9.422448184912962e-07,
                1.2098653950551882e-06,
                3.927862002606139e-07,
                3.4663257978780455e-07,
                1.553498495338299e-06,
                1.209865250822125e-06,
                3.927862002641863e-07
            ],
            [
                1.209865827740176e-06,
                1.994729721469003e-06,
                9.422445938964242e-07,
                1.9947299592407137e-06,
                2.260323758939877e-06,
                1.3709578605617394e-06,
                6.475947209985977e-07,
                6.475947981975644e-07,
                1.3709570434122812e-06,
                1.2098652508347793e-06
            ],
            [
                1.1478770860982112e-05,
                1.0677026154619133e-06,
                2.5612819052654485e-06,
                1.5534977545384963e-06,
                3.288750633192845e-06,
                1.5534977545102382e-06,
                7.338210679909462e-07,
                2.9023130229209922e-06,
                2.561281905100056e-06,
                4.222833444168322e-06
            ],
            [
                1.0677028700320085e-06,
                6.144175333926503e-06,
                9.4224425692559e-07,
                6.144172404520556e-06,
                8.315279285251204e-07,
                2.902313022984344e-06,
                6.475945666009864e-07,
                3.2887498493983645e-06,
                1.0677028700320085e-06,
                1.0677026154473471e-06
            ],
            [
                8.315282259009745e-07,
                1.7603425837062577e-06,
                5.043472278280699e-07,
                5.715005151574337e-07,
                9.422445938797133e-07,
                1.370957860567974e-06,
                7.338207180864763e-07,
                7.338212429420757e-07,
                1.2098655392662613e-06,
                5.71500651413193e-07
            ],
            [
                0.9999967112505427,
                0.9999990577551814,
                0.9999999123575568,
                0.9999996533674614,
                0.9999977396746244,
                0.9999990577555183,
                0.9999991684721706,
                0.9999999006880549,
                0.999999057755743,
                0.9999967112497584
            ],
            [
                3.2887506334201674e-06,
                0.00023050676905674014,
                2.5612815999423112e-06,
                2.2603234894745224e-06,
                1.1478764018576587e-05,
                3.2887482811579057e-06,
                1.1478769492893215e-05,
                2.144494073796001e-05,
                4.0063696957321844e-05,
                1.209866116149238e-06
            ],
            [
                0.9999998874648514,
                0.9999998144608319,
                0.9999998874647842,
                0.9999998724810027,
                0.9999999006880075,
                0.9999999006881259,
                0.9999999006881377,
                0.9999998724809115,
                0.9999996533672549,
                0.9999997897566338
            ],
            [
                0.9995694428254358,
                0.9980732656218819,
                0.06754668597767712,
                0.9994472214836695,
                0.11920292515117027,
                0.9998766054708684,
                0.0031726835295036713,
                0.5926665999540698,
                0.2942149783515162,
                0.9997388096614188
            ],
            [
                8.939700564679507e-06,
                4.222834450666572e-06,
                1.4738976695942536e-05,
                3.2887506333812835e-06,
                4.222833945815874e-06,
                1.0129990979031306e-05,
                4.785095061990212e-06,
                1.0129988562422337e-05,
                1.4738983720179032e-05,
                4.7850927822924614e-06
            ],
            [
                6.962253759157502e-06,
                4.785094494628999e-06,
                4.5397852367551086e-05,
                1.6701425824733193e-05,
                5.8291279365509446e-05,
                3.120191879107958e-05,
                4.539787943513799e-05,
                1.0129987357020188e-05,
                1.7603432133032607e-06,
                2.260325375615501e-06
            ],
            [
                NaN,
                2.4300232041998833e-05,
                1.6701423831188846e-05,
                1.8925143725892257e-05,
                1.6701415871049018e-05,
                1.6701429807964442e-05,
                1.994729008105057e-06,
                5.8291244679640374e-05,
                1.6701429794688725e-05,
                2.902313023039776e-06
            ],
            [
                2.753570092478113e-05,
                8.481106143026193e-05,
                3.1201918779615236e-05,
                1.4738980213020151e-05,
                4.539785780045566e-05,
                3.1201900207380036e-05,
                5.829128635171172e-05,
                8.93969736929749e-06,
                1.6701421842140854e-05,
                1.6701427787473256e-05
            ],
            [
                5.422221555133606e-06,
                6.144175334015912e-06,
                3.7266383954560706e-06,
                1.209865539274514e-06,
                2.260324836696773e-06,
                4.539789026296999e-05,
                4.785096776133645e-06,
                2.430024362932722e-05,
                1.01299946023704e-05,
                4.7850927830148924e-06
            ],
            [
                2.902313022984344e-06,
                1.5534981248881956e-06,
                1.5534979396984994e-06,
                3.28874867308036e-06,
                1.370956716519966e-06,
                1.3709572068179446e-06,
                3.726638395320497e-06,
                1.994730672496148e-06,
                3.7266397282926013e-06,
                1.7603430033158905e-06
            ],
            [
                1.0677028700130727e-06,
                2.1024329090781183e-07,
                6.475948753991907e-07,
                5.71500719531729e-07,
                1.0677029973114952e-06,
                1.0677028700320085e-06,
                1.3709573702722555e-06,
                2.5612834319655406e-06,
                5.715005832762133e-07,
                1.2098655392871682e-06
            ],
            [
                1.7603432132912532e-06,
                5.043474081957179e-07,
                8.315281267800897e-07,
                9.422447062150634e-07,
                7.338207180801359e-07,
                9.422450431800595e-07,
                3.726638395493353e-06,
                1.067702615468225e-06,
                1.9947301970287804e-06,
                2.2603234894560207e-06
            ],
            [
                9.42244930849811e-07,
                9.422443692330485e-07,
                8.315278293899016e-07,
                9.422443692527585e-07,
                1.2098653950403334e-06,
                7.338212429537553e-07,
                1.209866116170145e-06,
                1.067703251864202e-06,
                3.726640172385136e-06,
                4.785095635592258e-06
            ],
            [
                4.222833947774596e-06,
                4.5397874044343825e-05,
                NaN,
                2.4300232038993178e-05,
                1.473898021366358e-05,
                3.12019262448351e-05,
                1.7603430034311638e-06,
                3.535625070778844e-05,
                6.605212890195146e-05,
                2.9023133690637e-06
            ],
            [
                8.315278293951957e-07,
                9.422443692390473e-07,
                1.7603425837366772e-06,
                3.2887478891487563e-06,
                2.902311293034278e-06,
                9.4224425692559e-07,
                2.5612812946681295e-06,
                1.3709576971160984e-06,
                2.5612812946681295e-06,
                1.1478773598329648e-05
            ],
            [
                6.475950297768503e-07,
                9.422447062150634e-07,
                8.315283250260307e-07,
                6.475947209953583e-07,
                3.726639283752725e-06,
                5.04347227811786e-07,
                4.222831933795376e-06,
                1.2098652508144226e-06,
                1.2098658277082653e-06,
                1.3709575336860625e-06
            ],
            [
                2.753570422373059e-05,
                9.610241484924595e-05,
                1.3709570434054234e-06,
                1.147876949310201e-05,
                NaN,
                1.3709572068272963e-06,
                1.6701419849933667e-05,
                1.0677028700266676e-06,
                7.889265406904397e-06,
                1.0129993394664264e-05
            ],
            [
                6.962258739068529e-06,
                5.422221553654169e-06,
                8.939700563752626e-06,
                1.4738988995409548e-05,
                4.222835457364773e-06,
                4.785095063469892e-06,
                2.7535681235270997e-05,
                7.484621832590252e-05,
                1.1478765381674627e-05,
                1.473898372275276e-05
            ],
            [
                6.475947982002148e-07,
                8.315283250371857e-07,
                6.475948753991907e-07,
                6.47594798194325e-07,
                5.043474683204221e-07,
                6.475945666033422e-07,
                3.72664061671159e-06,
                1.2098658277082653e-06,
                5.043475885674441e-07,
                2.2603248367512505e-06
            ],
            [
                0.9999724643068227,
                0.999993855826131,
                0.9999984465022455,
                0.9999869928730862,
                0.9999151889486347,
                0.9999832985721836,
                0.9999962733589389,
                0.9999962733598274,
                0.9999599363030631,
                0.9999724643154663
            ],
            [
                4.2228324375973415e-06,
                2.2603242978007868e-06,
                4.450851049917114e-07,
                7.338212429537553e-07,
                1.2098661161861e-06,
                6.475948753930064e-07,
                1.7603440526806268e-06,
                5.715003789017068e-07,
                8.3152792852928e-07,
                7.338208055613267e-07
            ],
            [
                1.2098661161927025e-06,
                1.0677031245783732e-06,
                8.315283250343497e-07,
                2.9023123311055552e-06,
                2.902312677007974e-06,
                9.422445938964242e-07,
                1.209865539274514e-06,
                4.450851049941403e-07,
                2.5612822106841303e-06,
                1.994730434847717e-06
            ],
            [
                1.5534983101478522e-06,
                6.475945666009864e-07,
                1.0677027427413698e-06,
                9.422449308566668e-07,
                1.3709578605542582e-06,
                1.2098658277181688e-06,
                9.422449308673789e-07,
                5.829127239924071e-05,
                7.338209805170655e-07,
                8.315282259051341e-07
            ],
            [
                4.539789028295303e-05,
                2.4300252316291068e-05,
                0.00013982207399946956,
                6.144173869072478e-06,
                0.00010889692215579573,
                8.481108177927541e-05,
                4.7850939242083995e-06,
                0.00010889693518502668,
                2.1444945852673643e-05,
                NaN
            ],
            [
                4.222834451215781e-06,
                6.144175332440078e-06,
                8.93969630333567e-06,
                1.3007126912258525e-05,
                5.422221554847581e-06,
                1.0129988563730593e-05,
                1.1478769493728398e-05,
                4.7850950646797465e-06,
                3.7266410605974813e-06,
                3.2887478891487563e-06
            ],
            [
                1.0129992186774007e-05,
                1.0677033791107183e-06,
                1.994729483608425e-06,
                1.7603432131855856e-06,
                2.2603253754921562e-06,
                1.3709573701812335e-06,
                2.260324836567261e-06,
                2.561283431986506e-06,
                8.939695238089467e-06,
                1.7603436329554703e-06
            ],
            [
                6.144176066353646e-06,
                NaN,
                0.00043055715109146093,
                0.00023050668643219275,
                2.260324567268294e-06,
                6.962255419380732e-06,
                6.6052152530647e-05,
                8.481108177927541e-05,
                1.4738987226400411e-05,
                0.00017952800818209834
            ],
            [
                8.315284241597959e-07,
                2.260325375615501e-06,
                1.209865827698362e-06,
                7.889266346746518e-06,
                1.553498495281783e-06,
                6.962256249682458e-06,
                7.889259763857458e-06,
                3.0590215398829087e-07,
                2.699576809107705e-07,
                6.475948753847607e-07
            ],
            [
                7.484621824258834e-05,
                8.939700565834043e-06,
                1.4738985485461206e-05,
                1.012998977213635e-05,
                7.48462271283461e-05,
                4.2228319341064674e-06,
                7.889265405849647e-06,
                2.4300246525983375e-05,
                1.0129993394664264e-05,
                3.120190393260949e-05
            ],
            [
                0.0001233945890514007,
                9.610244921065592e-05,
                4.006371128770557e-05,
                1.1478769493331685e-05,
                2.4300252318589512e-05,
                7.48462272160166e-05,
                NaN,
                7.889265405333033e-06,
                1.3007123807727885e-05,
                0.00010889694746162803
            ],
            [
                2.5612822106841303e-06,
                4.222833444283541e-06,
                1.7603434230921292e-06,
                1.0129987355785634e-05,
                2.5612828212676906e-06,
                3.2887506334560605e-06,
                2.5612815999679353e-06,
                9.42244930862237e-07,
                2.561283431888668e-06,
                7.338208930315157e-07
            ],
            [
                0.9999998144609645,
                0.9999999317440116,
                0.9999998555019963,
                0.999999554914895,
                0.9999998724809115,
                0.9999999397643083,
                0.9999998724810026,
                0.9999998144609644,
                0.9999998874648379,
                0.9999997897566089
            ],
            [
                0.18242552158390105,
                0.3486451488696663,
                0.9998601778597607,
                0.9997040429845999,
                0.731058584489497,
                0.998299277510887,
                0.9525741271590256,
                0.5312093733737563,
                0.9740426420015996,
                0.37754066879814546
            ],
            [
                5.04347408197782e-07,
                2.561282210701601e-06,
                3.2887494573232236e-06,
                9.422444815563743e-07,
                4.2228344511197656e-06,
                0.9998415637455474,
                1.7603436330091044e-06,
                2.5612825159421147e-06,
                1.5534977545384963e-06,
                4.222833444383398e-06
            ],
            [
                0.9999921107402484,
                0.9999921107376507,
                0.9046505402422645,
                NaN,
                0.5312093733737562,
                0.9999724642991594,
                NaN,
                0.3486451285660856,
                0.9999852610234545,
                NaN
            ],
            [
                3.72664017246987e-06,
                1.7603432132079998e-06,
                9.422447062094932e-07,
                5.04347287945184e-07,
                3.2887498494282754e-06,
                1.3709572068354007e-06,
                1.0677027427166074e-06,
                1.5534977545603963e-06,
                3.288750633518874e-06,
                9.42244256915735e-07
            ],
            [
                1.3709576971242028e-06,
                2.9023112930949896e-06,
                3.927860597945825e-07,
                9.422447062240614e-07,
                9.422447062240614e-07,
                1.7603430034743913e-06,
                1.9947297214944016e-06,
                9.422447062240614e-07,
                1.209865827740176e-06,
                1.2098653950403334e-06
            ],
            [
                5.04347588554027e-07,
                0.9986749774333598,
                8.315278293301564e-07,
                2.699576809121209e-07,
                7.88926634455091e-06,
                8.315280276505193e-07,
                1.2098652508056196e-06,
                3.466325384589045e-07,
                5.715003107416295e-07,
                1.3709576970213355e-06
            ],
            [
                4.00636826326273e-05,
                6.962257079173776e-06,
                5.144223204149862e-05,
                2.1444940738662144e-05,
                4.006367784140681e-05,
                3.535624227734284e-05,
                6.605214468549049e-05,
                1.4738976699749503e-05,
                4.006368740052914e-05,
                4.5397879417962496e-05
            ],
            [
                3.927862002641863e-07,
                8.315280276580819e-07,
                1.2098652507957165e-06,
                1.2098653950606901e-06,
                8.315282259051341e-07,
                4.450850519360903e-07,
                5.043472879481655e-07,
                1.3709567165530083e-06,
                1.2098659719716573e-06,
                6.475949525981759e-07
            ],
            [
                0.9999998874648246,
                0.9999998874648917,
                0.9999998555019274,
                0.9999996072137998,
                0.9999997897567091,
                0.9999999317439221,
                0.9999999006880194,
                0.9999993524052018,
                0.9999994956525317,
                0.9999999123575464
            ],
            [
                0.9999986290421395,
                0.9999984465022455,
                0.9999998555019274,
                0.9999998555019446,
                0.9999998362623332,
                0.9999995549151072,
                0.9999986290421394,
                0.9999957771660523,
                0.9999995549147358,
                0.9999997617630332
            ],
            [
                0.9999982396572064,
                0.9999990577556307,
                0.9999957771680656,
                0.999998239656367,
                0.999998446502616,
                0.9999989322968755,
                0.999997438716568,
                0.9999982396559473,
                0.9999417087414438,
                0.9999970976887068
            ],
            [
                1.2098659719524008e-06,
                5.422218321441422e-06,
                1.6701421837158667e-05,
                4.222834450820197e-06,
                1.3709578605455302e-06,
                4.785095635017795e-06,
                3.288749849209925e-06,
                7.889264466344872e-06,
                2.2603240281935217e-06,
                6.1441775309064404e-06
            ],
            [
                0.9999984465015047,
                0.9999997897567341,
                0.9999997897565587,
                0.9999996940976636,
                0.9999993524051246,
                0.9999993524049702,
                0.9999997617629764,
                0.9999998874647306,
                0.9999996533672962,
                0.9999991684718732
            ],
            [
                0.9999984465024307,
                0.9999991684720715,
                0.9999986290429567,
                0.9999980052709919,
                0.9999990577551815,
                0.9999990577557432,
                0.9999987901346049,
                0.9999982396572065,
                0.9999982396559474,
                0.9999990577550693
            ],
            [
                0.999997097688713,
                0.9999986290423029,
                0.9999945777829694,
                0.9999998362623137,
                0.9999974387177893,
                0.9999986290432835,
                0.9999999468421692,
                0.9999938558246663,
                0.9999986290423029,
                0.9999970976869863
            ],
            [
                9.422450431654909e-07,
                1.0677028699955933e-06,
                1.9947290080343035e-06,
                1.760342583722268e-06,
                5.715003107689177e-07,
                1.3007130013572209e-05,
                3.288749849368453e-06,
                4.785096205717126e-06,
                9.422444815563743e-07,
                1.994729721436347e-06
            ],
            [
                7.889261645269683e-06,
                3.726638395415398e-06,
                3.7266388397721442e-06,
                6.475946437966953e-07,
                3.2887486732358968e-06,
                2.9023109471452223e-06,
                7.338211554641698e-07,
                2.9023112930949896e-06,
                2.9023130230846496e-06,
                4.222833947674739e-06
            ],
            [
                1.4738983727256784e-05,
                2.561283431942246e-06,
                2.90231163910023e-06,
                2.561282210618905e-06,
                3.7266410608720178e-06,
                1.2098659719441482e-06,
                4.785093924103951e-06,
                3.2887490649759413e-06,
                1.76034363298589e-06,
                3.1201900209877224e-05
            ],
            [
                8.315278294001114e-07,
                0.6224593382055109,
                1.067703379136937e-06,
                8.315280276456036e-07,
                5.7150044702099e-07,
                1.7603430033799313e-06,
                8.315284241597959e-07,
                7.338209805133949e-07,
                1.5534981249164537e-06,
                1.209866116170145e-06
            ],
            [
                2.3823693839057394e-07,
                2.561281294616881e-06,
                9.422444815679433e-07,
                9.422447062240614e-07,
                9.422444815495185e-07,
                5.043472278299047e-07,
                9.422443692446175e-07,
                7.338207180761315e-07,
                2.2603251061458426e-06,
                3.4663253846316044e-07
            ],
            [
                2.260325375650449e-06,
                1.209865539274514e-06,
                1.7603440527046419e-06,
                1.0677024881941248e-06,
                8.315282259051341e-07,
                2.5612825160096693e-06,
                1.0677031245783732e-06,
                6.475946437996402e-07,
                3.288749849209925e-06,
                2.9023116390421582e-06
            ],
            [
                7.484624486991525e-05,
                2.9023112930659533e-06,
                1.0129995809929273e-05,
                0.0001398221233172691,
                6.9622570780973205e-06,
                5.422219614438727e-06,
                6.605212887119557e-05,
                8.939700564679507e-06,
                1.8925143724239906e-05,
                1.3007130013856124e-05
            ],
            [
                4.7850927830845245e-06,
                1.5534971989907999e-06,
                4.785093924103951e-06,
                2.9023116391477434e-06,
                2.2603251062147097e-06,
                9.422443692489024e-07,
                4.22283394762097e-06,
                1.2098659719601033e-06,
                2.2603242978665707e-06,
                3.7266383955611403e-06
            ],
            [
                1.4738981970956057e-05,
                7.889260703763482e-06,
                6.96225541788636e-06,
                3.726641060536473e-06,
                5.422217030362759e-06,
                2.5612834318257725e-06,
                9.610243778831388e-05,
                8.939698432446272e-06,
                1.300712380408432e-05,
                3.28874867308036e-06
            ],
            [
                1.760342793583908e-06,
                6.475946438022905e-07,
                5.043474683220276e-07,
                4.450851580555361e-07,
                8.315283250305684e-07,
                6.475950297971703e-07,
                5.043475885606781e-07,
                1.0677024881829577e-06,
                5.715003107715166e-07,
                9.422448185435711e-07
            ],
            [
                0.9999970976883609,
                0.00017952794435509826,
                0.9999987901337396,
                0.00023050679741429107,
                0.9999967112493666,
                0.00015843627325363947,
                0.00048785722288971077,
                0.9999945777829696,
                0.9999885212305081,
                0.000295956992641387
            ],
            [
                1.0129994602057158e-05,
                4.539789028295303e-05,
                1.8925143728749452e-05,
                2.902310947190096e-06,
                1.067703379154416e-06,
                2.561283432005142e-06,
                1.9947290081177566e-06,
                2.260323489490968e-06,
                2.430023493052066e-05,
                7.889264466445326e-06
            ],
            [
                1.0677028700203557e-06,
                3.7266397280485686e-06,
                9.422448185388577e-07,
                4.4508526417014975e-07,
                2.9023133690821773e-06,
                5.043472278159142e-07,
                2.561282516042282e-06,
                8.315281267513512e-07,
                0.9999038975736046,
                5.715003107655392e-07
            ],
            [
                8.315281267706361e-07,
                1.209865539274514e-06,
                6.47594798194325e-07,
                1.0677033791437343e-06,
                1.0677028700203557e-06,
                1.0677031245623505e-06,
                3.466325384532298e-07,
                9.422449308566668e-07,
                9.422449308420983e-07,
                3.4663249714325014e-07
            ],
            [
                0.7310585903489891,
                0.9999756997507293,
                0.9999945777797997,
                0.9998415638491678,
                0.9999852610110749,
                0.9999930377422506,
                0.9999687980796316,
                1.0129988564578197e-05,
                NaN,
                0.9465966651155708
            ],
            [
                0.9933071481655668,
                0.9999945777823239,
                0.9999989322967482,
                0.999992110733654,
                0.7772998560157665,
                0.9999980052710022,
                0.999998629042304,
                0.9999980052702786,
                0.9999980052705164,
                0.9999852610197881
            ],
            [
                1.3709578605243332e-06,
                2.260323489435463e-06,
                1.7603436326432711e-06,
                1.370957370236096e-06,
                3.288749065209246e-06,
                1.5534973840150989e-06,
                2.260323758882316e-06,
                5.422221554670048e-06,
                2.2603242972087315e-06,
                2.1444953517061932e-05
            ],
            [
                1.3709572068354007e-06,
                8.315281267800897e-07,
                6.475946437996402e-07,
                9.422448185435711e-07,
                7.338208055613267e-07,
                1.3709573702722555e-06,
                1.5534981249574276e-06,
                3.288750633545794e-06,
                8.315277302788957e-07,
                3.726639728262097e-06
            ],
            [
                3.2887482811579057e-06,
                7.338211554725124e-07,
                6.475947209985977e-07,
                1.0677029973114952e-06,
                5.04347468318358e-07,
                1.2098656835076114e-06,
                4.22283545795623e-06,
                5.715005151550947e-07,
                5.715007195431641e-07,
                5.715003107619008e-07
            ],
            [
                2.6995774527184606e-07,
                6.475946437928669e-07,
                2.6995784182073116e-07,
                8.315280276580819e-07,
                1.3709570433661467e-06,
                4.450851580540182e-07,
                2.3823696679040834e-07,
                8.315284241560147e-07,
                4.450848927621807e-07,
                4.450849458200093e-07
            ],
            [
                5.04347528440776e-07,
                8.315281267834927e-07,
                1.0677027427525368e-06,
                9.422449308716635e-07,
                7.3382080556433e-07,
                7.338210679949506e-07,
                6.475947210012481e-07,
                6.475945666009864e-07,
                9.422449308716635e-07,
                7.338212429537553e-07
            ]
        ]
    },
    {
        "q_id": "7904_mmlu_math",
        "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": [
            [
                1.2098662604049616e-06,
                1.0677033791291683e-06,
                1.760344052650207e-06,
                1.3709568799368123e-06,
                4.78509506499309e-06,
                1.5534981249164537e-06,
                1.0677031245851707e-06,
                4.785095064044355e-06,
                9.42244818532859e-07,
                1.553497384180408e-06
            ],
            [
                0.9999962733616049,
                0.9999994284994848,
                0.9999996940978825,
                0.999998446502801,
                0.9999997897567091,
                0.9999997897565587,
                0.9999996072136125,
                0.9999992661790195,
                0.9999993524053563,
                0.9999998144609203
            ],
            [
                0.9902915249869724,
                0.999447221255861,
                0.9975273769691323,
                0.9924227596250706,
                0.9998204719485762,
                0.9990889487612006,
                0.9996200155151292,
                5.422221554758815e-06,
                0.9998766054694967,
                0.9940889306977416
            ],
            [
                0.9999977396765106,
                0.9999974387177897,
                0.9999996072137061,
                0.9999986290432837,
                0.9999991684717741,
                0.9999984465016899,
                0.9999992661788445,
                0.9999989322972573,
                0.9999997897567342,
                0.9999994284997574
            ],
            [
                0.9999982396561572,
                0.9999990577549569,
                0.9999986290424664,
                0.9999984465020603,
                0.9999996072138934,
                0.9999967112501508,
                0.9999998362622747,
                0.9999982396569966,
                0.9999994956526519,
                0.9999991684722698
            ],
            [
                0.9999997897565838,
                0.9999997300422547,
                0.9999990577552939,
                0.9999997617630332,
                0.9999996072138934,
                0.9999998144609645,
                0.9999996072138465,
                0.9999984465022455,
                0.9999998144609645,
                0.9999984465020604
            ],
            [
                0.99999862904312,
                0.999999057755743,
                0.9999991684715759,
                0.9999962733589395,
                0.999998239656577,
                0.999998790134605,
                0.9999974387177893,
                0.9999991684722697,
                0.9999994956524114,
                0.9999967112497589
            ],
            [
                0.9999986290432835,
                0.9999996940977001,
                0.9999993524051246,
                0.9999996940977731,
                0.9999996533672962,
                0.9999996533674201,
                0.999997097688361,
                0.9999997897565838,
                0.9999996940978095,
                0.9999996533674615
            ],
            [
                0.9999996533672962,
                0.9999984465015047,
                0.9999984465020603,
                0.9999996533672549,
                0.9999974387184003,
                0.9999970976887074,
                0.9999997897567091,
                0.9999990577551815,
                0.9999996533673375,
                0.9999994284994168
            ],
            [
                0.9999989322966211,
                0.9999994956527121,
                0.9999996072138465,
                0.9999993524054335,
                0.9999996533672549,
                0.9999994956527121,
                0.9999987901343166,
                0.9999996072137529,
                0.999999554914842,
                0.9999996940978825
            ],
            [
                0.9999997617631752,
                0.9999997617630332,
                0.9999995549147889,
                0.9999996072138934,
                0.9999994956527721,
                0.9999997897567341,
                0.9999997300421581,
                0.999999266178932,
                0.9999992661790195,
                0.9999996533674614
            ],
            [
                0.9999990577551815,
                0.9999994284993485,
                0.9999990577551815,
                0.999998790134605,
                0.999998790134605,
                0.9999993524052019,
                0.9999996533672549,
                0.9999994284996211,
                0.9999998362623332,
                0.9999997300422225
            ],
            [
                0.9999996940977002,
                0.9999974387165681,
                0.999999554914842,
                0.9999994956527721,
                0.9999994956524716,
                0.9999990577549569,
                0.9999994956527121,
                0.9999996533674201,
                0.9999996940978825,
                0.9999996940978825
            ],
            [
                0.9999997617630899,
                0.9999991684719723,
                0.9999998144608319,
                0.9999993524050474,
                0.9999994956524716,
                0.9999994284997573,
                0.999999694097773,
                0.9999996072137529,
                0.9999994956524115,
                0.9999993524051246
            ],
            [
                0.999999168471675,
                0.9999996072137529,
                0.9999991684718733,
                0.9999974387165682,
                0.9999992661787571,
                0.9999986290424665,
                0.9999996072137998,
                0.9999995549151073,
                0.9999986290427934,
                0.9999997617629763
            ],
            [
                0.9999995549150011,
                0.999999730042319,
                0.9999996533672962,
                0.9999998144609424,
                0.9999993524050474,
                0.9999996072137998,
                0.999999694097773,
                0.9999999006880549,
                0.9999997617630048,
                0.9999997617631468
            ],
            [
                0.9999974387177897,
                0.9999997617631184,
                0.9999986290432835,
                0.9999989322973847,
                0.9999986290431201,
                0.9999987901346049,
                0.9999999006881496,
                0.9999910602994365,
                0.9999974387184002,
                0.9999995549150542
            ],
            [
                0.999999352405279,
                0.9999987901337396,
                0.9999986290424664,
                0.9999989322968754,
                0.9999995549150542,
                0.9999984465018751,
                0.999999352405279,
                0.9999986290431201,
                0.9999967112493673,
                0.9999970976880153
            ],
            [
                0.9999994956525918,
                0.9999997897567091,
                0.9999997300422869,
                0.9999996940976272,
                0.9999997300421583,
                0.9999998362622552,
                0.9999998362623137,
                0.9999991684715759,
                0.9999998144609645,
                0.999999554914789
            ],
            [
                0.9999992661791945,
                0.9999993524051246,
                0.999997739674894,
                0.999998005270041,
                0.9999970976869772,
                0.9999990577555185,
                0.9999990577552939,
                0.999999057755743,
                0.9999996533672135,
                0.9999996072138934
            ],
            [
                0.9999996940978825,
                0.9999994956524716,
                0.9999995549147889,
                0.9999994956524114,
                0.9999995549147359,
                0.9999989322968755,
                0.9999987901341723,
                0.9999994284996211,
                0.9999993524051246,
                0.9999996072138934
            ],
            [
                0.9999998362623528,
                0.9999998144608981,
                0.9999993524051246,
                0.9999996940978825,
                0.9999996072136592,
                0.9999997897566089,
                0.9999990577556308,
                0.9999996072136125,
                0.999999789756684,
                0.9999996072138934
            ],
            [
                0.9999997617629763,
                0.9999993524050474,
                0.9999990577550693,
                0.9999990577555185,
                0.99999893229713,
                0.9999998362623138,
                0.9999994284994848,
                0.9999996533673375,
                0.9999990577552937,
                0.9999996072137529
            ],
            [
                0.9999998362622552,
                0.9999986290426297,
                0.9999992661786696,
                0.9999977396754329,
                0.9999982396574163,
                0.9999994284992805,
                0.9999995549148419,
                0.9999993524052019,
                0.9999970976890539,
                0.999999352404893
            ],
            [
                0.999999730042126,
                0.9999998555019963,
                0.9999998555020134,
                0.9999996533672962,
                0.9999998555019963,
                0.9999998362623137,
                0.9999995549151072,
                0.999999495652652,
                0.9999992661786695,
                0.9999996533672548
            ],
            [
                0.9999996940976271,
                0.9999990577554061,
                0.9999996940978825,
                0.9999998362623528,
                0.999999789756684,
                0.9999997617631469,
                0.9999986290431201,
                0.9999996940976636,
                0.999999855502048,
                0.9999991684722698
            ],
            [
                0.999999814460876,
                0.9999996072139402,
                0.9999990577556308,
                0.9999997300421581,
                0.9999996533675028,
                0.9999996940978095,
                0.9999996072137061,
                0.9999996533674202,
                0.9999997617630048,
                0.9999996940977002
            ],
            [
                0.9999996940977366,
                0.9999982396559474,
                0.9999974387174841,
                0.9999992661791071,
                0.9999997617630616,
                0.9999997897566338,
                0.9999996072137529,
                0.9999980052700408,
                0.9999994956524114,
                0.9999996940978825
            ],
            [
                0.9999998362622357,
                0.9999995549148419,
                0.9999989322970027,
                0.9999974387174841,
                0.9999998362623137,
                0.9999996072137529,
                0.9999998555020135,
                0.9999990577551815,
                0.9999996533672135,
                0.9999997300422225
            ],
            [
                0.9999996072139402,
                0.9999996072137529,
                0.9999996533672549,
                0.9999994956527721,
                0.9999996072138934,
                0.9999994284994167,
                0.9999995549148419,
                0.9999986290424664,
                0.9999997300422547,
                0.9999987901338839
            ],
            [
                0.999999266179107,
                0.9999986290421395,
                0.9999974387177897,
                0.9999995549150011,
                0.9999986290424663,
                0.999999789756634,
                0.9999996533672548,
                0.9999991684718732,
                0.9999992661787571,
                0.9999996533672962
            ],
            [
                3.4663249714451116e-07,
                6.475947209985977e-07,
                2.6995768091310296e-07,
                1.3709568799760888e-06,
                1.3709570434054234e-06,
                3.927862002654366e-07,
                1.6373772528677946e-07,
                9.422443692330485e-07,
                1.553497199007048e-06,
                5.715003107738556e-07
            ],
            [
                0.9999996072136125,
                0.9999995549149481,
                0.9999997617630616,
                0.9999998144609203,
                0.999999814460854,
                0.9999996940976271,
                0.9999995549147889,
                0.9999998362622746,
                0.9999998144609424,
                0.9999997897567091
            ],
            [
                0.9999996940978825,
                0.9999994284994167,
                0.9999995549151072,
                0.9999997300422547,
                0.9999991684715759,
                0.9999990577552937,
                0.9999997300422869,
                0.9999997300422225,
                0.9999995549150011,
                0.9999996533674202
            ],
            [
                0.99999893229713,
                0.9999998144608319,
                0.9999996533673376,
                0.9999997897565838,
                0.9999994284993486,
                0.9999998362623723,
                0.999999352404893,
                0.9999997617630332,
                0.9999994284995529,
                0.9999997300422225
            ],
            [
                0.999998932296621,
                0.9999995549149481,
                0.9999982396574165,
                0.9999998874648782,
                0.9999962733611608,
                0.9999997300422869,
                0.9999997300423191,
                0.9999996072137529,
                0.9999980052693276,
                0.9999996940977002
            ],
            [
                0.9999687980849195,
                0.9999967112509348,
                0.999986992869988,
                0.9999980052700408,
                0.999995777164542,
                0.9999885212332466,
                0.9999810748585323,
                0.9999038975853689,
                0.9999967112497585,
                0.999972464295789
            ],
            [
                0.9999996533673788,
                0.9999997897566589,
                0.9999998362622942,
                0.9999996072137998,
                0.9999998362622552,
                0.9999995549147359,
                0.9999998724809875,
                0.9999998144609202,
                0.9999997897565587,
                0.9999999123575151
            ],
            [
                0.9999991684718732,
                0.9999994284994849,
                0.9999986290427931,
                0.9999996940976271,
                0.9999998724809723,
                0.9999995549150542,
                0.9999996533675028,
                0.9999994956525317,
                0.9999989322968754,
                0.9999996940976272
            ],
            [
                0.9999998874649051,
                0.9999996533672962,
                0.9999967112505429,
                0.9999984465015047,
                0.99999976176309,
                0.9999984465018751,
                0.9999996940976636,
                0.9999995549151073,
                0.9999990577549569,
                0.9999997617631468
            ],
            [
                0.9999996940976636,
                0.9999992661790195,
                0.9999992661788445,
                0.9999994956527721,
                0.9999994956527721,
                0.9999996533675028,
                0.9999989322975119,
                0.9999996072137061,
                0.9999996072137061,
                0.9999997300420937
            ],
            [
                0.999999653367379,
                0.9999997897566089,
                0.9999996072138465,
                0.9999997617630049,
                0.9999996533672549,
                0.9999991684719725,
                0.9999997897566589,
                0.9999986290421394,
                0.9999998555019618,
                0.9999998874648245
            ],
            [
                0.9999984465024306,
                0.9999997897567091,
                0.9999997300422869,
                0.9999996072136125,
                0.9999957771675632,
                0.9999977396759717,
                0.9999991684718733,
                0.9999991684721706,
                0.9999982396569966,
                0.9999977396746245
            ],
            [
                0.9999987901343166,
                0.9999980052695655,
                0.999999266178757,
                0.9999997897565587,
                0.9999986290431201,
                0.9999987901347492,
                0.9999996072137529,
                0.9999994284992805,
                0.9999987901341724,
                0.9999994284992804
            ],
            [
                0.9999977396757023,
                0.9999990577554062,
                0.9999996940978095,
                0.9999989322970029,
                0.9999993524054334,
                0.9999996072137529,
                0.9999984465026159,
                0.9999997897566589,
                0.9999998724809267,
                0.9999996072137061
            ],
            [
                0.9999995549150011,
                0.9999996533672135,
                0.9999980052707543,
                0.999999789756634,
                0.9999996533672136,
                0.9999996533672962,
                0.9999998362622552,
                0.999999352404893,
                0.9999996940977366,
                0.9999997897565587
            ],
            [
                0.999998932296621,
                0.9999986290421395,
                0.999999939764258,
                0.9999996533673375,
                0.999999495652652,
                0.9999998144609645,
                0.9999995549147889,
                0.999998790134605,
                0.9999990577555185,
                0.9999994956523512
            ],
            [
                0.999999554914895,
                0.9999991684721706,
                0.9999967112521114,
                0.9999997300421581,
                0.9999994956526519,
                0.9999987901338839,
                0.9999980052698031,
                0.9999989322975119,
                0.9999994284995529,
                0.999999789756634
            ],
            [
                0.9999994284995529,
                0.9999996533674615,
                0.9999996940978095,
                0.9999992661791944,
                0.9999996533674202,
                0.9999997300421581,
                0.9999997300420937,
                0.9999994956525918,
                0.9999992661791071,
                0.9999962733616051
            ],
            [
                0.9999996940976272,
                0.9999997617631183,
                0.9999996072138934,
                0.999999168471675,
                0.999999554914895,
                0.9999989322973846,
                0.9999993524049703,
                0.9999996072137529,
                0.9999997897566089,
                0.999999855502048
            ],
            [
                0.9999997617630049,
                0.9999995549150011,
                0.999999730042319,
                0.9999989322972572,
                0.9999974387177895,
                0.9999997617630332,
                0.9999995549148419,
                0.9999990577555185,
                0.9999990577557432,
                0.9999994284994849
            ],
            [
                0.9999996072139402,
                0.9999980052709919,
                0.9999991684721706,
                0.9999986290424664,
                0.9999991684720715,
                0.9999986290431201,
                0.9999987901340281,
                0.9999996072136593,
                0.9999990577552939,
                0.9999994956527121
            ],
            [
                0.9999992661786695,
                0.9999996072136592,
                0.9999982396572065,
                0.9999994956526519,
                0.9999984465022456,
                0.9999991684720716,
                0.999999495652652,
                0.999999428499553,
                0.9999996940978825,
                0.9999974387168734
            ],
            [
                0.9959298620840191,
                0.99896776919745,
                0.9999785550464758,
                0.9999785550541487,
                0.8354835452961425,
                0.9999910603036964,
                0.9999938558268635,
                0.9999921107392967,
                0.999995214903224,
                0.9999938558268635
            ],
            [
                0.9999996533672549,
                0.9999977396748945,
                0.9999996072138934,
                0.9999994956527121,
                0.9999987901344608,
                0.9999992661790195,
                0.9999974387184002,
                0.9999998555019446,
                0.9999996072137998,
                0.9999996940977731
            ],
            [
                0.9999986290429568,
                0.9999997897565587,
                0.9999997617630616,
                0.9999997617629764,
                0.9999997617630332,
                0.9999994284996211,
                0.9999996533674201,
                0.9999997897567091,
                0.9999996940976636,
                0.9999984465015048
            ],
            [
                0.9999997897567091,
                0.9999995549150542,
                0.9999998362623723,
                0.9999998362623528,
                0.9999996940978095,
                0.9999994956527721,
                0.9999997897566089,
                0.999999814460854,
                0.9999982396574164,
                0.9999997617631184
            ],
            [
                0.9999994956527722,
                0.999999266178757,
                0.999999554914895,
                0.9999995549148419,
                0.9999994956524114,
                0.9999994956527722,
                0.9999957771650457,
                0.999999554914789,
                0.9999990577552939,
                0.999999057755743
            ],
            [
                0.9999996940978095,
                0.999999887464744,
                0.9999997300422547,
                0.9999997897566589,
                0.9999998362623528,
                0.9999997617631752,
                0.9999997617630616,
                0.9999998362623723,
                0.9999997617631468,
                0.9999995549150542
            ],
            [
                0.9999998555020307,
                0.9999998144608097,
                0.9999995549147889,
                0.9999996940978825,
                0.9999993524050473,
                0.9999997300421581,
                0.999999653367503,
                0.9999997300422225,
                0.9999998362622942,
                0.9999994284993485
            ],
            [
                0.9999996533672135,
                0.9999995549149481,
                0.9999987901338838,
                0.9999996533675028,
                0.9999982396563671,
                0.9999994956527121,
                0.9999977396759718,
                0.9999998144608097,
                0.999999495652712,
                0.9999997617631752
            ],
            [
                0.9999996072136125,
                0.9999998362623722,
                0.9999996072138934,
                0.9999995549149481,
                0.9999997897566089,
                0.9999996072136125,
                0.9999994956524114,
                0.9999998144608319,
                0.999999653367379,
                0.9999995549147358
            ],
            [
                0.9999996072137529,
                0.9996200154739502,
                0.9999984465015047,
                0.9999810748450086,
                0.9999921107345934,
                0.9999977396746245,
                0.9999995549150011,
                0.9999997617631468,
                0.9999986290432835,
                0.9999938558239349
            ],
            [
                0.9999990577551816,
                0.9999991684719725,
                0.9999997300421903,
                0.9999970976866313,
                0.9999994284992805,
                0.999999694097846,
                0.9999998724809571,
                0.9999991684720715,
                0.9999996072136592,
                0.9999984465028011
            ],
            [
                0.999999495652712,
                0.999999789756684,
                0.999999789756659,
                0.999999789756659,
                0.9999994956523514,
                0.9999996072137061,
                0.9999996940977366,
                0.9999997617631184,
                0.9999996533672136,
                0.9999995549150541
            ],
            [
                0.9999997300421903,
                0.9999974387168734,
                0.9999987901346049,
                0.9999980052705165,
                0.9999991684722697,
                0.9999993524053562,
                0.9999987901341725,
                0.999999653367503,
                0.9999993524054335,
                0.9999986290429567
            ],
            [
                0.9999990577550693,
                0.9999994956525918,
                0.9999996533675028,
                0.9999996072138934,
                0.9999995549148419,
                0.9999995549147358,
                0.9999996533672549,
                0.9999998724809723,
                0.999998629042303,
                0.9999997617629763
            ],
            [
                0.9999984465016899,
                0.9999994956524716,
                0.9999993524054334,
                0.9999987901340281,
                0.9999997300421581,
                0.9999989322966208,
                0.9999997617629764,
                0.9999998144609202,
                0.9999998144609645,
                0.999998790134605
            ],
            [
                0.9999996072138465,
                0.9999994956527121,
                0.9999995549147889,
                0.9999994956525917,
                0.999999266178757,
                0.9999994956524716,
                0.9999991684715759,
                0.9999994284994168,
                0.9999977396762413,
                0.999999428499553
            ],
            [
                0.9999997617631183,
                0.9999986290424664,
                0.999999730042126,
                0.9999984465024307,
                0.99999976176309,
                0.9999994956527721,
                0.9999994956525317,
                0.999999694097846,
                0.9999991684722698,
                0.9999997617631183
            ],
            [
                0.9999986290427931,
                0.99999976176309,
                0.9999995549147359,
                0.9999997617629764,
                0.9999996533672549,
                0.999998932296621,
                0.9999996940978825,
                0.999999730042126,
                0.999999694097773,
                0.9999993524051246
            ],
            [
                0.999999653367379,
                0.9999989322967482,
                0.9999986290432836,
                0.9999998362623137,
                0.9999994284994167,
                0.9999997300422869,
                0.9999996072137529,
                0.9999996533674202,
                0.9999994284996211,
                0.9999995549147358
            ],
            [
                0.9999996940977731,
                0.99999976176309,
                0.9999993524053563,
                0.9999996940976272,
                0.9999996072136592,
                0.9999994956525317,
                0.9999997897565838,
                0.9999991684718732,
                0.9999996533672136,
                0.9999998724809267
            ],
            [
                0.9999974387184,
                0.9999997300420937,
                0.9999996940978461,
                0.9999993524049702,
                0.9999998362623528,
                0.999999855502048,
                0.9999998362622552,
                0.9999987901341724,
                0.9999992661786696,
                0.9999996533672136
            ],
            [
                0.9999993524052789,
                0.9999995549149481,
                0.9999997617629764,
                0.9999996533672962,
                0.9999992661792819,
                0.9999992661791071,
                0.9999994284992805,
                0.9999967112497585,
                0.9999987901343165,
                0.9999986290432835
            ],
            [
                0.9999994956525918,
                0.9999997300421581,
                0.9999995549151073,
                0.9999995549148419,
                0.9999996533673375,
                0.9999994284997573,
                0.9999995549150542,
                0.9999974387187054,
                0.9999998362623332,
                0.9999996072139402
            ],
            [
                0.999999789756634,
                0.9999992661788445,
                0.9999991684720715,
                0.9999990577551815,
                0.9999996533672962,
                0.9999996533674201,
                0.9999998144608981,
                0.9999997897566589,
                0.9999995549148419,
                0.9999997897567091
            ],
            [
                0.9999989322972572,
                0.9999995549150542,
                0.9999998874648379,
                0.999999607213753,
                0.9999982396563671,
                0.9999997617631468,
                0.9999998874648514,
                0.9999998144608981,
                0.9999996072136592,
                0.9999997300422225
            ],
            [
                0.9999984465020603,
                0.9999996072136125,
                0.9999987901347491,
                0.9999987901340281,
                0.9999984465018752,
                0.9999987901340281,
                0.9999991684722698,
                0.9999990577557432,
                0.9999990577550691,
                0.9999952149072168
            ],
            [
                0.9999989322973846,
                0.9999991684715759,
                0.9999992661786696,
                0.9999980052695652,
                0.9999991684719723,
                0.9999990577550691,
                0.9999989322968755,
                0.9999994284992805,
                0.9999980052693275,
                0.9999977396765106
            ],
            [
                0.99999893229713,
                0.9999994284996893,
                0.9999994284996893,
                0.9999990577556308,
                0.9999996533672549,
                0.9999996072136592,
                0.9999995549148419,
                0.9999990577549568,
                0.9999991684717742,
                0.9999986290431201
            ],
            [
                0.9999996533672135,
                0.9999998144608097,
                0.9999994284994849,
                0.9999995549150011,
                0.999998790134605,
                0.9999989322970028,
                0.9999996940976271,
                0.9999991684717741,
                0.999999855501979,
                0.9999996940977366
            ],
            [
                0.9999996940976636,
                0.9999994956524114,
                0.999999855502048,
                0.9999990577552937,
                0.9999996072136125,
                0.9999996533674202,
                0.9999990577557432,
                0.9999974387174841,
                0.9999977396746245,
                0.999999855502048
            ],
            [
                0.9999930377412609,
                0.817574471748733,
                0.9999962733589399,
                0.9999952149072174,
                0.9999251537460276,
                0.999989870009022,
                0.9999957771655489,
                0.9999952149037947,
                0.9999756997592744,
                0.9999910603058317
            ],
            [
                0.9999995549147359,
                0.9999980052693275,
                0.9999995549149481,
                0.9999991684719723,
                0.9999994284996212,
                0.9999996072137998,
                0.9999998362622942,
                0.9999998144608317,
                0.9999998362623528,
                0.9999996072137061
            ],
            [
                0.9999989322968754,
                0.9999996533672549,
                0.9999952149037947,
                0.999996273359828,
                0.9999994284996211,
                0.9999990577551815,
                0.9999967112521111,
                0.9999930377462417,
                0.9999986290429567,
                0.9999982396559474
            ],
            [
                0.9998601779094202,
                0.9999546021097243,
                0.9999038975736445,
                0.999941708741465,
                0.9996200154712528,
                0.994779873397228,
                0.9998415638021905,
                0.9997388096908902,
                0.9990889488899464,
                0.9968273172289412
            ],
            [
                0.9999993524052019,
                0.9999986290426297,
                0.9999989322970027,
                0.9999987901343166,
                0.999999352404893,
                0.999999266179107,
                0.9999986290424664,
                0.9999986290429567,
                0.9999992661786696,
                0.9999980052707541
            ],
            [
                0.9999993524049702,
                0.9999994956524716,
                0.9999994284997573,
                0.9999991684719723,
                0.9999970976890528,
                0.9999989322970027,
                0.999999352405279,
                0.9999989322970027,
                0.999999495652652,
                0.9999962733620489
            ],
            [
                0.9999997897566589,
                0.9999996072137061,
                0.9999977396751636,
                0.9999996940976272,
                0.9999994956523514,
                0.9999998362622942,
                0.9999984465018751,
                0.9999994956525918,
                0.9999993524049703,
                0.9999997617630048
            ],
            [
                0.9999990577552937,
                0.9999957771650455,
                0.9999995549147359,
                0.9999991684720715,
                0.9999970976890529,
                0.9999980052693275,
                0.9999982396559473,
                0.9999938558239335,
                0.9999996072137529,
                0.9999986290432835
            ],
            [
                0.9999996072138934,
                0.9999994956526519,
                0.9999992661789321,
                0.9999994284995529,
                0.9999957771660524,
                0.999999266178757,
                0.9999994956525917,
                0.9999992661791071,
                0.99999893229713,
                0.9999996940978461
            ],
            [
                0.9999980052693276,
                0.9999994956525317,
                0.9999986290426298,
                0.9999987901346049,
                0.9999980052693275,
                0.9999996533673375,
                0.9999990577550691,
                0.9999994284993486,
                0.9999987901346049,
                0.9999974387184007
            ],
            [
                0.9999991684722697,
                0.9999996072138934,
                0.999999352405279,
                0.999999554914842,
                0.9999996072139402,
                0.99999893229713,
                0.999999653367379,
                0.9999986290427931,
                0.9999996072136125,
                0.9999990577550691
            ],
            [
                0.999999855501979,
                0.9999997897565838,
                0.9999998144608981,
                0.9999994284995529,
                0.9999962733593839,
                0.9999996072136125,
                0.9999994956527121,
                0.9999987901338839,
                0.9999998362622552,
                0.9999992661786695
            ],
            [
                0.9999996940976636,
                0.9999994284992804,
                0.9999998144608097,
                0.9999990577549569,
                0.9999996533672549,
                0.9999998362622942,
                0.9999998362622746,
                0.9999989322968754,
                0.9999997897565587,
                0.9999994956525917
            ],
            [
                0.9999996533672962,
                0.999999653367379,
                0.9999997897566589,
                0.9999987901337397,
                0.999999814460854,
                0.9999993524049702,
                0.9999994956523514,
                0.9999990577550693,
                0.9999982396567868,
                0.9999997897567341
            ],
            [
                0.9999995549149481,
                0.9999938558275976,
                0.999996273361161,
                0.9999998144609202,
                0.9999989322973847,
                0.9999989322972573,
                0.9999996072136125,
                0.9999996072137998,
                0.999999653367379,
                0.9999994284996211
            ],
            [
                0.9999974387180949,
                0.9999990577551816,
                0.9999996940976271,
                0.9999997300420937,
                0.9999977396759717,
                0.9999997300420937,
                0.9999997617631752,
                0.9999970976869772,
                0.9999998362622747,
                0.9999996533674201
            ],
            [
                0.9999997897565588,
                0.9999996533674202,
                0.9999992661789321,
                0.9999991684721706,
                0.9999996072136125,
                0.9999993524050476,
                0.9999984465015048,
                0.9999995549147358,
                0.9999995549150011,
                0.999999730042319
            ],
            [
                0.9999997617631183,
                0.999999730042319,
                0.9999977396762411,
                0.9999997300421903,
                0.9999998874649184,
                0.9999996072137061,
                0.9999996533674201,
                0.9999997617630616,
                0.9999990577549568,
                0.9999997897566589
            ],
            [
                1.7603432133032607e-06,
                1.2098662604192665e-06,
                3.7266383946527958e-06,
                3.2887506334201674e-06,
                1.9947306725868575e-06,
                3.2887498494282754e-06,
                1.9947292458004866e-06,
                2.260324297853209e-06,
                1.4738988994015443e-05,
                1.7603425837494853e-06
            ],
            [
                0.9999982396561572,
                0.9999996940977001,
                0.9999997897567091,
                0.9999987901347492,
                0.9999996940977366,
                0.9999980052702786,
                0.9999996072136125,
                0.9999980052698031,
                0.9999980052693275,
                0.9999993524054334
            ],
            [
                0.9999998874648781,
                0.9999998555019963,
                0.9999998874647977,
                0.9999998724808963,
                0.9999997300421903,
                0.9999998362623332,
                0.9999998362622552,
                0.999999900688043,
                0.9999998874647709,
                0.9999998144608981
            ],
            [
                0.9999992661792819,
                0.9999993524052018,
                0.9999991684718733,
                0.999999495652652,
                0.9999996533673375,
                0.9999987901344607,
                0.9999994956527121,
                0.9999994956526519,
                0.9999984465020603,
                0.9999994956525317
            ],
            [
                0.9999998362622747,
                0.9999997617630332,
                0.999999694097846,
                0.9999990577557432,
                0.9999995549150011,
                0.9999997300422225,
                0.9999996940977002,
                0.9999982396559474,
                0.999999554914789,
                0.9999998144609202
            ],
            [
                0.9999996072137998,
                0.9999998144608097,
                0.9999989322968754,
                0.99999976176309,
                0.9999993524051246,
                0.9999996072136592,
                0.9999994956524716,
                0.9999997300421581,
                0.9999991684716749,
                0.9999994956526519
            ],
            [
                0.9999996940977366,
                0.9999991684715759,
                0.9999991684722698,
                0.9999994956527721,
                0.9999990577557432,
                0.9999994956524716,
                0.9999993524049703,
                0.9999987901344608,
                0.9999982396572067,
                0.9999994956524715
            ],
            [
                0.9999996940977002,
                0.9999994956524716,
                0.9999994956527721,
                0.9999995549150542,
                0.9999996533672136,
                0.9999996533675028,
                0.9999994284997573,
                0.9999989322975119,
                0.9999982396572065,
                0.9999996072137061
            ],
            [
                0.9999996072138465,
                0.9999994956527121,
                0.9999994956524114,
                0.9999996940978825,
                0.999999352404893,
                0.9999996533672549,
                0.9999996940977366,
                0.9999998555019446,
                0.9999995549151073,
                0.9999995549147359
            ],
            [
                0.9999994284996211,
                0.9999982396567868,
                0.9999989322966211,
                0.9999993524052019,
                0.999999554914789,
                0.9999989322972572,
                0.9999952149037947,
                0.9999991684718733,
                0.9999995549149481,
                0.9999994284996891
            ],
            [
                0.9999998362623528,
                0.9999995549150542,
                0.9999994956527121,
                0.9999994956525918,
                0.9999997897567342,
                0.999999789756684,
                0.9999995549150011,
                0.9999996072137529,
                0.9999994284994168,
                0.999999653367379
            ],
            [
                0.999998932296621,
                0.9999997617630049,
                0.999999789756684,
                0.9999994956525918,
                0.9999984465020603,
                0.9999997617629763,
                0.9999990577551815,
                0.9999991684722698,
                0.9999987901337397,
                0.9999999123575987
            ],
            [
                0.9999910603068987,
                0.999999266179107,
                0.9999977396765106,
                0.9999982396559474,
                0.9999996072136593,
                0.9999991684721706,
                0.9999977396765111,
                0.9999999123574628,
                0.9999995549148419,
                0.9999980052695653
            ],
            [
                0.9999991684722697,
                0.9999987901344608,
                0.999999495652712,
                0.9999996940978825,
                0.9999974387180947,
                0.9999996533673788,
                0.9999994284994167,
                0.9999977396762413,
                0.9999991684719723,
                0.9999967112493667
            ],
            [
                0.9999996072137529,
                0.9999991684717742,
                0.9999996533673788,
                0.9999974387184001,
                0.9999995549150011,
                0.9999993524053562,
                0.9999995549147358,
                0.9999990577552939,
                0.9999986290421394,
                0.9999995549150011
            ],
            [
                0.9999995549151073,
                0.9999984465022456,
                0.9999994284995529,
                0.9999982396559474,
                0.9999991684722698,
                0.9999957771680668,
                0.9999994956527121,
                0.9999994956527121,
                0.9999957771680663,
                0.999998790134028
            ],
            [
                0.9999989322967482,
                0.9999990577555185,
                0.9999977396759718,
                0.9999974387177895,
                0.9999997617629764,
                0.9999986290427932,
                0.9999994956525318,
                0.999999653367503,
                0.9999996072139402,
                0.9999996940978825
            ],
            [
                0.9999992661788446,
                0.9999993524050474,
                0.9999994284997574,
                0.9999997617629764,
                0.9999994284996891,
                0.9999996940977366,
                0.9999997300422868,
                0.9999998555019962,
                0.9999989322968754,
                0.9999994956524114
            ],
            [
                0.9999997300422869,
                0.9999987901340281,
                0.9999989322966208,
                0.9999996072137529,
                0.9999987901347492,
                0.9999992661790195,
                0.9999996533674201,
                0.9999989322968755,
                0.9999995549147889,
                0.9999994956524716
            ],
            [
                0.9999993524048931,
                0.9999997617631184,
                0.999999352405279,
                0.9999995549151072,
                0.9999998555020306,
                0.9999984465022456,
                0.9999996533672135,
                0.9999994956527722,
                0.999995777166556,
                0.9999987901344607
            ],
            [
                0.9999982396565769,
                0.9999997300422225,
                0.9999982396572065,
                0.9999997617630899,
                0.9999993524049702,
                0.9999996533672962,
                0.9999998555019962,
                0.9999994956523514,
                0.9999990577551815,
                0.9999996533672549
            ],
            [
                0.9999995549149481,
                0.9999992661791945,
                0.999999266178932,
                0.9999998144609202,
                0.9999998362622943,
                0.9999995549149481,
                0.9999997617629764,
                0.9999986290421397,
                0.9999994284996893,
                0.9999991684716749
            ],
            [
                0.9999998144609645,
                0.999999814460876,
                0.9999998144609644,
                0.9999996533672962,
                0.9999997897566589,
                0.9999998724809267,
                0.9999999226557684,
                0.9999998144609645,
                0.9999997617629764,
                0.9999991684719725
            ],
            [
                0.9999998724808963,
                0.9999998362623137,
                0.9999991684717741,
                0.9999991684719723,
                0.9999997897565587,
                0.9999996940976272,
                0.9999997897566589,
                0.9999986290432835,
                0.9999998144609203,
                0.9999996533672549
            ],
            [
                0.9999993524050474,
                0.9999992661789321,
                0.9999977396757023,
                0.9999994284992805,
                0.9999996940977001,
                0.9999991684718733,
                0.999999352404893,
                0.9999990577549568,
                0.9999984465018752,
                0.9999993524052019
            ],
            [
                0.9999998144609423,
                0.9999997300422225,
                0.9999986290426298,
                0.9999996533673376,
                0.9999997300422225,
                0.9999997617631469,
                0.9999996940978095,
                0.9999996072139402,
                0.9999998144609202,
                0.9999996533672136
            ],
            [
                0.9999996533673375,
                0.999998239656367,
                0.9999984465020603,
                0.9999994284997574,
                0.9999996940977366,
                0.9999993524053562,
                0.9999994956525918,
                0.9999998555019446,
                0.9999994284993486,
                0.9999995549151072
            ]
        ]
    },
    {
        "q_id": "8427_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            10,
            11,
            12,
            13,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            33,
            34,
            35,
            36,
            37,
            38,
            40,
            41,
            42,
            43,
            46,
            47,
            48,
            49,
            50,
            51,
            53,
            54,
            55,
            56,
            57,
            59,
            61,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            74,
            75,
            76,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            93,
            94,
            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,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                5.04347408156499e-07,
                1.0129988563546333e-05,
                7.338209804600024e-07,
                1.012998856312253e-05,
                7.889266347248781e-06,
                1.8925152744771773e-05,
                1.0677031245429291e-06,
                3.7266392838544054e-06,
                3.726640172337686e-06,
                1.7603436329554703e-06
            ],
            [
                6.9622595668378125e-06,
                4.785095633181251e-06,
                0.998830489477924,
                0.006692850788072181,
                0.9964063969233655,
                0.9997040428322638,
                0.9984988180887695,
                0.9986749776305418,
                0.9875683472830811,
                6.962257075741783e-06
            ],
            [
                1.670142778941753e-05,
                3.726641061027928e-06,
                7.338213303776118e-07,
                6.962254587420098e-06,
                2.9023126769050284e-06,
                3.288748672760313e-06,
                1.147876675162131e-05,
                3.2887486731252264e-06,
                1.8925152738024674e-05,
                4.785095064436034e-06
            ],
            [
                0.9998415638032324,
                0.9998415637652545,
                5.04347528431602e-07,
                0.9984988174103203,
                0.9971990734679398,
                1.5534971985923634e-06,
                0.07585817270885642,
                0.11920292984474948,
                0.0011695103730313308,
                0.9992903295822826
            ],
            [
                6.475945665853783e-07,
                1.5534983100228109e-06,
                6.14417606210672e-06,
                2.4300231986394238e-05,
                3.7266406163624873e-06,
                0.8519528057272544,
                0.8807970873650401,
                0.7549149868676283,
                8.939697368305565e-06,
                0.9241418236349501
            ],
            [
                2.4300237795616407e-05,
                1.0129989770662257e-05,
                8.481107124843357e-05,
                2.4300252306390083e-05,
                3.535625480461658e-05,
                2.430024068917781e-05,
                2.753569107251144e-05,
                2.430023782010365e-05,
                1.1478772229781076e-05,
                2.1444950947650794e-05
            ],
            [
                6.9622562425398595e-06,
                4.2228324372555256e-06,
                6.962255419051463e-06,
                2.144494329496561e-05,
                1.9947301970451086e-06,
                1.7603434230312906e-06,
                1.3709576971061233e-06,
                1.7603438427852151e-06,
                1.3007125359792008e-05,
                1.0129990978441666e-05
            ],
            [
                3.120191878472311e-05,
                1.5534984952492866e-06,
                2.4300237779527314e-05,
                0.9994472212826166,
                1.9947294833018263e-06,
                6.962256248871951e-06,
                1.994730196616959e-06,
                1.8925145972677006e-05,
                4.222834952030037e-06,
                3.726640171768275e-06
            ],
            [
                1.3007128458384476e-05,
                3.2887486719886124e-06,
                3.72663839473414e-06,
                1.5534981246861515e-06,
                1.6373762768505704e-07,
                4.785096205717126e-06,
                6.144176061614971e-06,
                2.260325375615501e-06,
                1.5534979395006942e-06,
                2.2603237589028734e-06
            ],
            [
                1.760343422365266e-06,
                2.902311638596061e-06,
                3.7266379507909478e-06,
                3.2887478892055875e-06,
                3.4663270374206273e-07,
                6.144174600325954e-06,
                9.422447060393854e-07,
                NaN,
                3.288749847798131e-06,
                2.430023780560579e-05
            ],
            [
                0.0001088968695065005,
                3.120190389197351e-05,
                4.006368252433876e-05,
                0.9669140195852891,
                0.9959298631354075,
                1.0129995806022926e-05,
                1.1478766756214804e-05,
                1.473898722977843e-05,
                2.561281905100056e-06,
                1.0129995808178788e-05
            ],
            [
                0.2018132126589859,
                0.9999151889689127,
                0.9998911030393285,
                0.9994472213293746,
                0.9998601779269202,
                2.5612828208879873e-06,
                7.889265406567165e-06,
                0.9999810748562977,
                0.999841563747569,
                0.9999724643122028
            ],
            [
                1.7603427935678977e-06,
                2.9023116389365734e-06,
                4.222832436955956e-06,
                4.222833443461647e-06,
                3.466327037512053e-07,
                2.2603248365343694e-06,
                5.422218322664422e-06,
                6.144176798590883e-06,
                2.902311292002183e-06,
                1.994729721469003e-06
            ],
            [
                2.1024341621006495e-07,
                6.962254588585202e-06,
                NaN,
                6.962259569003389e-06,
                2.9023126767836054e-06,
                1.994729245878497e-06,
                4.785094493419144e-06,
                2.5612812938854287e-06,
                1.7603427935678977e-06,
                1.892515272983176e-05
            ],
            [
                3.726637951126493e-06,
                6.144176066353646e-06,
                5.422220907426478e-06,
                1.012999339309804e-05,
                9.422442569028803e-07,
                7.889266345770692e-06,
                1.2098656834613962e-06,
                1.553497939625029e-06,
                3.288749849368453e-06,
                1.9947297211279344e-06
            ],
            [
                7.484620031370475e-05,
                6.144176065940129e-06,
                1.8925141433805818e-05,
                0.04208772386048602,
                1.147876674819707e-05,
                5.82912653104079e-05,
                0.9149009625340367,
                4.785094491756681e-06,
                0.9947798742967692,
                4.006369685369712e-05
            ],
            [
                0.9998911031049706,
                0.01798620946860125,
                NaN,
                0.0004305570193235674,
                5.829125149535031e-05,
                1.300713463035057e-05,
                1.3007128432311684e-05,
                0.9964063973793963,
                0.994088931132811,
                NaN
            ],
            [
                1.0129990979031306e-05,
                9.422442568763144e-07,
                6.9622537584863015e-06,
                1.5534975693488444e-06,
                2.1444953521586782e-05,
                4.785095064819011e-06,
                2.1444943294263477e-05,
                5.422220262333096e-06,
                NaN,
                8.93970054731268e-06
            ],
            [
                0.9992903294664539,
                NaN,
                1.8925143702277406e-05,
                0.9999151889384766,
                0.9998204720171021,
                0.9980732654253247,
                NaN,
                0.9999687980774995,
                2.561283126160022e-06,
                2.7535700920674098e-05
            ],
            [
                4.0063706430021914e-05,
                4.785096203118982e-06,
                1.670141784666869e-05,
                6.9622562472889285e-06,
                8.939693101987369e-06,
                2.1444943297072005e-05,
                5.422219612998742e-06,
                6.144176797585032e-06,
                NaN,
                1.4738981957765705e-05
            ],
            [
                0.9579122749379931,
                0.9669140243523637,
                5.8291251396535027e-05,
                2.2603251051796405e-06,
                0.9997040428302661,
                0.8807970842359877,
                0.9988304898714782,
                0.9998204720338529,
                2.1444956020629035e-05,
                0.9875683518109231
            ],
            [
                3.7266392817462323e-06,
                3.535626334323525e-05,
                4.222831932021007e-06,
                4.006368232204473e-05,
                5.144221975938208e-05,
                3.2887486726287055e-06,
                6.144177530548804e-06,
                1.012998977022003e-05,
                6.144173132242205e-06,
                2.753570420840434e-05
            ],
            [
                1.0677024880178757e-06,
                2.1444950968441685e-05,
                6.962257909323729e-06,
                3.288750241410738e-06,
                1.0129994600638342e-05,
                4.7850944943330625e-06,
                6.962259566204604e-06,
                8.939700566143004e-06,
                1.7603440524628877e-06,
                1.9947301969217434e-06
            ],
            [
                6.96225541916544e-06,
                6.962259569313662e-06,
                8.939695234983602e-06,
                2.9023109468548636e-06,
                0.9982992774812389,
                1.8925141465820123e-05,
                1.8925143720384422e-05,
                1.8925141449434308e-05,
                0.9980732654324886,
                6.9622570784012604e-06
            ],
            [
                4.7850956351657615e-06,
                2.753568780461672e-05,
                6.962257908487893e-06,
                4.222832940942332e-06,
                1.3709578605455302e-06,
                4.006371127619171e-05,
                1.892514359356646e-05,
                6.96225375863827e-06,
                3.7266410609160796e-06,
                0.033085978388704126
            ],
            [
                2.7535681197606525e-05,
                6.144173136645595e-06,
                2.56128282048266e-06,
                4.222834447693925e-06,
                0.9989677688646894,
                1.553498495230919e-06,
                0.9959298625332659,
                NaN,
                0.020332355160653563,
                1.1478765384764794e-05
            ],
            [
                8.48110104253969e-05,
                3.535626332702904e-05,
                0.0002305067618667467,
                1.1478772226356834e-05,
                0.8807970670261976,
                6.962257077932685e-06,
                4.5397890190965e-05,
                1.4738980205754734e-05,
                1.012998856312253e-05,
                0.0
            ],
            [
                1.8925145966893773e-05,
                0.9982992776057605,
                0.9998911031170887,
                5.8291286228722664e-05,
                0.9996646499722618,
                0.9968273166958208,
                0.9995121427812825,
                0.000261190242567222,
                1.8925141462377723e-05,
                0.995390426942481
            ],
            [
                1.8925152738024674e-05,
                5.4222202614355715e-06,
                NaN,
                5.4222189669981275e-06,
                1.760344052402049e-06,
                NaN,
                5.4222196101976765e-06,
                6.144177530146464e-06,
                2.9023123296511196e-06,
                1.473898195905257e-05
            ],
            [
                1.3709572068179446e-06,
                7.889264466344872e-06,
                5.422219615898437e-06,
                0.9924227590507932,
                0.984093610737347,
                2.260324028372372e-06,
                6.144174601499446e-06,
                0.998073265726205,
                1.892515500715167e-05,
                1.8925157258585e-05
            ],
            [
                1.6701419850389357e-05,
                1.7603427931548347e-06,
                1.892514370819833e-05,
                1.370957860466977e-06,
                NaN,
                4.785095634460739e-06,
                6.962257908487893e-06,
                1.4738978421036199e-05,
                4.222833945815874e-06,
                4.7850944937411915e-06
            ],
            [
                1.4738981965808603e-05,
                3.059022998436399e-07,
                1.1478764015736973e-05,
                6.475949525663707e-07,
                3.2887478882574116e-06,
                5.422217671880454e-06,
                3.7266397280485686e-06,
                6.9622595668378125e-06,
                1.0129992186387057e-05,
                2.9023130228444433e-06
            ],
            [
                1.994729721482609e-06,
                6.144172403592939e-06,
                1.3007128464559612e-05,
                1.2098653949842147e-06,
                1.760343842833246e-06,
                5.422221554374162e-06,
                6.962258739271155e-06,
                1.0677024879557274e-06,
                1.0129987354882753e-05,
                1.3007130010543792e-05
            ],
            [
                0.9999898700078126,
                0.9991959139573227,
                0.9998766053663705,
                0.9999599363078477,
                0.9999417087066845,
                0.9999869928730869,
                0.9999852610127591,
                0.9999898700041914,
                0.9999930377445807,
                0.9999687980811924
            ],
            [
                4.7850933534310035e-06,
                NaN,
                4.222833444037741e-06,
                1.5534983088402167e-06,
                NaN,
                1.067702869764479e-06,
                1.994729007809344e-06,
                2.5612834319655406e-06,
                4.222835457595211e-06,
                4.785093924103951e-06
            ],
            [
                6.9622537584863015e-06,
                1.4738976695942536e-05,
                7.484621664709448e-05,
                1.994729245519287e-06,
                1.4738976686988113e-05,
                8.939699497042417e-06,
                4.222833943972373e-06,
                8.93970056350871e-06,
                1.0129994598777299e-05,
                0.9859363704386079
            ],
            [
                4.7850950649408664e-06,
                1.7603425836678333e-06,
                1.1478768123551712e-05,
                1.3709572067680694e-06,
                2.753570085726551e-05,
                2.561283431888668e-06,
                2.561283431888668e-06,
                2.753570418556523e-05,
                1.994729721482609e-06,
                NaN
            ],
            [
                6.962256245579263e-06,
                1.3007130006521673e-05,
                2.260324836250676e-06,
                2.9023109470871505e-06,
                3.120191508707442e-05,
                2.9023112927307205e-06,
                NaN,
                5.715003787319999e-07,
                5.422220906864292e-06,
                9.422448168416369e-07
            ],
            [
                0.9975273769065358,
                3.120192242584505e-05,
                0.9940889304159043,
                0.9986749777932171,
                5.422220905315815e-06,
                1.892515725149365e-05,
                0.9998911030656754,
                0.9998911030648404,
                7.889262584508638e-06,
                1.3007131558917768e-05
            ],
            [
                1.0129993386593603e-05,
                NaN,
                0.9964063973252062,
                0.9999339478241241,
                3.7266410605974813e-06,
                2.144495860587775e-05,
                4.7850956298041005e-06,
                0.9971990733118642,
                7.889261642134126e-06,
                1.5534979395289518e-06
            ],
            [
                5.42221767672807e-06,
                0.996406396742454,
                8.31528225655565e-07,
                6.9622537593854575e-06,
                NaN,
                2.753569436805389e-05,
                4.006370166357524e-05,
                1.0129989771288745e-05,
                1.3007131555983986e-05,
                4.7850950647493785e-06
            ],
            [
                8.481103106008262e-05,
                NaN,
                NaN,
                1.473898192141181e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                5.144221972794322e-05,
                NaN
            ],
            [
                3.726638391500705e-06,
                1.9947306720008733e-06,
                3.927860597576085e-07,
                NaN,
                4.2228319339950885e-06,
                7.889260703117714e-06,
                2.3823696677437438e-07,
                1.9947306725868575e-06,
                4.5397890028788624e-05,
                4.2228324370327694e-06
            ],
            [
                1.2098653949842147e-06,
                1.4738981861250941e-05,
                NaN,
                4.785093921819153e-06,
                9.422447060393854e-07,
                1.6701429796754513e-05,
                NaN,
                NaN,
                NaN,
                5.422217028109087e-06
            ],
            [
                2.144495096083526e-05,
                NaN,
                5.829125839291235e-05,
                NaN,
                0.9998601779092962,
                4.222834954461155e-06,
                7.889259750784274e-06,
                4.539788481371178e-05,
                0.00407013677210053,
                1.8925141467679015e-05
            ],
            [
                NaN,
                1.0129993394129904e-05,
                5.1442219756013625e-05,
                1.760343632444745e-06,
                NaN,
                1.012998977088337e-05,
                4.539787942390787e-05,
                6.144173136729416e-06,
                1.7603434230921292e-06,
                2.753570421361326e-05
            ],
            [
                2.144495857014705e-05,
                5.422218321441422e-06,
                2.9023126759653203e-06,
                1.0677031245312763e-06,
                5.422217670401019e-06,
                3.535626330593522e-05,
                4.222834954403545e-06,
                1.8925154993072253e-05,
                1.8925148227861472e-05,
                5.715005150225518e-07
            ],
            [
                6.144175333021237e-06,
                2.144495863411905e-05,
                6.962254588281262e-06,
                4.222833947498071e-06,
                8.315280275280036e-07,
                7.88926258185382e-06,
                1.3007133113703658e-05,
                2.4300252309307336e-05,
                2.144495349826041e-05,
                1.6701417857058377e-05
            ],
            [
                8.315282259051341e-07,
                NaN,
                2.260325104233996e-06,
                4.7850950647493785e-06,
                2.9023130215932583e-06,
                3.726639283440905e-06,
                8.315280276096808e-07,
                5.4222170304318e-06,
                2.5612815913442517e-06,
                2.9023109469023766e-06
            ],
            [
                3.5356250681935664e-05,
                NaN,
                4.006371123902672e-05,
                NaN,
                0.9796676473251761,
                5.1442231888421266e-05,
                NaN,
                2.1444950953735936e-05,
                3.5356267498715946e-05,
                0.00048785722186791647
            ],
            [
                1.1478766753082876e-05,
                1.994729245822257e-06,
                3.726639283752725e-06,
                2.4300234931404677e-05,
                4.785093924156175e-06,
                4.7850967754851966e-06,
                1.3007130012980722e-05,
                1.3007131552624333e-05,
                3.288749849114211e-06,
                7.889263525893087e-06
            ],
            [
                0.9971990732149673,
                0.9999970976869769,
                7.484621761854876e-05,
                0.9995121428878898,
                0.999512142828938,
                2.1444945852673643e-05,
                7.484624486174719e-05,
                0.9999930377445806,
                0.9975273771976952,
                0.9994472213261267
            ],
            [
                1.0129994600638342e-05,
                3.7266379504926854e-06,
                1.5534973840150989e-06,
                0.904650541527608,
                6.96225873320501e-06,
                0.9998415637297454,
                2.7535694345515298e-05,
                6.9622562472889285e-06,
                1.2098659710000347e-06,
                1.0129994590964606e-05
            ],
            [
                3.4663253836369585e-07,
                3.4663249713741784e-07,
                0.9947798739461415,
                0.02297736811196841,
                0.9997694933686195,
                0.9992903295671333,
                7.338207180761315e-07,
                3.288749456563487e-06,
                5.043472278159142e-07,
                2.382369099894428e-07
            ],
            [
                NaN,
                3.120192220541177e-05,
                1.0677031245783732e-06,
                1.9947297214182054e-06,
                3.927861534257969e-07,
                6.1441753335241615e-06,
                3.7266392836984955e-06,
                2.2603237589028734e-06,
                4.539787939913551e-05,
                4.4508515799046414e-07
            ],
            [
                1.1478765382509808e-05,
                2.2603251058292572e-06,
                1.1478772227964558e-05,
                3.288749843574711e-06,
                2.382370235766535e-07,
                2.26032348933062e-06,
                4.785095063826755e-06,
                1.2098653948576728e-06,
                3.726639727750306e-06,
                2.561283126535066e-06
            ],
            [
                6.9622570777680525e-06,
                1.1478770858372173e-05,
                5.422218967649081e-06,
                1.2098652508144226e-06,
                6.962255418924822e-06,
                0.006692849930551545,
                1.0129995803259e-05,
                1.9947306726213275e-06,
                1.4738985483128763e-05,
                1.3709573701812335e-06
            ],
            [
                6.144174598794825e-06,
                1.0129994598777299e-05,
                3.9278624706435693e-07,
                1.994730433764644e-06,
                6.962255419380732e-06,
                1.3007133113372426e-05,
                6.144173135025058e-06,
                7.889266330257934e-06,
                7.889262584006375e-06,
                1.300712845923622e-05
            ],
            [
                9.6102403101794e-05,
                4.222833947498071e-06,
                1.0129988561906404e-05,
                8.939699499823059e-06,
                1.670141586907437e-05,
                8.481108163797566e-05,
                2.4300246523066122e-05,
                3.5356246471407274e-05,
                3.5356246483883486e-05,
                2.902311984915459e-06
            ],
            [
                0.9990889489561737,
                5.043472878832595e-07,
                6.144173868044274e-06,
                NaN,
                0.9968273174027207,
                2.430025230320762e-05,
                1.7603425822012995e-06,
                0.0,
                NaN,
                2.2603237588597026e-06
            ],
            [
                5.422220906716348e-06,
                6.144176063224333e-06,
                4.006370157904312e-05,
                4.222834953420345e-06,
                9.422442566740706e-07,
                0.997817283863475,
                6.962259565976648e-06,
                0.970687767658707,
                6.962253758017727e-06,
                7.88926634455091e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                2.144494328864643e-05,
                1.892515048449202e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                3.120192251631124e-05,
                2.260324836651547e-06,
                2.430023491664161e-05,
                1.1478773594675732e-05,
                1.2098656834723998e-06,
                6.9622570786798724e-06,
                6.144173135628569e-06,
                2.260324836341129e-06,
                7.484622613619929e-05,
                1.2098658277264215e-06
            ],
            [
                4.006371126336615e-05,
                0.997817283420275,
                0.985936376004357,
                0.993307149233598,
                0.9980732653818941,
                0.9982992779745817,
                0.9998911031361611,
                0.9992903297127653,
                0.9980732652077238,
                0.9324533046369554
            ],
            [
                1.6701427805275476e-05,
                3.7266401719851935e-06,
                1.2098656832853378e-06,
                4.222833947498071e-06,
                1.994730672225833e-06,
                5.043474081629207e-07,
                1.9947292458603553e-06,
                7.338211554464836e-07,
                1.5534979397140412e-06,
                3.059023727694626e-07
            ],
            [
                0.9971990731200212,
                0.9990889489696311,
                0.9996200155632619,
                5.144223178811631e-05,
                0.9989677689381561,
                0.9947798736825663,
                0.5926665999540698,
                0.9859363726210016,
                0.9953904272843379,
                4.785093903610399e-06
            ],
            [
                5.04347287945184e-07,
                2.902311638759718e-06,
                1.067702997240607e-06,
                4.222833444229772e-06,
                4.222833444037741e-06,
                2.9023126767360923e-06,
                4.45085104982401e-07,
                3.7266401706904634e-06,
                3.2887494573232236e-06,
                1.0677026154376365e-06
            ],
            [
                9.610243764498401e-05,
                0.993307148837343,
                2.561282210460501e-06,
                5.4222176759932836e-06,
                0.974042645251108,
                4.22283193393364e-06,
                8.939699499432793e-06,
                0.9992903296260383,
                0.9999785550541526,
                0.9995694428632877
            ],
            [
                6.144176798132662e-06,
                1.0129995809247506e-05,
                0.03308598101059528,
                0.09534947004048375,
                0.7981867753392728,
                0.9964063980038331,
                0.006692849534296559,
                0.03308598136812591,
                4.222833443891798e-06,
                NaN
            ],
            [
                0.9999038976081353,
                6.144176066264237e-06,
                0.9997965731000351,
                6.605213635929352e-05,
                8.93969522730838e-06,
                1.6701421837705495e-05,
                0.9998415637838942,
                1.3007125362323574e-05,
                0.9990889490204407,
                8.939693105076969e-06
            ],
            [
                8.939696297969519e-06,
                1.99472900796355e-06,
                4.22283495284425e-06,
                6.144173135025058e-06,
                4.222835457906302e-06,
                4.222832940500659e-06,
                6.144175334239434e-06,
                0.00013982207270966346,
                1.067702615417244e-06,
                0.9669140183935203
            ],
            [
                1.4738988970101218e-05,
                1.5534979396448094e-06,
                1.0129992186589747e-05,
                NaN,
                5.8291244403975446e-05,
                1.5534981248528732e-06,
                2.561283126502453e-06,
                9.42244930849811e-07,
                NaN,
                2.144495096457996e-05
            ],
            [
                7.889261644057078e-06,
                5.422218323093458e-06,
                2.260324028255194e-06,
                2.2603248367173307e-06,
                2.2603245670174926e-06,
                4.22283344433731e-06,
                2.260324567268294e-06,
                6.475948753076037e-07,
                1.9947301970287804e-06,
                2.561281905058126e-06
            ],
            [
                3.288750241410738e-06,
                1.012999218277553e-05,
                2.2603251061232293e-06,
                5.422220261948442e-06,
                6.1441746017453204e-06,
                3.7266406165827946e-06,
                1.3709572068079696e-06,
                9.422442568428928e-07,
                4.222833947774596e-06,
                4.785093923603471e-06
            ],
            [
                0.9914225129547914,
                0.999620015562886,
                0.9984988180297891,
                NaN,
                0.9998415638397973,
                3.120190008331546e-05,
                0.9980732655054699,
                0.9982992772017569,
                0.9626731133251858,
                0.979667645655589
            ],
            [
                2.902313366519096e-06,
                NaN,
                3.2887486723295965e-06,
                0.997527377312551,
                4.222834945885029e-06,
                1.7603438423737528e-06,
                1.3007133025193357e-05,
                NaN,
                3.535624624773583e-05,
                6.144176787235942e-06
            ],
            [
                6.962257908487893e-06,
                1.7603427935967163e-06,
                8.31528424151477e-07,
                1.1478764018827141e-05,
                8.93969417167259e-06,
                6.962255418924822e-06,
                1.1478769487464542e-05,
                3.7266383952696564e-06,
                6.962254588977791e-06,
                5.422218969128516e-06
            ],
            [
                6.962255419279419e-06,
                3.7266383942867467e-06,
                7.889262583633267e-06,
                4.539787942093518e-05,
                4.222832437109582e-06,
                1.6701423823533284e-05,
                1.3007125357378736e-05,
                1.3007128461838766e-05,
                6.144173135762683e-06,
                6.144172404129392e-06
            ],
            [
                NaN,
                4.222832939548183e-06,
                3.2887502414436403e-06,
                NaN,
                1.5534983096766514e-06,
                1.209865392080352e-06,
                3.288749455331158e-06,
                1.2098652507715085e-06,
                3.927862470186306e-07,
                NaN
            ],
            [
                1.0129990979215566e-05,
                4.0063682496355735e-05,
                1.4738981965326028e-05,
                1.4738976675513583e-05,
                1.147877222702498e-05,
                1.1478773591084453e-05,
                2.430023201636237e-05,
                1.9947297176954825e-06,
                2.7535687779473676e-05,
                6.962254578922433e-06
            ],
            [
                4.785095634565186e-06,
                1.1478766754064213e-05,
                2.753570091316123e-05,
                6.96225707422208e-06,
                1.0129993390942177e-05,
                6.962254589528684e-06,
                1.1478773588244838e-05,
                1.4738981965808603e-05,
                3.2887486724851334e-06,
                1.670142382067764e-05
            ],
            [
                1.0129988512211066e-05,
                7.338209805040511e-07,
                1.147876949187012e-05,
                1.3709570433075437e-06,
                2.561282210530385e-06,
                1.1478773594675732e-05,
                3.2887482802097306e-06,
                1.0677031243419178e-06,
                3.12019076269651e-05,
                7.338207179866991e-07
            ],
            [
                3.535623805665442e-05,
                1.892514823488397e-05,
                1.0129995796478171e-05,
                4.785095626757702e-06,
                6.96225375863827e-06,
                1.8925148232956223e-05,
                6.144176065940129e-06,
                1.0677029970405669e-06,
                6.962259565748692e-06,
                1.670142582254589e-05
            ],
            [
                3.2887486729876365e-06,
                0.9996200155155605,
                1.3007131557971383e-05,
                8.315280268655114e-07,
                6.962256247098965e-06,
                0.9993736656977552,
                0.9953904278996801,
                8.481101083448713e-05,
                8.939695235487695e-06,
                0.0009110513215041023
            ],
            [
                0.0001584361784021822,
                0.0035936018244259885,
                0.00013982201691844102,
                0.00010889689582797596,
                0.0001233946327821131,
                4.006368735141308e-05,
                5.1442195212374294e-05,
                NaN,
                2.4300240700846825e-05,
                0.00010889696035142715
            ],
            [
                9.422450431012186e-07,
                1.892515500808112e-05,
                6.144173136455602e-06,
                NaN,
                1.3007133111929193e-05,
                4.450851580497677e-07,
                1.370957860466977e-06,
                5.4222202621161125e-06,
                3.5356259096177054e-05,
                6.475951069896949e-07
            ],
            [
                0.9971990736656355,
                2.7535700932494338e-05,
                0.9993736659730552,
                0.0008040857538017764,
                2.753570091616638e-05,
                2.5612828209345766e-06,
                0.998967768808029,
                0.00026119039765334733,
                0.9324533093296392,
                0.9770226290445921
            ],
            [
                1.6701427797619914e-05,
                3.7266397280960194e-06,
                3.2887494572095624e-06,
                5.422219615750493e-06,
                0.0004305571320277004,
                8.939694170518055e-06,
                9.422447061062286e-07,
                8.939695237813028e-06,
                1.0129988563730593e-05,
                2.1444953516281788e-05
            ],
            [
                5.422219613689145e-06,
                1.4738983725809062e-05,
                NaN,
                0.00012339456457822356,
                6.1441775291964935e-06,
                4.785096775171854e-06,
                NaN,
                5.422220905887864e-06,
                1.4738985472887472e-05,
                0.00010889693326938261
            ],
            [
                2.9023116378886404e-06,
                NaN,
                1.7603438421976406e-06,
                NaN,
                1.1478766751997141e-05,
                2.9023130219364104e-06,
                1.0129987354882753e-05,
                NaN,
                6.1441731309681274e-06,
                4.2228339464303755e-06
            ],
            [
                0.987568351822357,
                3.535625910878189e-05,
                3.1201926224857616e-05,
                0.00013982210635244866,
                0.9975273769542011,
                0.9579122674284875,
                1.3007134660776729e-05,
                4.539785228266453e-05,
                4.0063682158810334e-05,
                1.3709578599619916e-06
            ],
            [
                1.7603432129198161e-06,
                4.222833947728508e-06,
                7.338208930078229e-07,
                6.1441775309064404e-06,
                1.6701417841747264e-05,
                1.2098659718539182e-06,
                3.7266401724291984e-06,
                8.939699499823059e-06,
                6.475947981625199e-07,
                1.3709572067680694e-06
            ],
            [
                0.9984988177528604,
                0.998674977583095,
                0.9820137882284439,
                0.9959298627975287,
                0.9988304896398876,
                0.9890130588266817,
                0.9999417087346256,
                0.9947798743064415,
                0.9770226277901336,
                0.9982992773764825
            ],
            [
                7.889261643382609e-06,
                4.222832940500659e-06,
                0.00020342704452303584,
                2.1444940725789744e-05,
                4.785096205077381e-06,
                2.9023112929973233e-06,
                1.14787708580381e-05,
                7.889265405505236e-06,
                1.3007126906982452e-05,
                1.3007126909916233e-05
            ],
            [
                2.1444950965906214e-05,
                1.4738981962698681e-05,
                3.7266388388875246e-06,
                5.144222586675549e-05,
                6.144174600985344e-06,
                7.338210679542388e-07,
                3.2887482810801374e-06,
                5.422220907160179e-06,
                3.726640616630245e-06,
                2.9023112929973233e-06
            ],
            [
                2.561281294644835e-06,
                0.0002305066485908441,
                6.962257908196617e-06,
                6.144174600180663e-06,
                8.315282258900085e-07,
                8.939698433974813e-06,
                2.9023116390104826e-06,
                1.4738981964307261e-05,
                3.2887498492936755e-06,
                2.2603251055414524e-06
            ],
            [
                0.9947798732569769,
                0.00020342697136639773,
                1.4738985479697128e-05,
                9.610243732895915e-05,
                0.00029595723730392506,
                0.7057850154599563,
                0.000709670524464736,
                1.3007131563176482e-05,
                0.9990889489023441,
                9.610241470381859e-05
            ],
            [
                1.3007128460797749e-05,
                2.260325375634003e-06,
                4.785093353013212e-06,
                2.9023119850210436e-06,
                1.760343632444745e-06,
                4.78509620374567e-06,
                3.2887482794499933e-06,
                9.422445938557184e-07,
                8.315280276338815e-07,
                6.144172398016056e-06
            ],
            [
                0.9999251537371739,
                0.999997438716568,
                0.9999599363079151,
                0.994779875372833,
                0.9999967112501509,
                0.9999251538001661,
                0.999512142953086,
                0.00043055706656961736,
                0.9999921107392972,
                0.9986749774133334
            ],
            [
                0.00015843619614288354,
                0.9525741320396143,
                0.9989677688811355,
                3.72663839473414e-06,
                0.9993736659245972,
                8.481107136566915e-05,
                3.7266392836984955e-06,
                2.902311984915459e-06,
                0.9995694430174136,
                0.06754669207816588
            ],
            [
                7.889264465397747e-06,
                2.902312331125353e-06,
                2.2603242977555607e-06,
                1.0129994601688632e-05,
                3.927862470861484e-07,
                1.7603436326432711e-06,
                2.9023126770343703e-06,
                NaN,
                5.71500515151976e-07,
                5.71500242637956e-07
            ],
            [
                NaN,
                1.5534973836675267e-06,
                3.2887486728201357e-06,
                4.7850927830845245e-06,
                4.785093924047376e-06,
                3.288750241204353e-06,
                3.7266388393349185e-06,
                NaN,
                1.89251482355036e-05,
                1.9947290074646476e-06
            ],
            [
                1.1478773597390071e-05,
                6.962259567217739e-06,
                1.6701425697019e-05,
                7.889266347004826e-06,
                2.260325375520937e-06,
                5.422220908116881e-06,
                3.2887482807780376e-06,
                8.31528424064506e-07,
                2.75357009372024e-05,
                1.067702615417244e-06
            ],
            [
                3.466327863393773e-07,
                9.422448185101494e-07,
                8.939696300376156e-06,
                6.962259568078904e-06,
                7.338212422419668e-07,
                8.315277302059155e-07,
                3.2887498491620677e-06,
                3.726639283440905e-06,
                7.889263524960312e-06,
                5.715004470025379e-07
            ],
            [
                1.994729958696456e-06,
                1.1478765371735978e-05,
                3.2887482803712492e-06,
                3.7266401722360055e-06,
                3.2887502411026557e-06,
                5.04347528440776e-07,
                4.222833947428939e-06,
                NaN,
                5.04347348070562e-07,
                1.5534975692471157e-06
            ],
            [
                1.067702741991219e-06,
                1.473897669245728e-05,
                3.288748673035494e-06,
                1.147876810891517e-05,
                0.9999785550490472,
                1.8925143628403532e-05,
                0.9989677691990105,
                2.7535697661092444e-05,
                5.8291258551949844e-05,
                NaN
            ],
            [
                7.889262584508638e-06,
                1.0129988561077228e-05,
                1.1478764017720528e-05,
                3.2887490648622804e-06,
                8.93969310675186e-06,
                2.43002494076116e-05,
                1.4738987240475486e-05,
                7.889261642794245e-06,
                1.994730672496148e-06,
                7.889264464106214e-06
            ],
            [
                0.9995694429774199,
                1.760342793362967e-06,
                9.422445938728576e-07,
                0.9999599362982811,
                0.9998601779599728,
                NaN,
                0.9992903297302677,
                0.7772998663336158,
                4.222833947282995e-06,
                0.9997388096921669
            ],
            [
                NaN,
                2.1444956044501514e-05,
                NaN,
                1.4738978454950406e-05,
                3.1201907603241865e-05,
                5.422217026412668e-06,
                3.7266401719174067e-06,
                1.6701419846834993e-05,
                NaN,
                1.892514823364471e-05
            ]
        ]
    },
    {
        "q_id": "7736_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            18,
            19,
            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,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            111,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.999925153745996,
                0.9999417087553165,
                0.999993855825399,
                0.9999852610180284,
                0.999985261019786,
                0.9999990577555183,
                0.9999832985841328,
                0.9999869928699849,
                0.9999832985821409,
                0.9998601779259803
            ],
            [
                0.9999930377412606,
                0.9999992661787571,
                0.9999756997621686,
                0.9999832985841305,
                0.9999251537638503,
                0.9999687980737552,
                0.9999982396569966,
                0.999991060302631,
                0.9999957771670592,
                0.9999785550515884
            ],
            [
                0.9999869928746402,
                0.9999962733611603,
                0.9999921107383555,
                0.9999810748495058,
                0.9999970976873229,
                0.9999938558253983,
                0.9999970976890528,
                0.9999938558253986,
                0.9999251537728095,
                0.9999921107345932
            ],
            [
                4.222832940777184e-06,
                1.670142781086525e-05,
                4.22283344433731e-06,
                5.422218323093458e-06,
                1.6701425825128124e-05,
                3.726639727940109e-06,
                2.5612816000145246e-06,
                6.1441731363550164e-06,
                4.785096205717126e-06,
                3.5356246487099006e-05
            ],
            [
                0.9999599363030525,
                0.9999810748540198,
                0.9999974387171787,
                0.9999832985821381,
                0.9999885212359796,
                0.9999945777816769,
                0.9999869928668853,
                0.9999885212359801,
                0.9999687980774927,
                0.9999785550413688
            ],
            [
                0.999948557780254,
                0.9999724643089074,
                0.999925153746088,
                0.9999852610197867,
                0.9999885212305076,
                0.9999930377404309,
                0.9999038975507264,
                0.9999724643089118,
                0.9999687980886309,
                0.9996646498911933
            ],
            [
                0.9999885212332428,
                0.999985261016272,
                0.9999339478474597,
                0.999998239656367,
                0.999988521229138,
                0.9999646437535052,
                0.9999599362982967,
                0.9999921107355337,
                0.9999785550413632,
                0.999968798092358
            ],
            [
                0.9999038975852962,
                0.9999885212264016,
                0.9999869928715366,
                0.9999832985841296,
                0.9999910603015664,
                0.999972464312192,
                0.999992110737415,
                0.9999910603068932,
                0.9999930377412607,
                0.9999687980997901
            ],
            [
                0.9999930377412606,
                0.9999687980923566,
                0.9999945777829696,
                0.9999852610233023,
                0.9999930377437504,
                0.999996273360716,
                0.9998766054695147,
                0.9999485577986391,
                0.9999885212346129,
                0.9999957771665559
            ],
            [
                0.9999957771655487,
                0.999996273360716,
                0.9999957771680658,
                0.9999910603058275,
                0.9999910603068933,
                0.9999417087275401,
                0.9999885212264021,
                0.9999810748585295,
                0.9999987901341723,
                0.9999910603068942
            ],
            [
                0.9999038975967038,
                0.999985261014518,
                0.9999485577863629,
                0.9999646437535248,
                0.9997965729791986,
                0.9999977396748939,
                0.9999962733602719,
                0.9999810748562746,
                0.9999785550541502,
                0.9999756997563752
            ],
            [
                1.553498495091042e-06,
                2.9023126766305067e-06,
                1.2098658276290391e-06,
                2.2603245668941476e-06,
                1.5534977545243671e-06,
                1.99472900777306e-06,
                1.994729483080495e-06,
                1.3709570430407122e-06,
                2.2603245670174926e-06,
                1.7603434229000067e-06
            ],
            [
                0.9999546021097371,
                0.9999921107345938,
                0.9999687980849281,
                0.9999417087275736,
                0.9999898700041916,
                0.9997388096291354,
                0.9999485577741295,
                0.9999974387187054,
                0.9999938558261304,
                0.9998204720986045
            ],
            [
                0.9999832985701935,
                0.9999785550413652,
                0.9999885212291383,
                0.9999898700126437,
                0.9999930377404307,
                0.9999810748540172,
                0.9999967112501505,
                0.9999977396751634,
                0.9999970976883608,
                0.9999991684719723
            ],
            [
                0.9999724643056231,
                0.9999724643187533,
                0.9999898700041906,
                0.9999756997563729,
                0.9999339478553189,
                0.9999599363126329,
                0.9999898700078128,
                0.9999485577618238,
                0.9999970976866309,
                0.9999885212318744
            ],
            [
                0.9999980052700407,
                0.9999756997679594,
                0.9999957771670591,
                0.9999687980960907,
                0.999991060300499,
                0.9999724642957817,
                0.9999687980923528,
                0.9999251537549879,
                0.9999546021097508,
                0.9999970976880149
            ],
            [
                0.9999910603068932,
                0.9999898700041909,
                0.9999646437450735,
                0.9999687980737526,
                0.9999546021259581,
                0.9999485577618268,
                0.9999038975851613,
                0.9999957771680659,
                0.9999938558253988,
                0.9999986290432834
            ],
            [
                0.9999832985781563,
                0.9999980052705163,
                0.9999852610110012,
                0.9999151889891291,
                0.9999687980849222,
                0.9999930377462403,
                0.9999952149060757,
                0.9999599362887481,
                0.9999485577802313,
                0.999972464299064
            ],
            [
                0.9999885212332438,
                0.9999977396754328,
                0.9999898700078128,
                0.9999832985741748,
                0.9999832985721844,
                0.9999869928730867,
                0.9999869928746383,
                0.9999898700102277,
                0.9999038975507067,
                0.9999952149037943
            ],
            [
                0.9999885212332442,
                0.9999417087414566,
                0.9999339478474597,
                0.9999785550567005,
                0.999941708727552,
                0.9999869928684346,
                0.9999810748540158,
                0.9999599363078128,
                0.9999921107345932,
                0.9998766054398994
            ],
            [
                0.9999930377462404,
                0.9999885212359807,
                0.9999885212277702,
                0.9999852610233005,
                0.9999952149043648,
                0.9999974387168734,
                0.9999687980737538,
                0.9999921107374146,
                0.999959936288761,
                0.9999990577550691
            ],
            [
                0.9998415637645629,
                0.9999852610180293,
                0.9996646498121056,
                0.999975699753477,
                0.9999546021313669,
                0.9999962733598274,
                0.9999869928730863,
                0.9999898700041906,
                0.9999485577741157,
                0.9999724642957734
            ],
            [
                0.9999485577986563,
                0.999876605425276,
                0.9999938558232011,
                0.9999921107383553,
                0.9999339478396323,
                0.9999952149055054,
                0.9999687980923607,
                0.9999869928715373,
                0.9999957771655487,
                0.9999970976876692
            ],
            [
                0.9999546021259709,
                0.9998601779096806,
                0.9998601778594738,
                0.9998415637078668,
                0.9997388096606132,
                0.9999687980737538,
                0.9999977396765105,
                0.999933947878971,
                0.9999339478710885,
                0.9999599363173656
            ],
            [
                0.9999151889284615,
                0.9999869928684351,
                0.9982992776747416,
                0.9991959142472738,
                0.9986749778328076,
                0.9999756997679586,
                0.9953904270877703,
                0.9980732657271004,
                0.9998766053810748,
                0.9999646437450925
            ],
            [
                1.2098662603752517e-06,
                1.370957206753107e-06,
                1.3709573702111586e-06,
                1.2098655392464547e-06,
                1.0677031245623505e-06,
                8.93970056424046e-06,
                2.561283431986506e-06,
                3.7266410608720178e-06,
                2.2603248367173307e-06,
                5.715004470272272e-07
            ],
            [
                0.9999957771645419,
                0.9999962733602716,
                0.9999945777816767,
                0.9999980052707541,
                0.9999646437619372,
                0.9997965730295629,
                0.9999967112493665,
                0.9999687980811924,
                0.999991060304763,
                0.9999756997679626
            ],
            [
                0.999986992876188,
                0.9999756997505811,
                0.9999339478475102,
                0.9997040428661479,
                0.9999921107355335,
                0.9999967112493665,
                0.9999957771650454,
                0.999997097688015,
                0.9999810748585312,
                0.999972464315468
            ],
            [
                0.9999921107345936,
                0.9998601779429633,
                0.9999038975850983,
                0.9999417087066922,
                0.9999885212318764,
                0.9964063973919017,
                0.9999756997679619,
                0.9998766054105698,
                0.9999756997650627,
                0.999972464302344
            ],
            [
                0.9999687980774731,
                0.9999938558246659,
                0.9999952149032236,
                0.9999952149032237,
                0.9999687980997952,
                0.9999898700053984,
                0.9999339478318522,
                0.9999251537639298,
                0.9999869928653345,
                0.9999724643089054
            ],
            [
                0.9999810748562757,
                0.9999910603047618,
                0.9999832985761693,
                0.9999945777829694,
                0.9999687980849129,
                0.9999898700126433,
                0.9999970976890529,
                0.9999852610127608,
                0.9999930377437505,
                0.9999952149060758
            ],
            [
                0.9999832985741745,
                0.9999910603015664,
                0.99998329857418,
                0.9999885212291378,
                0.9999832985741761,
                0.9999957771665555,
                0.9999546021097193,
                0.9999930377462405,
                0.9999930377429208,
                0.9996646497753131
            ],
            [
                0.9999251537906192,
                0.9996200154276969,
                0.9999038975621809,
                0.999978555051593,
                0.9999930377445807,
                0.9999977396762412,
                0.9991959141730556,
                0.9999785550515917,
                0.9999852610180284,
                0.9999546021368017
            ],
            [
                0.9999724643187523,
                0.999993855824666,
                0.9998601778928643,
                0.999994577780384,
                0.9999970976866309,
                0.999968798081203,
                0.9999756997563835,
                0.9999038975507369,
                0.9999970976880149,
                0.9999599362935055
            ],
            [
                0.9999687980886555,
                0.999964643757734,
                0.9999885212346137,
                0.9999785550567023,
                0.9999852610127582,
                0.9999810748427396,
                0.9999724643089064,
                0.9999687980774796,
                0.9999869928684375,
                0.9999970976876689
            ],
            [
                0.9998601779428737,
                0.9999952149066464,
                0.999860177926084,
                0.9999687980998236,
                0.9999687980886323,
                0.9999339478789562,
                0.9999724643056241,
                0.9999885212264026,
                0.9999599362982728,
                0.9999885212359801
            ],
            [
                0.9999485577618268,
                0.9999910603047618,
                0.999997097686977,
                0.9999910603058286,
                0.9999756997650621,
                0.9999990577551814,
                0.9999930377437511,
                0.9999921107402361,
                0.9999938558246666,
                0.9999546021476133
            ],
            [
                0.9999646437492907,
                0.9999339478554337,
                0.9999910603068943,
                0.9999869928653355,
                0.9999339478554163,
                0.999994577780384,
                0.9999898700078128,
                0.9999785550541473,
                0.9999646437493069,
                0.9999945777829693
            ],
            [
                0.9999898700102289,
                0.9999485577802376,
                0.9999980052700408,
                0.9999885212291383,
                0.9999921107345933,
                0.9999038975965626,
                0.9999485577679585,
                0.9999852610197869,
                0.9999687980774927,
                0.999903897596573
            ],
            [
                0.9999962733607162,
                0.9998601778761356,
                0.9999339478632404,
                0.9999930377420904,
                0.9999921107336528,
                0.9999869928684356,
                0.9999151889688264,
                0.9998911030908894,
                0.999664649971091,
                0.999992110738355
            ],
            [
                0.9999417087484003,
                0.9999785550567057,
                0.9999687980737526,
                0.9999832985841309,
                0.9999832985801483,
                0.9999852610215446,
                0.9998601779099837,
                0.9999885212264018,
                0.9999885212277698,
                0.9999785550490328
            ],
            [
                0.9999967112521108,
                0.9999990577556308,
                0.9999996072138934,
                0.99997855505926,
                0.9999910603015666,
                0.9999885212359826,
                0.999993855823201,
                0.9999952149072169,
                0.9999977396751633,
                0.9999832985781563
            ],
            [
                0.999959936288716,
                0.9999339478318646,
                0.9999885212291378,
                0.9999921107392965,
                0.9999930377454118,
                0.9999251537460145,
                0.9999910603036963,
                0.9999151889485773,
                0.9999957771650454,
                0.9999921107345937
            ],
            [
                0.999948557780244,
                0.9999485577679526,
                0.9998204720986411,
                0.9999038976195891,
                0.9999339478790182,
                0.9998601778763776,
                0.9999339478632352,
                0.9998911030648799,
                0.9995694429648818,
                0.9999724643121888
            ],
            [
                0.999989870006606,
                0.9999546021476109,
                0.9999930377454105,
                0.9999724642957742,
                0.9999962733602716,
                0.9998911030388452,
                0.999991060300499,
                0.9999832985701927,
                0.9999967112501507,
                0.999991060304762
            ],
            [
                0.9986749774421405,
                0.9953904284445144,
                0.9999151889182929,
                0.9984988173893805,
                0.9840936085214388,
                0.4073334000459302,
                0.9990889487908704,
                0.999769493176958,
                0.999891103042404,
                0.9993736657556134
            ],
            [
                0.999948557774109,
                0.9999885212346113,
                0.9999938558246662,
                0.9999785550592574,
                0.9999646437493241,
                0.9999038976195121,
                0.9999151889586319,
                0.9998204720339836,
                0.9999417087136483,
                0.9999785550490354
            ],
            [
                0.9999930377462406,
                0.9999832985721853,
                0.9999251537371326,
                0.9999910603015651,
                0.9999546021098853,
                0.9999921107392962,
                0.999769493285311,
                0.9999810748495053,
                0.9999869928699853,
                0.9999646437408591
            ],
            [
                0.9998911031168464,
                0.9999952149066464,
                0.9999945777797377,
                0.9999910603026306,
                0.9999852610215451,
                0.9999756997592687,
                0.9999599363078321,
                0.9999852610127611,
                0.9999898700078133,
                0.9999832985841296
            ],
            [
                0.9999251537817575,
                0.9999251537995529,
                0.9998601779426642,
                0.9999546021205374,
                0.999992110739296,
                0.9999938558239335,
                0.9999724643187576,
                0.9999898700090204,
                0.999997438716568,
                0.9999646437492953
            ],
            [
                0.9999986290426297,
                0.9999832985801496,
                0.9999852610162737,
                0.9999038975509362,
                0.9999974387184,
                0.9999977396759716,
                0.9999952149037942,
                0.9999832985721915,
                0.9999832985801471,
                0.9999785550413672
            ],
            [
                0.99997246431547,
                0.9998415637088304,
                0.9999898700126436,
                0.9999869928668853,
                0.9999957771670589,
                0.9999869928699852,
                0.9999810748427365,
                0.9999962733607158,
                0.9999485577802474,
                0.9999832985821387
            ],
            [
                0.9999930377462405,
                0.9999957771665554,
                0.9999921107402363,
                0.9998911030390591,
                0.9999251537460401,
                0.9999756997650686,
                0.999993037746241,
                0.9999974387168734,
                0.9999984465024306,
                0.9999687980923528
            ],
            [
                0.9999938558261307,
                0.9998204719910657,
                0.9999599363125974,
                0.9999038975850886,
                0.999860177859368,
                0.9999485578047457,
                0.9999646437577323,
                0.999941708706696,
                0.9999339478632058,
                0.9999832985821384
            ],
            [
                7.889260704050487e-06,
                1.4738978455701077e-05,
                3.7266392839425286e-06,
                5.8291244643591885e-05,
                2.561281599914358e-06,
                1.0129995809044816e-05,
                3.5356250701614645e-05,
                4.7850944945245504e-06,
                4.785092783267308e-06,
                4.785096205778054e-06
            ],
            [
                0.9999756997621748,
                0.9999938558261309,
                0.9999417087066693,
                0.9999852610233002,
                0.9999898700066073,
                0.9999945777803839,
                0.999948557774109,
                0.9999898700114352,
                0.999996273360716,
                0.9999852610110015
            ],
            [
                0.9999980052705163,
                0.9999898700090204,
                0.999903897539223,
                0.99997569976506,
                0.9999251537638956,
                0.9999910603026313,
                0.9999945777810305,
                0.9999885212264013,
                0.9999962733620487,
                0.9999898700053984
            ],
            [
                0.9999898700114356,
                0.9999910603047621,
                0.9999930377445801,
                0.9999945777816768,
                0.999998629042303,
                0.999972464318766,
                0.9999898700066052,
                0.9999957771655491,
                0.999948557767984,
                0.9999921107336531
            ],
            [
                0.9999910603068933,
                0.9999756997534802,
                0.9998415637266933,
                0.9999832985721857,
                0.9999930377454104,
                0.9999921107392958,
                0.999989870006605,
                0.9999930377412608,
                0.9999810748495053,
                0.9999785550490391
            ],
            [
                1.0677029972920738e-06,
                2.2603237588597026e-06,
                3.7266401722360055e-06,
                4.222832940500659e-06,
                1.3007130010922344e-05,
                9.422445938917108e-07,
                6.962255417721724e-06,
                6.144174600471243e-06,
                5.422217676866151e-06,
                8.939695237504067e-06
            ],
            [
                0.9999885212305063,
                0.9999785550413666,
                0.9999832985821404,
                0.999975699747687,
                0.9999910603068932,
                0.999975699753489,
                0.9999930377437508,
                0.9999810748495092,
                0.9998601778931084,
                0.9999151889485693
            ],
            [
                0.9999546021313743,
                0.999997438716568,
                0.9999251537996058,
                0.9999810748495125,
                0.9999785550464758,
                0.9999599362935143,
                0.9999599363030465,
                0.9999687980997966,
                0.9999930377454103,
                0.999948557780219
            ],
            [
                0.9999832985801483,
                0.9999756997621719,
                0.9999724643089025,
                0.9998601778929295,
                0.9999687980849181,
                0.9999957771675623,
                0.9999785550567011,
                0.9999810748495044,
                0.9999687980737564,
                0.9999967112513267
            ],
            [
                0.9999151889485693,
                0.9999869928653335,
                0.9999921107345937,
                0.9999910603036964,
                0.9998204719707181,
                0.9996200154276969,
                0.999972464315472,
                0.9999869928715373,
                0.999997097688707,
                0.9999938558232012
            ],
            [
                0.9999930377420925,
                0.999959936298279,
                0.9999151889486014,
                0.9999852610215426,
                0.9999930377462409,
                0.9998415638401131,
                0.999959936317373,
                0.9999852610162724,
                0.9999974387180947,
                0.9999599363030484
            ],
            [
                0.999968798092365,
                0.9999970976887068,
                0.9999251537907651,
                0.9999945777790914,
                0.9999869928668843,
                0.9999945777797375,
                0.999941708706696,
                0.9999921107355336,
                0.999903897585194,
                0.9999687980774912
            ],
            [
                0.9999852610127591,
                0.9999957771665557,
                0.9999687980997901,
                0.999991060305828,
                0.9999945777829699,
                0.9999952149066462,
                0.9999852610197877,
                0.9999910603058275,
                0.9999151889891748,
                0.9999869928668853
            ],
            [
                0.9999921107364749,
                0.9999724642990576,
                0.9999599362887301,
                0.9999982396565767,
                0.9999967112517189,
                0.9999485577802837,
                0.99998107485853,
                0.9999930377462407,
                0.9999921107374147,
                0.9999646437535097
            ],
            [
                0.9996200155189874,
                0.999620015518302,
                0.9999417087066731,
                0.9999646437450763,
                0.9999957771675625,
                0.9996646499346009,
                0.9997388096911638,
                0.9999485577618328,
                0.9999485577679555,
                0.9998766053959857
            ],
            [
                0.9999724642957742,
                0.9991959141737103,
                0.9999980052700408,
                0.9999930377437504,
                0.9999898700102293,
                0.9999869928761876,
                0.9999599363078239,
                0.9999898700126442,
                0.9998766053813154,
                0.9999832985721955
            ],
            [
                0.9999546021205518,
                0.9999982396567867,
                0.9999810748585295,
                0.9999785550515884,
                0.9999921107374145,
                0.9999599362887388,
                0.9999930377404306,
                0.9999151889689127,
                0.9999646437535082,
                0.9999832985821401
            ],
            [
                0.9999952149055054,
                0.9999832985801511,
                0.999995777166052,
                0.9998204720778312,
                0.9999938558275955,
                0.9999869928668853,
                0.999996273360716,
                0.9999921107364743,
                0.9998911030908894,
                0.9999967112517189
            ],
            [
                0.9999984465018751,
                0.9999945777810304,
                0.9999687980849329,
                0.9999938558239335,
                0.9999910602994336,
                0.9999952149060758,
                0.9999921107364743,
                0.9999687980886347,
                0.9999962733593832,
                0.9999417087067668
            ],
            [
                0.9999945777797377,
                0.9999869928746372,
                0.9999885212332431,
                0.999978555054146,
                0.9999599362982671,
                0.9999898700102282,
                0.9999785550413672,
                0.9997388096600432,
                0.9999251537995594,
                0.9999546021313669
            ],
            [
                7.8892654060075e-06,
                2.2603251061232293e-06,
                1.994729245822257e-06,
                1.3007133114011233e-05,
                8.93969630348202e-06,
                6.144172404302622e-06,
                2.430024941459533e-05,
                1.9947306725669014e-06,
                3.7266397278180926e-06,
                1.76034300345598e-06
            ],
            [
                0.9999898700090215,
                0.9999785550567005,
                0.9999986290423029,
                0.9999938558275957,
                0.9999898700078143,
                0.9999599363030484,
                0.9999885212291378,
                0.9999687980811937,
                0.9999810748495068,
                0.9999546021097193
            ],
            [
                0.9999785550567141,
                0.9999952149060758,
                0.9999938558275953,
                0.9999957771645419,
                0.9999898700102289,
                0.9999982396572065,
                0.9999921107392965,
                0.9999962733620488,
                0.9999921107392957,
                0.9999785550413666
            ],
            [
                0.9999687980997854,
                0.9999869928699867,
                0.9999251537996416,
                0.9999646437493069,
                0.9999646437577242,
                0.9999952149060758,
                0.9999785550464806,
                0.9999852610180298,
                0.9998911031297709,
                0.9999785550592586
            ],
            [
                7.889265406438011e-06,
                2.260323758835034e-06,
                6.144174601097106e-06,
                2.5612819053166966e-06,
                8.93969417167259e-06,
                6.144176798590883e-06,
                1.3709572068272963e-06,
                1.9947294835866542e-06,
                2.561282210618905e-06,
                5.422217030121119e-06
            ],
            [
                0.9999930377420909,
                0.9999957771650454,
                0.9999957771665555,
                0.9999885212305069,
                0.999985261016272,
                0.9999810748472479,
                0.9999724643089107,
                0.99998107485853,
                0.9999810748472503,
                0.9999832985841317
            ],
            [
                0.9999989322972572,
                0.9999987901346049,
                0.9999967112517189,
                0.9999930377462405,
                0.9999921107355338,
                0.9999810748540193,
                0.9999898700053974,
                0.9999945777829694,
                0.9999970976873229,
                0.9999910603047619
            ],
            [
                0.9999832985721836,
                0.9999756997505803,
                0.9999832985801475,
                0.9999546021205704,
                0.9999339478238608,
                0.9999967112493665,
                0.9999869928699867,
                0.9999339478396323,
                0.9999724643121942,
                0.9999852610197874
            ],
            [
                0.9999957771660524,
                0.9999546021259903,
                0.9999952149043645,
                0.9999885212264016,
                0.9996646497311737,
                0.99995993630782,
                0.9999546021367857,
                0.999959936288716,
                0.9999038975966157,
                0.999986992873088
            ],
            [
                0.9999546021097124,
                0.9999756997592703,
                0.9999151889889872,
                0.9999785550464785,
                0.9999646437324344,
                0.9999756997621748,
                0.999972464299064,
                0.9999485577924795,
                0.9998911031297852,
                0.9999869928653352
            ],
            [
                0.9999810748472499,
                0.9999646437450779,
                0.9999974387184,
                0.9999724642990753,
                0.9999952149055056,
                0.9999810748562789,
                0.9999251537640033,
                0.999985261018032,
                0.999992110736474,
                0.9999546021367807
            ],
            [
                0.9999832985841296,
                0.9999967112497585,
                0.9999974387180947,
                0.9999898700090203,
                0.9999898700114356,
                0.9999869928699856,
                0.9999898700066053,
                0.9999952149032236,
                0.9999251537728863,
                0.9999724642957742
            ],
            [
                0.999997097686977,
                0.9999832985701927,
                0.999975699753477,
                0.9999785550541453,
                0.9997694932859279,
                0.9999038975736549,
                0.9999785550464758,
                0.9999938558224684,
                0.9986749775656875,
                0.9999898700126433
            ],
            [
                0.9999756997505781,
                0.9999339478395914,
                0.999978555054151,
                0.9996200154711754,
                0.9999038975621907,
                0.9999967112501505,
                0.9999599363173711,
                0.9999599363078182,
                0.999993037745411,
                0.9999546021205596
            ],
            [
                0.9999646437450779,
                0.9999952149066462,
                0.9999810748495053,
                0.9999485577679615,
                0.9999599363030609,
                0.9998911030907593,
                0.9999957771645421,
                0.9999599363078239,
                0.9999962733589393,
                0.9999910603036961
            ],
            [
                0.9999869928715369,
                0.9999687980886323,
                0.9999967112509347,
                0.9999930377462403,
                0.9999869928699856,
                0.9999869928684346,
                0.9999957771675625,
                0.99998329858413,
                0.9999910603004991,
                0.9999980052709919
            ],
            [
                0.9999869928699862,
                0.9999921107336528,
                0.9997388097850195,
                0.9999970976876689,
                0.9999785550490384,
                0.9999724643154838,
                0.999988521229139,
                0.9999646437619387,
                0.9999485577618361,
                0.9999756997505803
            ],
            [
                0.9999898700078145,
                0.9999869928715358,
                0.9999957771645419,
                0.9998766053958636,
                0.9999546021476033,
                0.9999646437619555,
                0.9999869928668845,
                0.9999646437408697,
                0.9999898700041926,
                0.9999810748562713
            ],
            [
                0.999991060305828,
                0.9999962733616047,
                0.9999921107355338,
                0.9999546021367783,
                0.9999938558246662,
                0.9999599362982708,
                0.99995993630783,
                0.999991060300499,
                0.9997694932850896,
                0.9999921107345929
            ],
            [
                0.9999810748585282,
                0.9999910603058279,
                0.9999810748495047,
                0.9999910603026309,
                0.9999646437577273,
                0.9999687980960733,
                0.9999756997505788,
                0.9999151889183892,
                0.9999785550490328,
                0.9999646437619356
            ],
            [
                0.9999930377420916,
                0.9999952149060757,
                0.9999898700041918,
                0.9999756997679633,
                0.9999546021151381,
                0.9999339478553674,
                0.9998766053668319,
                0.9999974387168733,
                0.9999967112501507,
                0.9998601779096136
            ],
            [
                0.9999417087275871,
                0.9999724643187533,
                0.9999646437619633,
                0.9992903294641835,
                0.999988521231878,
                0.9999930377412606,
                0.9999832985841309,
                0.9999885212359799,
                0.999941708734492,
                0.9999989322972572
            ],
            [
                0.9999945777810302,
                0.9999910603015651,
                0.9999646437535114,
                0.9999485577986323,
                0.9998415637463127,
                0.9999970976873229,
                0.999954602142192,
                0.9999910603026303,
                0.9999852610215436,
                0.9999921107336531
            ],
            [
                2.260325375572331e-06,
                6.1441760651689774e-06,
                1.3709576971160984e-06,
                1.0129994600398803e-05,
                5.422217030362759e-06,
                3.7266397273639203e-06,
                2.9023130230133794e-06,
                3.288750241204353e-06,
                1.9947306726213275e-06,
                3.2887494572873306e-06
            ],
            [
                0.9999957771665555,
                0.9999417087553654,
                0.99995993630782,
                0.9999994284992805,
                0.999964643732436,
                0.9999869928684346,
                0.9999687980923528,
                0.9999921107374143,
                0.999948557792504,
                0.9999687980923594
            ],
            [
                0.9999967112497585,
                0.9999756997563796,
                0.9999910603015654,
                0.9999930377437504,
                0.9999485578047577,
                0.9997388096603245,
                0.9999945777823229,
                0.9999599362887123,
                0.9999869928715408,
                0.9999945777784449
            ],
            [
                0.999983298576167,
                0.9999832985721828,
                0.9999952149043646,
                0.9999945777816783,
                0.9999417087067299,
                0.9999977396759717,
                0.999972464302337,
                0.9999898700114362,
                0.9998766053664531,
                0.9999921107336535
            ],
            [
                0.9999885212264016,
                0.9975273763833677,
                0.9999417087067168,
                0.9999646437450841,
                0.9999546021313669,
                0.999915188958804,
                0.9999339478474896,
                0.9999945777790913,
                0.9999832985781602,
                0.9999687980849142
            ],
            [
                0.9999724643056241,
                0.9999938558239333,
                0.9999852610162717,
                0.9999546021259605,
                0.9999251537372257,
                0.9999251537817236,
                0.9999810748540182,
                0.9999910603068932,
                0.9999785550541453,
                0.9999921107402366
            ],
            [
                0.9998601778594514,
                0.9999945777810304,
                0.9999646437535196,
                0.9999910603036961,
                0.9999785550567081,
                0.9999977396754328,
                0.999991060300499,
                0.9999756997621647,
                0.999996273362049,
                0.9999952149060765
            ],
            [
                0.9997965730032546,
                0.999993855826131,
                0.9999852610145155,
                0.9999977396748938,
                0.9999810748540172,
                0.9999962733598275,
                0.9999910603047621,
                0.9999852610180288,
                0.999975699767961,
                0.9999970976880149
            ],
            [
                0.9999921107364743,
                0.9999785550515939,
                0.9999038976082164,
                0.999820471970073,
                0.9999852610197867,
                0.9999646437619403,
                0.9999785550592677,
                0.9999921107336526,
                0.9999785550413729,
                0.9999810748585316
            ],
            [
                0.9999869928653345,
                0.9999756997476907,
                0.9999546021259682,
                0.999972464312199,
                0.9999646437619502,
                0.999988521231878,
                0.9999687980886347,
                0.9999038976079472,
                0.998830489753847,
                0.9999251537549417
            ],
            [
                0.9999921107355342,
                0.9998911031297852,
                0.9999852610215436,
                0.999997438716568,
                0.9999485577925504,
                0.9999898700114374,
                0.9999910603004992,
                0.9999952149055052,
                0.999985261016272,
                0.9999417087136911
            ],
            [
                0.999975699762166,
                0.9999885212318764,
                0.9999952149055057,
                0.9999785550439179,
                0.9999869928746369,
                0.9997040430081853,
                0.9999810748585336,
                0.9999687980997966,
                0.9999962733616047,
                0.9999599363078477
            ],
            [
                0.9998601778765159,
                0.999769493286223,
                0.9971990730744992,
                0.997199073375595,
                0.9994472212649619,
                0.9992903295644914,
                0.9902915242975189,
                0.9796676484011321,
                0.9990889486830523,
                0.6513548782017745
            ],
            [
                0.9999785550439251,
                0.999995777167059,
                0.9999646437408817,
                0.9999687980737735,
                0.9999417087344801,
                0.9999898700090208,
                0.9999952149072167,
                0.9997388095664079,
                0.9999852610145151,
                0.9995121428953829
            ],
            [
                0.9999756997534762,
                0.9999869928746379,
                0.9999546021097218,
                0.9999869928668841,
                0.9999546021151307,
                0.9998766053670707,
                0.9999938558224685,
                0.9998911030391892,
                0.9999910603036967,
                0.9999832985781566
            ],
            [
                0.9999646437535082,
                0.9999546021205622,
                0.999981074858529,
                0.9999938558239333,
                0.9999756997650636,
                0.9998204720131736,
                0.999933947863201,
                0.9999785550592568,
                0.9999785550464855,
                0.999925153746081
            ],
            [
                0.9999599362887179,
                0.9999921107374147,
                0.9999417087553878,
                0.9999832985781563,
                0.9999945777823233,
                0.9998766053957971,
                0.9998766054547386,
                0.9999852610162724,
                0.9999724643121858,
                0.9999339478317487
            ],
            [
                0.9999921107374143,
                0.9999646437408605,
                0.9999785550413666,
                0.9999869928653372,
                0.9999930377437506,
                0.9999724643154692,
                0.9999957771665556,
                0.9999417087553831,
                0.9999756997476845,
                0.9999417087553695
            ],
            [
                3.7266410609940346e-06,
                3.288747889038086e-06,
                5.4222202623972055e-06,
                2.5612815998491325e-06,
                2.902313368963394e-06,
                1.067703379154416e-06,
                9.422450431912e-07,
                8.939697369151141e-06,
                6.47594566594213e-07,
                1.2098659719524008e-06
            ],
            [
                0.9999967112521109,
                0.9999785550515867,
                0.9999910603026306,
                0.9999687980998037,
                0.9999885212332442,
                0.9999986290423029,
                0.9999852610110034,
                0.9999952149055054,
                0.9999991684715759,
                0.9999930377462408
            ],
            [
                0.9999980052702785,
                0.9999832985781578,
                0.9999952149066467,
                0.9999756997476845,
                0.9999921107383548,
                0.9992903295435629,
                0.9999417087066769,
                0.9999832985761665,
                0.9999687980849118,
                0.9999724643089045
            ],
            [
                0.9999967112513268,
                0.999995777166052,
                0.9999962733620487,
                0.9999984465026158,
                0.9999885212318768,
                0.9999993524051246,
                0.999998790134028,
                0.9999038975507067,
                0.9999869928653338,
                0.9999810748562722
            ],
            [
                0.9999485578047577,
                0.9999898700078128,
                0.9999485577925624,
                0.9999646437408679,
                0.9999945777823233,
                0.9999687980849129,
                0.9999952149066462,
                0.9999986290431201,
                0.999985261021543,
                0.9999930377412606
            ],
            [
                0.9999869928761873,
                0.9999832985701939,
                0.9999151889688264,
                0.9999898700066056,
                0.9999485577925108,
                0.9999945777803843,
                0.9999898700041905,
                0.9999756997563768,
                0.9999724643187544,
                0.9999339478553833
            ],
            [
                0.9999756997621669,
                0.9999599362935033,
                0.9999832985801487,
                0.9999974387177893,
                0.9999885212318746,
                0.9999038976195891,
                0.9999921107355343,
                0.9999646437366584,
                0.9997965729783995,
                0.9999869928746377
            ],
            [
                0.9999930377445811,
                0.9999646437450824,
                0.9999724642990617,
                0.9999967112509351,
                0.9999930377429207,
                0.9999869928761882,
                0.9999921107336528,
                0.999941708755344,
                0.9999980052700408,
                0.9999546021476057
            ]
        ]
    },
    {
        "q_id": "8054_mmlu_math",
        "cot_ids": [
            3,
            5,
            6,
            8,
            11,
            13,
            14,
            15,
            17,
            19,
            20,
            21,
            25,
            26,
            27,
            29,
            38,
            39,
            40,
            43,
            46,
            47,
            48,
            50,
            51,
            54,
            55,
            56,
            60,
            62,
            64,
            66,
            67,
            68,
            69,
            70,
            71,
            73,
            75,
            77,
            78,
            79,
            80,
            83,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            99,
            100,
            101,
            104,
            105,
            107,
            108,
            109,
            110,
            112,
            114,
            115,
            117,
            118,
            119,
            121,
            122,
            124,
            127
        ],
        "rewards": [
            [
                4.222831934052698e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                6.1441724044534996e-06,
                3.7266401719851935e-06,
                1.370957533676711e-06
            ],
            [
                1.1478773596575768e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                5.4222183222304545e-06,
                1.1478769493540482e-05,
                1.0129993393540266e-05,
                6.962257909412379e-06,
                1.8925155005051806e-05
            ],
            [
                6.475947982002148e-07,
                2.260324297702111e-06,
                1.9947297213746646e-06,
                2.6995777745711594e-07,
                2.9023123309973302e-06,
                3.466326211105621e-07,
                1.370957533676711e-06,
                8.315278293951957e-07,
                2.699577774579753e-07,
                3.4663278639738526e-07
            ],
            [
                6.962257079173776e-06,
                4.785096205434246e-06,
                NaN,
                1.670142582254589e-05,
                NaN,
                3.726640615752405e-06,
                4.7850927830148924e-06,
                4.0063711274151284e-05,
                NaN,
                5.422217030362759e-06
            ],
            [
                5.422217030121119e-06,
                1.2098662603631479e-06,
                1.4738985446345907e-05,
                NaN,
                1.553498495091042e-06,
                3.927863875459951e-07,
                1.0129987353537646e-05,
                6.144173136885882e-06,
                4.785093923420688e-06,
                1.3709578604495207e-06
            ],
            [
                6.144176798691468e-06,
                1.670142980380249e-05,
                9.422447057308776e-07,
                2.1444956075707356e-05,
                7.484620927188383e-05,
                5.422220261544064e-06,
                1.4738978435781506e-05,
                4.222835456696504e-06,
                5.422220908402905e-06,
                4.785096204415878e-06
            ],
            [
                5.043472879419732e-07,
                0.0003799844656906535,
                1.5534971989907999e-06,
                1.994729007841999e-06,
                1.209866116170145e-06,
                NaN,
                6.1441760667392215e-06,
                1.067703378997103e-06,
                8.315281267800897e-07,
                2.9023123308072772e-06
            ],
            [
                0.9999756997650613,
                0.9999251537638318,
                0.9999687980886276,
                0.9999974387171787,
                0.9999546021097193,
                0.9998766054546704,
                0.9999970976876689,
                0.9999952149060758,
                0.9999930377445804,
                0.9999980052702785
            ],
            [
                2.2603248367173307e-06,
                2.902313368860448e-06,
                1.0677033791204289e-06,
                9.422450431800595e-07,
                5.422220908762902e-06,
                1.1478764015736973e-05,
                2.2603251061232293e-06,
                5.422219615829396e-06,
                3.726639728224814e-06,
                1.6701419852090592e-05
            ],
            [
                0.9999038975622753,
                0.9990889486797145,
                NaN,
                0.9997694933132257,
                0.9998911031054348,
                NaN,
                NaN,
                0.9999646437493123,
                0.9999687980812203,
                0.9995121429411367
            ],
            [
                7.889265406681968e-06,
                1.8925152750692706e-05,
                1.012999339449843e-05,
                8.939698432690187e-06,
                1.892515045082535e-05,
                3.7266388395620047e-06,
                NaN,
                6.96225375863827e-06,
                6.1441760661636525e-06,
                NaN
            ],
            [
                0.9999945777816824,
                0.9999687980927745,
                0.7310585727705126,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999869928731319,
                0.9999724643124679,
                0.9999980052707629
            ],
            [
                7.484626254505505e-05,
                3.059021904484005e-07,
                1.2098662602663157e-06,
                9.422448184801556e-07,
                5.043472278195839e-07,
                1.8925150486764003e-05,
                5.715005151400212e-07,
                2.7535697619320912e-05,
                7.338208929524281e-07,
                7.338208055489796e-07
            ],
            [
                1.3709568798956654e-06,
                2.561282210701601e-06,
                1.1478765388105516e-05,
                1.5534973841154145e-06,
                6.962256249606473e-06,
                1.5534977545102382e-06,
                1.670142581762446e-05,
                3.726638395415398e-06,
                6.9622562484666964e-06,
                4.7850933535006355e-06
            ],
            [
                1.01299933928585e-05,
                5.422220907554695e-06,
                8.315283250150648e-07,
                4.22283394762097e-06,
                1.2098661161861e-06,
                4.450851580402549e-07,
                1.7603430032662588e-06,
                2.5612822106841303e-06,
                6.962254588724508e-06,
                5.71500583272315e-07
            ],
            [
                4.539788481668446e-05,
                3.5356242262551455e-05,
                6.605215252055522e-05,
                1.6701425802374098e-05,
                NaN,
                1.670142183059676e-05,
                2.1444958621558693e-05,
                6.962257908196617e-06,
                NaN,
                7.484622687241362e-05
            ],
            [
                NaN,
                1.99472995920443e-06,
                3.7266388393349185e-06,
                0.9999546021209916,
                0.04208773257151255,
                0.9399133473013075,
                4.785095634565186e-06,
                0.9999832985763507,
                0.9997388095982276,
                NaN
            ],
            [
                3.2887478891128633e-06,
                7.889263525663481e-06,
                NaN,
                1.300712846217e-05,
                NaN,
                1.6701427805275476e-05,
                NaN,
                7.338208930315157e-07,
                NaN,
                2.2603245672867952e-06
            ],
            [
                6.96225375833433e-06,
                5.42222090882208e-06,
                4.78509506425325e-06,
                6.962257909007124e-06,
                7.338208055055984e-07,
                6.962258737092915e-06,
                2.5612831264675113e-06,
                2.9023109470871505e-06,
                2.260324028331257e-06,
                2.5612834318583854e-06
            ],
            [
                6.144173136645595e-06,
                8.939698432690187e-06,
                0.00026119036777150326,
                1.4738987238035806e-05,
                2.1444948395559206e-05,
                2.561282515662579e-06,
                7.889260704050487e-06,
                4.5397852286628106e-05,
                NaN,
                6.144174601588856e-06
            ],
            [
                0.00010889690886829515,
                1.1478772221888615e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                6.144173867608406e-06
            ],
            [
                1.7603430027315182e-06,
                6.475946437781423e-07,
                1.5534983100920427e-06,
                1.1478768124324254e-05,
                2.2603242978665707e-06,
                3.7266379507909478e-06,
                1.5534973841450852e-06,
                1.9947301970287804e-06,
                1.3007126914245925e-05,
                6.475947209918244e-07
            ],
            [
                7.889261641416608e-06,
                1.1478772227964558e-05,
                1.8925152735477297e-05,
                NaN,
                NaN,
                4.222835457280279e-06,
                2.9023119850210436e-06,
                0.00017952793933482202,
                1.6701417860795016e-05,
                NaN
            ],
            [
                2.144495608105136e-05,
                3.288749065077638e-06,
                4.539789010145421e-05,
                NaN,
                6.605217605747206e-05,
                2.144495607336692e-05,
                NaN,
                NaN,
                6.144176798479122e-06,
                1.6701419845680582e-05
            ],
            [
                2.4300249387721226e-05,
                8.939697369004791e-06,
                2.9023126769050284e-06,
                2.2603248367358324e-06,
                3.288750633518874e-06,
                4.7850933529174686e-06,
                1.7603427932989266e-06,
                2.430023491549239e-05,
                1.370957206783032e-06,
                3.2887498483604557e-06
            ],
            [
                NaN,
                NaN,
                0.9999869928731026,
                0.09534945911506375,
                0.9998601778648872,
                NaN,
                0.9999810748562789,
                0.999925153757776,
                0.6224593312018545,
                0.5926665999540698
            ],
            [
                1.01299933920846e-05,
                1.0129989758408864e-05,
                3.726639283806955e-06,
                1.2098655392354511e-06,
                9.42244481511812e-07,
                NaN,
                2.561282821069686e-06,
                2.561283126535066e-06,
                2.9023126770343703e-06,
                3.2887486724851334e-06
            ],
            [
                8.31528424146183e-07,
                6.962257908348587e-06,
                1.892515725665725e-05,
                3.2887478887958082e-06,
                4.785093924251918e-06,
                1.5534981249291695e-06,
                9.422448185015797e-07,
                NaN,
                3.466327037472645e-07,
                9.422450431732037e-07
            ],
            [
                4.785094494576774e-06,
                6.144173136729416e-06,
                8.315277302701984e-07,
                1.3007126906036072e-05,
                4.222835457664342e-06,
                2.56128159959988e-06,
                8.315280276399315e-07,
                8.939700560874416e-06,
                1.473898371722997e-05,
                6.962257079059797e-06
            ],
            [
                NaN,
                1.0677026154619133e-06,
                2.902311292783513e-06,
                NaN,
                4.222833444229772e-06,
                2.5612822106421996e-06,
                NaN,
                NaN,
                0.0015011825806058117,
                5.422217030209884e-06
            ],
            [
                0.9999997617630049,
                0.9999989322966208,
                0.9999982396565769,
                0.9999982396569966,
                0.9999991684719723,
                0.9999995549151072,
                0.9999993524054334,
                0.9999977396765105,
                0.9999989322968754,
                0.9999869928730867
            ],
            [
                5.4222202623972055e-06,
                NaN,
                NaN,
                1.0129993394129904e-05,
                1.1478773596847203e-05,
                2.561282821069686e-06,
                8.93969417199781e-06,
                NaN,
                2.4300252311252174e-05,
                1.3007131563815288e-05
            ],
            [
                6.962254588585202e-06,
                2.9023126770343703e-06,
                4.2228324375973415e-06,
                1.6701425824307884e-05,
                3.726637949042046e-06,
                1.0129995800347667e-05,
                4.006368726425757e-05,
                2.1444943298944354e-05,
                4.2228349546493465e-06,
                5.422217030121119e-06
            ],
            [
                6.962256249517824e-06,
                6.962255419570695e-06,
                9.422447061782138e-07,
                1.2098652507285942e-06,
                2.9023130228444433e-06,
                1.3709573702248741e-06,
                NaN,
                4.785093924047376e-06,
                1.7603432132624344e-06,
                7.33821067986608e-07
            ],
            [
                NaN,
                NaN,
                1.1478769492893215e-05,
                NaN,
                1.3709576971160984e-06,
                2.2603245671490605e-06,
                6.144174601410037e-06,
                NaN,
                1.5534975693601474e-06,
                NaN
            ],
            [
                2.1444958618516124e-05,
                NaN,
                2.4300246506623417e-05,
                6.144177531459659e-06,
                8.939698434657777e-06,
                2.9023126769050284e-06,
                1.5534983099790112e-06,
                2.9023130228840374e-06,
                8.939694167639847e-06,
                2.902312330965655e-06
            ],
            [
                4.006371125185228e-05,
                NaN,
                NaN,
                4.5397884843438604e-05,
                2.144495351862222e-05,
                2.7535697658087296e-05,
                2.7535700938304286e-05,
                2.1444943241369593e-05,
                NaN,
                1.6701423828576233e-05
            ],
            [
                0.999999352404893,
                0.9999989322971299,
                0.9999997300421903,
                0.9999999006880194,
                0.9999987901337396,
                0.9999646437577657,
                0.9999994956527121,
                0.9999989322968754,
                0.9999987901341723,
                0.9999977396762411
            ],
            [
                NaN,
                4.0063706496627415e-05,
                5.422218968477564e-06,
                4.785092782597101e-06,
                NaN,
                0.9940889301094402,
                1.1478773591084453e-05,
                1.0,
                NaN,
                7.889265406151004e-06
            ],
            [
                0.9999485577926096,
                NaN,
                1.0129994601872894e-05,
                9.42244818532859e-07,
                1.994730672439908e-06,
                1.3007130009313495e-05,
                NaN,
                1.4738988996240646e-05,
                1.0677032518578904e-06,
                1.4738988993532872e-05
            ],
            [
                1.1478773576051192e-05,
                NaN,
                1.7603427932989266e-06,
                3.2887502414436403e-06,
                1.5534984952492866e-06,
                1.760343842833246e-06,
                NaN,
                NaN,
                2.3823693838927385e-07,
                4.222831933649433e-06
            ],
            [
                3.7266406163624873e-06,
                8.939695236983711e-06,
                7.889263525778283e-06,
                NaN,
                2.2603242974060834e-06,
                8.315284241174449e-07,
                1.2098662602861223e-06,
                2.5612812941789413e-06,
                NaN,
                8.939693103418341e-06
            ],
            [
                3.927861534257969e-07,
                1.7603430031445813e-06,
                NaN,
                NaN,
                NaN,
                7.338212428706634e-07,
                6.144176065940129e-06,
                1.5534973841154145e-06,
                6.962254588433232e-06,
                7.889265395847433e-06
            ],
            [
                NaN,
                2.9023126769050284e-06,
                6.144173135896795e-06,
                0.00012339454469590275,
                2.1444958632714784e-05,
                4.006368726804694e-05,
                NaN,
                7.889265404959923e-06,
                NaN,
                7.484625387601897e-05
            ],
            [
                0.9999646437367057,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999646437495691,
                0.9999151889814051,
                NaN,
                0.9999852610128406,
                0.9999724643056438
            ],
            [
                NaN,
                NaN,
                NaN,
                2.561282210460501e-06,
                6.144173863629707e-06,
                NaN,
                1.2098659718187066e-06,
                5.715004469297692e-07,
                NaN,
                3.7266392810548057e-06
            ],
            [
                1.2098652508056196e-06,
                3.726639728184142e-06,
                NaN,
                NaN,
                2.260324028404236e-06,
                5.715002426343175e-07,
                7.88926446470893e-06,
                5.422218969463855e-06,
                2.5612815999423112e-06,
                4.222834450743383e-06
            ],
            [
                7.889264465986113e-06,
                1.300712691308661e-05,
                5.422217030121119e-06,
                2.7535691076718644e-05,
                3.120191135560069e-05,
                4.785093923916815e-06,
                3.2887478889513447e-06,
                6.962254589617333e-06,
                5.1442213603354026e-05,
                8.315283249833015e-07
            ],
            [
                3.5356254905712496e-05,
                1.14787681240737e-05,
                3.120190391251851e-05,
                NaN,
                4.22283545710361e-06,
                1.8925141465820123e-05,
                1.892515725225098e-05,
                5.8291272451829125e-05,
                NaN,
                8.481101058829256e-05
            ],
            [
                2.9023126766305067e-06,
                NaN,
                1.9947299591354906e-06,
                6.962259568648793e-06,
                3.7266388384265735e-06,
                2.9023126768680736e-06,
                NaN,
                4.222833946537913e-06,
                7.889261641416608e-06,
                2.5612822093330395e-06
            ],
            [
                NaN,
                5.422218969128516e-06,
                NaN,
                5.422220907160179e-06,
                1.012998856048759e-05,
                NaN,
                7.889264465555602e-06,
                3.5356242262551455e-05,
                5.8291251541153115e-05,
                1.3007133113017532e-05
            ],
            [
                NaN,
                0.9999852610127575,
                0.999959936307828,
                0.9999930377420916,
                0.9999832985841309,
                0.9990889486727209,
                0.9999485578047517,
                0.9999810748472515,
                0.99999303774624,
                0.9999417087205692
            ],
            [
                7.889261644760245e-06,
                7.889260703906985e-06,
                1.8925150479534963e-05,
                1.0129987354366822e-05,
                4.7850933521167006e-06,
                NaN,
                NaN,
                4.222832436955956e-06,
                1.3007130000322877e-05,
                1.6701423833831836e-05
            ],
            [
                NaN,
                NaN,
                4.2228324354043435e-06,
                1.067703251753986e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                6.144177528838857e-06,
                NaN
            ],
            [
                NaN,
                0.9999339478790182,
                NaN,
                0.999941708741465,
                0.9997388096697479,
                0.9999898700090206,
                NaN,
                NaN,
                0.6224593312018546,
                NaN
            ],
            [
                0.9999810748495546,
                0.9999038975739151,
                0.9579122711832404,
                0.06754669301670264,
                0.9999724642990687,
                0.9465966705768132,
                0.9706877688246606,
                0.6791786861878392,
                1.7603432132912532e-06,
                0.16451646699291614
            ],
            [
                4.785093353352668e-06,
                1.0129992185981682e-05,
                5.422218323019487e-06,
                NaN,
                8.939698433974813e-06,
                7.484620023365781e-05,
                2.1444956078515887e-05,
                2.1444948402034417e-05,
                8.939699498099386e-06,
                8.481103108723191e-05
            ],
            [
                0.9999885212360617,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999898700090293,
                NaN,
                0.9241418163225626,
                NaN,
                0.999995214905507
            ],
            [
                1.012999459934851e-05,
                NaN,
                NaN,
                8.939697367492512e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.0,
                3.9278629390507954e-07,
                4.450848927599543e-07,
                1.9947299588742466e-06,
                NaN,
                NaN,
                NaN,
                7.338207180801359e-07,
                7.338212428706634e-07,
                2.699577130905084e-07
            ],
            [
                1.4738978456719842e-05,
                1.994729008056074e-06,
                5.422218322940583e-06,
                NaN,
                7.889260702141888e-06,
                2.7535681241281285e-05,
                1.0129990972361035e-05,
                6.1441731363550164e-06,
                1.473898547706978e-05,
                1.147876538716594e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                5.144222586675549e-05,
                8.939693102865466e-06,
                NaN,
                6.9622545830002985e-06,
                NaN,
                1.8925154974965226e-05
            ],
            [
                2.90231094702116e-06,
                1.7603440527046419e-06,
                4.785096776194573e-06,
                8.939698434966738e-06,
                2.1444948406091176e-05,
                7.88926164421493e-06,
                NaN,
                3.726641060956752e-06,
                1.7603432132912532e-06,
                3.9278615343222713e-07
            ],
            [
                0.9999852610145515,
                0.2942149721629888,
                0.9999921107364946,
                0.9796676448393464,
                0.9999646437494746,
                0.6224593312018546,
                0.22270013882530884,
                0.9995694429619008,
                0.9999832985822864,
                0.9999339478632615
            ],
            [
                NaN,
                8.939695232967228e-06,
                6.144176066521288e-06,
                2.430023203740195e-05,
                4.539787942390787e-05,
                8.93969523617066e-06,
                4.00636823663512e-05,
                8.93969842784439e-06,
                8.93969736427282e-06,
                4.006369691782494e-05
            ],
            [
                3.9278634073312583e-07,
                3.7266379512112265e-06,
                1.012998856312253e-05,
                NaN,
                NaN,
                NaN,
                1.670142781025767e-05,
                5.422218969128516e-06,
                4.785092782858221e-06,
                NaN
            ],
            [
                NaN,
                2.9023133687786197e-06,
                1.99472900790731e-06,
                1.0129994599624903e-05,
                6.962256247998122e-06,
                NaN,
                7.889264463890957e-06,
                NaN,
                NaN,
                3.726638395320497e-06
            ],
            [
                1.7603430031766016e-06,
                2.561281599734989e-06,
                4.5397868592445174e-05,
                6.144172404380855e-06,
                NaN,
                1.3007134663521234e-05,
                3.2887486729337966e-06,
                8.93969736427282e-06,
                NaN,
                2.2603242967194632e-06
            ],
            [
                0.9999852610232999,
                8.939697369151141e-06,
                NaN,
                NaN,
                0.9999646437619418,
                NaN,
                2.4300240716759115e-05,
                1.760343422928825e-06,
                NaN,
                0.9999687980923468
            ],
            [
                4.785093922889744e-06,
                1.1478772229300848e-05,
                2.1444945854624007e-05,
                8.939700564679507e-06,
                8.9396994983433e-06,
                NaN,
                4.222831934052698e-06,
                NaN,
                1.1478770858372173e-05,
                1.6701427813417103e-05
            ],
            [
                0.9999987901347491,
                NaN,
                0.9999980052695654,
                8.939698428917621e-06,
                0.999860177893495,
                NaN,
                0.9999974387187053,
                0.9999417087067002,
                0.9465966651155708,
                0.9999962733593876
            ],
            [
                6.962253758017727e-06,
                6.144176798870286e-06,
                0.00023050670472240378,
                NaN,
                9.422444815495185e-07,
                1.0677032518413822e-06,
                2.2603240283888175e-06,
                5.715004470077356e-07,
                2.2603253755949437e-06,
                5.422218323231539e-06
            ]
        ]
    },
    {
        "q_id": "8890_mmlu_math",
        "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,
            91,
            92,
            93,
            94,
            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": [
            [
                0.9999952149037948,
                0.999997097688707,
                0.9999938558261334,
                0.9999989322968754,
                0.9999945777797384,
                0.9999974387184001,
                0.9999945777784454,
                0.9999930377404321,
                0.9999930377420919,
                0.9999994956524716
            ],
            [
                0.9999986290426297,
                0.9999945777823233,
                0.9999990577549568,
                0.9999930377437511,
                0.9999599363078239,
                0.999993855824666,
                0.999975699767969,
                0.9999994956524115,
                0.9999945777797377,
                0.9999987901337396
            ],
            [
                0.9999945777790912,
                0.9999986290432835,
                0.9999977396757022,
                0.9999687980849298,
                0.9999938558239336,
                0.9999952149066464,
                0.9999952149055054,
                0.9999977396765105,
                0.9999945777810304,
                0.9999986290432834
            ],
            [
                0.9999987901337396,
                0.9999990577554061,
                0.9999957771665561,
                0.9999984465020603,
                0.9999970976890534,
                0.9999974387184,
                0.9999995549147358,
                0.9999984465022455,
                0.9999970976890531,
                0.9999974387184
            ],
            [
                0.9999980052693274,
                0.9999898700041907,
                0.9999970976880149,
                0.9999989322968754,
                0.9999546021313848,
                0.9999938558275958,
                0.9999785550541535,
                0.999997097687323,
                0.9999832985841309,
                0.9999945777797377
            ],
            [
                0.9999986290427931,
                0.9999852610127582,
                0.9999869928761888,
                0.999998446502801,
                0.9999910602994339,
                0.9999417087066922,
                0.9999810748585306,
                0.9999970976866309,
                0.9999832985821392,
                0.9999974387187053
            ],
            [
                0.9999984465020603,
                0.9999970976887069,
                0.999997438717484,
                0.9999990577556308,
                0.999998790134028,
                0.9999980052702786,
                0.9999962733611607,
                0.9999992661791945,
                0.9999957771680662,
                0.9999957771665561
            ],
            [
                0.9999986290421394,
                0.9999977396762411,
                0.9999995549147889,
                0.999997438717484,
                0.9999986290423029,
                0.9999910602994342,
                0.9999982396565767,
                0.9999982396567867,
                0.9999984465015046,
                0.9999945777816768
            ],
            [
                0.9999546021259734,
                0.9999945777784451,
                0.9999938558268633,
                0.9999417087484445,
                0.9999724643023473,
                0.9999724643154851,
                0.9999417087206875,
                0.9999930377420913,
                0.9999885212359824,
                0.9999910603068934
            ],
            [
                0.9999938558224686,
                0.9999852610215446,
                0.9999974387184,
                0.9999974387180947,
                0.9999885212318762,
                0.9999952149037942,
                0.9999945777790912,
                0.9999970976873229,
                0.9999977396759716,
                0.999995777167059
            ],
            [
                0.9999930377404309,
                0.9999977396765105,
                0.9999930377462404,
                0.9999974387187053,
                0.999997438717484,
                0.9999945777797377,
                0.9999980052695652,
                0.9999990577554061,
                0.9999930377412608,
                0.9999970976880148
            ],
            [
                0.9995121428838878,
                0.9999952149055052,
                0.9999970976880149,
                0.9999930377429205,
                0.999992110736474,
                0.9999687980886309,
                0.9999930377404305,
                0.9999930377412606,
                0.999991060300499,
                0.9999945777829694
            ],
            [
                0.9999957771670592,
                0.999972464315472,
                0.9999910603058276,
                0.9999952149043646,
                0.9999938558253981,
                0.9990889486876617,
                0.9999810748427385,
                0.9999987901344607,
                0.9999974387171787,
                0.9999980052707541
            ],
            [
                0.9999977396754328,
                0.9999967112513269,
                0.9999962733607163,
                0.9999970976866311,
                0.9999967112513267,
                0.9999852610145208,
                0.9999938558275967,
                0.9999938558275958,
                0.9999952149032241,
                0.9999945777803849
            ],
            [
                0.999995214906076,
                0.9999785550413659,
                0.9999852610233023,
                0.9999977396757022,
                0.9999151889587262,
                0.9999938558239333,
                0.9999898700126435,
                0.9999967112505425,
                0.9999869928746385,
                0.9999952149032236
            ],
            [
                0.9999967112521106,
                0.9999938558246657,
                0.999995214904935,
                0.9999938558253981,
                0.9999945777797375,
                0.9999977396748938,
                0.9999982396563669,
                0.9999945777790913,
                0.9999852610233002,
                0.9999990577549569
            ],
            [
                0.9999785550515963,
                0.9999930377445809,
                0.9999756997650724,
                0.9999952149049353,
                0.999994577781031,
                0.9999987901337396,
                0.9999990577549568,
                0.9999982396561572,
                0.9999974387168733,
                0.9999974387177893
            ],
            [
                0.9999930377420905,
                0.9999945777829694,
                0.9999974387177892,
                0.9999938558232008,
                0.9999599363078501,
                0.9999885212346133,
                0.9999980052707541,
                0.9999930377445804,
                0.9999417087275736,
                0.9999898700102287
            ],
            [
                0.9999977396759716,
                0.9999417087136605,
                0.999985261018032,
                0.9999885212264029,
                0.9999910603036967,
                0.9999986290432835,
                0.999972464315473,
                0.9998601778762657,
                0.9999832985701989,
                0.9999930377412606
            ],
            [
                0.9999885212264021,
                0.9999957771670588,
                0.999992110737415,
                0.9999962733620487,
                0.9999982396569966,
                0.9999970976880148,
                0.9999810748495139,
                0.9999945777803841,
                0.9999938558268632,
                0.9999982396572064
            ],
            [
                0.9999945777823247,
                0.9999967112493665,
                0.9999957771650456,
                0.9999995549149481,
                0.9999974387184001,
                0.9999989322968754,
                0.999998446502801,
                0.9999646437577469,
                0.9999984465018751,
                0.9999921107392965
            ],
            [
                0.999964643757729,
                0.9999938558261307,
                0.9999898700114362,
                0.9999967112513267,
                0.9999756997621702,
                0.9999921107355337,
                0.9999646437324474,
                0.9999957771670589,
                0.999992110739296,
                0.9999930377454106
            ],
            [
                0.9999957771675624,
                0.9999945777784447,
                0.9999957771670589,
                0.9999938558246657,
                0.9999921107355336,
                0.9999687980923468,
                0.9999785550413627,
                0.9999962733616043,
                0.9995694428611961,
                0.9999962733616045
            ],
            [
                0.9999996940977731,
                0.9999986290429567,
                0.9999982396567867,
                0.9999945777790911,
                0.9999994956527722,
                0.9999984465028011,
                0.9999987901341723,
                0.9999995549150011,
                0.9999980052695653,
                0.9999994284995529
            ],
            [
                0.9999967112521109,
                0.9999987901346049,
                0.9999687980997866,
                0.9999945777784449,
                0.9999967112497585,
                0.9999952149072169,
                0.9999945777790913,
                0.9999982396574163,
                0.9999974387168733,
                0.999997097687669
            ],
            [
                0.9999992661786695,
                0.9999997300422868,
                0.9999869928715439,
                0.9999986290429567,
                0.9999967112501509,
                0.9999974387180948,
                0.9999980052693275,
                0.9999885212359875,
                0.9999962733589393,
                0.9999938558261314
            ],
            [
                0.9999687980849362,
                0.9999756997563796,
                0.999986992869987,
                0.9999646437451037,
                0.999992110740236,
                0.9999869928730887,
                0.9999885212305063,
                0.9999921107355337,
                0.9999599362887278,
                0.999988521231875
            ],
            [
                0.9999967112509349,
                0.9999986290421394,
                0.9999984465022455,
                0.9999967112497585,
                0.9999930377420911,
                0.999997438716568,
                0.9999986290427932,
                0.9999990577549568,
                0.999993037740431,
                0.9999986290426297
            ],
            [
                0.9999967112517187,
                0.9999967112505427,
                0.9999921107336531,
                0.9999957771675623,
                0.9999982396567867,
                0.9999957771655489,
                0.9999930377420913,
                0.9999962733598274,
                0.9999980052702786,
                0.9999993524051246
            ],
            [
                0.9999980052702785,
                0.9999989322973845,
                0.9999992661788445,
                0.9999989322972572,
                0.9999997897567341,
                0.999999266179107,
                0.9999987901337396,
                0.9999898700126436,
                0.9999977396746244,
                0.9999989322966208
            ],
            [
                0.9999967112521109,
                0.9999992661786695,
                0.9999974387184,
                0.9999995549147358,
                0.999999495652652,
                0.9999986290421394,
                0.9999957771650453,
                0.9999987901337396,
                0.9999996940978095,
                0.9999984465015047
            ],
            [
                0.9999546021313743,
                0.999981074858529,
                0.9999687980886298,
                0.9998911030518618,
                0.9999810748517617,
                0.9999945777810303,
                0.9999898700041898,
                0.9994472212662482,
                0.999985261021544,
                0.9997965729542014
            ],
            [
                0.999995214906076,
                0.9999984465022455,
                0.9999984465018751,
                0.999999266178757,
                0.9999977396751633,
                0.999999057755743,
                0.999997097686977,
                0.9999980052705163,
                0.9999994284992805,
                0.9999967112517189
            ],
            [
                0.9999977396765105,
                0.9999910603026313,
                0.9999987901338838,
                0.9999982396574163,
                0.999996273358939,
                0.9999990577550691,
                0.9999970976873231,
                0.9999990577557432,
                0.9999986290429566,
                0.9999938558232012
            ],
            [
                0.9999967112505427,
                0.9999910603036963,
                0.9999938558275953,
                0.9999852610127585,
                0.9999980052693274,
                0.9999869928746379,
                0.9999930377454106,
                0.9999994284992805,
                0.9999832985841293,
                0.9999921107383558
            ],
            [
                0.9999982396561571,
                0.9999938558224684,
                0.9999852610180293,
                0.9999938558261305,
                0.9999970976880148,
                0.9999987901343165,
                0.9999962733589389,
                0.9999810748427356,
                0.9999977396762411,
                0.9999990577549569
            ],
            [
                0.9999910603047619,
                0.9999982396559473,
                0.9999980052705163,
                0.9999852610145168,
                0.9999938558268638,
                0.9999990577551815,
                0.9999996072137061,
                0.9999986290432834,
                0.9999984465022455,
                0.9999996533672135
            ],
            [
                0.9999945777797378,
                0.999996273360716,
                0.9999869928668863,
                0.9999930377420907,
                0.9999970976883608,
                0.9999974387168733,
                0.9999724643187587,
                0.9999852610180308,
                0.99997246431547,
                0.9999982396561571
            ],
            [
                0.9999852610162767,
                0.9999970976887068,
                0.999989870007816,
                0.9999938558253986,
                0.9999952149049351,
                0.9999251537818146,
                0.9999967112505427,
                0.9999977396746245,
                0.9999810748562817,
                0.9999945777810306
            ],
            [
                0.9999756997505845,
                0.999993855824666,
                0.9999724643089399,
                0.9999930377404308,
                0.9999898700090211,
                0.9999898700041916,
                0.9999962733607162,
                0.9999938558275957,
                0.999991060302631,
                0.9999962733607161
            ],
            [
                0.9999990577554061,
                0.9999970976890528,
                0.9999977396762411,
                0.9999962733607161,
                0.9999977396748938,
                0.9999885212318764,
                0.9999957771660521,
                0.9999994284994849,
                0.9999921107345932,
                0.9999982396565769
            ],
            [
                0.9990889487684591,
                0.9997694932030217,
                0.9999417087136563,
                0.9990889487994005,
                0.9996646499705251,
                0.9998415637645907,
                0.9999687980774756,
                0.9994472213273486,
                0.9993736659063435,
                0.9996200155173954
            ],
            [
                0.9999980052695652,
                0.9999996533672962,
                0.9999986290427931,
                0.9999986290426297,
                0.9999987901341724,
                0.9999990577555185,
                0.9999991684718732,
                0.9999980052707542,
                0.9999991684717741,
                0.9999938558224714
            ],
            [
                0.9999992661787571,
                0.999996273360716,
                0.999999266179107,
                0.99998987000419,
                0.9999869928730875,
                0.9999957771655488,
                0.9999646437535052,
                0.9999984465022455,
                0.9999251537995278,
                0.9999989322975118
            ],
            [
                0.9999990577556308,
                0.9999986290421394,
                0.9999980052702786,
                0.9999989322967482,
                0.9999996072137529,
                0.9999977396762412,
                0.999998790134028,
                0.9999993524053562,
                0.9999980052707541,
                0.9999986290429566
            ],
            [
                0.9999952149066462,
                0.9999945777823231,
                0.9999962733616043,
                0.9999952149032237,
                0.9999952149043646,
                0.9999982396559473,
                0.9999952149043644,
                0.9999967112509346,
                0.9999687980774852,
                0.9999957771650454
            ],
            [
                0.9999986290429566,
                0.9999984465015046,
                0.9999885212332433,
                0.9999977396757022,
                0.9999980052707541,
                0.999985261014516,
                0.999998005269803,
                0.9999945777797374,
                0.9999898700126439,
                0.9999990577555185
            ],
            [
                0.9999984465016899,
                0.9999989322970027,
                0.9999986290427932,
                0.9999977396746245,
                0.9999938558275957,
                0.9999785550515947,
                0.9999991684716749,
                0.9999977396746244,
                0.9999989322967482,
                0.9999967112497586
            ],
            [
                1.300712846361323e-05,
                2.902313023101807e-06,
                1.670142781478417e-05,
                4.7850950649408664e-06,
                2.5612816000145246e-06,
                2.561281905376098e-06,
                1.3007133114602719e-05,
                4.785093353739995e-06,
                2.561281905376098e-06,
                1.1478770862067849e-05
            ],
            [
                0.9999785550413794,
                0.9999945777797377,
                0.9999986290429566,
                0.9999957771650453,
                0.9999957771680659,
                0.9999952149060758,
                0.9999962733607161,
                0.9999832985701983,
                0.9999898700066077,
                0.9999974387168733
            ],
            [
                0.9999980052702785,
                0.9999993524053563,
                0.9999980052693275,
                0.9999993524054334,
                0.9999785550567011,
                0.9999987901338838,
                0.9999993524050474,
                0.9999994956523514,
                0.999998790134605,
                0.9999984465015046
            ],
            [
                0.9999982396561572,
                0.9999977396759716,
                0.9999992661789321,
                0.9999967112509347,
                0.9999994956523514,
                0.9999990577554061,
                0.99999893229713,
                0.9999852610127589,
                0.9999952149037941,
                0.9999869928653355
            ],
            [
                0.9999885212291387,
                0.9999687980886309,
                0.9999852610180293,
                0.9999910603058282,
                0.9999898700114362,
                0.9999852610110012,
                0.9999952149055056,
                0.9999724643121909,
                0.9999945777803843,
                0.9999938558253983
            ],
            [
                4.2228349546493465e-06,
                8.939695237504067e-06,
                1.6701417859944398e-05,
                1.0129992186202796e-05,
                7.889264465397747e-06,
                1.892515499864894e-05,
                2.1444953517842076e-05,
                1.0129988564099116e-05,
                7.88926164421493e-06,
                4.222831933864508e-06
            ],
            [
                0.9999967112497584,
                0.9999967112513266,
                0.9999962733616047,
                0.9999992661788445,
                0.999998790134605,
                0.9999852610110029,
                0.9999989322968753,
                0.9999984465016899,
                0.9999974387180947,
                0.9999987901338838
            ],
            [
                4.222832437677995e-06,
                1.5534975693601474e-06,
                3.2887502415243994e-06,
                1.0677029973114952e-06,
                1.5534979397500702e-06,
                3.288748673295719e-06,
                8.315280276505193e-07,
                1.5534979397677313e-06,
                1.2098655392662613e-06,
                7.338208930144969e-07
            ],
            [
                0.9999996072137529,
                0.999999266178932,
                0.9999930377412608,
                0.9999852610215458,
                0.9999991684719723,
                0.9999986290432834,
                0.9999930377420908,
                0.9999930377462403,
                0.9999974387187053,
                0.9999038976080066
            ],
            [
                0.9999910603068948,
                0.9999687980737645,
                0.9999945777797379,
                0.9999930377462406,
                0.9999962733602719,
                0.9999962733607162,
                0.9999977396757023,
                0.9999869928761891,
                0.9999980052700408,
                0.9999885212332442
            ],
            [
                0.9999910603036973,
                0.999998446502801,
                0.999997438717484,
                0.9999921107336539,
                0.9999977396748939,
                0.9999994284992805,
                0.9999980052705163,
                0.9999991684715758,
                0.9999974387171787,
                0.9999962733620489
            ],
            [
                0.9999997897566589,
                0.9999989322973845,
                0.9999984465016899,
                0.9999986290432834,
                0.9999962733598275,
                0.9999984465016899,
                0.9999982396572064,
                0.9999986290429567,
                0.9999974387184001,
                0.9999970976876689
            ],
            [
                0.9999974387168733,
                0.9999930377429205,
                0.99999862904312,
                0.9999869928761891,
                0.9999869928699877,
                0.9999930377437503,
                0.9999945777784449,
                0.9999993524052018,
                0.9999599363030699,
                0.9998601778759707
            ],
            [
                0.9999952149037942,
                0.999992110740236,
                0.9999756997534859,
                0.9999967112517186,
                0.9999974387177893,
                0.9999945777797377,
                0.9999967112509347,
                0.9999910603047645,
                0.9999970976887068,
                0.9999938558232012
            ],
            [
                0.9999724642990576,
                0.9999945777816766,
                0.9999785550515891,
                0.9999832985781566,
                0.9999756997592744,
                0.9999599363126035,
                0.9998766054547045,
                0.9998911030779789,
                0.9997040428313339,
                0.9999832985701931
            ],
            [
                0.9999952149060758,
                0.9999957771675625,
                0.9999832985721853,
                0.9999962733620487,
                0.9999930377412606,
                0.999997438716568,
                0.9999986290427931,
                0.9999970976880148,
                0.9999962733620487,
                0.9999952149055052
            ],
            [
                0.9999974387180945,
                0.9999987901338837,
                0.999981074842739,
                0.999948557798617,
                0.9999832985701967,
                0.9999921107392953,
                0.9999852610127573,
                0.9999756997650677,
                0.9999785550464821,
                0.9999785550592636
            ],
            [
                0.999991060301566,
                0.9999921107374152,
                0.9999898700090213,
                0.9999962733616046,
                0.9999989322968754,
                0.9999945777810305,
                0.9999938558232017,
                0.9999967112521109,
                0.9999977396746245,
                0.999995777168066
            ],
            [
                0.9999930377420906,
                0.9997040429356038,
                0.9999724643023419,
                0.9997040428661479,
                0.9999930377420906,
                0.9988304897565667,
                0.9999038975392727,
                0.9999151889889644,
                0.9999910603015647,
                0.9999599363125902
            ],
            [
                0.999985261023302,
                0.9999885212277717,
                0.9999930377404307,
                0.9999832985781612,
                0.9999930377412607,
                0.9999898700078145,
                0.9999938558261309,
                0.9999646437619434,
                0.9999599363078431,
                0.9999952149037942
            ],
            [
                0.9999996533672962,
                0.9999952149055055,
                0.9999938558275958,
                0.9999952149066464,
                0.9999987901344607,
                0.9999982396565769,
                0.9999982396561571,
                0.9999982396574163,
                0.9999991684717742,
                0.999998629042303
            ],
            [
                0.9999989322975118,
                0.9999993524049702,
                0.999999266178932,
                0.9999991684720715,
                0.99999893229713,
                0.999997438717484,
                0.9999996533672962,
                0.9999994956527121,
                0.999997097688707,
                0.9999962733611603
            ],
            [
                0.9999980052695652,
                0.9999962733620487,
                0.9999832985701935,
                0.9999910603004994,
                0.9999945777810302,
                0.9999885212318754,
                0.9999952149066461,
                0.9999810748585306,
                0.9999967112505427,
                0.9999962733589389
            ],
            [
                0.9998204720767369,
                0.9999898700126436,
                0.9999910603068931,
                0.9996200155629634,
                0.9996200155163675,
                0.9999339478396323,
                0.9997965729539883,
                0.9997694931752275,
                0.9999724643023353,
                0.9998601778928846
            ],
            [
                0.9999974387168733,
                0.9999687980737751,
                0.9999938558253986,
                0.9999724642957917,
                0.999995777166052,
                0.9999852610180315,
                0.999995214904935,
                0.9999977396751633,
                0.9999957771665555,
                0.9999930377420909
            ],
            [
                0.9999982396569965,
                0.9999970976869769,
                0.9999989322967481,
                0.9999962733611603,
                0.9999546021259605,
                0.9999945777823231,
                0.9999970976876689,
                0.9999991684721706,
                0.9999989322970027,
                0.9999982396567867
            ],
            [
                0.9999910603058283,
                0.9999980052705163,
                0.9999952149072169,
                0.9999984465022455,
                0.999993855823201,
                0.9999977396762411,
                0.9999982396561571,
                0.9999957771670592,
                0.9999974387168733,
                0.9999977396762411
            ],
            [
                0.9999977396748938,
                0.9999991684716749,
                0.9999724643089155,
                0.9999980052695652,
                0.999999789756684,
                0.9999989322967481,
                0.9999987901338838,
                0.9999996940977366,
                0.9999994284992805,
                0.9999980052705163
            ],
            [
                0.9999982396572065,
                0.99999862904312,
                0.9999990577549568,
                0.9999599362935143,
                0.999995214904935,
                0.9999977396754327,
                0.9999930377445806,
                0.9999994956527121,
                0.9999989322966208,
                0.999999266178932
            ],
            [
                0.9999957771670589,
                0.9999852610162754,
                0.9999990577554061,
                0.9999984465020603,
                0.9999980052695652,
                0.9999977396754327,
                0.9999977396751634,
                0.9999991684720715,
                0.9999986290432835,
                0.9999990577554061
            ],
            [
                0.9998766053960036,
                0.999925153772784,
                0.999704042797002,
                0.9995694429631032,
                0.9999151889183269,
                0.9999546021097171,
                0.9999646437408605,
                0.9999869928730862,
                0.9994472214525726,
                0.999088948786049
            ],
            [
                0.9999984465024306,
                0.9999980052700408,
                0.9999910603036976,
                0.9999957771655489,
                0.9999967112501507,
                0.9999957771675624,
                0.9999990577554061,
                0.9999980052705164,
                0.9999980052709919,
                0.9999967112497585
            ],
            [
                0.9999945777829701,
                0.999988521234614,
                0.9999980052695652,
                0.999997438717484,
                0.9999967112497589,
                0.9999962733620493,
                0.9999970976890531,
                0.9999952149037947,
                0.9999967112497588,
                0.9999977396765106
            ],
            [
                0.9999982396565769,
                0.9999962733593833,
                0.9999982396567867,
                0.9999957771670589,
                0.9999974387180948,
                0.9999945777797377,
                0.9998601779262996,
                0.9999952149055056,
                0.999991060305828,
                0.9999962733607161
            ],
            [
                0.9999962733607161,
                0.9999990577549568,
                0.9999993524052018,
                0.9999984465020603,
                0.9988304896791887,
                0.9999987901341723,
                0.9999980052709919,
                0.9999994956525918,
                0.9999989322973846,
                0.9999980052705163
            ],
            [
                0.9999989322972572,
                0.9999885212318754,
                0.9999952149055054,
                0.9999984465016898,
                0.9999930377437507,
                0.9999910603047626,
                0.9999945777790913,
                0.9999930377445804,
                0.9999987901341723,
                0.9998415637080029
            ],
            [
                0.999948557767984,
                0.9999646437492968,
                0.9999724642957762,
                0.9999785550439201,
                0.9999151889182762,
                0.9999485577986598,
                0.999989870005398,
                0.999968798077481,
                0.9998415638022965,
                0.9999724642957762
            ],
            [
                0.9999987901341723,
                0.9999930377445804,
                0.9999970976883608,
                0.9999910603015649,
                0.999999266179107,
                0.9999977396751633,
                0.9999910603036964,
                0.9999930377429209,
                0.9999982396569965,
                0.9999995549147889
            ],
            [
                0.9999785550567081,
                0.9999977396746244,
                0.9999938558268633,
                0.9988304896785087,
                0.9999980052702785,
                0.9999982396572064,
                0.9999910603004991,
                0.9999852610233015,
                0.9999945777797375,
                0.9999938558275958
            ],
            [
                0.9999952149055064,
                0.999998239656577,
                0.9999967112509347,
                0.999998629042303,
                0.9999986290426297,
                0.999998790134028,
                0.9999986290424663,
                0.9999962733589393,
                0.9999990577551815,
                0.9999980052707541
            ],
            [
                0.9999687980997901,
                0.9999417087553522,
                0.9999687980997926,
                0.9999151889891112,
                0.9999251537727775,
                0.9998601778760521,
                0.9924227604829851,
                0.9999885212291404,
                0.9997965730510352,
                0.9997965729810306
            ],
            [
                0.9999832985841337,
                0.9999962733589395,
                0.9999982396565769,
                0.99999862904312,
                0.9999982396569966,
                0.9999938558253996,
                0.9999994956524716,
                0.9999987901341723,
                0.9999970976866311,
                0.9999910603026327
            ],
            [
                0.9999977396751633,
                0.9999930377404305,
                0.9999869928699864,
                0.9999910603036958,
                0.999992110740236,
                0.9999251537460145,
                0.9999810748562726,
                0.999664649850108,
                0.9999945777797374,
                0.9998204720766403
            ],
            [
                0.9999977396765105,
                0.9999977396765105,
                0.999998005269803,
                0.9999994284995529,
                0.9999990577549568,
                0.999999730042319,
                0.9999989322966208,
                0.9999993524051246,
                0.9999986290426297,
                0.9999921107392967
            ],
            [
                0.9999546021259605,
                0.999998629042303,
                0.9999996940977366,
                0.9999974387180947,
                0.9999962733607161,
                0.9999898700053994,
                0.9999980052695652,
                0.9999885212332457,
                0.9999930377412619,
                0.9999977396748938
            ],
            [
                0.9999852610180324,
                0.9999945777790913,
                0.9999921107364745,
                0.9999852610162749,
                0.9999996072137061,
                0.9999970976880148,
                0.9999986290429566,
                0.9999945777797378,
                0.9999921107336545,
                0.9999785550541559
            ],
            [
                0.9999967112509347,
                0.9999980052702785,
                0.9999990577552937,
                0.9999986290424664,
                0.9999970976883608,
                0.9999977396762411,
                0.9999982396569966,
                0.9999977396751633,
                0.9999990577549568,
                0.999998005269803
            ],
            [
                0.9999977396757022,
                0.9999977396762411,
                0.9999962733607161,
                0.9999810748517651,
                0.99999862904312,
                0.9999945777797377,
                0.9999952149066468,
                0.9999921107374146,
                0.9999992661792819,
                0.9999957771650455
            ],
            [
                0.9999987901337396,
                0.9999990577555185,
                0.9999967112513268,
                0.9999980052695652,
                0.9999962733593833,
                0.9999938558261309,
                0.9999994956527121,
                0.9999980052698029,
                0.9999994956525318,
                0.9999996940978825
            ],
            [
                0.9999977396762411,
                0.9999982396565769,
                0.99999862904312,
                0.9999952149032235,
                0.9999990577552937,
                0.9999986290429567,
                0.9999987901343165,
                0.999999352404893,
                0.9999970976880149,
                0.999996273360716
            ],
            [
                0.9999962733620487,
                0.9999974387168733,
                0.9999974387177893,
                0.9999898700041912,
                0.9999646437450794,
                0.9999945777797377,
                0.9999724643023379,
                0.999998629042303,
                0.9999967112521109,
                0.9999970976873229
            ],
            [
                0.9999885212332438,
                0.999999057755743,
                0.9999967112501504,
                0.9999885212305071,
                0.9999962733611603,
                0.9999910603015649,
                0.9999938558268631,
                0.9999967112505427,
                0.9999967112521109,
                0.9999485578047577
            ],
            [
                0.9999952149072167,
                0.9999957771645419,
                0.9999921107355335,
                0.9999982396569965,
                0.9999724642957734,
                0.9999962733602717,
                0.9999970976880148,
                0.9999982396565767,
                0.9999938558224682,
                0.9999991684715759
            ],
            [
                3.726641061058432e-06,
                7.889266346603015e-06,
                5.422217030362759e-06,
                1.3709570434054234e-06,
                3.7266410609160796e-06,
                1.3007128462785148e-05,
                1.994729959270648e-06,
                3.5356246487099006e-05,
                3.7266392839425286e-06,
                4.785092783454444e-06
            ],
            [
                0.9999984465022455,
                0.99999862904312,
                0.9999987901343165,
                0.9999986290431201,
                0.999998790134605,
                0.9999987901347491,
                0.9999995549150542,
                0.9999993524049702,
                0.9999993524054335,
                0.9999994956524716
            ],
            [
                0.9999992661789321,
                0.9999987901341723,
                0.9999974387171787,
                0.9999986290424663,
                0.9999952149060769,
                0.9999967112509348,
                0.9999982396572065,
                0.9999952149049353,
                0.9999930377437518,
                0.9999970976873229
            ],
            [
                0.9999962733620488,
                0.9999967112505427,
                0.9999987901347491,
                0.9999980052705163,
                0.9999989322967481,
                0.9999984465022455,
                0.9999952149037943,
                0.9999930377420907,
                0.9999970976883609,
                0.9999994284996211
            ],
            [
                0.9999251537639157,
                0.9995694428613839,
                0.9999885212318746,
                0.9999687980960674,
                0.9997388096603245,
                0.9997965730030326,
                0.9998601779094202,
                0.9999546021205469,
                0.9999151889687554,
                0.9998911030648022
            ],
            [
                0.9999980052705163,
                0.9999921107336531,
                0.9999987901346049,
                0.999998239656367,
                0.9999982396561571,
                0.9999980052700407,
                0.9999982396567867,
                0.9999984465026158,
                0.9999977396757022,
                0.9999986290424663
            ],
            [
                0.9999930377437504,
                0.999999266178932,
                0.999999057755743,
                0.9999599363173789,
                0.9999982396574162,
                0.9999967112509347,
                0.9999977396765105,
                0.9999832985781566,
                0.9999989322971299,
                0.9999991684718732
            ],
            [
                0.9997694932038869,
                0.999997438716568,
                0.9999986290424663,
                0.9999970976890528,
                0.9999938558232008,
                0.9999967112517187,
                0.9999646437366568,
                0.9999962733598274,
                0.9999646437577242,
                0.9999996533674202
            ],
            [
                0.9999987901344607,
                0.9999869928684365,
                0.999999266179107,
                0.9999991684717741,
                0.9999994284994849,
                0.9999993524052019,
                0.9999987901337396,
                0.999999057755069,
                0.9999967112521109,
                0.9999980052705163
            ],
            [
                0.9999982396569966,
                0.9999986290421394,
                0.9999977396762411,
                0.9998601778599723,
                0.9999967112501507,
                0.9999987901343165,
                0.9999980052698029,
                0.9999990577552939,
                0.9999930377404308,
                0.999998629042303
            ],
            [
                0.9999984465015047,
                0.9999952149037946,
                0.9999977396746244,
                0.9999990577552939,
                0.9999980052698031,
                0.9999974387177895,
                0.9999984465022455,
                0.999998446502801,
                0.9999987901338839,
                0.9999989322966208
            ],
            [
                0.9999982396574163,
                0.9999980052700408,
                0.9999898700053991,
                0.9999952149066464,
                0.9999974387168734,
                0.9999984465024306,
                0.999996273358939,
                0.9999986290427931,
                0.9999967112513267,
                0.9999952149060762
            ],
            [
                0.9999980052702785,
                0.99999862904312,
                0.9999998555019446,
                0.9999970976866309,
                0.9999980052707541,
                0.9999992661791944,
                0.9999982396569965,
                0.9999970976887068,
                0.999999554914895,
                0.9999999317440278
            ],
            [
                0.9999980052693274,
                0.9999989322967482,
                0.9999952149066462,
                0.9999869928761888,
                0.9999962733598274,
                0.9999938558232011,
                0.9999921107364742,
                0.9999952149032236,
                0.9999756997679626,
                0.9999599363221628
            ],
            [
                0.9999992661787571,
                0.9999995549150541,
                0.9999957771680658,
                0.9999967112497585,
                0.9999990577556307,
                0.999998790134028,
                0.9999992661786695,
                0.9999977396765105,
                0.999998446502801,
                0.9999967112509347
            ],
            [
                0.9999957771680658,
                0.9999957771650457,
                0.9999945777829695,
                0.9999930377404308,
                0.9999910603068939,
                0.9999952149049349,
                0.9999987901344607,
                0.999981074858529,
                0.9999970976876689,
                0.9999832985821392
            ],
            [
                0.9999984465015047,
                0.9999980052709919,
                0.9999982396561572,
                0.9999957771650456,
                0.999998446502801,
                0.9999980052707541,
                0.9999967112501507,
                0.999998790134028,
                0.9999992661790195,
                0.9999952149066467
            ],
            [
                0.9999982396572065,
                0.9999810748562722,
                0.9999970976876689,
                0.9999977396748938,
                0.9999977396765105,
                0.999997097688015,
                0.9999724642957828,
                0.9999921107355342,
                0.9999991684722697,
                0.9999967112497586
            ],
            [
                0.99999862904312,
                0.9999984465022455,
                0.9999974387171787,
                0.9999982396572065,
                0.999997097687323,
                0.9999995549150011,
                0.999997097686977,
                0.9999992661786696,
                0.9999982396572065,
                0.999997438717484
            ],
            [
                0.9999982396574163,
                0.9999987901338838,
                0.9999930377404317,
                0.9999921107364742,
                0.999997097686977,
                0.9999977396757023,
                0.9999990577557432,
                0.999993037742092,
                0.9999987901340281,
                0.9999993524049702
            ],
            [
                0.9999992661789321,
                0.9999974387168734,
                0.9999938558275973,
                0.9999967112497585,
                0.9999991684719723,
                0.9999930377404317,
                0.9999984465016899,
                0.9999984465024306,
                0.9999921107392962,
                0.9999957771665561
            ],
            [
                0.9999910603047638,
                0.9999957771665555,
                0.9999962733598275,
                0.9999986290426297,
                0.9999977396748938,
                0.9999977396751634,
                0.9999989322973846,
                0.9999994284992805,
                0.9999930377462408,
                0.9999957771645422
            ],
            [
                0.9999984465026158,
                0.9999962733598275,
                0.9999986290426298,
                0.9999938558239336,
                0.999999057755069,
                0.9999995549150542,
                0.999999057755069,
                0.9999962733611605,
                0.9999980052695653,
                0.999995777166556
            ],
            [
                0.9999869928761884,
                0.9999930377445804,
                0.9999945777797375,
                0.9999869928715365,
                0.9999938558268633,
                0.9999485578048138,
                0.9999546021314138,
                0.9999967112513267,
                0.9999921107364743,
                0.9999967112493664
            ]
        ]
    },
    {
        "q_id": "8456_mmlu_math",
        "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,
            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": [
            [
                1.8925143721761383e-05,
                1.473898372500477e-05,
                6.605215250517728e-05,
                6.605216827142175e-05,
                1.0129987356375273e-05,
                1.6701417859944398e-05,
                4.5397863219323224e-05,
                3.120192624960245e-05,
                1.4738983726184394e-05,
                1.8925157258585e-05
            ],
            [
                1.4738980213020151e-05,
                5.422220908560712e-06,
                2.144494073796001e-05,
                8.939697368663308e-06,
                0.999999352405279,
                1.892515500388139e-05,
                2.753568452790729e-05,
                1.300712846217e-05,
                2.144495096457996e-05,
                1.3007123808532309e-05
            ],
            [
                1.3007130013288297e-05,
                1.4738976697631541e-05,
                6.962257079629686e-06,
                5.1442195225848094e-05,
                1.4738983725809062e-05,
                1.3007133114886634e-05,
                1.1478770861859053e-05,
                1.8925143725892257e-05,
                2.4300240727367308e-05,
                1.3007134665413997e-05
            ],
            [
                0.9993736658216329,
                0.9964063970084025,
                0.9995121428791761,
                0.9998601779092554,
                0.999959936303039,
                0.9986749773628055,
                0.9997965729781035,
                0.9999687980923468,
                0.9996200154688759,
                0.9998601779092168
            ],
            [
                0.9998911030777682,
                0.9995694429090684,
                0.9975273772476576,
                0.9999417087066884,
                0.9991959140504812,
                0.9968273171229062,
                0.9999885212264008,
                0.9996646497697713,
                0.9988304898649506,
                0.9933071496700977
            ],
            [
                0.9999687980774675,
                0.9995694430140943,
                0.9999687980849082,
                0.9996646498905104,
                0.999841563726562,
                0.99991518895867,
                0.9999785550541436,
                0.9999038975621215,
                0.99970404283018,
                0.9999038975506866
            ],
            [
                0.9988304897218895,
                0.9992903297038491,
                0.9988304898755578,
                0.999796573075106,
                0.9999151889889872,
                0.9995121429380712,
                0.9241418236349501,
                0.999569442858503,
                0.9999038975620929,
                0.9996646498900617
            ],
            [
                0.9992903296191034,
                0.9964063970142383,
                0.999088948763214,
                0.999290329450644,
                0.9999151889889644,
                0.9989677689193093,
                0.9999038975392132,
                0.9999038975849913,
                0.9996646498897299,
                0.9999251537995218
            ],
            [
                0.9998415637075303,
                0.9995121427635432,
                0.9997965729296244,
                0.9998911030388833,
                0.9999785550490294,
                0.999954602125951,
                0.9999339478395728,
                0.9980732657626956,
                0.9995694428583277,
                0.999933947855328
            ],
            [
                0.9999646437324302,
                0.9998601778759096,
                0.9999599363221395,
                0.9997040430064716,
                0.9998415637075787,
                0.999447221453473,
                0.9982992778688372,
                0.9999832985841282,
                0.9999785550592551,
                0.9994472213863268
            ],
            [
                3.2887502413389517e-06,
                1.1478769492392108e-05,
                8.939700565102295e-06,
                5.829125853074485e-05,
                0.0003353499887309223,
                1.0129987356541108e-05,
                3.5356246490314526e-05,
                3.53562591336057e-05,
                2.1444948406091176e-05,
                2.144495351940237e-05
            ],
            [
                0.9997388096905482,
                0.9999546021205374,
                0.9984988176785242,
                0.9995121428230627,
                0.9984988176903901,
                0.9997040429001783,
                0.9993736658223981,
                0.9997040428652609,
                0.9997040430069108,
                0.9982992779121233
            ],
            [
                2.1444948408977715e-05,
                1.3007130013288297e-05,
                3.12019076377484e-05,
                4.53978848619353e-05,
                3.535625068579429e-05,
                1.6701423832586287e-05,
                3.535624646754865e-05,
                5.1442195232584995e-05,
                1.670142582254589e-05,
                2.144494585197151e-05
            ],
            [
                2.4300243626409964e-05,
                3.120192623972722e-05,
                5.144222587386666e-05,
                2.144494329566774e-05,
                6.144175334239434e-06,
                6.9622570784012604e-06,
                1.4738981970312625e-05,
                3.2887498494551953e-06,
                6.962254589781966e-06,
                0.9999921107355334
            ],
            [
                8.481106152343337e-05,
                0.0002305067409473547,
                2.7535700941409604e-05,
                5.422220262333096e-06,
                3.5356254916002164e-05,
                3.120191507912884e-05,
                3.120191880504111e-05,
                6.144174601410037e-06,
                1.6701427813417103e-05,
                2.1444945847446664e-05
            ],
            [
                1.8925152744083297e-05,
                8.481101087089185e-05,
                1.8925143724239906e-05,
                1.3007123810638006e-05,
                1.3007131564383116e-05,
                4.0063692172075196e-05,
                1.4738976695942536e-05,
                4.5397852378781204e-05,
                1.4738976695942536e-05,
                1.3007126912258525e-05
            ],
            [
                7.484623611811155e-05,
                9.610243748836994e-05,
                2.4300249416363357e-05,
                4.539786317522845e-05,
                6.605216034072351e-05,
                7.484620930074429e-05,
                1.4738978456719842e-05,
                5.1442207479139826e-05,
                3.120190392795564e-05,
                5.144222587386666e-05
            ],
            [
                2.4300240728162926e-05,
                8.939699500489763e-06,
                6.14417606659952e-06,
                2.7535681242383173e-05,
                1.4738983727578497e-05,
                6.962254589433702e-06,
                2.4300232036606334e-05,
                1.3007133114886634e-05,
                1.3007134665674251e-05,
                3.535624648041073e-05
            ],
            [
                0.9997040429002644,
                0.9997040429000922,
                0.9997388097839099,
                0.9980732653424931,
                0.9997040427944791,
                0.9998766054398044,
                0.9994472212540602,
                0.9978172834238246,
                0.9999151889181831,
                0.9980732653319713
            ],
            [
                1.892514597770291e-05,
                3.1201915085825835e-05,
                0.999998790134028,
                3.5356259125502595e-05,
                1.4738976699427788e-05,
                0.00020342694789637583,
                0.000379984478525278,
                3.535623805665442e-05,
                6.144177531381426e-06,
                1.4738988998787566e-05
            ],
            [
                0.9999987901338838,
                5.1442219756013625e-05,
                1.6701425822059825e-05,
                2.144494585197151e-05,
                3.120191136263821e-05,
                3.5356238059741304e-05,
                2.753569437476538e-05,
                7.889264466230069e-06,
                4.785093353739995e-06,
                0.9999957771655487
            ],
            [
                6.144176066051891e-06,
                1.1478766756214804e-05,
                1.3007126912258525e-05,
                1.012999460150437e-05,
                8.93969736929749e-06,
                6.144173869240119e-06,
                7.889264465067689e-06,
                2.1444948407573453e-05,
                1.0129992185760567e-05,
                4.539786317820113e-05
            ],
            [
                1.6701417859944398e-05,
                1.6701419849933667e-05,
                3.5356254916002164e-05,
                3.535625068579429e-05,
                1.012999460150437e-05,
                2.7535687816036267e-05,
                1.473898021457511e-05,
                3.120190763332158e-05,
                3.535625066945945e-05,
                1.0129987355564522e-05
            ],
            [
                4.00636825989602e-05,
                3.1201911358551906e-05,
                9.610246055259474e-05,
                5.144220748250827e-05,
                1.4738976698757546e-05,
                2.7535694380675497e-05,
                3.120192621089609e-05,
                1.670142980608093e-05,
                9.610243773517696e-05,
                0.9999945777803839
            ],
            [
                0.9984988176827122,
                0.9989677691613169,
                0.9988304899927809,
                0.9947798744684557,
                0.9980732655392742,
                0.9994472213193091,
                0.9995121428792897,
                0.9992903295360914,
                0.9996200155598902,
                0.99937366582105
            ],
            [
                6.144176798590883e-06,
                6.962257079376403e-06,
                1.0129987356191011e-05,
                7.889264466115267e-06,
                1.4738987241172537e-05,
                3.535624648041073e-05,
                5.8291279387562654e-05,
                1.4738985481091229e-05,
                2.1444940738662144e-05,
                2.4300243625614346e-05
            ],
            [
                6.605212887119557e-05,
                1.6701417860795016e-05,
                2.699576809107705e-07,
                8.93969417214416e-06,
                3.288748281220719e-06,
                3.5356267547205986e-05,
                6.9622587393661365e-06,
                2.1444940742640888e-05,
                1.892515500560259e-05,
                1.4738985483504099e-05
            ],
            [
                0.99956944285824,
                0.999195913953862,
                0.9984988176947525,
                0.99908894876279,
                0.9995121429373901,
                0.9988304895841319,
                0.998967769156155,
                0.9997040429712185,
                0.9997694932297829,
                0.999769493257302
            ],
            [
                2.1444958627955892e-05,
                8.93969630317306e-06,
                6.144173869312763e-06,
                2.1444953523537147e-05,
                1.4738987241494252e-05,
                6.962253759670401e-06,
                2.7535684522397864e-05,
                1.892515500560259e-05,
                3.2887478891487563e-06,
                1.8925150490826034e-05
            ],
            [
                0.9975273765786226,
                0.9997040429710378,
                0.999796573026544,
                0.995929862689936,
                0.9914225134537443,
                0.9999038975735753,
                0.9988304898622308,
                0.9997040429005227,
                0.9999151889889569,
                0.9990889489864794
            ],
            [
                4.7850933534310035e-06,
                2.561283126639892e-06,
                4.5397890270732005e-05,
                1.147876538789672e-05,
                0.00037998448048197787,
                1.4738983726908257e-05,
                6.144173136556186e-06,
                1.012998977108606e-05,
                1.8925155000714377e-05,
                4.222833947774596e-06
            ],
            [
                3.120190392670705e-05,
                6.605216819645424e-05,
                2.430023492769181e-05,
                2.1444940742640888e-05,
                2.1444940738662144e-05,
                5.144220743759563e-05,
                4.785096205882502e-06,
                4.00636778258121e-05,
                7.889262585541864e-06,
                5.1442195245310235e-05
            ],
            [
                1.4738978456398127e-05,
                4.5397857775848465e-05,
                1.670142582300158e-05,
                1.8925143725341476e-05,
                2.4300240723831244e-05,
                8.939700566289352e-06,
                2.4300252315495453e-05,
                0.000179527900998409,
                0.9999990577555185,
                1.6701415868649062e-05
            ],
            [
                2.753569436805389e-05,
                2.4300240729754152e-05,
                2.75357009220765e-05,
                1.670142781560441e-05,
                1.3007123811797321e-05,
                2.4300249417247375e-05,
                1.473897845457507e-05,
                8.481107162358746e-05,
                3.535626334490732e-05,
                2.7535681242383173e-05
            ],
            [
                0.999841563745393,
                0.9971990735271185,
                0.9997040430062994,
                0.9959298620896819,
                0.9997040429710378,
                0.998299277480053,
                0.9995121428792897,
                0.9875683477976086,
                0.9997040430062994,
                0.9980732655231556
            ],
            [
                6.962255419380732e-06,
                7.88926540679677e-06,
                7.889265405677441e-06,
                1.4738980212644815e-05,
                6.144175334015912e-06,
                0.0002611903084106071,
                1.670141586949968e-05,
                1.3007126911974612e-05,
                7.88926258532661e-06,
                7.889265406567165e-06
            ],
            [
                2.5612819053166966e-06,
                1.3007131561047124e-05,
                1.4738983726559732e-05,
                5.4222215552470286e-06,
                5.8291244660131775e-05,
                4.2228349546493465e-06,
                6.60521604084826e-05,
                1.4738985484549675e-05,
                2.9023116390421582e-06,
                2.9023130230133794e-06
            ],
            [
                1.892514147143123e-05,
                6.962258739530771e-06,
                1.300712536258383e-05,
                1.4738983726559732e-05,
                1.1478765388523107e-05,
                2.7535687803514833e-05,
                1.1478764019328247e-05,
                3.120191507629113e-05,
                1.1478769492141554e-05,
                1.473898899846585e-05
            ],
            [
                6.962254589433702e-06,
                5.829126548301662e-05,
                2.7535700936100516e-05,
                0.9999417087275482,
                7.889260704050487e-06,
                1.8925148236123232e-05,
                2.1444945855248125e-05,
                7.889266346746518e-06,
                5.144221362431326e-05,
                1.0129992185760567e-05
            ],
            [
                3.120191508185304e-05,
                0.00012339453057324482,
                0.00013982203990505675,
                2.4300252309307336e-05,
                2.1444945852673643e-05,
                4.539785780309804e-05,
                5.8291293247581486e-05,
                1.892515725920463e-05,
                0.00012339461880846384,
                3.5356267550807374e-05
            ],
            [
                2.75357009372024e-05,
                7.889262585211807e-06,
                2.753568450797317e-05,
                2.7535691091443854e-05,
                1.3007134663876127e-05,
                2.7535704221626983e-05,
                3.5356246493272806e-05,
                1.6701421842140854e-05,
                1.4738976699427788e-05,
                6.605216035177641e-05
            ],
            [
                1.30071315640992e-05,
                5.422220908703723e-06,
                1.7603440526806268e-06,
                2.144495863411905e-05,
                2.2603248366762157e-06,
                1.0129994600398803e-05,
                8.939697369004791e-06,
                1.6701423830702777e-05,
                2.5612822106421996e-06,
                1.6701425823882575e-05
            ],
            [
                0.9994472213852655,
                0.9988304899980845,
                0.9994472214521223,
                0.998967768791463,
                0.9968273176000636,
                0.9978172836804141,
                0.9996646497697713,
                0.9964063969583807,
                0.99962001555968,
                0.9968273170890339
            ],
            [
                0.9999251537370814,
                0.9999251537549172,
                0.9971990729158223,
                0.9982992779530376,
                0.9998911030388326,
                0.9996200154238939,
                0.9999546021367712,
                0.9997694931749592,
                0.9998204720338529,
                0.9989677687903826
            ],
            [
                0.9994472213852655,
                0.9933071496731934,
                0.9964063967374519,
                0.999620015514278,
                0.9997694933396449,
                0.9992903297060369,
                0.99408893066217,
                0.9975273771620901,
                0.9924227604199546,
                0.9988304897265131
            ],
            [
                0.999195914240633,
                0.9996646498896129,
                0.997817283668751,
                0.9992903295331607,
                0.9995694428586032,
                0.999876605366243,
                0.9997965729537811,
                0.9995121429387809,
                0.9994472214521223,
                0.9971990725874132
            ],
            [
                5.829125853074485e-05,
                2.144495607789177e-05,
                1.1478766755985128e-05,
                1.8925141469400216e-05,
                1.6701419850845044e-05,
                1.3007131564383116e-05,
                0.9999994284994849,
                0.999998005269803,
                1.8925143726890553e-05,
                0.00017952796440747263
            ],
            [
                3.726640172503764e-06,
                1.4738983725406915e-05,
                4.785095065045315e-06,
                2.4300232031037035e-05,
                4.222832941072913e-06,
                1.6701415867707307e-05,
                1.3007126911974612e-05,
                7.889263525778283e-06,
                1.473897670007122e-05,
                4.7850950649408664e-06
            ],
            [
                0.9980732653823419,
                0.9859363707872744,
                0.9984988180341516,
                0.9991959141414883,
                0.9999785550439179,
                0.9997040428303522,
                0.9933071505214268,
                0.9984988175064688,
                0.9924227585220377,
                0.9989677690380322
            ],
            [
                1.1478769491598686e-05,
                0.00012339455991555511,
                6.1441775312976045e-06,
                1.1478770860982112e-05,
                3.726640172385136e-06,
                1.6701429804744246e-05,
                2.1444940742640888e-05,
                2.2603251062013478e-06,
                1.4738980211116665e-05,
                0.0024726236195036478
            ],
            [
                7.889261644631091e-06,
                7.889260704308795e-06,
                0.9999989322975118,
                1.6701425825492673e-05,
                5.829124465589078e-05,
                2.4300249418927004e-05,
                1.8925155005051806e-05,
                2.4300246521474893e-05,
                1.4738976694977387e-05,
                3.120191508060445e-05
            ],
            [
                0.9998911030907721,
                0.9998415638020614,
                0.998674977348479,
                0.999891103038808,
                0.9994472212537708,
                0.999088948654813,
                0.9998911031038012,
                0.9998911030907103,
                0.9999417087483575,
                0.9999724642957707
            ],
            [
                0.9902915216650597,
                0.9997694932851969,
                0.9999151889889569,
                0.9990889486523759,
                0.9997694933121257,
                0.9997965730024703,
                0.9997694932302121,
                0.999769493257302,
                0.9046505331728751,
                0.9995694428599811
            ],
            [
                0.999999266178757,
                1.8925155003330605e-05,
                2.144494073569759e-05,
                5.829126551609642e-05,
                4.0063696945516495e-05,
                0.9999990577549568,
                0.9999980052705163,
                2.430024072648329e-05,
                8.939697368110433e-06,
                0.9999982396574163
            ],
            [
                0.9999885212277695,
                4.539787936841779e-05,
                2.1444945850567248e-05,
                4.539785779797843e-05,
                2.430023781444595e-05,
                1.4738981970956057e-05,
                2.144495351004062e-05,
                1.0129993394314164e-05,
                1.4738987241172537e-05,
                2.1444945850567248e-05
            ],
            [
                0.9998204720338842,
                0.9984988178884456,
                0.9994472213851369,
                0.999704042759312,
                0.9990889488711908,
                0.9964063974702689,
                0.9975273762679376,
                0.9998911030907103,
                0.999860177875871,
                0.9996200155150629
            ],
            [
                1.8925150491445666e-05,
                2.4300243618542217e-05,
                6.605216035706259e-05,
                9.610246040856568e-05,
                1.8925143725892257e-05,
                2.1444948410303962e-05,
                6.605212886014267e-05,
                0.00037998456809129095,
                8.939695237813028e-06,
                3.535626334156318e-05
            ],
            [
                0.9982992774648336,
                0.9998204720125913,
                0.9998415637642725,
                0.9999687980849082,
                0.9940889304624211,
                0.9999785550413605,
                0.9998204719910343,
                0.9995121428799708,
                0.9999251537549052,
                0.9999339478789374
            ],
            [
                2.4300243623139103e-05,
                1.300712691308661e-05,
                4.539786320396437e-05,
                1.6701429804744246e-05,
                5.8291279365509446e-05,
                1.6701419849933667e-05,
                3.535626333989112e-05,
                2.4300249415479343e-05,
                0.9999990577551814,
                2.4300232038993178e-05
            ],
            [
                6.962257079465052e-06,
                5.4222215550004564e-06,
                2.1444958635523312e-05,
                2.144495863614743e-05,
                0.999997097687323,
                0.0001088969610517703,
                2.1444948410303962e-05,
                8.93969630348202e-06,
                7.484626286742124e-05,
                3.5356254907513187e-05
            ],
            [
                1.4738981969240237e-05,
                0.0001233945889939477,
                2.144495096457996e-05,
                1.892515500450102e-05,
                1.4738987241172537e-05,
                3.1201911358551906e-05,
                8.93969736942758e-06,
                1.4738988996240646e-05,
                2.144494840531103e-05,
                1.3007131563176482e-05
            ],
            [
                5.8291272451829125e-05,
                2.430023493052066e-05,
                1.8925145981283003e-05,
                5.144222587386666e-05,
                2.430024072648329e-05,
                7.484620930782328e-05,
                4.785093924047376e-06,
                4.539789028064095e-05,
                2.7535704221626983e-05,
                2.7535700941409604e-05
            ],
            [
                1.4738978455701077e-05,
                2.1444958621558693e-05,
                4.006369693006752e-05,
                3.5356238042506135e-05,
                4.006368262883792e-05,
                1.89251482355036e-05,
                5.422221555192784e-06,
                6.605212867704903e-05,
                1.3007131562845248e-05,
                1.0129992186939844e-05
            ],
            [
                0.9999038975965026,
                0.9993736659684644,
                0.9991959141449491,
                0.9997388096905482,
                0.9994472212540602,
                0.9990889487624192,
                0.998967768791463,
                0.9999038976193814,
                0.9998415637641733,
                0.9996200155591163
            ],
            [
                2.4300246521474893e-05,
                1.4738978450955768e-05,
                1.1478764019557924e-05,
                2.9023126768680736e-06,
                6.144172404218801e-06,
                2.1444950966608343e-05,
                1.892515500715167e-05,
                1.3007134663876127e-05,
                2.144495607640949e-05,
                1.892515274614874e-05
            ],
            [
                0.9997388096905482,
                0.9975273765700085,
                0.9999417087136174,
                0.9998766053956697,
                0.9993736658218151,
                0.9986749776685919,
                0.9840936101250567,
                0.9924227603114022,
                0.9984988174946029,
                0.9995694429606232
            ],
            [
                0.9999417087205802,
                0.9999810748540162,
                0.9997965729295415,
                0.9999756997592666,
                0.9978172839258476,
                0.9992903294548545,
                0.9996200154239604,
                0.9978172833868066,
                0.9998601779759897,
                0.9999339478474747
            ],
            [
                1.4738978453315019e-05,
                2.4300252313904224e-05,
                1.3007134665130082e-05,
                2.753568452349975e-05,
                1.1478766755734576e-05,
                5.422217030555087e-06,
                1.892515500715167e-05,
                4.006370171458602e-05,
                9.610244925260613e-05,
                2.4300237830711845e-05
            ],
            [
                1.473897669838221e-05,
                1.300712846115264e-05,
                6.1441738691562974e-06,
                1.0129988564099116e-05,
                0.00017952802946734746,
                7.889265406294507e-06,
                1.6701423831188846e-05,
                9.610238055986271e-05,
                2.4300234934056724e-05,
                1.147877086073156e-05
            ],
            [
                3.120190392670705e-05,
                6.962253759157502e-06,
                5.144221363703851e-05,
                5.144221976237626e-05,
                0.9999967112509347,
                4.00636778475281e-05,
                2.430023782717578e-05,
                7.889266347248781e-06,
                6.962258739454786e-06,
                2.1444943294263477e-05
            ],
            [
                4.0063677818524845e-05,
                1.0129995809763438e-05,
                1.8925145980732218e-05,
                8.939693106329072e-06,
                1.0129992185760567e-05,
                1.4738987240100149e-05,
                1.892514372479069e-05,
                2.7535700934898458e-05,
                1.0129992186202796e-05,
                8.939698432917844e-06
            ],
            [
                3.2887478892055875e-06,
                8.481102108950948e-05,
                2.7535687811228037e-05,
                1.4738978456049602e-05,
                3.120190019784534e-05,
                2.4300240728162926e-05,
                8.93969630333567e-06,
                4.539785238670836e-05,
                4.0063706492255065e-05,
                1.0129987356541108e-05
            ],
            [
                2.7535681250497054e-05,
                4.539785781036459e-05,
                8.93969310647542e-06,
                1.1478772230198667e-05,
                8.939698434657777e-06,
                1.6701421842140854e-05,
                1.1478768124553928e-05,
                1.6701423833831836e-05,
                8.93969417214416e-06,
                7.889260704423598e-06
            ],
            [
                5.144221363067589e-05,
                7.484623608435025e-05,
                4.006370642681552e-05,
                2.7535700934898458e-05,
                6.605216035706259e-05,
                1.0129988563914856e-05,
                0.9999974387168733,
                0.9999982396569966,
                3.1201918802543923e-05,
                3.120192251631124e-05
            ],
            [
                0.9999646437492881,
                0.999903897539223,
                0.9998911031036888,
                0.99997569975637,
                0.9999898700090201,
                0.9995121427655299,
                0.996827316727484,
                0.9997040429012288,
                0.9999724642957716,
                0.9997388097531997
            ],
            [
                7.88926258532661e-06,
                4.222831934156396e-06,
                1.0129994601688632e-05,
                1.3007130012010681e-05,
                1.892515500450102e-05,
                4.785096776251149e-06,
                2.430024072648329e-05,
                2.430025231469984e-05,
                3.7266401724291984e-06,
                1.1478766756214804e-05
            ],
            [
                0.00023050671507143103,
                1.4738985482351282e-05,
                2.4300232040584407e-05,
                3.535623805819787e-05,
                1.4738978456049602e-05,
                3.5356250696598434e-05,
                6.605213669905004e-05,
                3.5356238024242e-05,
                2.4300234934056724e-05,
                2.430025231469984e-05
            ],
            [
                0.9999339478474597,
                0.9947798744200933,
                0.9980732653621937,
                0.9998766053957809,
                0.9978172837077972,
                0.9953904285299785,
                0.9995694429096069,
                0.9999339478631961,
                0.9992903294477132,
                0.9971990729379331
            ],
            [
                3.535623806128476e-05,
                2.4300234931404677e-05,
                3.1201922511884416e-05,
                8.939696303758459e-06,
                1.1478773596575768e-05,
                5.8291272448012225e-05,
                4.7850933538313875e-06,
                1.4738983724575818e-05,
                1.4738976700661033e-05,
                2.43002523073625e-05
            ],
            [
                1.1478764019328247e-05,
                5.829127242214212e-05,
                6.1441738691562974e-06,
                5.422218969601935e-06,
                1.0129994600638342e-05,
                1.1478764019996392e-05,
                4.222832941072913e-06,
                2.1444956075707356e-05,
                1.8925141469950998e-05,
                8.315279285149107e-07
            ],
            [
                2.7535681246690542e-05,
                4.006370172712009e-05,
                2.7535687805818776e-05,
                2.1444953520182517e-05,
                1.6701421841259862e-05,
                1.1478766756653273e-05,
                1.6701429806475863e-05,
                1.6701419850845044e-05,
                4.006371126336615e-05,
                2.1444948409679848e-05
            ],
            [
                4.539785235863304e-05,
                2.7535681242383173e-05,
                1.4738978456049602e-05,
                2.1444953524161264e-05,
                4.006369217615605e-05,
                2.7535684529910724e-05,
                4.006369694959736e-05,
                3.726638395527247e-06,
                6.605212095972449e-05,
                1.6701419852090592e-05
            ],
            [
                0.9999646437324287,
                0.9975273771913783,
                0.9994472213188589,
                0.9999339478474415,
                0.996406396663253,
                0.9998415638396958,
                0.9996646497292712,
                0.999860177909178,
                0.998299277700239,
                0.9992903295324176
            ],
            [
                0.9996646497299249,
                0.998073265548229,
                0.997817283653031,
                0.993307149821789,
                0.9995694429603477,
                0.9984988180493329,
                0.9991959139563873,
                0.9982992779022407,
                0.9980732650637758,
                0.9933071506050118
            ],
            [
                8.939695237813028e-06,
                6.144174601309452e-06,
                1.8925141465820123e-05,
                1.1478765386623071e-05,
                2.260323489490968e-06,
                1.0129995809044816e-05,
                1.1478768123823146e-05,
                1.6701415863393463e-05,
                6.144176066443055e-06,
                0.00012339456000173458
            ],
            [
                6.962253759043525e-06,
                1.0129993394129904e-05,
                2.7535697655983693e-05,
                8.481103105082719e-05,
                1.670141985166528e-05,
                3.535624646549072e-05,
                1.473897669838221e-05,
                2.753568781022632e-05,
                7.889259763728304e-06,
                3.12019113570763e-05
            ],
            [
                2.1444953520884646e-05,
                2.4300246523773334e-05,
                0.9999992661791944,
                0.0001398221236671851,
                0.9999993524050473,
                3.1201900204769344e-05,
                0.9999990577554061,
                0.00012339461859481044,
                4.006368740446426e-05,
                3.5356267506175954e-05
            ],
            [
                0.9993736658285919,
                0.9997388097534734,
                0.9993736658208678,
                0.9997694932295716,
                0.9990889487684591,
                0.9995121428837458,
                0.9964063976061611,
                0.9820137906958956,
                0.9964063975569731,
                0.9986749773876074
            ],
            [
                2.144495863614743e-05,
                5.144221358089769e-05,
                1.1478769492642663e-05,
                6.962257909412379e-06,
                1.0129994601872894e-05,
                1.0129992187253088e-05,
                2.2603234894745224e-06,
                5.144220137064579e-05,
                2.4300237829827827e-05,
                2.4300234936443568e-05
            ],
            [
                5.829127243062412e-05,
                4.539785779269366e-05,
                3.120191506868607e-05,
                2.753569437266178e-05,
                1.3007126911643378e-05,
                1.670141586949968e-05,
                1.4738978455325741e-05,
                3.53562506877236e-05,
                1.3007123811513407e-05,
                6.605216823009351e-05
            ],
            [
                4.539785239182798e-05,
                0.000139822090473997,
                0.00012339461859481044,
                2.1444953521586782e-05,
                5.422220262505697e-06,
                1.4738981970956057e-05,
                2.5612822106841303e-06,
                1.8925157262578186e-05,
                2.9023133690425823e-06,
                0.00012339463344461816
            ],
            [
                1.6701417859944398e-05,
                1.892514823364471e-05,
                2.1444945850567248e-05,
                8.939698433584547e-06,
                2.753570094040789e-05,
                1.1478765388105516e-05,
                8.93969630333567e-06,
                8.939698433584547e-06,
                6.962254589617333e-06,
                6.144175333289463e-06
            ],
            [
                1.892514147046736e-05,
                2.4300240723831244e-05,
                1.0129990979381404e-05,
                2.4300243621371074e-05,
                4.785096205830278e-06,
                1.8925150491445666e-05,
                1.1478773598099973e-05,
                1.3007128463352975e-05,
                2.4300249418927004e-05,
                1.4738988998117324e-05
            ],
            [
                8.481103119027577e-05,
                1.4738983724575818e-05,
                4.006368739659403e-05,
                3.5356250691324983e-05,
                2.753570421601738e-05,
                2.144494073796001e-05,
                7.889260704308795e-06,
                2.753569108453202e-05,
                7.88926164421493e-06,
                1.0129988563546333e-05
            ],
            [
                1.6701417861949427e-05,
                4.539786319306454e-05,
                2.753569108924008e-05,
                1.1478766755233466e-05,
                1.1478773597870298e-05,
                4.785093353787868e-06,
                1.4738980212644815e-05,
                3.726638839806038e-06,
                1.1478765387416494e-05,
                2.144495096387783e-05
            ],
            [
                0.9994472214515435,
                0.9989677690405532,
                0.9999151889485459,
                0.9933071492243107,
                0.9997388095971864,
                0.9980732650870582,
                0.9980732653230164,
                0.9995694429619008,
                0.999769493257302,
                0.9995694430122656
            ],
            [
                8.93969630348202e-06,
                1.012998856312253e-05,
                6.144172404380855e-06,
                6.144174601410037e-06,
                1.6701415868649062e-05,
                8.939693106020111e-06,
                3.120192623257619e-05,
                1.3007130012980722e-05,
                4.222832437677995e-06,
                7.889259763728304e-06
            ],
            [
                0.9991959142396977,
                0.9988304897231133,
                0.9999038975964927,
                0.98201378585969,
                0.9995121429382132,
                0.9959298627295754,
                0.9993736658216329,
                0.9991959142418958,
                0.99951214282153,
                0.9997040429711238
            ],
            [
                6.962257909323729e-06,
                2.144495352474637e-05,
                4.00636826148464e-05,
                1.0129992186589747e-05,
                2.7535681246690542e-05,
                8.939695237666677e-06,
                3.1201922517673344e-05,
                3.5356242271040426e-05,
                0.00026119027722163314,
                3.7266397280960194e-06
            ],
            [
                1.4738980213341866e-05,
                2.1444948403750736e-05,
                1.6701417859944398e-05,
                1.8925150490206403e-05,
                2.1444950959196957e-05,
                1.3007133115430804e-05,
                4.0063706496627415e-05,
                1.8925150493166868e-05,
                3.288749065167371e-06,
                1.0129987355785634e-05
            ],
            [
                5.144223204748698e-05,
                1.3007126913346863e-05,
                4.0063687398634466e-05,
                4.0063696951637786e-05,
                1.892514372479069e-05,
                4.539789026561238e-05,
                1.3007134665413997e-05,
                1.3007131563507714e-05,
                7.484623600430327e-05,
                4.222832940942332e-06
            ],
            [
                0.997527376616525,
                0.9997694931746943,
                0.9993736658946478,
                0.9990889487607767,
                0.9940889303283431,
                0.9998204720765749,
                0.998830489716586,
                0.9999038975735753,
                0.999195914233431,
                0.999876605395702
            ],
            [
                1.6701423834226767e-05,
                3.7266410609940346e-06,
                2.1444953520884646e-05,
                1.147877086020957e-05,
                1.6701415868649062e-05,
                3.7266397283231055e-06,
                0.9999957771680656,
                2.144494329496561e-05,
                2.1444940736477737e-05,
                4.7850956352353935e-06
            ],
            [
                6.144176066443055e-06,
                6.962258739169842e-06,
                4.785092783267308e-06,
                3.120191134788212e-05,
                2.1444958633416914e-05,
                7.889262585082652e-06,
                3.1201911361276113e-05,
                3.28875024125221e-06,
                1.47389819699641e-05,
                8.939696303758459e-06
            ],
            [
                4.539787404186659e-05,
                6.605212100345552e-05,
                1.0129992185060374e-05,
                1.0129988562901417e-05,
                4.006370171677219e-05,
                1.1478764019557924e-05,
                4.539789026561238e-05,
                1.3007131561804229e-05,
                1.0129995809431767e-05,
                1.3007130012673148e-05
            ],
            [
                0.00013982202350580785,
                0.9978172834785908,
                8.939695237959376e-06,
                0.9994472213878061,
                1.0129990979381404e-05,
                0.9947798742097168,
                0.000123394530503224,
                2.7535697662094155e-05,
                2.1444953524161264e-05,
                5.829125158695591e-05
            ],
            [
                6.1441753335241615e-06,
                9.422450431860582e-07,
                5.422220907909759e-06,
                5.422220262264056e-06,
                1.1478773595343877e-05,
                1.300712691308661e-05,
                6.962257078819179e-06,
                8.939700565996655e-06,
                1.0129995809597604e-05,
                2.1444940736477737e-05
            ],
            [
                0.9940889320385214,
                0.9990889486527997,
                0.9914225139922965,
                0.9988304898562473,
                0.9999251537370575,
                0.9998415638209155,
                0.9999151889586244,
                0.9964063971751413,
                0.9997388096908217,
                0.9980732655694966
            ],
            [
                2.144495096387783e-05,
                0.00012339453024827647,
                1.892515725920463e-05,
                2.144494074076854e-05,
                3.120191136774608e-05,
                1.3007126913346863e-05,
                6.962255419279419e-06,
                7.484623611811155e-05,
                9.610244902887168e-05,
                6.96225707894582e-06
            ],
            [
                0.9993736658967611,
                0.9995694430116269,
                0.9996200155154167,
                0.9999687980849072,
                0.999860177909178,
                0.9999417087483575,
                0.10669059749614015,
                0.9999756997564291,
                0.9992903297062846,
                0.9998766053956697
            ],
            [
                0.9968273164145334,
                0.9994472213195986,
                0.9978172836504956,
                0.9998911030517628,
                0.999704042759312,
                0.9993736658206491,
                0.9998204719482784,
                0.9993736659684644,
                0.9992903297040554,
                0.9998415637831289
            ],
            [
                0.997199072941835,
                0.9997388095970496,
                0.9964063982114229,
                0.9992903296200941,
                0.9999038975964458,
                0.9982992774676008,
                0.9997040428296547,
                0.9999151889182053,
                0.9980732653319713,
                0.9995694429607108
            ],
            [
                0.9999810748427351,
                0.9990889486576211,
                0.9990889487652271,
                0.9998415638397973,
                0.9988304899941408,
                0.9975273765728798,
                0.999088948975989,
                0.9982992772794348,
                0.9980732653015251,
                0.9971990728442877
            ],
            [
                5.144223201604811e-05,
                2.56128282131428e-06,
                1.473898899908247e-05,
                1.0129988564264954e-05,
                6.144173868983067e-06,
                8.939695237162584e-06,
                3.726639728262097e-06,
                2.260324297853209e-06,
                2.4300252315495453e-05,
                1.0129995809597604e-05
            ],
            [
                7.889264466344872e-06,
                6.1441746018123775e-06,
                2.753568124769226e-05,
                3.1201922520397544e-05,
                4.006370173105521e-05,
                1.473898724181597e-05,
                0.9999938558275956,
                2.1444953524161264e-05,
                3.535625491754561e-05,
                9.610244928336962e-05
            ],
            [
                1.1478770861650256e-05,
                2.144494329566774e-05,
                2.4300246522270504e-05,
                8.939697368500698e-06,
                6.962257909121104e-06,
                1.1478765387416494e-05,
                1.6701419850389357e-05,
                2.4300232038993178e-05,
                2.753568452790729e-05,
                7.484620038721724e-05
            ],
            [
                1.0129995809044816e-05,
                1.6701421844419295e-05,
                6.605216029987583e-05,
                6.144177531381426e-06,
                2.4300243626409964e-05,
                4.006368737181739e-05,
                0.9999993524051246,
                2.4300249420429837e-05,
                1.1478770859332632e-05,
                1.300713311517055e-05
            ],
            [
                0.00012339454504780223,
                3.1201915085825835e-05,
                1.6701421842566163e-05,
                2.7535691095550887e-05,
                1.473898724181597e-05,
                4.006370173105521e-05,
                2.1444950965906214e-05,
                3.120192252175965e-05,
                0.0002611904326725625,
                1.892515275165658e-05
            ],
            [
                0.9984988177406455,
                0.9982992772640178,
                0.9999151889181905,
                0.9984988175151938,
                0.9998766053956554,
                0.9975273766257136,
                0.9993736658216329,
                0.9996646498097153,
                0.9940889318551903,
                0.9989677689163081
            ],
            [
                1.1478766756214804e-05,
                1.892514823426434e-05,
                7.889261644982674e-06,
                1.0129987356375273e-05,
                2.144494585583323e-05,
                2.1444945853375776e-05,
                4.5397863198349305e-05,
                6.9622545892184106e-06,
                8.93969630388855e-06,
                1.892514147046736e-05
            ],
            [
                4.222833947820683e-06,
                1.6701425822059825e-05,
                1.892514597770291e-05,
                2.7535697651475977e-05,
                0.00013982212379942078,
                6.144174600605357e-06,
                1.4738976696371488e-05,
                5.422220262195015e-06,
                4.7850956352353935e-06,
                1.670141984792864e-05
            ],
            [
                2.7535694373763664e-05,
                0.0001398221237566985,
                4.5397874031792504e-05,
                2.4300240723831244e-05,
                0.99999893229713,
                4.539788485433845e-05,
                8.48110513985993e-05,
                8.481108152444222e-05,
                3.535625912022914e-05,
                0.9999994284992805
            ],
            [
                5.144221360709674e-05,
                1.892514372479069e-05,
                4.006370170554982e-05,
                0.9999974387187053,
                1.6701425824307884e-05,
                5.829125855619084e-05,
                1.4738983726908257e-05,
                4.5397863211726375e-05,
                4.0063692179945426e-05,
                1.6701415866735174e-05
            ],
            [
                0.9980732653319713,
                0.9995121429405406,
                0.9971990732097646,
                0.9988304898795015,
                0.9999038976193912,
                0.9940889313298237,
                0.9997694933396986,
                0.999769493174852,
                0.9997694933672178,
                0.9971990725574987
            ],
            [
                1.0129987356541108e-05,
                1.3007128462785148e-05,
                2.144494329769612e-05,
                1.3007123811797321e-05,
                1.6701429805199933e-05,
                2.753570422573402e-05,
                0.00010889689617180939,
                6.9622537593854575e-06,
                8.939700565834043e-06,
                2.4300243626409964e-05
            ],
            [
                0.999796573050825,
                0.9999151889788488,
                0.9998601779259395,
                0.998830489860871,
                0.999841563839772,
                0.9933071497567785,
                0.9997040428653471,
                0.9997388097839707,
                0.991422513897258,
                0.9993736658223981
            ],
            [
                0.9999962733616045,
                3.120191508060445e-05,
                2.4300232033865884e-05,
                1.0129989771473008e-05,
                3.53562675293277e-05,
                6.605212884380361e-05,
                0.9999974387184,
                3.12019002110123e-05,
                2.1444945850567248e-05,
                0.9999996533672136
            ]
        ]
    },
    {
        "q_id": "8295_mmlu_math",
        "cot_ids": [
            1,
            2,
            3,
            4,
            5,
            6,
            9,
            13,
            14,
            15,
            16,
            17,
            20,
            21,
            22,
            23,
            25,
            26,
            27,
            28,
            29,
            30,
            32,
            33,
            34,
            35,
            36,
            38,
            39,
            42,
            43,
            44,
            45,
            47,
            49,
            50,
            51,
            52,
            54,
            55,
            60,
            61,
            62,
            63,
            64,
            65,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            88,
            89,
            90,
            91,
            93,
            94,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            115,
            116,
            118,
            119,
            120,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.5534984951164742e-06,
                1.892515271055432e-05,
                1.2098658270370427e-06,
                3.726638394957837e-06,
                NaN,
                0.4378234991142019,
                6.962258732597129e-06,
                0.7057850278370112,
                2.90231233014737e-06,
                1.8925141440966004e-05
            ],
            [
                1.1478773581396351e-05,
                2.4300234903469775e-05,
                0.03732688787958169,
                0.00013982203938425186,
                0.22270013882530884,
                1.1478765381257036e-05,
                0.9740426422370713,
                8.481107101026021e-05,
                0.0002611903025816733,
                1.3007129996348077e-05
            ],
            [
                4.222833947282995e-06,
                1.1478765357203838e-05,
                7.338213302981904e-07,
                8.939698385890826e-06,
                1.6701417837251142e-05,
                3.120191488412147e-05,
                1.8925143702277406e-05,
                1.0129989763162812e-05,
                7.889259761030436e-06,
                1.1478773595009805e-05
            ],
            [
                1.0129994599901296e-05,
                0.00013982205500229526,
                NaN,
                2.90231336827709e-06,
                1.4738978451920916e-05,
                2.4300243621371074e-05,
                0.00026119042722360877,
                2.1444943252135606e-05,
                8.939700562110258e-06,
                3.535625067794842e-05
            ],
            [
                1.8925145974191664e-05,
                1.3007128457012223e-05,
                2.4300246513165137e-05,
                3.7266383951544193e-06,
                3.7266397280960194e-06,
                2.4300231958282535e-05,
                1.9947301968382903e-06,
                1.6701421834059987e-05,
                5.422220255507965e-06,
                1.2098653948994866e-06
            ],
            [
                6.144174600325954e-06,
                6.144173135628569e-06,
                0.00037998454475460003,
                NaN,
                2.5612812941789413e-06,
                5.422219612623952e-06,
                7.889260701697028e-06,
                4.785093352595421e-06,
                0.04742587469223235,
                1.0129989765595064e-05
            ],
            [
                0.00033535005799371583,
                4.785095064148803e-06,
                0.02033235371367809,
                2.5612831263510383e-06,
                3.120190382227939e-05,
                0.6791787121629466,
                0.04208772566276723,
                0.985936373692828,
                4.006370648788271e-05,
                6.144177529364136e-06
            ],
            [
                NaN,
                7.889263522779056e-06,
                1.3007123805078022e-05,
                6.144174596313726e-06,
                4.22283344189467e-06,
                2.4300232030064617e-05,
                1.1478765381674627e-05,
                4.539788991813875e-05,
                1.8925152744771773e-05,
                5.829127911529036e-05
            ],
            [
                6.605216019559409e-05,
                5.82912652667256e-05,
                1.8925143696838414e-05,
                0.0011695103100681017,
                3.5356254894393866e-05,
                4.539788983688541e-05,
                9.610238038856615e-05,
                2.144495096387783e-05,
                0.060086649332446,
                7.889263523869684e-06
            ],
            [
                0.9988304899200264,
                0.9959298626446339,
                0.9999546021456537,
                0.00012339453052117807,
                0.00017952802340487781,
                9.610242556891941e-05,
                0.32082130731838393,
                5.829125829918625e-05,
                0.9992903295620972,
                0.9998415638266416
            ],
            [
                3.7266410589163644e-06,
                9.610243738349442e-05,
                4.222834951722786e-06,
                0.8933094124452287,
                6.962253756890615e-06,
                1.6701415860173268e-05,
                1.0129990973871981e-05,
                2.2603251058292572e-06,
                3.535623795375786e-05,
                1.0129990976156825e-05
            ],
            [
                1.0677028699489821e-06,
                3.2887478877249985e-06,
                7.88926070097951e-06,
                8.939700562988356e-06,
                1.3007125356479674e-05,
                1.9947292455918548e-06,
                4.785096775580942e-06,
                8.9396941718352e-06,
                1.9947292455918548e-06,
                1.1478772218380856e-05
            ],
            [
                2.5612831259923004e-06,
                4.785093922654737e-06,
                0.9875683467456855,
                8.93969523264201e-06,
                1.1478766745733287e-05,
                6.144176064364297e-06,
                6.962253757295868e-06,
                1.994729958830706e-06,
                3.2887494564079503e-06,
                2.1444945840269323e-05
            ],
            [
                1.4738980164521487e-05,
                2.7535694358938284e-05,
                1.5534977535212112e-06,
                1.5534984949356236e-06,
                4.22283344293164e-06,
                4.222833944970936e-06,
                1.1478770844842243e-05,
                1.1478772221888615e-05,
                1.4738976647202596e-05,
                6.144176790655836e-06
            ],
            [
                7.338210674670325e-07,
                4.0063692129517645e-05,
                0.0035936021537350767,
                2.56128159807175e-06,
                1.0129995805359584e-05,
                1.760343632307057e-06,
                6.962257907880012e-06,
                2.1444940727740105e-05,
                2.2603234886501675e-06,
                0.9991959142155196
            ],
            [
                1.3007126896099073e-05,
                1.012999215661038e-05,
                4.006368730943852e-05,
                2.144494838924002e-05,
                3.5356267498715946e-05,
                4.78509563374701e-06,
                4.006371117314994e-05,
                0.9998415637282702,
                1.473898722495269e-05,
                2.902311289848246e-06
            ],
            [
                0.00020342692240195656,
                5.8291272369553704e-05,
                8.481101071663458e-05,
                1.4738978453743973e-05,
                1.8925155002710973e-05,
                2.144495607336692e-05,
                0.952574127663914,
                0.00013982214005220497,
                2.7535684514885004e-05,
                0.4073334000459302
            ],
            [
                3.5356254877415924e-05,
                2.902311639073834e-06,
                2.2603251057881422e-06,
                3.7266383943816487e-06,
                1.0677033790621648e-06,
                9.422445938642879e-07,
                1.3709572067181944e-06,
                NaN,
                6.475947209638476e-07,
                4.006367760515421e-05
            ],
            [
                8.93969310418261e-06,
                4.0063711205213854e-05,
                1.8925150485318196e-05,
                4.785096205173126e-06,
                5.422218967797024e-06,
                NaN,
                1.8925145964139856e-05,
                1.3007131560621253e-05,
                6.962253756232077e-06,
                0.042087728366189174
            ],
            [
                6.1441738684354385e-06,
                3.288749849060371e-06,
                5.4222176759932836e-06,
                NaN,
                4.7850944945245504e-06,
                6.962254588585202e-06,
                NaN,
                8.939700549589229e-06,
                6.962259567217739e-06,
                8.315281267142941e-07
            ],
            [
                1.1478764004044448e-05,
                2.753569075717155e-05,
                1.0129987355785634e-05,
                NaN,
                1.3007128443762892e-05,
                NaN,
                6.962253759670401e-06,
                2.902313022802209e-06,
                7.889260692082281e-06,
                4.006370170554982e-05
            ],
            [
                0.9996200155205239,
                0.9975273772844114,
                0.43782349911420193,
                0.24508500761839527,
                0.8354835330070839,
                0.5,
                0.9902915251570972,
                0.02033235308294522,
                0.9996646498140179,
                1.1478770731508191e-05
            ],
            [
                NaN,
                0.00015843623299818262,
                2.561283431627768e-06,
                0.00033535023718528334,
                1.6701429769656252e-05,
                7.484626239585179e-05,
                5.1442207239605705e-05,
                3.726640614816945e-06,
                1.6701429784906616e-05,
                6.962253758017727e-06
            ],
            [
                1.147876940006287e-05,
                0.6224593312018546,
                NaN,
                NaN,
                1.0129995736298305e-05,
                0.004609573262633005,
                0.9902915226768554,
                NaN,
                2.9023123310290063e-06,
                7.88926352407059e-06
            ],
            [
                3.120190391853445e-05,
                5.422218319715415e-06,
                1.4738987231065292e-05,
                4.22283294025486e-06,
                1.4738985454496043e-05,
                3.2887506327561457e-06,
                2.4300249326547287e-05,
                6.475946437587058e-07,
                1.3007126901209531e-05,
                6.144175332283612e-06
            ],
            [
                5.4222208958868744e-06,
                6.1441724013465395e-06,
                6.144173866177863e-06,
                2.260323758746637e-06,
                9.42244592515424e-07,
                1.7603432131631714e-06,
                3.288747887916428e-06,
                1.994729482634204e-06,
                4.222833945554712e-06,
                0.004609572632334463
            ],
            [
                0.9465966690702636,
                7.88926257376021e-06,
                NaN,
                NaN,
                9.422447061782138e-07,
                7.889262572468676e-06,
                1.1478773587743728e-05,
                NaN,
                NaN,
                1.0677029971065997e-06
            ],
            [
                2.561281904871769e-06,
                2.1444948365991674e-05,
                1.0129989769464556e-05,
                5.829126464329852e-05,
                2.1444948393530826e-05,
                3.288750633488963e-06,
                6.962257904410026e-06,
                4.0063682500145096e-05,
                6.962258737472841e-06,
                4.785092781953005e-06
            ],
            [
                8.481101029952298e-05,
                1.892514371095225e-05,
                0.9924227570513268,
                3.53562420932866e-05,
                1.1478765382092217e-05,
                3.2887482797610674e-06,
                1.8925148220012804e-05,
                0.9984988174822135,
                2.7535681222849733e-05,
                0.00048785704137934615
            ],
            [
                2.9023112925037123e-06,
                8.939697367037201e-06,
                5.144223778919782e-05,
                3.5356263160336484e-05,
                4.006370165453905e-05,
                NaN,
                6.605214424049113e-05,
                1.0129990974903845e-05,
                0.32082129433083023,
                NaN
            ],
            [
                1.670142581883963e-05,
                8.939697365736316e-06,
                0.0008040860791083398,
                5.144223194306502e-05,
                6.962255418658875e-06,
                4.539786852010991e-05,
                8.48110609144254e-05,
                1.473898723610551e-05,
                2.7535691044062732e-05,
                2.1444940689981053e-05
            ],
            [
                2.7535694299837088e-05,
                1.147876948232818e-05,
                3.288747888089911e-06,
                5.144223177089979e-05,
                1.473898899256772e-05,
                6.962256229875678e-06,
                8.939698431389304e-06,
                1.1478769488257963e-05,
                0.3486451217982255,
                2.4300234924597754e-05
            ],
            [
                1.1478765382927399e-05,
                0.00015843619386997132,
                NaN,
                0.0017007221366970554,
                2.7535691080725503e-05,
                0.962673113726775,
                0.0002034270191588291,
                0.0001233945289053134,
                NaN,
                1.1478772222807315e-05
            ],
            [
                8.939695219275413e-06,
                2.4300231997886442e-05,
                NaN,
                NaN,
                0.40733340004593027,
                0.0009110513203914834,
                NaN,
                6.9622587329010695e-06,
                1.8925154930764804e-05,
                4.539785233683338e-05
            ],
            [
                2.2603234888763e-06,
                0.9626731122542814,
                5.715004468299721e-07,
                0.9890130579664848,
                1.0677029972134173e-06,
                1.3007130007515371e-05,
                2.260324028255194e-06,
                1.1478768116055965e-05,
                1.2098658271514805e-06,
                1.370957370146321e-06
            ],
            [
                2.430024336739321e-05,
                3.7266401659047057e-06,
                5.144219459969108e-05,
                3.120191117943573e-05,
                2.4300231894987002e-05,
                NaN,
                1.4738988823398708e-05,
                0.007577242241331297,
                0.7310585786300049,
                3.535624218306386e-05
            ],
            [
                0.00017952796472352542,
                0.0005527786157635272,
                1.670142581075876e-05,
                0.0031726828638394596,
                0.992422757447018,
                0.5,
                0.29421498454004374,
                4.006368730943852e-05,
                0.00010889689537322853,
                3.53562675293277e-05
            ],
            [
                1.5534971982250105e-06,
                4.4508505189581243e-07,
                0.18242552602881165,
                NaN,
                2.9023123304218908e-06,
                6.1441745989959955e-06,
                1.892514141783309e-05,
                1.209866260246509e-06,
                1.5534984946134832e-06,
                4.785095062930243e-06
            ],
            [
                0.00020342698348320458,
                6.962254570564075e-06,
                2.1444956025465942e-05,
                4.785096204972935e-06,
                1.2098652507439992e-06,
                9.610238461854262e-05,
                3.2887506328937356e-06,
                1.147876536781063e-05,
                1.1478773570789552e-05,
                1.3007130000322877e-05
            ],
            [
                1.670142578341747e-05,
                1.8925141444270707e-05,
                2.4300246501849726e-05,
                3.1201903840894755e-05,
                0.00010889695868930055,
                1.6701427795007302e-05,
                0.9933071484318007,
                5.422220905315815e-06,
                2.1444953514565465e-05,
                5.422220260202708e-06
            ],
            [
                4.450849458011859e-07,
                NaN,
                1.5534983098151152e-06,
                1.067703251641342e-06,
                9.422444813172807e-07,
                1.067702615136605e-06,
                6.475947209402883e-07,
                1.0129993388178253e-05,
                7.338207180287456e-07,
                5.422220907554695e-06
            ],
            [
                0.9959298626200951,
                0.9999810748525918,
                0.00023050671389769165,
                1.892515498164348e-05,
                0.00010889690862903777,
                0.9740426442150328,
                NaN,
                0.9924227596565859,
                6.605214457784486e-05,
                3.1201907583945445e-05
            ],
            [
                0.999876605389068,
                5.1442213526628236e-05,
                4.006370160848361e-05,
                4.539785232659414e-05,
                0.7772998611746912,
                0.9988304896381198,
                0.0004878571373712147,
                0.012431649115226305,
                0.320821300824607,
                0.9968273175455734
            ],
            [
                1.9947304346826253e-06,
                0.00023050670360232113,
                3.7266410591603975e-06,
                4.785095061084996e-06,
                1.0129993360133632e-05,
                NaN,
                0.053403333001242094,
                NaN,
                1.209865250613056e-06,
                0.0002305068231627894
            ],
            [
                4.785095634756674e-06,
                NaN,
                8.315279283568503e-07,
                0.16451646699291614,
                1.994729721004569e-06,
                1.147876538330323e-05,
                7.88926164035468e-06,
                6.605214372436877e-05,
                7.484626223140146e-05,
                8.939699491123385e-06
            ],
            [
                4.222834450029027e-06,
                7.889261642578988e-06,
                4.0063677828144015e-05,
                1.553497383879461e-06,
                1.7603434229576435e-06,
                2.260325375391425e-06,
                8.939696301611998e-06,
                2.260324297155282e-06,
                1.9947297204167715e-06,
                1.3709568797522746e-06
            ],
            [
                5.71500651364594e-07,
                0.00023050671389769165,
                0.004070137940519512,
                1.3007130012673148e-05,
                1.4738978433261398e-05,
                0.06754669395523943,
                0.00010889690862903777,
                5.043475885012763e-07,
                2.561281599269096e-06,
                1.0677029971978802e-06
            ],
            [
                5.422221553368145e-06,
                8.939698426706115e-06,
                4.785093923420688e-06,
                0.00029595712810000365,
                6.144175332115971e-06,
                0.009708474833948886,
                0.022977369742764476,
                7.484625363315528e-05,
                2.753568773760199e-05,
                7.889264463446097e-06
            ],
            [
                NaN,
                2.4300231996295212e-05,
                4.539786317192547e-05,
                6.9622554187981796e-06,
                4.222832436272325e-06,
                0.00010889694586288107,
                8.93969949678224e-06,
                6.14417679836736e-06,
                3.2887490648622804e-06,
                NaN
            ],
            [
                4.5397863055000004e-05,
                5.14422257009529e-05,
                3.5356246441695886e-05,
                0.9984988179526609,
                0.0001584361711131888,
                1.2098658274331742e-06,
                3.7266383938732464e-06,
                NaN,
                2.4300246522270504e-05,
                4.006369692540368e-05
            ],
            [
                5.422221553910605e-06,
                1.760342793362967e-06,
                2.430025227845516e-05,
                0.00017952804318300018,
                0.00043055701321114136,
                1.6701419835108622e-05,
                0.00043055716506988233,
                6.144173134164498e-06,
                8.93969310367852e-06,
                4.006370639416863e-05
            ],
            [
                8.939696301611998e-06,
                3.5356267506175954e-05,
                0.9902915241721636,
                1.7603436327425345e-06,
                6.962258736497698e-06,
                4.222834953197588e-06,
                NaN,
                4.7850967749455485e-06,
                2.4300246467284693e-05,
                1.0677031245050577e-06
            ],
            [
                0.6513548714339145,
                5.82912922691822e-05,
                3.535625069312567e-05,
                1.300712535865635e-05,
                0.00012339458638522277,
                1.4738978450419574e-05,
                7.889260698138136e-06,
                1.3007126907455643e-05,
                6.144177529855884e-06,
                0.2689414096510108
            ],
            [
                1.3007125358230479e-05,
                2.7535704192176552e-05,
                1.6701421834059987e-05,
                1.300712534701587e-05,
                1.670141983978702e-05,
                1.1478765384054893e-05,
                7.88926070097951e-06,
                2.4300243556219075e-05,
                5.422217670657454e-06,
                6.144172399580713e-06
            ],
            [
                2.90231198483099e-06,
                3.7266410604686857e-06,
                7.484623473770956e-05,
                1.1478769487046951e-05,
                6.962256246035174e-06,
                5.829124266813458e-05,
                3.1201911314056636e-05,
                2.9023126766305067e-06,
                1.5534979396448094e-06,
                1.670142581574095e-05
            ],
            [
                5.1442201347440924e-05,
                0.005911069822152616,
                4.222833442171196e-06,
                5.829125820121915e-05,
                3.726640170066823e-06,
                4.785093922115089e-06,
                1.3007123807727885e-05,
                1.147876948575242e-05,
                5.422218969306048e-06,
                3.5356259098234985e-05
            ],
            [
                3.1201910630282336e-05,
                3.5356250345592426e-05,
                4.539786315904385e-05,
                1.6701417833423363e-05,
                NaN,
                7.484626198853775e-05,
                2.7535687779473676e-05,
                5.1442207296120786e-05,
                2.7535691082027735e-05,
                2.4300237736387333e-05
            ],
            [
                0.00012339463294908592,
                6.144175332596544e-06,
                2.902311637529651e-06,
                1.473898723508674e-05,
                8.481101038837516e-05,
                7.889264457390238e-06,
                0.999841563731585,
                2.9023116336757916e-06,
                1.4738980190151517e-05,
                6.14417459774427e-06
            ],
            [
                1.6701425817016872e-05,
                5.829125833184195e-05,
                2.430025190805223e-05,
                3.7266401719174067e-06,
                1.8925141402548846e-05,
                1.3007123731638893e-05,
                2.2603240280866228e-06,
                6.144175332596544e-06,
                4.2228344501365644e-06,
                0.000139822139856903
            ],
            [
                0.9999546021477249,
                0.8175744695262775,
                NaN,
                0.7981867801399695,
                0.9997965730791963,
                0.999769493376165,
                0.9968273174969741,
                0.9968273171575148,
                0.9980732653348816,
                0.999903897573697
            ],
            [
                1.01299873472359e-05,
                1.4738978447095178e-05,
                3.7266383940901643e-06,
                2.7535704143893865e-05,
                2.753568452349975e-05,
                1.1478766749992709e-05,
                8.939699496489538e-06,
                7.889266345397582e-06,
                8.481103094408114e-05,
                2.260324297607547e-06
            ],
            [
                0.9998601778962292,
                6.605212087322356e-05,
                4.222833943419322e-06,
                0.0004878570733387893,
                2.9023123304852425e-06,
                0.7772998560157665,
                0.9993736657246075,
                1.670141976882121e-05,
                0.014063628476651944,
                0.999860177859901
            ],
            [
                7.889262584666493e-06,
                8.939693096068342e-06,
                4.785094493932679e-06,
                1.994729721396435e-06,
                NaN,
                0.0003799845098435321,
                NaN,
                5.422221549225722e-06,
                2.9023123304852425e-06,
                1.7603430031766016e-06
            ],
            [
                2.260323489266892e-06,
                1.3007125332346968e-05,
                9.610243756248196e-05,
                2.1444958575139983e-05,
                5.422219611144516e-06,
                1.670141586084161e-05,
                1.0129987351621326e-05,
                0.012431652659749253,
                1.067703378938839e-06,
                2.7535697624529836e-05
            ],
            [
                8.939693105662367e-06,
                2.561283431888668e-06,
                3.288749456563487e-06,
                1.892514144530343e-05,
                1.3709576970537545e-06,
                1.0677033790883835e-06,
                0.08509903978628845,
                7.889264461063935e-06,
                1.2098661161239298e-06,
                2.260324027202651e-06
            ],
            [
                7.484620904971269e-05,
                0.017986206145766886,
                8.939697355784541e-06,
                6.962253755548213e-06,
                6.605212018842459e-05,
                3.1201907643310305e-05,
                0.11920292984474948,
                7.88926258417858e-06,
                3.7266383948154845e-06,
                1.012998852776274e-05
            ],
            [
                3.2887506310811342e-06,
                1.892515032331887e-05,
                7.484620829607338e-05,
                1.3709578599993979e-06,
                4.222833443553821e-06,
                5.715003106860134e-07,
                7.338212429006964e-07,
                0.009708475881559975,
                5.4222196128014845e-06,
                3.288749065029781e-06
            ],
            [
                6.962255405994694e-06,
                1.670142780910326e-05,
                2.1444945822247952e-05,
                7.889262581595514e-06,
                6.962257908196617e-06,
                4.006368736948546e-05,
                0.0005527785322809396,
                6.96225541655662e-06,
                1.0129987351952995e-05,
                6.605216810947268e-05
            ],
            [
                1.3007133095130927e-05,
                1.8925152537195053e-05,
                6.144176065012512e-06,
                1.6701421837158667e-05,
                NaN,
                NaN,
                1.67014178554179e-05,
                1.670142581373592e-05,
                NaN,
                1.7603434211805112e-06
            ],
            [
                4.539785757337586e-05,
                1.3007125357378736e-05,
                4.222833442816421e-06,
                1.892514141783309e-05,
                6.96225870876313e-06,
                4.006368257301759e-05,
                7.484621548723039e-05,
                2.1444958573423664e-05,
                3.535623795375786e-05,
                4.006369669192012e-05
            ],
            [
                6.96225541098438e-06,
                9.610241364527538e-05,
                6.475948753276293e-07,
                8.481103056645933e-05,
                1.994730434356071e-06,
                1.5534973837805584e-06,
                3.2887502400378273e-06,
                1.892515725665725e-05,
                5.144220718496198e-05,
                1.3007131559390956e-05
            ],
            [
                8.315278293067121e-07,
                6.962253757295868e-06,
                1.553497754391555e-06,
                2.7535690996781786e-05,
                0.7310585727705127,
                0.9525741254760639,
                0.0001584362895628308,
                0.7310585727705127,
                0.37754066879814546,
                6.144173863897934e-06
            ],
            [
                2.9023130224326608e-06,
                2.1444940727740105e-05,
                3.120191874363308e-05,
                1.9947297212331575e-06,
                1.0677031245429291e-06,
                2.561283431888668e-06,
                8.939694166989405e-06,
                3.28874906467085e-06,
                4.785094493305991e-06,
                8.3152822584917e-07
            ],
            [
                1.5534981247680996e-06,
                1.3709568798220997e-06,
                5.4222202614355715e-06,
                4.222832940646604e-06,
                4.785092782501357e-06,
                3.726640171768275e-06,
                2.2603237580312362e-06,
                8.939700562402957e-06,
                7.889260703619978e-06,
                5.422218965873757e-06
            ],
            [
                1.3007134633189714e-05,
                2.5612825153504304e-06,
                1.6701425819447213e-05,
                3.7266397207885882e-06,
                0.5,
                0.7549149868676283,
                0.9669140204195272,
                2.4300231968183514e-05,
                2.1444950930643612e-05,
                5.8291279168302876e-05
            ],
            [
                1.0677031244603883e-06,
                1.0129988559160908e-05,
                1.3709573696849766e-06,
                1.9947304344830644e-06,
                2.7535700806578716e-05,
                0.00023050668270305571,
                7.338210679622478e-07,
                1.3709572062593438e-06,
                1.7603427927353679e-06,
                1.1478765380839446e-05
            ],
            [
                0.9993736656940024,
                1.0129995779857767e-05,
                8.939694169591174e-06,
                6.962255416961874e-06,
                0.0001233945578867468,
                3.726640171842841e-06,
                0.0001233945718962973,
                2.2603237587774727e-06,
                0.7981867777396212,
                0.9525741293468757
            ],
            [
                1.1478772225271098e-05,
                1.1478773593548236e-05,
                NaN,
                5.829128626561938e-05,
                0.00012339461809748284,
                2.144494838463716e-05,
                2.7535687762043832e-05,
                1.4738976697229395e-05,
                5.1442231703530785e-05,
                9.610238008932154e-05
            ],
            [
                1.8925141462377723e-05,
                4.0063711256516126e-05,
                5.1442218751467176e-05,
                1.6701417852987564e-05,
                4.785093919486482e-06,
                2.7535700909955743e-05,
                3.120190389560577e-05,
                2.1444953520182517e-05,
                4.006370170554982e-05,
                4.0063682424940686e-05
            ],
            [
                1.892514145845339e-05,
                1.994729957785731e-06,
                NaN,
                2.1444958599324522e-05,
                1.1478772206270732e-05,
                2.902313368820854e-06,
                3.726639282234298e-06,
                1.1478765364971017e-05,
                6.962259568230874e-06,
                2.430023492663099e-05
            ],
            [
                2.7535703388400046e-05,
                6.605214360518968e-05,
                1.8925154989561007e-05,
                7.88926445282682e-06,
                NaN,
                3.5356237965848203e-05,
                6.962256244008905e-06,
                7.484626243723662e-05,
                1.0129994591443684e-05,
                8.939694169591174e-06
            ],
            [
                0.13296422645481662,
                5.144220122131125e-05,
                1.3007126909159127e-05,
                1.1478772225981004e-05,
                NaN,
                5.422217671880454e-06,
                2.1444953469238977e-05,
                1.3007134652969082e-05,
                1.3007134660350856e-05,
                3.53562590400984e-05
            ],
            [
                1.4738985483128763e-05,
                9.610244780112891e-05,
                2.9023116387069255e-06,
                5.422218315375735e-06,
                1.0129990968896918e-05,
                1.1478765386623071e-05,
                6.1441760651689774e-06,
                5.1442231677331724e-05,
                1.4738981951170529e-05,
                5.422217023256539e-06
            ],
            [
                6.144175332596544e-06,
                2.9023116380522973e-06,
                2.561282515406337e-06,
                7.889262582341733e-06,
                1.147876401460948e-05,
                1.4738978443234588e-05,
                1.9947304345193483e-06,
                6.9622545872301346e-06,
                2.561283431478682e-06,
                6.475950297574138e-07
            ],
            [
                0.2942149597859341,
                1.0129995806317745e-05,
                4.0063711151871155e-05,
                3.2887502409830123e-06,
                8.93969736547614e-06,
                1.1478766752748805e-05,
                NaN,
                1.6701419836749094e-05,
                1.0677031242953065e-06,
                0.003593602027847295
            ],
            [
                0.9626731150654055,
                NaN,
                0.9998911031056156,
                0.9890130559627316,
                0.9989677688201534,
                NaN,
                0.8933094074745443,
                NaN,
                0.9995121427746977,
                0.13296423847995262
            ],
            [
                4.006368733421517e-05,
                3.1201911281593244e-05,
                1.0129994588458645e-05,
                1.147876538330323e-05,
                5.14422010147131e-05,
                1.1478768117893363e-05,
                1.1478765367142486e-05,
                4.006368261266023e-05,
                3.535624215888317e-05,
                0.9968273174203932
            ],
            [
                1.0677033786203283e-06,
                2.902313021213151e-06,
                0.99477987495208,
                7.484622665024243e-05,
                2.9023126767836054e-06,
                3.2887478854876635e-06,
                3.2887506306863106e-06,
                2.260324296916815e-06,
                1.3007126909159127e-05,
                5.422218968931258e-06
            ],
            [
                2.1444950959196957e-05,
                2.4300237809495462e-05,
                3.120190389560577e-05,
                0.00015843615919308046,
                0.00013982210534135435,
                5.8291244568526206e-05,
                3.120191134118513e-05,
                1.3007134663521234e-05,
                8.481101088878567e-05,
                4.0063692144966625e-05
            ],
            [
                6.962255413517216e-06,
                4.450848925381227e-07,
                1.3709568797522746e-06,
                4.222831931882744e-06,
                7.889262580791891e-06,
                4.539785230545508e-05,
                0.014063624047297283,
                0.007577240427454735,
                6.475947202423429e-07,
                4.4508494553644535e-07
            ],
            [
                1.4738981945326025e-05,
                2.9023119850210436e-06,
                8.481106015547928e-05,
                3.2887478884069663e-06,
                3.535623779786957e-05,
                3.2887506330851655e-06,
                1.89251413196559e-05,
                6.962257909121104e-06,
                NaN,
                1.3007131546094302e-05
            ],
            [
                NaN,
                2.7535691054881254e-05,
                6.144173135025058e-06,
                3.5356246419315886e-05,
                2.1444955991763626e-05,
                4.006370407769647e-05,
                1.473898020682712e-05,
                2.4300234854672095e-05,
                7.889261644057078e-06,
                4.78509563128378e-06
            ]
        ]
    },
    {
        "q_id": "8375_mmlu_math",
        "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": [
            [
                0.9999832985701977,
                0.999995214904935,
                0.9999987901337396,
                0.9999910602994339,
                0.9999980052705164,
                0.9999599363078321,
                0.9999982396569966,
                0.9999885212318756,
                0.9999852610180304,
                0.9999977396748939
            ],
            [
                0.999999554914789,
                0.9999810748495092,
                0.9999687980960907,
                0.9999980052702785,
                0.9999957771650474,
                0.999995214904935,
                0.9999646437619594,
                0.9999785550515954,
                0.9999938558239347,
                0.9999885212318752
            ],
            [
                1.5534981249023245e-06,
                1.2098652507285942e-06,
                7.338211554725124e-07,
                1.3709570433075437e-06,
                7.338211554725124e-07,
                9.422444815495185e-07,
                2.9023109467598367e-06,
                1.2098662603862553e-06,
                1.5534971989258068e-06,
                8.315281267800897e-07
            ],
            [
                0.9999996072137529,
                0.9999995549150011,
                0.9999994284992805,
                0.9999991684722698,
                0.9999984465015047,
                0.999995777168066,
                0.99999893229713,
                0.9999992661788446,
                0.999997438717484,
                0.9999962733607163
            ],
            [
                0.999999653367379,
                0.9999989322972572,
                0.9999982396569967,
                0.9999990577557432,
                0.9999980052695655,
                0.9999980052695653,
                0.9999980052705167,
                0.9999938558224716,
                0.9999996072136125,
                0.9999980052698035
            ],
            [
                0.9999986290432834,
                0.999998005270992,
                0.9999982396559474,
                0.999998932296621,
                0.9999980052700408,
                0.9999952149060769,
                0.9999992661786695,
                0.9999996072137529,
                0.999997739675433,
                0.9999974387177893
            ],
            [
                0.9999991684720715,
                0.9999980052698029,
                0.9999869928761911,
                0.9999962733620491,
                0.9999962733611605,
                0.9999994284994849,
                0.9999986290429568,
                0.9999986290427931,
                0.9999945777823237,
                0.9999987901344607
            ],
            [
                0.9999989322966208,
                0.9999967112505427,
                0.9999994956526519,
                0.9999987901338839,
                0.9999957771665555,
                0.999994577780384,
                0.9999977396765105,
                0.999993855826131,
                0.9999991684720715,
                0.9999984465026159
            ],
            [
                0.9999974387171788,
                0.9999982396569966,
                0.9999995549151073,
                0.9999980052695652,
                0.9999974387180947,
                0.9999945777790915,
                0.9999984465016899,
                0.9999957771670593,
                0.9999977396746244,
                0.9999989322968754
            ],
            [
                0.9999910603026332,
                0.9999938558239336,
                0.9999962733589398,
                0.9999938558261308,
                0.9999898700114378,
                0.9999987901340281,
                0.9999546021206072,
                0.9999977396757023,
                0.9999982396574163,
                0.9999921107345942
            ],
            [
                8.3152792852928e-07,
                6.475951069631906e-07,
                4.450851580497677e-07,
                2.2603245671490605e-06,
                4.4508505193386385e-07,
                2.260325375391425e-06,
                6.475949525722606e-07,
                3.4663274507098256e-07,
                4.4508489275752546e-07,
                2.3823699518764604e-07
            ],
            [
                0.9999982396565769,
                0.9999599363126164,
                0.9999756997534859,
                0.9999885212305093,
                0.9999980052707541,
                0.9999945777829702,
                0.9999852610197937,
                0.9999921107336541,
                0.999991060302631,
                0.9999921107383646
            ],
            [
                0.9999938558224694,
                0.9999810748517651,
                0.9999910603004999,
                0.999996273361605,
                0.9999898700114681,
                0.9999945777790923,
                0.9999967112509347,
                0.9999938558239339,
                0.999988521235985,
                0.999993855823934
            ],
            [
                0.9999989322968754,
                0.9999957771680662,
                0.9999970976873231,
                0.9999984465024306,
                0.999996273360716,
                0.9999957771670596,
                0.9999982396563671,
                0.9999485577865156,
                0.9999952149037947,
                0.9999967112521111
            ],
            [
                0.9999991684719723,
                0.9999993524050473,
                0.9999990577551814,
                0.9999974387174843,
                0.9999994956527722,
                0.9999986290429567,
                0.9999991684720715,
                0.9999996533672136,
                0.9999957771655507,
                0.9999992661788446
            ],
            [
                0.9999974387177893,
                0.999989870011436,
                0.9999921107355343,
                0.9999984465018752,
                0.9999832985841337,
                0.9999991684715759,
                0.9999921107336528,
                0.9999952149043648,
                0.9999991684722698,
                0.9999898700114386
            ],
            [
                0.9999251537371462,
                0.9999952149055061,
                0.9999957771650463,
                0.9999930377437518,
                0.999997097689053,
                0.9999921107392962,
                0.9999485577863694,
                0.999997097687323,
                0.9999938558224688,
                0.9999980052693274
            ],
            [
                0.9999986290424664,
                0.9999998362623528,
                0.9999986290431201,
                0.9999982396574163,
                0.9999991684720715,
                0.9999982396561573,
                0.9999991684718732,
                0.9999986290429567,
                0.9999986290426298,
                0.9999996940977001
            ],
            [
                0.9999987901343166,
                0.9999938558268644,
                0.9999785550413712,
                0.9999967112501508,
                0.9999810748517663,
                0.9999986290421395,
                0.9999962733607164,
                0.99995993629351,
                0.9999945777829703,
                0.9999977396746245
            ],
            [
                0.9999945777784449,
                0.9999756997592866,
                0.9999910603004993,
                0.9999869928653375,
                0.9999756997534868,
                0.9999151889385092,
                0.9999810748540204,
                0.9999038975736549,
                0.999995777166556,
                0.9999485578047674
            ],
            [
                0.9999982396569966,
                0.9999989322968754,
                0.9999967112521109,
                0.9999994284994167,
                0.9999995549150011,
                0.9999970976890528,
                0.9999974387165681,
                0.9999910603036978,
                0.9999967112497585,
                0.9999970976890528
            ],
            [
                0.9999599362891609,
                0.9999785550541804,
                0.8354835411997898,
                0.9999151889487705,
                0.904650538956921,
                0.9999910603037047,
                0.9998766054566004,
                0.9992903296321063,
                0.9840936058390232,
                0.9999977396762443
            ],
            [
                0.9999989322972573,
                0.9999990577550691,
                0.9999970976890534,
                0.9999977396746245,
                0.9999986290424665,
                0.9999990577555185,
                0.999999428499553,
                0.9999994284994848,
                0.9999995549147889,
                0.9999987901344608
            ],
            [
                6.144177531532303e-06,
                6.475947209826952e-07,
                5.422221555192784e-06,
                6.962255419570695e-06,
                4.785093353687772e-06,
                2.9023119847359636e-06,
                8.939695237959376e-06,
                4.450852641596248e-07,
                6.144176065940129e-06,
                5.422218323231539e-06
            ],
            [
                0.9999957771670592,
                0.9999962733593832,
                0.9999885212277729,
                0.9999974387171787,
                0.9999962733616051,
                0.9999980052695652,
                0.9999977396746244,
                0.999993037742921,
                0.999999057755743,
                0.999989870011436
            ],
            [
                0.9999984465016899,
                0.9999952149055056,
                0.9999938558239334,
                0.9999921107355347,
                0.9999974387184,
                0.999996273360272,
                0.999983298580152,
                0.9999980052707541,
                0.9999980052693276,
                0.9999977396751634
            ],
            [
                0.9999962733611603,
                0.9999999123575151,
                0.9999982396569966,
                0.9999987901337396,
                0.9999957771675625,
                0.9999993524054334,
                0.9999962733602719,
                0.9999957771645422,
                0.9999898700041931,
                0.9999989322966208
            ],
            [
                0.9999957771670603,
                0.9999952149060765,
                0.9999984465018752,
                0.9999974387177893,
                0.9999994284994167,
                0.9999974387184001,
                0.9999993524049702,
                0.9999974387177895,
                0.9999952149049361,
                0.9999957771655534
            ],
            [
                0.999993855826131,
                0.999997097687669,
                0.999997438717484,
                0.9999962733620494,
                0.9999987901337398,
                0.9999974387168733,
                0.9999957771675625,
                0.9999970976873229,
                0.9999986290427932,
                0.9999991684717742
            ],
            [
                0.9999989322966208,
                0.9999952149066466,
                0.9999977396748939,
                0.9999952149060769,
                0.9999967112517189,
                0.9999993524053562,
                0.999992110733653,
                0.999992110740236,
                0.9999957771680664,
                0.9999967112501507
            ],
            [
                0.9999997300420937,
                0.9999993524053562,
                0.999999266178932,
                0.9999970976866313,
                0.9999990577556307,
                0.9999977396762412,
                0.9999986290421394,
                0.999999352404893,
                0.9999996533674201,
                0.999999352405279
            ],
            [
                0.9999938558246667,
                0.9999974387180948,
                0.9999962733607162,
                0.9999982396567868,
                0.9999869928653361,
                0.999997438717484,
                0.9999945777829694,
                0.9999910603005017,
                0.9999970976876689,
                0.9999993524052789
            ],
            [
                0.9999546021422271,
                0.9999982396567867,
                0.9999921107374152,
                0.9999980052693275,
                0.9999990577556308,
                0.9999962733598277,
                0.9999967112509347,
                0.9999991684718733,
                0.9999921107392983,
                0.9999957771675624
            ],
            [
                1.2098659719441482e-06,
                1.067703251864202e-06,
                7.338213304016384e-07,
                7.338208930315157e-07,
                1.7603430034151537e-06,
                1.370957370146321e-06,
                5.715005832853093e-07,
                5.043474683156057e-07,
                1.0129988541987731e-05,
                6.475947209826952e-07
            ],
            [
                0.999954602126097,
                0.99999893229713,
                0.999978555054146,
                0.9999945777790913,
                0.9999974387168736,
                0.9999898700078163,
                0.9999945777784456,
                0.9999756997592744,
                0.999995777164542,
                0.9999974387165682
            ],
            [
                0.999996711250935,
                0.9999982396572065,
                0.9999977396757024,
                0.99999893229713,
                0.9999984465015047,
                0.9999977396746245,
                0.9999992661787571,
                0.9968273167805015,
                0.9999724643158778,
                0.9999962733616045
            ],
            [
                1.2098655392871682e-06,
                5.4222196154940574e-06,
                1.2098652508056196e-06,
                1.5534973841592143e-06,
                1.7603427935678977e-06,
                4.785096775920397e-06,
                1.7603425836678333e-06,
                2.5612834318257725e-06,
                2.9023126769050284e-06,
                3.7266406161591266e-06
            ],
            [
                0.9999980052698033,
                0.9999994284997574,
                0.9999991684720716,
                0.9999996533674201,
                0.999999352404893,
                0.9999997897565587,
                0.9999967112513272,
                0.9999980052709921,
                0.9999998555020134,
                0.9999989322975118
            ],
            [
                0.9999962733598275,
                0.9999910602994355,
                0.9999977396757023,
                0.9999962733607161,
                0.9999970976883613,
                0.9999952149060761,
                0.9999957771680659,
                0.9999977396754327,
                0.9999938558275958,
                0.9999962733616046
            ],
            [
                0.9999952149055065,
                0.9999910603068946,
                0.9999938558224688,
                0.9999952149037954,
                0.99999862904312,
                0.9999952149055057,
                0.9999967112513268,
                0.9999980052702786,
                0.9999980052702786,
                0.99999862904312
            ],
            [
                0.9999930377462416,
                0.9999599363221586,
                0.9998911030983648,
                0.9999810748585312,
                0.9999724642958017,
                0.9997388096011155,
                0.999948557774109,
                0.9998911030522595,
                0.7772998560157665,
                0.9998766053816152
            ],
            [
                0.9999982396572065,
                0.9999986290429567,
                0.9999952149049353,
                0.9999995549151072,
                0.9999957771680673,
                0.9999984465020603,
                0.9999982396572065,
                0.9999984465016899,
                0.9999991684719723,
                0.999996711249367
            ],
            [
                0.9999982396572068,
                0.9999991684715759,
                0.9999990577549569,
                0.9999957771645422,
                0.9999967112509347,
                0.9999970976883619,
                0.9999962733611603,
                0.9999970976890531,
                0.9999910603068967,
                0.9999993524054335
            ],
            [
                0.9999980052698033,
                0.9999984465016899,
                0.9999987901344607,
                0.9999991684718732,
                0.9999991684718732,
                0.9999990577551815,
                0.9999996072136125,
                0.9999984465022456,
                0.9999982396574164,
                0.999997438717484
            ],
            [
                0.9999957771645422,
                0.999997097689053,
                0.999996711251327,
                0.9999984465020606,
                0.9999980052707541,
                0.999997097688707,
                0.9999989322966208,
                0.9999990577554061,
                0.9999945777790918,
                0.9999930377412606
            ],
            [
                0.999996711251327,
                0.9999982396574163,
                0.9999992661792819,
                0.9999993524049703,
                0.9999977396757023,
                0.9999251537460276,
                0.999997097687323,
                0.9999994284996891,
                0.9999982396561573,
                0.9999986290429568
            ],
            [
                0.9999898700053986,
                0.9999885212332466,
                0.9999977396757023,
                0.9999977396765105,
                0.9999869928715408,
                0.9998415637463428,
                0.9999970976873234,
                0.999988521233246,
                0.9999986290432835,
                0.999995214903795
            ],
            [
                0.9999970976869771,
                0.9999990577555185,
                0.9999980052695653,
                0.9999977396759716,
                0.9999967112517193,
                0.9999994956525918,
                0.9999930377420919,
                0.9999977396754328,
                0.9999957771670591,
                0.9999987901341724
            ],
            [
                0.9999982396569966,
                0.9999982396561572,
                0.9999970976876692,
                0.9999982396559474,
                0.999996273360272,
                0.999996273361605,
                0.9999962733616053,
                0.999997739674894,
                0.9999982396565769,
                0.9999980052698031
            ],
            [
                0.9999994956524716,
                0.999998790134028,
                0.9999957771655494,
                0.9999992661792819,
                0.9999980052700408,
                0.9999982396561572,
                0.9999957771680659,
                0.9999984465024307,
                0.9999986290432834,
                0.9999989322972572
            ],
            [
                0.9999974387184001,
                0.9999982396572065,
                0.9999921107383561,
                0.9999990577554061,
                0.99999844650169,
                0.9999921107345944,
                0.9999967112509357,
                0.9999982396559479,
                0.9999977396759717,
                0.9999974387187053
            ],
            [
                0.9999994284996891,
                0.9999957771665557,
                0.9999977396765105,
                0.9999993524049703,
                0.9999986290427931,
                0.9999996533673788,
                0.9999982396574169,
                0.9999994284994168,
                0.9999977396746246,
                0.9999996072136592
            ],
            [
                0.9999982396569966,
                0.9999992661791973,
                0.9999957771665567,
                0.9999957771650564,
                0.999998629042303,
                0.9999990577554062,
                0.9999756997535103,
                0.9999952149072224,
                0.9999977396762413,
                0.9999986290424664
            ],
            [
                0.9999984465020604,
                0.9999952149049356,
                0.9999996072137529,
                0.999998629042303,
                0.9999987901340281,
                0.9999952149055058,
                0.999999495652712,
                0.9999980052709919,
                0.9999986290421394,
                0.9999945777810314
            ],
            [
                0.9999986290431201,
                0.9999986290427932,
                0.9999945777790918,
                0.9999957771665574,
                0.9999921107355365,
                0.9999957771670593,
                0.9999986290427932,
                0.9999967112497586,
                0.999988521234612,
                0.9999989322975119
            ],
            [
                0.9999974387168737,
                0.9999991684720715,
                0.999988521231884,
                0.999999352405279,
                0.9999987901343165,
                0.9999998555019618,
                0.9999977396748938,
                0.9999984465016899,
                0.9999993524053562,
                0.999999266178757
            ],
            [
                0.9999869928715373,
                0.9999984465016899,
                0.9999952149049355,
                0.9999974387168733,
                0.9999417087067621,
                0.9999974387187055,
                0.9999996940976272,
                0.9999980052695655,
                0.9999974387184,
                0.999998005270041
            ],
            [
                0.9999885212291401,
                0.9999974387168734,
                0.9999977396762415,
                0.9999980052693274,
                0.9999852610127639,
                0.9999910603047636,
                0.999989870007814,
                0.9999952149032242,
                0.9999938558232021,
                0.9999982396572065
            ],
            [
                0.9999945777797381,
                0.9999938558246657,
                0.9999810748540177,
                0.9999938558232019,
                0.9999930377404317,
                0.9999832985781587,
                0.9999930377420914,
                0.9999945777803854,
                0.9999910603036979,
                0.9999974387165682
            ],
            [
                0.9999989322970027,
                0.9999724643121964,
                0.9953904276732001,
                0.9999977396765105,
                0.9999974387184009,
                0.9999977396754328,
                0.9999992661786695,
                0.9999980052700409,
                0.9999980052695652,
                0.9999967112517193
            ],
            [
                0.9999986290427931,
                0.9999990577557432,
                0.9999980052709919,
                0.9999945777816783,
                0.9999974387187053,
                0.9999952149055052,
                0.9999974387184001,
                0.9999982396569966,
                0.9999984465015047,
                0.9999974387171787
            ],
            [
                0.9999995549151072,
                0.9999994956524716,
                0.9999996533672549,
                0.9999994284997573,
                0.9999986290432835,
                0.9999989322966208,
                0.9999980052693275,
                0.9999986290424664,
                0.9999998144609645,
                0.9999996533672135
            ],
            [
                0.9999546021152791,
                0.9999832985821435,
                0.9999945777797395,
                0.9999756997506166,
                0.9999938558246663,
                0.9999251537728863,
                0.9999251537372807,
                0.9999962733607172,
                0.9999546021151652,
                0.9999952149072173
            ],
            [
                0.9999687980960746,
                0.9999938558261308,
                0.9999852610233055,
                0.9999938558275957,
                0.9999646437366672,
                0.9999885212291383,
                0.9999930377437531,
                0.9999832985741761,
                0.9999910602994346,
                0.9999938558224687
            ],
            [
                0.9999869928684397,
                0.9999989322970027,
                0.999989870012645,
                0.9999910603015656,
                0.9999852610215472,
                0.9999974387180948,
                0.9999977396757022,
                0.999998005269803,
                0.9999938558246659,
                0.9999982396574163
            ],
            [
                0.9999984465026159,
                0.9999982396572065,
                0.9999994284995529,
                0.9999970976883611,
                0.9999996533672136,
                0.9999962733589404,
                0.9999980052700409,
                0.9999967112497589,
                0.9999997617631184,
                0.9999952149060765
            ],
            [
                0.9999982396559474,
                0.9999974387174841,
                0.9999986290429567,
                0.9999974387177895,
                0.9999977396751634,
                0.9999992661791944,
                0.9999990577556308,
                0.9999980052702786,
                0.9999987901341724,
                0.9999987901347492
            ],
            [
                0.9999898700066088,
                0.9999957771665567,
                0.9999980052698032,
                0.999999352405279,
                0.9999989322968754,
                0.9999980052695652,
                0.9999977396757023,
                0.9999977396748939,
                0.9999938558275963,
                0.9999974387168734
            ],
            [
                0.9999989322967481,
                0.9999989322968754,
                0.9999687980887184,
                0.9999930377420916,
                0.9999970976883612,
                0.9999974387168737,
                0.9999938558253991,
                0.9999945777797381,
                0.9999970976883609,
                0.9999989322970029
            ],
            [
                9.422449308138184e-07,
                3.726639283806955e-06,
                4.222834451065997e-06,
                4.450851580362069e-07,
                1.7603430034439723e-06,
                4.222832941111319e-06,
                1.5534975693036317e-06,
                6.962254588977791e-06,
                8.315284241174449e-07,
                1.2098658277264215e-06
            ],
            [
                0.999997438717484,
                0.9999982396559474,
                0.9999986290432834,
                0.9999957771655488,
                0.9999938558232014,
                0.9999962733589395,
                0.9999962733593833,
                0.9999989322972572,
                0.9999990577556308,
                0.9999938558239343
            ],
            [
                0.9999957771680668,
                0.9999989322968754,
                0.9999962733620501,
                0.9999982396559474,
                0.999999168471675,
                0.9999980052693275,
                0.9999982396567868,
                0.9999996940977001,
                0.9999967112501512,
                0.9999970976887071
            ],
            [
                0.9999938558275958,
                0.9999869928730878,
                0.9999885212305106,
                0.9999921107355355,
                0.999986992876195,
                0.9999957771670611,
                0.9999724643056241,
                0.9999945777829694,
                0.9999989322973845,
                0.9999810748427593
            ],
            [
                0.9999992661791945,
                0.9999993524051246,
                0.9999987901346049,
                0.9999993524053563,
                0.9999995549150542,
                0.9999992661791071,
                0.9999991684717741,
                0.9999996072137061,
                0.9999980052707543,
                0.9999990577556311
            ],
            [
                0.9999930377437506,
                0.9999992661788445,
                0.999999495652712,
                0.9999970976887071,
                0.9999982396561572,
                0.9999986290426297,
                0.9999996072137061,
                0.9999930377404331,
                0.9999974387165681,
                0.9999994956525318
            ],
            [
                0.999998005270992,
                0.9999921107402369,
                0.9999938558261311,
                0.9999982396561572,
                0.9999967112505438,
                0.9999970976866313,
                0.9999987901337396,
                0.9999945777823237,
                0.9999967112509354,
                0.9999962733593835
            ],
            [
                0.9999898700053991,
                0.9999990577555185,
                0.9999599363173874,
                0.9999869928715388,
                0.9999967112505427,
                0.9999687980849312,
                0.9995121428352106,
                0.9999977396748939,
                0.9999852610110147,
                0.9999810748517715
            ],
            [
                0.9999986290424665,
                0.9999986290421395,
                0.9999991684719723,
                0.9999980052702792,
                0.9999994956523514,
                0.9999991684715759,
                0.9999993524050474,
                0.9999994284996211,
                0.9999987901338838,
                0.9999989322966211
            ],
            [
                0.9999990577552937,
                0.9999994284995529,
                0.9999993524052019,
                0.999997739674894,
                0.999999266179107,
                0.9999832985821457,
                0.999999495652652,
                0.9999977396746248,
                0.999998005270992,
                0.9999991684715759
            ],
            [
                0.999995777167059,
                0.9999991684718732,
                0.9999952149060773,
                0.9999952149043652,
                0.9999977396748939,
                0.9999962733593838,
                0.9999992661791944,
                0.9999987901337397,
                0.9999921107355336,
                0.9999251537995529
            ],
            [
                0.9999485577741262,
                0.9999995549147889,
                0.9999945777829702,
                0.9999938558268655,
                0.9999938558261312,
                0.9999910603026315,
                0.9999994284992804,
                0.999997438717484,
                0.9999898700041918,
                0.9999952149066462
            ],
            [
                0.9999974387168735,
                0.9999957771675629,
                0.9999724642958198,
                0.9999982396559474,
                0.9999898700078134,
                0.9999980052695652,
                0.9999982396565769,
                0.9999832985721872,
                0.9999957771655492,
                0.9999898700114368
            ],
            [
                0.9999957771675624,
                0.9999970976869773,
                0.9999974387171787,
                0.999997097687323,
                0.9999962733620488,
                0.9999921107374196,
                0.9999952149066468,
                0.9999921107393047,
                0.9999962733620491,
                0.999998629042303
            ],
            [
                0.9999898700126474,
                0.9999687980960955,
                0.9999962733598274,
                0.9999417087066845,
                0.9999724643121839,
                0.9999982396574163,
                0.9999785550516034,
                0.9999832985721934,
                0.9999957771680662,
                0.9999970976890528
            ],
            [
                0.9999977396765108,
                0.9999993524052019,
                0.9999984465028012,
                0.999998005270992,
                0.9999993524052019,
                0.9999980052709919,
                0.9999938558232021,
                0.9999993524052018,
                0.9999997897566089,
                0.9999989322972572
            ],
            [
                0.999997097686977,
                0.9999938558268642,
                0.9999952149066468,
                0.9999967112501505,
                0.9999930377412617,
                0.9999910603015668,
                0.9999974387168735,
                0.9999970976887069,
                0.999986992868439,
                0.9999832985841324
            ],
            [
                0.9999995549148419,
                0.9999599363221628,
                0.9999957771675632,
                0.9999930377437518,
                0.9999957771645431,
                0.9999832985781765,
                0.9999987901341723,
                0.9999990577555185,
                0.9999982396572065,
                0.9999962733616047
            ],
            [
                0.9999974387187054,
                0.9999974387168734,
                0.9999989322968754,
                0.9999982396563675,
                0.9999984465015047,
                0.9999987901338839,
                0.9999989322975119,
                0.9999987901343166,
                0.9999994956525318,
                0.99999844650169
            ],
            [
                0.9999982396561572,
                0.9999998144609645,
                0.9999995549147358,
                0.9999982396572065,
                0.9999990577549568,
                0.9999994956526519,
                0.9999974387187053,
                0.9999957771675627,
                0.9999977396757023,
                0.9999921107364753
            ],
            [
                0.9999982396565767,
                0.9999485577741123,
                0.9999967112521109,
                0.999948557804806,
                0.9999945777790913,
                0.9999967112521109,
                0.9999990577552937,
                0.999995777164542,
                0.9999687980811937,
                0.9999952149032236
            ],
            [
                0.999997097686631,
                0.9999962733611605,
                0.9999974387177893,
                0.9999957771660524,
                0.9999952149032243,
                0.9999974387180949,
                0.9999957771675624,
                0.9999910603036993,
                0.9999970976873237,
                0.9999910603026315
            ],
            [
                0.9999785550413638,
                0.999997097687323,
                0.9999938558275958,
                0.9999957771670589,
                0.9999982396559474,
                0.999983298574179,
                0.999999352405279,
                0.999999428499553,
                0.9999952149066464,
                0.9999977396762413
            ],
            [
                0.9999938558253986,
                0.9999962733598277,
                0.9999980052707546,
                0.9999982396569966,
                0.9999945777810307,
                0.9999952149060778,
                0.9999938558246658,
                0.9999987901343165,
                0.999997097687669,
                0.9999980052700459
            ],
            [
                3.2887494573561262e-06,
                7.889260704179641e-06,
                7.338208055579897e-07,
                3.7266383955882547e-06,
                4.222832437677995e-06,
                3.2887494573561262e-06,
                9.422447061953531e-07,
                7.889259763857458e-06,
                2.902312677060767e-06,
                3.2887494572873306e-06
            ],
            [
                0.9999991684718733,
                0.9999962733598278,
                0.9999974387184,
                0.9999962733620489,
                0.9999898700053997,
                0.9999984465024306,
                0.9999977396751634,
                0.9999990577552937,
                0.9999957771670596,
                0.9999930377437529
            ],
            [
                0.9999980052695653,
                0.9999989322975118,
                0.9999898700078154,
                0.9999945777784459,
                0.9999980052700409,
                0.9999646437535129,
                0.9999910603015666,
                0.9999970976876691,
                0.9999921107355343,
                0.9999756997476967
            ],
            [
                0.9999869928746399,
                0.9999945777810317,
                0.9999885212305091,
                0.9999994956523514,
                0.9999852610197955,
                0.9999957771665557,
                0.9999991684720715,
                0.9999982396565769,
                0.999997097688015,
                0.9999852610233055
            ],
            [
                0.957912268029248,
                0.9999921107364834,
                0.8519528057272543,
                0.9626731101124724,
                0.9999339478759748,
                0.9740426427551088,
                0.651354857898194,
                0.7057850278370112,
                0.9999687980895614,
                0.999820472024562
            ],
            [
                0.9999977396757022,
                0.9999984465018751,
                0.9999962733589395,
                0.9999991684722698,
                0.999997438717484,
                0.9999984465015047,
                0.9999974387171787,
                0.9999852610127611,
                0.9999962733589393,
                0.9999987901340281
            ],
            [
                0.9999957771660528,
                0.9999930377462405,
                0.9999938558254017,
                0.9999977396757022,
                0.9999977396748938,
                0.9999852610215454,
                0.9999962733611614,
                0.9999977396762414,
                0.9999980052705171,
                0.999993037743751
            ],
            [
                0.9999852610215482,
                0.9999724643023589,
                0.9999756997534839,
                0.9999921107345938,
                0.9999785550413666,
                0.9999921107355338,
                0.9999938558261312,
                0.999992110737415,
                0.9999989322972573,
                0.9999885212359809
            ],
            [
                0.9999967112513275,
                0.9999986290426298,
                0.9999993524051247,
                0.9999957771660526,
                0.9999970976869789,
                0.9999989322972572,
                0.9999967112493665,
                0.9999984465020603,
                0.9999987901337396,
                0.9999996533673375
            ],
            [
                0.9999974387171787,
                0.9999945777816778,
                0.9999980052702786,
                0.999999352405279,
                0.9999599363221742,
                0.9999967112501507,
                0.999997438717484,
                0.99998329858015,
                0.9999982396574163,
                0.9999930377454105
            ],
            [
                0.9999989322975118,
                0.9999967112509354,
                0.9999980052702786,
                0.9999986290432835,
                0.9999980052698033,
                0.9999984465022455,
                0.999999352404893,
                0.9999930377429231,
                0.9999982396565769,
                0.9999977396757022
            ],
            [
                0.9999945777797377,
                0.9999898700102295,
                0.9999756997534786,
                0.9999991684718733,
                0.9999962733602722,
                0.999997097688707,
                0.9998911030779789,
                0.9999980052702786,
                0.9999930377420916,
                0.9999930377454104
            ],
            [
                0.999997097689053,
                0.9999989322972573,
                0.9999982396567868,
                0.9999980052695653,
                0.9999938558268638,
                0.9999957771655491,
                0.9999957771680662,
                0.9999989322972573,
                0.9999977396751634,
                0.9999991684720715
            ],
            [
                0.999998239656367,
                0.9999982396567868,
                0.9999852610110046,
                0.999998239656577,
                0.9999977396757023,
                0.999996273360272,
                0.9999938558232019,
                0.9999980052700408,
                0.9999869928715388,
                0.9999986290421395
            ],
            [
                0.9999989322972573,
                0.9999962733611607,
                0.9999993524050474,
                0.999998932296621,
                0.9999996533674614,
                0.9999970976887071,
                0.99999862904312,
                0.999997097687323,
                0.9999991684719725,
                0.9999982396565771
            ],
            [
                0.999997097687323,
                0.999999266178757,
                0.999998239656367,
                0.9999991684719723,
                0.9999986290427931,
                0.9999977396762411,
                0.9999994956523514,
                0.9999991684722698,
                0.999999168471675,
                0.9999980052709919
            ],
            [
                0.9999992661791945,
                0.9999992661788445,
                0.999999352404893,
                0.9999980052705163,
                0.9999984465015047,
                0.9999986290421394,
                0.9999991684715759,
                0.9999982396567868,
                0.9999992661792819,
                0.9999957771645422
            ],
            [
                1.067702615468225e-06,
                2.902311292920774e-06,
                2.561282821209454e-06,
                2.2603251060985603e-06,
                1.76034363298589e-06,
                1.3007125360478133e-05,
                0.9999996072137529,
                1.3709578604108674e-06,
                3.2887482809933958e-06,
                0.9999994284996893
            ],
            [
                0.9999898700114359,
                0.9999930377445807,
                0.9999869928715378,
                0.9999852610197881,
                0.9999885212305076,
                0.9999992661788445,
                0.99998107485853,
                0.9999970976869778,
                0.9999930377412614,
                0.9999885212359814
            ],
            [
                0.9999952149037947,
                0.9999982396569966,
                0.9999977396751634,
                0.9999957771650482,
                0.9999962733602719,
                0.999997097688015,
                0.9999993524051246,
                0.9999967112501511,
                0.9999952149060768,
                0.999998446502801
            ],
            [
                1.4738985483504099e-05,
                1.7603438427467903e-06,
                7.889264466344872e-06,
                1.0677029972833341e-06,
                1.3709578605243332e-06,
                2.5612812946890944e-06,
                3.2887502414436403e-06,
                1.9947301969707264e-06,
                2.260324297853209e-06,
                2.561283431916622e-06
            ],
            [
                0.9999546021259818,
                0.9999869928669192,
                0.9998601779778491,
                0.9999921107365359,
                0.9999910603069027,
                0.9999687980849524,
                0.9998601778773867,
                0.9998766054548427,
                0.9875683472716471,
                0.999972464302379
            ],
            [
                0.9999980052695652,
                0.9999989322973845,
                0.9999996072139402,
                0.9999957771645424,
                0.9999995549149481,
                0.9999977396762414,
                0.9999991684717742,
                0.9999989322971302,
                0.9999989322975119,
                0.9999990577550691
            ],
            [
                0.9999993524053562,
                0.9999921107364796,
                0.9999921107392958,
                0.9999974387171788,
                0.9999967112517189,
                0.9999910603036993,
                0.999998005270992,
                0.9999910603068951,
                0.9999957771675639,
                0.9999982396569966
            ],
            [
                0.9999982396574165,
                0.9999974387165681,
                0.9999810748472573,
                0.9999945777797379,
                0.9999982396572065,
                0.9999974387187056,
                0.9999970976869772,
                0.9999977396765106,
                0.9999982396565769,
                0.999995214905506
            ],
            [
                0.999964643749675,
                0.9999646437603207,
                0.9399133523506772,
                0.8175744828610095,
                0.999998629043295,
                0.9149009544128984,
                0.999999352405281,
                0.9999957771655635,
                0.9999962733607576,
                0.9999982396574163
            ],
            [
                0.9999952149072168,
                0.9999974387180947,
                0.9999982396561571,
                0.999998790134028,
                0.9999987901347491,
                0.9999989322970028,
                0.9999930377420914,
                0.999997097688707,
                0.9999992661787571,
                0.999996711249367
            ],
            [
                0.9999724643154864,
                0.9999756997592822,
                0.9999852610162783,
                0.999975699759271,
                0.9999785550413659,
                0.9999974387174841,
                0.9999962733602726,
                0.9999756997650704,
                0.9999756997621748,
                0.9999921107336557
            ],
            [
                0.9999995549147889,
                0.9999996072136125,
                0.9999991684717741,
                0.9999993524049702,
                0.99999893229713,
                0.9999994956525317,
                0.9999982396567868,
                0.9999993524050474,
                0.9999991684717742,
                0.9999991684722698
            ],
            [
                0.9999987901343166,
                0.9999993524049702,
                0.9999996072137061,
                0.9999991684716749,
                0.9999952149032242,
                0.9999990577555185,
                0.9999989322973846,
                0.999997097688015,
                0.9999852610110042,
                0.9999982396561572
            ],
            [
                0.9999952149066468,
                0.9999962733611607,
                0.9999962733589389,
                0.9999952149043646,
                0.9999970976883611,
                0.9999992661790195,
                0.999995777167564,
                0.9999990577554061,
                0.9999987901341723,
                0.9999967112497586
            ],
            [
                0.9999989322972572,
                0.9999967112513269,
                0.9999982396574163,
                0.9999989322975118,
                0.999999554914842,
                0.9999967112505429,
                0.9999989322971301,
                0.9999938558246665,
                0.9999982396574163,
                0.9999987901341724
            ],
            [
                0.9999938558224705,
                0.9999980052707542,
                0.9999962733593835,
                0.99999893229713,
                0.999996273362049,
                0.9999989322966208,
                0.99999893229713,
                0.9999952149037943,
                0.999997739674894,
                0.9999967112501509
            ],
            [
                0.9999982396567867,
                0.9999994956525918,
                0.9890130581284042,
                0.9999957771655491,
                0.9999970976887097,
                0.9978172837539427,
                0.9999991684722698,
                0.9999962733621026,
                0.9999977396754329,
                0.999996711250151
            ],
            [
                0.9999994284996891,
                0.9999977396759717,
                0.9999980052702786,
                0.9999962733593833,
                0.9999974387171787,
                0.9999989322968754,
                0.9999885212359836,
                0.9999930377445814,
                0.9999938558224685,
                0.9999982396569966
            ]
        ]
    },
    {
        "q_id": "8901_mmlu_math",
        "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": [
            [
                0.9999599362934879,
                0.999941708755344,
                0.9996646499706324,
                0.9999339478553524,
                0.9999646437366446,
                0.9999038975622117,
                0.999841563745393,
                0.9999599363125995,
                0.9999417087136211,
                0.9999251537460145
            ],
            [
                0.9999599363221485,
                0.9998766053810263,
                0.9995121429394904,
                0.9999339478632202,
                0.999948557774106,
                0.9998766054692957,
                0.9998601779428107,
                0.9998766053957648,
                0.9998601779092757,
                0.9998911031297583
            ],
            [
                0.9997388095666206,
                0.9999724643187494,
                0.9999810748449929,
                0.9999485578047517,
                0.9997040428654331,
                0.9999724642990531,
                0.9999485577679615,
                0.9999724643056201,
                0.9999599363173711,
                0.9999687980997901
            ],
            [
                0.9999339478395968,
                0.9999251537370755,
                0.9997388096599749,
                0.9999724642990617,
                0.9996646500100201,
                0.9997388096911638,
                0.9996646497711177,
                0.9998415637077608,
                0.9999339478553375,
                0.9997965729299618
            ],
            [
                0.9999546021367759,
                0.9999038976080584,
                0.9999546021313743,
                0.9999646437408605,
                0.9997694933121795,
                0.9999151889485539,
                0.9998911031297076,
                0.9999756997476807,
                0.9998766054692795,
                0.9999251537905833
            ],
            [
                0.9998415637644016,
                0.9996200154713965,
                0.9998601779760303,
                0.9993736658954131,
                0.9989677687980654,
                0.9990889488703962,
                0.9996646497722788,
                0.9998415637266403,
                0.9997965730268786,
                0.9996200154244688
            ],
            [
                0.9992903294511394,
                0.9998766054693945,
                0.9996200155149193,
                0.99989110311668,
                0.9999038975850585,
                0.999796573099902,
                0.9999151889687863,
                0.9996646498107299,
                0.9999151889282987,
                0.9988304895940591
            ],
            [
                0.9998601779261043,
                0.9998601779093368,
                0.9999852610145148,
                0.9999687980960746,
                0.999841563821259,
                0.9999339478553524,
                0.9999151889587096,
                0.9999832985721839,
                0.9999687980886254,
                0.9999852610180288
            ],
            [
                0.9999485577863536,
                0.9999151889283524,
                0.9988304897290969,
                0.9999251537727964,
                0.998830489462965,
                0.9998766053812794,
                0.9999038976195891,
                0.9999485577863506,
                0.9999151889485612,
                0.9999417087483762
            ],
            [
                0.9999852610127573,
                0.9999038975850585,
                0.9988304898815413,
                0.9997388096909586,
                0.9999546021421944,
                0.9999038976079563,
                0.9995121429393768,
                0.9999038976194206,
                0.9993736658944657,
                0.9998911030778315
            ],
            [
                0.9999038975507067,
                0.9998415637643255,
                0.9997694932577917,
                0.9999339478395968,
                0.9999646437450735,
                0.9999339478553375,
                0.9999687980737576,
                0.9999599363125902,
                0.9999646437535052,
                0.9999687980737526
            ],
            [
                0.9997694932848212,
                0.9999599362887106,
                0.999841563764616,
                0.9999646437535068,
                0.9999151889283443,
                0.9999151889687937,
                0.999972464312183,
                0.9999038975850683,
                0.9998766054545571,
                0.9998911030388833
            ],
            [
                0.9999251537817236,
                0.9998415638210446,
                0.9988304894569816,
                0.9999687980811879,
                0.999933947863251,
                0.9999646437492968,
                0.9996646497714592,
                0.9999485577740787,
                0.9997694933402419,
                0.999925153781686
            ],
            [
                0.9999417087483646,
                0.9999038975851299,
                0.999941708755328,
                0.9998911031299215,
                0.999964643732433,
                0.9998911031167291,
                0.9995121428835189,
                0.9999339478553327,
                0.9997694932301049,
                0.9998601778759707
            ],
            [
                0.9998601778758892,
                0.9999251537370629,
                0.9999724643056231,
                0.9999756997563714,
                0.9999785550464746,
                0.9999485577986055,
                0.9998204720767369,
                0.9998911031167164,
                0.9999485577863596,
                0.9999832985801468
            ],
            [
                0.9999251537906257,
                0.9997694932297829,
                0.9999485577740902,
                0.9997388097217372,
                0.9999417087205764,
                0.9998204719911963,
                0.9999251537995338,
                0.9999687980811868,
                0.9999417087344838,
                0.9999599362982728
            ],
            [
                0.9999251537729087,
                0.9998204720980013,
                0.9999885212277702,
                0.9999885212264015,
                0.999903897596522,
                0.999941708748396,
                0.9999852610127573,
                0.9999485577802218,
                0.9999417087553479,
                0.999959936298269
            ],
            [
                0.9997040428315234,
                0.9997388097225656,
                0.9997388097525158,
                0.9997965729295415,
                0.998498817679571,
                0.9997694932300513,
                0.9998601778760113,
                0.9998911030518491,
                0.9989677691597564,
                0.9997388095977412
            ],
            [
                0.9998766054398994,
                0.9998911031167544,
                0.9999251537994984,
                0.99996879809608,
                0.9995121428815036,
                0.9999599363221628,
                0.9999832985741738,
                0.9999546021097344,
                0.9999852610233012,
                0.999941708741448
            ],
            [
                0.9992903296210848,
                0.9997694933399132,
                0.9998204720770398,
                0.9996200155156378,
                0.9994472212569223,
                0.9994472212589162,
                0.9902915230439671,
                0.9999251537549172,
                0.9997965729787457,
                0.9998911030907721
            ],
            [
                0.9998911031167418,
                0.9999546021259631,
                0.9998601778594107,
                0.9999724643121898,
                0.9999599363030408,
                0.9999546021205493,
                0.999512142765899,
                0.9999038975735851,
                0.9997694931749592,
                0.9999724643187504
            ],
            [
                0.9999646437324287,
                0.9999038976079864,
                0.9998415638208648,
                0.9999687980960759,
                0.9999599363126013,
                0.9999869928684344,
                0.9999251537995039,
                0.9999646437619449,
                0.9999485578047674,
                0.9999251537638694
            ],
            [
                0.9996200155617695,
                0.9999599362887198,
                0.9999251537727589,
                0.9995694428581399,
                0.999891103038808,
                0.9994472212551214,
                0.9999251537370689,
                0.9999724642990576,
                0.9999756997621694,
                0.9999756997679594
            ],
            [
                0.9999251537816681,
                0.9997040429709516,
                0.999903897562102,
                0.9999251537549356,
                0.9997965730996001,
                0.9999810748427365,
                0.9999687980960662,
                0.999925153746002,
                0.9996200155151292,
                0.9994472212546711
            ],
            [
                0.9990889488728333,
                0.9999339478317487,
                0.9999687980886335,
                0.9999646437408605,
                0.9999485577740932,
                0.9999151889688097,
                0.9999599362982653,
                0.9999546021421896,
                0.9996646498908519,
                0.9997965730997274
            ],
            [
                0.9997965730991,
                0.9996200155600339,
                0.9999038975621404,
                0.9999417087066808,
                0.999941708755328,
                0.9999485577863596,
                0.999959936322143,
                0.9999646437450779,
                0.9992903297028585,
                0.9998415637645076
            ],
            [
                0.9995694429099702,
                0.9998204719915358,
                0.9999546021151307,
                0.9999599362887237,
                0.9996200154698709,
                0.9999417087136483,
                0.9997965730514673,
                0.9998415638021121,
                0.9999756997476854,
                0.9999417087066731
            ],
            [
                0.9999724643121839,
                0.999796572929876,
                0.9999339478317647,
                0.9999646437535068,
                0.9999785550439215,
                0.9999724643089034,
                0.9999599363078162,
                0.9999485577924977,
                0.9999785550515903,
                0.9999785550515897
            ],
            [
                0.9997388096287174,
                0.9998415638400048,
                0.9986749778405101,
                0.9999038975621705,
                0.999841563745628,
                0.9995121429412501,
                0.9996200154691524,
                0.9999151889890107,
                0.9999038975965423,
                0.9999151889587016
            ],
            [
                0.99973880959746,
                0.9998766054397576,
                0.9998601779092371,
                0.9999251537906066,
                0.9997965729297074,
                0.9999151889586775,
                0.9999599363078182,
                0.999948557798617,
                0.9998766054546057,
                0.9997965729784852
            ],
            [
                0.9999339478474645,
                0.99979657295416,
                0.9998204719914993,
                0.9999038976079275,
                0.9999339478710932,
                0.9999038975965528,
                0.9996200155152066,
                0.9997694932575167,
                0.9998415637266403,
                0.9997965730991827
            ],
            [
                0.9999546021367831,
                0.9999038975506579,
                0.9998766054104549,
                0.9999151889687863,
                0.9999417087275282,
                0.9986749775211675,
                0.9999785550592574,
                0.99973880959746,
                0.9999251537817236,
                0.9999599363173711
            ],
            [
                0.9999810748540172,
                0.9999646437366521,
                0.9999417087136211,
                0.9997040428666903,
                0.9998911031296585,
                0.9995121429383267,
                0.9994472213916329,
                0.9999417087553089,
                0.9999756997534754,
                0.9997694931753348
            ],
            [
                0.998674977506841,
                0.9995694429096069,
                0.9999646437535129,
                0.9997040429363098,
                0.9998415638211505,
                0.9998766054397883,
                0.9975273763822192,
                0.9997694931749592,
                0.9999339478553236,
                0.99989110311668
            ],
            [
                0.999978555056703,
                0.999860177959389,
                0.999972464315468,
                0.9999599363030504,
                0.9999646437619372,
                0.9999251537371604,
                0.9999485578047399,
                0.9999756997563736,
                0.9999646437366535,
                0.9999038975392935
            ],
            [
                0.9999832985841286,
                0.99956944301318,
                0.9999038975965026,
                0.9999724643023353,
                0.999876605439851,
                0.999925153745996,
                0.9995121429383267,
                0.9994472213195986,
                0.9999785550464806,
                0.9989677687980654
            ],
            [
                0.9996646499296739,
                0.9999599362982708,
                0.9997388097838416,
                0.9999038975965026,
                0.9998415638021121,
                0.9999151889485385,
                0.998674977379905,
                0.9997694933396449,
                0.9998204719697047,
                0.9978172834603354
            ],
            [
                0.9998766053662573,
                0.9998415637453423,
                0.9998204720553445,
                0.9999724643023452,
                0.9999646437366584,
                0.9999417087483685,
                0.9999938558275954,
                0.999903897608017,
                0.9999687980774769,
                0.9999038976194807
            ],
            [
                0.9998204720341167,
                0.9998601779426847,
                0.9995694429618006,
                0.9999417087205882,
                0.9995694429097949,
                0.999959936303039,
                0.9999339478238459,
                0.9997965729299204,
                0.9999251537370814,
                0.9999038975393573
            ],
            [
                0.9933071503945013,
                0.9992903297045509,
                0.999195914062313,
                0.9993736659742211,
                0.9991959141487373,
                0.9993736658245113,
                0.9968273172237867,
                0.9940889320932472,
                0.9993736658971619,
                0.9997040428666903
            ],
            [
                0.9997040429005227,
                0.9978172839212838,
                0.999569443012441,
                0.9980732651067588,
                0.9998766053956697,
                0.9999546021367736,
                0.9997040427956243,
                0.9994472212627751,
                0.9996646498897299,
                0.9971990736851449
            ],
            [
                0.9999485577802278,
                0.9999756997679633,
                0.9999599362934992,
                0.9999339478239084,
                0.999959936298269,
                0.9999687980886287,
                0.999876605410392,
                0.9998204720556789,
                0.9998601778928846,
                0.9998766054252419
            ],
            [
                0.9997388097527894,
                0.9997965729540741,
                0.9999646437492907,
                0.9999646437577213,
                0.999981074858529,
                0.9999151889283524,
                0.9999038975507264,
                0.999860177892614,
                0.9997388096289302,
                0.9999038975622012
            ],
            [
                0.9998911031297583,
                0.9999339478553424,
                0.9999687980886287,
                0.9999339478474549,
                0.999941708755328,
                0.9996200155146319,
                0.9999930377412604,
                0.999964643732436,
                0.99995460213136,
                0.9999646437324375
            ],
            [
                0.99992515374599,
                0.9999339478238508,
                0.9997694932026393,
                0.9999251537816621,
                0.9999485577863724,
                0.9998911031167045,
                0.9998766053662573,
                0.99982047196977,
                0.9997040428660531,
                0.9998911031166673
            ],
            [
                0.9999038975850683,
                0.9989677689423576,
                0.9998601779430304,
                0.9998415638211505,
                0.9999251537549112,
                0.9996646499709837,
                0.9998415638209155,
                0.9986749775110003,
                0.9999339478238556,
                0.999948557798617
            ],
            [
                0.9993736658303772,
                0.9997040427960807,
                0.9999251537549613,
                0.9997694933121257,
                0.9999038975851299,
                0.9997388096909586,
                0.9998766053664029,
                0.9999485577802218,
                0.9999546021476009,
                0.9998415637267463
            ],
            [
                0.9999785550439207,
                0.9999038975623089,
                0.999796572978145,
                0.9999646437408712,
                0.9999599363030465,
                0.9999151889485854,
                0.9999339478553674,
                0.9999339478710831,
                0.999959936307828,
                0.9999646437450841
            ],
            [
                0.9998911030387961,
                0.9996646500099129,
                0.999891103038858,
                0.9997965730757956,
                0.9999417087136322,
                0.9999417087344962,
                0.9997040429715629,
                0.9999724643089016,
                0.9998911030517628,
                0.9998911030518237
            ],
            [
                0.9999485577740932,
                0.999972464312192,
                0.9995121428236302,
                0.9997040427609136,
                0.9999546021205518,
                0.9999251537638889,
                0.999972464315472,
                0.9999687980737504,
                0.9999546021421896,
                0.9999646437450908
            ],
            [
                0.999373665828009,
                0.9999251537728232,
                0.9999151889384377,
                0.9999251537638694,
                0.9997965730996001,
                0.9999251537460401,
                0.9988304895867156,
                0.9997040429357845,
                0.9997965729788819,
                0.9999251537727964
            ],
            [
                0.9997388095982276,
                0.9999646437535068,
                0.9999417087275401,
                0.9998415638400048,
                0.99979657295416,
                0.9996200155170307,
                0.9998766054252095,
                0.9999687980774709,
                0.9999339478396064,
                0.9999339478474896
            ],
            [
                0.9999038975392034,
                0.9995121427651894,
                0.9999546021367807,
                0.9996646497701029,
                0.9999339478553626,
                0.9999151889890348,
                0.9999417087205764,
                0.9998911030907974,
                0.9999151889889872,
                0.9998601779761158
            ],
            [
                0.9999417087553016,
                0.9999251537727715,
                0.998674977665973,
                0.9999417087483837,
                0.9997965730508666,
                0.999841563745393,
                0.9997965729299618,
                0.9993736658971619,
                0.9998911031296949,
                0.9996646499714423
            ],
            [
                0.9997388096909586,
                0.9998415638209662,
                0.9998601779092554,
                0.999941708755344,
                0.9999251537817176,
                0.9998911031297203,
                0.9999339478789562,
                0.9994472214575892,
                0.9999251537995719,
                0.9998911030648404
            ],
            [
                0.9997388096603245,
                0.9999646437535082,
                0.9999724643056184,
                0.9999417087275282,
                0.9999852610197857,
                0.9999251537460472,
                0.9999417087206002,
                0.9999485578047517,
                0.9999546021151355,
                0.9999546021313848
            ],
            [
                0.999620015470081,
                0.9999038975850787,
                0.9996200154699372,
                0.9988304898702542,
                0.99989110311668,
                0.9998601779426847,
                0.999933947831781,
                0.9999417087205725,
                0.9997965729782308,
                0.9996200155169533
            ],
            [
                0.9999724643089045,
                0.9997694932030821,
                0.9999251537549232,
                0.9999339478396064,
                0.9997965730996415,
                0.9982992772920846,
                0.9994472214580716,
                0.9998601779260615,
                0.9999756997476821,
                0.9999251537727649
            ],
            [
                0.9999599363030427,
                0.9998601778759707,
                0.9975273771052364,
                0.9999417087136283,
                0.9999785550515878,
                0.9999646437535052,
                0.9996200155601113,
                0.9999724643089034,
                0.9999151889789265,
                0.9999546021151381
            ],
            [
                0.9996200155153504,
                0.9999151889789345,
                0.9999038975506963,
                0.9986749778465179,
                0.9999251537460145,
                0.999941708713625,
                0.9995694429115358,
                0.9998204719701774,
                0.999954602142192,
                0.9998601778760521
            ],
            [
                0.9980732654092062,
                0.9989677690427139,
                0.9994472212551214,
                0.9947798750633136,
                0.9998601778926528,
                0.9990889488837477,
                0.9990889489893404,
                0.9998601779594093,
                0.9996646499293421,
                0.9993736658996759
            ],
            [
                0.9999251537638378,
                0.9999417087553165,
                0.9999417087066808,
                0.999769493284714,
                0.9994472213873559,
                0.999975699759268,
                0.9997040428299991,
                0.9999646437535052,
                0.9998601779425625,
                0.999933947855328
            ],
            [
                0.9999687980811924,
                0.9999599363125938,
                0.9998415637835254,
                0.9999832985761654,
                0.9999151889182207,
                0.9995121427643663,
                0.9999485577924913,
                0.999959936288716,
                0.999933947823871,
                0.9999599363173656
            ],
            [
                0.9998601779426236,
                0.999964643732439,
                0.9999724642957795,
                0.9999930377429205,
                0.9999417087553398,
                0.9997388095664763,
                0.9999339478396165,
                0.9999546021259682,
                0.998073265096013,
                0.9999646437366552
            ],
            [
                0.9996646497308322,
                0.999841563745393,
                0.9997040430081853,
                0.9997388097533365,
                0.9991959139567147,
                0.9998766054251287,
                0.9994472213239721,
                0.9989677690478758,
                0.9978172840105324,
                0.9998766054105537
            ],
            [
                0.9999546021476212,
                0.9998204719912301,
                0.9995694429102457,
                0.999891103038808,
                0.9999339478789965,
                0.9997694933122868,
                0.9998766054695488,
                0.9999546021421969,
                0.9999038975507789,
                0.9999485578047517
            ],
            [
                0.9999485577679555,
                0.9999151889485693,
                0.9999599363125995,
                0.9999339478395871,
                0.9999599363173656,
                0.999738809597118,
                0.9999038975507166,
                0.9999251537370755,
                0.9996200154692297,
                0.9980732653319713
            ],
            [
                0.9999485577925007,
                0.999903897619401,
                0.9999646437619328,
                0.9999687980960696,
                0.9999151889587867,
                0.9999485577740932,
                0.99986017797601,
                0.999903897608017,
                0.9999151889687937,
                0.9999832985741745
            ],
            [
                0.999796572978145,
                0.9989677689193093,
                0.9991959140581509,
                0.9982992778897885,
                0.99919591395765,
                0.9933071495307894,
                0.9995694428587786,
                0.9998204720125233,
                0.9992903297062846,
                0.9999599363173831
            ],
            [
                0.9997965729539054,
                0.9998601779260412,
                0.9999151889586547,
                0.9995694429616252,
                0.9995694428597932,
                0.9999339478553424,
                0.999664649850908,
                0.9999038975621508,
                0.999569442962264,
                0.9999151889283845
            ],
            [
                0.9998204719485109,
                0.9999339478238556,
                0.9996646498896129,
                0.9999869928715365,
                0.999968798077472,
                0.9999724643056193,
                0.9999885212346115,
                0.9998911030777563,
                0.999941708713625,
                0.9998766054545895
            ],
            [
                0.999876605366322,
                0.9997694933123403,
                0.9999485577802407,
                0.9996646500103618,
                0.999841563783258,
                0.9998204720126225,
                0.9998911031296703,
                0.9999599363125938,
                0.9998415638020614,
                0.999841563726668
            ],
            [
                0.9999646437492907,
                0.9998601779759103,
                0.9999485577924709,
                0.9999251537727649,
                0.9995121428802264,
                0.9998204720981632,
                0.9999546021097423,
                0.9998415638022159,
                0.9999251537995403,
                0.999820471970039
            ],
            [
                0.9999038976194401,
                0.9997694933400205,
                0.999903897585039,
                0.9997965731000351,
                0.9992903297052939,
                0.9998911030907847,
                0.9993736659692295,
                0.9999785550592586,
                0.999933947878971,
                0.9998415637455751
            ],
            [
                0.9999599363030446,
                0.9998911030778189,
                0.999972464302337,
                0.9999417087414129,
                0.9999724642957752,
                0.9999251537817236,
                0.9998911031038409,
                0.9997965730025976,
                0.9999599362934953,
                0.9999599362934974
            ],
            [
                0.9999546021421873,
                0.9999485578047547,
                0.9999251537995464,
                0.9984988175162407,
                0.9999724642957716,
                0.9998911031037506,
                0.9999485577740814,
                0.9999339478238656,
                0.999891103064815,
                0.9999485577802376
            ],
            [
                0.9998601779593687,
                0.9999810748540188,
                0.9998766054545105,
                0.9998601779260412,
                0.9998204720126225,
                0.9999646437366602,
                0.9999785550413652,
                0.9999417087275321,
                0.9999038976194807,
                0.9999832985761689
            ],
            [
                0.9999599363173749,
                0.9999599363126035,
                0.999925153737113,
                0.9999687980811868,
                0.9999546021367934,
                0.9999646437577213,
                0.9999546021205596,
                0.9999038975737515,
                0.9999417087275358,
                0.9998911031038012
            ],
            [
                0.9999151889687863,
                0.9998766054103616,
                0.9999687980960685,
                0.9999251537995464,
                0.9999038975965122,
                0.9999599363078145,
                0.9999038975392727,
                0.9993736658201027,
                0.9999151889890266,
                0.9999724643121868
            ],
            [
                0.9999832985701931,
                0.999959936298269,
                0.9999038975507166,
                0.9999417087553165,
                0.9999852610232999,
                0.9999869928730875,
                0.9999646437408679,
                0.9999910603026306,
                0.9999687980923515,
                0.9999417087205692
            ],
            [
                0.9999417087205764,
                0.9999038976194401,
                0.9998415637644823,
                0.9999151889182516,
                0.9997965730032546,
                0.9999724643154637,
                0.999876605469328,
                0.9999151889384766,
                0.9998911031038679,
                0.9998204720562509
            ],
            [
                0.9999910603047619,
                0.9999038975735655,
                0.9999339478789562,
                0.9999546021421849,
                0.9999151889687629,
                0.9999339478789913,
                0.9999038975736046,
                0.9999251537905887,
                0.999891103103726,
                0.9999810748427351
            ],
            [
                0.9999785550541442,
                0.9999869928699859,
                0.9998766054104549,
                0.9999038975965626,
                0.9999687980923515,
                0.9998911031166918,
                0.9998911031037759,
                0.9999869928730862,
                0.9999599362887123,
                0.999915188978879
            ],
            [
                0.9999785550490299,
                0.9991959141493452,
                0.9999546021259605,
                0.9999417087206043,
                0.9999251537995218,
                0.9999852610232997,
                0.9999151889283684,
                0.9999646437450749,
                0.9999599363078182,
                0.9999339478238364
            ],
            [
                0.9990889487823403,
                0.9998601779092168,
                0.9998911030778315,
                0.9998911031297076,
                0.9998601779592466,
                0.9999546021313577,
                0.9998204719483437,
                0.9998766053662896,
                0.9999339478317002,
                0.9999417087483837
            ],
            [
                0.9999417087275321,
                0.9997388095973233,
                0.9999832985781578,
                0.9999599363030504,
                0.9999724643121868,
                0.9999810748517622,
                0.9999756997534777,
                0.9997694932027467,
                0.9999417087344686,
                0.9999038975964829
            ],
            [
                0.9999151889789512,
                0.9999151889283214,
                0.9997388096595644,
                0.999876605454541,
                0.9997694933121795,
                0.9999599363221504,
                0.9995121428807939,
                0.9995121429409095,
                0.9999038975850683,
                0.9998204719484768
            ],
            [
                0.9997694932573558,
                0.999941708755328,
                0.9998601778927158,
                0.9999151889688264,
                0.9999485577924853,
                0.999903897607966,
                0.9999417087344652,
                0.9998911030517865,
                0.9998601778759911,
                0.999941708734492
            ],
            [
                0.9998766053957809,
                0.9992903295398066,
                0.9997965730028551,
                0.9999251537549356,
                0.9997388097848751,
                0.9997965729539054,
                0.999569442912563,
                0.9999339478710649,
                0.9998766053957809,
                0.9995694429114481
            ],
            [
                0.9999251537816801,
                0.9999339478710932,
                0.9999646437408634,
                0.9999339478238608,
                0.9997388096596329,
                0.9999251537995529,
                0.9998911030648404,
                0.999447221319888,
                0.9997040428650026,
                0.9999339478474645
            ],
            [
                0.9999038975736046,
                0.9999038975735949,
                0.9994472213245831,
                0.9999339478553885,
                0.9997965729785296,
                0.9999038975965325,
                0.9996200155608298,
                0.9993736658981092,
                0.9998415638021905,
                0.9999339478632404
            ],
            [
                0.9999038975965122,
                0.999903897585039,
                0.9997040427949182,
                0.9995694428613839,
                0.9991959141446217,
                0.9992903294501487,
                0.999915188928401,
                0.9998204719485762,
                0.9998601779594521,
                0.9990889486714493
            ],
            [
                0.9999339478789859,
                0.9999339478396218,
                0.9999038976194401,
                0.9999785550592561,
                0.9999038976195339,
                0.99997246431547,
                0.9999724642957734,
                0.999964643732433,
                0.9999485578047611,
                0.9999599363126256
            ],
            [
                0.9999546021475963,
                0.9999417087483536,
                0.9999417087275205,
                0.9999852610180288,
                0.9998766054544782,
                0.9999038976194206,
                0.999820471991097,
                0.9997694932572485,
                0.9999038976194108,
                0.999972464302337
            ],
            [
                0.9999599363125918,
                0.9999687980737538,
                0.9998415637455474,
                0.9999151889889724,
                0.999447221385555,
                0.9999485577863596,
                0.9999038975391943,
                0.9999756997650643,
                0.999915188978871,
                0.9999832985801496
            ],
            [
                0.999876605469328,
                0.9999646437408634,
                0.9999785550464753,
                0.9999339478553424,
                0.9999646437408712,
                0.9999852610145177,
                0.9999756997650652,
                0.9999687980997877,
                0.9999687980886323,
                0.9999832985781587
            ],
            [
                0.9999417087275401,
                0.9999646437408728,
                0.9997040429720107,
                0.9988304895980029,
                0.999841563802165,
                0.99992515374599,
                0.9995121427676871,
                0.9999485577863858,
                0.999948557774106,
                0.9999038976079563
            ],
            [
                0.9999339478710885,
                0.9999151889890767,
                0.9999038976194913,
                0.9998415638399263,
                0.999664649890286,
                0.9999251537370629,
                0.9999251537995278,
                0.9998415637077608,
                0.9999417087066845,
                0.9982992779698382
            ],
            [
                0.9996646499700762,
                0.999569443012441,
                0.9998766054251126,
                0.9999646437577213,
                0.9999151889182516,
                0.9999546021313669,
                0.9999417087136283,
                0.9999339478710788,
                0.9999038975736144,
                0.9998601779093368
            ],
            [
                0.9999417087344724,
                0.9996646497696542,
                0.9995694429615251,
                0.999891103064815,
                0.9999546021151239,
                0.9997388095662711,
                0.9999417087553318,
                0.9991959140482831,
                0.999512142940796,
                0.9997965729539469
            ],
            [
                0.9998204720125913,
                0.9998601779258804,
                0.9998415637265112,
                0.999841563745393,
                0.9999687980774697,
                0.9999038976195017,
                0.9997040429006089,
                0.9999485577924884,
                0.9999417087205654,
                0.9994472213200488
            ],
            [
                0.9999485577802131,
                0.9999151889283604,
                0.999903897608017,
                0.99995993630782,
                0.9999038975621606,
                0.9998415637831543,
                0.999959936317373,
                0.9998911031038679,
                0.9997694933129441,
                0.9997388096604004
            ],
            [
                0.9998204719487146,
                0.9999485577924853,
                0.9989677690645619,
                0.9998766054251287,
                0.9999339478396323,
                0.9999251537995039,
                0.9989677690577193,
                0.9998766053810586,
                0.999933947878961,
                0.9999038975507579
            ],
            [
                0.9999485577741157,
                0.9999810748517622,
                0.9999546021476057,
                0.9999339478553236,
                0.9998601779259598,
                0.9999417087275172,
                0.9999810748472484,
                0.9995694430120777,
                0.9997965729299618,
                0.9999546021367883
            ],
            [
                0.9993736657466504,
                0.9998911031296949,
                0.9990889487563792,
                0.9988304900126354,
                0.9997388097220792,
                0.9995694430135433,
                0.9993736659699947,
                0.9998415637643762,
                0.9998204719910003,
                0.9980732653711484
            ],
            [
                0.9998204720770059,
                0.9999251537995403,
                0.9998204720767708,
                0.9999724643121839,
                0.9998204719482784,
                0.9999724642990576,
                0.9995694428591543,
                0.9999756997592687,
                0.9998766053810263,
                0.9999756997650627
            ],
            [
                0.9999038975965626,
                0.9999038975964927,
                0.9999417087414129,
                0.9999251537460085,
                0.999891103064815,
                0.9998415638021374,
                0.9998204720982624,
                0.999796572978145,
                0.99929032970162,
                0.9990889486665749
            ],
            [
                0.9999646437535068,
                0.9999339478710885,
                0.9999485577802343,
                0.9999339478317237,
                0.9999251537638759,
                0.999915188948618,
                0.9998204720127244,
                0.9998204720125233,
                0.9999724643056253,
                0.9999546021421873
            ],
            [
                0.9999151889384531,
                0.9997388096289986,
                0.999968798081195,
                0.999964643736646,
                0.9984988178699488,
                0.999972464312183,
                0.9998911030648926,
                0.9999417087275321,
                0.9999785550515891,
                0.999964643753501
            ],
            [
                0.9999687980960651,
                0.9997965730025117,
                0.9998766054694268,
                0.9999251537638563,
                0.9999546021151381,
                0.9999599363126097,
                0.9999724643023379,
                0.9999646437450749,
                0.9999485577618425,
                0.9998601779093775
            ],
            [
                0.9999546021259464,
                0.9994472214537946,
                0.9995694429611617,
                0.9999687980849082,
                0.9996646500108106,
                0.9995121428234033,
                0.999088948763214,
                0.9998601779759694,
                0.9999339478789513,
                0.9999546021421827
            ],
            [
                0.9996200155161462,
                0.9999810748472489,
                0.9999485577618238,
                0.9997965730761124,
                0.9999339478632668,
                0.9998204720770738,
                0.9999339478238508,
                0.9998911030648656,
                0.999915188958662,
                0.9989677691628774
            ],
            [
                0.999972464315468,
                0.9997388096909586,
                0.9998204719914993,
                0.9994472212548321,
                0.9999687980997901,
                0.9999724643154672,
                0.999975699762166,
                0.9999852610180298,
                0.9999546021367759,
                0.9999038975507264
            ],
            [
                0.9997388095661343,
                0.9997040430066525,
                0.9998911030389752,
                0.9999038975507893,
                0.9996200154255522,
                0.9996200154246788,
                0.9998601778592663,
                0.9998601779760934,
                0.9980732653639846,
                0.9997965730993071
            ],
            [
                0.9988304898969083,
                0.9997694932574094,
                0.9997388095978781,
                0.9997388097531315,
                0.9999251537460085,
                0.9994472212555717,
                0.9998766053662735,
                0.9997965729295829,
                0.999820471970073,
                0.9999038975621705
            ],
            [
                0.9999151889687703,
                0.9999546021151355,
                0.9999151889586856,
                0.99994170874838,
                0.9998601779092962,
                0.9999251537727589,
                0.9998766054104549,
                0.9998204720981319,
                0.9999724643056213,
                0.9999485577986323
            ],
            [
                0.9995694430144701,
                0.999195914239043,
                0.9980732655766603,
                0.9997040428661479,
                0.98756835162798,
                0.9994472213210779,
                0.9940889307278409,
                0.9995121428260144,
                0.9989677691664788,
                0.9997965729539883
            ],
            [
                0.999941708741432,
                0.9999485577924977,
                0.9999151889384297,
                0.9999646437577197,
                0.9999151889891112,
                0.9999417087483723,
                0.9998601779095057,
                0.999968798081195,
                0.9998601779093998,
                0.9998766054692634
            ],
            [
                0.9999251537995464,
                0.9999599363078145,
                0.9997040428657001,
                0.9998911030648404,
                0.9997388096596329,
                0.9998415637833893,
                0.9999646437619328,
                0.9997694932299439,
                0.9998204720125573,
                0.9997388096601193
            ],
            [
                0.9999038975965122,
                0.9998601778761356,
                0.9998911030517865,
                0.9999251537727529,
                0.9999251537370873,
                0.9998911030648656,
                0.9997388096601193,
                0.999925153737113,
                0.9999339478474795,
                0.9999417087483918
            ],
            [
                0.9998415637834425,
                0.9993736659701768,
                0.9999339478632303,
                0.9998415637268017,
                0.999876605425082,
                0.9999151889485385,
                0.999820472055543,
                0.99989110309081,
                0.9999485577679776,
                0.9999417087205921
            ],
            [
                0.9999852610197869,
                0.9999810748562741,
                0.9999687980737564,
                0.999985261016272,
                0.9999810748472489,
                0.9998204719697386,
                0.999981074847252,
                0.9999852610180304,
                0.9999599362982653,
                0.9999832985801492
            ],
            [
                0.9999785550515897,
                0.9999038975621809,
                0.999975699762166,
                0.9999599363125918,
                0.9999756997679633,
                0.9999546021205596,
                0.9999832985761661,
                0.999975699762166,
                0.9998766054398044,
                0.9999756997650636
            ],
            [
                0.9986749775407316,
                0.9993736658201027,
                0.9997694932298903,
                0.9996646499722618,
                0.9994472213866161,
                0.9999417087205921,
                0.9999038975506768,
                0.9999339478710885,
                0.9993736658208678,
                0.9999339478632105
            ],
            [
                0.9999810748427365,
                0.999860177959389,
                0.9999599362934934,
                0.9998601779425625,
                0.9999785550592593,
                0.9999756997534754,
                0.9999485577802313,
                0.9999687980886298,
                0.9999832985801483,
                0.9990889489812341
            ],
            [
                0.9998911030519014,
                0.999769493312555,
                0.9998911031167291,
                0.9997388095662711,
                0.9998204719698691,
                0.9998766054692957,
                0.9999038975392328,
                0.9998911030647897,
                0.999948557780225,
                0.99970404283018
            ],
            [
                0.9999038976194807,
                0.9996200155146319,
                0.9997040429007811,
                0.9999339478553327,
                0.9999485578047517,
                0.9999339478474795,
                0.9999417087345085,
                0.9999724643187533,
                0.9999646437450749,
                0.999975699762164
            ],
            [
                0.9998415638400323,
                0.9986749778703955,
                0.9988304897224335,
                0.9997388095973917,
                0.9997694931752275,
                0.9992903295370822,
                0.999860177909463,
                0.9997965730756625,
                0.9997965730508666,
                0.9998911030777808
            ]
        ]
    },
    {
        "q_id": "7894_mmlu_math",
        "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": [
            [
                0.9999832985801937,
                1.0129992185760567e-05,
                0.9999898700078189,
                0.9999810748562882,
                4.5397873923454754e-05,
                1.6701415868649062e-05,
                1.1478764017428212e-05,
                0.9999485577987738,
                0.9999724643155059,
                1.0129992186202796e-05
            ],
            [
                0.9988304897358964,
                0.9999339478555154,
                0.999959936317411,
                0.9999251537907886,
                0.9999251537554344,
                0.9997694932594148,
                0.9996646498166522,
                0.9995694430193551,
                0.9997965730048498,
                0.9993736657765269
            ],
            [
                2.753570417835288e-05,
                0.9997388096988394,
                3.535625486069523e-05,
                5.8291244568526206e-05,
                2.9023133687786197e-06,
                0.9999339478554703,
                1.4738980201465192e-05,
                1.0129989767363975e-05,
                1.892515048042999e-05,
                0.9993736657683655
            ],
            [
                4.539785226284666e-05,
                6.144175333401224e-06,
                2.1444956053317158e-05,
                4.222831933649433e-06,
                2.1444940692945607e-05,
                4.006367763255427e-05,
                6.144173134868593e-06,
                1.7603430033399058e-06,
                1.3007126908733257e-05,
                5.4222209070122355e-06
            ],
            [
                0.014063626139295524,
                0.00020342704432769888,
                4.539787380124449e-05,
                0.9994472214613196,
                0.02595735738617415,
                0.003172682752649986,
                2.7535681233968765e-05,
                7.484624497718912e-05,
                0.9997694933700817,
                0.0001398220732792939
            ],
            [
                0.9999724643188062,
                0.9999546021260848,
                0.9998766054430845,
                0.9999485577869023,
                0.9999038975761636,
                0.9999756997535163,
                0.9999417087068924,
                0.999941708741982,
                0.9999898700054173,
                0.999925153737382
            ],
            [
                0.999948557768061,
                1.0129993394129904e-05,
                0.9999810748540331,
                0.9999485577805037,
                0.9998911030398688,
                0.9998911030395091,
                0.9999038975624613,
                0.9999785550414335,
                0.9999810748585516,
                0.9999339478636321
            ],
            [
                7.889260700721204e-06,
                1.147876812069122e-05,
                8.93969736183366e-06,
                1.0129992183991656e-05,
                1.1478768120315386e-05,
                3.5356267531385634e-05,
                6.962253757485831e-06,
                3.535625064399255e-05,
                5.422220260044902e-06,
                1.8925154999337424e-05
            ],
            [
                3.535623798797096e-05,
                6.9622537587775775e-06,
                6.14417753110761e-06,
                1.0129995801637498e-05,
                6.144176065314267e-06,
                0.999903897597087,
                6.14417606300081e-06,
                0.9999646437451162,
                1.1478770856952364e-05,
                3.288749065125496e-06
            ],
            [
                4.22283344041987e-06,
                4.785095064044355e-06,
                1.0129995805359584e-05,
                2.902312330891746e-06,
                4.785095064601411e-06,
                6.1441753335241615e-06,
                5.422221552579112e-06,
                3.7266410609160796e-06,
                7.889263523238269e-06,
                8.939693104637921e-06
            ],
            [
                2.1444940632406306e-05,
                2.2603253591304477e-06,
                1.3007131554942966e-05,
                4.539786314219866e-05,
                1.473898899256772e-05,
                5.422218321855664e-06,
                1.0129993386593603e-05,
                1.8925141449434308e-05,
                1.4738988982594524e-05,
                8.939696291139872e-06
            ],
            [
                0.999988521235985,
                0.9999646437451394,
                0.9999546021152204,
                0.99997569974772,
                0.9999810748472895,
                0.9999687980812275,
                0.999988521226405,
                0.999948557761856,
                0.9999785550439516,
                0.9994472212741913
            ],
            [
                8.939696302457574e-06,
                0.9964063981505632,
                0.9984988177977064,
                0.18242552602881168,
                0.998967769098294,
                0.9996646498608599,
                0.9991959139920232,
                0.999195914024105,
                0.9999546021098393,
                6.144172401748879e-06
            ],
            [
                3.535624646549072e-05,
                4.5397857612020705e-05,
                2.753569434230981e-05,
                2.430023201636237e-05,
                1.8925145971093502e-05,
                1.6701415858775822e-05,
                4.222833946537913e-06,
                4.0063701703217896e-05,
                6.962253754763033e-06,
                0.1480471923932738
            ],
            [
                0.9990889488558262,
                0.99987660536762,
                0.9998601779266475,
                1.300712381094558e-05,
                0.9990889489399614,
                1.3007134663521234e-05,
                0.999876605470091,
                0.9995121429567474,
                0.9998415637097733,
                4.006369210969633e-05
            ],
            [
                5.1442238057176775e-05,
                0.00012339460299272932,
                7.889260703619978e-06,
                2.4300249374107374e-05,
                4.0063692068304736e-05,
                3.120191507481552e-05,
                4.785093923768848e-06,
                4.006368256747928e-05,
                4.222834450820197e-06,
                2.1444953516281788e-05
            ],
            [
                7.88926634305847e-06,
                8.939694171135975e-06,
                2.9023130229209922e-06,
                0.9998766054273532,
                1.3007130009313495e-05,
                7.88926446470893e-06,
                5.4222209064007344e-06,
                5.422219615286937e-06,
                0.9999151889287515,
                0.9995694429412714
            ],
            [
                4.006369679977145e-05,
                2.1444943216873018e-05,
                1.670142978217249e-05,
                1.3007123807302014e-05,
                4.539785744654147e-05,
                1.6701423811563878e-05,
                5.8291258356863845e-05,
                4.00636968073502e-05,
                1.0129995788923442e-05,
                6.962258737979408e-06
            ],
            [
                0.9992903296818475,
                0.4378234991142019,
                0.998299277475507,
                0.998967768741885,
                0.9996646497761912,
                0.9997694932947679,
                0.9980732656380006,
                0.9995121428163641,
                0.46879062662624377,
                0.9989677690302294
            ],
            [
                0.999988521231908,
                0.9999938558275997,
                0.9999251537908969,
                0.9999852610215486,
                0.9999687980924558,
                0.9999930377445836,
                0.9999687980812371,
                0.9999869928746761,
                0.999948557768088,
                0.9999724642959031
            ],
            [
                6.144176797998549e-06,
                1.4738976692993472e-05,
                4.222832436871463e-06,
                5.829128594669602e-05,
                7.88925976359915e-06,
                2.7535691071008866e-05,
                6.144174600325954e-06,
                3.7266410608245674e-06,
                1.147876812106705e-05,
                1.670141586150995e-05
            ],
            [
                2.4300234920177672e-05,
                3.120192619704807e-05,
                5.422218966071015e-06,
                2.1444940734059286e-05,
                1.6701415859504925e-05,
                1.670142382796865e-05,
                2.4300246507772637e-05,
                7.484624457532056e-05,
                3.5356238036718197e-05,
                5.8291279270086916e-05
            ],
            [
                3.28875024125221e-06,
                0.999948557804925,
                0.9999417087485908,
                0.9999852610145229,
                0.9999599363079494,
                2.1444943270937118e-05,
                6.144174601309452e-06,
                0.9999687980998393,
                4.2228324372555256e-06,
                0.9999417087347663
            ],
            [
                0.14804720367010532,
                0.24508502416032488,
                0.9998911030849982,
                0.13296423332632276,
                1.4738988989189704e-05,
                0.40733340004593027,
                0.22270013366638425,
                0.0002959570234685284,
                7.889264465067689e-06,
                0.06754668785475053
            ],
            [
                6.605212867704903e-05,
                0.999876605426829,
                2.7535681206621957e-05,
                1.67014178590634e-05,
                2.7535704202894907e-05,
                2.430023487960134e-05,
                0.9999251537906645,
                1.3007125359034903e-05,
                0.2450850021044189,
                2.7535704187167975e-05
            ],
            [
                1.473898195905257e-05,
                5.8291265499980624e-05,
                1.8925145971919677e-05,
                1.0129989765595064e-05,
                2.753570419988976e-05,
                7.484624340674342e-05,
                3.53562464244607e-05,
                0.06754669536304463,
                1.892514821904893e-05,
                4.5397890039027863e-05
            ],
            [
                0.9998911030526985,
                0.9999687980849942,
                0.9999417087346595,
                7.889259762106714e-06,
                0.999569442869325,
                0.9999885212305093,
                0.9999687980924301,
                0.9999417087276669,
                0.9999251537999471,
                0.9999724643122624
            ],
            [
                1.670142581574095e-05,
                7.889261639780667e-06,
                1.3007123801954964e-05,
                0.9999417087347396,
                4.222831933795376e-06,
                1.7603434229832599e-06,
                2.5612811556782268e-06,
                6.96225956837018e-06,
                4.785096775580942e-06,
                3.2887486731641103e-06
            ],
            [
                3.535625059357322e-05,
                6.962259567749634e-06,
                0.999738809787345,
                2.7535684510878145e-05,
                0.999769493313863,
                8.939696302652706e-06,
                0.9998415637668129,
                1.0129988550869138e-05,
                5.422217676575195e-06,
                0.999704042973578
            ],
            [
                5.144221969687863e-05,
                5.829126543170052e-05,
                1.473898020838208e-05,
                1.4738988995838502e-05,
                2.753568121974442e-05,
                1.4738978452886064e-05,
                2.4300232013798725e-05,
                9.610243700594259e-05,
                5.144222579863794e-05,
                4.0063711186267e-05
            ],
            [
                0.9999869928700105,
                0.999985261014532,
                0.9999785550413993,
                2.4300240681044865e-05,
                1.6701429800582296e-05,
                1.670142383015595e-05,
                7.889263522291142e-06,
                0.9999810748585959,
                3.535625486815523e-05,
                1.8925143719695944e-05
            ],
            [
                6.9622554173544636e-06,
                0.999985261016284,
                0.9999785550567367,
                0.9999417087207939,
                0.9999599363031813,
                8.939696301611998e-06,
                2.9023116388072315e-06,
                4.222835457280279e-06,
                2.14449560556576e-05,
                8.939695234463248e-06
            ],
            [
                4.222831932888989e-06,
                1.8925141447437712e-05,
                3.535624222962456e-05,
                1.6701421834728333e-05,
                3.726640172120768e-06,
                1.012999218369684e-05,
                0.9999852610233412,
                4.53978574584322e-05,
                1.6701427797619914e-05,
                2.430023781329673e-05
            ],
            [
                5.1442207399419876e-05,
                2.1444943264773968e-05,
                1.4738976692993472e-05,
                1.0129995805691255e-05,
                7.484624456551887e-05,
                6.605212873904136e-05,
                0.0002034268983932842,
                0.9997965731040691,
                2.7535697600689013e-05,
                0.29421497216298875
            ],
            [
                2.4300243616508983e-05,
                5.144221969687863e-05,
                0.9999852610110367,
                0.9999724643122159,
                1.4738976694494812e-05,
                2.753570419988976e-05,
                4.539788482626311e-05,
                0.999986992873094,
                2.7535700934898458e-05,
                1.6701425809239798e-05
            ],
            [
                0.999664649780972,
                0.9999339478476293,
                0.9998415637671125,
                0.9998204719973607,
                0.9999417087347396,
                0.9999687980999349,
                0.9998601779769866,
                0.9996646498589573,
                0.4073334000459302,
                0.9996646497422769
            ],
            [
                1.3007126910294786e-05,
                0.999964643757854,
                0.9999724643155059,
                1.0129994600398803e-05,
                5.422218322457301e-06,
                2.7535687797204028e-05,
                8.93969841372978e-06,
                2.4300249362084747e-05,
                4.785093353100252e-06,
                0.9999852610215486
            ],
            [
                6.962257904663309e-06,
                7.889264465239894e-06,
                7.484624481164976e-05,
                4.785095634843714e-06,
                3.7266379509129646e-06,
                6.962255416759247e-06,
                8.939698432917844e-06,
                1.0129990973871981e-05,
                NaN,
                4.5397873629819826e-05
            ],
            [
                0.9993736657937604,
                0.5312093733737563,
                0.9991959141684258,
                0.999968798081359,
                0.9997388096963772,
                0.9998911031039929,
                0.9997965730545069,
                0.9997388096933677,
                0.9997388097899897,
                0.9998601779439805
            ],
            [
                4.785093923603471e-06,
                7.889259762666377e-06,
                7.88926257539615e-06,
                4.222835457526079e-06,
                0.9999038976196115,
                5.422220261849814e-06,
                0.9998766054261036,
                1.6701425815072606e-05,
                1.4738983710366698e-05,
                2.144494073569759e-05
            ],
            [
                2.7535687797204028e-05,
                0.9999646437369003,
                0.9999646437620782,
                6.144172403592939e-06,
                1.30071253611406e-05,
                2.7535697630940815e-05,
                3.1201907620154606e-05,
                0.9999687980998543,
                3.120192249167993e-05,
                0.9999687980998543
            ],
            [
                1.0129990977004428e-05,
                6.962253756687988e-06,
                5.829129312544061e-05,
                8.939694169330997e-06,
                8.93969310418261e-06,
                2.1444940727740105e-05,
                4.5397863124032274e-05,
                2.1444953513707305e-05,
                5.422217029844958e-06,
                1.8925141468298646e-05
            ],
            [
                1.1478773596283455e-05,
                3.288750241204353e-06,
                1.3007123806876143e-05,
                1.473898372500477e-05,
                1.892515500450102e-05,
                6.144173134164498e-06,
                1.012998856078241e-05,
                3.2887502413389517e-06,
                3.7266388388875246e-06,
                8.939696300376156e-06
            ],
            [
                2.4300246497960055e-05,
                3.120190009761751e-05,
                1.3007130010117919e-05,
                3.5356237965848203e-05,
                3.12019150568812e-05,
                5.144219514537961e-05,
                2.7535694350223355e-05,
                7.484620930782328e-05,
                0.9998601779604551,
                3.5356250658398075e-05
            ],
            [
                6.962258715855074e-06,
                0.9994472212652834,
                0.06754668456987209,
                NaN,
                0.9986749775866381,
                0.03732689055684297,
                1.892514595147183e-05,
                4.222832940777184e-06,
                0.9993736659089303,
                0.16451645880021026
            ],
            [
                1.4738983718463215e-05,
                1.1478772225271098e-05,
                1.1478768119146135e-05,
                1.473898899256772e-05,
                1.8925148215055747e-05,
                3.535624222962456e-05,
                1.4738983716586539e-05,
                3.1201922481918207e-05,
                1.892514823488397e-05,
                1.0129993386188227e-05
            ],
            [
                0.9999646437494065,
                1.8925148220012804e-05,
                4.006368732517898e-05,
                1.4738985481520185e-05,
                1.8925143710057227e-05,
                1.47389854563191e-05,
                3.1201922481918207e-05,
                3.726637950411341e-06,
                0.9999546021305061,
                6.144176798255599e-06
            ],
            [
                0.9999852610145515,
                0.9999724643090657,
                0.9999546021152625,
                0.9995121429063957,
                0.9999417087556024,
                0.9996646500153766,
                0.999954602115292,
                0.6224593312018546,
                0.3775406687981454,
                0.9999785550464971
            ],
            [
                0.9999151889291749,
                0.9999756997680357,
                0.9999832985801913,
                0.999978555056734,
                0.9999599363176382,
                0.9999869928653431,
                0.9999810748586022,
                0.9999852610180979,
                0.9999151889616775,
                0.9999810748495402
            ],
            [
                0.9999869928700097,
                0.9996646499777353,
                0.9999251537910755,
                0.9998415637654412,
                0.9999852610198027,
                0.9999038975401997,
                0.9999546021369318,
                0.9999417087346655,
                0.9999945777810432,
                0.9999599363174296
            ],
            [
                1.670142581762446e-05,
                1.0129990975862006e-05,
                1.892515500450102e-05,
                1.1478768117893363e-05,
                2.7535704065559712e-05,
                1.6701429803316423e-05,
                5.422220905887864e-06,
                5.422219614438727e-06,
                5.14422074125194e-05,
                1.4738988994498018e-05
            ],
            [
                7.88926446430712e-06,
                0.9999756997622469,
                6.1441753319483296e-06,
                7.889259762106714e-06,
                8.93970056424046e-06,
                7.88926446470893e-06,
                5.144221351278017e-05,
                0.00013982212147817588,
                0.9999756997593239,
                0.9999832985781947
            ],
            [
                1.8925143721072897e-05,
                5.829125842132705e-05,
                7.889261643727018e-06,
                4.539785778179383e-05,
                1.892515726099468e-05,
                2.753569107251144e-05,
                0.00012339458893469933,
                5.8291265491498626e-05,
                7.889262584809997e-06,
                2.7535704212311033e-05
            ],
            [
                0.9998204719797399,
                3.1201903900940664e-05,
                0.9999251537818837,
                0.9999038975858079,
                1.6701423812475255e-05,
                0.9999038975966262,
                0.29421497216298875,
                0.9998415638214826,
                2.75356812012127e-05,
                3.535624646549072e-05
            ],
            [
                6.9622570784012604e-06,
                0.9991959139929119,
                0.9992903296787514,
                6.144175332887123e-06,
                0.9996646500210647,
                6.9622579086271995e-06,
                0.9992903295471129,
                0.9998601778615834,
                0.9990889488249907,
                0.00029595722103785974
            ],
            [
                1.670142182755884e-05,
                5.422218967649081e-06,
                2.144494057233509e-05,
                3.120190759915557e-05,
                1.4738983712565087e-05,
                3.7266383556143174e-06,
                1.6701425802374098e-05,
                1.1478766745190422e-05,
                2.4300237810821485e-05,
                3.535625065376772e-05
            ],
            [
                0.9997388097883102,
                0.999769493316539,
                1.3007130013288297e-05,
                0.9995694429158196,
                0.9989677691674391,
                2.753569097394268e-05,
                0.9998766054129289,
                0.9989677687578508,
                0.9994472213536219,
                7.88926258185382e-06
            ],
            [
                0.9999724642958978,
                0.9999599363223587,
                2.4300246493981982e-05,
                1.1478765380380096e-05,
                0.9999339478715931,
                0.9999832985821696,
                1.0129993388915298e-05,
                7.889264463675704e-06,
                8.939699497855469e-06,
                0.9999785550465643
            ],
            [
                1.3007126900026555e-05,
                2.1444940715959902e-05,
                0.9999910603005258,
                4.0063701635592195e-05,
                1.8925154997134284e-05,
                6.144176797115634e-06,
                2.430024072091399e-05,
                4.785092782936557e-06,
                6.1441753335241615e-06,
                4.785093353274332e-06
            ],
            [
                1.670141784666869e-05,
                6.144177531208195e-06,
                1.892515048889829e-05,
                4.539786295326824e-05,
                8.939699500164542e-06,
                2.1444948401176257e-05,
                0.9998766054557134,
                2.14449586130551e-05,
                2.1444943229667413e-05,
                0.9999687980812332
            ],
            [
                2.4300246430156e-05,
                2.2603249499541457e-06,
                6.144174600325954e-06,
                1.6701425819447213e-05,
                0.9999756997593239,
                0.9999151889694595,
                1.14787667504103e-05,
                8.93969310367852e-06,
                1.6701425808449937e-05,
                0.9998766054123543
            ],
            [
                8.939698433974813e-06,
                4.22283193338827e-06,
                8.93969630089651e-06,
                5.422217676101776e-06,
                6.144175333021237e-06,
                5.422217029844958e-06,
                6.144177530146464e-06,
                1.8925143714394646e-05,
                0.9999646437536464,
                4.785094493932679e-06
            ],
            [
                6.962258729962979e-06,
                4.785095634930755e-06,
                0.9999687980923798,
                0.9999852610215536,
                0.9999339478792247,
                0.9992903295800949,
                1.8925154923880002e-05,
                0.0010322311596793377,
                3.7266392829528392e-06,
                5.4222215541571775e-06
            ],
            [
                0.9990889488010959,
                0.999704043008366,
                0.9998204720996102,
                0.9999339478712095,
                0.9994472214667542,
                0.9999646437451921,
                0.999841563821342,
                0.999948557768173,
                0.9997965730766746,
                1.0129987353537646e-05
            ],
            [
                1.8925150472994405e-05,
                1.670142176594982e-05,
                4.539786853134004e-05,
                3.5356263286899354e-05,
                3.120192247170245e-05,
                9.610240282771945e-05,
                4.0063682527545155e-05,
                2.4300234891270352e-05,
                7.889259760542522e-06,
                0.00012339457242414658
            ],
            [
                2.2603240283888175e-06,
                6.962258738435319e-06,
                2.2603253754284284e-06,
                1.9947290080343035e-06,
                1.1478772227964558e-05,
                1.4738987226400411e-05,
                1.7603432132464244e-06,
                7.889265402907818e-06,
                1.3007123803043302e-05,
                0.9980732649202757
            ],
            [
                0.9998766053811916,
                0.999820472082977,
                0.9999756997651188,
                1.1478770854906172e-05,
                0.9997388096358155,
                0.9999785550439367,
                0.9999151889892229,
                0.9999646437577571,
                0.999954602121018,
                1.3007133100619938e-05
            ],
            [
                6.144173135762683e-06,
                2.9023109468548636e-06,
                3.2887478888496478e-06,
                1.3007125355533295e-05,
                4.78509563509613e-06,
                2.902312676941983e-06,
                1.0129994600638342e-05,
                8.939698433974813e-06,
                4.539786282709443e-05,
                6.962255413795828e-06
            ],
            [
                7.88926446470893e-06,
                2.4300232027942982e-05,
                1.3007130008887624e-05,
                4.006369677995013e-05,
                1.670142975094265e-05,
                8.939698434332555e-06,
                2.144495594167824e-05,
                3.120190756487605e-05,
                2.753570415270896e-05,
                2.4300237781295346e-05
            ],
            [
                3.120190017639228e-05,
                2.1444956072586775e-05,
                4.22283294007051e-06,
                3.1201907620154606e-05,
                2.430024939965545e-05,
                6.962254588281262e-06,
                2.7535700923478902e-05,
                2.4300249381886717e-05,
                2.7535687803514833e-05,
                4.222831933795376e-06
            ],
            [
                0.9998601779283259,
                0.679178699175393,
                5.829129319244845e-05,
                0.9999339478714133,
                0.9999785550490502,
                4.539786311280214e-05,
                0.22270012850745968,
                0.99973880966303,
                0.9988304894904351,
                0.9999945777803896
            ],
            [
                2.1444940722669156e-05,
                2.753568117757223e-05,
                0.999876605469714,
                6.962255419051463e-06,
                0.9999921107392996,
                5.829129303765185e-05,
                0.9999832985702116,
                0.999964643753547,
                6.144173457780155e-06,
                0.9999852610197921
            ],
            [
                6.144173136455602e-06,
                1.1478769489719528e-05,
                0.9999646437367795,
                1.6701425818232042e-05,
                2.4300249394528152e-05,
                1.0129993392342568e-05,
                1.6701423823533284e-05,
                8.939700562695657e-06,
                1.6701421840318107e-05,
                1.012999460150437e-05
            ],
            [
                2.9023116384112864e-06,
                0.9999885212277838,
                0.9998204720832016,
                0.999925153755477,
                0.9995694429777454,
                0.9999339478319458,
                0.9998766053825165,
                0.999664649830858,
                0.904650527388829,
                0.999968798092387
            ],
            [
                2.2603242977308917e-06,
                0.9953904268228312,
                0.9995694429222577,
                6.962257077413455e-06,
                6.144176797730321e-06,
                0.9982992772270566,
                0.9953904281859852,
                0.9993736659222653,
                0.9964063981889131,
                0.9993736658638607
            ],
            [
                8.939693103158165e-06,
                2.4300243694479212e-05,
                0.003593603109982145,
                2.430023202476052e-05,
                4.222835457794923e-06,
                1.8925141455974863e-05,
                1.3007125352457558e-05,
                2.4300231905241586e-05,
                1.4738980199481274e-05,
                7.889265404959923e-06
            ],
            [
                0.9999974387187065,
                0.9999785550593026,
                0.9999885212291499,
                0.9999724643023645,
                0.9999898700102803,
                0.9999546021476384,
                0.9999885212305261,
                0.9996646500158742,
                0.999985261018038,
                0.9999967112517207
            ],
            [
                0.0010322309127499248,
                1.670142978022822e-05,
                4.539786843885661e-05,
                1.4738978450419574e-05,
                0.0005527785216687472,
                1.4738980202752053e-05,
                1.1478766745190422e-05,
                1.3007130005527972e-05,
                1.3007133103695677e-05,
                4.006371118306061e-05
            ],
            [
                7.48462179518055e-05,
                1.6701429787579988e-05,
                0.9990889489395374,
                0.2450850131323717,
                0.9989677687903826,
                8.939699499627926e-06,
                0.9991959141204904,
                5.422220904724041e-06,
                0.9993736657147338,
                0.9991959140482364
            ],
            [
                3.535625900948665e-05,
                1.1478765375285496e-05,
                4.006369682950345e-05,
                2.430024650998268e-05,
                4.222832938511214e-06,
                0.9999756997680261,
                7.484620922668724e-05,
                0.9999852610180373,
                2.1444950951785568e-05,
                2.753570085726551e-05
            ],
            [
                1.6701421836551084e-05,
                6.962253758182361e-06,
                1.8925143715220825e-05,
                8.939697366289195e-06,
                1.1478772223224906e-05,
                6.9622595668378125e-06,
                4.006370638746435e-05,
                1.4738981965326028e-05,
                5.4222202621161125e-06,
                1.8925141467059383e-05
            ],
            [
                0.9999962733589493,
                0.9999982396561583,
                0.9999952149066484,
                0.9999938558254122,
                0.9999910603068974,
                0.9999967112493685,
                0.9999977396754335,
                0.9999967112493678,
                0.9999898700078329,
                0.9999974387187099
            ],
            [
                5.144221349406656e-05,
                1.0129989747500578e-05,
                2.1444955958061307e-05,
                1.3007131561047124e-05,
                9.610240308920897e-05,
                3.7266406155693803e-06,
                2.144494327788042e-05,
                2.7535694293025422e-05,
                1.3007134655335035e-05,
                3.120191506868607e-05
            ],
            [
                0.9998911030661191,
                0.9997388095798441,
                0.9998911031174278,
                0.999903897609521,
                0.9995121429606358,
                0.9999546021478428,
                0.9996200155032012,
                0.9993736658043993,
                0.9997694933202012,
                0.9992903295993721
            ],
            [
                1.4738987240475486e-05,
                3.120191504757351e-05,
                2.144494583831896e-05,
                4.006369693006752e-05,
                4.5397890221682726e-05,
                1.0129990975567187e-05,
                1.3007125357378736e-05,
                1.473897845240349e-05,
                1.1478772226690907e-05,
                8.481101083448713e-05
            ],
            [
                1.3007128446602034e-05,
                6.962255418367598e-06,
                1.0129995802042874e-05,
                4.222834450328596e-06,
                9.610241448987261e-05,
                6.144175333837093e-06,
                4.0063677765182186e-05,
                0.9999546021155609,
                3.535626332111248e-05,
                1.4738987235622935e-05
            ],
            [
                6.9622545872301346e-06,
                8.939694164159978e-06,
                1.0129990975862006e-05,
                6.962257908753841e-06,
                1.4738985472887472e-05,
                2.1444943281001e-05,
                6.962257907702715e-06,
                6.144176065940129e-06,
                2.7535697602692443e-05,
                1.1478773582022739e-05
            ],
            [
                0.9999852610180443,
                2.144494581132591e-05,
                0.9999885212346163,
                1.3007128446602034e-05,
                2.144494329348333e-05,
                8.939697365736316e-06,
                5.422220908018252e-06,
                4.785096775580942e-06,
                3.726641059804374e-06,
                0.9999898700078178
            ],
            [
                6.962254586166343e-06,
                7.889261641416608e-06,
                1.6701423823533284e-05,
                0.9999756997477791,
                1.6701415858775822e-05,
                2.144495350169305e-05,
                1.6701419838268058e-05,
                1.3007131557498195e-05,
                6.962254587420098e-06,
                0.9999810748563078
            ],
            [
                0.0001584362336597708,
                1.8925154984741643e-05,
                1.1478770856952364e-05,
                4.0063677627890424e-05,
                2.430023202246208e-05,
                4.006368257301759e-05,
                1.670141785596473e-05,
                2.144494838924002e-05,
                1.1478773596575768e-05,
                2.4300234912928744e-05
            ],
            [
                8.48110810406911e-05,
                0.9999151889801439,
                8.939696302051047e-06,
                3.120190761300358e-05,
                0.9999810748427871,
                0.9999832985781849,
                1.0129987350552609e-05,
                4.006371115915841e-05,
                1.1478766755233466e-05,
                0.9999756997478639
            ],
            [
                5.8291272333081096e-05,
                0.9999687981001126,
                0.9998911030804792,
                1.1478765385432939e-05,
                7.889265403166124e-06,
                1.3007134659451795e-05,
                3.726637950723161e-06,
                2.14449432697669e-05,
                6.962253759043525e-06,
                0.9998601778931084
            ],
            [
                0.9999810748562882,
                0.9999724643155298,
                0.9999869928699966,
                5.829127156885272e-05,
                1.4738987173853463e-05,
                4.006370165453905e-05,
                1.6701421835335913e-05,
                0.9999852610162822,
                4.539787939913551e-05,
                0.9999910603015678
            ],
            [
                1.0129995807939249e-05,
                2.561283126502453e-06,
                1.3007131561047124e-05,
                0.9999724643023973,
                1.1478772224477678e-05,
                0.999941708734919,
                0.999975699762253,
                1.30071346612026e-05,
                4.785095635413826e-06,
                6.962257908487893e-06
            ],
            [
                0.9995121427881514,
                0.9990889487411734,
                0.14804719803168945,
                0.9994472212701071,
                0.010986944998665251,
                0.999195914163983,
                0.9998911030522754,
                1.0129995796478171e-05,
                0.4378234991142019,
                0.03732688975366457
            ],
            [
                0.9999251537561935,
                0.997817283431431,
                0.9999885212277895,
                7.88926258381982e-06,
                0.9999646437325374,
                0.9999599363175299,
                2.5612834318257725e-06,
                0.9999785550567353,
                0.9992903297438483,
                0.9999646437535832
            ],
            [
                8.939695236593446e-06,
                2.9023119850527192e-06,
                0.9994472213928549,
                0.9999485577986458,
                0.9999251537728575,
                0.9996646499331374,
                0.999290329729731,
                0.999925153799579,
                0.9999339478711851,
                5.422217029943586e-06
            ],
            [
                0.9964063965823846,
                0.9995694430000659,
                0.9994472214901976,
                0.34864514886966624,
                0.9971990724293867,
                0.9982992774454637,
                0.004070138006585215,
                0.9998911031185242,
                0.999195913924212,
                0.9988304897781892
            ],
            [
                8.939695236398313e-06,
                1.892515047774492e-05,
                0.9999687980924876,
                1.3007126899411407e-05,
                2.7535687790192025e-05,
                1.4738981962698681e-05,
                0.999738809634744,
                8.939694171331106e-06,
                6.144174598191315e-06,
                2.144494073796001e-05
            ],
            [
                1.1478770859332632e-05,
                2.1444945829581326e-05,
                5.422218153209867e-06,
                3.1201922480102066e-05,
                4.222834954514924e-06,
                1.012999339031569e-05,
                1.6701415864001047e-05,
                2.1444945828411102e-05,
                1.0129995807441742e-05,
                1.8925157247225074e-05
            ],
            [
                2.753570091766895e-05,
                1.3007133113703658e-05,
                5.422218322664422e-06,
                3.1201900178208404e-05,
                3.5356250658398075e-05,
                1.6701423831188846e-05,
                7.88926352407059e-06,
                2.5612815990734206e-06,
                1.4738976695459959e-05,
                1.3007134661628471e-05
            ],
            [
                4.539785207127391e-05,
                0.999993037741262,
                6.962256246035174e-06,
                4.222832940777184e-06,
                0.9999599362937874,
                6.144176065940129e-06,
                7.889265405505236e-06,
                3.7266379491640618e-06,
                8.939698432446272e-06,
                0.9998911031180712
            ],
            [
                0.9999251537817438,
                6.144173868558375e-06,
                0.999876605367261,
                0.9992903294885381,
                0.9999646437451097,
                0.999986992874646,
                0.9999885212277806,
                0.9993736658386114,
                0.9999251537460603,
                0.9998204720349343
            ],
            [
                0.9999038975742074,
                2.4300237810821485e-05,
                1.8925152736303473e-05,
                3.1201926195004916e-05,
                1.6701429783995243e-05,
                2.7535695217608515e-05,
                4.785093923420688e-06,
                5.422219615069953e-06,
                1.0129987350921133e-05,
                6.144172314776347e-06
            ],
            [
                8.939700563248534e-06,
                1.3007130005527972e-05,
                2.1444950953735936e-05,
                6.144172404302622e-06,
                1.0129990975862006e-05,
                1.3007126908307386e-05,
                7.484620014653187e-05,
                1.67014178554179e-05,
                8.939696300636336e-06,
                1.4738987241494252e-05
            ],
            [
                1.0129990977262395e-05,
                0.9999810748472692,
                0.9999485577987319,
                1.1478764015361142e-05,
                0.9999724643189699,
                0.9999756997476992,
                0.9999599363032666,
                1.3007128457485415e-05,
                1.4738988988010078e-05,
                0.9999832985741933
            ],
            [
                0.2942149659744614,
                0.9999038975509013,
                8.93969736654937e-06,
                2.144494839142443e-05,
                7.889264464508026e-06,
                0.999903897623875,
                1.4738988990959142e-05,
                1.3007133108948093e-05,
                3.535626333809042e-05,
                0.9999339478492882
            ],
            [
                1.3007125352978066e-05,
                1.0129987355343409e-05,
                3.5356250658398075e-05,
                2.4300249397180202e-05,
                1.0129994576702751e-05,
                4.785093923768848e-06,
                3.120191506868607e-05,
                0.9998601779597145,
                1.89251527371985e-05,
                6.9622562484666964e-06
            ],
            [
                0.998498818002742,
                8.939699497335115e-06,
                0.9998415637457642,
                0.9996646500226064,
                3.2887482810382622e-06,
                3.726640615664282e-06,
                0.9998415637470481,
                4.006370169593065e-05,
                0.9999724643057286,
                5.829127049248668e-05
            ],
            [
                2.7535687793096995e-05,
                0.998498817439636,
                0.9982992779832786,
                0.9975273763822192,
                0.9994472213395045,
                0.9997388095993296,
                1.3007131556504496e-05,
                0.9997388095750563,
                0.9995694429720839,
                0.9999038975739403
            ],
            [
                0.9995121429872309,
                0.9999546021207254,
                0.9999038975398473,
                0.9999756997650924,
                0.9999810748450078,
                0.9999852610180633,
                0.99996464375782,
                0.9998204719702453,
                0.9999417087488541,
                0.9999898700126449
            ],
            [
                1.0129993386593603e-05,
                4.785096203588998e-06,
                1.670142181698688e-05,
                2.561281904708706e-06,
                4.0063701700885974e-05,
                6.144173134343315e-06,
                0.9999869928715471,
                4.222833947029514e-06,
                8.939698432690187e-06,
                7.8892607025437e-06
            ],
            [
                0.0229773705372549,
                0.9992903295033573,
                0.9997040429444644,
                7.8892607025437e-06,
                0.9995121428218705,
                0.999447221411185,
                0.9996646499427185,
                0.22270012850745968,
                6.962257907158154e-06,
                1.0129994597524319e-05
            ],
            [
                9.61024419896269e-05,
                1.8925150467761954e-05,
                3.535625906762324e-05,
                6.1441738667590205e-06,
                0.004070138520010149,
                6.605214437024256e-05,
                7.484621809175153e-05,
                0.9975273772120522,
                1.8925150410480426e-05,
                1.670142976734743e-05
            ],
            [
                0.9997965730314748,
                1.0129987353242826e-05,
                2.4300243613326524e-05,
                2.4300237812059105e-05,
                3.120191507027519e-05,
                4.00636873566599e-05,
                0.9999852610198201,
                4.5397890221682726e-05,
                3.120190009761751e-05,
                1.1478765382092217e-05
            ],
            [
                0.999447221425817,
                0.999290329503894,
                0.9991959139109772,
                0.9999339478318714,
                0.24508501313237172,
                0.9993736658041807,
                0.9995694428744355,
                0.9999251538038525,
                0.9997694932066167,
                0.9959298619764264
            ],
            [
                1.3007125360478133e-05,
                0.999903897573785,
                0.9998911030914217,
                0.9933071504564162,
                0.9998766054558984,
                0.9997040430159867,
                0.9998911030539422,
                0.9994472214661112,
                0.9995694429774199,
                0.9997965730295097
            ],
            [
                0.9994472213634623,
                3.1201907623673364e-05,
                1.1478765380380096e-05,
                6.144174596559601e-06,
                1.670142580759932e-05,
                1.8925143714394646e-05,
                0.10669059465574898,
                0.03308598101059529,
                0.6224593312018546,
                1.3007126905042372e-05
            ],
            [
                0.9999885212264108,
                0.9999646437496246,
                0.9999885212277845,
                0.9999485578050175,
                0.9953904275941458,
                0.99990389758532,
                0.9999930377454131,
                0.9996200153961685,
                0.9996646499400647,
                0.9999869928684942
            ],
            [
                0.9999724643122099,
                0.9991959139485306,
                0.9984988180636417,
                0.998498817946728,
                0.9998766054698289,
                0.9997694932383681,
                0.9988304898120507,
                0.9998204719526795,
                6.144172403827636e-06,
                0.9999151889794664
            ],
            [
                0.9999038975511627,
                0.9999485577926672,
                0.9989677690885705,
                0.9998911031043828,
                0.0017007227134497413,
                0.9990889489248085,
                0.9991959141169829,
                0.99990389755182,
                0.9875683494212288,
                1.3007133105966991e-05
            ],
            [
                0.9984988174731396,
                0.9993736658462627,
                3.535626748276697e-05,
                0.9994472214089983,
                0.9975273763563767,
                0.9986749777847445,
                0.9986749776376281,
                0.9978172831631782,
                0.9991959142025185,
                0.9994472212649619
            ],
            [
                4.22283394762097e-06,
                0.9986749777000178,
                7.889261642134126e-06,
                1.3709573702248741e-06,
                6.144177529855884e-06,
                0.9990889487614125,
                0.9997040429383162,
                6.605212857805352e-05,
                0.9998415637275854,
                0.9991959141366248
            ],
            [
                1.3007134654199377e-05,
                7.889259762106714e-06,
                2.1444945836212564e-05,
                8.939700561817559e-06,
                3.120192622315499e-05,
                2.144494328950459e-05,
                2.430024939965545e-05,
                1.012999338780973e-05,
                0.00010889694730159487,
                4.539785231965789e-05
            ],
            [
                0.9998415638410236,
                0.9997040430187681,
                0.9999151889797132,
                0.9998766054109289,
                1.3007133106487501e-05,
                0.9999724643023589,
                0.9989677691301057,
                7.889263522291142e-06,
                0.9997388097550692,
                0.9996200154041058
            ],
            [
                0.9999339478555707,
                0.9999485577988247,
                6.144176797585032e-06,
                3.1201900190126774e-05,
                1.3007131561047124e-05,
                2.43002523073625e-05,
                1.8925145971093502e-05,
                0.999985261021573,
                0.9999417087346145,
                7.889260701697028e-06
            ],
            [
                1.1478769489009626e-05,
                0.9997694933714633,
                1.1478772219424831e-05,
                4.2228349539810764e-06,
                0.9996200154800192,
                0.9994472212771819,
                4.222835457526079e-06,
                2.753569434230981e-05,
                3.726637950851956e-06,
                2.1444948365991674e-05
            ],
            [
                3.120191503962793e-05,
                0.005911068385602728,
                3.120190017276001e-05,
                1.670141785651155e-05,
                7.484620881011638e-05,
                4.785092638781052e-06,
                8.481101074748604e-05,
                0.0009110513839697094,
                8.481102078408009e-05,
                3.5356246408511744e-05
            ]
        ]
    },
    {
        "q_id": "8085_mmlu_math",
        "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,
            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,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                3.5356267537559426e-05,
                1.1478765388105516e-05,
                1.6701423829669885e-05,
                2.902312676941983e-06,
                6.144173136556186e-06,
                2.9023116390421582e-06,
                2.5612825159421147e-06,
                1.1478773597390071e-05,
                3.2887478890769702e-06,
                1.3007125360809367e-05
            ],
            [
                7.484626282603639e-05,
                1.670142781560441e-05,
                1.3007130012980722e-05,
                4.785094494185095e-06,
                1.1478770860982112e-05,
                1.3007130003871806e-05,
                5.422218969029887e-06,
                2.7535704220525098e-05,
                1.553497198908852e-06,
                4.006367782348017e-05
            ],
            [
                0.0021827166912857902,
                0.9994472214591328,
                0.9997388096923874,
                0.9999599362936694,
                0.9999724643089319,
                0.9997040428683696,
                0.9999646437450925,
                0.9999251537728232,
                0.9859363722206809,
                0.9999869928681341
            ],
            [
                9.422442569097361e-07,
                2.9023126766305067e-06,
                1.9947297213492663e-06,
                2.260323489435463e-06,
                4.7850933534310035e-06,
                3.7266392836984955e-06,
                1.0677032518093368e-06,
                3.2887486729876365e-06,
                1.4738981968060613e-05,
                8.939698434153684e-06
            ],
            [
                1.4738980207363312e-05,
                2.2603248364644736e-06,
                0.999933947823931,
                2.7535691075316245e-05,
                6.962257079173776e-06,
                2.9023116389365734e-06,
                0.9996646497344911,
                0.9999546021422212,
                6.962257908196617e-06,
                0.9999952149032237
            ],
            [
                6.144176064364297e-06,
                2.260325375572331e-06,
                0.999997097688361,
                5.42222090821551e-06,
                1.0129994601301684e-05,
                0.9999417087067168,
                1.9947290081177566e-06,
                6.1441746016670885e-06,
                1.4738987241494252e-05,
                3.53562421293004e-05
            ],
            [
                1.0129992182112188e-05,
                3.7266388397721442e-06,
                4.222833444283541e-06,
                5.422217030495909e-06,
                2.260325375615501e-06,
                2.5612831265909735e-06,
                1.1478764018012839e-05,
                1.3007133111929193e-05,
                2.1444940737257882e-05,
                3.2887498494282754e-06
            ],
            [
                1.4738988997768797e-05,
                4.0063696945516495e-05,
                8.939697367703906e-06,
                5.422217030032353e-06,
                8.93969417167259e-06,
                2.260324566939374e-06,
                5.1442238144007945e-05,
                5.422220908018252e-06,
                5.422217030032353e-06,
                2.430023783150746e-05
            ],
            [
                6.144177531532303e-06,
                1.2098661161789477e-06,
                6.144175334015912e-06,
                4.78509563546605e-06,
                1.3709576971242028e-06,
                2.260323489490968e-06,
                2.561283431888668e-06,
                4.785096776133645e-06,
                3.726641060956752e-06,
                1.994729483666479e-06
            ],
            [
                0.9999038975850291,
                0.9999810748427375,
                0.9999980052710093,
                0.9999756997593695,
                0.9999921107336528,
                0.9999885212264156,
                0.9999546021105059,
                0.4378234991142019,
                0.9999687980774995,
                0.9995694428698261
            ],
            [
                4.22283344433731e-06,
                3.28874906467085e-06,
                7.889264465397747e-06,
                7.889262585082652e-06,
                1.3007125357804606e-05,
                2.902312676398219e-06,
                4.539787400668985e-05,
                6.962259568775433e-06,
                1.6701423825538316e-05,
                1.0129990977520359e-05
            ],
            [
                1.892515500663531e-05,
                2.753570421481532e-05,
                4.785092781709294e-06,
                1.6701421834059987e-05,
                1.89251527491092e-05,
                1.1478769489719528e-05,
                5.8291279365509446e-05,
                2.1444950959196957e-05,
                8.93969630348202e-06,
                1.3007128460797749e-05
            ],
            [
                0.9999339478636666,
                0.5621765008857982,
                0.9999832985821496,
                0.9999646437366749,
                0.9999724643056384,
                0.9999898700102293,
                0.46879062662624377,
                0.7981867753392728,
                0.9999970976887068,
                0.9999898700066064
            ],
            [
                0.9999945777810328,
                0.999948557774109,
                0.9999417087554264,
                0.9999987901338839,
                0.9998415637078139,
                0.9998766054108176,
                0.999925153772803,
                0.9999869928653401,
                0.9999038976081129,
                0.9998204720559609
            ],
            [
                0.9999417087484445,
                0.999738809723432,
                0.9999724643154813,
                0.9999599363030699,
                0.9999785550592593,
                0.9999885212305084,
                0.9999938558275958,
                0.9999785550413688,
                0.9999962733593835,
                0.9999546021259818
            ],
            [
                0.7057850154599563,
                0.9999417087414828,
                2.7535697629338066e-05,
                0.9999810748472732,
                0.9999599363030484,
                0.320821300824607,
                0.999968798081195,
                7.338208930355202e-07,
                0.1329642436335826,
                0.0031726823012649466
            ],
            [
                1.473897845457507e-05,
                5.422217029844958e-06,
                6.144172403335888e-06,
                7.889261644501938e-06,
                6.144174601208867e-06,
                2.1444945849006956e-05,
                8.939698433584547e-06,
                1.892514371900746e-05,
                1.1478769492893215e-05,
                1.670141785809127e-05
            ],
            [
                1.3709575336405514e-06,
                8.939698434332555e-06,
                8.315279285149107e-07,
                1.3709578605455302e-06,
                6.14417606031854e-06,
                4.222835457364773e-06,
                6.962255418924822e-06,
                1.994729483680993e-06,
                1.4738983715996728e-05,
                3.2887482807780376e-06
            ],
            [
                5.4222202621161125e-06,
                5.42221767672807e-06,
                2.430024651705481e-05,
                0.00012339454465460842,
                6.144173135896795e-06,
                1.0129994600159262e-05,
                3.5356267541418054e-05,
                3.120191877428034e-05,
                4.222833947674739e-06,
                1.0129987355564522e-05
            ],
            [
                5.422217676654099e-06,
                2.9023109465275493e-06,
                4.22283193393364e-06,
                6.144176064856046e-06,
                1.3007125359792008e-05,
                1.6701427813417103e-05,
                1.6701423825538316e-05,
                1.0129990976156825e-05,
                2.7535684457586915e-05,
                2.5612831264675113e-06
            ],
            [
                0.9999646437603207,
                0.46879062662624377,
                0.9998415637651945,
                0.9999756997679633,
                0.999981074845043,
                0.9999251537995992,
                0.9999756997477506,
                0.9999945777803845,
                0.9465966730249561,
                0.5
            ],
            [
                0.9999724643023399,
                0.9999546021097657,
                0.9999885212277702,
                0.9999756997566026,
                0.9999724643155059,
                0.999903897573855,
                0.9999546021422393,
                0.9999852610180368,
                0.9999485577679982,
                0.999891103039235
            ],
            [
                1.0677026154055912e-06,
                2.26032537546132e-06,
                1.370957533574467e-06,
                1.8925148238291944e-05,
                4.2228334433617906e-06,
                4.222832940162684e-06,
                2.260324836341129e-06,
                1.9947301968382903e-06,
                6.96225956837018e-06,
                1.3709570433387154e-06
            ],
            [
                5.422217030032353e-06,
                1.3007134659924986e-05,
                5.422218968221128e-06,
                6.1441731319963306e-06,
                2.4300243618542217e-05,
                5.422220908018252e-06,
                2.144494328950459e-05,
                1.0129989768027317e-05,
                6.144174599532449e-06,
                7.889261644875049e-06
            ],
            [
                1.3007133113372426e-05,
                0.00033535022604312816,
                2.1444940738662144e-05,
                1.8925141465820123e-05,
                8.481108156331507e-05,
                2.4300232009732255e-05,
                2.7535687779473676e-05,
                1.1478765386330758e-05,
                1.4738985483504099e-05,
                1.1478769492893215e-05
            ],
            [
                0.9999687980851895,
                0.9999785550425039,
                0.9999898700066072,
                0.9999898700115686,
                0.9999885212359998,
                0.9999832985801831,
                0.9999977396757042,
                0.8175744828610095,
                0.6513548646660543,
                0.9999546021259903
            ],
            [
                5.422217030209884e-06,
                7.889265404113251e-06,
                1.7603434229000067e-06,
                2.5612828208879873e-06,
                2.561283126535066e-06,
                1.89251503840428e-05,
                3.2887482809455384e-06,
                6.1441738691562974e-06,
                2.902311984989368e-06,
                1.994729483630195e-06
            ],
            [
                0.9996200154834131,
                0.9999724643123162,
                0.9995694428708782,
                0.9993736658692166,
                0.9997694932323853,
                0.9995121429484879,
                0.9999832985801625,
                0.9999599363079568,
                0.9999885212278096,
                0.9999339478475554
            ],
            [
                0.9999756997650764,
                0.999985261023306,
                0.9999945777803848,
                0.99991518894794,
                0.9999945777797382,
                0.9999885212305076,
                0.9241418267688302,
                0.9999898700054018,
                0.9999599363126013,
                0.9997965729551455
            ],
            [
                0.0002959571680203096,
                0.00015843629194178295,
                0.0002959570969370248,
                0.00013982213952122777,
                0.00029595716501509226,
                7.88925976316864e-06,
                0.00010889688301423978,
                2.1444940740066406e-05,
                4.539785779269366e-05,
                0.00010889694784665827
            ],
            [
                0.9999724643131839,
                0.5,
                0.7981867705385762,
                0.9998911030911016,
                0.9999756997477506,
                0.9999485577986705,
                0.07585817740967664,
                0.9999646437372343,
                0.999981074852258,
                0.9999974387169913
            ],
            [
                2.9023123309287002e-06,
                2.144494329348333e-05,
                1.3007130013572209e-05,
                0.00010889693502657802,
                6.9622554171645e-06,
                2.1444958637356654e-05,
                7.889265406438011e-06,
                3.2887482811579057e-06,
                6.1441738684354385e-06,
                2.902311293034278e-06
            ],
            [
                0.8519528057272543,
                0.9971990725496949,
                0.9999339478790235,
                0.9999910603005024,
                0.9995694430155098,
                0.999975699765101,
                0.9999251537549879,
                0.9998766054255219,
                0.999664649931147,
                0.9999599362936574
            ],
            [
                6.962258738435319e-06,
                3.7266392836984955e-06,
                1.3007130011300897e-05,
                2.144494839938192e-05,
                2.4300234933172706e-05,
                6.962253759157502e-06,
                3.2887478887419687e-06,
                5.42222090821551e-06,
                8.93969417199781e-06,
                4.222835457595211e-06
            ],
            [
                8.93969310418261e-06,
                1.3007134655902864e-05,
                1.670142582254589e-05,
                1.994729007936337e-06,
                1.3007131559390956e-05,
                1.6701425819447213e-05,
                8.939693105076969e-06,
                4.222834953896582e-06,
                6.144173867753695e-06,
                8.939693106182721e-06
            ],
            [
                2.2603253751406236e-06,
                1.2098659718693234e-06,
                1.6701421800703626e-05,
                1.4738976694494812e-05,
                1.3709578602063795e-06,
                6.1441760657054305e-06,
                1.2098659719122375e-06,
                1.473898899742027e-05,
                1.5534983100765009e-06,
                3.2887490653109436e-06
            ],
            [
                0.9999910603068974,
                7.889264465699106e-06,
                5.829127933242964e-05,
                0.0001233945890514007,
                1.0129987351952995e-05,
                1.4738976697229395e-05,
                2.1444958631232504e-05,
                1.3007133112307748e-05,
                6.605217593396786e-05,
                1.300712845923622e-05
            ],
            [
                0.9999921107383555,
                0.9999974387177893,
                0.9999417087136733,
                0.9999756997679626,
                0.999997097687669,
                0.9999977396765105,
                0.9999962733602719,
                0.9999952149066464,
                0.9999952149066464,
                0.9999952149072169
            ],
            [
                1.67014297980912e-05,
                4.785092782597101e-06,
                8.939695232967228e-06,
                1.6701415865641523e-05,
                2.4300234904884198e-05,
                3.120190388402792e-05,
                1.670141586949968e-05,
                8.939700566435704e-06,
                1.01299946023704e-05,
                3.535625063370289e-05
            ],
            [
                2.430024072091399e-05,
                4.7850967757637256e-06,
                0.6224593312018546,
                1.6701429800582296e-05,
                3.1201926179794786e-05,
                1.012998977022003e-05,
                1.3007128462477575e-05,
                1.1478768122069266e-05,
                1.4738985480608657e-05,
                2.430024651705481e-05
            ],
            [
                1.8925154957064743e-05,
                1.0129988556912918e-05,
                3.1201907628667734e-05,
                1.4738988971066366e-05,
                6.9622587372828785e-06,
                3.535625490018181e-05,
                1.0129988558055338e-05,
                5.4222183221120994e-06,
                2.75356811755688e-05,
                1.8925155002022494e-05
            ],
            [
                0.9999852610162734,
                0.9999930377404307,
                0.9999957771675627,
                0.9998415637265112,
                0.9999724643023645,
                0.9999910603036963,
                0.9999910603036963,
                0.9998766054693442,
                0.9999599363030588,
                1.3709568796450432e-06
            ],
            [
                0.00026119021273099364,
                4.006368737910463e-05,
                0.99929032954282,
                2.7535700920674098e-05,
                2.1444953514565465e-05,
                6.605216037820727e-05,
                4.5397852330227426e-05,
                0.00013982204016952795,
                5.8291293247581486e-05,
                0.00010889692203379031
            ],
            [
                1.9947301969707264e-06,
                2.561282210590951e-06,
                2.4300234920177672e-05,
                2.7535687811228037e-05,
                4.539785237316614e-05,
                7.8892654060075e-06,
                2.561281599881745e-06,
                5.422220262195015e-06,
                3.7266388393349185e-06,
                1.2098658276598493e-06
            ],
            [
                5.144221363404434e-05,
                3.726639283040963e-06,
                5.1442213596242845e-05,
                6.962259568775433e-06,
                4.006369218184011e-05,
                0.9999852610197864,
                0.9999756997621677,
                3.535625063370289e-05,
                6.9622579075254155e-06,
                1.3007134663521234e-05
            ],
            [
                1.1478766754064213e-05,
                1.1478764019787597e-05,
                0.00012339453048526995,
                1.670142582254589e-05,
                2.1444948400318094e-05,
                3.72663839489005e-06,
                1.3007123808910861e-05,
                1.300713156215912e-05,
                1.8925152742706337e-05,
                2.5612831266608576e-06
            ],
            [
                0.00010889693428820737,
                0.00010889690800633475,
                0.0003799845720710205,
                0.0002959572369164327,
                0.001032231143473468,
                0.0004305570829028235,
                0.0004305571384282138,
                0.9984988180769037,
                0.0007096704969316796,
                0.00020342706968894909
            ],
            [
                0.9999417087553318,
                0.9995121427683967,
                0.9999724642957807,
                0.9999967112521114,
                0.9999952149049389,
                0.9999898700066067,
                0.9999832985741748,
                0.9999756997534934,
                0.9999977396754328,
                0.9999977396757023
            ],
            [
                1.9947306726049992e-06,
                1.994730434816876e-06,
                3.2887478889962107e-06,
                5.144221973168594e-05,
                6.144173868558375e-06,
                2.144494073569759e-05,
                3.2887478891487563e-06,
                1.6701419849933667e-05,
                1.6701419849447602e-05,
                2.260324027708365e-06
            ],
            [
                0.9999974387180965,
                0.9999952149055097,
                0.9999852610180362,
                0.6791787056691698,
                0.9999952149055056,
                0.9999852610110981,
                0.9999910603001375,
                0.9999251537641983,
                NaN,
                0.9999898700042046
            ],
            [
                1.0129992185539456e-05,
                2.7535684519993744e-05,
                3.535625066508635e-05,
                1.8925157234281645e-05,
                8.4811010852998e-05,
                0.03308598017635717,
                5.1442207485876726e-05,
                2.753570420840434e-05,
                1.4738981964843453e-05,
                1.0129994601872894e-05
            ],
            [
                6.144174600985344e-06,
                1.0677026152550755e-06,
                4.785094493532295e-06,
                9.422449307915373e-07,
                2.260324028331257e-06,
                6.962256921036117e-06,
                1.5534975693488444e-06,
                5.422218322565793e-06,
                1.4738981969240237e-05,
                4.222833444229772e-06
            ],
            [
                4.539789024909747e-05,
                1.4738983720715225e-05,
                4.222833444383398e-06,
                1.300713156215912e-05,
                2.1444945848226808e-05,
                6.962256249112569e-06,
                2.260324297702111e-06,
                1.1478773596575768e-05,
                1.892515274546026e-05,
                2.2603245672025095e-06
            ],
            [
                0.2689414330889798,
                0.999954602136796,
                0.9149009636941992,
                0.9997694933408589,
                0.9999832985832576,
                0.8519527982093666,
                0.9998766053667189,
                0.8354835309589073,
                0.6224593382055109,
                0.9998601779762012
            ],
            [
                0.5312093733737563,
                0.999769493235987,
                7.484621818541193e-05,
                7.48462093285157e-05,
                0.00013982205678442458,
                0.9998911031388327,
                0.9996646498629673,
                7.484620025053846e-05,
                0.0002305066591410812,
                2.1444950959196957e-05
            ],
            [
                8.939695237959376e-06,
                0.9998911031037886,
                2.144494584573034e-05,
                1.8925150482908516e-05,
                0.9999599363173673,
                6.144175332283612e-06,
                1.670142781636389e-05,
                0.0001398221225299582,
                1.6701415863393463e-05,
                2.430024938029549e-05
            ],
            [
                1.8925157212938766e-05,
                2.144495352474637e-05,
                6.9622545892184106e-06,
                1.067702488159652e-06,
                5.422218319103914e-06,
                1.892515048889829e-05,
                0.9999852610145165,
                1.1478768119939555e-05,
                1.1478764017428212e-05,
                1.0129994601301684e-05
            ],
            [
                6.144172402765906e-06,
                1.8925141467679015e-05,
                1.9947299588742466e-06,
                4.7850962047640385e-06,
                2.4300234925658572e-05,
                1.994729483630195e-06,
                1.9947306723745965e-06,
                2.9023112930949896e-06,
                6.9622562492265485e-06,
                2.5612822106421996e-06
            ],
            [
                0.9997388097198145,
                0.9996646500123227,
                0.9994472212629358,
                0.9999957771680894,
                0.8670357701094303,
                0.9999852610216999,
                0.9998415638213973,
                0.9999832985835297,
                0.9998766054706028,
                0.9999869928684505
            ],
            [
                0.0021827165051822753,
                1.4738976699106073e-05,
                5.1442238107329257e-05,
                3.12019113204131e-05,
                0.0001584362543718626,
                7.484625369741068e-05,
                6.605212102411961e-05,
                0.0001398221236224284,
                1.67014238321306e-05,
                0.0001795279655750396
            ],
            [
                0.651354857898194,
                0.9999938558232014,
                0.9999987901347491,
                0.9999977396762441,
                0.9999974387168733,
                0.9999945777803854,
                0.9999910603036979,
                0.9999910603068933,
                0.9999990577549568,
                0.9999974387171787
            ],
            [
                3.2887486732000038e-06,
                2.144494073483943e-05,
                1.7603434231241496e-06,
                2.2603234894560207e-06,
                8.939696303010449e-06,
                1.0677033791291683e-06,
                2.260324028255194e-06,
                6.962257078819179e-06,
                3.2887478889513447e-06,
                2.1444945828411102e-05
            ],
            [
                5.422218969532895e-06,
                2.1444948406091176e-05,
                5.82912931135658e-05,
                8.939698433145498e-06,
                1.8925145981283003e-05,
                1.892514823488397e-05,
                1.147877086020957e-05,
                6.962257906334983e-06,
                1.3007131559390956e-05,
                1.0129990977262395e-05
            ],
            [
                0.9999967112501507,
                0.9999898700114359,
                0.9999810748517707,
                0.9999994284996211,
                0.9999485577802376,
                0.9997965730523404,
                0.9999810748495241,
                0.999993037740431,
                0.9999930377412611,
                0.9999967112517189
            ],
            [
                0.9999980052698031,
                0.9999417087600749,
                0.9820137930317494,
                0.4378234991142019,
                0.8354835350552603,
                0.9999930377429761,
                0.9999785550517414,
                0.651354857898194,
                0.9999869928762511,
                0.998299277344858
            ],
            [
                1.994729008105057e-06,
                4.222833444229772e-06,
                1.3709575336093795e-06,
                1.0677033791204289e-06,
                1.2098653950205268e-06,
                1.370957533676711e-06,
                4.222834451012227e-06,
                1.0129987355988324e-05,
                1.2098653950403334e-06,
                1.7603425836005905e-06
            ],
            [
                1.670142781086525e-05,
                4.222832940834793e-06,
                1.4738976682001517e-05,
                2.753569108924008e-05,
                6.144173136455602e-06,
                6.144176798132662e-06,
                1.4738985481091229e-05,
                2.7535684510878145e-05,
                2.4300243618542217e-05,
                1.4738980213020151e-05
            ],
            [
                4.222835457906302e-06,
                0.9999756997651473,
                2.5612819052374947e-06,
                1.5534975693601474e-06,
                2.902311639126627e-06,
                1.9947297212331575e-06,
                6.962253759043525e-06,
                3.2887498493983645e-06,
                1.1478769493331685e-05,
                3.7266379512112265e-06
            ],
            [
                0.9999869928761926,
                0.9999869928746392,
                0.9998911031171965,
                0.9999810748495792,
                6.9622562484666964e-06,
                0.9999756997679731,
                0.9999485577863824,
                0.9999785550592704,
                0.9999930377454107,
                0.9999485578049403
            ],
            [
                0.9999832985781849,
                0.9997965730280062,
                0.9999992661791992,
                0.9999599363079641,
                0.5312093733737563,
                0.9999038976084709,
                0.9995694430160734,
                0.9999251537462509,
                0.5,
                0.9999852610189881
            ],
            [
                3.5356263276609686e-05,
                8.939697368110433e-06,
                2.5612831265909735e-06,
                1.0129989771288745e-05,
                8.939693098117235e-06,
                2.4300246514137558e-05,
                1.8925143723620274e-05,
                2.561282515820982e-06,
                2.7535687811228037e-05,
                3.288749849368453e-06
            ],
            [
                1.670142980112912e-05,
                8.481103109648735e-05,
                8.939694169330997e-06,
                1.6701429804744246e-05,
                6.144173136556186e-06,
                2.1444956079218013e-05,
                3.120191880118183e-05,
                3.5356246478738656e-05,
                1.6701429805655623e-05,
                1.0129987355122296e-05
            ],
            [
                0.9999898700126462,
                0.9999938558239373,
                0.9997694932302659,
                0.34864513533394575,
                0.9999852610110431,
                0.9999599363222645,
                0.9997965730097569,
                0.99999627335988,
                0.29421497216298875,
                0.9999756997679989
            ],
            [
                3.7266410608245674e-06,
                6.144176797864436e-06,
                4.222833942436121e-06,
                1.892515499864894e-05,
                6.962255419380732e-06,
                1.5534973839896667e-06,
                6.962254588585202e-06,
                0.00023050682328351694,
                2.9023126765777146e-06,
                2.90231198483099e-06
            ],
            [
                3.120190392137216e-05,
                1.892514823488397e-05,
                1.6701419833468143e-05,
                1.012998977108606e-05,
                6.605212886590941e-05,
                1.3007131563176482e-05,
                1.3007128455545335e-05,
                2.1444948393530826e-05,
                6.962258739169842e-06,
                2.430024361951464e-05
            ],
            [
                0.9999687980776334,
                0.9999546021205942,
                0.9999962733607162,
                0.999995214904366,
                0.9999989322973846,
                0.9999977396762414,
                0.9999991684719723,
                0.999968798092365,
                0.9999898700054067,
                0.9999724643154813
            ],
            [
                4.006370637667922e-05,
                2.7535681246690542e-05,
                0.9998911031167418,
                0.00012339455931948047,
                0.9997694932304335,
                5.144223201941656e-05,
                1.0129992187253088e-05,
                2.4300243628620005e-05,
                1.892515048889829e-05,
                9.61024375498969e-05
            ],
            [
                0.9997040427975704,
                0.9998601779594724,
                0.9940889324517005,
                0.9999756997679626,
                0.999769493312555,
                0.9999038975396697,
                0.9999417087275358,
                0.9999546021205734,
                0.9999687980849583,
                0.9999910603036997
            ],
            [
                0.9999251537460674,
                0.999959936303095,
                0.99976949337976,
                0.9999485577891561,
                0.99999627336077,
                0.9999852610110357,
                0.46879062662624377,
                0.9998601779431668,
                0.9999952149061925,
                0.9999724643095594
            ],
            [
                2.4300243626409964e-05,
                5.42222090767305e-06,
                7.889259763469998e-06,
                1.0129994589969591e-05,
                1.4738976693529666e-05,
                4.785096775058701e-06,
                6.1441731363550164e-06,
                3.1201903930339314e-05,
                2.2603242977802297e-06,
                7.889260704179641e-06
            ],
            [
                0.9999997617630616,
                0.9999991684720715,
                0.9999957771645424,
                0.999995214905506,
                0.9999992661788445,
                0.9997965730031214,
                0.9999974387180949,
                0.9999974387184005,
                0.9999945777829702,
                0.9999810748562825
            ],
            [
                0.09534946425643773,
                0.1329642316084462,
                0.08509905022775231,
                0.9998601779165365,
                0.9998911031145901,
                0.9997694933794917,
                9.422443692446175e-07,
                0.9999832985768449,
                0.5312093733737563,
                0.6791786861878392
            ],
            [
                2.144495096083526e-05,
                1.8925150489517924e-05,
                4.5397873994468824e-05,
                6.60521523571645e-05,
                6.962257079376403e-06,
                4.785096205512581e-06,
                1.8925152748558416e-05,
                1.0129995807939249e-05,
                8.939695237813028e-06,
                1.8925150490206403e-05
            ],
            [
                4.006369692044835e-05,
                7.889259763326495e-06,
                2.4300243627117176e-05,
                1.0129992186387057e-05,
                1.0129990978441666e-05,
                6.962258739271155e-06,
                4.7850956352353935e-06,
                1.892514372737249e-05,
                4.785092783371756e-06,
                1.012998977022003e-05
            ],
            [
                0.9999832985781624,
                0.999891103104096,
                0.9998204720352765,
                0.999933947834289,
                0.8175744761936437,
                0.9999251537479613,
                0.9914225159247485,
                0.9997388096007127,
                0.9999756997563889,
                0.9999724643090008
            ],
            [
                1.0129992176400077e-05,
                6.96225458885115e-06,
                5.422220261849814e-06,
                7.889260702342794e-06,
                4.785095064523075e-06,
                6.962253759271479e-06,
                5.422218322940583e-06,
                5.4222215550004564e-06,
                1.5534981248133121e-06,
                1.67014178554179e-05
            ],
            [
                0.9996646498673871,
                0.999975699747731,
                0.9999339478556144,
                0.9999852610145247,
                0.00029595708966939497,
                0.7549149813536518,
                0.9999339478396323,
                0.4378234991142019,
                0.9999952149038214,
                0.9999810748472868
            ],
            [
                2.753570419988976e-05,
                2.7535687776067845e-05,
                2.4300252298610736e-05,
                6.962257906765564e-06,
                8.48110513985993e-05,
                2.1444953513707305e-05,
                1.0129990975567187e-05,
                7.48462533336597e-05,
                2.1444953509026425e-05,
                0.00013982202350580785
            ],
            [
                6.605214460043122e-05,
                1.4738985479697128e-05,
                1.6701423830702777e-05,
                1.670142979875954e-05,
                5.422217676866151e-06,
                2.1444945848226808e-05,
                7.889265405146477e-06,
                5.1442195225848094e-05,
                2.430023782010365e-05,
                1.4738976694494812e-05
            ],
            [
                2.561282821239737e-06,
                4.222832938926002e-06,
                6.144176066521288e-06,
                4.785092781953005e-06,
                2.2603245668530326e-06,
                3.288750241042834e-06,
                6.605215913115156e-05,
                3.7266388393349185e-06,
                3.7266392802820347e-06,
                3.726638395215427e-06
            ],
            [
                5.422219615188307e-06,
                9.422450431372112e-07,
                7.889260699630574e-06,
                1.3007126911974612e-05,
                0.9525741261492485,
                8.939699500327152e-06,
                6.144177531007026e-06,
                4.222835456466066e-06,
                1.147876812069122e-05,
                6.96225873895455e-06
            ],
            [
                1.3007131561804229e-05,
                1.300712845966209e-05,
                7.889264465239894e-06,
                5.422220908314139e-06,
                9.610241489119613e-05,
                1.3007130013288297e-05,
                6.1441775309064404e-06,
                7.889259759222289e-06,
                1.3007133114011233e-05,
                5.422217676654099e-06
            ],
            [
                6.144175334015912e-06,
                2.902312677060767e-06,
                3.5356242257020764e-05,
                1.4738976697229395e-05,
                2.753569765908901e-05,
                2.4300240723831244e-05,
                2.7535684525803696e-05,
                1.1478770860982112e-05,
                1.3007126901777358e-05,
                8.939699500164542e-06
            ],
            [
                6.1441775248378034e-06,
                1.4738981969240237e-05,
                1.1478766749992709e-05,
                6.962257907702715e-06,
                3.120192622644674e-05,
                3.5356259136692605e-05,
                5.422219614951598e-06,
                6.962257907880012e-06,
                1.6701419840455358e-05,
                1.1478770854029233e-05
            ],
            [
                1.3709573698620332e-06,
                1.3007128460797749e-05,
                3.288750633025344e-06,
                3.2887506314400653e-06,
                6.9622570780973205e-06,
                2.902311292831027e-06,
                1.670141785651155e-05,
                2.1444943296369872e-05,
                8.939699487513427e-06,
                6.144173135762683e-06
            ],
            [
                6.962257908487893e-06,
                8.939696302652706e-06,
                1.0129990976728036e-05,
                3.2887486732000038e-06,
                2.144494328864643e-05,
                1.994729007562614e-06,
                3.2887490652451393e-06,
                6.605212888657352e-05,
                2.4300237825230942e-05,
                1.8925157257345735e-05
            ],
            [
                2.4300252306390083e-05,
                1.473897669245728e-05,
                2.753568452349975e-05,
                1.147876401711502e-05,
                2.144494583730477e-05,
                2.144495096083526e-05,
                3.535623801986889e-05,
                7.889263523453522e-06,
                1.0129993387404356e-05,
                4.222831933104063e-06
            ],
            [
                3.5356259091803945e-05,
                3.5356267434662786e-05,
                3.5356259112640515e-05,
                3.120192618864844e-05,
                3.1201907595069264e-05,
                4.5397863134932104e-05,
                3.1201903888114227e-05,
                4.539789016057757e-05,
                0.00010889686937974167,
                2.430024940080467e-05
            ],
            [
                2.9023126767836054e-06,
                1.2098662603356388e-06,
                2.902311293034278e-06,
                0.00012339457322130677,
                1.0677028700130727e-06,
                1.2098659718990333e-06,
                2.9023119850527192e-06,
                6.962256248314727e-06,
                1.7603432132464244e-06,
                1.5534981246268099e-06
            ],
            [
                0.9999952149060762,
                0.9999952149032239,
                0.9999957771670591,
                0.9999957771670593,
                0.9999869928684362,
                0.9999852610145177,
                0.9999687980997966,
                0.9999898700078134,
                0.9999930377429207,
                0.9999962733602719
            ],
            [
                0.9995694428642522,
                0.9990889486735156,
                0.9999546021152351,
                0.9996646499354791,
                0.9999687980812073,
                0.9999869928653361,
                0.9999962733602717,
                0.999964643753573,
                0.9999945777791701,
                0.9999957771656468
            ],
            [
                4.222832437186393e-06,
                6.962257906765564e-06,
                1.0129988561648438e-05,
                6.144173136455602e-06,
                6.962255418215627e-06,
                3.2887506316554234e-06,
                2.9023123304852425e-06,
                1.4738988998117324e-05,
                1.760343632854606e-06,
                6.962255418924822e-06
            ],
            [
                0.3775406687981454,
                0.6513548646660543,
                0.8354835330070839,
                0.999954602115206,
                0.880797071719777,
                0.9525741234565096,
                0.9999756997681241,
                0.679178699175393,
                0.9999417087353678,
                0.9999724642991056
            ],
            [
                0.9997965730758843,
                0.9999599363223765,
                0.9982992774668102,
                0.00037998451981496417,
                9.422444814304002e-07,
                0.9991959141780129,
                0.5312093733737563,
                0.9999546021369627,
                0.9399133523506772,
                0.9999339478318099
            ],
            [
                1.3007123810638006e-05,
                8.939699499026267e-06,
                1.760344052632596e-06,
                1.3007131564643372e-05,
                1.8925152746768368e-05,
                1.8925141469400216e-05,
                1.6701427809710842e-05,
                1.1478773595970265e-05,
                4.222833444037741e-06,
                6.144177530291754e-06
            ],
            [
                1.8925143726890553e-05,
                1.8925148237775583e-05,
                1.4738987241172537e-05,
                1.6701419847381817e-05,
                1.1478766756214804e-05,
                1.0129992186202796e-05,
                8.939696302831578e-06,
                1.0129987355988324e-05,
                1.0129993393742954e-05,
                1.3007128463069061e-05
            ],
            [
                0.9999987901340283,
                0.9999952149049351,
                0.9999987901347454,
                0.9999938558253987,
                0.9999921107374156,
                0.999995214903224,
                0.9999989322975118,
                0.9999952149032247,
                0.9999984465022458,
                0.9999989322967482
            ],
            [
                0.5,
                0.9669140235181257,
                0.9465966685053075,
                0.9999832985783028,
                0.9999898700103093,
                0.9998766054404974,
                0.7772998560157665,
                0.9324533018213449,
                0.9998766054403591,
                0.9706877676057092
            ],
            [
                0.999925153737113,
                0.7549149923816048,
                0.7549149813536518,
                0.9999810748570915,
                0.9999952149043729,
                0.9999984465015047,
                0.9999967112497818,
                0.9999599363078994,
                0.9999970976873265,
                0.8519528057272543
            ],
            [
                1.3007126911335805e-05,
                2.561283431124603e-06,
                1.994729483608425e-06,
                1.1478765386330758e-05,
                2.2603253755476615e-06,
                4.785093924103951e-06,
                4.785092783267308e-06,
                5.422218322348809e-06,
                4.222834954514924e-06,
                6.144175333635923e-06
            ],
            [
                1.0129990976156825e-05,
                5.1442195149496606e-05,
                1.4738987229134998e-05,
                1.1478764005840086e-05,
                6.144176796601534e-06,
                7.889265404759017e-06,
                7.484621809175153e-05,
                7.889265403395731e-06,
                6.962253757840428e-06,
                6.605214460571739e-05
            ],
            [
                4.539785229422496e-05,
                9.610238020678204e-05,
                2.144494328302938e-05,
                7.484622690835306e-05,
                6.605214452354149e-05,
                4.5397863198349305e-05,
                4.006367775556302e-05,
                3.120190386700167e-05,
                1.4738980204575109e-05,
                4.539787932217606e-05
            ],
            [
                3.120191507333991e-05,
                8.939693106020111e-06,
                4.785096775676685e-06,
                4.785092783210732e-06,
                2.430023203572232e-05,
                2.902312677084523e-06,
                2.5612816000145246e-06,
                3.1201918788014855e-05,
                4.785096776133645e-06,
                3.288749457409966e-06
            ],
            [
                0.9999724643023452,
                0.9999646437366749,
                0.9999921107355344,
                0.9999810748495196,
                0.999999352405279,
                0.9999962733593833,
                0.9999724643023452,
                0.9999938558275955,
                0.9999852610110022,
                0.9999910603058283
            ],
            [
                4.222833947498071e-06,
                2.5612834318257725e-06,
                1.8925143717561654e-05,
                2.5612812945889277e-06,
                7.88926164421493e-06,
                3.2887502411564953e-06,
                0.9149009457116781,
                1.1478770849018147e-05,
                4.785096776133645e-06,
                3.288748281220719e-06
            ],
            [
                1.5534973840150989e-06,
                1.8925150495232307e-05,
                1.300713466281145e-05,
                7.889265406567165e-06,
                6.962257909121104e-06,
                1.4738978457336465e-05,
                2.7535694380675497e-05,
                3.2887490652451393e-06,
                4.785094494576774e-06,
                3.7266397282926013e-06
            ],
            [
                3.120191506039996e-05,
                1.8925143720384422e-05,
                4.785093353274332e-06,
                1.3007128461838766e-05,
                7.48462093933156e-05,
                5.829125844846945e-05,
                1.3007131560621253e-05,
                8.939695235243779e-06,
                4.0063711254184204e-05,
                2.7535694358938284e-05
            ],
            [
                0.9999945777823236,
                0.9999952149032251,
                0.9999756997534821,
                0.9999930377420927,
                0.999993037740431,
                0.9999852610197898,
                0.9999980052695653,
                0.9999967112505427,
                0.999991060301566,
                0.99997569974772
            ],
            [
                3.5356242266024216e-05,
                5.144221975264518e-05,
                5.144221973879711e-05,
                0.00013982202384351717,
                2.7535684528909006e-05,
                0.00013982212348408955,
                2.7535684521195802e-05,
                0.00015843615991460315,
                0.9999485577802758,
                1.4738981969240237e-05
            ],
            [
                1.1478770854906172e-05,
                1.1478766755734576e-05,
                1.0129993382982077e-05,
                2.753569108924008e-05,
                3.1201915067096954e-05,
                1.670142781478417e-05,
                4.222832939663403e-06,
                4.785093922654737e-06,
                2.9023112925670636e-06,
                1.01299933920846e-05
            ],
            [
                3.7266397281434697e-06,
                4.785093339487208e-06,
                2.144495863482118e-05,
                2.430024071781994e-05,
                8.93970056529743e-06,
                7.889261644631091e-06,
                6.962253758916883e-06,
                1.1478764019077695e-05,
                2.430023203298187e-05,
                7.889263525405172e-06
            ]
        ]
    },
    {
        "q_id": "7910_mmlu_math",
        "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": [
            [
                0.9999967112497594,
                0.9999977396748939,
                0.9999982396567868,
                0.9999984465028011,
                0.9999980052702786,
                0.99999844650169,
                0.99999709768767,
                0.999996711249367,
                0.8354835330070838,
                0.9999910603047638
            ],
            [
                0.9999785550490348,
                0.9999885212359809,
                0.9999810748540182,
                0.9999869928715373,
                0.999975699747698,
                0.9999910603015663,
                0.9890130549406149,
                0.7310585786300049,
                0.999993855825399,
                0.9999546021205543
            ],
            [
                0.9999996072137998,
                0.999999789756684,
                0.9999991684722697,
                0.9999970976869775,
                0.9999987901343166,
                0.9999993524052019,
                0.0009110513965793914,
                0.9999980052693274,
                0.9999989322970028,
                0.03732689055684297
            ],
            [
                0.9999994956527121,
                0.9999996533672136,
                0.9999998144608983,
                0.9999885212264031,
                0.9999984465016899,
                0.9999945777829709,
                0.9999994284996211,
                0.9999996940978096,
                0.9999970976866311,
                0.9999990577555186
            ],
            [
                0.999998790134605,
                0.9999962733611624,
                0.9999952149055074,
                0.010986940373841205,
                0.9999993524050474,
                0.9999992661791948,
                0.9999980052702786,
                0.9999984465026158,
                0.9999998144609202,
                0.999999266179107
            ],
            [
                0.9999967112513267,
                0.9999977396751634,
                0.9999996072138934,
                0.9999982396559475,
                0.9999982396574166,
                0.9999990577550693,
                0.9999957771665556,
                0.9999991684718733,
                0.9999994284996893,
                0.9999992661791945
            ],
            [
                0.9999994284996893,
                0.9999990577556309,
                0.9999996072138466,
                0.99999893229713,
                0.9999991684719725,
                0.9999970976873235,
                0.9999992661791944,
                0.999993855827596,
                0.9999982396574163,
                0.9999967112497591
            ],
            [
                9.610239180740553e-05,
                6.144176798479122e-06,
                1.012999460251781e-05,
                5.8291279378656556e-05,
                7.889259764359722e-06,
                7.88926634644516e-06,
                4.785095065045315e-06,
                5.1442213588757405e-05,
                0.0008040857556256627,
                0.0005527785324417303
            ],
            [
                0.9999993524051247,
                0.9999996940978825,
                0.9999980052695652,
                0.9999991684721706,
                0.9999957771660528,
                0.9999996533672549,
                0.9999977396757032,
                0.9999952149060773,
                0.9999977396751634,
                0.9999997897567341
            ],
            [
                1.370956716529941e-06,
                1.2098658277082653e-06,
                1.2098655392354511e-06,
                4.222834450820197e-06,
                1.760343842833246e-06,
                4.785095065045315e-06,
                3.288749065167371e-06,
                7.338209805133949e-07,
                5.043475885634304e-07,
                1.5534975693707442e-06
            ],
            [
                0.9999980052695652,
                0.9999994284996211,
                0.9999993524050474,
                0.999999266178932,
                0.99999844650169,
                0.9999996533672136,
                0.9999952149032245,
                0.9999957771680661,
                0.9999989322970029,
                0.9999974387180947
            ],
            [
                0.9999996940978825,
                0.9999995549148419,
                0.9999996533674615,
                0.9999994284992805,
                0.9999991684721706,
                0.9999995549149481,
                0.9999996533672963,
                0.9999996940977367,
                0.9999984465024307,
                0.9999996533672549
            ],
            [
                0.0001398221221820766,
                0.00020342702056762278,
                0.9947798735519877,
                0.00012339455903760178,
                0.9924227599682365,
                0.0009110511252063574,
                1.473898723042186e-05,
                0.00015843623383265972,
                5.8291279387562654e-05,
                0.0017007221813667216
            ],
            [
                0.0004305571264162915,
                9.610239169833504e-05,
                0.005911067717949185,
                0.009708478218538959,
                5.8291286217696064e-05,
                0.00013982202362176826,
                5.1442232005568484e-05,
                7.48462449477841e-05,
                0.0011695102968771018,
                2.4300240708626165e-05
            ],
            [
                4.006369694959736e-05,
                5.144220137064579e-05,
                3.7266397282926013e-06,
                0.00013982212291039007,
                0.00048785715811931177,
                0.00026119040045002054,
                5.144219514088835e-05,
                2.9023123311055552e-06,
                1.670142781636389e-05,
                2.4300237817893614e-05
            ],
            [
                0.9999957771675625,
                0.9999957771655488,
                0.9999984465022455,
                0.9999910603015656,
                0.9999994284994167,
                0.0002959571648084298,
                0.9999992661790195,
                0.0015011825685654289,
                0.9999984465016905,
                0.9999952149037952
            ],
            [
                0.9999996940976638,
                0.999997097687323,
                0.9999992661791944,
                0.9999970976887075,
                0.9999982396569969,
                0.9999987901343167,
                0.9999980052700408,
                0.001501182034600713,
                0.9999974387180949,
                0.9999970976873244
            ],
            [
                0.9999991684721706,
                0.999998239656997,
                0.9999982396565769,
                0.999997097687323,
                0.9999994284997573,
                0.9999994284997575,
                0.9999994956524115,
                0.9999996072136592,
                0.9999990577556308,
                0.9999994956525918
            ],
            [
                0.9999977396762414,
                0.9999938558261331,
                0.9999987901341724,
                0.9999898700054043,
                0.9999898700054018,
                0.9999986290426297,
                0.999999266178932,
                0.9999994284994849,
                0.9999987901346049,
                0.9999945777829699
            ],
            [
                6.605216808208071e-05,
                6.144175333021237e-06,
                6.1441760661636525e-06,
                8.939694168225243e-06,
                2.7535691088138193e-05,
                5.422218322851817e-06,
                5.422217030362759e-06,
                3.7266379512518984e-06,
                0.0006263342268615364,
                3.2887506334201674e-06
            ],
            [
                0.00010889694797658617,
                4.0063677828144015e-05,
                1.3007128457958606e-05,
                3.2887486723295965e-06,
                4.539786320660675e-05,
                3.120192250053358e-05,
                0.00037998456761593444,
                0.0001088969215394306,
                1.670142979997471e-05,
                0.012431648829377724
            ],
            [
                7.484623606311329e-05,
                2.430023781444595e-05,
                0.00048785710461703857,
                0.00013982203988064398,
                0.00023050676729948426,
                3.7266379513162962e-06,
                0.0003353502638796249,
                1.670142183825232e-05,
                4.539787401263522e-05,
                0.0005527787165472226
            ],
            [
                0.9999938558253988,
                0.9999910603068958,
                0.999992110738357,
                0.9999980052693277,
                0.9999957771665569,
                0.9999990577554061,
                0.9999962733616058,
                0.9999898700066134,
                0.9999910602994343,
                0.9999990577555186
            ],
            [
                0.9999962733593836,
                0.9999994284993486,
                0.9999994956527121,
                0.999999694097846,
                0.999999730042126,
                0.999997097686977,
                0.999997739676511,
                0.9999998362622357,
                0.9999980052695654,
                0.9999952149072169
            ],
            [
                0.9999989322971301,
                0.9999982396565769,
                0.9999885212346149,
                0.9999977396751634,
                0.999998932296621,
                0.9999957771650465,
                0.9999921107336547,
                0.9999986290427932,
                0.9999952149066468,
                0.9999970976887085
            ],
            [
                0.9999990577549568,
                0.9999986290432835,
                0.9999993524050474,
                0.9999989322966208,
                0.9999957771645427,
                0.9999993524050474,
                0.9999991684722698,
                0.999998932297512,
                0.9999994284996893,
                0.9999984465020604
            ],
            [
                0.9999993524052019,
                0.9999995549149481,
                0.9999996533675028,
                0.9999994956524716,
                0.9999977396757022,
                0.9999994284997573,
                0.9999995549150541,
                0.9999997617630048,
                0.9999996533673375,
                0.9999993524052019
            ],
            [
                2.260324028331257e-06,
                7.338211554725124e-07,
                2.2603234893861252e-06,
                1.2098653950205268e-06,
                9.422449308716635e-07,
                1.2098662604049616e-06,
                1.0677033791583005e-06,
                9.422443692261927e-07,
                2.902311639126627e-06,
                1.760344052650207e-06
            ],
            [
                0.9999996072138466,
                0.9999997300422869,
                0.9999992661786696,
                0.9999990577557432,
                0.9999994956524716,
                0.9999996072137529,
                0.9999982396574164,
                0.9999995549148419,
                0.9999994284996893,
                0.9999994284996211
            ],
            [
                0.9999980052702786,
                0.9999970976883615,
                0.00033535002690887676,
                0.9999989322968754,
                0.9999945777790915,
                0.999991060304767,
                0.0002034269950968716,
                0.9999962733616046,
                0.9999885212332448,
                0.9999974387171787
            ],
            [
                0.9999998362623332,
                0.9999982396567868,
                0.9999974387171787,
                0.003172682594333856,
                0.9999980052693275,
                0.999999730042126,
                0.9999987901343167,
                0.999999428499553,
                0.9999996533672548,
                0.9999994284994168
            ],
            [
                0.9999970976876693,
                0.9999986290429567,
                0.9999938558239347,
                0.9999974387171787,
                0.9999982396559474,
                0.9999980052698031,
                0.9999151889789105,
                0.9999993524049702,
                0.9999980052709919,
                0.9999967112521114
            ],
            [
                0.9999885212264026,
                0.9999952149049358,
                0.9999898700114368,
                0.9999957771665557,
                0.9999967112517197,
                0.9999945777810312,
                0.9999967112509353,
                0.9999938558246684,
                0.9999852610233023,
                0.9999962733598278
            ],
            [
                0.9999930377412627,
                0.22270013366638422,
                0.8933094145755219,
                0.9999687980998037,
                3.120192252800261e-05,
                0.9999832985703765,
                0.07585818106587035,
                0.9999785550439179,
                0.04742587401904765,
                0.0002959570953956673
            ],
            [
                0.02033235434441098,
                0.9999997300422547,
                0.9999996533675028,
                0.00669285140412498,
                0.9999996533674615,
                0.9999991684719723,
                0.0008040858345204427,
                0.9999994284994848,
                0.001700722349569768,
                0.9999930377420911
            ],
            [
                0.9999251537817236,
                0.999995214906647,
                0.9999962733607163,
                0.9999898700126459,
                0.9999967112521111,
                0.9999987901337396,
                0.9999984465022458,
                0.999998239656577,
                0.999991060302632,
                0.999999607213753
            ],
            [
                0.9999994284994167,
                0.9999994956523512,
                0.9999997300421903,
                0.9999993524049703,
                0.9999980052695652,
                0.9999995549147359,
                0.9999997300421583,
                0.99999844650169,
                0.9999957771675623,
                0.9999997300422225
            ],
            [
                9.422449308566668e-07,
                8.939700566435704e-06,
                1.3709572068179446e-06,
                2.260325375650449e-06,
                2.9023126770343703e-06,
                4.450849988811838e-07,
                1.2098658277264215e-06,
                1.3709578605355551e-06,
                3.7266385141272173e-06,
                1.9947306725669014e-06
            ],
            [
                0.9999994284993486,
                0.9999989322966208,
                0.9999970976887069,
                0.9999990577556309,
                0.9999938558246659,
                0.9999996533672963,
                0.9999993524052019,
                0.9999994956524115,
                0.9999967112493667,
                0.9999991684715758
            ],
            [
                0.9999986290421395,
                0.9999977396759722,
                0.9999997897565838,
                0.999999266178757,
                0.9999989322967483,
                0.0017007222849371034,
                0.9999990577550691,
                0.999999352404893,
                0.9999990577549569,
                0.9999991684721706
            ],
            [
                2.9023112925670636e-06,
                1.3709575336405514e-06,
                8.939699499627926e-06,
                2.561282821352716e-06,
                1.2098655392662613e-06,
                1.0677027426952437e-06,
                1.3709578605455302e-06,
                6.47594720987407e-07,
                3.28875024125221e-06,
                1.3709576970537545e-06
            ],
            [
                0.9984988177516388,
                1.670141785651155e-05,
                5.422217030032353e-06,
                1.300713466316634e-05,
                6.9622570786798724e-06,
                4.7850950646797465e-06,
                6.605217614445361e-05,
                1.994729483630195e-06,
                1.670142183983204e-05,
                6.962258738701267e-06
            ],
            [
                0.0015011822930326316,
                7.484622708369406e-05,
                9.610246056517981e-05,
                0.0004305570787694201,
                0.000203426899920463,
                0.00029595709336348644,
                0.0005527786583409379,
                0.00010889696057483979,
                5.14422319797437e-05,
                0.00037998451939488164
            ],
            [
                2.4300252313904224e-05,
                3.1201903888114227e-05,
                7.484620042097855e-05,
                5.8291286313118594e-05,
                0.0005527787297320723,
                3.535625910055016e-05,
                0.000295957236726992,
                1.012999097799944e-05,
                1.892515499389843e-05,
                0.0005527786634219284
            ],
            [
                1.473898899742027e-05,
                9.610243779880144e-05,
                8.481103114893482e-05,
                0.000709670529170536,
                0.00043055703152336885,
                0.00013982214056894142,
                0.000261190337904862,
                1.892514597832254e-05,
                8.481104101029498e-05,
                5.82912515996789e-05
            ],
            [
                0.9999996072138934,
                0.9999992661787571,
                0.9999930377462407,
                0.9999994956526519,
                0.9999991684722697,
                0.003172682449272106,
                0.9999989322968754,
                0.04742587637519415,
                0.9999980052707543,
                0.9999977396757023
            ],
            [
                4.5397857795336036e-05,
                2.1444958622572883e-05,
                8.939694172290508e-06,
                0.00012339463372649704,
                5.144223201941656e-05,
                5.144220137064579e-05,
                5.144222587049821e-05,
                0.0009110513712540637,
                0.00015843629223915196,
                1.4738985484549675e-05
            ],
            [
                0.9999987901344607,
                0.9999990577551815,
                0.9999993524051246,
                0.9999986290424671,
                0.9999986290421399,
                0.9999962733620499,
                0.9999997300422547,
                0.9999967112497585,
                0.9999989322968754,
                0.9999982396567868
            ],
            [
                3.12019262070368e-05,
                2.1444956079218013e-05,
                1.4738978451438343e-05,
                2.7535681235270997e-05,
                4.006368259662828e-05,
                1.9947299592570416e-06,
                1.1478766755734576e-05,
                8.939695232316787e-06,
                5.422220908703723e-06,
                5.1442232001825764e-05
            ],
            [
                4.7850933535006355e-06,
                1.5534975693707442e-06,
                8.315277302819205e-07,
                1.012999580884213e-05,
                8.93969630348202e-06,
                6.962258739068529e-06,
                4.222833444506298e-06,
                6.14417753110761e-06,
                9.422450431912e-07,
                1.3709572068272963e-06
            ],
            [
                0.0003353501809866762,
                8.93969417199781e-06,
                1.3007126906036072e-05,
                0.0009110510552703289,
                0.00015843617813478082,
                0.0005527786578264075,
                0.0009110510460514891,
                0.0001795280046349924,
                0.00023050682184820075,
                0.0013250226224058087
            ],
            [
                0.9999962733589398,
                0.9999974387187055,
                0.9999987901340281,
                0.9999910603058291,
                0.9999952149060765,
                0.9999996072139402,
                0.999999352404893,
                0.9999992661789321,
                0.999999266178757,
                0.9999898700078143
            ],
            [
                0.9999996940977731,
                0.9999996533674202,
                0.9999995549147359,
                0.9999989322970028,
                0.9999997300422547,
                0.9999997300421583,
                0.9999997617631752,
                0.9999987901341724,
                0.9999995549151073,
                0.9999977396765106
            ],
            [
                3.7266410609160796e-06,
                5.422217675628357e-06,
                2.5612812945889277e-06,
                6.144175333401224e-06,
                1.994729721482609e-06,
                1.3709573702647743e-06,
                1.3709570433885908e-06,
                4.2228319341064674e-06,
                6.144176798479122e-06,
                1.0677028699955933e-06
            ],
            [
                2.430024941371131e-05,
                7.48462272410653e-05,
                2.1444956075707356e-05,
                4.006368738595465e-05,
                7.484624490204296e-05,
                7.484623605603429e-05,
                6.962256249606473e-06,
                1.4738987238893715e-05,
                2.430025231213619e-05,
                2.1444948402034417e-05
            ],
            [
                0.999997097688015,
                0.9999996940978095,
                0.9999921107374158,
                0.9999977396748944,
                0.999999428499553,
                0.9999991684717742,
                0.9999989322968754,
                0.9999996940978825,
                0.9999990577555185,
                0.9999984465018755
            ],
            [
                0.9999990577554062,
                0.9999989322973847,
                0.9999986290424664,
                0.9999984465024307,
                0.9999982396563679,
                0.9999993524052019,
                0.999999730042126,
                0.9999990577555186,
                0.9999986290431201,
                0.9999994956525918
            ],
            [
                5.422217030614265e-06,
                3.2887482812506295e-06,
                2.2603242977555607e-06,
                5.422220908762902e-06,
                3.2887498488809053e-06,
                2.9023112931213857e-06,
                7.338209805200689e-07,
                6.962257908880483e-06,
                1.7603425837494853e-06,
                8.315280276505193e-07
            ],
            [
                0.9999885212264085,
                0.9999982396574163,
                0.9999967112505429,
                0.9999930377445827,
                0.9999957771670596,
                0.9999938558232017,
                0.9999980052705165,
                0.9999970976873231,
                0.9999687980774852,
                0.9999869928684397
            ],
            [
                0.9999992661787571,
                0.9999996072138934,
                0.9999989322970027,
                0.9999974387177893,
                0.9999970976883615,
                0.9999995549150542,
                0.9999646437324408,
                0.9999945777823255,
                0.9999980052702787,
                0.999999168471675
            ],
            [
                8.31528126775552e-07,
                3.7266379512857925e-06,
                2.2603237588597026e-06,
                1.8925145971093502e-05,
                6.962258738827909e-06,
                4.785094494402695e-06,
                1.0129988562661878e-05,
                2.9023109470554753e-06,
                7.338208930443633e-07,
                2.902312677060767e-06
            ],
            [
                7.484621815546239e-05,
                0.9999945777784478,
                0.9999962733598278,
                0.9999832985821401,
                0.9999885212305079,
                0.9999938558224711,
                0.9999810748585424,
                0.999988521229139,
                0.999995214905507,
                0.9999990577552937
            ],
            [
                0.999996273360272,
                0.999999168471675,
                0.0019267345473631989,
                0.9999945777816776,
                0.9999998144608098,
                0.999999554914842,
                0.9999997617630332,
                0.9999987901343165,
                0.0002611903391740042,
                0.9999992661792819
            ],
            [
                0.9999997617630616,
                0.9999977396759716,
                0.9999986290424663,
                0.9999997300422869,
                0.9999986290424664,
                0.99999976176309,
                0.99999976176309,
                0.999998790134605,
                0.9999962733589395,
                0.999999694097846
            ],
            [
                2.9023116389761676e-06,
                2.5612828213352452e-06,
                2.260325375615501e-06,
                1.3709576971160984e-06,
                1.370957533676711e-06,
                1.7603436329978976e-06,
                3.726639283752725e-06,
                3.726639728184142e-06,
                1.3709576971160984e-06,
                1.5534983101301911e-06
            ],
            [
                1.9947299592824403e-06,
                3.2887486726287055e-06,
                3.726639284017094e-06,
                1.5534984953298217e-06,
                3.288750633518874e-06,
                1.0677028700266676e-06,
                4.785092782858221e-06,
                3.2887498493983645e-06,
                1.4738980211116665e-05,
                2.561281294616881e-06
            ],
            [
                0.9999930377454176,
                0.9999957771675664,
                0.9999930377462407,
                0.9999687980998037,
                0.9999832985821441,
                0.999994577778446,
                0.9999989322967482,
                0.9999980052702806,
                0.9999987901340281,
                0.9999885212305071
            ],
            [
                4.5397852399094525e-05,
                1.6701417859944398e-05,
                0.0010322309798542174,
                1.8925155005051806e-05,
                7.889260703619978e-06,
                4.0063711272110856e-05,
                0.0001795279214608635,
                0.00033535018812858204,
                0.0002959571332235112,
                6.605216826132997e-05
            ],
            [
                4.53978793499211e-05,
                0.9999810748540267,
                2.753569765708558e-05,
                0.000804085927258063,
                0.00020342689893785958,
                0.002800927054913503,
                3.120190760732817e-05,
                0.00023050666003312292,
                9.610239188711088e-05,
                5.1442232005568484e-05
            ],
            [
                0.9999852610197889,
                0.0007096703468001748,
                0.9999724643056561,
                0.9999599363221447,
                0.9999724643024414,
                0.9999945777784449,
                0.999989870012648,
                0.9999945777829704,
                0.9999938558275955,
                0.9999756997476829
            ],
            [
                0.9999832985821445,
                0.9999945777829695,
                0.999959936298325,
                0.999998790134605,
                0.9999994956524716,
                0.9999977396762411,
                0.9999989322972573,
                0.9999994284994849,
                0.999999266179282,
                0.9999984465018752
            ],
            [
                0.9999938558246662,
                0.9999977396751634,
                0.9999977396746244,
                0.9999990577551816,
                0.999998239656577,
                0.9999930377429219,
                0.9999967112517191,
                0.9999962733593833,
                0.9999952149072169,
                0.9999980052695656
            ],
            [
                3.059021175247079e-07,
                1.0677028700266676e-06,
                1.7603438428460541e-06,
                3.927863875584984e-07,
                3.4663249714325014e-07,
                1.9947290080905435e-06,
                2.561283431916622e-06,
                9.422449308566668e-07,
                1.2098653950551882e-06,
                8.315281267706361e-07
            ],
            [
                0.9999991684718733,
                0.9999997897566589,
                0.9999980052700408,
                0.999999789756684,
                0.999999168471675,
                0.9999996072137998,
                0.9999997300422225,
                0.9999957771660524,
                0.999999266178932,
                0.9999987901338842
            ],
            [
                0.9999957771680658,
                0.9999991684716751,
                0.9999898700126524,
                0.9999987901344607,
                0.9999957771645429,
                0.9999996940976272,
                0.005911067622179214,
                0.9999967112517189,
                0.999999352405279,
                0.9999989322967482
            ],
            [
                3.120190764966677e-05,
                2.7535700926183532e-05,
                0.0013250221272938733,
                0.0002611903393183976,
                3.535626333461766e-05,
                8.48110715112881e-05,
                7.889259763469998e-06,
                0.0004305571341820806,
                2.7535694360340682e-05,
                0.00026119024113088795
            ],
            [
                0.9999687980849506,
                0.13296425222296632,
                0.3486451285660856,
                0.9998766054556452,
                0.9995121428290514,
                0.9997694933671104,
                0.9999646437536852,
                0.9999038975508214,
                0.1066905854244781,
                0.10669060175672707
            ],
            [
                2.2603242978377903e-06,
                2.1444943292703185e-05,
                1.7603436330091044e-06,
                1.2098652508287273e-06,
                5.043475284447896e-07,
                7.338207180838067e-07,
                2.5612819053586272e-06,
                5.422220908634683e-06,
                8.315282259089153e-07,
                1.2098658277264215e-06
            ],
            [
                0.9999987901338839,
                0.9999986290427934,
                0.9999930377429228,
                0.9999993524052019,
                0.9999938558275958,
                0.999968798081212,
                0.9999974387171787,
                0.9999989322975119,
                0.9999945777829694,
                8.481104122255304e-05
            ],
            [
                0.18242552602881168,
                0.017986207659136923,
                0.11920292202211755,
                0.2942149659744614,
                0.9964063971109468,
                0.04742587688008271,
                0.13296425050508956,
                0.999664649791597,
                0.7981867825403177,
                0.11920292984474948
            ],
            [
                0.9999982396574163,
                0.9999994284994167,
                0.9999980052707542,
                0.9999990577550691,
                0.9999994284996211,
                0.9999980052693276,
                0.9999970976880155,
                0.999999352404893,
                0.9999994956524114,
                0.012431651573524372
            ],
            [
                0.999999428499553,
                0.9999984465028011,
                0.9999998144609424,
                0.9999996533674615,
                0.9999986290424665,
                0.9999996072137061,
                0.9999989322975119,
                0.9999982396567868,
                0.9999991684719723,
                0.9999967112505427
            ],
            [
                1.8925152739677025e-05,
                7.484621825620178e-05,
                0.00029595723532340883,
                3.120191135412508e-05,
                2.430024072471526e-05,
                1.670142582300158e-05,
                4.5397879378987325e-05,
                1.1478766755985128e-05,
                1.3007126909537681e-05,
                0.00015843621604585045
            ],
            [
                0.9999910603037002,
                0.9999921107402365,
                0.9999993524051246,
                0.9999984465015047,
                0.9999986290432838,
                0.9999898700126444,
                0.9999938558253991,
                0.9999957771660523,
                0.9999970976869783,
                0.9999990577554061
            ],
            [
                0.9999785550464846,
                0.9999921107345966,
                0.9999986290427935,
                0.9999994284996893,
                0.9999724643089352,
                0.9525741249711752,
                0.9995694429412714,
                0.8354835350552604,
                0.8933094103149355,
                0.9999038976084177
            ],
            [
                0.9999986290431201,
                0.9999952149066464,
                0.9999810748427519,
                0.9999945777823233,
                0.99999893229713,
                0.9999984465015049,
                0.9999977396757023,
                0.9999991684722698,
                0.9999980052698033,
                0.9999910603026323
            ],
            [
                0.0006263342854848357,
                0.0003799844809352247,
                0.002182716602037236,
                0.9999967112501505,
                0.999988521229142,
                0.999959936317534,
                0.9525741301883566,
                0.9999970976883619,
                0.0010322308875407998,
                0.9999977396757023
            ],
            [
                2.2603251062013478e-06,
                2.902312330849511e-06,
                5.422219615750493e-06,
                1.9947297214544894e-06,
                7.88926258343236e-06,
                5.422217030209884e-06,
                3.726639284050988e-06,
                5.043472278299047e-07,
                6.144173136952939e-06,
                1.2098662603961589e-06
            ],
            [
                1.8925157255968775e-05,
                4.785092783149804e-06,
                0.00037998457379557,
                4.785094494463623e-06,
                3.2887494573232236e-06,
                0.0031726829882833115,
                3.535623802218407e-05,
                1.1478769489343698e-05,
                2.7535681250497054e-05,
                5.422218968931258e-06
            ],
            [
                0.9999987901343166,
                0.9999995549150543,
                0.9999995549147889,
                0.9999984465024307,
                0.9999994956525318,
                0.999998629042303,
                0.999998239656367,
                0.9999993524051246,
                0.9999967112517187,
                0.9999994956524114
            ],
            [
                3.2887478890769702e-06,
                2.902313022984344e-06,
                5.04347528440776e-07,
                5.043475885674441e-07,
                9.422445938964242e-07,
                4.785093924156175e-06,
                1.2098652508287273e-06,
                5.715004470295662e-07,
                1.0677024881499412e-06,
                9.422447062094932e-07
            ],
            [
                8.315283250343497e-07,
                4.22283545795623e-06,
                1.3007130012980722e-05,
                1.7603427936263351e-06,
                6.962255419570695e-06,
                2.9023109470554753e-06,
                2.902312677060767e-06,
                4.785094494463623e-06,
                2.9023133690188264e-06,
                1.0677026153784014e-06
            ],
            [
                1.0129987355785634e-05,
                4.0063677828144015e-05,
                1.3007126907881513e-05,
                4.222833443968609e-06,
                7.484624505832518e-05,
                0.0010322311643610335,
                4.785093924047376e-06,
                8.93969630388855e-06,
                5.422218968595919e-06,
                1.4738987237124277e-05
            ],
            [
                0.999998790134606,
                0.999996711249367,
                0.9999984465015048,
                0.999981074851767,
                0.9999986290426298,
                0.9999930377454106,
                0.9999599363030631,
                0.9999991684719723,
                0.9999724642990617,
                0.9999756997534839
            ],
            [
                8.315280276399315e-07,
                2.9023116390421582e-06,
                6.144172404218801e-06,
                1.5534975693707442e-06,
                1.5534975693707442e-06,
                5.715005832762133e-07,
                1.5534981249397663e-06,
                1.2098653950403334e-06,
                9.422444815563743e-07,
                1.370957370236096e-06
            ],
            [
                0.9999990577549569,
                0.9999996940977002,
                0.9999991684720715,
                0.9999994284993488,
                0.9999986290427931,
                0.9999982396563671,
                0.9999974387171787,
                0.9999992661791072,
                0.9999990577549568,
                0.9999996533672136
            ],
            [
                0.00017952804981488825,
                0.00026119024281041084,
                0.02297736823741426,
                1.0129987355564522e-05,
                0.00015843619734157965,
                2.4300237828943813e-05,
                2.7535694375867267e-05,
                8.9396941702904e-06,
                0.00017952790062228017,
                0.00013982209018104417
            ],
            [
                0.9999952149055066,
                0.9999997300422547,
                0.9999994284994168,
                0.999993037746242,
                0.9999984465026168,
                0.9999996940977731,
                0.9999991684719725,
                0.999998629042303,
                0.9999997300421903,
                0.9999962733620491
            ],
            [
                0.9999997617630332,
                0.999999168471675,
                0.9999996072138466,
                0.999999495652652,
                0.9999986290424664,
                0.9999991684722698,
                0.9999997300420939,
                0.9999992661792825,
                0.9999994284996891,
                0.9999994284994849
            ],
            [
                0.9999970976880155,
                0.9999980052698033,
                0.999997097686631,
                0.9999977396754329,
                0.9999982396574163,
                0.9999984465028013,
                0.9999967112509349,
                0.9999984465024309,
                0.9999989322972573,
                0.99999893229713
            ],
            [
                0.9999885212264035,
                0.9999910603036979,
                0.9999810748472546,
                0.9999945777784456,
                0.999925153781868,
                0.9999852610162783,
                0.9999977396762412,
                0.9999756997477003,
                0.999986992868442,
                0.9999982396561572
            ],
            [
                0.9999980052698031,
                0.9999997300422869,
                0.9999984465024307,
                0.9999990577551815,
                0.9999995549151073,
                0.9999996940976271,
                0.9999997897566089,
                0.9999996533674202,
                0.9999970976876692,
                0.9999997617631469
            ],
            [
                6.605215244462661e-05,
                7.48462272160166e-05,
                0.00033534998587221034,
                3.120191508185304e-05,
                7.484625386839543e-05,
                0.0009110512825624411,
                5.144223815074485e-05,
                3.120190765193695e-05,
                1.4738978454950406e-05,
                0.00017952802932107503
            ],
            [
                0.9999986290429568,
                0.9999987901341724,
                0.9999989322970027,
                0.9999930377454109,
                0.9999945777810313,
                0.9999996533673788,
                0.9999987901338839,
                0.9999994284996211,
                0.9999930377404309,
                0.9999962733620493
            ],
            [
                0.9999987901337396,
                0.9999992661789321,
                0.005220124953613327,
                0.9999885212359801,
                0.9999996533674204,
                0.999999428499553,
                0.9999869928684365,
                0.9999994284992804,
                0.9999996940977001,
                0.9999974387168733
            ],
            [
                2.1444945840269323e-05,
                1.3007125359792008e-05,
                7.48462628538078e-05,
                7.889264465239894e-06,
                0.0021827168018323,
                0.00020342701706339652,
                0.0005527785248524049,
                5.144220127670351e-05,
                0.00857748507315692,
                0.00013982210734726777
            ],
            [
                0.9999970976880151,
                0.9999756997563805,
                0.9999952149055067,
                0.9999952149072169,
                0.9999832985781592,
                0.9999970976887075,
                0.9999957771680659,
                0.9999898700053994,
                0.9999921107364745,
                0.9999938558224688
            ],
            [
                0.9999989322968754,
                0.9999994284996894,
                0.9999987901347491,
                0.9999994956526519,
                0.9999996072136593,
                0.999999789756684,
                0.9999984465020603,
                0.999999554914895,
                0.9999991684715759,
                0.999996273361161
            ],
            [
                0.9999994956525318,
                0.9999997617629764,
                0.9999984465018751,
                0.9999989322972572,
                0.9999996072138934,
                0.9999974387171787,
                0.9999986290424664,
                0.999999730042126,
                0.9999987901347491,
                0.9999994284992805
            ],
            [
                0.9998204719486101,
                0.9999885212305069,
                3.535625067383256e-05,
                0.999925153781868,
                0.9999921107355361,
                9.610240341642045e-05,
                0.9999417087414739,
                0.00012339453062351613,
                0.9999485577618208,
                0.9999151889489136
            ],
            [
                0.9999987901347497,
                0.9999952149049353,
                0.9999993524052019,
                0.9999987901337397,
                0.9999974387180947,
                0.9999977396757023,
                0.9999952149037948,
                0.9999986290427932,
                0.9999980052693274,
                0.9999967112517224
            ],
            [
                0.9999957771650484,
                0.9999996940978095,
                0.0001398220403526234,
                0.9999938558275964,
                0.999998790134028,
                0.9999994284996893,
                0.9999995549150011,
                0.9999898700102313,
                0.999998446502801,
                0.999992110739296
            ],
            [
                8.315282259117513e-07,
                6.9622562487453084e-06,
                2.260323489299784e-06,
                3.466327037548308e-07,
                1.3709570433979422e-06,
                1.5534973841592143e-06,
                2.9023133690425823e-06,
                5.043476486883855e-07,
                1.0677032518700286e-06,
                4.4508526417014975e-07
            ],
            [
                0.9999992661787571,
                0.9999994284995529,
                0.9999986290423029,
                0.9999992661786696,
                0.9999980052709919,
                0.9999989322968754,
                0.9999990577554061,
                0.0008040857716665095,
                0.9999980052695653,
                0.9999977396759725
            ],
            [
                3.726637951170554e-06,
                1.8925157262061825e-05,
                0.0001088969475123316,
                8.939698434966738e-06,
                0.000295957052452933,
                5.4222215550004564e-06,
                6.144173869312763e-06,
                5.422217676397663e-06,
                3.726641060956752e-06,
                5.422218323231539e-06
            ],
            [
                5.829129323782717e-05,
                0.00020342707012401784,
                0.00013982212250147666,
                0.0002305068244974993,
                0.00010889696044015842,
                6.1441746017453204e-06,
                7.484620928658632e-05,
                1.1478766755734576e-05,
                5.422217676925328e-06,
                0.0008040859213187396
            ],
            [
                2.144494074076854e-05,
                0.008577486435377259,
                0.0017007227146356618,
                2.4300246504236573e-05,
                0.0004305571343824881,
                1.6701419852819694e-05,
                1.4738985485997396e-05,
                5.144219520863158e-05,
                8.481102063969529e-05,
                4.539787944306515e-05
            ],
            [
                9.422448185388577e-07,
                3.2887506334201674e-06,
                3.288750241374845e-06,
                2.260324836651547e-06,
                2.561281294616881e-06,
                1.3709572068179446e-06,
                3.72664017246987e-06,
                1.7603440526662173e-06,
                1.2098662604192665e-06,
                8.315283250343497e-07
            ],
            [
                3.2887494572095624e-06,
                1.994729008105057e-06,
                4.7850939242083995e-06,
                8.93969310584124e-06,
                1.2098661161982042e-06,
                1.5534975693792215e-06,
                1.1478765388314311e-05,
                1.0129995809431767e-05,
                1.3709573702647743e-06,
                1.553498495338299e-06
            ],
            [
                0.9999982396563669,
                0.9999974387168733,
                0.9999962733611604,
                0.9999945777797387,
                0.9999945777829696,
                0.9999982396574164,
                0.999988521234614,
                0.999997097686977,
                0.9999986290429567,
                0.9999957771655489
            ],
            [
                2.1444958632714784e-05,
                5.144223816384438e-05,
                1.3007125362323574e-05,
                6.605217602719671e-05,
                2.144495608046625e-05,
                1.1478764018305152e-05,
                1.6701423833011596e-05,
                7.484625385369293e-05,
                4.222834954753043e-06,
                8.93969630317306e-06
            ],
            [
                4.7850939242083995e-06,
                4.222833444506298e-06,
                7.338211554641698e-07,
                4.785092782936557e-06,
                2.260324836651547e-06,
                8.939695237813028e-06,
                1.6701425823457267e-05,
                1.2098661161861e-06,
                1.994730197071414e-06,
                3.7266410608720178e-06
            ],
            [
                0.9999957771655515,
                0.9999970976880149,
                0.9999957771655493,
                0.9999991684717742,
                0.9999885212332442,
                0.9999945777816768,
                0.999998005269328,
                0.9999992661791947,
                0.9999992661786696,
                0.9999974387171787
            ],
            [
                3.2887494571676872e-06,
                2.2603248367656408e-06,
                2.902313368583287e-06,
                4.222831934156396e-06,
                2.5612812945260317e-06,
                7.338210679979539e-07,
                4.785096776251149e-06,
                1.3709567165461505e-06,
                1.994729483705484e-06,
                7.338208930443633e-07
            ],
            [
                0.9999997300422869,
                0.9999885212359833,
                0.9999967112493665,
                0.9999997300422547,
                0.9999990577556308,
                0.9999998724810026,
                0.9999996072136125,
                0.9999996940977731,
                0.9999984465016899,
                0.9999999123574942
            ],
            [
                2.5612822104977725e-06,
                4.22283545795623e-06,
                2.2603251061664e-06,
                5.422218323093458e-06,
                1.370956879949281e-06,
                7.88926070293116e-06,
                5.422218969306048e-06,
                4.7850956352353935e-06,
                5.42221702914469e-06,
                1.994729008105057e-06
            ],
            [
                5.8291251550907405e-05,
                2.1444950954750122e-05,
                0.0009110512794894937,
                1.8925155000714377e-05,
                3.1201911328358685e-05,
                5.1442201347440924e-05,
                8.939693105272102e-06,
                1.3007131561804229e-05,
                3.12019076269651e-05,
                7.889264466115267e-06
            ],
            [
                0.999999495652652,
                0.999999554914895,
                0.999999352404893,
                0.9999993524049702,
                0.9999993524049703,
                0.9999993524049703,
                0.9999996533673376,
                0.9999992661790196,
                0.9999990577555185,
                0.9999996072138934
            ]
        ]
    },
    {
        "q_id": "7993_mmlu_math",
        "cot_ids": [
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            36,
            37,
            38,
            40,
            41,
            42,
            43,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            58,
            60,
            61,
            62,
            63,
            64,
            66,
            67,
            70,
            71,
            74,
            78,
            79,
            80,
            81,
            82,
            83,
            85,
            86,
            88,
            89,
            90,
            91,
            92,
            94,
            95,
            96,
            97,
            99,
            100,
            101,
            102,
            103,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            116,
            117,
            118,
            119,
            120,
            122,
            123,
            125,
            127
        ],
        "rewards": [
            [
                0.9999967112505429,
                0.9999967112509348,
                0.9999980052709921,
                0.9999724643056319,
                0.9999986290424663,
                0.9999991684719723,
                0.999999554914789,
                0.9999984465024307,
                0.9999986290427935,
                0.9999989322968754
            ],
            [
                0.00015843621658295862,
                6.60521682560438e-05,
                5.829125158695591e-05,
                9.610239198289712e-05,
                8.481102081493154e-05,
                8.939694169835089e-06,
                9.610239202344896e-05,
                0.00023050671512508768,
                6.605216828583859e-05,
                6.605215254506384e-05
            ],
            [
                1.4738987242700688e-05,
                1.4738976699106073e-05,
                1.4738978455325741e-05,
                6.962256249606473e-06,
                1.4738988995838502e-05,
                1.8925152741191683e-05,
                5.42221767672807e-06,
                6.962257079059797e-06,
                8.93969950101825e-06,
                3.288750633545794e-06
            ],
            [
                1.8925148238291944e-05,
                2.561281599881745e-06,
                NaN,
                8.93969630317306e-06,
                4.222834451012227e-06,
                2.753568119580344e-05,
                2.5612834318257725e-06,
                4.78509563466093e-06,
                2.4300232029003796e-05,
                1.3007130014376633e-05
            ],
            [
                1.0129993393742954e-05,
                3.5356267533443565e-05,
                4.785092782597101e-06,
                1.0129992184544441e-05,
                6.144173869240119e-06,
                4.222833444467892e-06,
                1.8925145980732218e-05,
                1.1478770855323762e-05,
                3.5356267537559426e-05,
                7.889263524960312e-06
            ],
            [
                2.260323758835034e-06,
                2.1444953506061874e-05,
                1.0129987354366822e-05,
                6.962256244287517e-06,
                NaN,
                NaN,
                3.2887494572514376e-06,
                3.7266410608245674e-06,
                1.4738978452886064e-05,
                NaN
            ],
            [
                1.8925148237775583e-05,
                3.535623803478889e-05,
                6.14417386791016e-06,
                4.7850944945245504e-06,
                1.5534984952662413e-06,
                1.01299946023704e-05,
                1.76034258364702e-06,
                4.222833444168322e-06,
                NaN,
                3.2887498491620677e-06
            ],
            [
                5.422220262333096e-06,
                8.939700565834043e-06,
                2.430023493564795e-05,
                1.0129990978220553e-05,
                2.2603248355311635e-06,
                3.726639728262097e-06,
                5.422219615967477e-06,
                3.2887482812506295e-06,
                7.338212429367364e-07,
                6.475950297421001e-07
            ],
            [
                3.120190392670705e-05,
                7.889265407090955e-06,
                4.2228349547223175e-06,
                7.889260704631679e-06,
                3.2887498488151014e-06,
                5.422217674937953e-06,
                1.1478764018827141e-05,
                1.1478766756653273e-05,
                2.5612825157045092e-06,
                6.962255419380732e-06
            ],
            [
                1.2098658274595828e-06,
                4.785093923916815e-06,
                2.2603240283888175e-06,
                1.370957697068717e-06,
                1.0129992186202796e-05,
                2.2603242978213447e-06,
                8.315283250343497e-07,
                2.2603251061849014e-06,
                4.785093353787868e-06,
                2.9023116390421582e-06
            ],
            [
                4.0063682603624035e-05,
                7.889266346129453e-06,
                2.1444940724775554e-05,
                1.670141587031992e-05,
                6.962259568078904e-06,
                2.144494581132591e-05,
                1.892514595271109e-05,
                4.22283394762097e-06,
                3.120191508321514e-05,
                5.422218967944967e-06
            ],
            [
                3.2887478891128633e-06,
                6.144177530146464e-06,
                4.222834954280646e-06,
                2.9023116388969785e-06,
                7.889265406438011e-06,
                3.726637951126493e-06,
                3.2887502414436403e-06,
                3.2887498492936755e-06,
                1.2098662602663157e-06,
                2.2603242977802297e-06
            ],
            [
                6.14417679836736e-06,
                7.484623553817936e-05,
                1.4738988997044936e-05,
                1.0129990974903845e-05,
                7.889260703763482e-06,
                7.484623586490171e-05,
                5.422221554374162e-06,
                1.4738987235622935e-05,
                2.7535704201392335e-05,
                3.5356238040705445e-05
            ],
            [
                3.535624648041073e-05,
                1.8925152733687252e-05,
                1.0129995803996048e-05,
                7.889261644875049e-06,
                6.962255419653012e-06,
                1.5534975693601474e-06,
                6.962257078819179e-06,
                1.670142581883963e-05,
                1.1478772226690907e-05,
                1.0129994597524319e-05
            ],
            [
                1.0129992185299915e-05,
                4.785095064523075e-06,
                9.422443692446175e-07,
                2.260324028045508e-06,
                2.2603237589542675e-06,
                4.222832437747125e-06,
                4.222832941111319e-06,
                6.1441775312976045e-06,
                3.2887486733420804e-06,
                6.1441738691562974e-06
            ],
            [
                3.120192621804711e-05,
                1.0129992186939844e-05,
                6.144176797283277e-06,
                8.939700564468113e-06,
                1.7603438427660027e-06,
                1.0129993394664264e-05,
                1.7603440518929245e-06,
                5.4222202621161125e-06,
                8.939698434332555e-06,
                1.5534984952662413e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                7.889265394125388e-06,
                1.0129990971550284e-05,
                NaN,
                NaN,
                NaN,
                3.535626751337872e-05
            ],
            [
                3.2887494572514376e-06,
                5.422219615286937e-06,
                1.892514823013346e-05,
                4.222834954461155e-06,
                2.5612816000145246e-06,
                3.726640616477725e-06,
                2.5612819053399912e-06,
                6.144172403470001e-06,
                6.96225873895455e-06,
                1.5534971989696065e-06
            ],
            [
                1.7603434231241496e-06,
                1.6701415858046724e-05,
                3.726639283806955e-06,
                4.785093353274332e-06,
                2.1444945835198374e-05,
                3.7266392838544054e-06,
                7.889260704179641e-06,
                0.00029595717099969423,
                1.8925145981283003e-05,
                3.2887482809455384e-06
            ],
            [
                2.5612831266608576e-06,
                1.3709570433786157e-06,
                4.222834954514924e-06,
                1.3709576971242028e-06,
                6.962256248606003e-06,
                3.726638395493353e-06,
                1.0677026153919963e-06,
                6.14417753110761e-06,
                1.5534975693205863e-06,
                4.785092783415276e-06
            ],
            [
                2.4300243618542217e-05,
                1.8925154965188806e-05,
                1.0129990978220553e-05,
                1.4738983720179032e-05,
                5.144222574736265e-05,
                5.422218969463855e-06,
                3.1201907628667734e-05,
                2.4300246501849726e-05,
                5.144223817619536e-05,
                1.8925157257965367e-05
            ],
            [
                2.9023126770343703e-06,
                5.422218969532895e-06,
                4.785092782858221e-06,
                8.31528324227788e-07,
                2.14449533973095e-05,
                1.5534977534646952e-06,
                2.902312676044509e-06,
                NaN,
                3.726639283901856e-06,
                1.67014178576052e-05
            ],
            [
                9.610238045498727e-05,
                0.00020342694656453353,
                8.481102086552792e-05,
                1.8925145982350146e-05,
                0.00020342694702623886,
                8.481103099344347e-05,
                6.605216823537969e-05,
                0.0001398221239682756,
                0.0002034268973988422,
                6.605215252055522e-05
            ],
            [
                8.939694170940841e-06,
                9.610242629256036e-05,
                1.1478764018305152e-05,
                1.01299933928585e-05,
                2.7535691079423274e-05,
                4.539787393897876e-05,
                0.0002611903052947494,
                4.785096775998733e-06,
                3.1201926235527406e-05,
                1.6701425825492673e-05
            ],
            [
                3.5356246488642456e-05,
                3.7266379512112265e-06,
                5.422218969128516e-06,
                1.473898371326214e-05,
                1.5534973841450852e-06,
                1.3007131562845248e-05,
                1.2098656834349874e-06,
                7.88925976397226e-06,
                4.222834953896582e-06,
                3.2887486731252264e-06
            ],
            [
                4.5397884871679096e-05,
                8.481108148371828e-05,
                NaN,
                6.605212100874168e-05,
                9.610244931343393e-05,
                2.2603245671490605e-06,
                NaN,
                NaN,
                NaN,
                3.1201903857921005e-05
            ],
            [
                6.9622562489985925e-06,
                2.2603240274082256e-06,
                1.3709572066558505e-06,
                1.1478766743561818e-05,
                2.260324297097721e-06,
                1.5534981247144094e-06,
                2.4300234937946394e-05,
                4.7850933521167006e-06,
                1.3709576966834319e-06,
                3.7266401722360055e-06
            ],
            [
                4.785096776251149e-06,
                7.338209805040511e-07,
                8.31528424151477e-07,
                7.338210679816025e-07,
                2.902311292831027e-06,
                2.9023126768680736e-06,
                9.422447061679302e-07,
                4.785095064523075e-06,
                9.422444815409489e-07,
                8.315279284430651e-07
            ],
            [
                7.889261644760245e-06,
                2.260325105870372e-06,
                1.1478769493916314e-05,
                6.144172403827636e-06,
                1.3709575336860625e-06,
                2.144494581132591e-05,
                1.3007128463069061e-05,
                2.5612831265630198e-06,
                1.1478769487840372e-05,
                1.9947292458930106e-06
            ],
            [
                3.726639728224814e-06,
                2.2603251060142746e-06,
                6.144177531208195e-06,
                2.561282821352716e-06,
                5.422218323290717e-06,
                1.3007131542403415e-05,
                3.72664017246987e-06,
                3.726639728348526e-06,
                1.3007130015299356e-05,
                5.422217676979575e-06
            ],
            [
                1.4738980188435699e-05,
                2.7535681236473055e-05,
                3.120190388993035e-05,
                0.00013982214030853883,
                2.7535684524701807e-05,
                3.5356246482211416e-05,
                2.144495606813994e-05,
                1.147876538789672e-05,
                4.785094494019719e-06,
                1.0129995809247506e-05
            ],
            [
                1.5534977545497995e-06,
                3.7266383954560706e-06,
                2.9023112930659533e-06,
                1.7603430034439723e-06,
                3.4663266242969896e-07,
                6.962257908880483e-06,
                3.288749457409966e-06,
                4.7850967742927495e-06,
                1.3709578605118645e-06,
                4.222834450328596e-06
            ],
            [
                2.561281599914358e-06,
                4.785096775842062e-06,
                4.785095064819011e-06,
                9.610246075745164e-05,
                1.6701419845680582e-05,
                2.144495096723246e-05,
                6.144176066443055e-06,
                3.288750241204353e-06,
                2.1444940715959902e-05,
                3.53562591107112e-05
            ],
            [
                7.48462272410653e-05,
                4.0063701693307245e-05,
                7.48462182289749e-05,
                2.7535700931292276e-05,
                4.5397863219323224e-05,
                8.481105146153628e-05,
                4.539786323088365e-05,
                8.48110210734667e-05,
                0.00012339454537815678,
                9.610241477233725e-05
            ],
            [
                2.9023133690821773e-06,
                8.315284241401329e-07,
                1.553498495295912e-06,
                2.2603234893861252e-06,
                3.9278605978261504e-07,
                1.2098659719601033e-06,
                1.1478769490053603e-05,
                7.338208930078229e-07,
                1.3709570434054234e-06,
                7.338211554725124e-07
            ],
            [
                4.5397868609620665e-05,
                0.00023050682421580176,
                0.00023050671287150817,
                0.0001398220905167193,
                0.0002305068230420619,
                0.0001088969221019232,
                0.00013982213941340482,
                0.0008040858074427433,
                5.829125155557251e-05,
                3.1201922523121745e-05
            ],
            [
                6.962259568078904e-06,
                1.5534975693036317e-06,
                6.144172404380855e-06,
                1.3709570434054234e-06,
                1.2098662602046953e-06,
                9.422445938861406e-07,
                1.3709578603659798e-06,
                6.475950297906914e-07,
                1.760343842833246e-06,
                1.994729245842213e-06
            ],
            [
                0.9999977396749247,
                0.9999980052700448,
                0.9998601779470037,
                0.4687906266262437,
                0.9999945777804327,
                0.6791787056691697,
                NaN,
                0.9999910603058371,
                0.7057850216484837,
                0.9999885212361195
            ],
            [
                3.288749065209246e-06,
                8.93969523358515e-06,
                6.962259567914269e-06,
                6.962256249429175e-06,
                1.1478765386623071e-05,
                1.8925148216088467e-05,
                7.889263525663481e-06,
                5.829129331543752e-05,
                NaN,
                7.88926258343236e-06
            ],
            [
                0.9999993524050474,
                0.9999982396565769,
                0.9999970976883621,
                0.9999832985742226,
                0.9999898700114376,
                0.9999962733607167,
                0.9999987901341724,
                0.9999987901344607,
                0.9999756997592727,
                0.9999987901344608
            ],
            [
                1.7603430033158905e-06,
                1.6701415862785876e-05,
                2.561282515820982e-06,
                NaN,
                5.422218323290717e-06,
                2.561282820785491e-06,
                3.7266401690635765e-06,
                6.962257078819179e-06,
                3.1201918802543923e-05,
                2.2603240281935217e-06
            ],
            [
                3.2887494567788457e-06,
                2.9023112931213857e-06,
                1.1478765383679059e-05,
                2.260324567227179e-06,
                6.9622537570932415e-06,
                1.3709567164962755e-06,
                3.7266379506485954e-06,
                4.785096775920397e-06,
                1.3007128458384476e-05,
                1.5534973841705173e-06
            ],
            [
                5.144220132161615e-05,
                2.7535681228559507e-05,
                2.144495863045236e-05,
                1.8925155003330605e-05,
                1.1478768123551712e-05,
                8.939698434332555e-06,
                2.7535697658087296e-05,
                3.7266397278791014e-06,
                NaN,
                5.422218322457301e-06
            ],
            [
                1.209865395009523e-06,
                2.9023130230133794e-06,
                4.4508489275145346e-07,
                2.2603248367512505e-06,
                3.7266392836984955e-06,
                5.4222183222304545e-06,
                9.422447062150634e-07,
                2.9023116391477434e-06,
                6.962257909501028e-06,
                2.9023112931688987e-06
            ],
            [
                0.999988521227774,
                0.9999945777784452,
                0.9999898700126623,
                0.9999938558268652,
                0.9999957771665565,
                0.9999852610233075,
                0.999978555041611,
                0.9999852610233815,
                0.9999910603015691,
                0.9999687980812496
            ],
            [
                2.4300240728958537e-05,
                0.00010889696094085623,
                1.4738976695942536e-05,
                1.0129990977759901e-05,
                4.539789028526512e-05,
                7.889265405505236e-06,
                4.222832437497486e-06,
                0.00017952790125438557,
                6.605216828103296e-05,
                3.535626334156318e-05
            ],
            [
                2.430023493052066e-05,
                5.8291286322448804e-05,
                1.892514597343433e-05,
                NaN,
                3.7266379506485954e-06,
                9.422444811750245e-07,
                4.785096204537733e-06,
                1.1478772229781076e-05,
                1.1478773599102191e-05,
                NaN
            ],
            [
                0.9999989322972572,
                0.9999994284993486,
                0.9999999226557684,
                0.999999352404893,
                0.9999992661791944,
                0.9999991684718732,
                0.9999945777810305,
                0.999999694097846,
                0.999999352404893,
                0.9999989322968754
            ],
            [
                0.00020342694499000003,
                0.006692849506434881,
                0.001032231163520729,
                0.0001233945737204296,
                2.4300232011058275e-05,
                5.829128625501688e-05,
                2.430023781329673e-05,
                2.753568450797317e-05,
                8.939699496489538e-06,
                1.3007125361755747e-05
            ],
            [
                2.75357009372024e-05,
                2.902312330759764e-06,
                1.1478772224060087e-05,
                1.0129992185060374e-05,
                4.7850967754851966e-06,
                3.5356242243001115e-05,
                8.939693105662367e-06,
                2.561282210194942e-06,
                2.5612825155181522e-06,
                1.0129987356541108e-05
            ],
            [
                1.300712535865635e-05,
                1.3709578603435361e-06,
                1.1478768123551712e-05,
                5.4222183231674305e-06,
                2.1444943291142893e-05,
                1.3007123797838208e-05,
                2.260323758746637e-06,
                1.2098661153987887e-06,
                4.785096205778054e-06,
                9.422443692489024e-07
            ],
            [
                0.003172682736450196,
                2.4300246523066122e-05,
                2.561281905376098e-06,
                3.2887478891487563e-06,
                9.42244256886598e-07,
                8.939699499026267e-06,
                7.889263526180094e-06,
                3.1201918794144304e-05,
                3.2887506333812835e-06,
                1.6701429806475863e-05
            ],
            [
                1.3007126911335805e-05,
                6.96225458885115e-06,
                2.430024650998268e-05,
                2.1444953522913026e-05,
                3.2887494572095624e-06,
                1.1478769488257963e-05,
                8.48110512764275e-05,
                5.422221554670048e-06,
                2.4300232032009452e-05,
                7.484625371483588e-05
            ],
            [
                0.9999996072138934,
                0.9999986290432834,
                0.9999996072138934,
                0.999998239656367,
                0.9999993524050474,
                0.9999992661791944,
                0.9999980052693274,
                0.9999910602994336,
                0.9999989322975118,
                0.9999989322975119
            ],
            [
                5.144220134032976e-05,
                1.8925143720384422e-05,
                5.1442219775101506e-05,
                2.430024360881804e-05,
                6.144177531532303e-06,
                2.4300252308334918e-05,
                6.962253759670401e-06,
                6.962258738827909e-06,
                2.430023782010365e-05,
                0.9669140239948331
            ],
            [
                5.1442201281194775e-05,
                6.144176799099397e-06,
                4.222834943365576e-06,
                1.892515049423401e-05,
                1.0129994602222992e-05,
                4.785094494672519e-06,
                1.300712381094558e-05,
                6.962254589705982e-06,
                1.3007131564903626e-05,
                4.222834450950777e-06
            ],
            [
                NaN,
                NaN,
                0.9998601779435066,
                0.9998415638509935,
                NaN,
                0.5621765008857981,
                0.9998601779434821,
                0.8933094032139576,
                0.32082129433083023,
                0.9990889489947445
            ],
            [
                3.726639283806955e-06,
                1.3007131561425676e-05,
                8.939697368305565e-06,
                4.0063701700885974e-05,
                2.2603237584218285e-06,
                1.994729483608425e-06,
                1.892515049423401e-05,
                6.9622545892184106e-06,
                6.1441746016670885e-06,
                2.1444958636771547e-05
            ],
            [
                7.889262584809997e-06,
                3.535623802655717e-05,
                1.6701421837158667e-05,
                2.1444950958338794e-05,
                1.3007131561425676e-05,
                2.1444956077189637e-05,
                7.889264466639056e-06,
                1.6701423823533284e-05,
                5.144219521911119e-05,
                4.222834451292594e-06
            ],
            [
                6.144175333635923e-06,
                1.3007131561425676e-05,
                1.4738988997768797e-05,
                8.939693103418341e-06,
                1.0129993390610508e-05,
                1.3007134665934505e-05,
                8.939694171135975e-06,
                2.9023116390104826e-06,
                1.0129988563914856e-05,
                2.4300246525983375e-05
            ],
            [
                1.209865683518615e-06,
                2.7535694354731078e-05,
                3.7266392836374875e-06,
                2.561282210194942e-06,
                2.902311293034278e-06,
                1.3709578605455302e-06,
                1.0677029972745947e-06,
                2.561282210618905e-06,
                1.1478773597390071e-05,
                1.3709567164962755e-06
            ],
            [
                3.726640171327661e-06,
                2.260324297570543e-06,
                1.6701421840804172e-05,
                7.338209804506587e-07,
                2.7535697590471516e-05,
                8.315283248842301e-07,
                8.939699497335115e-06,
                4.222831934202483e-06,
                5.043474081629207e-07,
                2.2603251059484907e-06
            ],
            [
                1.0129990979031306e-05,
                2.144494072961245e-05,
                1.0129989769464556e-05,
                1.4738976696371488e-05,
                3.7266383955611403e-06,
                NaN,
                3.726638839395927e-06,
                8.93969310675186e-06,
                5.422221555192784e-06,
                4.222831934156396e-06
            ],
            [
                0.9999930377429258,
                0.9999962733616093,
                NaN,
                0.9999417087451721,
                0.9999151889192825,
                0.9999885212346604,
                NaN,
                0.9999832985742657,
                0.9998911031050927,
                NaN
            ],
            [
                0.9999998555019962,
                0.9999992661792819,
                0.9999997617631184,
                0.9999997300421903,
                0.9999993524054335,
                0.9999997617630332,
                0.9999997617631468,
                0.9999994956523514,
                0.9999996533675028,
                0.9999898700066139
            ],
            [
                5.422217029509618e-06,
                4.785096205582214e-06,
                4.2228334438149845e-06,
                2.5612815999423112e-06,
                8.939700566435704e-06,
                5.422220907554695e-06,
                7.889263525663481e-06,
                0.0001398221226967786,
                8.939693106020111e-06,
                5.144221973168594e-05
            ],
            [
                0.9999251537553245,
                0.9998601779433335,
                0.08509904616718289,
                0.999999730042319,
                0.9999898700054144,
                0.9999977396765105,
                0.999998446502616,
                0.9999938558239365,
                0.9999962733611729,
                0.7772998560157665
            ],
            [
                1.0129993394959082e-05,
                1.0129995809431767e-05,
                4.539786857692116e-05,
                1.892515275165658e-05,
                7.889264466445326e-06,
                1.3007125360478133e-05,
                8.939700566289352e-06,
                2.4300234931404677e-05,
                4.222834954211514e-06,
                6.962258738827909e-06
            ],
            [
                0.9999885212291578,
                0.9999785550490321,
                0.9999756997563912,
                0.9999756997564893,
                0.9999910603068946,
                0.9999921107383631,
                0.9999832985761714,
                0.9999974387177893,
                0.9999930377420909,
                0.9999687980960875
            ],
            [
                0.9999852610238863,
                0.9997388096047861,
                0.9999885212346283,
                0.9999417087227287,
                0.9998415638507815,
                0.9999485577835227,
                0.9999869928669034,
                0.9999930377437515,
                NaN,
                0.6513548782017745
            ],
            [
                1.1478772229300848e-05,
                3.288750241204353e-06,
                4.222834451292594e-06,
                3.2887498494282754e-06,
                1.5534979397140412e-06,
                NaN,
                1.5534977545102382e-06,
                6.1441767989541075e-06,
                1.994730434798734e-06,
                4.785096776133645e-06
            ],
            [
                NaN,
                0.9999885212332738,
                0.9999952149049364,
                NaN,
                NaN,
                0.9999832985702107,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                6.475951069696694e-07,
                1.0677026154551157e-06,
                1.3007125361755747e-05,
                3.7266392829528392e-06,
                1.5534971989907999e-06,
                6.144174601879434e-06,
                4.222835457794923e-06,
                1.2098656834834034e-06,
                2.5612815999679353e-06,
                8.939697369151141e-06
            ],
            [
                2.1444956081636468e-05,
                5.422220908402905e-06,
                3.7266392835086923e-06,
                7.889260702744606e-06,
                6.475949525516461e-07,
                7.889261644875049e-06,
                1.0129988563914856e-05,
                3.726640172290235e-06,
                1.0129989768322136e-05,
                1.300713311517055e-05
            ],
            [
                3.7266410608720178e-06,
                4.785092783267308e-06,
                3.1201900194894126e-05,
                1.9947301970813926e-06,
                4.0063682591672956e-05,
                6.962257078819179e-06,
                5.422217030555087e-06,
                1.4738988997768797e-05,
                2.2603245672867952e-06,
                6.144173869312763e-06
            ],
            [
                6.144173135762683e-06,
                3.535625486558282e-05,
                NaN,
                8.93969310418261e-06,
                2.1444956067203762e-05,
                NaN,
                1.473898020838208e-05,
                7.88926352407059e-06,
                2.561282210530385e-06,
                2.4300249365620815e-05
            ],
            [
                2.561282821239737e-06,
                2.902311293147782e-06,
                1.3709572068272963e-06,
                5.043472879337165e-07,
                4.222834451292594e-06,
                7.338208930391909e-07,
                6.475950297332654e-07,
                5.71500583272315e-07,
                2.9023116390421582e-06,
                3.288749457409966e-06
            ],
            [
                6.144172401547709e-06,
                1.4738987236641703e-05,
                2.5612819035765855e-06,
                1.0129993394811673e-05,
                5.04347528431602e-07,
                2.75357009372024e-05,
                4.006369696286016e-05,
                1.2098661161789477e-06,
                1.8925143697939984e-05,
                2.1444956074147067e-05
            ],
            [
                7.889264466445326e-06,
                1.994729483630195e-06,
                5.422218323093458e-06,
                1.1478770861650256e-05,
                5.422217030495909e-06,
                1.9947304348703948e-06,
                1.209865539274514e-06,
                4.2228324375512536e-06,
                1.300712381094558e-05,
                1.2098658277335738e-06
            ],
            [
                2.1444958614225316e-05,
                1.0129987355564522e-05,
                8.939695237813028e-06,
                2.902311639126627e-06,
                3.2887482809455384e-06,
                4.78509563546605e-06,
                9.422442568951678e-07,
                2.260323758882316e-06,
                8.939698435096828e-06,
                8.93969417214416e-06
            ],
            [
                0.9998766053662735,
                0.9993736657518971,
                0.9999687980775139,
                1.4738981968060613e-05,
                2.5612831265909735e-06,
                6.60521524950855e-05,
                1.0129990979215566e-05,
                1.3007123808910861e-05,
                0.9997694933672178,
                5.422220908703723e-06
            ],
            [
                3.927861066113479e-07,
                1.855391239505118e-07,
                2.561283431986506e-06,
                5.043472277902271e-07,
                5.422218969720291e-06,
                1.6373774480535133e-07,
                3.9278638755456876e-07,
                2.3823699518764604e-07,
                9.422448185388577e-07,
                6.475950297709604e-07
            ],
            [
                9.610246065397443e-05,
                1.1478770861211786e-05,
                1.012999460108057e-05,
                2.4300246506623417e-05,
                1.4738981957068655e-05,
                5.144219522247965e-05,
                1.1478769481785311e-05,
                0.00012339456000173458,
                5.8291258386974944e-05,
                1.3007125362820425e-05
            ],
            [
                7.889263525663481e-06,
                3.120191879107958e-05,
                2.4300232033865884e-05,
                1.4738987237124277e-05,
                1.8925148230890784e-05,
                1.8925143718318983e-05,
                2.753569436805389e-05,
                3.535626334323525e-05,
                5.144223815074485e-05,
                1.1478766754064213e-05
            ],
            [
                2.5612834318583854e-06,
                1.0677031245710902e-06,
                2.5612815999423112e-06,
                3.2887494572514376e-06,
                4.785096775998733e-06,
                1.0129989769722525e-05,
                2.2603242978213447e-06,
                6.144172404520556e-06,
                6.9622562489985925e-06,
                1.01299946023704e-05
            ],
            [
                3.726639283440905e-06,
                1.0129993394129904e-05,
                1.8925157254522964e-05,
                1.0129994589490511e-05,
                NaN,
                3.726637950973972e-06,
                3.7266406162269133e-06,
                1.1478766752372975e-05,
                1.370957697068717e-06,
                5.422220906716348e-06
            ],
            [
                1.1478765388314311e-05,
                2.5612831266165976e-06,
                7.88925976283858e-06,
                4.222833444283541e-06,
                2.2603234894560207e-06,
                4.0063706414281447e-05,
                1.892515274339482e-05,
                4.785095635413826e-06,
                6.1441760667392215e-06,
                1.8925157257965367e-05
            ],
            [
                2.4300232039788792e-05,
                1.5534977543661227e-06,
                4.222833444383398e-06,
                1.6701417859944398e-05,
                6.144173868781898e-06,
                2.9023126768680736e-06,
                8.93969416907082e-06,
                2.430023203572232e-05,
                2.4300232038993178e-05,
                1.4738987234550548e-05
            ],
            [
                3.7266388397382506e-06,
                7.889261644982674e-06,
                1.012999097799944e-05,
                1.3709575336947905e-06,
                3.7266388394569345e-06,
                2.561282516042282e-06,
                1.7603430034655858e-06,
                7.889264464508026e-06,
                1.0677028700053041e-06,
                7.88926540679677e-06
            ],
            [
                3.726638839656906e-06,
                4.2228349546493465e-06,
                1.5534981249291695e-06,
                5.422218969661113e-06,
                1.994729483705484e-06,
                3.726639284103523e-06,
                4.222832437186393e-06,
                1.2098652507957165e-06,
                2.260325375650449e-06,
                4.222833947774596e-06
            ],
            [
                0.9999974387168733,
                0.9999962733598274,
                0.9999982396565769,
                0.9999982396569965,
                0.9999852610145148,
                0.9999992661787571,
                0.9999974387187053,
                0.9999987901347491,
                0.9999987901341723,
                0.9999952149072184
            ],
            [
                2.561283431478682e-06,
                NaN,
                1.147876949187012e-05,
                NaN,
                3.7266392835086923e-06,
                2.753569760850239e-05,
                1.0129990966427814e-05,
                NaN,
                4.222832437497486e-06,
                6.144173868178388e-06
            ],
            [
                1.5534981249164537e-06,
                2.902313023039776e-06,
                2.2603248364644736e-06,
                1.7603425836246058e-06,
                4.222834954753043e-06,
                5.4222202624563834e-06,
                6.962257909007124e-06,
                3.726640616670918e-06,
                4.222832940777184e-06,
                1.99472924590571e-06
            ],
            [
                2.561281599914358e-06,
                4.0063706483364614e-05,
                1.7603440522963817e-06,
                1.067703124384645e-06,
                8.939698435096828e-06,
                4.7850950646797465e-06,
                1.760343632854606e-06,
                5.14422197242005e-05,
                1.2098661159577745e-06,
                4.222834954280646e-06
            ],
            [
                8.93969417214416e-06,
                1.5534973841450852e-06,
                1.5534971987760398e-06,
                2.5612815998491325e-06,
                3.7266410609940346e-06,
                1.6701429805655623e-05,
                1.3709578604981489e-06,
                2.9023130223693095e-06,
                1.994730434816876e-06,
                1.2098661161789477e-06
            ],
            [
                2.561282210590951e-06,
                6.962257909412379e-06,
                1.0129995809763438e-05,
                1.2098658277335738e-06,
                5.422221555069497e-06,
                1.6701427815999337e-05,
                1.6701423828576233e-05,
                6.1441767990323395e-06,
                2.5612819047646128e-06,
                2.5612815999423112e-06
            ],
            [
                1.1478768122695653e-05,
                7.88925976397226e-06,
                8.939695237504067e-06,
                6.14417313680765e-06,
                3.120191135412508e-05,
                4.006368260814213e-05,
                1.4738983724146862e-05,
                NaN,
                2.5612834318257725e-06,
                3.1201918807538294e-05
            ],
            [
                6.144173136131494e-06,
                1.7603432132079998e-06,
                0.00012339454176221037,
                6.962257079173776e-06,
                3.2887506332466845e-06,
                6.475947209918244e-07,
                1.5534977544932838e-06,
                3.2887494573561262e-06,
                6.144173136729416e-06,
                2.260323489435463e-06
            ],
            [
                3.2887494572095624e-06,
                6.144173136556186e-06,
                7.88926540679677e-06,
                8.939695234723424e-06,
                4.222835458044565e-06,
                1.473897845457507e-05,
                1.5534971986912662e-06,
                2.2603251060985603e-06,
                5.71500719517695e-07,
                6.144174600325954e-06
            ]
        ]
    },
    {
        "q_id": "8958_mmlu_math",
        "cot_ids": [
            2,
            3,
            7,
            9,
            10,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            24,
            25,
            27,
            29,
            30,
            31,
            33,
            35,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            56,
            57,
            58,
            61,
            62,
            63,
            66,
            67,
            69,
            70,
            72,
            73,
            75,
            76,
            77,
            78,
            79,
            81,
            82,
            83,
            84,
            86,
            87,
            88,
            89,
            91,
            92,
            93,
            95,
            96,
            97,
            99,
            101,
            103,
            105,
            106,
            107,
            108,
            109,
            111,
            112,
            113,
            114,
            115,
            117,
            118,
            119,
            120,
            121,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999992661786696,
                0.9999991684719723,
                0.9999997897565838,
                0.9999994284994168,
                0.9999996072139402,
                0.9999991684717742,
                0.9999992661786695,
                0.9999996072136593,
                0.9999997617630048,
                0.9999995549150541
            ],
            [
                6.962253758017727e-06,
                1.0129992185060374e-05,
                1.0129987356706945e-05,
                2.902312330965655e-06,
                8.939698434820389e-06,
                7.889266346129453e-06,
                7.338209804506587e-07,
                8.939693106020111e-06,
                6.144176794031025e-06,
                1.0129987351289655e-05
            ],
            [
                0.999972464296047,
                NaN,
                0.999903897548882,
                0.9999646437451684,
                0.9999938558269261,
                0.9999930377420938,
                0.9999885212279158,
                0.9999945777803854,
                0.9999970976883702,
                0.4073334000459302
            ],
            [
                0.9999995549149481,
                0.9999996940977731,
                0.9999996533673375,
                0.9999994956527722,
                0.999999352405279,
                0.9999967112517196,
                0.9999994956524716,
                0.9999992661792819,
                0.9999996072138934,
                0.9999995549149481
            ],
            [
                0.9999945777823309,
                0.9999810748562746,
                0.9999810748450086,
                0.9999930377437549,
                0.9525741264858408,
                0.9998601779100814,
                0.999948557774137,
                0.9996646497336422,
                0.9998204720135028,
                0.9999785550413904
            ],
            [
                4.785095064436034e-06,
                5.422217676866151e-06,
                1.5534981249023245e-06,
                4.222835457794923e-06,
                2.9023112929973233e-06,
                5.42221767672807e-06,
                7.889259764273619e-06,
                4.222834451012227e-06,
                5.42221961567159e-06,
                2.902313368963394e-06
            ],
            [
                6.144173868044274e-06,
                2.561281294369958e-06,
                2.2603234892298883e-06,
                1.670142582102693e-05,
                2.902313022659669e-06,
                1.8925145970336176e-05,
                1.1478765384764794e-05,
                1.892514821712119e-05,
                1.3007123810638006e-05,
                1.670142383015595e-05
            ],
            [
                2.144494327218535e-05,
                5.829129321322935e-05,
                2.7535703964586788e-05,
                3.1201922511884416e-05,
                8.939696301839653e-06,
                4.222834450236421e-06,
                2.1444945840269323e-05,
                0.00010889688304276053,
                3.12019224737456e-05,
                5.422217672551131e-06
            ],
            [
                2.902312677060767e-06,
                6.144176064856046e-06,
                1.760343422928825e-06,
                1.5534975692866768e-06,
                5.42221702914469e-06,
                1.9947299590520376e-06,
                2.5612828206131103e-06,
                8.315284241333265e-07,
                3.28875024040274e-06,
                1.473898196763166e-05
            ],
            [
                0.9999974387184011,
                0.9999993524052019,
                0.999999814460876,
                0.9999984465020604,
                0.9999999226558515,
                0.9999898700078241,
                0.9999921107349744,
                0.9999997897565838,
                0.9999997300421903,
                0.9999996072136125
            ],
            [
                0.9999546021379979,
                NaN,
                NaN,
                0.9999957771675626,
                0.9999832985763965,
                0.9999724643188521,
                0.9149009619539554,
                0.1480471999111614,
                0.9998911030656389,
                NaN
            ],
            [
                2.1444945853375776e-05,
                4.222833947359807e-06,
                3.1201918796982014e-05,
                3.535624226936835e-05,
                7.484623524086198e-05,
                3.7266406153660187e-06,
                3.7266401716055872e-06,
                1.1478766756214804e-05,
                NaN,
                5.422221554670048e-06
            ],
            [
                0.9999885212318801,
                0.9999945777784451,
                5.422218322565793e-06,
                2.2603251061458426e-06,
                9.42244930849811e-07,
                1.0129995809597604e-05,
                2.2603251059484907e-06,
                1.3709575336860625e-06,
                8.939693106329072e-06,
                3.7266406160845606e-06
            ],
            [
                1.9947299592407137e-06,
                3.2887478890769702e-06,
                1.4738988996240646e-05,
                5.422218969217281e-06,
                7.889264466230069e-06,
                3.7266401716055872e-06,
                6.144174600471243e-06,
                1.7603440525701563e-06,
                4.785093924047376e-06,
                1.370957860466977e-06
            ],
            [
                6.47594566560052e-07,
                3.120192248986379e-05,
                1.3709572067181944e-06,
                1.2098662603752517e-06,
                2.5612828211442287e-06,
                2.2603242977308917e-06,
                6.962254588433232e-06,
                1.3007131564383116e-05,
                1.2098661157002888e-06,
                1.994730672468935e-06
            ],
            [
                1.0129987355988324e-05,
                1.6701419849933667e-05,
                1.5534977545102382e-06,
                NaN,
                5.422219615967477e-06,
                1.3007133113703658e-05,
                7.338208055229508e-07,
                1.892514597494899e-05,
                2.4300246508833455e-05,
                1.0129992186387057e-05
            ],
            [
                0.7310585727705126,
                NaN,
                0.9149009596336303,
                0.9999485577682591,
                0.9999724643155748,
                0.9999687980887039,
                0.999954602112016,
                NaN,
                0.9999869928775567,
                NaN
            ],
            [
                3.2887506334560605e-06,
                6.144173136556186e-06,
                7.889262584508638e-06,
                4.2228344508893285e-06,
                3.726637951126493e-06,
                6.144172404028807e-06,
                1.3709567164663505e-06,
                4.222835457794923e-06,
                7.889264466344872e-06,
                4.450849458153541e-07
            ],
            [
                1.3007130008414434e-05,
                2.144494327998681e-05,
                1.0129987355785634e-05,
                8.93969310584124e-06,
                2.9023112931213857e-06,
                0.0,
                1.0129995797510037e-05,
                2.4300234928664224e-05,
                1.0129995808639442e-05,
                6.144173134700951e-06
            ],
            [
                0.6224593312018546,
                0.012431649904168424,
                0.015906389466749785,
                0.022977367944707283,
                0.0011695103912539506,
                0.012431650407261973,
                0.07585817375348311,
                0.01406362881240483,
                0.00010889686932428466,
                0.999954602127873
            ],
            [
                7.88926258381982e-06,
                1.7603438427660027e-06,
                1.892515274546026e-05,
                3.2887498491620677e-06,
                4.222834450328596e-06,
                6.962259567027776e-06,
                4.785092782692845e-06,
                1.4738985480179701e-05,
                2.2603251035432644e-06,
                2.56128159959988e-06
            ],
            [
                0.9998204720129125,
                NaN,
                0.010986943946188713,
                NaN,
                0.9999756997564273,
                NaN,
                0.9999417087068236,
                NaN,
                0.9997965731065197,
                0.9998601778601696
            ],
            [
                4.785093351707613e-06,
                4.222831933726245e-06,
                1.7603425836870455e-06,
                3.2887494549841913e-06,
                4.785094494463623e-06,
                1.89251482218717e-05,
                5.422217030288788e-06,
                2.5612819043220148e-06,
                4.785094494019719e-06,
                1.5534971987506078e-06
            ],
            [
                0.999941708727918,
                0.999915188920998,
                0.43782349911420193,
                0.9999599363032492,
                0.9999646437658967,
                0.9999810748517699,
                0.9999687980887184,
                0.9999852610180706,
                0.9149009538328171,
                0.9999974387175018
            ],
            [
                0.9999910603015705,
                0.999992110737415,
                0.9999921107336746,
                NaN,
                0.9999930377462442,
                0.9999910603047814,
                0.9999852610180706,
                0.9999810748517763,
                0.9999646437410106,
                0.9999546021154466
            ],
            [
                0.999999855502048,
                0.9999997300422225,
                0.9999998362622357,
                0.9999997897565838,
                0.9999996940978825,
                0.9999998555019274,
                0.9999997617630616,
                0.9999998874649184,
                0.9999996533674614,
                0.9999984465024307
            ],
            [
                8.939697361085651e-06,
                1.7603434230088762e-06,
                1.3007133104263505e-05,
                1.1478773590165753e-05,
                8.939700543735243e-06,
                2.7535684500460307e-05,
                NaN,
                6.962257908348587e-06,
                1.994729483608425e-06,
                3.2887506332466845e-06
            ],
            [
                6.1441775309064404e-06,
                1.4738983725809062e-05,
                3.7266401706904634e-06,
                3.7266392833663395e-06,
                2.5612815994461346e-06,
                4.7850967733701265e-06,
                8.93969310418261e-06,
                5.422220907426478e-06,
                2.5612834317116285e-06,
                5.422218322457301e-06
            ],
            [
                3.7266388393349185e-06,
                1.637377448031548e-07,
                4.45085104982401e-07,
                1.7603434230537046e-06,
                3.2887486729876365e-06,
                8.315280275900177e-07,
                5.715005151400212e-07,
                7.3382106794623e-07,
                5.422218322851817e-06,
                6.475949525781504e-07
            ],
            [
                0.9999997617630049,
                0.9999991684716749,
                0.9999991684718732,
                0.9999994956524715,
                0.9999994284994168,
                0.9999991684719723,
                0.9999992661791945,
                0.9999997300422869,
                0.9999993524049702,
                0.999999694097846
            ],
            [
                8.315279285012978e-07,
                2.2603253755949437e-06,
                2.56128129449109e-06,
                5.422220262195015e-06,
                7.889266346603015e-06,
                2.2603253755949437e-06,
                2.4300249408672413e-05,
                6.962258738574625e-06,
                7.889259762307618e-06,
                1.0129992185539456e-05
            ],
            [
                1.370956716481313e-06,
                6.1441760667392215e-06,
                1.4738987237553233e-05,
                1.6701417859519093e-05,
                5.422220261849814e-06,
                1.0129994600638342e-05,
                2.2603234893594005e-06,
                1.3007126912258525e-05,
                3.1201907631845964e-05,
                1.0129988562661878e-05
            ],
            [
                5.422218969384951e-06,
                2.902311985079115e-06,
                1.3007126911004571e-05,
                2.2603234894560207e-06,
                1.553498495281783e-06,
                5.422218323231539e-06,
                1.7603430033799313e-06,
                1.4738988995838502e-05,
                1.473898548194914e-05,
                9.422448184912962e-07
            ],
            [
                0.9999485577986634,
                0.9999687980774866,
                0.9999785550592607,
                0.9999339478632352,
                0.9999485577803375,
                0.9999724643023361,
                0.9999756997563761,
                0.9999832985821424,
                0.9995694428624236,
                0.9998911031297709
            ],
            [
                1.3007133114602719e-05,
                1.0129989769188164e-05,
                5.422220907909759e-06,
                1.4738976695459959e-05,
                2.1444958620544503e-05,
                2.7535697622726747e-05,
                2.1444945853375776e-05,
                1.1478773589706403e-05,
                5.422218322664422e-06,
                8.939693101044227e-06
            ],
            [
                0.9999898700041916,
                0.999993037740431,
                0.9999977396751633,
                0.9999957771675625,
                0.9999974387168735,
                0.9999990577555185,
                0.9999930377437515,
                0.9999885212346129,
                0.9996200154721371,
                0.999988521234614
            ],
            [
                3.7266410604686857e-06,
                1.2098653949842147e-06,
                6.962253759157502e-06,
                0.9994472212605884,
                8.939693105272102e-06,
                6.962255419570695e-06,
                6.144174601588856e-06,
                9.422448185478557e-07,
                3.7266397278180926e-06,
                0.9998204720984661
            ],
            [
                1.370957370236096e-06,
                1.0129990976451642e-05,
                2.43002435523294e-05,
                1.0129993392600532e-05,
                2.902311638654133e-06,
                1.3007126911974612e-05,
                1.0677026153919963e-06,
                2.561281599881745e-06,
                1.760343002872408e-06,
                1.4738981959696002e-05
            ],
            [
                1.473898021151881e-05,
                1.4738981931599482e-05,
                1.0129995809597604e-05,
                6.96225541788636e-06,
                NaN,
                NaN,
                NaN,
                1.0129994596824126e-05,
                6.962258738701267e-06,
                NaN
            ],
            [
                0.9999987901337396,
                0.9999980052700408,
                0.9999996533672135,
                0.9999991684720715,
                0.9999995549147358,
                0.9999992661792819,
                0.9999989322968754,
                0.9999982396567868,
                0.9999996940978095,
                0.9999996533672549
            ],
            [
                1.7603436327425345e-06,
                2.561282821176841e-06,
                1.7603436324895734e-06,
                1.4738983723664288e-05,
                2.56128129423019e-06,
                1.4738976698757546e-05,
                6.9622562487453084e-06,
                1.1478766753082876e-05,
                1.5534973837805584e-06,
                1.3007131554375137e-05
            ],
            [
                1.5534973840377051e-06,
                1.67014158650947e-05,
                2.144495351097679e-05,
                7.889260701926633e-06,
                1.0129987353832463e-05,
                8.9396973679153e-06,
                4.450851580402549e-07,
                1.6701419841852803e-05,
                2.561281599914358e-06,
                6.144173134343315e-06
            ],
            [
                0.9999810748428508,
                0.9997694932963105,
                0.9999910603068949,
                0.9999785550413672,
                0.9999339478720765,
                0.9999599362911407,
                0.9999885212277838,
                0.9999938558276008,
                0.9999339478239488,
                0.9999832985702
            ],
            [
                3.288749064736654e-06,
                5.4222176759932836e-06,
                7.889260704050487e-06,
                2.2603240283888175e-06,
                5.422220262333096e-06,
                2.9023109471188266e-06,
                1.760342793583908e-06,
                6.1441738691562974e-06,
                3.2887502413389517e-06,
                1.5534971989258068e-06
            ],
            [
                6.144173136645595e-06,
                1.5534971989907999e-06,
                1.0677026154279257e-06,
                1.7603430033799313e-06,
                1.3709572068422585e-06,
                6.144172404302622e-06,
                3.726639728224814e-06,
                2.9023112930659533e-06,
                6.1441731363550164e-06,
                1.9947290080343035e-06
            ],
            [
                9.422450430566563e-07,
                6.9622554185195676e-06,
                6.962253756890615e-06,
                2.561281904969606e-06,
                1.3709578603185986e-06,
                4.785095063939907e-06,
                1.3709572066782945e-06,
                1.7603430025778205e-06,
                1.553497754476329e-06,
                7.889266341623432e-06
            ],
            [
                4.222834954280646e-06,
                4.785092782858221e-06,
                0.0009110511788239829,
                6.144174591820927e-06,
                2.4300231991521528e-05,
                7.88926634455091e-06,
                7.484625372354849e-05,
                2.430023201636237e-05,
                7.889265404959923e-06,
                2.5612828193365626e-06
            ],
            [
                8.315279285012978e-07,
                5.422221554670048e-06,
                NaN,
                2.4300234922476113e-05,
                1.3007130007515371e-05,
                1.6701429805199933e-05,
                NaN,
                1.0129994601301684e-05,
                6.605214447116035e-05,
                1.3007123809644304e-05
            ],
            [
                4.222835457595211e-06,
                1.0129988556507541e-05,
                1.4738976695942536e-05,
                5.422221553910605e-06,
                2.902310946184398e-06,
                1.4738983702216562e-05,
                4.785096775389454e-06,
                1.4738985483128763e-05,
                7.88926070328992e-06,
                4.785094494185095e-06
            ],
            [
                6.144175332440078e-06,
                4.539785752118879e-05,
                4.222832437186393e-06,
                4.222835457852533e-06,
                NaN,
                3.1201911365248895e-05,
                6.144173133762157e-06,
                NaN,
                3.7266392839425286e-06,
                4.222834954514924e-06
            ],
            [
                0.9999995549150011,
                0.9999995549149481,
                0.9999986290421394,
                0.9999997617630332,
                0.999999814460876,
                0.9999998144608981,
                0.9999993524054335,
                0.9999996533675028,
                0.9999995549147359,
                0.9999998362622942
            ],
            [
                8.939700167909281e-06,
                6.9622537584863015e-06,
                1.1478773597118638e-05,
                NaN,
                7.889266346603015e-06,
                6.96225872884853e-06,
                4.785096773196046e-06,
                8.939695236398313e-06,
                6.144177530794679e-06,
                2.9023112930659533e-06
            ],
            [
                7.88926258532661e-06,
                6.144176798691468e-06,
                4.785096775842062e-06,
                0.00037998445992004734,
                2.1444948408977715e-05,
                1.9947294833417385e-06,
                4.5397868457023003e-05,
                6.962253759043525e-06,
                4.78509563509613e-06,
                5.422220908018252e-06
            ],
            [
                NaN,
                4.22283293977094e-06,
                1.012998856312253e-05,
                4.222831933564939e-06,
                1.6701423830702777e-05,
                NaN,
                2.9023130222373278e-06,
                1.7603430033399058e-06,
                8.939693105467234e-06,
                8.939699496489538e-06
            ],
            [
                6.962258737814774e-06,
                1.2098662602267027e-06,
                4.222833946845163e-06,
                1.9947294834469616e-06,
                3.7266379509129646e-06,
                2.4300249408672413e-05,
                1.6701417852987564e-05,
                0.00015843615824564974,
                1.147876538716594e-05,
                2.561281294558644e-06
            ],
            [
                0.9999994956524716,
                0.9999982396561572,
                0.9999989322968755,
                0.9999990577550691,
                0.9999991684718732,
                0.999998005270041,
                0.9999986290421395,
                0.999999352405279,
                0.9999991684718732,
                0.9999980052693275
            ],
            [
                4.785093353626844e-06,
                5.422221554670048e-06,
                6.144177531459659e-06,
                2.7535704202894907e-05,
                1.3007134665413997e-05,
                4.785096205582214e-06,
                3.7266392839425286e-06,
                4.7850950648799385e-06,
                2.902312677060767e-06,
                2.144495863482118e-05
            ],
            [
                6.144176797115634e-06,
                1.0129993393742954e-05,
                3.7266392838544054e-06,
                2.5612812944118885e-06,
                1.2098662602046953e-06,
                7.889264464106214e-06,
                1.0677033791000363e-06,
                7.889264465067689e-06,
                4.785096205582214e-06,
                2.561281599390228e-06
            ],
            [
                6.144173135025058e-06,
                1.8925141467059383e-05,
                2.2603245671202796e-06,
                4.006371123115648e-05,
                4.785092782858221e-06,
                3.2887494570181325e-06,
                3.120192616798991e-05,
                2.4300240719941574e-05,
                0.6791787056691698,
                3.7266379501469723e-06
            ],
            [
                7.889261644358435e-06,
                3.288749064736654e-06,
                1.2098652507439992e-06,
                2.9023109470554753e-06,
                7.338212429167144e-07,
                1.7603425836678333e-06,
                9.422443691996268e-07,
                1.3007133110746217e-05,
                9.422449308335287e-07,
                3.288748280293481e-06
            ],
            [
                7.889262585211807e-06,
                6.144173136131494e-06,
                1.30071315640992e-05,
                8.939700564679507e-06,
                1.8925143712742298e-05,
                0.42250463481418826,
                1.994729007841999e-06,
                1.8925143710057227e-05,
                4.222833444168322e-06,
                1.8925152750176348e-05
            ],
            [
                5.422218320642526e-06,
                3.726640616423495e-06,
                1.209865250613056e-06,
                2.561282515564741e-06,
                8.939696301839653e-06,
                3.7266410592824143e-06,
                3.726640607821332e-06,
                8.315283250006957e-07,
                1.3709568797522746e-06,
                2.561283431627768e-06
            ],
            [
                0.999999352405279,
                0.9999990577557432,
                0.9999962733602723,
                0.9999977396751634,
                0.9999980052705163,
                0.9999992661790195,
                0.9999992661786695,
                0.9999990577557432,
                0.999996711251327,
                0.9999991684716749
            ],
            [
                1.6701419838268058e-05,
                4.785096775842062e-06,
                7.889265396651054e-06,
                3.288748280658394e-06,
                4.2228349539810764e-06,
                5.422218966643064e-06,
                6.144176796780352e-06,
                6.1441760661636525e-06,
                1.670142979875954e-05,
                5.422220906223202e-06
            ],
            [
                NaN,
                0.9999546021356456,
                NaN,
                0.9999687980774927,
                0.999985261020975,
                0.9999785550465643,
                NaN,
                0.6224593312018546,
                0.9999810748462638,
                NaN
            ],
            [
                1.2098658277082653e-06,
                1.1478773596847203e-05,
                5.422218969601935e-06,
                8.315283249833015e-07,
                2.9023126768680736e-06,
                1.8925141465200488e-05,
                3.726640172503764e-06,
                2.260323489435463e-06,
                1.3007125361448172e-05,
                1.2098656834481918e-06
            ],
            [
                3.1201926212712214e-05,
                8.939700563248534e-06,
                1.3007123811229494e-05,
                2.1444942069902756e-05,
                1.670142979323052e-05,
                4.5397879426550244e-05,
                6.605216819645424e-05,
                3.120190392137216e-05,
                4.785095064819011e-06,
                1.8925155000714377e-05
            ],
            [
                2.2603248365343694e-06,
                1.0129992185760567e-05,
                6.9622554187981796e-06,
                9.422447060582385e-07,
                3.7266388395111645e-06,
                1.5534981248712412e-06,
                9.422443692090534e-07,
                1.3007131563815288e-05,
                4.222834954514924e-06,
                NaN
            ],
            [
                2.1444958621558693e-05,
                NaN,
                3.120192252175965e-05,
                6.9622554173544636e-06,
                NaN,
                1.0129988535649135e-05,
                8.939697359004234e-06,
                4.0063692132141055e-05,
                2.4300240709863792e-05,
                3.535625912717466e-05
            ],
            [
                2.902311638596061e-06,
                8.939697367037201e-06,
                1.6701427774227924e-05,
                5.422217029943586e-06,
                1.6701417857058377e-05,
                2.9023109467598367e-06,
                2.5612815994461346e-06,
                7.889264463675704e-06,
                3.2887486731252264e-06,
                4.222834450420771e-06
            ],
            [
                0.9999977396765107,
                NaN,
                0.9999885212359875,
                0.9999938558268744,
                0.9465966707651318,
                0.5,
                0.9999339478421317,
                0.9999151889690979,
                NaN,
                NaN
            ],
            [
                7.88926164299515e-06,
                5.422219613689145e-06,
                7.88926069905656e-06,
                1.300712381094558e-05,
                7.88925976126004e-06,
                1.0129994600398803e-05,
                1.1478773586115126e-05,
                4.222835455690258e-06,
                1.473898372275276e-05,
                4.785096204650886e-06
            ],
            [
                1.1478765377456965e-05,
                1.670142781478417e-05,
                5.14422135311195e-05,
                NaN,
                1.1478764016780948e-05,
                1.3007123809644304e-05,
                1.4738980207363312e-05,
                2.902312676941983e-06,
                2.144494328864643e-05,
                4.7850962029623105e-06
            ],
            [
                2.5612819053166966e-06,
                2.9023109467598367e-06,
                3.72663839473414e-06,
                4.785092782692845e-06,
                6.144173135896795e-06,
                3.7266392839832006e-06,
                2.260323758882316e-06,
                3.288749065077638e-06,
                2.4300237828943813e-05,
                1.994729008056074e-06
            ],
            [
                4.2228339475595195e-06,
                2.753570420569971e-05,
                7.88925976283858e-06,
                1.4738976691867467e-05,
                1.9947290078746543e-06,
                4.7850956342431385e-06,
                0.00033534997638870185,
                7.889262584350785e-06,
                2.1444940741392653e-05,
                1.300713156215912e-05
            ],
            [
                2.26032429753354e-06,
                2.561282210087786e-06,
                1.0129990958320302e-05,
                7.889260703117714e-06,
                NaN,
                0.9999687980812073,
                5.422217675874929e-06,
                0.9999251537488346,
                0.9999687980849966,
                8.939699500327152e-06
            ],
            [
                1.0129994592807221e-05,
                1.8925148236123232e-05,
                7.889266346746518e-06,
                3.2887486729876365e-06,
                1.4738980212644815e-05,
                2.2603248363822436e-06,
                8.939700564468113e-06,
                1.4738980211920955e-05,
                1.30071284492519e-05,
                3.5356267531385634e-05
            ],
            [
                0.999991060300515,
                0.40733340004593027,
                0.9999646437493611,
                0.9997965729398678,
                0.9999251537795946,
                NaN,
                0.9998766054070651,
                0.9999251537798777,
                0.9995694430027463,
                0.9998911030793052
            ],
            [
                1.5534977545102382e-06,
                2.2603240281606297e-06,
                2.2603253752763026e-06,
                1.9947301970106386e-06,
                3.288748280293481e-06,
                1.0129987353537646e-05,
                1.9947299591100915e-06,
                3.288750241374845e-06,
                1.0129988563730593e-05,
                1.6701419843189485e-05
            ],
            [
                0.9999687980895431,
                0.99992515378086,
                0.9999724643131696,
                0.5312093733737563,
                0.9999546021326636,
                0.9999687980818124,
                0.999988521229291,
                0.9999599362982006,
                0.999968798093762,
                0.7981867849406659
            ],
            [
                0.731058584489497,
                0.9999852610172367,
                0.8175744850834648,
                0.9999930377407674,
                0.9999810748428117,
                0.914900952092573,
                0.9999832985856489,
                0.9998204719934687,
                0.9999646437545667,
                0.9999251537573381
            ],
            [
                0.9999998144608317,
                0.9999994956524716,
                0.999999789756684,
                0.9999994956527722,
                0.9999997617631183,
                0.9999996940978825,
                0.9999996533672962,
                0.9999996940977001,
                0.9999995549147359,
                0.9999997300421903
            ],
            [
                0.999999266179107,
                0.9999998874647306,
                0.9999921107345932,
                0.9999998362623722,
                0.9999996533674202,
                0.9999974387184,
                0.9999996072137998,
                0.999998239656367,
                0.9999992661786695,
                0.9999989322966208
            ],
            [
                4.222834450743383e-06,
                2.260325106045111e-06,
                1.4738978453315019e-05,
                2.561281294369958e-06,
                6.962258738435319e-06,
                7.48462357451035e-05,
                4.7850956351657615e-06,
                4.785096775580942e-06,
                1.0129990978220553e-05,
                1.5534975693347152e-06
            ],
            [
                8.939700561199636e-06,
                2.1444958627955892e-05,
                1.0129994600859455e-05,
                2.5612812943280275e-06,
                1.3007125357804606e-05,
                3.7266401719174067e-06,
                1.3709568799243436e-06,
                3.288747887090887e-06,
                1.994729721004569e-06,
                2.4300243582562758e-05
            ],
            [
                1.9947292456281383e-06,
                6.962255417721724e-06,
                2.260325374750031e-06,
                0.0008040859751000164,
                4.006368257039418e-05,
                1.553497939554384e-06,
                5.422217030288788e-06,
                2.2603240281606297e-06,
                3.726641061058432e-06,
                4.222834954211514e-06
            ],
            [
                0.999964643762994,
                NaN,
                0.9999832985821424,
                1.3007126900594382e-05,
                0.9999339478796002,
                0.9999251538043427,
                0.9999687980879794,
                0.999995777167568,
                0.9999810748454998,
                0.9999832985821656
            ],
            [
                2.902311984783477e-06,
                1.0129994598482479e-05,
                2.561281599138645e-06,
                6.962257908348587e-06,
                8.939699499026267e-06,
                8.93969630317306e-06,
                2.2603245671490605e-06,
                1.0129995806612563e-05,
                1.9947299578582988e-06,
                1.3709570433786157e-06
            ],
            [
                1.0129989768322136e-05,
                NaN,
                1.892515272680245e-05,
                1.892515722725915e-05,
                8.939695235243779e-06,
                1.0129990977759901e-05,
                NaN,
                2.75356812012127e-05,
                1.1478770854906172e-05,
                1.3007123808532309e-05
            ],
            [
                1.3007134665130082e-05,
                4.222832941072913e-06,
                3.726641060658489e-06,
                3.7266410608720178e-06,
                1.1478770861211786e-05,
                2.9023126764615702e-06,
                1.2098661160788147e-06,
                4.7850933535659155e-06,
                4.2228339475595195e-06,
                7.88926070328992e-06
            ],
            [
                4.222833444037741e-06,
                4.222834451169694e-06,
                3.7266397280960194e-06,
                6.144173136243255e-06,
                1.3709572067680694e-06,
                1.994730434798734e-06,
                6.962253758916883e-06,
                4.785096776068365e-06,
                6.144173134868593e-06,
                6.475945665800774e-07
            ],
            [
                2.753568780461672e-05,
                8.939696301611998e-06,
                8.939696298945184e-06,
                1.0129992185981682e-05,
                1.6701419835959236e-05,
                2.1444958600728787e-05,
                1.670141784666869e-05,
                0.00017952791593124672,
                7.889263525405172e-06,
                1.670142379382242e-05
            ],
            [
                4.539785780805251e-05,
                1.670142582254589e-05,
                2.430024360395595e-05,
                2.561281294558644e-06,
                1.5534984953298217e-06,
                6.144173136645595e-06,
                7.889265406294507e-06,
                7.889263524788109e-06,
                8.939697368663308e-06,
                1.1478765387667046e-05
            ]
        ]
    },
    {
        "q_id": "8270_mmlu_math",
        "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,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.999999730042319,
                0.999999352404893,
                0.9999996940976636,
                0.9999993524051246,
                0.9999990577556308,
                0.9999994956523514,
                0.9999982396574163,
                0.9999970976876693,
                0.999999352404893,
                0.999999266178757
            ],
            [
                0.9999989322970027,
                0.9999984465015047,
                0.9999990577557432,
                0.9999970976890531,
                0.9999992661790195,
                0.9999980052700408,
                0.9999982396561572,
                0.9999994284994848,
                0.9999980052705164,
                0.9999992661790196
            ],
            [
                0.9999687980774881,
                0.9996646497319738,
                0.9998601778930637,
                0.9997388097252635,
                0.9998601778594514,
                0.9997694932871889,
                0.9999785550592762,
                0.9997388097225656,
                0.9999599362935498,
                0.9999852610162749
            ],
            [
                0.9999921107364803,
                0.9875683472716471,
                0.9999810748457884,
                0.999975699753483,
                0.9669140191085815,
                0.9999921107346418,
                0.999998005270992,
                0.9999339478553327,
                0.9999970976890551,
                0.9999646437621098
            ],
            [
                0.999999730042126,
                0.9999997897566589,
                0.9999994284993486,
                0.9999996533675028,
                0.9999994956527121,
                0.9999998144608097,
                0.9999993524052789,
                0.9999987901343166,
                0.9999997300422225,
                0.999999554914895
            ],
            [
                0.99999893229713,
                0.999999730042319,
                0.9999998144609202,
                0.9999994956524115,
                0.9999987901341725,
                0.9999999006879838,
                0.9999993524050474,
                0.9999998555019274,
                0.9999993524054335,
                0.999999428499553
            ],
            [
                0.9999987901338838,
                0.9999998362623332,
                0.9999996940977366,
                0.9999994956524715,
                0.9999998724809115,
                0.9999994956525317,
                0.9999995549151073,
                0.9999994956525918,
                0.9999997300422547,
                0.9999992661790195
            ],
            [
                0.999998239656367,
                0.9999993524053562,
                0.999999057755743,
                0.9999998724808963,
                0.9999995549147358,
                0.9999989322966208,
                0.9999990577554061,
                0.9999992661792819,
                0.9999998144609423,
                0.9999991684717742
            ],
            [
                0.9999991684720715,
                0.9999997617629763,
                0.9999992661790195,
                0.9999996072139402,
                0.9999999123575045,
                0.9999995549149481,
                0.9999996533672962,
                0.9999989322966208,
                0.9999998874648514,
                0.9999996533672962
            ],
            [
                0.9999982396565769,
                0.9999996533673375,
                0.9999993524049703,
                0.9999998874648245,
                0.9999996072137998,
                0.9999991684718732,
                0.9999995549150542,
                0.999999730042126,
                0.999999554914789,
                0.9999998362622746
            ],
            [
                0.9999982396574163,
                0.9999994956525918,
                0.9999989322975118,
                0.9999992661790195,
                0.9999989322972572,
                0.9999980052695653,
                0.9999996940978461,
                0.9999984465016899,
                0.999999168471675,
                0.9999999006880549
            ],
            [
                0.9999986290432835,
                0.9999986290432835,
                0.9999998724809875,
                0.9999991684722697,
                0.9999996072138934,
                0.99999976176309,
                0.9999970976883611,
                0.9999998724809267,
                0.9999999006879957,
                0.9999989322973845
            ],
            [
                0.9999990577549569,
                0.9999994284994848,
                0.9999995549151072,
                0.9999994284995529,
                0.9999997300421903,
                0.9999997300422547,
                0.9999995549148419,
                0.9999994284996891,
                0.9999998144609202,
                0.9999987901346049
            ],
            [
                0.9999974387187054,
                0.9999991684718732,
                0.9999996072137061,
                0.9999995549149481,
                0.9999987901340281,
                0.999999352404893,
                0.9999996072137529,
                0.9999982396572065,
                0.9999994284996891,
                0.999999554914895
            ],
            [
                0.999999789756684,
                0.9999997897567091,
                0.9999989322967481,
                0.9999991684719723,
                0.9999994284992805,
                0.9999992661790196,
                0.9999998362622747,
                0.9999993524049703,
                0.9999998362622552,
                0.9999987901343165
            ],
            [
                0.9999998874649318,
                0.9999997617630333,
                0.9999996072137061,
                0.9999995549150011,
                0.9999998724808963,
                0.999999352404893,
                0.999999495652652,
                0.9999996072137529,
                0.9999994284994849,
                0.9999998362622357
            ],
            [
                0.9999995549150011,
                0.9999996072139402,
                0.9999998724808963,
                0.9999997617631469,
                0.9999986290427931,
                0.9999993524051246,
                0.999999554914895,
                0.9999990577554061,
                0.9999997617629763,
                0.9999993524051246
            ],
            [
                0.999999789756684,
                0.9999991684719725,
                0.9999996072136592,
                0.9999990577555185,
                0.9999991684717741,
                0.9999998724809723,
                0.9999998362622746,
                0.999999855502048,
                0.9999994956524716,
                0.9999991684718733
            ],
            [
                0.9999996940978825,
                0.9999998144609202,
                0.9999996533672549,
                0.9999989322973846,
                0.9999998724809571,
                0.9999990577549569,
                0.9999991684718732,
                0.9999990577549568,
                0.9999987901344608,
                0.9999991684716749
            ],
            [
                0.9999997300420937,
                0.9999996940977366,
                0.999999730042126,
                0.999999730042126,
                0.9999999006879721,
                0.9999977396746245,
                0.9999997300421581,
                0.999999352404893,
                0.9999995549150542,
                0.9999996533673376
            ],
            [
                0.999999730042126,
                0.9999991684720715,
                0.9999990577556307,
                0.9999997300420939,
                0.9999982396574163,
                0.9999980052707543,
                0.9999997897565587,
                0.9999986290432835,
                0.9999991684721706,
                0.9999996940977731
            ],
            [
                0.999999855501979,
                0.9999994284996211,
                0.9999996940978095,
                0.999999694097773,
                0.9999998555019962,
                0.9999997300422547,
                0.9999998555019962,
                0.9999998874647709,
                0.9999995549147358,
                0.9999998555019446
            ],
            [
                0.9999998362623528,
                0.999999730042126,
                0.9999998144608317,
                0.9999996533674202,
                0.9999998362623138,
                0.9999996072137998,
                0.9999987901347492,
                0.9999994284994849,
                0.9999986290426298,
                0.9999992661786696
            ],
            [
                0.9999995549150542,
                0.9999980052693275,
                0.9999996072137529,
                0.9999991684722698,
                0.999999789756684,
                0.9999982396559474,
                0.9999989322973846,
                0.99999976176309,
                0.9999997617630616,
                0.999998790133884
            ],
            [
                0.9999991684717741,
                0.9999987901340281,
                0.9999989322967482,
                0.9999997617631183,
                0.9999992661786695,
                0.9999993524053563,
                0.999999352405279,
                0.9999993524049702,
                0.9999996533672962,
                0.9999993524053562
            ],
            [
                0.9999998874647842,
                0.9999980052700409,
                0.9999996072138934,
                0.9999992661792819,
                0.9999999006879721,
                0.9999993524052789,
                0.99999893229713,
                0.9999997300422225,
                0.9999996940978825,
                0.999999814460876
            ],
            [
                0.9999999006880785,
                0.9999997617629764,
                0.9999989322970028,
                0.9999998874647976,
                0.999999266179107,
                0.9999990577552939,
                0.9999998724810027,
                0.9999999226558145,
                0.9999998362623723,
                0.9999996533672135
            ],
            [
                0.9999991684715759,
                0.9999999123575359,
                0.9999990577552939,
                0.9999986290427931,
                0.9999986290421395,
                0.9999996072136125,
                0.9999984465016899,
                0.9999999317440034,
                0.999999495652712,
                0.9999996940977366
            ],
            [
                0.9999996940977731,
                0.9999997897567091,
                0.999999554914789,
                0.9999995549149481,
                0.9999997897565587,
                0.9999996940977731,
                0.9999994284992805,
                0.9999997897567091,
                0.9999993524051246,
                0.9999993524053563
            ],
            [
                0.9999977396746245,
                0.9999977396759717,
                0.9999986290429567,
                0.9999977396746247,
                0.9999970976873234,
                0.9999989322972572,
                0.9999974387174843,
                0.9999977396754328,
                0.9999962733616052,
                0.9999987901338839
            ],
            [
                0.9999989322966208,
                0.9999992661786695,
                0.9999984465026158,
                0.9999994956526519,
                0.9999987901346051,
                0.9999997897565838,
                0.9999990577551815,
                0.9999996940977731,
                0.999998790134028,
                0.9999982396567867
            ],
            [
                0.9999994956527721,
                0.9999991684722698,
                0.9999991684717742,
                0.9999974387187053,
                0.9999995549147359,
                0.9999996533672136,
                0.999998790134605,
                0.9999996533674201,
                0.9999990577550691,
                0.9999984465016899
            ],
            [
                0.9999996940976636,
                0.9999998144609203,
                0.9999982396569966,
                0.9999989322975118,
                0.9999994284997574,
                0.9999996072138465,
                0.9999991684721706,
                0.9999967112509349,
                0.9999987901341724,
                0.9999995549151073
            ],
            [
                0.9999991684718732,
                0.9999994956525317,
                0.9999982396574163,
                0.9999997617631752,
                0.9999994956524716,
                0.99999893229713,
                0.9999993524051246,
                0.9999992661789321,
                0.9999996072139402,
                0.999999266178757
            ],
            [
                0.9999990577555185,
                0.9999998144608319,
                0.9999996940976636,
                0.999999554914842,
                0.9999987901337396,
                0.9999994284996891,
                0.9999992661791944,
                0.9999996072138465,
                0.9999998555020307,
                0.99999893229713
            ],
            [
                0.9999991684722697,
                0.9999992661790195,
                0.999999352404893,
                0.9999990577552939,
                0.9999997300422225,
                0.9999977396746246,
                0.9999996940977002,
                0.9999996533672962,
                0.9999987901343165,
                0.9999986290424664
            ],
            [
                0.9999994956525917,
                0.9999996072138465,
                0.9999997897565838,
                0.9999999123574836,
                0.9999996940977366,
                0.9999998144608319,
                0.9999999397642222,
                0.9999998555019274,
                0.9999997897567091,
                0.9999997617631752
            ],
            [
                0.9999990577551815,
                0.9999996533675028,
                0.9999998724810027,
                0.9999997617631184,
                0.9999996940978095,
                0.9999987901344608,
                0.9999998362622357,
                0.9999998724809267,
                0.999999694097846,
                0.9999996533673788
            ],
            [
                0.9999977396754328,
                0.9999957771670589,
                0.9999885212305071,
                0.9999974387184,
                0.9999997617629764,
                0.9999852610145185,
                0.9999957771650455,
                0.999997097687669,
                0.9999852610197889,
                0.9999546021314297
            ],
            [
                0.9999998362623722,
                0.9999996940978095,
                0.9999998362622746,
                0.9999998724810027,
                0.9999997617630616,
                0.9999999397642437,
                0.9999999006880549,
                0.9999997617631183,
                0.9999998724809875,
                0.9999996533672549
            ],
            [
                0.999998629042303,
                0.999999789756634,
                0.9999998144609645,
                0.999999554914895,
                0.9999987901347492,
                0.9999977396748939,
                0.999999495652652,
                0.9999998144609644,
                0.9999990577557432,
                0.9999994956523514
            ],
            [
                0.9999991684715758,
                0.9999995549149481,
                0.9999994956527722,
                0.9999998362622746,
                0.9999995549150542,
                0.9999997617631183,
                0.9999999123574628,
                0.9999997300421903,
                0.9999995549149481,
                0.999999814460854
            ],
            [
                0.9999997897567342,
                0.9999991684717741,
                0.9999997897565838,
                0.9999997300422869,
                0.9999991684719723,
                0.999999495652712,
                0.9999997617631752,
                0.9999991684715758,
                0.9999974387174841,
                0.9999980052702787
            ],
            [
                0.999999266179107,
                0.999999057755743,
                0.9999992661791944,
                0.9999992661786695,
                0.9999997300420937,
                0.9999994956527722,
                0.999999266179107,
                0.999999653367379,
                0.999999789756634,
                0.9999998362623528
            ],
            [
                0.9999996072136125,
                0.9999987901347491,
                0.9999995549147358,
                0.9999994284992805,
                0.9999997897565838,
                0.9999992661790195,
                0.9999984465016899,
                0.9999997300422225,
                0.9999997897566338,
                0.9999993524049702
            ],
            [
                0.9999992661790196,
                0.9999997897567341,
                0.9999996533672549,
                0.9999991684719725,
                0.9999999397642868,
                0.9999999226557592,
                0.999999694097846,
                0.9999994956526519,
                0.9999998362622357,
                0.9999997617629763
            ],
            [
                0.9999962733593833,
                0.9999980052707541,
                0.999998005269803,
                0.9999982396559474,
                0.9999980052709919,
                0.9999990577556307,
                0.999996273358939,
                0.9999991684719723,
                0.9999952149055056,
                0.9999974387184
            ],
            [
                0.9999994956527721,
                0.9999996533673788,
                0.9999994956523514,
                0.9999997897565838,
                0.9999998362623528,
                0.9999996533673375,
                0.999999554914895,
                0.999999789756684,
                0.9999991684721706,
                0.999999730042319
            ],
            [
                0.9999996533674614,
                0.9999991684719723,
                0.9999998144608098,
                0.9999997300420937,
                0.999998790134605,
                0.9999993524049702,
                0.9999997897566089,
                0.9999989322970028,
                0.9999998144608538,
                0.9999993524050474
            ],
            [
                0.9999987901340281,
                0.999999352404893,
                0.9999994956525317,
                0.9999996940977366,
                0.999999694097773,
                0.999999266178932,
                0.9999997897566589,
                0.9999996940976272,
                0.9999998724809571,
                0.9999986290421395
            ],
            [
                0.9999998144609202,
                0.9999999397642725,
                0.99999862904312,
                0.9999994956525318,
                0.9999994284993485,
                0.9999995549148419,
                0.9999996940978095,
                0.9999994284996211,
                0.9999997300422225,
                0.9999996533672549
            ],
            [
                0.9999994284995529,
                0.9999998362623137,
                0.9999990577550691,
                0.9999996533672136,
                0.9999977396762411,
                0.9999994284995529,
                0.9999994284993485,
                0.9999995549148419,
                0.9999998362622942,
                0.9999980052693274
            ],
            [
                0.9999967112497585,
                0.9999997300421581,
                0.9999990577550691,
                0.9999991684721706,
                0.9999993524053562,
                0.9999995549147358,
                0.9999989322975119,
                0.9999994956524716,
                0.9999991684719723,
                0.9999994956525918
            ],
            [
                0.999999352405279,
                0.9999993524054335,
                0.9999995549147889,
                0.9999996940976272,
                0.9999994284996211,
                0.9999994284994168,
                0.9999998144608098,
                0.9999993524051246,
                0.9999992661789321,
                0.9999996072139402
            ],
            [
                0.9999987901341724,
                0.9999993524053562,
                0.9999991684719725,
                0.9999986290421395,
                0.9999993524049703,
                0.9999984465018751,
                0.9999996940978825,
                0.999998629042303,
                0.999998932296621,
                0.9999990577557432
            ],
            [
                0.9999990577556307,
                0.9999996072138466,
                0.9999999123575987,
                0.9999995549150011,
                0.9999989322973845,
                0.999999266179107,
                0.999999730042126,
                0.9999996533674615,
                0.999999855501979,
                0.9999986290426298
            ],
            [
                0.9999997300422225,
                0.9999997897565838,
                0.9999993524054334,
                0.9999991684719723,
                0.9999997897565587,
                0.9999998362623332,
                0.9999993524053563,
                0.9999997617630616,
                0.9999997897567091,
                0.9999994284996891
            ],
            [
                0.9999997897566338,
                0.9999996072138465,
                0.9999987901346049,
                0.9999997897566089,
                0.9999994284994848,
                0.9999990577550691,
                0.9999977396746245,
                0.9999996533674202,
                0.9999996940978825,
                0.9999996940978825
            ],
            [
                0.9999997617630049,
                0.9999996940978825,
                0.999999887464811,
                0.9999998724809571,
                0.9999996533673376,
                0.999999789756684,
                0.9999992661786696,
                0.9999994956525317,
                0.9999998555019446,
                0.9999998724809419
            ],
            [
                0.9999997617631468,
                0.9999992661789321,
                0.9999997300420937,
                0.9999992661792819,
                0.9999997617631752,
                0.9999992661786695,
                0.9999999006880668,
                0.9999998555019962,
                0.9999997300422225,
                0.999999887464744
            ],
            [
                0.9999994956525917,
                0.9999998724809267,
                0.9999986290427931,
                0.9999996072138934,
                0.9999994956524115,
                0.9999998362622552,
                0.9999994284997574,
                0.9999997617631183,
                0.9999994284993486,
                0.9999995549147889
            ],
            [
                0.9999998362622746,
                0.9999992661788446,
                0.9999993524054335,
                0.999999266179107,
                0.9999993524050474,
                0.9999997300422225,
                0.9999994284994849,
                0.99999976176309,
                0.9999998144608097,
                0.999999057755743
            ],
            [
                0.9999994956524114,
                0.999998239656367,
                0.9999994284997574,
                0.9999986290424663,
                0.999998005269803,
                0.9999996533672549,
                0.9999977396759717,
                0.9999996072138934,
                0.9999990577555185,
                0.9999992661792819
            ],
            [
                0.9999990577555185,
                0.9999994284996891,
                0.9999998144609423,
                0.9999996072136125,
                0.9999977396765106,
                0.99999893229713,
                0.9999984465022455,
                0.99999862904312,
                0.9999997617629763,
                0.9999994284993485
            ],
            [
                0.9999980052709919,
                0.9999991684715758,
                0.9999986290432834,
                0.9999986290426298,
                0.9999952149055064,
                0.9999977396754328,
                0.9999989322972572,
                0.999999266178757,
                0.999998629042303,
                0.9999997897565838
            ],
            [
                0.9999997300420937,
                0.9999962733611603,
                0.9999997617630049,
                0.9999994956525918,
                0.9999989322968754,
                0.9999991684719723,
                0.9999994284997573,
                0.9999982396572065,
                0.9999991684722698,
                0.9999977396759716
            ],
            [
                0.9999999226557408,
                0.9999998874647709,
                0.999999554914895,
                0.999999554914895,
                0.9999995549147359,
                0.9999998555019619,
                0.9999993524052019,
                0.9999994956527722,
                0.9999990577552939,
                0.9999998362622552
            ],
            [
                0.9999991684722697,
                0.9999998144609644,
                0.9999998144609645,
                0.9999991684722697,
                0.9999989322967482,
                0.9999974387177893,
                0.9999987901341723,
                0.9999997897566589,
                0.999999428499553,
                0.9999996940978095
            ],
            [
                0.9999984465026158,
                0.999998005269803,
                0.9999994284993485,
                0.9999998144608097,
                0.9999995549151073,
                0.9999997897566089,
                0.9999990577552939,
                0.9999990577549569,
                0.9999997897567341,
                0.9999980052693275
            ],
            [
                0.9999989322967482,
                0.9999997300421581,
                0.9999982396569967,
                0.9999992661791944,
                0.9999994284996891,
                0.9999987901341724,
                0.9999996940978825,
                0.999999266179107,
                0.9999998362622747,
                0.9999990577550691
            ],
            [
                0.9999986290429567,
                0.9999997897567341,
                0.9999997300421581,
                0.9999977396762412,
                0.9999992661786695,
                0.9999996072137998,
                0.9999997617630048,
                0.999999730042126,
                0.9999993524050474,
                0.9999996533673375
            ],
            [
                0.9999982396561572,
                0.99999893229713,
                0.9999977396751634,
                0.9999952149043647,
                0.9999957771650458,
                0.9999945777810307,
                0.9999980052693275,
                0.9999984465026158,
                0.9999982396574163,
                0.9999989322966208
            ],
            [
                0.9999996072139402,
                0.9999996940976272,
                0.9999998144609202,
                0.9999992661791944,
                0.9999992661791945,
                0.999999352405279,
                0.9999990577556307,
                0.9999994956524716,
                0.9999997617629763,
                0.9999995549150011
            ],
            [
                0.9999993524054335,
                0.9999995549148419,
                0.9999994956527721,
                0.9999998144609645,
                0.9999987901344608,
                0.9999994284994167,
                0.9999997617630332,
                0.999999855502048,
                0.9999993524052019,
                0.9999999006880312
            ],
            [
                0.9999998362622552,
                0.999999814460876,
                0.999999730042126,
                0.9999996533674615,
                0.9999996940978825,
                0.9999997897566089,
                0.9999994956525918,
                0.9999996072137061,
                0.9999995549148419,
                0.9999996940977002
            ],
            [
                0.9999998874647709,
                0.9999991684718732,
                0.999999730042126,
                0.9999996072139402,
                0.9999996940976636,
                0.9999993524054335,
                0.9999997300422546,
                0.9999994284994849,
                0.9999995549147359,
                0.9999990577549568
            ],
            [
                0.9999996940977002,
                0.9999995549147889,
                0.9999997897567091,
                0.9999992661786696,
                0.9999977396762412,
                0.9999998144608317,
                0.999999653367379,
                0.9999994284995529,
                0.9999996072137061,
                0.9999994956523514
            ],
            [
                0.9996200154732647,
                0.9999810748517602,
                0.9999546021313874,
                0.9997388096613428,
                0.9999599363030408,
                0.9999852610162742,
                0.9998415637456812,
                0.9999724643056309,
                0.9999869928653361,
                0.999620015520137
            ],
            [
                0.9999998144609645,
                0.9999994956525918,
                0.9999998362622943,
                0.9999984465024309,
                0.9999998555019618,
                0.9999997617630332,
                0.9999996072138465,
                0.9999997617631184,
                0.9999996072137998,
                0.9999986290427932
            ],
            [
                0.9999997897567341,
                0.9999992661788446,
                0.9999989322975119,
                0.9999967112509357,
                0.999999266179107,
                0.9999996940977731,
                0.9999996072137061,
                0.9999997300422547,
                0.9999998144609423,
                0.9999998144609424
            ],
            [
                0.9999982396574163,
                0.9999992661792819,
                0.9999989322967482,
                0.9999984465016899,
                0.9999993524051246,
                0.9999999226558053,
                0.9999994284994167,
                0.9999991684720715,
                0.99999893229713,
                0.9999997897566338
            ],
            [
                0.9999997897566089,
                0.9999996072137061,
                0.9999995549151073,
                0.9999991684720715,
                0.9999984465022456,
                0.9999998724808963,
                0.9999997897565838,
                0.9999995549150011,
                0.9999996940976271,
                0.9999989322975119
            ],
            [
                0.9999986290424664,
                0.9999997617630899,
                0.9999998874649184,
                0.9999998144608319,
                0.999999814460876,
                0.9999994956523514,
                0.9999998144608981,
                0.9999998362622357,
                0.999999694097773,
                0.999999855502048
            ],
            [
                0.9999994956525318,
                0.9999993524052021,
                0.9999970976866317,
                0.999998790133884,
                0.99999879013374,
                0.9999945777797401,
                0.9999974387171794,
                0.9999967112505447,
                0.9999977396765111,
                0.9999992661790197
            ],
            [
                0.9999987901341723,
                0.9999990577551815,
                0.9999990577554062,
                0.999999554915001,
                0.999999931743979,
                0.9999997617631752,
                0.999998932296621,
                0.9999997300423191,
                0.9999991684721706,
                0.9999997617631753
            ],
            [
                0.999999789756634,
                0.9999998362623722,
                0.9999993524052789,
                0.9999996940976636,
                0.9999997617630616,
                0.9999995549150542,
                0.9999994956523514,
                0.9999997897566089,
                0.9999930377462417,
                0.9999998724809723
            ],
            [
                0.9999996533673788,
                0.9999996072137061,
                0.9999996940977731,
                0.9999998555020307,
                0.9999997617631468,
                0.9999997897567091,
                0.999999653367379,
                0.9999998362623137,
                0.9999998555020307,
                0.9999991684721706
            ],
            [
                0.9999998555019274,
                0.9999996533674615,
                0.9999982396572065,
                0.9999998724809723,
                0.9999990577550691,
                0.9999990577555185,
                0.9999986290431201,
                0.9999996072138934,
                0.9999994284994848,
                0.9999996072138934
            ],
            [
                0.999999554914842,
                0.9999984465018751,
                0.9999993524053562,
                0.9999991684719723,
                0.999999266178932,
                0.9999996072136125,
                0.9999995549147358,
                0.9999994956524716,
                0.999999653367379,
                0.99999976176309
            ],
            [
                0.999999554914789,
                0.9999996940977366,
                0.9999998144608317,
                0.9999996533674202,
                0.9999995549151073,
                0.9999996940976636,
                0.9999996072136125,
                0.9999996072139402,
                0.9999998874649051,
                0.9999998724810027
            ],
            [
                0.9999991684719723,
                0.9999998555019618,
                0.9999974387174841,
                0.9999995549151073,
                0.999999730042319,
                0.9999994956523514,
                0.9999996940978095,
                0.9999999123575881,
                0.9999996940978825,
                0.9999996533675028
            ],
            [
                0.9999998144609423,
                0.9999994956527121,
                0.9999994284997573,
                0.9999993524049703,
                0.9999987901340281,
                0.9999995549151073,
                0.9999996940978825,
                0.9999992661786696,
                0.9999987901340281,
                0.999999789756684
            ],
            [
                0.9999994284996211,
                0.9999980052702786,
                0.9999993524054334,
                0.9999974387168734,
                0.9999997617631183,
                0.9999982396574163,
                0.9999990577550691,
                0.9999994284994167,
                0.9999994284997573,
                0.9999998874647842
            ],
            [
                0.9999996072137061,
                0.9999994284994167,
                0.9999995549150011,
                0.9999997617630332,
                0.9999996533674614,
                0.9999984465016899,
                0.9999991684722698,
                0.9999994284996211,
                0.9999995549150011,
                0.9999998362623332
            ],
            [
                0.9999984465026159,
                0.9999996072136125,
                0.9999990577554061,
                0.9999997617631468,
                0.9999996533672549,
                0.9999998362623332,
                0.9999994956525317,
                0.9999987901344607,
                0.9999987901340281,
                0.9999997300422225
            ],
            [
                0.999999352405279,
                0.9999996072137998,
                0.999999554914895,
                0.9999995549147359,
                0.9999989322970028,
                0.9999998555019446,
                0.9999996940976636,
                0.9999997897566089,
                0.9999997300422547,
                0.9999993524054334
            ],
            [
                0.9999852610110079,
                0.9999910603015666,
                0.9999967112505429,
                0.9999930377404328,
                0.9999957771650465,
                0.9999980052702786,
                0.9999989322967482,
                0.9999986290423029,
                0.9999982396572065,
                0.9999810748472628
            ],
            [
                0.9999991684715759,
                0.9999995549148419,
                0.9999997617631183,
                0.9999996940978095,
                0.9999991684719725,
                0.9999996072137061,
                0.9999989322972573,
                0.9999994956527721,
                0.999999266179107,
                0.9999997617631752
            ],
            [
                0.9999996072137061,
                0.9999998555020134,
                0.999999694097773,
                0.9999998144609202,
                0.9999999123574941,
                0.9999996940976272,
                0.9999998555020307,
                0.999999554914895,
                0.9999998555019446,
                0.9999995549147359
            ],
            [
                0.9999982396567867,
                0.9999997617631468,
                0.9999993524053562,
                0.9999996940978825,
                0.9999999006880785,
                0.9999996940978825,
                0.9999992661788445,
                0.9999996072138934,
                0.9999994956524114,
                0.9999996940978095
            ],
            [
                0.9999982396567867,
                0.999999554914842,
                0.999999352405279,
                0.9999982396572065,
                0.9999994284992805,
                0.9999994956526519,
                0.9999987901340281,
                0.9999998362623137,
                0.9999996072136125,
                0.9999994284996891
            ],
            [
                0.9999989322968754,
                0.9999996533672962,
                0.9999999006880904,
                0.9999994956525918,
                0.999999789756684,
                0.9999996533673375,
                0.9999990577551815,
                0.9999994956527121,
                0.9999996940977366,
                0.9999989322970027
            ],
            [
                0.9999990577550691,
                0.9999994284997573,
                0.9999991684718732,
                0.9999980052702787,
                0.9999997300421903,
                0.9999996072137061,
                0.9999990577549568,
                0.9999987901340281,
                0.9999992661786695,
                0.9999996072136125
            ],
            [
                0.9999982396569966,
                0.9999986290426297,
                0.9999990577549569,
                0.9999989322973845,
                0.9999982396574163,
                0.9999991684720715,
                0.9999996940976272,
                0.9999974387184001,
                0.9999998724809571,
                0.9999992661792819
            ],
            [
                0.9999998874647574,
                0.9999986290421394,
                0.9999990577556308,
                0.9999997617631184,
                0.9999997300421903,
                0.9999995549149481,
                0.9999998724809875,
                0.9999997617631183,
                0.999999855502048,
                0.9999994284994167
            ],
            [
                0.9998601778762881,
                0.9999869928699864,
                0.9997040428680853,
                0.9999339478553375,
                0.9998204720344955,
                0.9995121428865275,
                0.9997388096918782,
                0.9999485577863791,
                0.9984988174148572,
                0.9999756997476916
            ],
            [
                0.9999996533672135,
                0.9999987901340281,
                0.9999997897566589,
                0.9999998555020307,
                0.9999996072138934,
                0.9999991684718732,
                0.9999996533673788,
                0.999998790134605,
                0.9999991684715759,
                0.9999995549150542
            ],
            [
                0.9999984465018751,
                0.9999993524053562,
                0.9999994956525918,
                0.9999989322970027,
                0.9999991684716749,
                0.999995214904935,
                0.9999898700053984,
                0.9999997300421903,
                0.9999996072137529,
                0.9999990577554061
            ],
            [
                0.9999994284992804,
                0.9999997617631469,
                0.9999997300421903,
                0.9999999006881496,
                0.9999999123575359,
                0.9999994284996891,
                0.999999789756684,
                0.9999997300422225,
                0.999999789756684,
                0.9999996072139402
            ],
            [
                0.999999653367379,
                0.9999996533674202,
                0.9999998724809875,
                0.999999730042126,
                0.9999997300420937,
                0.9999998724809116,
                0.9999998724809419,
                0.9999996072138465,
                0.9999999123575359,
                0.9999997897565587
            ],
            [
                0.9999982396561572,
                0.9999997897566589,
                0.999999887464811,
                0.9999991684720715,
                0.999998446502801,
                0.9999998874647709,
                0.9999998874649051,
                0.9999984465015047,
                0.999998790134605,
                0.9999999123575045
            ],
            [
                0.9999991684719723,
                0.9999984465026159,
                0.9999996533672962,
                0.9999999006881377,
                0.9999997897565587,
                0.9999998874648514,
                0.9999993524049703,
                0.9999986290432835,
                0.9999996533672135,
                0.9999992661787571
            ],
            [
                0.9999996072136125,
                0.9999992661788446,
                0.999999730042126,
                0.9999998362623332,
                0.9999997897567091,
                0.9999994956524114,
                0.9999994956524114,
                0.9999993524053563,
                0.9999997897566089,
                0.9999982396574163
            ],
            [
                0.9999997617630049,
                0.9999998144609645,
                0.9999998362623528,
                0.999999554914842,
                0.9999993524054335,
                0.9999998724809875,
                0.9999998362622357,
                0.9999995549151072,
                0.9999992661792819,
                0.9999997897565587
            ],
            [
                0.9999987901338839,
                0.9999989322967482,
                0.9999998144608981,
                0.9999982396569966,
                0.9999994284992805,
                0.9999998144609645,
                0.999999266179107,
                0.9999997617630899,
                0.9999996940978461,
                0.9999994956525317
            ],
            [
                0.9999984465026159,
                0.9999994956524114,
                0.999999694097846,
                0.9999999530883732,
                0.9999998362622942,
                0.9999998724809571,
                0.9999998874648112,
                0.9999997617630616,
                0.999999789756684,
                0.9999996533672135
            ],
            [
                0.9999990577549569,
                0.9999997617631752,
                0.9999980052693274,
                0.9999989322968754,
                0.9999990577552939,
                0.9999996072137061,
                0.9999996072137061,
                0.9999986290421395,
                0.9999996072138934,
                0.999998629042303
            ],
            [
                0.9999997617631469,
                0.9999999123574523,
                0.9999996533674202,
                0.9999996533672549,
                0.9999998362623137,
                0.9999996533675028,
                0.9999998144609424,
                0.9999998362622746,
                0.9999996533672962,
                0.9999995549149481
            ],
            [
                0.9999970976876691,
                0.9999996072137061,
                0.9999997617630899,
                0.9999980052693274,
                0.9999994284992805,
                0.9999990577555185,
                0.9999998144609644,
                0.9999993524052018,
                0.9999997617630332,
                0.9999998144609202
            ],
            [
                0.9999980052707541,
                0.9999989322970028,
                0.9999996072138934,
                0.99999976176309,
                0.9999998362623528,
                0.9999991684715759,
                0.9999994284996211,
                0.9999996072138934,
                0.9999997897566338,
                0.9999997617631183
            ],
            [
                0.999999814460854,
                0.9999991684715759,
                0.999999946842182,
                0.999999789756684,
                0.9999984465015047,
                0.9999996940977366,
                0.9999996533672548,
                0.9999998555020135,
                0.9999998874647976,
                0.9999995549147889
            ],
            [
                0.9999997300422225,
                0.9999996533672135,
                0.999999352405279,
                0.9999999530883843,
                0.9999995549149481,
                0.9999998362623137,
                0.9999999006881496,
                0.9999998874647976,
                0.9999994284992805,
                0.9999999123574628
            ],
            [
                0.9999997617630616,
                0.9999990577549569,
                0.9999999006879721,
                0.999999789756684,
                0.9999987901343166,
                0.9999990577556308,
                0.9999997300422547,
                0.9999991684722697,
                0.9999994284997573,
                0.9999974387171787
            ],
            [
                0.9999998144608098,
                0.9999984465026159,
                0.9999994956525917,
                0.9999994284995529,
                0.9999991684720715,
                0.9999987901338839,
                0.9999994956527722,
                0.9999993524050474,
                0.9999997300420937,
                0.9999997617630332
            ],
            [
                0.9999977396748939,
                0.999999266179107,
                0.9999994284994849,
                0.9999992661786695,
                0.9999994284992805,
                0.9999986290424664,
                0.999999789756684,
                0.9999996940976272,
                0.9999987901338838,
                0.9999994284993486
            ],
            [
                8.939694169835089e-06,
                7.889259763857458e-06,
                3.726640616477725e-06,
                1.2098659719661556e-06,
                8.939699498587217e-06,
                4.2228329408924035e-06,
                6.962253758182361e-06,
                3.2887506328937356e-06,
                7.889266345397582e-06,
                3.288748672879957e-06
            ],
            [
                1.5534977545102382e-06,
                7.338212429367364e-07,
                9.422442568951678e-07,
                1.5534971987760398e-06,
                1.9947292458930106e-06,
                1.9947306725215466e-06,
                1.3709567165087443e-06,
                1.3709570433661467e-06,
                1.2098653949688097e-06,
                3.927862470840049e-07
            ]
        ]
    },
    {
        "q_id": "8902_mmlu_math",
        "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,
            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,
            52
        ],
        "rewards": [
            [
                0.9999832985841411,
                0.9998766054257319,
                0.9999832985742014,
                0.9999417087276563,
                0.9999485577986525,
                0.9999967112517191,
                0.9999832985741862,
                0.9999251537374746,
                0.9999251537817999,
                0.999992110738357
            ],
            [
                0.9999810748562796,
                0.9999785550490361,
                0.9999832985841344,
                0.9999724643121964,
                0.9999910603026347,
                0.9999885212318754,
                0.9999921107392977,
                0.9999038975508111,
                0.9999898700090248,
                0.9999599363078407
            ],
            [
                0.9999967112505433,
                0.9999852610145203,
                0.9999945777784451,
                0.999992110735536,
                0.9999989322970028,
                0.9999952149066478,
                0.9999852610145177,
                0.9999980052705164,
                0.999996711250543,
                0.9999687980961591
            ],
            [
                0.9999910603058276,
                0.9999930377420935,
                0.9999938558261318,
                0.9999921107336532,
                0.9999785550490348,
                0.9999945777823233,
                0.9999852610110026,
                0.9999885212305063,
                0.9999852610110056,
                0.9999952149037944
            ],
            [
                0.9999930377454114,
                0.9999417087275647,
                0.9992903294608811,
                0.9999599363221586,
                0.999941708748413,
                0.9999785550567073,
                0.9999599363126054,
                0.9999785550515924,
                0.9999852610197894,
                0.9999910603058286
            ],
            [
                0.9999885212332488,
                0.999959936317411,
                0.999978555056715,
                0.9999952149072171,
                0.999991060302631,
                0.9999599362935014,
                0.9999339478475852,
                0.9999546021422155,
                0.9999646437493142,
                0.9999885212318756
            ],
            [
                0.9999251537460145,
                0.9999251537818445,
                0.9999251537817111,
                0.9999339478711851,
                0.9998415638022159,
                0.9999756997592727,
                0.999769493314044,
                0.9999756997534811,
                0.9996200155181473,
                0.9999251537640268
            ],
            [
                0.9999982396572065,
                0.9999810748472596,
                0.9999646437324645,
                0.9999832985801568,
                0.9999957771655489,
                0.9999910603058286,
                0.9999938558253998,
                0.9999646437619537,
                0.9999962733620489,
                0.9999921107402396
            ],
            [
                0.9999938558253986,
                0.9999485577741157,
                0.9999869928715366,
                0.999975699762171,
                0.9999852610180304,
                0.9999038975852165,
                0.9999546021313769,
                0.9999599363126054,
                0.9999756997650704,
                0.9999921107392957
            ],
            [
                0.9999852610197889,
                0.9999962733593832,
                0.9999756997476854,
                0.9999885212346123,
                0.999995214903224,
                0.9999921107355343,
                0.9999898700078131,
                0.9999945777790915,
                0.9999756997679787,
                0.999972464312199
            ],
            [
                0.9999921107345949,
                0.9999724643023661,
                0.9998204719926093,
                0.9999599363221765,
                0.9999832985801537,
                0.9999898700078153,
                0.9999930377445817,
                0.9999898700090217,
                0.9999898700066094,
                0.9999810748585398
            ],
            [
                0.9999687980998132,
                0.9999810748495187,
                0.9995121428953829,
                0.9999546021476413,
                0.9999898700102283,
                0.9999910603036978,
                0.9999485577680282,
                0.9999687980997952,
                0.9999852610233037,
                0.9999885212277713
            ],
            [
                0.9999930377454104,
                0.9999921107383583,
                0.9999938558268633,
                0.9999810748449961,
                0.9999810748585377,
                0.9999810748517622,
                0.9999930377420909,
                0.9999038975623662,
                0.9999962733602719,
                0.9997040427627908
            ],
            [
                0.9999977396748938,
                0.999998790134605,
                0.9999986290426297,
                0.9999991684715759,
                0.9999898700054012,
                0.9999980052700408,
                0.9999970976890532,
                0.9999910603058285,
                0.9999810748495098,
                0.9999962733593835
            ],
            [
                0.9999599362935468,
                0.9999832985721976,
                0.9999832985781694,
                0.999954602136865,
                0.9999898700126519,
                0.999948557761917,
                0.9999785550567463,
                0.9999724643154996,
                0.9999921107364748,
                0.9999885212360011
            ],
            [
                0.9999038975966815,
                0.9999724643187533,
                0.9999687980775102,
                0.9999687980737616,
                0.9999339478396017,
                0.9999485577925141,
                0.9999339478239136,
                0.9998415637456558,
                0.9997040429401589,
                0.999975699759268
            ],
            [
                0.999860177909703,
                0.9999945777797382,
                0.9999038976082038,
                0.9999962733611607,
                0.9999038975853451,
                0.9999945777803839,
                0.9999599363030677,
                0.9999485577680282,
                0.9999756997650714,
                0.9999957771655494
            ],
            [
                0.9999810748450013,
                0.9999546021259992,
                0.9999646437408994,
                0.9999687980886489,
                0.9999938558254005,
                0.9998766054255417,
                0.9999930377412609,
                0.9999339478398471,
                0.9999646437493199,
                0.9999339478633308
            ],
            [
                0.999997097686631,
                0.9999938558275964,
                0.999993855827596,
                0.999994577780384,
                0.9999930377420906,
                0.9999687980886537,
                0.9999810748540259,
                0.9999885212305093,
                0.9999898700066062,
                0.9999832985781667
            ],
            [
                0.9999852610127634,
                0.9999832985702006,
                0.9999869928699895,
                0.9999038975395174,
                0.9999251537554039,
                0.9999921107402382,
                0.9999869928668915,
                0.9999687980961062,
                0.9999810748563009,
                0.9999785550439251
            ],
            [
                0.9999485578047641,
                0.9994472213922438,
                0.9999485577863629,
                0.9990889489958571,
                0.9997694932302121,
                0.9999038975622648,
                0.9996646498518251,
                0.9999785550541578,
                0.9999151889486261,
                0.9998911031299215
            ],
            [
                0.9999417087067817,
                0.9999910603068933,
                0.9999810748427408,
                0.9999957771680668,
                0.9999810748427408,
                0.999978555056715,
                0.9999974387165682,
                0.999992110733654,
                0.9999852610233064,
                0.9999869928684375
            ],
            [
                0.9999869928746405,
                0.9999957771655489,
                0.9999910603058321,
                0.9999832985841317,
                0.9999417087067299,
                0.999954602109809,
                0.9999756997506015,
                0.999981074847252,
                0.9999810748427421,
                0.9999832985821424
            ],
            [
                0.9999485577925747,
                0.999948557798626,
                0.9998911031039929,
                0.9999885212346126,
                0.9999417087067668,
                0.9998911030652222,
                0.9999251537817575,
                0.9999785550567089,
                0.9997388096310506,
                0.9999756997563877
            ],
            [
                0.9999687980812073,
                0.9999952149072169,
                0.9999832985701962,
                0.9999646437619555,
                0.9999151889487236,
                0.999985261014516,
                0.9999417087414693,
                0.9999921107345937,
                0.9998911030389752,
                0.9999687980886335
            ],
            [
                0.9999990577550693,
                0.9997694932044838,
                0.9999898700078134,
                0.9996200154251874,
                0.9999038975737075,
                0.9999869928653361,
                0.9999417087206043,
                0.9999785550592742,
                0.9999546021422182,
                0.9999938558253986
            ],
            [
                0.999981074847252,
                0.9999687980849298,
                0.9999687980997877,
                0.9999930377437505,
                0.9999687980886605,
                0.9999952149043647,
                0.9999251537818069,
                0.9999930377412606,
                0.999948557792528,
                0.999993037746241
            ],
            [
                0.999964643749305,
                0.9999724643023485,
                0.9998601779096583,
                0.9999852610162764,
                0.9999687980774978,
                0.9999832985741811,
                0.9997965729551929,
                0.999981074856281,
                0.9999687980812043,
                0.9999810748472566
            ],
            [
                0.9999251537729316,
                0.9999785550515947,
                0.9999885212318825,
                0.9999151889184756,
                0.9999646437493369,
                0.9999910603005017,
                0.9999687980849379,
                0.9992903297214338,
                0.9999832985781653,
                0.9999785550413756
            ],
            [
                0.9999687980737629,
                0.9999910603047624,
                0.9999251537995921,
                0.9999910603036967,
                0.999975699759271,
                0.9999852610145172,
                0.9998415638403066,
                0.9999599363030631,
                0.9999785550490417,
                0.9999785550490348
            ],
            [
                0.999994577782324,
                0.9999810748517651,
                0.9999756997476845,
                0.9999938558246663,
                0.9999810748517651,
                0.9999938558268644,
                0.9999898700078163,
                0.9999945777803846,
                0.999996273360272,
                0.9999921107355355
            ],
            [
                0.9999852610110337,
                0.9999646437577874,
                0.9998204719527318,
                0.9999921107383711,
                0.9999485578047371,
                0.9999974387184033,
                0.9999417087066731,
                0.9992903295385682,
                0.9859363755265549,
                0.9999546021097124
            ],
            [
                0.999796573003438,
                0.999986992868439,
                0.9999756997505835,
                0.9997694932312318,
                0.9997965729556724,
                0.9999724642990765,
                0.9999646437408679,
                0.9996646497349887,
                0.9994472214656287,
                0.9999646437324686
            ],
            [
                0.9999938558239335,
                0.9999810748472645,
                0.9999810748450036,
                0.9999251537730296,
                0.9999339478554764,
                0.9999646437577393,
                0.9999885212346179,
                0.9999485577986672,
                0.9999687980997993,
                0.9999485577986784
            ],
            [
                0.9999339478475977,
                0.9994472212668913,
                0.9999599363174034,
                0.999995214904935,
                0.9999810748540162,
                0.9999869928761901,
                0.999986992869988,
                0.9999724643056438,
                0.999985261016272,
                0.999991060300501
            ],
            [
                0.9998204719702819,
                0.9997040429377564,
                0.9999930377445811,
                0.9999869928746383,
                0.9999646437450749,
                0.9999756997621821,
                0.9997040429375756,
                0.9999952149032236,
                0.9999910603015649,
                0.9999417087276105
            ],
            [
                0.9999852610215467,
                0.9999687980812073,
                0.9999785550413746,
                0.9999852610127832,
                0.9999930377454107,
                0.999991060305831,
                0.9999962733611607,
                0.9999970976887069,
                0.9996646498952815,
                0.9999898700126464
            ],
            [
                0.9999485577740962,
                0.9998415637838666,
                0.999988521234612,
                0.9999869928761884,
                0.9994472214572999,
                0.9999646437619434,
                0.9999869928730869,
                0.9999546021421996,
                0.9999810748562776,
                0.9999485577802376
            ],
            [
                0.9999869928668866,
                0.9999756997476897,
                0.9999974387180947,
                0.9999724643056358,
                0.9999724643121931,
                0.9999417087136483,
                0.9999898700078133,
                0.9999898700041914,
                0.9999869928668863,
                0.999975699765066
            ],
            [
                0.9997388096925318,
                0.9998911031040214,
                0.9999724643155093,
                0.999948557780265,
                0.9999687980923566,
                0.9999810748517645,
                0.9999546021476734,
                0.999968798092365,
                0.9999038975508111,
                0.9999756997563889
            ],
            [
                5.422219616140078e-06,
                1.4738987241494252e-05,
                1.6701421842140854e-05,
                2.1444940743772097e-05,
                2.9023116391477434e-06,
                1.0129992186589747e-05,
                4.006370651557427e-05,
                1.670141985245514e-05,
                5.8291272486605336e-05,
                1.8925141471913163e-05
            ],
            [
                0.9999898700041905,
                0.9999869928668841,
                0.9999599362934897,
                0.999995777166052,
                0.9999687980960662,
                0.9997388097531997,
                0.9999974387184,
                0.999983298570192,
                0.9999810748517881,
                0.9998601778926955
            ],
            [
                0.9999251537819502,
                0.9999852610197902,
                0.99998329857418,
                0.9999785550515963,
                0.999993855826864,
                0.9999785550541495,
                0.999820472077719,
                0.9999599363174215,
                0.9999898700041916,
                0.9999724643121942
            ],
            [
                0.9999756997621767,
                0.9999339478318457,
                0.9999810748585295,
                0.9999898700041918,
                0.9999646437619502,
                0.9980732650169871,
                0.9999151889890027,
                0.9999898700041912,
                0.9999546021476109,
                0.9999898700041909
            ],
            [
                0.999954602120585,
                0.9999869928653355,
                0.9999832985801483,
                0.9999930377404309,
                0.9998766054253442,
                0.9999885212305071,
                0.9999898700090208,
                0.9999852610180315,
                0.9999724643154743,
                0.9999910603036978
            ],
            [
                0.9999938558275956,
                0.999988521231879,
                0.9999810748472509,
                0.9999898700066064,
                0.9999832985761674,
                0.9999485577925467,
                0.9999599362935014,
                0.9999869928730917,
                0.9999417087136441,
                0.9999869928715366
            ],
            [
                0.9999485577986821,
                0.9999930377454114,
                0.9999810748540244,
                0.9999974387187053,
                0.9999852610233111,
                0.9999687980849298,
                0.9999599362935554,
                0.9999921107355347,
                0.9999687980774756,
                0.9996646499364937
            ],
            [
                0.9999151889387635,
                0.9999485577986746,
                0.9999485577741635,
                0.9999646437366619,
                0.9999898700102364,
                0.9999885212277806,
                0.9997040428351917,
                0.9999898700126474,
                0.999991060304768,
                0.9999785550464864
            ],
            [
                0.9997694932867596,
                0.9999785550464778,
                0.9999339478711851,
                0.9998204720344249,
                0.9999417087275647,
                0.9999945777790916,
                0.9986749778981241,
                0.9999910603004994,
                0.9999339478790639,
                0.9998766054401562
            ],
            [
                0.9999910603047638,
                0.999964643757743,
                0.9999251537728504,
                0.999915188928435,
                0.9999599363174135,
                0.9999485577925789,
                0.99998329858413,
                0.999948557780254,
                0.9998204720132834,
                0.9999945777810322
            ],
            [
                0.9999898700102295,
                0.9999339478554222,
                0.9999885212277717,
                0.9999898700114376,
                0.9999930377429218,
                0.9999724643187554,
                0.9999869928746372,
                0.9999852610215443,
                0.9999785550515972,
                0.999954602115177
            ],
            [
                0.9999952149043648,
                0.9999832985781634,
                0.9999687980886323,
                0.9999832985741766,
                0.9998766054104549,
                0.9999910602994335,
                0.9999898700114356,
                0.9999910603047634,
                0.9999251537548992,
                0.9999962733598275
            ],
            [
                0.9999980052695652,
                0.9999945777790913,
                0.9999832985821387,
                0.9999885212346123,
                0.9999832985821424,
                0.9999921107392962,
                0.9999251537460401,
                0.9999952149037941,
                0.9999885212318756,
                0.9999980052695652
            ],
            [
                0.999985261023302,
                0.9997965729304471,
                0.9999869928761891,
                0.9999885212346123,
                0.9999952149043648,
                0.9999646437493069,
                0.9999810748540237,
                0.9998601779595598,
                0.9999930377445809,
                0.9998911030910287
            ],
            [
                0.9999952149066462,
                0.9999251537996058,
                0.9997388095994055,
                0.9999885212346187,
                0.9999930377429237,
                0.9999898700053986,
                0.9999251537461387,
                0.9999810748540198,
                0.9999869928684375,
                0.9999038975853325
            ],
            [
                0.9999339478396271,
                0.9999810748427385,
                0.999769493314775,
                0.9993736657654873,
                0.9999251537638378,
                0.999891103064815,
                0.9999151889283764,
                0.9995121429491124,
                0.9999599363078845,
                0.9998204719485422
            ],
            [
                0.9999151889485854,
                0.9999417087066731,
                0.999999057755294,
                0.9706877697786226,
                0.9999251537995278,
                0.9999952149072164,
                0.999915188918557,
                0.9999885212332431,
                0.99998107485853,
                0.9999921107374145
            ],
            [
                0.9999852610145218,
                0.9998601779764942,
                0.9999756997534786,
                0.9999546021476569,
                0.9999646437451097,
                0.9999974387171787,
                0.9999852610197881,
                0.9999339478633428,
                0.9999785550439235,
                0.9999952149037942
            ],
            [
                0.9999869928730897,
                0.9999546021422182,
                0.9999910603036978,
                0.9999038975624249,
                0.9999810748495086,
                0.9999599363030588,
                0.9999898700114366,
                0.9999869928746395,
                0.9999910603015654,
                0.9999938558253986
            ],
            [
                0.9999038975739151,
                0.9999832985702006,
                0.9999756997650787,
                0.9999921107355346,
                0.9999756997563877,
                0.9999945777816772,
                0.999993855822469,
                0.9999785550490384,
                0.9999945777810305,
                0.9999599363221651
            ],
            [
                0.999972464312199,
                0.9999599362887508,
                0.9999546021422588,
                0.9999898700078172,
                0.9999151889893031,
                0.999964643757743,
                0.9999910603015663,
                0.9999646437366851,
                0.9999869928668915,
                0.9999151889893352
            ],
            [
                0.9999756997621777,
                0.9999599363078678,
                0.9999785550592636,
                0.9999339478318714,
                0.9999339478318036,
                0.9999885212277727,
                0.9999885212332451,
                0.99994855779869,
                0.9999938558224692,
                0.999996273359828
            ],
            [
                0.9999546021314075,
                0.9995694429628151,
                0.9998766054108356,
                0.999972464302344,
                0.9999885212264024,
                0.9999339478553524,
                0.9999339478554827,
                0.9999599363078321,
                0.9999646437577657,
                0.9999910603058276
            ],
            [
                0.9999339478554337,
                0.9999151889891383,
                0.9998766054548786,
                0.9999687980812059,
                0.9999599362887435,
                0.9997040427629802,
                0.9999810748562764,
                0.9999810748495133,
                0.9999687980849346,
                0.9999339478790292
            ],
            [
                0.9999756997563846,
                0.9999546021313848,
                0.9999756997592901,
                0.9999885212305091,
                0.9999967112497586,
                0.9999038975395789,
                0.9999599363174162,
                0.999993855826131,
                0.9997388096617151,
                0.9999785550464871
            ],
            [
                0.9999599363030898,
                0.9998911030780946,
                0.9999599362983397,
                0.9999546021476873,
                0.999991060303697,
                0.9999921107336545,
                0.9999546021097657,
                0.9999852610127629,
                0.9999898700090265,
                0.9999251537372807
            ],
            [
                0.9999151889587515,
                0.99984156372691,
                0.9999485577986672,
                0.9999832985801543,
                0.9999339478395968,
                0.9999151889587954,
                0.9999885212305079,
                0.9999251537461316,
                0.9998911030391304,
                0.9990889488032151
            ],
            [
                0.9998601779435838,
                0.99997246431548,
                0.9999952149032237,
                0.9999646437451076,
                0.9999832985821429,
                0.9999785550464871,
                0.9998911030910002,
                0.9999957771670592,
                0.9998601779429186,
                0.9999251537460739
            ],
            [
                0.9999251537460472,
                0.9999756997621777,
                0.9999810748427379,
                0.9999930377462405,
                0.9999599362935078,
                0.9999599363173852,
                0.9998601778929518,
                0.9999687980998067,
                0.9999038975851507,
                0.9999898700066072
            ],
            [
                0.9999646437367131,
                0.9999687980849379,
                0.9999910603015658,
                0.9999885212277744,
                0.9999339478476293,
                0.999975699762171,
                0.9999756997563856,
                0.9998601779271825,
                0.9999724642990868,
                0.9999785550515979
            ],
            [
                0.999915188928435,
                0.9999646437408665,
                0.9999646437450908,
                0.9999417087345988,
                0.9999938558246665,
                0.9999599363078321,
                0.9999930377420905,
                0.9999646437619434,
                0.9999869928699856,
                0.9999885212277733
            ],
            [
                0.999941708741613,
                0.9999832985721844,
                0.9998415637645907,
                0.999959936312614,
                0.9999687980737504,
                0.9999151889487328,
                0.999964643757729,
                0.9999756997563752,
                0.999985261014516,
                0.9997694933410937
            ],
            [
                0.9999599363221995,
                0.999948557774137,
                0.9998911030913045,
                0.9999898700078149,
                0.9997965730275858,
                0.9999852610197885,
                0.9999832985721947,
                0.9999930377404326,
                0.9998204719710603,
                0.9999599362935166
            ],
            [
                3.535625492783527e-05,
                7.88925976397226e-06,
                4.7850956352353935e-06,
                1.8925150493717652e-05,
                4.222834451215781e-06,
                5.829125856000775e-05,
                1.8925145983348442e-05,
                4.222832437324657e-06,
                1.4738981968864903e-05,
                1.670142781520948e-05
            ],
            [
                0.9997040427645733,
                0.9999785550464791,
                0.9999756997621686,
                0.99997855505926,
                0.9999339478238656,
                0.9999756997563736,
                0.9999546021205493,
                0.9999945777790911,
                0.9999546021097396,
                0.9999687980997901
            ],
            [
                0.9996200155683249,
                0.9999485577742242,
                0.9999756997592761,
                0.999988521231878,
                0.9999910603004999,
                0.9999910602994357,
                0.9998766053816942,
                0.9999251537551137,
                0.9999724643155044,
                0.9999810748585516
            ],
            [
                0.9999339478317756,
                0.9999832985801492,
                0.9999785550439201,
                0.9999485577741191,
                0.9998601778763104,
                0.9996646498557084,
                0.9999546021205761,
                0.9999945777810304,
                0.9999546021476009,
                0.9999756997592791
            ],
            [
                0.9998415638412494,
                0.9999687980923697,
                0.9999038975737075,
                0.9999852610180342,
                0.9999724642990738,
                0.9999687980886605,
                0.9999724642991094,
                0.999981074851773,
                0.9999485577802474,
                0.9999852610127677
            ],
            [
                0.9999038975851507,
                0.999933947871197,
                0.999972464299064,
                0.9999417087553741,
                0.9999485577741295,
                0.9998204719701774,
                0.9999546021476632,
                0.9998766054553454,
                0.9999785550515947,
                0.9999646437493417
            ],
            [
                0.9999952149072173,
                0.9999967112501513,
                0.9999945777784466,
                0.9999989322970028,
                0.9999974387187054,
                0.9999986290431201,
                0.999999266178757,
                0.9999977396748939,
                0.999996273358939,
                0.9999995549147359
            ],
            [
                2.144494585583323e-05,
                8.93969630362837e-06,
                1.4738976700661033e-05,
                4.222834451254188e-06,
                1.3007126911974612e-05,
                8.939697369671496e-06,
                5.422218323349895e-06,
                8.939700566435704e-06,
                6.962254589781966e-06,
                2.2603251062147097e-06
            ],
            [
                0.9999724642957865,
                0.9997965730033463,
                0.999983298572192,
                0.9999599362982967,
                0.9999852610162727,
                0.9999785550515996,
                0.9999251537907575,
                0.999993855826864,
                0.9999417087344686,
                0.9999724643187624
            ],
            [
                0.9998204720568646,
                0.9999832985821557,
                0.9999646437451295,
                0.9998911030780359,
                0.9999832985781694,
                0.9999869928684402,
                0.999981074849511,
                0.9999938558268634,
                0.9999756997506137,
                0.9999921107364793
            ],
            [
                0.9999599363221943,
                0.9999810748450013,
                0.9999832985741842,
                0.9999910603036983,
                0.9999852610127608,
                0.9999910603004994,
                0.9999898700126439,
                0.999941708741465,
                0.9999921107355344,
                0.9999810748517721
            ],
            [
                0.999981074842744,
                0.9999251537551547,
                0.9999910603058317,
                0.9999339478477572,
                0.9999952149049374,
                0.9999646437535178,
                0.9999687980886623,
                0.9999885212264057,
                0.9999756997563815,
                0.9999869928668877
            ],
            [
                0.9999546021314502,
                0.9999810748517628,
                0.9999724642990808,
                0.9999599363174442,
                0.9999952149032242,
                0.9999945777810308,
                0.9999832985821424,
                0.9999832985721862,
                0.9999724643089206,
                0.9999038975624739
            ],
            [
                0.9999852610145172,
                0.9998204719916403,
                0.9998766053811413,
                0.9999251537728575,
                0.9999339478632668,
                0.999978555049031,
                0.9998911030518871,
                0.9995121428866693,
                0.9999599363126013,
                0.9999251537461021
            ],
            [
                0.9999852610162767,
                0.9999417087138586,
                0.999925153772901,
                0.9999756997534839,
                0.9999885212264044,
                0.9996646498538448,
                0.9999885212277717,
                0.9999945777803838,
                0.9999974387184001,
                0.9999417087415464
            ],
            [
                0.9998766053663866,
                0.9999832985721941,
                0.999903897608352,
                0.9998204720144849,
                0.9999251537550745,
                0.9999646437450925,
                0.9997388096001655,
                0.9998766054257715,
                0.9998911030780359,
                0.9999151889891562
            ],
            [
                0.9999599362887689,
                0.9994472214579109,
                0.9999038975965836,
                0.9994472213276703,
                0.9999832985761679,
                0.9980732649072912,
                0.9999724643121888,
                0.9998601779760934,
                0.999959936298279,
                0.9999599363173749
            ],
            [
                0.9998911030652539,
                0.999991060299434,
                0.9999898700090227,
                0.9999810748427408,
                0.9999646437619537,
                0.9998911030910144,
                0.9998601779764474,
                0.9998601779262548,
                0.9999646437408912,
                0.9999952149049355
            ],
            [
                0.9999832985761679,
                0.9999910603047625,
                0.9999921107383563,
                0.9999962733589395,
                0.9999898700102313,
                0.9999687980774823,
                0.9999970976866311,
                0.9999921107374153,
                0.999988521233244,
                0.9999910603026321
            ],
            [
                0.9999646437408781,
                0.9999599363078845,
                0.9999832985761709,
                0.9999852610162727,
                0.9999687980886474,
                0.9999756997621738,
                0.9999832985721927,
                0.9999810748472588,
                0.999925153790781,
                0.999993855823202
            ],
            [
                0.9999957771675624,
                0.9999687980923566,
                0.9999646437366602,
                0.9999945777790911,
                0.9999724643056309,
                0.9999967112505427,
                0.9998766053958313,
                0.9999485577802578,
                0.9999810748517715,
                0.9999756997505854
            ],
            [
                0.9999869928699883,
                0.9998911030391447,
                0.9999921107345934,
                0.9999938558268633,
                0.9997965730522931,
                0.9999756997679626,
                0.9998204720779462,
                0.9999810748585323,
                0.9999785550413729,
                0.999995777167059
            ],
            [
                0.9999687980849222,
                0.9999974387177895,
                0.9998911031039089,
                0.9999485577986598,
                0.9999724643187728,
                0.9999785550541535,
                0.9999898700078143,
                0.999981074851773,
                0.9999898700114374,
                0.9998601779263891
            ],
            [
                0.9999910603036969,
                0.9999756997592761,
                0.9999810748427421,
                0.999978555046477,
                0.9999485577619046,
                0.9999832985801511,
                0.9999930377462408,
                0.9999952149066462,
                0.999915188948705,
                0.9999957771670592
            ],
            [
                0.9999898700114365,
                0.9999957771655487,
                0.9999990577550691,
                0.9999756997476845,
                0.9999687980812002,
                0.9999852610215454,
                0.9999339478238921,
                0.9999962733593832,
                0.9999938558253983,
                0.9999724643089016
            ],
            [
                0.9998766054408529,
                0.9999417087276945,
                0.9999251537551465,
                0.9999417087415261,
                0.9999756997621758,
                0.9999038975852054,
                0.9999957771680662,
                0.9999339478318396,
                0.9999151889184082,
                0.9997694932324457
            ],
            [
                0.9999945777803843,
                0.9998415638407447,
                0.999993037740433,
                0.9999339478714296,
                0.9999898700078175,
                0.9999485578048722,
                0.9999938558268638,
                0.9999785550592695,
                0.9999546021097598,
                0.9999151889284265
            ],
            [
                0.9999910602994345,
                0.9999852610110034,
                0.9999898700053989,
                0.9999957771645419,
                0.9999785550515903,
                0.9999957771680663,
                0.9999687980960814,
                0.9999869928715388,
                0.9999485578047809,
                0.9999869928699887
            ],
            [
                0.9999646437324474,
                0.9999810748495139,
                0.9999921107392967,
                0.9999724642990699,
                0.9998911030911934,
                0.9999599362983198,
                0.9999832985741892,
                0.9999952149072168,
                0.9997040428321691,
                0.9999785550413773
            ],
            [
                0.9999938558275973,
                0.9999810748495105,
                0.9999151889792702,
                0.9999898700090281,
                0.9999832985721915,
                0.9998415638219251,
                0.9999417087276458,
                0.9999724643122003,
                0.9998911030780803,
                0.9999885212346129
            ],
            [
                0.9996646500223234,
                0.9999646437535561,
                0.9999485577619084,
                0.999860177860194,
                0.9995121428859314,
                0.9998415637473225,
                0.9999546021097627,
                0.9995694429665227,
                0.9993736657620259,
                0.9999339478633682
            ],
            [
                0.9999417087346256,
                0.999915188948618,
                0.9999251537817236,
                0.9999832985841344,
                0.9999756997534786,
                0.9999898700126436,
                0.9999687980811962,
                0.9999869928684354,
                0.9999546021259761,
                0.9999945777784447
            ],
            [
                0.9999930377404309,
                0.9999756997563856,
                0.9999852610145168,
                0.9996200155629634,
                0.9999724643089016,
                0.9999724643056253,
                0.999985261023306,
                0.9999810748472515,
                0.9999785550439243,
                0.9999599363030566
            ],
            [
                1.3007130014636887e-05,
                4.22283394786293e-06,
                1.6701419853184244e-05,
                1.1478773597390071e-05,
                3.288749457383046e-06,
                2.902312676941983e-06,
                3.726638395527247e-06,
                7.889263525893087e-06,
                8.939694172290508e-06,
                1.4738978456398127e-05
            ],
            [
                0.999959936298299,
                0.9999898700102298,
                0.9999921107364749,
                0.9991959139656471,
                0.9999869928761884,
                0.9999485577679911,
                0.9999910603068982,
                0.9999417087484003,
                0.9999921107383551,
                0.9999687980737629
            ],
            [
                0.9999646437408817,
                0.9999546021421969,
                0.9999785550592574,
                0.9999952149066462,
                0.9999967112501507,
                0.9999485577618268,
                0.9999869928653343,
                0.9999546021422125,
                0.9999810748517617,
                0.9999646437324458
            ],
            [
                0.9999885212264029,
                0.9998601779600705,
                0.9999852610127649,
                0.9999687980961026,
                0.9999724643122128,
                0.9999785550465006,
                0.9999852610127585,
                0.9997965730529738,
                0.9999869928746435,
                0.9999980052700408
            ],
            [
                0.9997965729304916,
                0.9999910603047624,
                0.9998911031168874,
                0.9999756997534777,
                0.9999599363078431,
                0.9999910603068967,
                0.9999921107364752,
                0.9998415637647842,
                0.9999687980998037,
                0.9999962733593835
            ],
            [
                0.9996646500111618,
                0.9999898700090217,
                0.9998415637268294,
                0.9999756997592832,
                0.9999251537995403,
                0.9999687980849281,
                0.9993736657658879,
                0.9999785550592677,
                0.9999646437535196,
                0.9999910603026312
            ],
            [
                0.9999687980811988,
                0.9999546021476354,
                0.9999810748449967,
                0.9999832985781574,
                0.9999038975507579,
                0.9999485577925318,
                0.9999852610233012,
                0.9999810748427448,
                0.999933947839665,
                0.9998766053664531
            ],
            [
                0.9999945777803846,
                0.999985261012762,
                0.9989677688619284,
                0.99998699287154,
                0.9999724643122028,
                0.9999546021422518,
                0.9999038976082038,
                0.9999546021368508,
                0.9999687980849395,
                0.9999546021259992
            ],
            [
                0.9999785550464881,
                0.9999832985721908,
                0.9999339478317487,
                0.9999251537371533,
                0.9999898700102303,
                0.9999898700078128,
                0.9999599362982876,
                0.9999938558232018,
                0.9999724642990628,
                0.9999756997505854
            ],
            [
                0.9999546021152134,
                0.9999785550490444,
                0.9998204720130666,
                0.9999687980737689,
                0.9999646437577469,
                0.999988521227772,
                0.9999957771670593,
                0.9999485577802407,
                0.9999724642990652,
                0.9997965730762514
            ],
            [
                0.9999756997650734,
                0.9999251537817438,
                0.9998204720771418,
                0.9997388097235079,
                0.9999810748585323,
                0.9999885212277695,
                0.9999785550413652,
                0.9999852610145185,
                0.9999485577986746,
                0.9999898700041906
            ],
            [
                0.9999810748517607,
                0.999994577780384,
                0.9999546021313795,
                0.9999921107336535,
                0.99956944296403,
                0.9997694933126087,
                0.9999756997505828,
                0.9999898700066064,
                0.9999921107402359,
                0.9999687980849181
            ],
            [
                0.9999869928699862,
                0.9999417087414739,
                0.9998415637080859,
                0.9999646437324408,
                0.9999957771650457,
                0.9999885212318776,
                0.9999910603058283,
                0.9999756997650686,
                0.9999810748562856,
                0.9999938558253983
            ],
            [
                0.9999885212346183,
                0.9999756997563937,
                0.9999546021206008,
                0.9999599363221917,
                0.999975699765091,
                0.999986992876197,
                0.9999785550413632,
                0.9999251537640109,
                0.9999646437451225,
                0.9999785550541551
            ],
            [
                0.9999251537460739,
                0.9999546021313769,
                0.999948557780244,
                0.9999251537818293,
                0.9999724643056201,
                0.9998766054548786,
                0.9999646437408619,
                0.9999339478475977,
                0.9999832985721927,
                0.9999599363030525
            ],
            [
                0.9999756997505863,
                0.9999832985761737,
                0.9999599362935078,
                0.9999885212359804,
                0.9999687980886309,
                0.9999810748427379,
                0.9999885212318764,
                0.999981074849511,
                0.9999546021476599,
                0.9999945777790911
            ],
            [
                0.9999810748495053,
                0.9999339478633364,
                0.9999945777829694,
                0.999941708706696,
                0.9999852610180324,
                0.9999869928761911,
                0.9999885212291385,
                0.9999485577925429,
                0.9999832985721857,
                0.999988521229139
            ],
            [
                0.9999910603068956,
                0.9998911031299643,
                0.999981074847252,
                0.9999810748495092,
                0.9999810748427401,
                0.9999151889687937,
                0.9998766054698289,
                0.9999910603015649,
                0.9999852610145235,
                0.999986992869987
            ],
            [
                0.9999832985701983,
                0.9999810748585343,
                0.999876605410638,
                0.9999546021151535,
                0.9999810748540177,
                0.9999980052693274,
                0.9999756997534821,
                0.999860177926322,
                0.9999785550515891,
                0.9999810748472532
            ],
            [
                0.9999151889588594,
                0.9999038975626026,
                0.9999485577803994,
                0.9999756997534958,
                0.9999945777829717,
                0.9998601778931329,
                0.9999910603026332,
                0.9999724642990838,
                0.9997388096020959,
                0.999972464315472
            ],
            [
                0.9999952149049348,
                0.9999984465015046,
                0.9999910603036961,
                0.999997097686631,
                0.9999832985781563,
                0.9999984465024306,
                0.9999898700102318,
                0.9999930377420928,
                0.9999986290429566,
                0.9999957771660521
            ],
            [
                0.9999724643056319,
                0.9999546021313986,
                0.9999687980886387,
                0.9998911030650004,
                0.9999646437493241,
                0.9999251537638889,
                0.9999724643023561,
                0.9999339478554053,
                0.9999417087206302,
                0.9999724643089193
            ]
        ]
    },
    {
        "q_id": "8964_mmlu_math",
        "cot_ids": [
            3,
            4,
            5,
            6,
            7,
            8,
            18,
            21,
            22,
            24,
            25,
            26,
            27,
            29,
            31,
            32,
            35,
            36,
            38,
            40,
            44,
            45,
            49,
            50,
            51,
            54,
            56,
            59,
            60,
            63,
            65,
            67,
            70,
            71,
            72,
            73,
            74,
            76,
            77,
            79,
            81,
            83,
            88,
            90,
            94,
            98,
            100,
            101,
            102,
            103,
            104,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            116,
            118,
            119,
            123
        ],
        "rewards": [
            [
                4.539785768600744e-05,
                0.9796676477332973,
                4.006368234711286e-05,
                NaN,
                6.144173856544049e-06,
                NaN,
                0.16451646494473965,
                NaN,
                6.6052160167241e-05,
                0.01590639349037286
            ],
            [
                8.481108128750289e-05,
                3.288750633025344e-06,
                1.4738985458142157e-05,
                1.3007126909537681e-05,
                0.00010889692168995679,
                NaN,
                NaN,
                6.962254581404613e-06,
                1.370957697068717e-06,
                1.3709567163491442e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.5534979387066465e-06,
                NaN,
                NaN
            ],
            [
                1.0129987335148346e-05,
                NaN,
                3.5356246475137275e-05,
                NaN,
                NaN,
                NaN,
                1.670141583301427e-05,
                NaN,
                4.785095634121282e-06,
                NaN
            ],
            [
                NaN,
                2.7535694360340682e-05,
                NaN,
                5.1442195089987364e-05,
                NaN,
                4.006370643585172e-05,
                2.753570413007019e-05,
                NaN,
                2.4300252207203426e-05,
                2.1444953502863275e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                0.9997040429026841,
                0.00023050676257769753,
                NaN,
                NaN,
                1.1478764009139048e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                1.5534984945682705e-06,
                NaN,
                1.1478766682468357e-05,
                NaN,
                1.9947297210880223e-06,
                NaN,
                3.2887478881736613e-06
            ],
            [
                NaN,
                2.902310941058239e-06,
                NaN,
                2.2603242972087315e-06,
                NaN,
                3.120191863103277e-05,
                NaN,
                1.67014218359435e-05,
                NaN,
                NaN
            ],
            [
                NaN,
                2.7535690999185903e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                2.9023112925037123e-06,
                NaN,
                NaN,
                NaN,
                3.7266379505740294e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.7603425836678333e-06,
                4.785092781953005e-06,
                NaN,
                NaN,
                6.144173864881432e-06,
                NaN,
                8.939700563752626e-06,
                6.96225624314774e-06,
                2.7535694358938284e-05,
                NaN
            ],
            [
                4.222834953082369e-06,
                NaN,
                8.939696299237883e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                0.0,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                8.481102023122205e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                3.120192250393883e-05,
                NaN,
                NaN
            ],
            [
                NaN,
                3.535623799851786e-05,
                2.14449483436795e-05,
                3.5356242224994204e-05,
                3.1201907609144296e-05,
                5.1442195113940765e-05,
                0.00029595720252434025,
                0.22270014398423357,
                0.09534945911506375,
                9.610244823181772e-05
            ],
            [
                NaN,
                3.2887490612610076e-06,
                NaN,
                1.6701423712406153e-05,
                1.3007134643315992e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                2.902311291748779e-06,
                NaN,
                NaN,
                NaN,
                1.0129994583336173e-05,
                NaN,
                2.260325104414902e-06,
                NaN,
                NaN,
                2.1444943262121474e-05
            ],
            [
                0.00015843624843370446,
                NaN,
                4.5397873902976276e-05,
                0.00033535018004027614,
                NaN,
                2.4300237787837067e-05,
                3.726639283291774e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                3.7266379506485954e-06,
                NaN,
                1.0129995792019037e-05,
                3.288749065077638e-06,
                2.260324564772615e-06,
                NaN,
                NaN,
                1.4738983707256776e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.994729245392294e-06,
                2.1444943267270435e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                6.605215234370881e-05,
                NaN,
                NaN,
                NaN,
                6.605217584506407e-05,
                NaN,
                2.1444956047154008e-05,
                2.4300243557987107e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                8.9396994898225e-06,
                NaN,
                1.4738988989779516e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                4.222832940777184e-06,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                6.144173135483279e-06,
                NaN,
                NaN,
                1.8925143673705497e-05,
                NaN,
                2.1444958618516124e-05,
                8.939699493497501e-06,
                7.889266332726198e-06,
                NaN,
                NaN
            ],
            [
                0.00023050662979089953,
                1.670142979997471e-05,
                NaN,
                NaN,
                0.00010889696084103356,
                NaN,
                NaN,
                NaN,
                NaN,
                9.610244866949822e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                2.753568123767511e-05,
                NaN,
                NaN,
                6.962255416328664e-06,
                2.753570394134699e-05,
                NaN,
                NaN,
                1.4738988970101218e-05,
                NaN,
                7.889265395847433e-06
            ],
            [
                0.0,
                3.120191878472311e-05,
                NaN,
                NaN,
                4.22283344293164e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                1.4738980201465192e-05,
                6.962253742174839e-06,
                3.2887478883351803e-06,
                1.473898017363677e-05,
                2.4300246493981982e-05,
                NaN,
                NaN,
                NaN,
                2.9023133666352393e-06
            ],
            [
                NaN,
                NaN,
                1.147876401460948e-05,
                NaN,
                2.144495090489879e-05,
                NaN,
                3.535625045723523e-05,
                NaN,
                NaN,
                3.288750628879691e-06
            ],
            [
                NaN,
                6.962258733787562e-06,
                NaN,
                3.535624222267904e-05,
                NaN,
                3.5356246441695886e-05,
                NaN,
                NaN,
                6.9622554153915155e-06,
                NaN
            ],
            [
                NaN,
                8.939695213161252e-06,
                NaN,
                3.726639726997871e-06,
                NaN,
                NaN,
                1.0129988563343644e-05,
                6.60521680181661e-05,
                NaN,
                3.2887506313204215e-06
            ],
            [
                2.7535694331891973e-05,
                NaN,
                NaN,
                NaN,
                2.9023119840232638e-06,
                NaN,
                NaN,
                NaN,
                2.4300240706150922e-05,
                NaN
            ],
            [
                2.1444945844014022e-05,
                1.8925145958150083e-05,
                1.994729007562614e-06,
                NaN,
                3.2887498463624074e-06,
                6.962257075741783e-06,
                1.4738988971066366e-05,
                NaN,
                5.144219501139025e-05,
                2.5612815990734206e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999546021332687,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                1.6701415793764356e-05,
                3.726639281203937e-06,
                4.78509563466093e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                6.144172400944199e-06,
                NaN,
                NaN,
                2.430023201636237e-05,
                NaN,
                2.9023130224326608e-06,
                NaN,
                NaN,
                2.753568773760199e-05,
                NaN
            ],
            [
                1.0677026138101252e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.6701415845530497e-05,
                NaN,
                NaN
            ],
            [
                NaN,
                4.785095064601411e-06,
                1.0129992176400077e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.1478765386330758e-05
            ],
            [
                NaN,
                NaN,
                1.670141984792864e-05,
                NaN,
                3.12019149930895e-05,
                NaN,
                4.785092781709294e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                NaN,
                4.539787398158721e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                3.7266388395111645e-06,
                9.610241435283532e-05,
                NaN,
                7.484620868705099e-05
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                0.00012339463228478546,
                9.610240284170286e-05,
                9.610242567519328e-05,
                0.0001398221218789517,
                8.939697364890742e-06,
                NaN,
                1.6701429779256086e-05,
                NaN,
                1.892514821299031e-05,
                8.481106116247119e-05
            ],
            [
                1.1478770818450524e-05,
                1.0129995799905438e-05,
                NaN,
                3.120191874590325e-05,
                7.889263524257144e-06,
                NaN,
                7.889262576544182e-06,
                2.7535704094208775e-05,
                1.473898723610551e-05,
                4.7850967748236935e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.147876810891517e-05,
                NaN,
                3.1201903802301935e-05,
                8.939700525652926e-06,
                5.829126517851279e-05,
                3.288749062947982e-06,
                1.3007134657984903e-05,
                1.892515272473701e-05,
                4.539787869791275e-05,
                2.902311983500617e-06
            ],
            [
                NaN,
                NaN,
                1.3007126905042372e-05,
                1.892514584048889e-05,
                NaN,
                NaN,
                6.962254581733882e-06,
                1.0129992166413098e-05,
                1.3007133108948093e-05,
                NaN
            ],
            [
                NaN,
                1.3007130004439633e-05,
                NaN,
                1.4738985452565748e-05,
                NaN,
                NaN,
                7.889265400583057e-06,
                NaN,
                NaN,
                4.222833945954137e-06
            ],
            [
                1.1478770847306026e-05,
                1.8925145968614975e-05,
                3.12019150514328e-05,
                NaN,
                2.144494327335557e-05,
                7.484624482036237e-05,
                NaN,
                2.430024360395595e-05,
                9.61024490400584e-05,
                NaN
            ],
            [
                NaN,
                NaN,
                1.4738985469509454e-05,
                3.7266379499571688e-06,
                NaN,
                2.144494072680393e-05,
                NaN,
                6.1441775261789395e-06,
                NaN,
                1.670142381836882e-05
            ],
            [
                3.2887482800422294e-06,
                NaN,
                NaN,
                3.1201907453183846e-05,
                NaN,
                NaN,
                NaN,
                2.4300249298965976e-05,
                NaN,
                NaN
            ],
            [
                8.939694170940841e-06,
                0.00013982202353022053,
                6.9622545846972985e-06,
                NaN,
                0.00010889693489823463,
                2.753569108924008e-05,
                6.9622570747539755e-06,
                3.1201903857921005e-05,
                1.1478768107662397e-05,
                0.0001233945443098906
            ],
            [
                NaN,
                2.753569754859982e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                6.475950769591715e-07,
                NaN,
                NaN
            ],
            [
                NaN,
                1.0677032511305593e-06,
                1.0129994596455602e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                5.422218968714274e-06
            ],
            [
                NaN,
                NaN,
                4.0063677515375304e-05,
                NaN,
                NaN,
                1.670142968836147e-05,
                NaN,
                NaN,
                NaN,
                5.422220903362958e-06
            ],
            [
                5.4222209070122355e-06,
                3.7266406152643387e-06,
                6.1441731363550164e-06,
                NaN,
                NaN,
                NaN,
                2.56128159807175e-06,
                NaN,
                6.962253757485831e-06,
                NaN
            ],
            [
                7.88926257993087e-06,
                8.315283247980153e-07,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                4.78509505845639e-06,
                NaN,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.4738983708061067e-05,
                NaN
            ],
            [
                1.1478766751997141e-05,
                1.1478766753751021e-05,
                NaN,
                1.892514597563747e-05,
                NaN,
                1.147877084091689e-05,
                NaN,
                NaN,
                5.8291243716509506e-05,
                3.1201926179794786e-05
            ]
        ]
    },
    {
        "q_id": "8450_mmlu_math",
        "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,
            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": [
            [
                0.9998415637643508,
                0.9978172834349807,
                0.9997694933670065,
                0.9997040430059551,
                0.9999151889181979,
                0.9990889489775784,
                0.9998911031167418,
                0.9988304897205296,
                0.9997965730753162,
                0.9998204720553445
            ],
            [
                0.9999852610232999,
                0.9999724642990617,
                0.9997965729295829,
                0.9999151889586775,
                0.9999687980998037,
                0.9999785550490321,
                0.9999687980886359,
                0.9999417087276202,
                0.999933947878961,
                0.9999151889587182
            ],
            [
                0.9999038975621215,
                0.9999151889384605,
                0.9990889488952975,
                0.9990889486604292,
                0.9986749778218702,
                0.9997694933668488,
                0.9988304898795015,
                0.9975273770960479,
                0.9995121427716891,
                0.9995121427663813
            ],
            [
                0.9997965729296658,
                0.9999417087553016,
                0.999903897550639,
                0.9999251537459726,
                0.9996200154705231,
                0.9999038975621705,
                0.9996200155608962,
                0.9975273771655356,
                0.9995694429111727,
                0.9998415637643508
            ],
            [
                0.9998766053957163,
                0.999948557798626,
                0.9999724643187504,
                0.9999251537817047,
                0.9999339478789758,
                0.9995121428817306,
                0.9999038975850983,
                0.9999546021151307,
                0.99989110309081,
                0.999891103129733
            ],
            [
                0.9978172832103379,
                0.9999546021421896,
                0.9999599363221565,
                0.99998329858413,
                0.9990889486673696,
                0.9996646498097153,
                0.9999546021421873,
                0.999915188928435,
                0.9998601779758696,
                0.9999724643154765
            ],
            [
                0.9998601779260005,
                0.9998911030518491,
                0.9996646500100201,
                0.9999038975507166,
                0.9995121428255319,
                0.9999599362934934,
                0.9996646498899543,
                0.9999038975392426,
                0.999738809659496,
                0.9992903295413339
            ],
            [
                0.9998911030777682,
                0.9999687980849095,
                0.9993736657520793,
                0.999195914236845,
                0.9975273768893076,
                0.9980732648902771,
                0.9996200154249663,
                0.9999339478474549,
                0.9999546021205351,
                0.9999546021421873
            ],
            [
                0.999704042901048,
                0.9998415637077331,
                0.9982992779289238,
                0.9999646437577143,
                0.9986749775160838,
                0.9999038976079563,
                0.9995694429607108,
                0.9997388096289986,
                0.9996646498900617,
                0.9992903294533685
            ],
            [
                0.9998415637453423,
                0.9999898700041899,
                0.998299277891172,
                0.9990889487696777,
                0.9997388097845256,
                0.9995121427644797,
                0.9990889486739395,
                0.999915188978879,
                0.9997694933404095,
                0.9984988177296522
            ],
            [
                0.999981074842739,
                0.9999038975737291,
                0.9999251537460401,
                0.9999832985821392,
                0.9999417087345305,
                0.9999687980960733,
                0.9999910603015646,
                0.9999724642990576,
                0.9996200154246125,
                0.999991060305829
            ],
            [
                0.999841563783417,
                0.9998766054107798,
                0.9999869928699859,
                0.9999417087483837,
                0.9999885212318741,
                0.9996200155613383,
                0.9998911031297203,
                0.9999417087066769,
                0.9999417087205921,
                0.9999785550515911
            ],
            [
                0.9993736658971619,
                0.9997388097526526,
                0.997817283275246,
                0.9991959139510092,
                0.9998911030388452,
                0.99982047196977,
                0.9997040430071777,
                0.9998415637452915,
                0.9996646499291274,
                0.9991959139701834
            ],
            [
                0.9995121428809076,
                0.9997388097215321,
                0.9978172832336644,
                0.9996646500108106,
                0.9964063973793963,
                0.9995694430122656,
                0.999738809597118,
                0.9999251537459726,
                0.9996646499297909,
                0.999964643736646
            ],
            [
                2.2603242978665707e-06,
                2.260325375634003e-06,
                4.222834451254188e-06,
                1.8925150493717652e-05,
                4.222834451215781e-06,
                1.209865250822125e-06,
                2.260324028404236e-06,
                1.1478764019328247e-05,
                5.422218969661113e-06,
                8.93969417214416e-06
            ],
            [
                0.9995694429621763,
                0.9999251537548992,
                0.9998601779259192,
                0.9999151889384605,
                0.999860177975949,
                0.9998911031036888,
                0.9998911031038535,
                0.9997965729537811,
                0.9998601779759897,
                0.9998601779092168
            ],
            [
                0.9991959140594134,
                0.9996646497705518,
                0.9997965730754879,
                0.9997388095970496,
                0.9995694429607108,
                0.9953904270343552,
                0.9993736657510955,
                0.9999151889384001,
                0.999860177959389,
                0.9998601779093572
            ],
            [
                0.9947798741565181,
                0.9980732650691488,
                0.9993736658977084,
                0.999738809721874,
                0.998073264899232,
                0.9988304899986284,
                0.9998911030648404,
                0.9996200155598238,
                0.9989677688017867,
                0.9996646497300419
            ],
            [
                0.9997388095666206,
                0.9999038975391943,
                0.9993736659705776,
                0.999195913953862,
                0.9997040429363098,
                0.9995121429384402,
                0.9998766053662896,
                0.9998204719911309,
                0.9999417087136139,
                0.9992903297060369
            ],
            [
                0.9999151889587349,
                0.9998204720771078,
                0.9998766054691844,
                0.9999038975392628,
                0.9999339478395824,
                0.9999724643023344,
                0.999891103116832,
                0.9999785550592551,
                0.9988304895940591,
                0.9999921107345928
            ],
            [
                0.9990889486564025,
                0.9998766054692149,
                0.9994472214525726,
                0.9996646497703273,
                0.9995694430118022,
                0.9988304897324967,
                0.9991959140517438,
                0.9997040428298269,
                0.9984988175424154,
                0.9997040429710378
            ],
            [
                0.9999251537816741,
                0.9999646437408591,
                0.9999339478317045,
                0.9996200155144881,
                0.9999599362934879,
                0.9999485577924824,
                0.9997040430068247,
                0.9999251537460085,
                0.9997040430063856,
                0.9998204720124919
            ],
            [
                0.9995121429405406,
                0.9995121428815036,
                0.9998601779092757,
                0.9997965730512482,
                0.9998601778759707,
                0.9992903294496533,
                0.9998415637832303,
                0.9998601778927158,
                0.9947798733464474,
                0.9992903297127653
            ],
            [
                0.9999832985721833,
                0.999968798081189,
                0.9999599362887198,
                0.9999251537816986,
                0.999891103116859,
                0.999959936298279,
                0.9999756997621654,
                0.9999898700053974,
                0.9999485577863536,
                0.9999724642957734
            ],
            [
                0.9999038975391943,
                0.9999251537995338,
                0.998967769161797,
                0.999933947871074,
                0.9992903296230663,
                0.9995121429382132,
                0.99990389758502,
                0.9997694933669528,
                0.9971990723949199,
                0.9998601779592853
            ],
            [
                0.9997965730266685,
                0.9999599363173656,
                0.9999869928699849,
                0.9999339478632668,
                0.9999687980811924,
                0.9999962733611601,
                0.9998766053958313,
                0.9999687980811924,
                0.9999898700090202,
                0.9999852610145143
            ],
            [
                0.9999756997621633,
                0.9999251537906132,
                0.9999832985781555,
                0.9999339478238364,
                0.9999687980737504,
                0.9991959142393704,
                0.9994472213207883,
                0.9999898700114352,
                0.9999785550413615,
                0.9999339478238094
            ],
            [
                0.9999251537459726,
                0.9980732653621937,
                0.9975273764178245,
                0.9991959140448224,
                0.9995121428829227,
                0.9996646498498932,
                0.9995121427663813,
                0.9995121428235167,
                0.9986749778395857,
                0.9995694428593297
            ],
            [
                0.9998204720562144,
                0.999933947871098,
                0.9993736658988743,
                0.9998204719913635,
                0.9997694932299439,
                0.9980732653122708,
                0.9999852610197855,
                0.9997694932296253,
                0.9999251537995099,
                0.999903897550667
            ],
            [
                0.9998911030647778,
                0.9997694932845563,
                0.9984988175087373,
                0.999891103064765,
                0.9999038976079374,
                0.9988304897324967,
                0.9998415638397465,
                0.9995694429106089,
                0.9998415637832303,
                0.9997040427595703
            ],
            [
                0.9999869928730862,
                0.9992903294568359,
                0.9995694429636544,
                0.9996646499706324,
                0.9999038975621404,
                0.9999151889890767,
                0.9999038975506866,
                0.9998415637076571,
                0.9998911030778189,
                0.9992903297110316
            ],
            [
                0.9999251537906066,
                0.9999785550566994,
                0.9999832985781563,
                0.9999687980811924,
                0.9998766053811251,
                0.9998766054692634,
                0.9995694429127508,
                0.9999599362887218,
                0.9999599362887367,
                0.9999251537370689
            ],
            [
                0.9999151889687937,
                0.9997965729781864,
                0.9999151889283289,
                0.9996200154246125,
                0.9999417087136139,
                0.9997040429007811,
                0.9991959140467399,
                0.9999546021205679,
                0.9999869928653333,
                0.9998601779258804
            ],
            [
                0.9999785550515924,
                0.9999724642990617,
                0.9999646437577323,
                0.9999785550541453,
                0.9999952149066462,
                0.9999724643023419,
                0.9999339478238608,
                0.9999810748585336,
                0.9999756997505903,
                0.9999810748517663
            ],
            [
                0.9999151889182362,
                0.9991959139614848,
                0.999620015517694,
                0.9996200155154941,
                0.9999339478553236,
                0.9997694932849822,
                0.9998766054252419,
                0.9998911031167045,
                0.9999151889889569,
                0.9996200154243251
            ],
            [
                0.9999756997679602,
                0.9995694429628151,
                0.9975273766607445,
                0.9975273771684071,
                0.9994472213852655,
                0.9995694430130798,
                0.987568348357872,
                0.9859363759010484,
                0.999820471991097,
                0.9989677690375521
            ],
            [
                0.9996646498500006,
                0.9998766054104387,
                0.994779873697075,
                0.9998766053809329,
                0.9997388097217372,
                0.9995121428229208,
                0.9990889489848369,
                0.9999810748562713,
                0.9997694932844523,
                0.9796676449877542
            ],
            [
                0.9995121428836323,
                0.9990889489787971,
                0.9999151889485539,
                0.9996646498904032,
                0.9999810748585273,
                0.9999756997505788,
                0.9998766054692634,
                0.9997388096287174,
                0.999841563726668,
                0.9997388096915893
            ],
            [
                0.9999785550515891,
                0.9999898700066062,
                0.9999852610197857,
                0.9998204720985366,
                0.9999687980811913,
                0.9999898700114355,
                0.9971990730140199,
                0.9999852610162717,
                0.9999930377412604,
                0.9999151889789265
            ],
            [
                6.475948754012522e-07,
                1.2098659719716573e-06,
                1.9947304348595095e-06,
                1.2098662604192665e-06,
                3.72664061681327e-06,
                1.0677027427413698e-06,
                3.2887506334201674e-06,
                3.927860597945825e-07,
                1.994729483694599e-06,
                3.9278634073732336e-07
            ],
            [
                0.999860177875871,
                0.9995694428598808,
                0.999769493202693,
                0.9993736659730552,
                0.999704042901048,
                0.99986017787593,
                0.9997694931751202,
                0.9998601778760948,
                0.9999038975506201,
                0.9995121429383267
            ],
            [
                0.9999038976193724,
                0.9980732648920682,
                0.9989677690359915,
                0.9998911030777436,
                0.9999251537905887,
                0.99970404283018,
                0.9999869928668839,
                0.9999417087136211,
                0.99781728344208,
                0.999876605454525
            ],
            [
                0.9999251537816801,
                0.9999945777803839,
                0.9999646437619328,
                0.999954602115126,
                0.9999485577679644,
                0.9999038975851088,
                0.9998415637458196,
                0.9947798754502128,
                0.9997388095973917,
                0.9999646437408591
            ],
            [
                0.9990889488890987,
                0.9997040430060411,
                0.9989677691842451,
                0.9997694933402419,
                0.9992903294474655,
                0.9996646500102446,
                0.9997965729296658,
                0.9995694428597932,
                0.9984988177088868,
                0.9770226305499425
            ],
            [
                0.9999417087066587,
                0.9980732656523281,
                0.9999417087275134,
                0.9999151889384531,
                0.9999339478789562,
                0.9997694933123403,
                0.9995121428238858,
                0.9997694933397523,
                0.9999151889384377,
                0.9999646437619301
            ],
            [
                0.9999251537905948,
                0.9998911030907721,
                0.9998204720554777,
                0.9997388096599749,
                0.9999546021259464,
                0.9999038975391754,
                0.9999038976194708,
                0.9998415638209408,
                0.99995460213136,
                0.9999339478710649
            ],
            [
                0.9998911030518871,
                0.9998911030517992,
                0.9999339478710831,
                0.9999417087136483,
                0.9997388095669019,
                0.999925153745984,
                0.9999417087344801,
                0.9999339478317237,
                0.9999485577863596,
                0.9993736657583825
            ],
            [
                0.9999485577618238,
                0.9997388096600432,
                0.9998204720771078,
                0.9999151889889952,
                0.9999339478238862,
                0.9982992772072913,
                0.9999898700102277,
                0.999841563726562,
                0.9999038976194206,
                0.9999810748517589
            ],
            [
                0.9984988178666333,
                0.99991518896874,
                0.9991959139525992,
                0.9988304898635907,
                0.9999417087553055,
                0.999704042759312,
                0.9999038975621306,
                0.9998601779426236,
                0.9998204720553105,
                0.9982992778660701
            ],
            [
                0.9994472212537708,
                0.9998766054544944,
                0.9989677687872615,
                0.9999339478632058,
                0.9992903297043032,
                0.998299277510887,
                0.9998415637643255,
                0.9999151889283443,
                0.9997965730028551,
                0.9995694430129921
            ],
            [
                0.9999756997505761,
                0.9996200154259834,
                0.9999930377437503,
                0.9998204719484768,
                0.9999724642990521,
                0.9999251537905887,
                0.9991959139532072,
                0.9998204719483776,
                0.9993736657513141,
                0.9999485577679497
            ],
            [
                0.9995694428604445,
                0.9999687980960696,
                0.9999417087205802,
                0.9999810748585286,
                0.9999646437450808,
                0.9995694429137028,
                0.999903897596573,
                0.999569442968865,
                0.9999852610180284,
                0.9999339478553779
            ],
            [
                0.9988304898661745,
                0.9991959139522719,
                0.9959298621085578,
                0.999447221257694,
                0.9998204720986045,
                0.9996646499715593,
                0.9993736658266609,
                0.9902915220590333,
                0.997527377365959,
                0.9986749773840642
            ],
            [
                0.9999898700053974,
                0.9998911030518871,
                0.9999785550464758,
                0.9999485577924795,
                0.9999151889384377,
                0.9999339478789562,
                0.9998601778759911,
                0.9999974387168732,
                0.9999910603026305,
                0.9999151889384686
            ],
            [
                0.9998601779425035,
                0.9996646497694395,
                0.9990889489756181,
                0.9991959140498733,
                0.9994472212534813,
                0.9984988180526484,
                0.9996200154692297,
                0.9971990725874132,
                0.9995694429603477,
                0.9992903294568359
            ],
            [
                0.999975699756372,
                0.9999417087553165,
                0.9999251537816801,
                0.9995694430129921,
                0.9997040428658723,
                0.9997965729784409,
                0.9998601778759096,
                0.9997388095972548,
                0.9998766054692634,
                0.9999646437619314
            ],
            [
                0.9998766053957325,
                0.9999756997679586,
                0.999903897539223,
                0.9998601778925327,
                0.9998415637077608,
                0.9999646437450749,
                0.9999646437535068,
                0.9998911030777318,
                0.9984988176870745,
                0.999841563745317
            ],
            [
                0.9996200155593926,
                0.9994472214569782,
                0.999876605381109,
                0.9999417087414166,
                0.9998766054692149,
                0.9999251537995218,
                0.9999485577924947,
                0.9998911031297203,
                0.9993736659709419,
                0.9997388096287174
            ],
            [
                0.9999339478789758,
                0.9999151889789345,
                0.99991518895867,
                0.9998601779425829,
                0.9998766054105196,
                0.999820472034391,
                0.9999646437324458,
                0.9999251537905712,
                0.9998601779092757,
                0.9997040428307913
            ],
            [
                0.9993736658243291,
                0.9998601779761789,
                0.9999151889687629,
                0.9996646499690811,
                0.9993736659025906,
                0.9998601778592663,
                0.9993736659703589,
                0.9998911031166673,
                0.9999810748472479,
                0.9984988178774522
            ],
            [
                0.9997965730749018,
                0.9990889488841714,
                0.9999038975621705,
                0.9947798747949022,
                0.999512142822353,
                0.9997965729783995,
                0.9997694932298903,
                0.9994472214536338,
                0.9997694932028004,
                0.9989677690375521
            ],
            [
                0.9999724643089025,
                0.9999599362982616,
                0.999820471970039,
                0.9999869928761873,
                0.9999756997476807,
                0.9999251537638443,
                0.9999756997505788,
                0.9999151889182126,
                0.9999832985741741,
                0.9999852610162715
            ],
            [
                0.9953904279552319,
                0.9989677689199095,
                0.9984988177055714,
                0.9996646499707494,
                0.9998204720552792,
                0.9989677690427139,
                0.9998204719913294,
                0.9990889489844661,
                0.9997388095659975,
                0.9975273769720038
            ],
            [
                0.9999599363030371,
                0.999769493312555,
                0.9997040428654331,
                0.9997388097217372,
                0.9982992773312199,
                0.9992903297043032,
                0.9999417087483536,
                0.9993736659763708,
                0.9996200154705231,
                0.9947798743378772
            ],
            [
                0.989013059008841,
                0.999664649851591,
                0.9968273176957896,
                0.999088948999142,
                0.9997694931757305,
                0.9999599362938393,
                0.9902915254257154,
                0.998967769172721,
                0.9993736657495652,
                0.9997694932579526
            ],
            [
                0.9982992774828201,
                0.9995694428601689,
                0.9997965730753162,
                0.9991959142418958,
                0.9990889488878801,
                0.9999546021476033,
                0.9999599363173692,
                0.999820471969804,
                0.9998204720982624,
                0.9993736658225802
            ],
            [
                1.6701421843356024e-05,
                1.1478772229989872e-05,
                4.785093353787868e-06,
                1.3007123811797321e-05,
                2.260324567302214e-06,
                2.9023112931873767e-06,
                1.892515049423401e-05,
                1.4738981971250963e-05,
                3.7266406167827664e-06,
                5.422217676979575e-06
            ],
            [
                0.9992903294472179,
                0.9997965730267513,
                0.998830489874198,
                0.9996646499695202,
                0.9998766054398672,
                0.9989677690436742,
                0.9999251537906008,
                0.9999785550490304,
                0.9999151889889644,
                0.9991959140442145
            ],
            [
                0.999891103064815,
                0.9999339478789374,
                0.9992903294578266,
                0.9996646499701837,
                0.999959936298269,
                0.9980732649896752,
                0.9999756997679566,
                0.9971990735310203,
                0.9999339478789813,
                0.9999038975621705
            ],
            [
                0.9996200154698709,
                0.999796573002639,
                0.9994472213259659,
                0.9998766054105033,
                0.9999151889485773,
                0.9992903294538638,
                0.999738809628649,
                0.9840936095710796,
                0.9996200155150629,
                0.9986749778405101
            ],
            [
                0.9990889486551838,
                0.9995121428218705,
                0.9998601778925327,
                0.9820137875375573,
                0.9997694933394873,
                0.9978172831900541,
                0.9993736658262602,
                0.9991959142438132,
                0.9997388097839707,
                0.9986749773661946
            ],
            [
                0.9999251537816921,
                0.9997388095662026,
                0.9998415637076825,
                0.9999687980849082,
                0.998073265587406,
                0.9990889487757706,
                0.9995694428601689,
                0.9988304894655489,
                0.9998601779759897,
                0.9997965730996858
            ],
            [
                0.9999038976194206,
                0.9997694932299439,
                0.9994472213221391,
                0.9997388097218056,
                0.9996646500110447,
                0.9992903294521301,
                0.9998415638210446,
                0.9988304897397041,
                0.999447221256472,
                0.9995121429390079
            ],
            [
                0.9999151889890187,
                0.9999646437450749,
                0.9992903295360914,
                0.9996200154252537,
                0.9997965729542457,
                0.9997694931750128,
                0.9999646437408619,
                0.9991959142485832,
                0.9996200154708106,
                0.9997040428657862
            ],
            [
                0.9998204720343571,
                0.9991959139627474,
                0.9997694932299439,
                0.998830489886845,
                0.9997965729297074,
                0.9997965731000796,
                0.9999810748495053,
                0.9999151889283443,
                0.9997040429721915,
                0.9997040427600956
            ],
            [
                0.9992903297125176,
                0.9991959141433592,
                0.9902915214949348,
                0.9996200154247563,
                0.9995121427642527,
                0.9989677690463152,
                0.9996646497705518,
                0.999195914156407,
                0.9998766054692311,
                0.9971990723949199
            ],
            [
                0.9998911031166554,
                0.9997965730750646,
                0.9993736659686465,
                0.9997040429714769,
                0.9971990731837521,
                0.9984988175282811,
                0.9998601778925734,
                0.9959298621689608,
                0.9993736657479986,
                0.9991959141484099
            ],
            [
                0.9999251537459726,
                0.9982992779247731,
                0.9999417087066587,
                0.9992903294551022,
                0.9997694933126624,
                0.9998911030388706,
                0.9995694429634664,
                0.9995694429112603,
                0.9975273765424431,
                0.9990889486677935
            ],
            [
                0.9984988175043749,
                0.9998204720984661,
                0.9998911031166673,
                0.9999687980737515,
                0.9999810748562709,
                0.9997694933671104,
                0.9999151889182207,
                0.9999038976079864,
                0.999704042794832,
                0.9997388097227099
            ],
            [
                0.9995121427643663,
                0.9997040428300853,
                0.9997040429362151,
                0.9997388096282387,
                0.9995121429379576,
                0.9996646498112958,
                0.9999151889889872,
                0.9996646499305715,
                0.9990889489979234,
                0.9997388097842443
            ],
            [
                0.9994472214562065,
                0.9997388095666206,
                0.9997388097217372,
                0.9999546021313555,
                0.9997388096595644,
                0.9997040429005227,
                0.9999832985701924,
                0.9993736659717071,
                0.9997388096594276,
                0.9995694429616252
            ],
            [
                0.9999038975965026,
                0.9999921107364741,
                0.9999546021476109,
                0.999954602147616,
                0.9999339478395728,
                0.999985261016272,
                0.9999930377462403,
                0.9999810748517607,
                0.9999546021367908,
                0.9999930377454103
            ],
            [
                0.9998204720980326,
                0.9993736659730552,
                0.9986749775279455,
                4.222835458117536e-06,
                0.9997965729537811,
                0.9968273170853521,
                0.9999151889889353,
                0.9991959139563873,
                0.9999038976193814,
                0.9999485577863421
            ],
            [
                0.9998204720767369,
                0.99986017797589,
                0.9999151889182516,
                0.9998204720342866,
                0.9999724642957716,
                0.999933947878961,
                0.9999687980849105,
                0.9999599362887106,
                0.9999785550464741,
                0.9999852610127568
            ],
            [
                0.9984988176893431,
                0.9998601778925327,
                0.9998415637642217,
                0.9993736657472334,
                0.9998911030907593,
                0.9997388097839099,
                0.999796573050825,
                0.9996646497297103,
                0.9890130585635626,
                0.9996200155160025
            ],
            [
                0.9999869928684346,
                0.9993736659014247,
                0.9998601778594107,
                0.9997694933131117,
                0.9997965729788375,
                0.9999646437619403,
                0.9999599363030446,
                0.9999885212264008,
                0.9997965730509494,
                0.9998415638209662
            ],
            [
                0.9988304896000427,
                0.9996200155602549,
                0.9994472213851369,
                0.9989677690333505,
                0.9999599363173673,
                0.9994472212560218,
                0.9997965729297902,
                0.9999151889283289,
                0.9991959140448224,
                0.9997040429713047
            ],
            [
                0.9998601778593477,
                0.9997040427944791,
                0.9999546021205351,
                0.9997388096289986,
                0.9999910603058273,
                0.9998601778927362,
                0.9999151889485693,
                0.999704042794393,
                0.9999885212332426,
                0.9998415638400577
            ],
            [
                0.9998911031166918,
                0.9997388097839099,
                0.9953904273292066,
                0.999569442912851,
                0.9995121428824402,
                0.9997965730026834,
                0.9978172839258476,
                0.9991959140476753,
                0.999876605366322,
                0.9997694933123941
            ],
            [
                0.9997388096913081,
                0.9997388097219424,
                0.99962001542511,
                0.9940889315131547,
                0.9998415638399263,
                0.9999251537906066,
                0.999954602147616,
                0.9990889488732042,
                0.9997965730992656,
                0.9999810748449907
            ],
            [
                0.9994472214596152,
                0.9989677688127107,
                0.9999832985701956,
                0.9991959141612239,
                0.9992903295473606,
                0.9998415638401407,
                0.9995694428617596,
                0.9997694932025857,
                0.9995694428639517,
                0.9997965730755767
            ],
            [
                0.9998415637455751,
                0.9998911030647175,
                0.9995694429109848,
                0.999373665746104,
                0.9997040429007811,
                0.9924227573664791,
                0.9988304895880756,
                0.9991959140464125,
                0.999704042865967,
                0.9994472213215281
            ],
            [
                0.9980732648920682,
                0.9997694931749592,
                0.9993736658206491,
                0.9968273169204088,
                0.9986749775656875,
                0.9982992773270692,
                0.9968273175801821,
                0.9999417087414166,
                0.9993736657552127,
                0.9992903297013723
            ],
            [
                0.9997694931753952,
                0.9993736659699947,
                0.9999724642957725,
                0.9996200155591827,
                0.999704042935354,
                0.9999852610162724,
                0.999915188978871,
                0.9994472214542448,
                0.9995121428236302,
                0.9996646498109543
            ],
            [
                0.9999151889181905,
                0.9998601779426032,
                0.999915188978879,
                0.9999251537905887,
                0.9998204720983304,
                0.9997965730752333,
                0.9999832985821392,
                0.9998415638399794,
                0.9998415637079199,
                0.9996200154706668
            ],
            [
                0.9982992778743716,
                0.999975699759266,
                0.999991060300499,
                0.9978172839324397,
                0.9997694932574094,
                0.9982992776751369,
                0.9998415637454438,
                0.9999151889385346,
                0.9998766054397721,
                0.9999546021367646
            ],
            [
                0.9999038975735851,
                0.9998204720124606,
                0.9999038975622648,
                0.9999251537994924,
                0.9997965730998575,
                0.9999599362934916,
                0.9997040427950044,
                0.9999687980886287,
                0.9999251537816741,
                0.9998766054692795
            ],
            [
                0.9998415638399263,
                0.9997388096592909,
                0.9998601778926528,
                0.9997965729542457,
                0.9999852610162715,
                0.9999417087483609,
                0.9999339478632202,
                0.9998911030907467,
                0.9999339478710885,
                0.999860177975949
            ],
            [
                0.9999339478238608,
                0.9998204720983304,
                0.9997694931751202,
                0.9999251537548818,
                0.9999646437366552,
                0.9998911030647532,
                0.9999038975621306,
                0.9999151889687481,
                0.9998601779260209,
                0.9924227602553751
            ],
            [
                0.9989677691628774,
                0.999820471948409,
                0.9998911031037759,
                0.9994472213885778,
                0.9999832985721833,
                0.9859363712650766,
                0.9998766053957163,
                0.9998204720338529,
                0.9993736658272439,
                0.9998204720981319
            ],
            [
                0.999948557761818,
                0.9999785550515873,
                0.9999339478710831,
                0.999981074849503,
                0.9999599362887106,
                0.999915188978879,
                0.9998415638021374,
                0.9998911030518237,
                0.9998911031036649,
                0.9998415638398733
            ],
            [
                0.9991959139504012,
                0.9998204720125233,
                0.9993736658202849,
                0.9998204719696734,
                0.9992903297006293,
                0.9986749773458602,
                0.998498818047239,
                0.9998601779758696,
                0.9999038976079275,
                0.9978172831875187
            ],
            [
                0.9991959140658674,
                0.9999038975736144,
                0.9997965730759761,
                0.9924227587776612,
                0.9995694428627117,
                0.9996646498137837,
                0.8933093996634686,
                0.9975273767669861,
                0.8519527982093666,
                0.9995694429104336
            ],
            [
                0.9999832985841279,
                0.9990889488752175,
                0.9997965730267098,
                0.9995694428575135,
                0.9994472212572438,
                0.9998204719482471,
                0.9992903294513871,
                0.9998766054692311,
                0.9991959141430318,
                0.999569442960072
            ],
            [
                0.999664649930913,
                0.9999151889283214,
                0.9999810748540149,
                0.9999251537816801,
                0.9999151889586936,
                0.9999885212291375,
                0.9997965730267098,
                0.9998911030518491,
                0.9999485577924824,
                0.9997040427596564
            ],
            [
                0.9999038976194604,
                0.996827317320249,
                0.9999417087553356,
                0.9997965729541156,
                0.9998415637642725,
                0.9993736658973441,
                0.9997040430060411,
                0.99979657309939,
                0.999769493285311,
                0.9978172838046521
            ],
            [
                0.9990889488780785,
                0.9994472214583611,
                0.9998911031297709,
                0.9988304898854851,
                0.998674977688002,
                0.9997388096599749,
                0.999769493257624,
                0.998967768835519,
                0.9998415637454438,
                0.9998911031296949
            ],
            [
                0.999978555041362,
                0.9999687980737526,
                0.999933947831754,
                0.9998601779260615,
                0.9999687980960721,
                0.9999687980737603,
                0.9998911030390449,
                0.9999785550464785,
                0.9999869928715373,
                0.9999810748517645
            ],
            [
                0.9998415637076571,
                0.9995694428592421,
                0.9998911030906626,
                0.9998766054546057,
                0.9998204720126564,
                0.9999599363173656,
                0.9991959142440937,
                0.9998911030777682,
                0.999876605439851,
                0.9997040429007811
            ],
            [
                0.9998204720770059,
                0.9997694932853645,
                0.999993855826863,
                0.9999417087066808,
                0.9999852610127573,
                0.9999756997563707,
                0.9999885212332428,
                0.999796573050908,
                0.9999339478238556,
                0.9999151889890107
            ],
            [
                0.9984988178589553,
                0.9995694428598808,
                0.9993736657462862,
                0.9997388097529262,
                0.9991959139601754,
                0.9996200154246788,
                0.9995694429604353,
                0.9991959140530534,
                0.9993736657485816,
                0.9999599363125974
            ],
            [
                0.9999038975735753,
                0.9968273165014232,
                0.9998601778926324,
                0.9996200155607524,
                0.9959298626389711,
                0.9997040429710378,
                0.9980732651678751,
                0.9991959140603955,
                0.9990889487753468,
                0.9999251537905604
            ],
            [
                0.9999038975965122,
                0.999876605439851,
                0.9997965729540741,
                0.9998911030648404,
                0.9997388097531315,
                0.9978172840313231,
                0.9999832985781553,
                0.999876605410392,
                0.9998204719483776,
                0.9984988175392745
            ],
            [
                0.9999151889789432,
                0.9999869928715358,
                0.9999832985821371,
                0.9997965729297074,
                0.9993736658272439,
                0.9999869928715361,
                0.9999852610145143,
                0.9999687980849129,
                0.9999810748540162,
                0.9999885212332428
            ],
            [
                0.9992903296220755,
                0.9988304897224335,
                0.9964063966757585,
                0.9975273773688303,
                0.999925153745996,
                0.9998204720126225,
                0.9996200154241041,
                0.9998601779425239,
                0.9999646437408564,
                0.9999038976194108
            ],
            [
                0.9999339478710788,
                0.999985261021543,
                0.9999417087484003,
                0.9999869928761888,
                0.9999151889586856,
                0.9999869928761882,
                0.9999599363221565,
                0.9999485578047914,
                0.9999599363125974,
                0.9998204720768701
            ],
            [
                0.9999151889788864,
                0.9997388097526526,
                0.9999417087136139,
                0.999860177859246,
                0.9997040430068247,
                0.9999599362887088,
                0.9991959141396178,
                0.9998601779259192,
                0.9999546021151193,
                0.9999251537727241
            ],
            [
                0.9999151889687703,
                0.9999038975392328,
                0.9999151889586171,
                0.9999485577679709,
                0.9993736658288106,
                0.999820471991097,
                0.9999417087205921,
                0.9994472213872272,
                0.9933071506112032,
                0.9999546021313795
            ],
            [
                0.999985261021543,
                0.9999038975735655,
                0.9999785550439179,
                0.9999687980811962,
                0.9998415637643255,
                0.9997694932571948,
                0.9999869928715353,
                0.9999038975850487,
                0.9998766054252095,
                0.9999977396765105
            ],
            [
                0.9995121429439182,
                0.9997040428306192,
                0.9997694931749056,
                0.999820471970005,
                0.9997040429709516,
                0.9998415638025179,
                0.9998204720982624,
                0.9998204720126564,
                0.9995121428232897,
                0.9953904275279108
            ],
            [
                0.9968273168725458,
                0.9994472213870663,
                0.9986749776668974,
                0.9978172831393448,
                0.9982992772683661,
                0.9988304896269686,
                0.9995121428248224,
                0.9996200155153504,
                0.9964063973593876,
                0.9933071496329489
            ],
            [
                0.9998204719484768,
                0.9997040428657862,
                0.9999251537906066,
                0.999903897596573,
                0.9999546021151215,
                0.9964063979229647,
                0.9999810748562717,
                0.9997965730509494,
                0.9999599363173692,
                0.9996646499297909
            ],
            [
                0.9995694429618006,
                0.9999038975850886,
                0.9999339478238272,
                0.9998766054250353,
                0.9999785550515862,
                0.9982992775630675,
                0.9996200154706668,
                0.9999485577679644,
                0.9999724642990531,
                0.9999646437492968
            ],
            [
                0.9997694933405168,
                0.9997040429035365,
                0.9997040429725532,
                0.999738809753063,
                0.9940889319153886,
                0.9995694429618006,
                0.9998601779093572,
                0.9998766053957809,
                0.9994472212569223,
                0.9997040427950904
            ],
            [
                0.9997388095664763,
                0.9998911031167045,
                0.9994472213216888,
                0.9998204719699032,
                0.9998766053809959,
                0.9997040430064716,
                0.9986749778422046,
                0.9999810748472471,
                0.9997965730995142,
                0.9997965729294587
            ],
            [
                0.9998766054398349,
                0.9999724642990531,
                0.9997694933398595,
                0.9999546021259487,
                0.9999485578047517,
                0.9997965730993486,
                0.9999038975735753,
                0.9998601779093165,
                0.9996200154238166,
                0.999860177942705
            ]
        ]
    },
    {
        "q_id": "8028_mmlu_math",
        "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,
            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": [
            [
                3.2887506333812835e-06,
                2.1444940719392548e-05,
                1.5534973841592143e-06,
                1.3709578605355551e-06,
                3.726639283901856e-06,
                3.288750633139005e-06,
                1.994730434778778e-06,
                1.0677028700130727e-06,
                3.726638395527247e-06,
                1.5534984953199313e-06
            ],
            [
                0.0017007223404777113,
                0.012431648532095208,
                0.0009110511861354775,
                0.9980732654074151,
                0.0015011825132494672,
                0.00317268325631624,
                0.01243165152778859,
                0.005220125270387185,
                0.0003799845193064432,
                0.0017007222363143663
            ],
            [
                0.0019267344945300558,
                0.00029595706177857543,
                4.539788483220847e-05,
                1.370957533625589e-06,
                0.00037998448116737557,
                1.4738988981843854e-05,
                0.00010889696068733835,
                0.9859363743514202,
                0.9706877665457513,
                0.0015011819649759157
            ],
            [
                0.9989677688237547,
                0.0009110509892549614,
                0.014063626255517657,
                0.005220125787865128,
                0.9999599362935078,
                0.002182716286117667,
                0.0010322309264348785,
                0.9980732652784665,
                0.00247262279196767,
                0.00029595699218500754
            ],
            [
                0.0420877273148584,
                0.010986943784269254,
                0.9999987901347492,
                0.002800927553054874,
                NaN,
                0.002472622832167191,
                0.9999952149060773,
                0.0021827165822605682,
                0.9999921107345938,
                0.029312227677479034
            ],
            [
                6.144173132689249e-06,
                1.9947299592407137e-06,
                2.90231163910023e-06,
                1.3709570433661467e-06,
                1.7603440527046419e-06,
                2.2603251061849014e-06,
                4.222832941034507e-06,
                3.2887486731641103e-06,
                1.5534981249496567e-06,
                2.9023109470871505e-06
            ],
            [
                0.014063629845490687,
                0.00033535014504298873,
                0.005911069042311205,
                0.020332351932785337,
                0.0004878571698415613,
                0.9991959139585853,
                0.0008040857960785276,
                0.0035936033350795734,
                0.0159063933445894,
                0.00020342692086293903
            ],
            [
                0.979667644505429,
                0.0675466977093867,
                0.0009110512953840491,
                0.11920291263495984,
                0.01098694273179283,
                0.029312228419449384,
                0.02931223409022338,
                0.007577241425436959,
                0.012431649115226305,
                0.029312229744396484
            ],
            [
                0.0017007226571185074,
                0.05340332829327472,
                0.010986940434560983,
                0.06008665690650098,
                0.0004305569800562419,
                0.0013250227083649007,
                0.004070137485609981,
                0.0035936028632086838,
                0.0330859762435206,
                0.00970847488767253
            ],
            [
                7.889262584350785e-06,
                1.3007131562845248e-05,
                2.5612825160271407e-06,
                1.7603425837494853e-06,
                1.4738985484871391e-05,
                2.2603237589028734e-06,
                1.147876812106705e-05,
                7.889259762666377e-06,
                7.889260704423598e-06,
                2.9023112929973233e-06
            ],
            [
                0.008577484209889493,
                0.0046095711666236105,
                0.0021827160173578776,
                0.015906390720487305,
                0.022977371540821797,
                0.0002611904328853529,
                0.9995121428836323,
                0.012431652716918986,
                0.004070138016023173,
                0.0015011820822387336
            ],
            [
                0.0028009273495062355,
                0.9978172831236248,
                0.0021827160153295015,
                0.02033235193278534,
                0.009708477878289113,
                0.0024726230176592735,
                0.010986942094235046,
                0.9982992774940863,
                0.010986943015151858,
                0.009708474395205814
            ],
            [
                0.00757724126786081,
                0.001169510025849681,
                0.0028009263109531877,
                0.0028009273885251425,
                0.005220126087712186,
                0.03732688506845755,
                0.9975273774302783,
                0.015906389525063156,
                0.999569442966911,
                0.03732688506845755
            ],
            [
                0.022977371833528822,
                0.005911068224161905,
                0.0203323526006201,
                0.9999038975508551,
                0.047425874019047645,
                0.060086648490884395,
                0.014063628618701241,
                0.014063627417739045,
                0.004070136915557446,
                0.01243164854352915
            ],
            [
                0.00023050674181927547,
                0.002800927540048571,
                0.9980732653021968,
                0.006692849939838772,
                0.0004305570827149416,
                0.001700722496030954,
                0.9978172840267593,
                0.009708474529514918,
                0.00970847657996743,
                0.9992903295473606
            ],
            [
                0.9999991684722697,
                0.000709670433403387,
                0.9999993524049703,
                0.004070136989173498,
                0.0019267344063255746,
                0.005220126295670638,
                0.007577242290354993,
                0.0017007220186979863,
                0.999999352405279,
                0.9999990577554062
            ],
            [
                0.0066928521161458724,
                0.1824255304737224,
                0.0035936023763313636,
                0.001032230954405004,
                0.006692849416658365,
                0.0028009270139436556,
                0.060086644283076515,
                0.9999977396762412,
                0.00460957201699224,
                0.07585818681131791
            ],
            [
                0.009708476964986945,
                0.11920292045759122,
                0.0015011820073789874,
                0.004609572410127541,
                0.04742587637519415,
                0.0010322312553539973,
                0.9999945777829711,
                0.0017007225375381748,
                0.012431651299109682,
                0.0013250223703824109
            ],
            [
                0.9994472213213994,
                0.00010889693504083841,
                0.003172683460286368,
                0.0004878571092434949,
                0.0019267347407862432,
                0.9990889486669459,
                0.0004878572259267104,
                0.01798621032398446,
                0.005911069950758051,
                0.0059110694445451825
            ],
            [
                0.07585817793199001,
                0.0179862123308452,
                0.9999970976883612,
                0.025957355737872837,
                0.9999977396754328,
                0.999975699759268,
                0.9999984465018751,
                0.9999417087067388,
                0.07585817218654307,
                0.02033235523485744
            ],
            [
                0.003593602211259959,
                0.07585818106587035,
                0.008577485968103978,
                0.0534033311180551,
                0.002800926312253817,
                0.0046095716965015325,
                0.9996200155148418,
                0.009708476293441287,
                0.012431653151408963,
                0.02297737246075816
            ],
            [
                0.017986208843513554,
                0.006692849605498625,
                0.020332353453964558,
                0.010986944259907672,
                0.022977367777446158,
                0.0075772406305528615,
                0.0004878571136996522,
                0.9999977396746245,
                0.0046095713012296894,
                0.0011695100981961816
            ],
            [
                9.422443692176231e-07,
                8.315279285251204e-07,
                4.785093353787868e-06,
                3.288750633518874e-06,
                3.726638395527247e-06,
                7.338208055536515e-07,
                1.209865971934245e-06,
                1.994729959270648e-06,
                1.2098653950480359e-06,
                2.9023133689924295e-06
            ],
            [
                4.222834954211514e-06,
                3.7266401719851935e-06,
                7.338213304083124e-07,
                3.2887506330851655e-06,
                5.422217030362759e-06,
                1.3709578604981489e-06,
                1.994729721436347e-06,
                2.902312330965655e-06,
                8.315283250082584e-07,
                9.422442569097361e-07
            ],
            [
                0.9999991684718732,
                0.008577487084807957,
                0.005220125966806113,
                0.010986940414321057,
                0.005220126834911782,
                0.9999957771660524,
                0.012431650155715195,
                0.9999938558268643,
                0.002800927392427033,
                0.9984988176177988
            ],
            [
                0.020332351190746736,
                0.006692850521838325,
                0.03308598208318718,
                0.04208772626352764,
                0.9991959142415684,
                0.007577241919175583,
                0.007577241141799893,
                0.06008664596619963,
                0.9996200155218616,
                0.004070137153393925
            ],
            [
                0.014063627688924045,
                0.007577241057759283,
                0.9998766054254501,
                0.9940889305226194,
                0.0006263340789734484,
                0.0010322312349466036,
                0.005220126017586663,
                0.9997388096303742,
                0.9999869928684406,
                0.01243165160782621
            ],
            [
                0.014063626965764048,
                0.0017007224323865506,
                0.22270012850745968,
                0.0007096705355687727,
                0.004070138063212963,
                0.9997694932038266,
                0.06008664554541885,
                0.9875683471001379,
                0.0009110510639593504,
                0.004609573027606419
            ],
            [
                0.9999987901341723,
                0.006692849651934755,
                0.006692851054306047,
                0.9999977396754328,
                0.003593601868611763,
                0.007577241919175583,
                0.01798620752753952,
                0.0031726827069960316,
                0.03732689136002139,
                0.0024726232427766176
            ],
            [
                0.05340333130637379,
                0.9999984465015047,
                0.005220126394813625,
                0.999978555051613,
                0.01590639200338161,
                0.006692852366901075,
                0.01098694507962499,
                0.025957356303004706,
                0.9971990726817089,
                0.9988304898682143
            ],
            [
                0.0031726833829691698,
                0.0013250222965931733,
                0.0052201245763864685,
                0.01406362870909625,
                0.01798621150836126,
                0.04742587115801276,
                0.9999945777803846,
                0.012431653277182384,
                0.004609572269111613,
                0.00857748700560909
            ],
            [
                0.00013982205620869103,
                0.995929862019841,
                0.004070137927306371,
                0.015906388387952462,
                0.007577239888194219,
                0.07585817218654306,
                0.00669284951881785,
                0.9840936116120476,
                0.0031726835250855453,
                0.012431649801262929
            ],
            [
                4.222832940834793e-06,
                1.3709578605243332e-06,
                1.76034363298589e-06,
                5.422221554038823e-06,
                1.209866116170145e-06,
                1.2098652508144226e-06,
                9.422447062150634e-07,
                1.5534983101393749e-06,
                6.144175333837093e-06,
                2.561283431669698e-06
            ],
            [
                1.2098655392662613e-06,
                8.315284241560147e-07,
                4.785096205830278e-06,
                1.1478769490387674e-05,
                7.889264464895484e-06,
                5.71500515151976e-07,
                3.7266383954560706e-06,
                2.260324028351814e-06,
                1.2098653950403334e-06,
                1.2098656835076114e-06
            ],
            [
                0.006692852407145737,
                0.9990889488716148,
                0.008577486364098282,
                0.005220125577488576,
                0.001700722674116704,
                0.0006263341420417566,
                0.004070138350126892,
                0.053403331871329895,
                0.0017007227711645513,
                0.004609572273384823
            ],
            [
                0.9980732657271004,
                0.00970847801259826,
                0.005911067835609435,
                0.0028009263532236543,
                0.9968273171972779,
                0.9991959141654796,
                0.9902915227126712,
                0.002472623523599048,
                0.006692849930551545,
                0.010986941193558235
            ],
            [
                0.009708475380139267,
                0.0035936021879165283,
                0.025957357244891174,
                0.0008040861146975217,
                0.0006263340434497075,
                0.9997040427964424,
                0.9999952149060765,
                0.9968273173342398,
                0.9993736659730552,
                0.008577486562095438
            ],
            [
                0.0075772404344581195,
                0.0015011821780382747,
                0.9999724642957807,
                0.009708478370756002,
                0.009708477466407732,
                0.04208772386048601,
                0.0007096704386870915,
                0.008577484558364408,
                0.0007096702593713944,
                0.9999970976883611
            ],
            [
                0.01243164841775578,
                0.001169510206715941,
                0.001700722322491251,
                0.0035936032892263927,
                0.002800926586686708,
                0.9998415637839242,
                0.13296424019782926,
                0.0004878570474533431,
                0.004609571854610279,
                0.9998204719923377
            ],
            [
                7.889263523238269e-06,
                1.2098659719524008e-06,
                3.7266410608245674e-06,
                9.422448185388577e-07,
                3.2887494572095624e-06,
                6.9622562481627565e-06,
                2.56128282131428e-06,
                1.9947301970106386e-06,
                2.2603242978007868e-06,
                3.2887478889962107e-06
            ],
            [
                0.9993736658323811,
                0.0035936025405690825,
                0.9770226292954839,
                0.00048785711381318486,
                8.481103103169929e-05,
                0.002800926871524666,
                0.004070137134518014,
                0.0017007227855932539,
                0.006692851939688514,
                0.9953904285641643
            ],
            [
                0.037326891226158315,
                0.005220124796435466,
                0.0024726226438037285,
                0.0006263342952493138,
                0.003593602548072329,
                0.9933071494812574,
                0.9947798741178281,
                0.01590639433591697,
                0.022977367359293347,
                0.002800927185626831
            ],
            [
                2.2603251061458426e-06,
                1.0677026154376365e-06,
                2.5612831263929686e-06,
                1.0129993388546776e-05,
                6.144173135762683e-06,
                3.288749849368453e-06,
                4.222835457852533e-06,
                1.9947290080125335e-06,
                6.475946437966953e-07,
                6.962255419279419e-06
            ],
            [
                0.042087726413717746,
                0.03308598089141841,
                0.07585817584273653,
                0.002800926486538209,
                0.012431648978018985,
                0.9999991684720715,
                0.01590638882530272,
                0.003593601793579316,
                0.0028009273143892194,
                0.014063627133640472
            ],
            [
                0.007577241449948806,
                0.004070137070339915,
                0.002800927260413066,
                0.0850990461671829,
                0.9999930377420916,
                0.9999962733607164,
                0.9999945777829704,
                0.9997388097843887,
                0.053403329046549465,
                0.005220124784344862
            ],
            [
                1.6701419845073e-05,
                8.939695236983711e-06,
                7.889266344321303e-06,
                4.222834954134701e-06,
                6.1441767989541075e-06,
                2.902313368820854e-06,
                2.5612831264302397e-06,
                1.9947294836483373e-06,
                6.14417753110761e-06,
                4.222833444229772e-06
            ],
            [
                0.9999599363125995,
                0.0021827167359100685,
                0.04208772325972563,
                0.03732688694254029,
                0.9940889306156531,
                0.9940889321835445,
                0.022977371958974684,
                0.015906393286276015,
                0.0013250225242768883,
                0.0013250226934221907
            ],
            [
                0.01798621062007865,
                0.02033235464122646,
                0.999860177959267,
                0.9999967112505428,
                0.042087728215999064,
                0.004070138138716626,
                0.00970847658892137,
                0.9997965730515117,
                0.9982992775025854,
                0.012431653162842912
            ],
            [
                0.022977370077286757,
                0.9999970976869775,
                0.047425874692232355,
                0.11920291732853862,
                0.9999967112501513,
                0.005220125659704699,
                0.03732689015525376,
                0.015906389116869566,
                0.00247262272707416,
                0.012431650544469309
            ],
            [
                0.0017007227996266498,
                0.00460957185461028,
                0.0008040860076493824,
                0.000804085771292379,
                0.00033535006539904983,
                0.00043055707899487843,
                0.0006263340700834043,
                0.0001795279441800938,
                0.0002959571297533035,
                0.00023050665818867585
            ],
            [
                0.0015011825729278863,
                0.0021827165381433865,
                0.0035936021403959735,
                0.007577241082271128,
                0.0035936030282801186,
                0.9999251537370873,
                0.9999984465018751,
                0.04742587788985982,
                0.004609573211354476,
                0.9999885212277744
            ],
            [
                0.037326888147307814,
                0.0006263341520612747,
                0.008577483639657844,
                0.01798621042268252,
                0.0028009267791799367,
                0.00970847538909321,
                0.0009110510482767262,
                0.0028009269944342047,
                0.05340333431947304,
                0.0031726830788548757
            ],
            [
                8.315278293838516e-07,
                6.962256248606003e-06,
                9.422450431800595e-07,
                7.338207180838067e-07,
                1.5534977545497995e-06,
                6.9622537570932415e-06,
                1.760343842833246e-06,
                1.9947297214544894e-06,
                2.5612822104232297e-06,
                3.288750633192845e-06
            ],
            [
                0.033085975409282604,
                0.999993855825402,
                0.11920292045759122,
                0.9992903297040554,
                0.9975273764706581,
                0.0035936018369313962,
                0.9999885212332466,
                0.9999986290431201,
                0.005911070191551214,
                0.9984988178685528
            ],
            [
                1.9947304348332037e-06,
                1.5534975693707442e-06,
                3.726639283901856e-06,
                4.450850519360903e-07,
                8.939693105467234e-06,
                4.78509563509613e-06,
                1.3709578605455302e-06,
                3.726637951079042e-06,
                3.7266388397382506e-06,
                1.5534979397394734e-06
            ],
            [
                0.9995121427666085,
                0.04208772461143651,
                0.1192029235866439,
                0.04208772521219691,
                0.005220125289732152,
                0.003172682768113423,
                0.03308597969964969,
                0.9999974387180947,
                0.005911068087347653,
                0.06754669348597103
            ],
            [
                0.9986749775804761,
                0.9989677689679268,
                0.029312231546324636,
                0.9975273769691323,
                0.0011695101621113269,
                0.002182716924549074,
                0.0035936025539081867,
                0.999993037746242,
                0.9996646497332812,
                0.00757724006678049
            ],
            [
                5.715002426439334e-07,
                3.2887490649759413e-06,
                2.561281905293402e-06,
                1.5534984952492866e-06,
                6.9622554185195676e-06,
                1.760342793515064e-06,
                2.2603251061664e-06,
                4.7850950647493785e-06,
                1.7603427935518875e-06,
                3.2887502412970765e-06
            ],
            [
                0.0011695103953336416,
                0.9980732649028139,
                0.9994472214545342,
                0.9995121428841148,
                0.004609572619514834,
                0.00023050663190362958,
                0.0024726226282982006,
                0.9706877669167365,
                0.9902915232051379,
                0.997199072878104
            ],
            [
                0.020332351895683404,
                0.0011695101493282975,
                0.0013250226053064204,
                0.014063628592874097,
                0.9975273772947484,
                0.007577241835134963,
                0.0011695100537275614,
                NaN,
                0.012431648394887893,
                0.009708476687414733
            ],
            [
                0.004070137647942836,
                0.002182715955999515,
                0.0015011822605759534,
                0.025957360164739443,
                0.0019267343781180508,
                0.017986212462442634,
                0.10669058471438035,
                0.0040701382746232235,
                0.009708476991848772,
                0.0011695103492331339
            ],
            [
                0.9999339478632202,
                0.9933071490168961,
                0.9999962733616047,
                0.007577242752578437,
                0.0035936019194670894,
                0.002800926511250176,
                0.009708474977211935,
                0.037326883863690125,
                0.0035936017285511965,
                0.022977367986522567
            ],
            [
                0.015906394015193337,
                0.9999251537906715,
                0.9997040429722862,
                0.004609572170827789,
                0.9975273770070348,
                0.9999952149060763,
                0.029312230698358435,
                0.9875683462425918,
                0.006692850992391194,
                0.0021827164194833863
            ],
            [
                0.005911069912450048,
                0.0046095726280612525,
                0.0007096705008119003,
                0.010986942792512621,
                0.9997040428665956,
                0.0021827160939290598,
                0.015906394569170524,
                0.0019267345643772622,
                0.006692849946030257,
                0.0011695105430184667
            ],
            [
                0.0001398221236671851,
                0.00460957241012754,
                0.0004305571817538054,
                0.0015011821326687282,
                0.9999852610110103,
                0.005220125666959063,
                0.0021827166167429635,
                0.001926735032264062,
                0.002800926680982376,
                0.9947798744031664
            ],
            [
                0.9975273769806179,
                0.008577484930598992,
                0.004609572399444516,
                0.9999967112497595,
                0.014063627895541195,
                0.9998415637463428,
                0.004609571102525478,
                0.9998766054545105,
                0.9994472214555955,
                0.020332352415110444
            ],
            [
                0.08509904500702024,
                0.00048785722198144924,
                0.07585818054355695,
                0.05340333205964859,
                0.008577486799692035,
                0.08509904964767094,
                0.03308597755446608,
                0.010986942478793704,
                0.9999970976883611,
                0.0953494616857507
            ],
            [
                0.9999962733611605,
                0.004070136807964758,
                0.005220126513301586,
                0.003593601846102029,
                0.9999038975621215,
                0.007577239587048752,
                0.008577483615898194,
                0.005911067526409248,
                0.999996711249759,
                0.9994472212569223
            ],
            [
                0.060086644703857287,
                0.015906388971086143,
                0.9999938558261318,
                0.09534946875514018,
                0.006692849915072835,
                0.998967769167079,
                0.02931222831345362,
                0.007577241863148503,
                0.005911068106501647,
                0.047425872336085924
            ],
            [
                0.8933094145755218,
                0.9933071493729064,
                3.2887478891128633e-06,
                0.2018132246607271,
                0.9998415637083141,
                1.3007123812317831e-05,
                0.06008664617659003,
                3.535626334490732e-05,
                0.9820137859583881,
                0.9988304895767884
            ],
            [
                0.9999251537373559,
                0.9992903297117747,
                0.04742586829697802,
                0.0002034269963754405,
                0.9999869928761931,
                0.006692851710603529,
                0.9999251537818761,
                0.9998601779266962,
                0.07585817793199001,
                0.9998766054402837
            ],
            [
                0.017986210027890265,
                0.0013250225110287143,
                0.060086651857130885,
                0.033085978269527264,
                0.012431651459184916,
                0.0004305569801439202,
                0.04742587418734382,
                0.9982992774065259,
                0.0052201248568884894,
                0.007577241481464036
            ],
            [
                6.144177530548804e-06,
                4.222831933649433e-06,
                3.2887502414436403e-06,
                2.2603251062147097e-06,
                7.338212429167144e-07,
                2.9023116389365734e-06,
                3.2887478889962107e-06,
                8.939696299530582e-06,
                4.785093923982095e-06,
                2.902313368860448e-06
            ],
            [
                0.0017007227308432453,
                0.003593603001601907,
                0.9988304897357605,
                0.9914225136755012,
                0.03308597922294221,
                NaN,
                0.00170072203589383,
                0.0035936026322754265,
                0.008577484257408799,
                0.9998601779764698
            ],
            [
                0.033085981248949035,
                0.017986210521380584,
                0.07585817166422973,
                0.029312231016345756,
                0.020332351079440945,
                0.009708477430591961,
                0.0011695104619685972,
                0.00669285128339101,
                0.007577241674057112,
                0.9999994284992804
            ],
            [
                0.0017007223673585754,
                0.00522012596196987,
                0.014063624680062151,
                0.0024726230170849946,
                0.06008664428307652,
                0.001501181936009209,
                0.0011695105241158958,
                0.0013250225339819463,
                0.004609572044768103,
                0.0024726230021537426
            ],
            [
                1.5534977545384963e-06,
                4.222833444229772e-06,
                5.422220907554695e-06,
                2.5612822106421996e-06,
                4.7850950646797465e-06,
                6.475948753847607e-07,
                5.422219615069953e-06,
                2.9023119850210436e-06,
                1.0677031245783732e-06,
                4.785096776068365e-06
            ],
            [
                1.5534981248881956e-06,
                1.5534979397140412e-06,
                1.994729959160889e-06,
                1.0677029973056687e-06,
                1.7603432133032607e-06,
                1.7603430034311638e-06,
                3.2887486732000038e-06,
                7.338212429537553e-07,
                1.994729245878497e-06,
                8.315279285251204e-07
            ],
            [
                0.03308597552845946,
                0.10669058968506456,
                0.9995694429635666,
                0.02931222831345362,
                0.005911069269422904,
                0.022977370119102045,
                0.002472622622555412,
                0.00037998456873246963,
                0.0031726832010896735,
                0.0035936025422364706
            ],
            [
                0.9995121427663813,
                0.14804720179063335,
                0.9999251537643246,
                0.9999417087498236,
                0.007577241667053729,
                0.999876605410911,
                0.9984988180275206,
                0.6791787056691698,
                0.9989677692033321,
                0.9859363735378652
            ],
            [
                0.05340332885823078,
                0.020332354641226458,
                0.9999994956525317,
                0.03732688881662312,
                0.004609572771213796,
                0.9999991684717742,
                0.047425871662901256,
                0.06008665648572012,
                0.005911069529370039,
                0.008577484740521755
            ],
            [
                0.0040701382481969405,
                0.0031726832408528016,
                0.0015011820729903267,
                0.022977371666267666,
                0.9989677690458352,
                0.006692851527954695,
                0.10669060033653141,
                0.0011695104890305497,
                0.0015011821372056828,
                0.001032231133749946
            ],
            [
                0.9999785550490417,
                0.0011695102169151667,
                0.00013982209006304925,
                0.9995121428934245,
                7.484625391195843e-05,
                8.48110513393645e-05,
                0.002182716303865956,
                0.00012339455980783077,
                0.06008665648572011,
                0.004070137336490271
            ],
            [
                2.9023130228444433e-06,
                7.338213304283347e-07,
                2.9023116391477434e-06,
                1.3709567165087443e-06,
                6.9622537587775775e-06,
                3.2887498492518007e-06,
                2.561283431888668e-06,
                2.5612812945889277e-06,
                3.2887478889513447e-06,
                2.561282210460501e-06
            ],
            [
                0.04742587536541707,
                0.02297737162445238,
                0.1066905889749668,
                0.08509904848750825,
                0.00591106783287315,
                0.007577242199310985,
                0.03732688787958169,
                0.09534947389651462,
                0.006692850178210923,
                0.042087728065808946
            ],
            [
                0.02931222863144092,
                0.0024726228821294535,
                0.0015011822525490331,
                0.9999417087275605,
                0.001501182289542666,
                0.009708474583238558,
                0.0004305570262626741,
                0.009708476391934649,
                0.0008040859092530275,
                0.009708476391934649
            ],
            [
                0.9999982396574163,
                0.02595735813968335,
                0.012431651893674853,
                0.010986940981039,
                0.9996200155195181,
                0.9924227572754352,
                0.9999984465020604,
                0.9999986290429567,
                0.9999930377454117,
                0.012431649744093207
            ],
            [
                0.012431651219072064,
                0.0005527785343712199,
                0.0008040858405532981,
                0.0021827166618743343,
                0.000552778598430277,
                0.002182715995045745,
                0.0017007226662105659,
                0.022977367526554472,
                0.003172682323355567,
                0.0010322307918661745
            ],
            [
                0.014063626074727671,
                0.10669058258408719,
                0.9996200155190648,
                0.0179862130546311,
                0.9988304895975949,
                0.05340332829327471,
                0.9994472214580716,
                0.005220125857990649,
                0.010986942843112447,
                0.022977369993656183
            ],
            [
                0.9997040430074533,
                0.000709670362775123,
                0.004070137714008535,
                0.002182716178613747,
                0.0003799844808578411,
                0.008577484423726372,
                0.006692850834508319,
                0.0040701369627472225,
                0.9706877671287282,
                0.0021827160457551366
            ],
            [
                0.09534946875514017,
                0.02931223228829508,
                0.017986210323984453,
                0.014063623776112349,
                0.9980732649426626,
                0.9999938558246698,
                0.022977368488305956,
                0.0015011820122649378,
                0.9999974387165682,
                0.006692849593115658
            ],
            [
                0.9993736657616251,
                0.003172682107603848,
                0.02595735978798481,
                0.004609573151529527,
                0.005220125901516834,
                0.006692852125433102,
                0.014063628773664112,
                0.9953904277971232,
                0.9991959141490645,
                0.9999970976887085
            ],
            [
                0.01406362549361702,
                0.24508500761839527,
                0.0035936024071780413,
                0.0019267342531990228,
                0.9959298619160235,
                0.9924227589037221,
                0.037326884131416216,
                0.003172683265152491,
                0.020332354641226458,
                0.002800926509949546
            ],
            [
                3.726639728262097e-06,
                4.222833444429485e-06,
                2.5612834320214477e-06,
                1.5534973841450852e-06,
                6.144177531208195e-06,
                4.450852111120808e-07,
                4.7850956351657615e-06,
                3.2887490649221017e-06,
                2.902313023039776e-06,
                2.5612825159421147e-06
            ],
            [
                0.0021827167708995602,
                3.535625910878189e-05,
                0.005220126769622493,
                0.001325022208631478,
                0.015906390691330614,
                0.9999832985701989,
                0.001501182212937927,
                0.9933071493109916,
                0.9997694932312318,
                0.0017007221189082504
            ],
            [
                0.0017007222908667055,
                0.00012339461880846384,
                0.0002959570255609853,
                0.014063624602580736,
                0.00017952790110811325,
                0.0006263342365531442,
                0.0003353499892968107,
                0.001325022533057655,
                0.0006263342453703215,
                0.0001584362918011666
            ],
            [
                0.9999982396559474,
                0.9999869928699877,
                0.0013250221061892305,
                0.00970847824540079,
                0.0017007227863838677,
                0.9947798741541,
                0.006692850023423812,
                0.0010322308582501984,
                0.9992903297036013,
                0.009708475675619326
            ],
            [
                0.9968273168187919,
                0.9984988177561759,
                0.6513548714339145,
                0.9875683482549664,
                0.9991959141767034,
                0.9993736657594027,
                0.9770226309680954,
                0.9992903296437057,
                0.9706877667577428,
                0.9994472212622927
            ],
            [
                0.9999599362887278,
                0.00020342704413236188,
                8.481107143601051e-05,
                9.610240327239146e-05,
                6.605215227306636e-05,
                0.9999251537550445,
                0.0010322311862089476,
                7.484621811625572e-05,
                6.60521761026448e-05,
                0.9999810748472596
            ],
            [
                0.022977368321044824,
                0.007577241141799893,
                0.9971990734100616,
                0.003593602865709766,
                0.9999869928730966,
                0.0017007222485688769,
                0.9999945777790935,
                0.002800926857868051,
                0.06754669583231306,
                0.015906390399763742
            ],
            [
                0.999512142826866,
                0.0006263340176904422,
                0.000552778541638964,
                0.001501182198280073,
                0.0021827165995017654,
                0.00043055698373872776,
                0.0003799845633819444,
                0.0017007225901139894,
                0.006692851577486581,
                0.020332355531672935
            ],
            [
                0.0019267350685308903,
                0.0035936032375373525,
                0.0017007223179452224,
                0.005220125229279125,
                0.0021827166010230476,
                0.06008665059478843,
                0.007577242206314371,
                0.001926734267974391,
                0.0035936029457444003,
                0.004070136938208539
            ],
            [
                0.007577240504491955,
                0.9959298622444644,
                0.9999957771660531,
                0.0024726226903203138,
                0.009708478227492904,
                0.0017007223541157968,
                0.9999980052702787,
                0.009708475693527207,
                0.010986940535760614,
                0.04208772656390786
            ],
            [
                0.006692849450711526,
                0.9968273166074583,
                0.07585818054355695,
                0.0035936017819076026,
                0.004070137549788086,
                0.01098694201327533,
                0.000911051251197186,
                0.0006263343049773574,
                0.02595735917575854,
                0.025957356821042256
            ],
            [
                0.0052201260296772705,
                0.0035936027306513246,
                0.007577240168329546,
                0.029312229002426103,
                0.0019267348674962572,
                0.9999992661791071,
                0.002472622951617199,
                0.009708474619054318,
                0.01590639042892043,
                0.9990889489840422
            ],
            [
                0.9914225132240676,
                0.004609572431493589,
                0.06754668973182398,
                0.008577484273248566,
                0.037326887879581695,
                0.05340332622176919,
                0.025957359693796152,
                0.9992903295443473,
                0.012431652145221664,
                0.002182716944832839
            ],
            [
                0.9999646437450858,
                0.0017007220859001353,
                0.003593602205424101,
                0.004070138057550188,
                0.003593603308401359,
                0.0004878571051563188,
                0.003172683002274041,
                0.9989677692038123,
                0.06008664512463807,
                0.0031726827843132134
            ],
            [
                5.715006513999389e-07,
                1.209866116170145e-06,
                1.209865971934245e-06,
                8.315284241401329e-07,
                5.043472278159142e-07,
                2.38237023590304e-07,
                1.7603438428188364e-06,
                1.0677029972993568e-06,
                9.42244256915735e-07,
                4.450849458153541e-07
            ],
            [
                0.9996200154692297,
                0.012431647937530193,
                0.009708477385822247,
                0.012431649972772088,
                0.008577485389952328,
                0.02931222810146209,
                0.9914225156237929,
                0.010986941325117766,
                0.03732688399755318,
                0.0013250225225823545
            ],
            [
                0.014063623995643008,
                0.0066928513143484384,
                0.006692850305136358,
                0.0015011820930576252,
                0.010986942812752552,
                0.008577484399966718,
                0.0013250226468995278,
                0.9740426448743534,
                0.00857748352085959,
                0.0006263342409981674
            ],
            [
                0.006692852026369321,
                0.9998911030388833,
                0.9999930377437568,
                0.07585817427579647,
                0.002800926723903163,
                0.002472622790819113,
                0.0035936027765044987,
                0.000804086010689194,
                0.037326890958432175,
                0.0009110512056327967
            ],
            [
                0.00023050668547308019,
                0.0003353501844893322,
                0.002800927185626831,
                5.144223195167328e-05,
                0.00010889694740933997,
                0.0003799844368928975,
                0.002800927384623252,
                0.00043055698326276024,
                0.00033535022568213015,
                0.00013982207367803525
            ],
            [
                1.1478765388105516e-05,
                2.902312676941983e-06,
                8.939697368110433e-06,
                3.7266401722360055e-06,
                2.56128282131428e-06,
                1.067702742726318e-06,
                3.2887494572514376e-06,
                6.144172404028807e-06,
                4.7850950646797465e-06,
                8.315277302444853e-07
            ],
            [
                0.0035936026431134488,
                0.0024726236464947633,
                0.9996200154269562,
                0.0005527785225048593,
                0.9998204719492134,
                0.004070138367115217,
                0.9995694430134556,
                0.010986943025271824,
                0.001325022699584133,
                0.008577485540430151
            ],
            [
                0.005220126610026455,
                0.0059110676002889365,
                0.0010322309916184767,
                0.004609573123753658,
                0.0010322312749210868,
                0.0046095720447681034,
                0.010986940697680025,
                0.0010322310503197314,
                0.0015011824701483883,
                0.00192673472019027
            ],
            [
                0.06008665311947338,
                0.01798620910670837,
                0.0028009272766709435,
                0.9999957771665566,
                0.006692849791243149,
                0.10669058613457583,
                0.00015843623513047908,
                0.029312228790434564,
                0.025957357904211723,
                0.99999893229713
            ],
            [
                0.022977367442923908,
                0.014063626836628337,
                0.9989677691644381,
                0.04208772851637929,
                0.999796573050908,
                0.012431651527788587,
                0.09534946425643774,
                0.003172682793885817,
                0.017986207363042774,
                0.015906391216151
            ],
            [
                0.9992903295341513,
                0.9999974387165681,
                0.01798621094907221,
                0.005911068571670123,
                0.9997965729787457,
                0.0675466845698721,
                0.008577484099011115,
                0.9999910603015654,
                0.012431649801262929,
                0.9995694429104336
            ],
            [
                0.02931223091034998,
                0.9996200155154167,
                0.042087727765428726,
                0.0021827165381433865,
                0.07585818785594478,
                0.02595735578496716,
                0.07585817427579646,
                0.012431648897981384,
                0.0028009276317430103,
                0.9994472213242616
            ],
            [
                0.004070138182131233,
                0.9999991684716749,
                0.9999986290431203,
                0.9999990577556308,
                0.0015011823560265093,
                0.9999987901340285,
                0.9999984465016908,
                0.002800926813646631,
                0.06754668597767712,
                0.9999970976873244
            ],
            [
                3.72663839489005e-06,
                1.7603430034311638e-06,
                6.9622562492265485e-06,
                1.7603438428188364e-06,
                3.9278629390507954e-07,
                2.9023109471188266e-06,
                1.5534981249574276e-06,
                3.7266397280960194e-06,
                6.47594875389178e-07,
                5.422220908634683e-06
            ],
            [
                0.9999910603005,
                0.012431652293862965,
                0.022977370077286757,
                0.01590639404435003,
                0.9995694430145703,
                0.004070137840477162,
                0.0007096704508643792,
                0.999841563821259,
                0.9999832985801568,
                0.9982992779431549
            ],
            [
                0.004070138603064188,
                0.004609572632334463,
                0.004070136832503441,
                0.015906388008915584,
                0.025957354560514824,
                0.004070137347815818,
                0.005220125942624898,
                0.06008665227791172,
                0.06754669677084987,
                0.0009110510583432754
            ],
            [
                0.9988304897324967,
                0.06754669301670264,
                0.006692851422699437,
                0.9997040430064716,
                0.9984988179589429,
                0.9999967112493676,
                0.9999952149049357,
                0.01590639494820756,
                0.24508502416032485,
                0.014063625312827045
            ],
            [
                0.0179862066392571,
                0.006692850125583304,
                0.0011695103152357103,
                0.005220125168826098,
                0.07585817532042317,
                0.9999982396572065,
                0.03308598124894904,
                0.9999151889384766,
                0.000911050983373978,
                0.9999991684716749
            ],
            [
                0.014063624279741517,
                0.00013982210674915566,
                0.0015011823288047779,
                0.005911070021901484,
                0.009708474619054318,
                0.004070137510148668,
                0.0031726831996169644,
                0.0534033354493853,
                0.0019267345907938343,
                0.015906395123147725
            ],
            [
                0.0024726228166616617,
                0.9968273166803573,
                0.9991959142549903,
                0.008577483465420406,
                0.004070136806077167,
                0.015906389845786698,
                0.9995121429412501,
                0.012431651722165664,
                0.022977369199165775,
                0.033085975051752044
            ]
        ]
    },
    {
        "q_id": "8624_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            39,
            40,
            41,
            44,
            45,
            46,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            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,
            92,
            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,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.6701425823457267e-05,
                2.7535697649071857e-05,
                2.1444950958338794e-05,
                3.535624224711697e-05,
                3.120191135264947e-05,
                1.473898548194914e-05,
                1.1478773595343877e-05,
                1.1478765383679059e-05,
                1.1478766755734576e-05,
                1.1478773597870298e-05
            ],
            [
                4.539787402650773e-05,
                8.939697369151141e-06,
                4.006370648569653e-05,
                1.670141586949968e-05,
                6.962256248871951e-06,
                3.535624219155282e-05,
                3.726637951126493e-06,
                1.4738988996240646e-05,
                1.3007133112662637e-05,
                1.473897669838221e-05
            ],
            [
                0.9999970976876719,
                1.8925155002710973e-05,
                1.1478766752748805e-05,
                6.1441760661636525e-06,
                2.902313368860448e-06,
                0.00013982212343729845,
                0.9999938558239417,
                1.1478765386330758e-05,
                0.9999038975394585,
                0.9999945777797385
            ],
            [
                1.3007128461838766e-05,
                1.892514372640862e-05,
                6.9622545892184106e-06,
                1.1478770859917257e-05,
                3.7266410603195545e-06,
                1.4738980213020151e-05,
                1.1478765385746131e-05,
                1.3007126911004571e-05,
                1.473898899742027e-05,
                6.605213671635022e-05
            ],
            [
                1.5534984951673385e-06,
                1.994729959224386e-06,
                1.3709568798607528e-06,
                1.7603436328289897e-06,
                1.0129995808418327e-05,
                7.88926164421493e-06,
                5.422218969532895e-06,
                2.4300243618542217e-05,
                5.422218323231539e-06,
                5.422218969463855e-06
            ],
            [
                1.4738981967202704e-05,
                4.222834451012227e-06,
                3.2887478889513447e-06,
                1.0129992185760567e-05,
                2.9023119850527192e-06,
                1.994730434798734e-06,
                6.96225375833433e-06,
                1.1478768123823146e-05,
                2.9023116389761676e-06,
                6.144173868178388e-06
            ],
            [
                3.120190019330501e-05,
                1.8925150492616083e-05,
                1.1478770858372173e-05,
                2.753570094040789e-05,
                6.60521209179157e-05,
                3.535626334156318e-05,
                1.67014238321306e-05,
                1.0129987356541108e-05,
                6.962253759271479e-06,
                2.2603242977555607e-06
            ],
            [
                0.8933093982432729,
                0.9998766054459465,
                0.904650538956921,
                0.9999930377437616,
                0.9046505248181417,
                0.9999921107349753,
                0.9999339478292796,
                0.9999417087084128,
                0.9999938558276413,
                0.939913352771458
            ],
            [
                8.939698434495167e-06,
                6.962254583304239e-06,
                4.785095064819011e-06,
                1.4738981965808603e-05,
                2.4300246516082393e-05,
                4.7850967757637256e-06,
                6.144177531532303e-06,
                2.7535684529910724e-05,
                1.6701421840318107e-05,
                2.7535684518791692e-05
            ],
            [
                6.1441775296994185e-06,
                5.422217030288788e-06,
                6.144175332887123e-06,
                1.994729483508644e-06,
                4.222832940500659e-06,
                6.475947209314536e-07,
                1.0129988563914856e-05,
                6.962253759043525e-06,
                5.144222575222819e-05,
                8.939699497595294e-06
            ],
            [
                3.2887502412970765e-06,
                2.5612812946681295e-06,
                2.9023116390421582e-06,
                5.8291251536063904e-05,
                2.5612812945889277e-06,
                1.9947290079889487e-06,
                4.2228324375512536e-06,
                1.0677028700130727e-06,
                1.7603436329554703e-06,
                2.9023112930949896e-06
            ],
            [
                3.288748672760313e-06,
                2.5612834313109603e-06,
                6.144172404129392e-06,
                7.889261643181705e-06,
                5.422218968083048e-06,
                1.67014178590634e-05,
                1.4738976697229395e-05,
                3.7266401724291984e-06,
                1.4738987239698005e-05,
                4.7850950646797465e-06
            ],
            [
                1.6701417852987564e-05,
                1.3007134662054344e-05,
                2.2603245671490605e-06,
                5.422218322348809e-06,
                4.7850950649408664e-06,
                1.1478773597390071e-05,
                4.222832939978334e-06,
                1.4738988993532872e-05,
                7.889260704179641e-06,
                1.300712535865635e-05
            ],
            [
                3.726640616477725e-06,
                2.2603240281606297e-06,
                1.994729245722476e-06,
                2.561281294369958e-06,
                1.2098656834723998e-06,
                2.5612815996464693e-06,
                1.1478770850103883e-05,
                1.5534973841154145e-06,
                2.9023116387069255e-06,
                3.2887482807780376e-06
            ],
            [
                7.889260703619978e-06,
                1.3709568798607528e-06,
                1.5534983100765009e-06,
                9.422445938642879e-07,
                8.315280276338815e-07,
                3.2887502407856003e-06,
                3.7266401714225625e-06,
                1.2098652507715085e-06,
                2.9023133685252154e-06,
                2.2603240281606297e-06
            ],
            [
                0.9995121427752086,
                0.9999339478255207,
                0.904650530602188,
                0.9999724643024033,
                0.8175744806385543,
                0.9997040427991291,
                0.9999038975534965,
                0.9999599362995893,
                0.9999992661792819,
                0.32082131381216084
            ],
            [
                0.5926665999540698,
                0.9999339478475212,
                0.9997040430082713,
                0.9999957771645426,
                0.977022629295484,
                0.99937366583781,
                0.9324533055754921,
                0.9993736659840949,
                0.9997388096932918,
                0.9999038975855228
            ],
            [
                0.9999852610233136,
                0.999994577778446,
                0.9999974387174846,
                0.9999038975623662,
                0.9999921107383576,
                0.9999984465015047,
                0.9999938558224694,
                0.9999980052707542,
                0.9999785550439609,
                0.9999921107374191
            ],
            [
                1.209865971934245e-06,
                1.5534973837805584e-06,
                2.260323758746637e-06,
                1.2098658276444443e-06,
                4.785096775676685e-06,
                6.144176794031025e-06,
                1.7603427934462202e-06,
                3.288749063629951e-06,
                6.144173863093253e-06,
                2.90231094680735e-06
            ],
            [
                7.889261644501938e-06,
                1.1478773597640625e-05,
                3.120190020204515e-05,
                5.4222183222304545e-06,
                1.3709570432888404e-06,
                7.889260703763482e-06,
                4.5397890204837524e-05,
                3.535625067589049e-05,
                6.144176798870286e-06,
                2.75356878022126e-05
            ],
            [
                3.72663839489005e-06,
                2.902313368897403e-06,
                6.144173136455602e-06,
                7.889266346129453e-06,
                5.422218969463855e-06,
                4.222834451169694e-06,
                8.939696302457574e-06,
                6.144175333635923e-06,
                8.939696302652706e-06,
                2.902311292920774e-06
            ],
            [
                0.9995121429857834,
                0.924141814233309,
                0.6791786861878392,
                0.8519527944504227,
                0.9999832985783366,
                0.9149009567332237,
                0.9999930377430084,
                0.9999785550573,
                0.9999832985841314,
                0.7772998508568416
            ],
            [
                7.338208055436404e-07,
                6.144172403928222e-06,
                7.338207180661203e-07,
                2.9023116388547446e-06,
                1.2098658277082653e-06,
                3.9278634073098236e-07,
                3.2887506330851655e-06,
                3.7266397278180926e-06,
                4.7850956351657615e-06,
                2.2603242976733308e-06
            ],
            [
                2.902313022802209e-06,
                1.9947306726049992e-06,
                1.0677029972993568e-06,
                1.1478764016780948e-05,
                8.3152773023541e-07,
                4.2228319339950885e-06,
                1.7603430033607189e-06,
                2.9023130228444433e-06,
                1.0129994599624903e-05,
                4.785096776068365e-06
            ],
            [
                8.93969949923766e-06,
                8.939698434332555e-06,
                1.8925150493166868e-05,
                5.422217676797111e-06,
                1.300712846115264e-05,
                1.6701423832586287e-05,
                3.1201911339482505e-05,
                1.8925148237775583e-05,
                3.120192250723057e-05,
                0.999993855826865
            ],
            [
                9.422448184133123e-07,
                2.5612828207295832e-06,
                7.889264465842609e-06,
                1.3709570433075437e-06,
                1.4738980205164923e-05,
                1.6701421837705495e-05,
                2.1444956070870452e-05,
                1.14787681240737e-05,
                6.9622595675850006e-06,
                2.7535697630940815e-05
            ],
            [
                0.9997694933689683,
                0.9999921107370677,
                0.9999546021151355,
                0.9975273773717018,
                0.999796573080611,
                0.9999785550541817,
                0.9999417087350005,
                0.9999599363078454,
                0.9997388096037222,
                0.7772998560157665
            ],
            [
                1.5534977544141614e-06,
                2.902311292831027e-06,
                2.2603248365960415e-06,
                0.0009110509942352539,
                1.76034258364702e-06,
                2.5612815998491325e-06,
                3.2887494570719725e-06,
                2.902312330965655e-06,
                1.370957533676711e-06,
                5.829127240390582e-05
            ],
            [
                2.2603242978007868e-06,
                7.889266346603015e-06,
                8.939699499823059e-06,
                1.892515274194901e-05,
                1.99472900790731e-06,
                6.962256248871951e-06,
                4.222833444283541e-06,
                1.3007133114011233e-05,
                1.0129989771473008e-05,
                3.288748672879957e-06
            ],
            [
                5.422220261544064e-06,
                7.889266346287306e-06,
                5.422220908560712e-06,
                1.4738987241172537e-05,
                1.30071253611406e-05,
                2.7535694366751658e-05,
                1.1478773598329648e-05,
                4.222834954403545e-06,
                2.4300252309307336e-05,
                2.1444956079218013e-05
            ],
            [
                3.726639283440905e-06,
                3.2887478877249985e-06,
                1.3007123809644304e-05,
                1.0129995808418327e-05,
                1.8925141465200488e-05,
                0.0006263343033013648,
                1.1478765385746131e-05,
                1.4738976691867467e-05,
                3.1201926243586504e-05,
                1.0129989771288745e-05
            ],
            [
                1.553498495189945e-06,
                3.288749849209925e-06,
                1.7603430033158905e-06,
                2.5612834317535587e-06,
                7.8892607025437e-06,
                1.2098658276290391e-06,
                1.9947297210880223e-06,
                2.9023133684671433e-06,
                5.422220261652556e-06,
                6.962259566635186e-06
            ],
            [
                0.9999869928746389,
                0.7981867729389246,
                0.9999910603026361,
                0.7057850402140659,
                0.9999852610170299,
                0.8670357477770337,
                0.7310585786300049,
                0.9324533093296393,
                0.999988521227772,
                0.7981867849406659
            ],
            [
                8.939698431129126e-06,
                1.2098658277181688e-06,
                1.7603434231097403e-06,
                3.28875024092319e-06,
                9.422450431012186e-07,
                1.2098653950315304e-06,
                4.7850950647493785e-06,
                2.2603253754921562e-06,
                2.561281294369958e-06,
                1.2098653949534047e-06
            ],
            [
                1.3709567164663505e-06,
                3.7266388388875246e-06,
                6.962258738283349e-06,
                2.260323489435463e-06,
                1.7603432131855856e-06,
                5.422217030032353e-06,
                4.2228354571957855e-06,
                1.99472900796355e-06,
                3.726639727940109e-06,
                3.288749065209246e-06
            ],
            [
                8.939699499627926e-06,
                4.785094494402695e-06,
                3.726640172290235e-06,
                7.889259762307618e-06,
                6.962254588281262e-06,
                4.5397873994468824e-05,
                4.222834954211514e-06,
                1.7603434230729168e-06,
                6.96225873895455e-06,
                2.1444953514565465e-05
            ],
            [
                5.422218322348809e-06,
                6.962257907702715e-06,
                2.5612822106654943e-06,
                1.3709575336654889e-06,
                3.2887498493325602e-06,
                2.561283431916622e-06,
                8.939699498099386e-06,
                2.2603251060985603e-06,
                2.260325105981383e-06,
                4.450852641681257e-07
            ],
            [
                3.2887502411564953e-06,
                3.2887502412970765e-06,
                4.222831934052698e-06,
                1.553497569203316e-06,
                3.7266397278791014e-06,
                2.260325375572331e-06,
                3.726640616423495e-06,
                2.902311984915459e-06,
                3.1201922493496056e-05,
                2.2603245669804887e-06
            ],
            [
                0.6791787056691698,
                0.9999989322972573,
                0.8354835330070838,
                0.9999785550592659,
                0.9998911030400035,
                0.7772998560157663,
                0.9997040428306192,
                0.7981867729389246,
                8.939695236983711e-06,
                0.9999785550592668
            ],
            [
                1.2098661159797817e-06,
                5.715006514074756e-07,
                5.043475284068321e-07,
                2.69957713081915e-07,
                1.0677028699858827e-06,
                6.475945665853783e-07,
                1.067702997240607e-06,
                6.475949525663707e-07,
                1.2098656833491588e-06,
                1.9947301970106386e-06
            ],
            [
                4.222833444168322e-06,
                5.4222202617511845e-06,
                1.5534979397140412e-06,
                1.2098662604126641e-06,
                4.785094493836935e-06,
                2.561282821106957e-06,
                4.7850950647493785e-06,
                1.7603430033607189e-06,
                3.2887478888496478e-06,
                2.902312330759764e-06
            ],
            [
                7.889266346746518e-06,
                8.939696302457574e-06,
                1.6701417860795016e-05,
                4.5397890270732005e-05,
                2.5612834317908303e-06,
                2.7535697638353506e-05,
                1.892515274194901e-05,
                2.5612834317116285e-06,
                1.3007126913346863e-05,
                6.962255418658875e-06
            ],
            [
                1.0677029972522599e-06,
                1.9947299591826594e-06,
                7.338209804773549e-07,
                3.4663253846473677e-07,
                1.553497754476329e-06,
                3.0590219045271286e-07,
                2.260323758746637e-06,
                9.422447061953531e-07,
                8.31528126775552e-07,
                1.0677033791291683e-06
            ],
            [
                1.0129995803627524e-05,
                2.4300246514137558e-05,
                1.3007123810638006e-05,
                1.6701429768562597e-05,
                1.6701429805199933e-05,
                5.8291265334581605e-05,
                8.939694169330997e-06,
                1.8925141464512013e-05,
                1.4738980209829803e-05,
                0.9999898700054022
            ],
            [
                0.9999967112513307,
                0.9999984465028139,
                0.9999974387187087,
                0.9999921107383649,
                0.9999957771665706,
                0.9999974387187055,
                0.9999984465019093,
                0.9999970976883625,
                0.9999945777823913,
                0.9840936061597468
            ],
            [
                8.315283250006957e-07,
                1.760343632774555e-06,
                7.338207180714596e-07,
                4.4508489275752546e-07,
                1.2098656834723998e-06,
                1.7603438428188364e-06,
                1.209866116149238e-06,
                3.726641060536473e-06,
                9.422445938797133e-07,
                2.561281599734989e-06
            ],
            [
                4.222832436779288e-06,
                6.1441775291964935e-06,
                4.785096204868486e-06,
                2.26032429753354e-06,
                1.5534983100920427e-06,
                4.222832436871463e-06,
                9.422449308335287e-07,
                3.726640172385136e-06,
                1.9947301967693507e-06,
                3.7266392835764795e-06
            ],
            [
                1.7603432131375548e-06,
                6.475947981860793e-07,
                1.2098653950205268e-06,
                6.144176065582494e-06,
                3.726637950851956e-06,
                6.96225873350895e-06,
                1.7603430033158905e-06,
                4.785096204972935e-06,
                5.422217029006611e-06,
                8.315279285088606e-07
            ],
            [
                6.9622579086271995e-06,
                7.889265406681968e-06,
                2.43002494076116e-05,
                7.88926446430712e-06,
                3.5356242266024216e-05,
                4.539786319570692e-05,
                1.0129988563343644e-05,
                0.0001795279656089957,
                1.012998977108606e-05,
                2.7535687803514833e-05
            ],
            [
                3.2887478885505384e-06,
                1.0677028700053041e-06,
                1.760343213227212e-06,
                1.3709570432501875e-06,
                2.5612815996930587e-06,
                1.7603440526133836e-06,
                1.5534981248881956e-06,
                1.0677031245050577e-06,
                1.7603427935518875e-06,
                2.9023112925037123e-06
            ],
            [
                3.726640171686931e-06,
                6.962253755776166e-06,
                1.3709576971061233e-06,
                6.144174599700092e-06,
                2.9023109466489728e-06,
                2.2603234893861252e-06,
                1.3709567165087443e-06,
                4.7850967754851966e-06,
                2.9023119843875324e-06,
                1.3709578605243332e-06
            ],
            [
                0.20181322466072713,
                0.9399133521402868,
                0.1329642384799526,
                0.8807970732843033,
                0.9046505402422645,
                0.9998766054006448,
                0.9241418131886822,
                0.7981867729389246,
                0.9999785550541588,
                0.7549149868676284
            ],
            [
                1.3007130012341915e-05,
                1.012999459934851e-05,
                1.6701429800582296e-05,
                1.670142979608617e-05,
                3.535624224711697e-05,
                2.4300243620398656e-05,
                7.889264465555602e-06,
                3.120190391410763e-05,
                9.610238020678204e-05,
                1.1478764012939119e-05
            ],
            [
                6.475945665853783e-07,
                7.338212429504183e-07,
                3.2887494567070593e-06,
                2.2603251061232293e-06,
                1.9947297213492663e-06,
                1.209865827698362e-06,
                1.5534983100595462e-06,
                7.338212429464139e-07,
                1.5534973841309562e-06,
                1.3709578605118645e-06
            ],
            [
                4.785094493184135e-06,
                2.4300249415479343e-05,
                8.939700566143004e-06,
                2.7535694375867267e-05,
                1.0129993393945642e-05,
                2.260324297570543e-06,
                7.889262584809997e-06,
                6.962257079275089e-06,
                6.962257075260544e-06,
                6.1441775309064404e-06
            ],
            [
                6.962256246491084e-06,
                1.3007131561425676e-05,
                2.7535700934898458e-05,
                0.9999832985761714,
                8.939695234170549e-06,
                7.889262584350785e-06,
                2.1444948397509574e-05,
                7.889264463675704e-06,
                6.144173136019732e-06,
                1.1478766756214804e-05
            ],
            [
                6.144177530291754e-06,
                5.422217676575195e-06,
                7.88926446470893e-06,
                2.1444953517842076e-05,
                4.785093923324944e-06,
                1.0129995806317745e-05,
                1.8925141467059383e-05,
                1.1478764019996392e-05,
                4.785096776251149e-06,
                1.5534984951164742e-06
            ],
            [
                9.422445938454347e-07,
                9.422450431654909e-07,
                2.699577452746696e-07,
                4.7850956352353935e-06,
                1.0677032518501217e-06,
                1.994729245693449e-06,
                6.475948753741589e-07,
                2.1024331597066579e-07,
                1.3709576970537545e-06,
                5.715005832676369e-07
            ],
            [
                0.9998766054719475,
                0.9626731118526922,
                0.8807970889295664,
                0.9998911030403315,
                0.9999485577986634,
                0.9999151889693348,
                0.9999885212360005,
                0.9999852610146415,
                0.8933094103149354,
                0.9998601778971407
            ],
            [
                1.994729245822257e-06,
                4.785095633999427e-06,
                7.338208929831288e-07,
                2.5612834318257725e-06,
                1.3709567162743315e-06,
                6.144174600471243e-06,
                1.7603436328994344e-06,
                1.5534975693488444e-06,
                4.22283193320392e-06,
                1.370957696865476e-06
            ],
            [
                6.962259567027776e-06,
                6.962254588724508e-06,
                3.7266410605974813e-06,
                2.902311984683171e-06,
                6.9622537593854575e-06,
                6.144172403201774e-06,
                5.422217029943586e-06,
                6.962259567407701e-06,
                3.7266388395620047e-06,
                8.939700561199636e-06
            ],
            [
                2.561281905293402e-06,
                1.7603432132624344e-06,
                5.422218969463855e-06,
                3.288749065167371e-06,
                2.2603251060142746e-06,
                1.370956879949281e-06,
                1.2098656834922064e-06,
                3.2887502411026557e-06,
                1.7603427935967163e-06,
                4.7850933534310035e-06
            ],
            [
                1.5534983100228109e-06,
                2.561281599776919e-06,
                1.2098655392871682e-06,
                0.0031726825280619896,
                4.785093923116048e-06,
                2.5612834317535587e-06,
                2.5612822106654943e-06,
                3.2887502412970765e-06,
                8.31527730252048e-07,
                6.144175333021237e-06
            ],
            [
                6.144173135896795e-06,
                4.222833947428939e-06,
                1.8925148236123232e-05,
                1.3007131562845248e-05,
                0.9999885212332632,
                1.6701421840318107e-05,
                7.889260704308795e-06,
                7.889261644760245e-06,
                1.0129993390610508e-05,
                6.962258736497698e-06
            ],
            [
                3.2887494564857185e-06,
                2.260323489490968e-06,
                2.561283431888668e-06,
                4.785096205582214e-06,
                1.994729007841999e-06,
                6.1441746017453204e-06,
                2.260325375572331e-06,
                1.9947297213746646e-06,
                3.7266401720529807e-06,
                2.699577452655852e-07
            ],
            [
                2.260324296916815e-06,
                2.260324836567261e-06,
                2.2603251061232293e-06,
                4.222831933864508e-06,
                2.2603251058292572e-06,
                1.2098656834613962e-06,
                4.7850933521167006e-06,
                2.5612831262112703e-06,
                4.222832436587256e-06,
                2.902311292371731e-06
            ],
            [
                1.4738985483504099e-05,
                2.144495096387783e-05,
                2.4300252313904224e-05,
                1.3007130006521673e-05,
                1.8925141464512013e-05,
                1.670141786036971e-05,
                1.67014178576052e-05,
                2.144495607640949e-05,
                2.430024360395595e-05,
                4.0063677828144015e-05
            ],
            [
                0.999993037742924,
                0.9999987901341725,
                0.9999599362887345,
                0.9999930377446005,
                0.999989870008015,
                0.9999977396754328,
                0.9999910603047636,
                0.9999910603068948,
                0.9999921107383708,
                0.9959298618140936
            ],
            [
                1.9947290081177566e-06,
                4.450848927437622e-07,
                2.2603251059484907e-06,
                3.2887478889962107e-06,
                2.2603251061458426e-06,
                1.2098662604192665e-06,
                1.760343632854606e-06,
                2.5612825160271407e-06,
                1.5534975693601474e-06,
                1.0129990979694647e-05
            ],
            [
                1.5534983100595462e-06,
                1.994730672496148e-06,
                2.5612812943280275e-06,
                2.902311292960369e-06,
                2.9023130227599746e-06,
                1.2098662603202336e-06,
                1.553497384058899e-06,
                3.7266388395111645e-06,
                4.222832939978334e-06,
                1.5534981248528732e-06
            ],
            [
                3.288749849209925e-06,
                2.5612834317535587e-06,
                3.7266392838544054e-06,
                3.2887486731252264e-06,
                5.422220908560712e-06,
                1.01299933928585e-05,
                1.9947306725669014e-06,
                8.93969950000193e-06,
                4.222835457794923e-06,
                1.147877359872636e-05
            ],
            [
                6.605212873279408e-05,
                7.889264464508026e-06,
                1.6701415868193372e-05,
                8.939693104865575e-06,
                7.889265405677441e-06,
                0.999876605470969,
                3.2887502412970765e-06,
                2.9023116389365734e-06,
                1.8925143724239906e-05,
                7.889266347004826e-06
            ],
            [
                3.2887478863371333e-06,
                1.1478769491598686e-05,
                1.3007133113703658e-05,
                3.2887498493325602e-06,
                4.7850950647493785e-06,
                8.939693106329072e-06,
                5.422219613846953e-06,
                6.144173868558375e-06,
                4.222835457906302e-06,
                6.962254589104433e-06
            ],
            [
                5.4222202621161125e-06,
                5.422220908560712e-06,
                2.753569108693614e-05,
                1.3709572067680694e-06,
                6.1441724044534996e-06,
                4.7850933534310035e-06,
                5.422218969661113e-06,
                1.892515274194901e-05,
                2.1444948412137308e-05,
                1.4738988994015443e-05
            ],
            [
                0.9997965729325515,
                0.9978172830835644,
                0.7310585786300048,
                0.7772998663336158,
                0.2450850021044189,
                0.9978172833497888,
                0.6513548646660543,
                0.9992903296403207,
                0.047425871831197425,
                0.9997965729791986
            ],
            [
                0.9999930377454128,
                0.9999984465018753,
                0.9999952149066467,
                0.9999898700078197,
                0.9999921107336575,
                0.9999938558253995,
                0.9999996072138466,
                0.9999986290432835,
                0.9998601778597382,
                0.9999898700114386
            ],
            [
                1.5534984950006168e-06,
                1.0677033791291683e-06,
                3.4663262110630603e-07,
                6.962259565976648e-06,
                2.5612828208879873e-06,
                2.260324836651547e-06,
                1.5534975692866768e-06,
                3.2887486729876365e-06,
                2.2603240282243575e-06,
                1.5534975692471157e-06
            ],
            [
                0.9999982396563671,
                0.9999989322973846,
                0.9999038975401452,
                0.9999687980856979,
                0.9999974387168734,
                0.9999984465026209,
                0.6513548714339144,
                0.9999885212292892,
                0.9149009602137116,
                0.9999967112501538
            ],
            [
                0.6224593241981982,
                0.999986992870056,
                0.9875683474545902,
                0.9999339478721023,
                0.9975273767813431,
                0.9997694933783515,
                0.6513548782017745,
                0.9993736658997852,
                0.8807970826714614,
                0.998498817992621
            ],
            [
                3.120191879561992e-05,
                4.0063696885178056e-05,
                1.1478764017720528e-05,
                2.4300234917879235e-05,
                8.93969630226244e-06,
                8.93969736427282e-06,
                4.222834954134701e-06,
                4.0063682527545155e-05,
                0.00043055718040105486,
                6.144175333155351e-06
            ],
            [
                1.30071315640992e-05,
                2.2603248367358324e-06,
                2.26032348933062e-06,
                1.5534975693347152e-06,
                1.5534973841309562e-06,
                9.42244256886598e-07,
                2.5612822099713135e-06,
                1.3709576971242028e-06,
                2.5612815999679353e-06,
                8.315277302444853e-07
            ],
            [
                2.2603234893861252e-06,
                5.1442238118931704e-05,
                4.222834954403545e-06,
                6.475946437966953e-07,
                2.260324028255194e-06,
                5.043476486883855e-07,
                2.902313368860448e-06,
                6.1441753317695124e-06,
                1.7603440525925705e-06,
                1.2098652507715085e-06
            ],
            [
                5.42222155426567e-06,
                4.222831934286977e-06,
                2.9023109470554753e-06,
                6.962253759271479e-06,
                4.785093923116048e-06,
                5.422217029391264e-06,
                1.1478765384764794e-05,
                6.144174601208867e-06,
                3.2887494572873306e-06,
                5.422220262037209e-06
            ],
            [
                7.889266347133978e-06,
                1.3007130010922344e-05,
                1.6701415866735174e-05,
                5.422219614833243e-06,
                6.962258738574625e-06,
                1.8925141461620395e-05,
                8.93969310584124e-06,
                3.288750241410738e-06,
                2.7535691079423274e-05,
                6.144173135483279e-06
            ],
            [
                1.1478772223642496e-05,
                2.9023123309287002e-06,
                1.76034279349265e-06,
                4.78509506425325e-06,
                2.9023130227599746e-06,
                1.0677032518209896e-06,
                3.288749848677511e-06,
                6.144174599867732e-06,
                5.715004469900632e-07,
                3.726641060956752e-06
            ],
            [
                3.2887506310811342e-06,
                5.422217676575195e-06,
                2.2603251060142746e-06,
                9.422450431372112e-07,
                3.7266401719851935e-06,
                2.56128129449109e-06,
                1.1478765381257036e-05,
                1.3709575336093795e-06,
                1.9947301966967833e-06,
                3.288749848749297e-06
            ],
            [
                1.5534971989258068e-06,
                1.5534975692866768e-06,
                1.2098658276862581e-06,
                1.2098656834481918e-06,
                1.5534975693601474e-06,
                1.3709567165386693e-06,
                1.7603425837062577e-06,
                5.422220907426478e-06,
                1.9947297213492663e-06,
                2.561283126535066e-06
            ],
            [
                6.144174601208867e-06,
                8.939694166989405e-06,
                4.222833947674739e-06,
                2.9023109470871505e-06,
                2.2603245672867952e-06,
                3.7266397278180926e-06,
                4.785096204972935e-06,
                4.2228324372555256e-06,
                2.561282515886208e-06,
                1.7603432132464244e-06
            ],
            [
                4.222833443461647e-06,
                3.7266406165827946e-06,
                8.93969417199781e-06,
                7.889264463446097e-06,
                1.1478765385432939e-05,
                1.3007133115430804e-05,
                4.785093924103951e-06,
                1.1478766756444477e-05,
                1.3007131563815288e-05,
                7.889265405146477e-06
            ],
            [
                1.5534979396448094e-06,
                1.9947301968673173e-06,
                1.3709573702111586e-06,
                1.3709578603659798e-06,
                2.3823685318502406e-07,
                2.3823690998803445e-07,
                9.422447061953531e-07,
                2.3823685318675746e-07,
                6.475949525722606e-07,
                1.20986611609532e-06
            ],
            [
                1.9947290080125335e-06,
                3.2887494566352732e-06,
                9.422450431732037e-07,
                1.9947299591354906e-06,
                7.338210679542388e-07,
                3.9278605978261504e-07,
                2.5612828209345766e-06,
                5.7150044702099e-07,
                5.043476486764593e-07,
                1.0677027427166074e-06
            ],
            [
                2.1444953517842076e-05,
                5.4222183231674305e-06,
                3.2887494573232236e-06,
                1.8925145982350146e-05,
                7.889264465239894e-06,
                1.012998977108606e-05,
                4.2228344508893285e-06,
                2.4300249411766472e-05,
                2.753569433890398e-05,
                3.5356267531385634e-05
            ],
            [
                2.2603251061458426e-06,
                1.6701419852090592e-05,
                4.78509563466093e-06,
                6.962258737092915e-06,
                5.422219614705025e-06,
                6.144177531007026e-06,
                6.144175333635923e-06,
                8.939693105662367e-06,
                2.5612828210277558e-06,
                4.785095634460739e-06
            ],
            [
                1.3709568799243436e-06,
                2.2603234893861252e-06,
                9.422447062150634e-07,
                2.5612834317116285e-06,
                4.785093923420688e-06,
                1.760343632920248e-06,
                1.9947306725868575e-06,
                4.222835457449267e-06,
                1.0677027427413698e-06,
                2.2603237588597026e-06
            ],
            [
                0.0005527786693711892,
                1.7603425835173373e-06,
                7.338208930078229e-07,
                0.0009110512842578603,
                0.0009110514029372144,
                1.2098659719122375e-06,
                1.3709570431803621e-06,
                1.370957370247318e-06,
                4.222835457526079e-06,
                1.9947292456607935e-06
            ],
            [
                1.994729959224386e-06,
                1.892515274614874e-05,
                6.96225873895455e-06,
                1.6701421834059987e-05,
                1.1478768124553928e-05,
                1.6701419851270353e-05,
                1.6701425821573757e-05,
                2.7535700936100516e-05,
                7.8892654060075e-06,
                5.1442238087492836e-05
            ],
            [
                0.999941708745072,
                1.1478768124324254e-05,
                2.1444945843077847e-05,
                8.939699500489763e-06,
                2.4300246513165137e-05,
                0.000179527962994377,
                8.939693104865575e-06,
                2.1444945850567248e-05,
                2.1444956072586775e-05,
                1.0129988563730593e-05
            ],
            [
                7.338207180714596e-07,
                1.370957533676711e-06,
                7.338209805090567e-07,
                5.043472278159142e-07,
                4.222832437109582e-06,
                3.288749065125496e-06,
                1.9947297214182054e-06,
                1.5534975693036317e-06,
                7.338211554591642e-07,
                1.7603434230088762e-06
            ],
            [
                0.9999646437535943,
                0.9465966690702636,
                0.9996200155654729,
                0.9999930377404314,
                0.9999151889587602,
                0.9999417087137606,
                0.9999599363126355,
                0.9999852610145218,
                0.9999646437324774,
                0.9999756997650966
            ],
            [
                1.7603425837062577e-06,
                3.7266401719851935e-06,
                4.785096775171854e-06,
                1.3709576970537545e-06,
                5.043476486571938e-07,
                3.059023363033496e-07,
                1.7603438428028262e-06,
                1.3709568799679844e-06,
                1.2098662604126641e-06,
                3.726640171131078e-06
            ],
            [
                2.5612812945889277e-06,
                6.144172404218801e-06,
                1.5534983101301911e-06,
                9.422450431800595e-07,
                3.4663274506641133e-07,
                2.9023109471188266e-06,
                5.715005151550947e-07,
                1.994729483680993e-06,
                1.553498495281783e-06,
                5.043472278255469e-07
            ],
            [
                1.7603425831394971e-06,
                2.5612822104977725e-06,
                6.1441745960455e-06,
                3.7266383940901643e-06,
                5.043474683126242e-07,
                1.2098658277181688e-06,
                1.2098653949842147e-06,
                1.7603438427467903e-06,
                4.222835457364773e-06,
                1.370957370146321e-06
            ],
            [
                0.9999910603047636,
                0.9796676458039968,
                0.9999151889487328,
                0.9999910603058285,
                0.9999151889284177,
                0.9999785550464846,
                0.9999724642990779,
                0.9999852610147802,
                0.999915188948652,
                0.9999485578047775
            ],
            [
                2.561282515820982e-06,
                2.5612812945260317e-06,
                1.3709570433979422e-06,
                2.902311292920774e-06,
                3.726639283291774e-06,
                5.04347528438253e-07,
                3.2887494573232236e-06,
                1.3709576970824327e-06,
                1.3709572064688193e-06,
                1.760342793515064e-06
            ],
            [
                1.2098661161602417e-06,
                3.0590222691880844e-07,
                1.5534971989258068e-06,
                1.7603436329714805e-06,
                6.962258739068529e-06,
                1.5534977544932838e-06,
                2.9023109469842055e-06,
                6.475946437966953e-07,
                8.315284241333265e-07,
                2.260324028306588e-06
            ],
            [
                1.760342793583908e-06,
                9.422448184912962e-07,
                8.315283250150648e-07,
                2.902311984989368e-06,
                1.3709576969153512e-06,
                5.715005151400212e-07,
                1.3709570433536782e-06,
                5.04347287945184e-07,
                1.7603434231097403e-06,
                1.9947292457750883e-06
            ],
            [
                8.315283250082584e-07,
                2.102433159684668e-07,
                5.422219614705025e-06,
                6.475951069696694e-07,
                6.475950297768503e-07,
                2.3823688158484836e-07,
                1.0677026154473471e-06,
                1.2098652506746763e-06,
                7.338212428346234e-07,
                1.553497384180408e-06
            ],
            [
                2.561282515853595e-06,
                4.785094493419144e-06,
                4.222833947121688e-06,
                3.7266401721817755e-06,
                1.2098656834481918e-06,
                2.260323489266892e-06,
                5.4222170296279735e-06,
                3.726640171517464e-06,
                3.7266379509129646e-06,
                2.56128129449109e-06
            ],
            [
                3.726640171842841e-06,
                2.561282821209454e-06,
                1.9947306723745965e-06,
                4.785096203884934e-06,
                1.994729721323867e-06,
                1.370957043323753e-06,
                3.288749848749297e-06,
                1.2098653949192932e-06,
                3.726640172290235e-06,
                4.785095634356291e-06
            ],
            [
                0.9999967112513499,
                0.9975273771678328,
                0.9999885212319842,
                0.8354835411997897,
                0.9999869928655222,
                0.932453310268176,
                0.7981867825403177,
                0.9149009584734676,
                0.9999930377430531,
                0.9999810748518236
            ],
            [
                6.962257077413455e-06,
                3.2887478889513447e-06,
                1.1478770861650256e-05,
                0.001501182490041194,
                1.3007133108474901e-05,
                5.1442238107329257e-05,
                8.939698433373153e-06,
                1.9947290080343035e-06,
                1.473898372275276e-05,
                0.999998446502431
            ],
            [
                1.3709572067680694e-06,
                2.9023109470871505e-06,
                3.7266379507909478e-06,
                1.2098659719524008e-06,
                2.561281905100056e-06,
                0.00017952798456432952,
                3.726640616630245e-06,
                1.5534981249291695e-06,
                5.422217029006611e-06,
                5.422217029844958e-06
            ],
            [
                2.561282515662579e-06,
                1.553498495308628e-06,
                1.994729245822257e-06,
                2.5612834317535587e-06,
                1.067702742656401e-06,
                1.5534975692683091e-06,
                2.902311292960369e-06,
                1.5534983100016177e-06,
                1.9947306725669014e-06,
                1.994729721396435e-06
            ],
            [
                5.04347528431602e-07,
                2.5612812945260317e-06,
                2.561282821069686e-06,
                3.28875024092319e-06,
                2.260323758806253e-06,
                5.422218969029887e-06,
                1.209865539274514e-06,
                5.422219615286937e-06,
                1.5534984952111384e-06,
                4.785092782188013e-06
            ],
            [
                3.288749849209925e-06,
                4.4508515804389805e-07,
                3.7266410603195545e-06,
                4.22283294007051e-06,
                5.422220908314139e-06,
                9.422444815679433e-07,
                3.927861534257969e-07,
                9.422442568428928e-07,
                2.9023116388072315e-06,
                4.785094494463623e-06
            ],
            [
                4.539786317522845e-05,
                1.7603440525925705e-06,
                7.88925976397226e-06,
                0.0002034270450853695,
                0.9999810748585449,
                1.1478769491598686e-05,
                1.8925148236674017e-05,
                6.144175334015912e-06,
                4.785093923768848e-06,
                1.3007130009739366e-05
            ],
            [
                1.012999339309804e-05,
                3.1201926212712214e-05,
                3.12019187926687e-05,
                1.1478765386038447e-05,
                6.962257909121104e-06,
                1.1478765386330758e-05,
                3.1201907603241865e-05,
                2.7535704207102113e-05,
                1.300712536203966e-05,
                2.7535697653779924e-05
            ],
            [
                8.315278293838516e-07,
                5.422218319715415e-06,
                3.726638394957837e-06,
                2.2603242977308917e-06,
                3.7266406162947e-06,
                1.5534973841592143e-06,
                2.260323758746637e-06,
                1.5534979396984994e-06,
                6.962253757840428e-06,
                5.422221551060224e-06
            ]
        ]
    },
    {
        "q_id": "7854_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            6,
            7,
            8,
            13,
            17,
            20,
            22,
            23,
            24,
            29,
            32,
            33,
            37,
            39,
            45,
            48,
            51,
            53,
            54,
            55,
            56,
            57,
            59,
            61,
            63,
            65,
            66,
            67,
            69,
            71,
            72,
            75,
            77,
            78,
            80,
            82,
            83,
            84,
            86,
            89,
            90,
            91,
            93,
            95,
            96,
            97,
            99,
            101,
            103,
            104,
            107,
            108,
            109,
            113,
            117,
            118,
            124
        ],
        "rewards": [
            [
                8.939699498814873e-06,
                3.726639283752725e-06,
                1.7603425836005905e-06,
                1.7603438426203097e-06,
                4.785095634756674e-06,
                1.8925152751174644e-05,
                1.9947301968673173e-06,
                2.144494581694296e-05,
                1.0129992183991656e-05,
                4.22283294025486e-06
            ],
            [
                0.3486451285660856,
                0.0007096704304725822,
                0.0006263342475199637,
                0.13296423504419935,
                0.0011695104521773382,
                0.9796676465831374,
                0.00010889688297145868,
                0.020332351487562173,
                0.00029595702575903684,
                0.00048785710606458015
            ],
            [
                0.999999352404893,
                0.9999970976887069,
                0.9999986290424663,
                0.999999814460876,
                0.9999996533672549,
                0.9999980052705164,
                0.9999984465020604,
                0.9999984465024306,
                0.9999982396574163,
                0.9999984465028011
            ],
            [
                0.9999995549147358,
                0.9999984465022456,
                0.9999970976883621,
                0.9999898700114362,
                0.9999957771675626,
                0.9999996533673375,
                0.9999832985801492,
                0.9999945777810304,
                0.9999910602994339,
                0.9999756997650652
            ],
            [
                0.9999986290427931,
                0.9999986290431201,
                0.9999957771655489,
                0.999996273358939,
                0.9999982396561572,
                0.9999992661792819,
                0.9999991684722697,
                0.9999992661788445,
                0.999997097687669,
                0.9999990577554061
            ],
            [
                0.9999995549151072,
                0.999993037746241,
                0.9999997617631753,
                0.9999994284997573,
                0.9999991684721706,
                0.9999995549150541,
                0.9999967112497589,
                0.9999995549147889,
                0.9999991684722697,
                0.9999996072138465
            ],
            [
                4.785094492383368e-06,
                2.260325375091285e-06,
                3.5356242177147305e-05,
                5.422219615286937e-06,
                1.3007128460419196e-05,
                0.00023050665751126075,
                5.829127936084435e-05,
                1.473898898859989e-05,
                1.473897845457507e-05,
                7.889261643382609e-06
            ],
            [
                0.6513548714339144,
                0.0001584362153911779,
                0.00023050682410178131,
                3.12019150568812e-05,
                0.0010322311692828163,
                0.0003353500666186372,
                0.00048785702165304786,
                0.7549149923816048,
                0.06008664596619964,
                0.0006263340541979161
            ],
            [
                0.00010889692200685404,
                5.1442225836439433e-05,
                0.00023050668619744495,
                0.0002034269975711392,
                9.610240330734994e-05,
                3.120192624846737e-05,
                5.1442201289803036e-05,
                0.00013982209022783522,
                5.1442238087492836e-05,
                0.0001584362919971074
            ],
            [
                3.120191136649749e-05,
                1.8925152732723376e-05,
                1.300713311517055e-05,
                5.144220122617679e-05,
                5.1442219708855337e-05,
                8.481103117361599e-05,
                1.147876675466972e-05,
                5.8291265499980624e-05,
                2.1444948352105077e-05,
                4.0063711274151284e-05
            ],
            [
                0.0003353501858552705,
                0.00010889688174031335,
                0.0001233946187725557,
                0.0001398220738102709,
                1.892515725225098e-05,
                0.00010889693502657802,
                0.00037998456456480846,
                4.539786857692116e-05,
                3.535626751800907e-05,
                5.829125852607975e-05
            ],
            [
                0.9999992661790195,
                0.9999996533675028,
                0.9999989322970029,
                0.9999910603047638,
                0.9999977396751634,
                0.9999977396759716,
                0.9999994284992805,
                0.999994577778445,
                0.999995777167059,
                0.9999998144609645
            ],
            [
                4.539785235863304e-05,
                0.00013982210665353909,
                0.000123394574531953,
                5.144220739530288e-05,
                8.481104129042625e-05,
                0.00023050679675028972,
                7.484621811625572e-05,
                0.00026119027604368705,
                5.144221363404434e-05,
                0.00010889696085529394
            ],
            [
                0.9999982396561572,
                0.9999910603047626,
                0.9999852610180362,
                0.9999910603026309,
                0.9999989322972573,
                0.9999417087067817,
                0.9999992661791944,
                0.9999986290424664,
                0.9999977396754328,
                0.9999980052705164
            ],
            [
                7.484620043459196e-05,
                4.785096776303374e-06,
                7.484621813204729e-05,
                1.8925152750176348e-05,
                5.144222589407736e-05,
                5.829129321831856e-05,
                2.430023781444595e-05,
                4.00637017209988e-05,
                5.422217676397663e-06,
                4.539785776395774e-05
            ],
            [
                5.422220262195015e-06,
                3.120192618433512e-05,
                6.14417753110761e-06,
                8.93969310367852e-06,
                3.72664017246987e-06,
                4.2228329408924035e-06,
                6.144177527609484e-06,
                8.939696303010449e-06,
                2.1444945854624007e-05,
                1.4738987237124277e-05
            ],
            [
                0.9999151889793035,
                0.0004305570804227815,
                6.144173867608406e-06,
                0.00023050679605275296,
                0.9999785550413729,
                3.1201922508819695e-05,
                0.00029595723900028025,
                0.00012339454532968083,
                5.1442201250130194e-05,
                8.4811031131658e-05
            ],
            [
                1.3007125360478133e-05,
                5.1442237979702405e-05,
                0.0009110513790953785,
                1.670142581574095e-05,
                5.42222155351609e-06,
                0.008577483402061336,
                1.3007123798453357e-05,
                1.6701429803316423e-05,
                6.1441753294672295e-06,
                2.260323758835034e-06
            ],
            [
                0.0159063923241052,
                0.00043055718020064735,
                2.4300234906298624e-05,
                0.00012339458908910424,
                0.0002611903395995848,
                0.00015843623546473096,
                0.0066928498903068975,
                0.000108896882881143,
                0.012431648406321836,
                0.000158436215866046
            ],
            [
                0.9999885212359814,
                0.9999938558239364,
                0.9999832985781617,
                0.9999832985801581,
                0.9999945777810311,
                0.9999832985801511,
                0.999933947831781,
                0.9999910602994382,
                0.9999930377454147,
                0.9999724643023691
            ],
            [
                0.999933947855452,
                0.7057850278370112,
                0.025957358751909597,
                0.7772998611746912,
                0.9968273172694406,
                0.05340332452690107,
                0.11920291732853862,
                0.0003799845238720768,
                0.0024726229786083075,
                0.0019267347980967786
            ],
            [
                5.829127246412803e-05,
                7.484623602717382e-05,
                6.605216826132997e-05,
                1.4738980210258757e-05,
                3.1201907645920996e-05,
                1.4738987236641703e-05,
                7.484620938678116e-05,
                1.8925150485318196e-05,
                0.00017952803016475351,
                1.3007130012980722e-05
            ],
            [
                0.9999962733607161,
                0.9999945777816768,
                0.999998446502801,
                0.9999989322973846,
                0.9999967112521109,
                0.9999986290426297,
                0.9999992661786696,
                0.9999974387168735,
                0.9999957771665555,
                0.9999994956525917
            ],
            [
                5.144223204149862e-05,
                0.06008665017400762,
                1.4738988993050295e-05,
                6.144176063224333e-06,
                1.4738976690741464e-05,
                2.4300246506623417e-05,
                7.484620031370475e-05,
                1.1478772222347966e-05,
                1.1478765384054893e-05,
                2.1444950959196957e-05
            ],
            [
                8.939698433145498e-06,
                7.484620934866355e-05,
                7.484620937425679e-05,
                5.4222202613172164e-06,
                1.670141985166528e-05,
                1.4738988998117324e-05,
                7.889259763010786e-06,
                1.4738988994015443e-05,
                5.422217028582506e-06,
                2.9023116389365734e-06
            ],
            [
                1.892515048889829e-05,
                2.1444953520182517e-05,
                0.00012339453019082351,
                0.00015843621574156602,
                2.753569765708558e-05,
                4.0063692172075196e-05,
                0.00010889686997709268,
                3.1201922511884416e-05,
                7.484620938678116e-05,
                4.006370166911356e-05
            ],
            [
                0.9998911030778569,
                0.5312093733737563,
                0.9986749775880245,
                0.9840936109414438,
                0.9999921107369998,
                0.9999687980849329,
                0.9399133433038894,
                0.9999546021260729,
                0.9997040428315234,
                0.9999417087554018
            ],
            [
                4.0063701703217896e-05,
                1.1478770858372173e-05,
                3.535626334799422e-05,
                1.8925150490206403e-05,
                3.535625492063251e-05,
                2.430023493228869e-05,
                0.00023050663126645703,
                6.962253759043525e-06,
                4.006368261047406e-05,
                6.144176794522774e-06
            ],
            [
                5.829127940791947e-05,
                0.00013982202392692734,
                6.605216036234875e-05,
                1.0129992182443859e-05,
                3.5356267555952205e-05,
                4.53978523645784e-05,
                2.1444948402034417e-05,
                0.00012339458914655723,
                0.00012339461898800447,
                1.0129994600398803e-05
            ],
            [
                0.9999832985841378,
                0.9999962733620493,
                0.9999982396567867,
                0.9999974387180948,
                0.9999970976887079,
                0.9999982396572067,
                0.999999168471675,
                0.9999957771660526,
                0.9999990577557432,
                0.999996273360272
            ],
            [
                0.9999994956525917,
                0.9999992661790196,
                0.9999987901347492,
                0.999991060299435,
                0.9999852610127611,
                0.9999990577555185,
                0.9999997617631752,
                0.9999930377412614,
                0.9999852610145198,
                0.9999989322968754
            ],
            [
                0.9999990577551815,
                0.999998239656577,
                0.999997438716568,
                0.9999957771645422,
                0.999998005269328,
                0.9999962733607165,
                0.9999485577741262,
                0.9999938558275968,
                0.9999990577552939,
                0.999997097688707
            ],
            [
                4.222832436871463e-06,
                4.006368739659403e-05,
                3.5356242224994204e-05,
                5.8291279382897555e-05,
                2.4300252296223892e-05,
                4.222834450589758e-06,
                1.01299933920846e-05,
                3.1201900190126774e-05,
                6.605212069781891e-05,
                0.00012339455967856158
            ],
            [
                3.288749456964293e-06,
                1.3007134662432895e-05,
                1.3007128457958606e-05,
                1.4738983723235332e-05,
                8.939694168517944e-06,
                2.9023116390104826e-06,
                8.93969310584124e-06,
                1.0129995808418327e-05,
                1.147876401711502e-05,
                5.422221554758815e-06
            ],
            [
                1.4738987237124277e-05,
                0.00043055698421469533,
                1.4738978453315019e-05,
                0.00015843615943512485,
                3.5356238040705445e-05,
                7.889261643899223e-06,
                2.1444945843077847e-05,
                1.0129995807939249e-05,
                0.0001233946042513091,
                0.00023050674165159843
            ],
            [
                4.5397868567012224e-05,
                4.785095063469892e-06,
                6.9622537593854575e-06,
                5.422220905887864e-06,
                1.012999580244825e-05,
                4.222834953896582e-06,
                6.144177530794679e-06,
                6.962257076628275e-06,
                6.962259567027776e-06,
                4.785095064148803e-06
            ],
            [
                0.9241418272911436,
                0.8354835350552603,
                0.6791786861878392,
                0.9999957771680658,
                0.999447221257694,
                0.9999546021159507,
                0.999983298570245,
                0.9999485577802313,
                0.9997388095668258,
                0.8519528000888387
            ],
            [
                2.144495096083526e-05,
                6.962257079173776e-06,
                3.7266410604686857e-06,
                2.7535697654881812e-05,
                1.89251482355036e-05,
                2.9023123309973302e-06,
                9.422447061876404e-07,
                1.1478768120315386e-05,
                2.1444953511912968e-05,
                1.300713311517055e-05
            ],
            [
                3.28875024092319e-06,
                1.0129993388178253e-05,
                8.9396994983433e-06,
                2.90231336806592e-06,
                5.4222183209778656e-06,
                1.0129992180674948e-05,
                1.9947294834143063e-06,
                4.5397890254712545e-05,
                2.1444953504969666e-05,
                1.012999459535003e-05
            ],
            [
                0.014063625132037074,
                0.0002611902395349612,
                0.00023050674002848438,
                2.4300234928664224e-05,
                0.9999938558268642,
                0.00048785717216898124,
                7.484624503872184e-05,
                1.4738983721251418e-05,
                1.670142182986766e-05,
                0.9999938558275963
            ],
            [
                2.1444953517061932e-05,
                9.610246071689974e-05,
                2.4300246515109972e-05,
                2.144494840531103e-05,
                0.0003799845617568882,
                0.00013982209057978554,
                3.120191506550783e-05,
                6.605212100874168e-05,
                4.5397884829235786e-05,
                0.00017952790107154517
            ],
            [
                1.670142980112912e-05,
                1.0129995804696242e-05,
                7.889259762494174e-06,
                1.6701421834728333e-05,
                7.484625363315528e-05,
                2.4300249410794055e-05,
                4.222831933104063e-06,
                3.1201922511884416e-05,
                1.3007134657464394e-05,
                8.939694168225243e-06
            ],
            [
                7.484620047815493e-05,
                0.001032231084051947,
                3.535626754334737e-05,
                0.0009110512155933839,
                1.8925145968614975e-05,
                0.00043055701328629413,
                7.484622717027548e-05,
                1.8925143723620274e-05,
                7.484621813204729e-05,
                2.1444958627955892e-05
            ],
            [
                3.2887490649759413e-06,
                4.539785778179383e-05,
                7.484620040083068e-05,
                5.8291286280462885e-05,
                2.4300234922476113e-05,
                8.939699496164318e-06,
                3.120192622644674e-05,
                1.012999218369684e-05,
                1.3007131563176482e-05,
                4.785094492383368e-06
            ],
            [
                0.00013982202362176826,
                1.300712846217e-05,
                2.144494329192304e-05,
                4.785096205717126e-06,
                1.1478773595657069e-05,
                2.4300252300909177e-05,
                7.889266344981421e-06,
                3.535626755428014e-05,
                1.0129995806888955e-05,
                6.962255419380732e-06
            ],
            [
                4.539789012787806e-05,
                8.939694170940841e-06,
                5.829129299693822e-05,
                0.02595735536111827,
                3.120190017457614e-05,
                0.00010889688312673828,
                0.0006263342803839891,
                2.144494837847401e-05,
                5.144223806615931e-05,
                9.610243770231598e-05
            ],
            [
                3.7266397281434697e-06,
                4.222835457595211e-06,
                6.962255419279419e-06,
                1.1478769491598686e-05,
                7.484620922668724e-05,
                1.76034363298589e-06,
                7.889262585211807e-06,
                1.147876675548402e-05,
                1.4738987238464762e-05,
                1.3007128460040644e-05
            ],
            [
                0.999978555054167,
                0.0001233945453117268,
                0.00048785704961046365,
                9.610242621495249e-05,
                5.14422258772351e-05,
                0.9999930377454114,
                0.00012339454513936787,
                1.1478772225271098e-05,
                9.610241465487671e-05,
                0.9999810748585369
            ],
            [
                2.4300243623139103e-05,
                7.484622650430645e-05,
                1.6701425819447213e-05,
                5.829127248999813e-05,
                2.5612834318257725e-06,
                8.48110513480029e-05,
                1.892514823013346e-05,
                2.7535704218321328e-05,
                7.889266345584138e-06,
                2.7535681228559507e-05
            ],
            [
                0.9999977396751636,
                0.9999994284995529,
                0.9999991684718732,
                0.9999986290429566,
                0.9999987901337398,
                0.9999982396574163,
                0.9999974387184001,
                0.9999977396748939,
                0.9999038976194708,
                0.9999930377404308
            ],
            [
                0.00017952792209296897,
                0.05340332659840655,
                0.00029595705464011043,
                0.00026119043216338555,
                0.46879062662624377,
                0.00015843621589601344,
                0.2450850021044189,
                0.007577239474994627,
                0.001032231187289339,
                0.003172682089194999
            ],
            [
                0.00010889688308554166,
                0.0007096704188319211,
                8.48110411016153e-05,
                3.1201907610960436e-05,
                3.120192622962497e-05,
                1.8925148232267744e-05,
                3.12019113570763e-05,
                0.00017952802935764314,
                2.7535697650273915e-05,
                4.0063692159249626e-05
            ],
            [
                2.1444940741392653e-05,
                1.3007130007988564e-05,
                3.120190020862863e-05,
                0.00015843625426351888,
                2.7535704201392335e-05,
                0.00010889693308082876,
                NaN,
                7.889259763469998e-06,
                2.430023492769181e-05,
                4.539786861787811e-05
            ],
            [
                0.0021827169646095102,
                0.0002034270447124535,
                0.000158436178074846,
                9.610244915612066e-05,
                4.006371122853307e-05,
                5.144220118088988e-05,
                0.00029595709796172625,
                5.829124444893003e-05,
                0.00017952796506569833,
                1.0129992183070348e-05
            ],
            [
                5.144223190264361e-05,
                2.7535700909955743e-05,
                3.120192250564146e-05,
                9.610242426426827e-05,
                0.00023050681582523842,
                2.1444950959977102e-05,
                0.00010889694790686876,
                8.481106150677358e-05,
                3.120192251903545e-05,
                2.1444953513707305e-05
            ],
            [
                4.006371123377989e-05,
                7.484622722255103e-05,
                3.5356242257020764e-05,
                0.989013055557933,
                0.9999151889183892,
                0.00015843627123890696,
                1.0129993390610508e-05,
                4.539789027568648e-05,
                0.0001584362349852524,
                2.1444940732342966e-05
            ],
            [
                0.9999810748562825,
                0.9999938558253988,
                0.9999724643056384,
                0.9999869928730878,
                0.9999339478790182,
                0.9999910603015656,
                0.9999910603026315,
                0.9999930377437514,
                0.9999910603068937,
                0.9999756997592719
            ],
            [
                0.9999898700090265,
                0.999994577779738,
                0.999620015571542,
                0.9999417087207414,
                0.9999921107355368,
                0.999997739674625,
                0.9999724643056594,
                0.9999724642958652,
                0.9999485577802613,
                NaN
            ],
            [
                1.3007123808153756e-05,
                1.9947304346826253e-06,
                1.6701429806475863e-05,
                1.3007131565613412e-05,
                1.3709578604831862e-06,
                7.889264465397747e-06,
                2.1444950957402623e-05,
                3.1201911361276113e-05,
                4.222833443968609e-06,
                7.338208055489796e-07
            ],
            [
                3.535625905424669e-05,
                0.0009110513100070403,
                0.006692849902689867,
                0.0006263341173390909,
                0.00026119042221543526,
                0.002800927010041765,
                0.00015843621558481343,
                0.003593602971588918,
                0.00091105097823474,
                0.0002034269657371438
            ],
            [
                4.53978523645784e-05,
                2.753569436424737e-05,
                1.3007133113372426e-05,
                0.00017952800860263153,
                2.430024940080467e-05,
                4.0063706496627415e-05,
                6.605217615406483e-05,
                5.829126551609642e-05,
                7.889265405505236e-06,
                1.6701423824262386e-05
            ],
            [
                5.1442213603354026e-05,
                0.00012339454230442278,
                3.5356267231441916e-05,
                8.481104104114645e-05,
                1.8925141469950998e-05,
                5.1442219692761636e-05,
                5.144221364040696e-05,
                5.42222155351609e-06,
                1.3007130012673148e-05,
                1.1478768118310953e-05
            ]
        ]
    },
    {
        "q_id": "9027_mmlu_math",
        "cot_ids": [
            0,
            1,
            2,
            3,
            5,
            6,
            7,
            8,
            12,
            15,
            16,
            17,
            19,
            20,
            21,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            37,
            39,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            49,
            50,
            53,
            55,
            56,
            57,
            60,
            61,
            62,
            63,
            64,
            66,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            80,
            81,
            82,
            84,
            85,
            86,
            87,
            88,
            89,
            91,
            92,
            94,
            96,
            97,
            98,
            99,
            101,
            103,
            104,
            105,
            106,
            108,
            109,
            111,
            113,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.2098662603862553e-06,
                1.0677024881140118e-06,
                9.422444812967136e-07,
                2.9023133689924295e-06,
                1.6701425824733193e-05,
                6.14417533430649e-06,
                4.785093353352668e-06,
                5.4222170304318e-06,
                1.3709576970213355e-06,
                3.726640172537657e-06
            ],
            [
                6.962255411338977e-06,
                1.1478773592378984e-05,
                1.0129995808178788e-05,
                1.892515725920463e-05,
                3.5356242272712497e-05,
                2.430025231469984e-05,
                1.9947301968673173e-06,
                3.7266392826613557e-06,
                8.3152822584917e-07,
                1.2098655391045077e-06
            ],
            [
                0.000626334071795831,
                5.829126542194621e-05,
                0.0004305571799000361,
                0.000158436178012606,
                0.0001398220395714161,
                3.535626327403727e-05,
                NaN,
                4.539786316895279e-05,
                0.00010889696101057365,
                NaN
            ],
            [
                4.785096773021966e-06,
                1.9947306723745965e-06,
                2.9023116389761676e-06,
                4.5397857748103446e-05,
                3.2887506283532587e-06,
                4.785094494463623e-06,
                5.715006513843456e-07,
                6.144173868781898e-06,
                9.422444814458256e-07,
                4.2228324356808684e-06
            ],
            [
                1.8925148232956223e-05,
                2.260324567177841e-06,
                1.0129989757856078e-05,
                1.3007131563176482e-05,
                4.785095633477187e-06,
                1.3709576970824327e-06,
                1.4738978454950406e-05,
                1.1478765388711023e-05,
                1.6701421834728333e-05,
                1.670141983261753e-05
            ],
            [
                NaN,
                1.4738980211116665e-05,
                5.144221346936461e-05,
                7.484625311911196e-05,
                0.00013982212266829705,
                1.8925154986738235e-05,
                3.2887494572095624e-06,
                2.7535681242383173e-05,
                5.144222587049821e-05,
                0.00015843621385131426
            ],
            [
                1.892514371356847e-05,
                0.00020342706712293146,
                NaN,
                NaN,
                7.484622694429252e-05,
                4.539788362265688e-05,
                3.120192615550398e-05,
                0.0001398221236224284,
                0.0001398220730026163,
                0.002472622885000848
            ],
            [
                2.430024362791279e-05,
                7.889263512877297e-06,
                NaN,
                2.9023112892886446e-06,
                8.939694169591174e-06,
                NaN,
                NaN,
                4.7850944856987e-06,
                NaN,
                4.7850956288640684e-06
            ],
            [
                1.7603427934206038e-06,
                2.260323758835034e-06,
                3.7266392836984955e-06,
                8.939695236983711e-06,
                4.7850939242083995e-06,
                4.7850950648799385e-06,
                8.939693105662367e-06,
                1.3709576969402887e-06,
                1.76034300345598e-06,
                1.994729721323867e-06
            ],
            [
                7.338208055536515e-07,
                2.260325375615501e-06,
                2.561282210562998e-06,
                2.2603248365960415e-06,
                6.475946437966953e-07,
                0.00020342705853402374,
                1.5534977543406908e-06,
                2.2603242977555607e-06,
                9.422447061782138e-07,
                6.475951069561228e-07
            ],
            [
                9.610244927358124e-05,
                2.1444940731484803e-05,
                3.2887478891487563e-06,
                NaN,
                4.7850956352353935e-06,
                1.0129987354108855e-05,
                0.00010889689611952136,
                2.5612822106654943e-06,
                1.1478773598538445e-05,
                6.962253759752719e-06
            ],
            [
                1.9947292458004866e-06,
                6.962258736902953e-06,
                6.475947209709154e-07,
                3.72664017246987e-06,
                8.315281267513512e-07,
                5.715004469963006e-07,
                1.7603427931932593e-06,
                5.715002426254813e-07,
                5.7150044702099e-07,
                4.222831933726245e-06
            ],
            [
                1.0677029972522599e-06,
                NaN,
                4.785096205830278e-06,
                1.2098655392464547e-06,
                4.22283394762097e-06,
                1.5534983101478522e-06,
                2.5612828213352452e-06,
                4.785096776194573e-06,
                1.3007128439125628e-05,
                1.0129995809431767e-05
            ],
            [
                0.9924227600277652,
                4.5397879429522924e-05,
                7.88926258343236e-06,
                0.0002959570269817894,
                0.9324533158993962,
                5.829125146227052e-05,
                0.9820137922092657,
                5.422220904921299e-06,
                0.9669140226838876,
                2.430024625989446e-05
            ],
            [
                7.889260703763482e-06,
                1.892514141783309e-05,
                5.829124453120541e-05,
                0.00012339454388617493,
                1.8925148202663113e-05,
                8.481101066480413e-05,
                NaN,
                0.00013982202353022053,
                2.4300234912928744e-05,
                6.605217599499912e-05
            ],
            [
                8.315283249280938e-07,
                1.1478772229781076e-05,
                4.4508521108961425e-07,
                8.93969630317306e-06,
                2.561282210618905e-06,
                8.939699500164542e-06,
                3.4663253845638233e-07,
                4.222835457733473e-06,
                3.120192623972722e-05,
                1.3007134664822509e-05
            ],
            [
                1.7603440523668265e-06,
                1.2098656834195822e-06,
                1.3709575336530204e-06,
                1.553498495295912e-06,
                8.315278293604072e-07,
                2.699577774530648e-07,
                4.45085104982401e-07,
                1.5534979397267575e-06,
                3.7266388396128453e-06,
                1.370956716519966e-06
            ],
            [
                2.3823685317830715e-07,
                2.561282515886208e-06,
                7.338209804506587e-07,
                5.043475885453117e-07,
                1.370957370247318e-06,
                5.715002426254813e-07,
                1.370956716519966e-06,
                8.315282258956806e-07,
                6.47594720987407e-07,
                1.5534977545384963e-06
            ],
            [
                0.9999921107403112,
                1.1478770856576534e-05,
                1.8925150486764003e-05,
                4.539787932646994e-05,
                NaN,
                6.962258738701267e-06,
                1.4738981964843453e-05,
                7.889260701237816e-06,
                0.999769493261816,
                2.430023780286534e-05
            ],
            [
                4.22283444919945e-06,
                6.144172395937299e-06,
                2.9023133687311063e-06,
                2.2603251057881422e-06,
                4.785095064523075e-06,
                8.939699486537762e-06,
                5.422220907298259e-06,
                3.7266397266860513e-06,
                7.889260698453844e-06,
                1.1478764016446877e-05
            ],
            [
                2.260323757126707e-06,
                8.315279284657531e-07,
                7.338211554641698e-07,
                9.422450431474948e-07,
                1.9947290079889487e-06,
                9.422447061953531e-07,
                9.422445938861406e-07,
                2.902312677007974e-06,
                8.315283249923769e-07,
                3.2887494572514376e-06
            ],
            [
                4.785096775389454e-06,
                1.3007123807302014e-05,
                7.889261640067674e-06,
                8.93970055911822e-06,
                1.7603436320989248e-06,
                1.760343002958863e-06,
                1.4738983707256776e-05,
                2.75356942132889e-05,
                3.7266388375114506e-06,
                1.4738976686988113e-05
            ],
            [
                1.67014258067487e-05,
                6.9622545849505825e-06,
                1.3007125348293483e-05,
                7.88926445328603e-06,
                6.144177525128383e-06,
                3.2887498463624074e-06,
                6.144173868312501e-06,
                7.889265405333033e-06,
                NaN,
                1.4738985477605971e-05
            ],
            [
                1.3709578605118645e-06,
                6.962258736902953e-06,
                0.00013982214041839615,
                3.7266397276079535e-06,
                4.222832437186393e-06,
                1.3007131561425676e-05,
                8.93970056529743e-06,
                2.753569109254574e-05,
                7.889265405505236e-06,
                4.222833444283541e-06
            ],
            [
                4.539785234971499e-05,
                1.8925143723620274e-05,
                1.0129995809763438e-05,
                NaN,
                7.889262576171072e-06,
                NaN,
                0.00015843627048972158,
                5.4222196113615e-06,
                2.430023781568357e-05,
                1.0129994597155795e-05
            ],
            [
                8.939695237341456e-06,
                8.93969417150998e-06,
                2.9023119850527192e-06,
                1.892515274194901e-05,
                1.1478765353779597e-05,
                0.00010889694733803808,
                5.144220737696355e-05,
                5.1442219648971794e-05,
                0.00033535014170619706,
                3.7266388391247794e-06
            ],
            [
                0.0002959571653164751,
                5.829125158695591e-05,
                0.00012339455998378054,
                0.00017952804952495535,
                3.120190762537599e-05,
                0.00020342692303532148,
                4.5397868567012224e-05,
                4.539785238406597e-05,
                0.0004305570216032018,
                3.5356267550807374e-05
            ],
            [
                1.7603425837062577e-06,
                7.889263523668778e-06,
                5.422217030209884e-06,
                2.7535684518791692e-05,
                5.715006513781082e-07,
                2.9023126765777146e-06,
                1.3007126902913016e-05,
                2.2603242977555607e-06,
                1.0129989762757436e-05,
                2.902311984873224e-06
            ],
            [
                0.001032231059923209,
                0.0013250222286577825,
                8.481101063271864e-05,
                NaN,
                0.0002959569820585506,
                NaN,
                9.610242597024299e-05,
                0.0008040857629679743,
                6.605214435486462e-05,
                0.00023050676945245808
            ],
            [
                3.288748280520804e-06,
                NaN,
                3.1201907609144296e-05,
                NaN,
                2.144495093719684e-05,
                1.9947306703717274e-06,
                2.1444940717130123e-05,
                5.4222196124266945e-06,
                8.481107076961873e-05,
                6.9622562489985925e-06
            ],
            [
                2.753570081479278e-05,
                3.2887486714861093e-06,
                NaN,
                1.0129988559492579e-05,
                5.42222155240158e-06,
                6.9622554173544636e-06,
                NaN,
                2.5612825155181522e-06,
                1.553498123468235e-06,
                1.0129994590964606e-05
            ],
            [
                5.829125857188255e-05,
                2.1444945836212564e-05,
                0.00033535026021110423,
                5.144221356106128e-05,
                0.0002305067919815528,
                4.006369679598209e-05,
                8.481102086552792e-05,
                5.144221971634078e-05,
                0.00010889689512763323,
                1.1478770859019436e-05
            ],
            [
                3.12019150080726e-05,
                NaN,
                2.4300237808257835e-05,
                NaN,
                NaN,
                1.892514595147183e-05,
                2.7535704190573806e-05,
                2.1444945827162874e-05,
                NaN,
                NaN
            ],
            [
                3.120192250564146e-05,
                9.610242605973675e-05,
                9.610240270746225e-05,
                0.00020342690000925244,
                0.0003799845734970903,
                9.610242627088607e-05,
                0.0003353501847430065,
                1.1478772214998373e-05,
                3.1201900190126774e-05,
                5.144223806166804e-05
            ],
            [
                2.144495095654446e-05,
                4.785094493636744e-06,
                NaN,
                6.605212828298922e-05,
                3.726640614559354e-06,
                NaN,
                5.422217029736466e-06,
                0.00012339461811902776,
                2.4300240729754152e-05,
                0.00033535013185192954
            ],
            [
                0.9999921107364745,
                0.9999417087067719,
                0.9999810748540182,
                0.8519528057272543,
                0.9999810748585699,
                0.9998415637652844,
                0.999512142890501,
                0.9999251537909971,
                0.9999967112513268,
                0.6513548646660543
            ],
            [
                4.785093919486482e-06,
                5.422221554670048e-06,
                2.260324567177841e-06,
                2.1444943276710197e-05,
                4.45085157792111e-07,
                1.1478770841585035e-05,
                4.785096775580942e-06,
                4.222834448800026e-06,
                6.144172396876092e-06,
                1.0129989764415789e-05
            ],
            [
                2.2603242978213447e-06,
                2.260325106045111e-06,
                1.2098662600770527e-06,
                4.222835458002318e-06,
                1.9947306723745965e-06,
                4.785092782597101e-06,
                1.2098659718187066e-06,
                2.5612828211442287e-06,
                1.9947304346535984e-06,
                6.962258739169842e-06
            ],
            [
                NaN,
                0.9999251537463385,
                8.939696297644297e-06,
                NaN,
                7.484619994287504e-05,
                8.939696297969519e-06,
                2.56128129423019e-06,
                7.889265398545302e-06,
                NaN,
                1.67014218283487e-05
            ],
            [
                3.120192623700302e-05,
                0.00020342694826337235,
                7.484620904971269e-05,
                0.0001233945743452308,
                0.0003353502169206109,
                5.144220136091472e-05,
                1.8925141463066202e-05,
                0.00012339461840449737,
                9.610239073907419e-05,
                0.00012339452971504112
            ],
            [
                NaN,
                2.1444953511912968e-05,
                4.006368737181739e-05,
                6.962256232307201e-06,
                NaN,
                NaN,
                1.1478764004670832e-05,
                2.7535681183983206e-05,
                1.4738978425004027e-05,
                1.4738976665218677e-05
            ],
            [
                2.561283126535066e-06,
                4.785095635296322e-06,
                1.2098653950315304e-06,
                1.067702615330819e-06,
                7.338212429087055e-07,
                2.9023123310580418e-06,
                5.043474081188854e-07,
                2.2603242977555607e-06,
                5.422220908116881e-06,
                6.9622579086271995e-06
            ],
            [
                8.939698429568063e-06,
                4.5397879346287815e-05,
                1.3709570433536782e-06,
                5.4222202613172164e-06,
                1.3007123808153756e-05,
                3.7266401721817755e-06,
                3.120190389197351e-05,
                3.5356267527012524e-05,
                1.067703251784089e-06,
                0.00012339453062351613
            ],
            [
                6.96225956921868e-06,
                6.144177529364136e-06,
                2.260324028281919e-06,
                NaN,
                4.222833947121688e-06,
                5.422219615395428e-06,
                3.5356267471448335e-05,
                6.96225458885115e-06,
                1.3007126883654165e-05,
                NaN
            ],
            [
                6.96225458545715e-06,
                8.939695232967228e-06,
                4.785094493836935e-06,
                5.422218321135672e-06,
                4.222833947029514e-06,
                7.889259762494174e-06,
                2.9023126730036544e-06,
                1.1478773556842028e-05,
                2.2603234892298883e-06,
                3.726640612634205e-06
            ],
            [
                3.120191134288775e-05,
                0.00012339463226144516,
                6.605212092416299e-05,
                0.00029595708955745283,
                8.481104108187037e-05,
                NaN,
                8.939693105662367e-06,
                3.120190391853445e-05,
                0.00012339452858752667,
                1.4738980210687712e-05
            ],
            [
                7.889262584350785e-06,
                4.222831933864508e-06,
                3.4663270374206273e-07,
                1.5534977545603963e-06,
                1.760343632854606e-06,
                1.0129992186202796e-05,
                1.0677028699858827e-06,
                8.315279285088606e-07,
                1.9947299592407137e-06,
                1.994729008074216e-06
            ],
            [
                8.93969629582306e-06,
                1.5534981246268099e-06,
                1.473897844934719e-05,
                2.9023133676594165e-06,
                1.3007126895436607e-05,
                4.222834447693925e-06,
                4.222832936867425e-06,
                6.14417532387917e-06,
                1.1478765385746131e-05,
                2.430023203298187e-05
            ],
            [
                2.1444956077189637e-05,
                9.42244256886598e-07,
                2.260323758939877e-06,
                8.315278293301564e-07,
                1.2098659717989e-06,
                2.260323489410794e-06,
                1.0677031245429291e-06,
                6.475949525878687e-07,
                4.785096776133645e-06,
                1.994729483608425e-06
            ],
            [
                NaN,
                7.484626278955236e-05,
                1.892514597494899e-05,
                6.605214461148412e-05,
                7.48462092936653e-05,
                0.0003353500649014583,
                0.00037998443215038816,
                0.0003353500569985326,
                8.48110614123681e-05,
                1.0129989768322136e-05
            ],
            [
                1.3709575330707286e-06,
                NaN,
                1.6701429727246864e-05,
                1.670141784666869e-05,
                1.012998976360504e-05,
                NaN,
                2.4300249389135656e-05,
                7.889260698138136e-06,
                7.889262583231455e-06,
                6.605216029987583e-05
            ],
            [
                4.006368253104304e-05,
                1.6701419840455358e-05,
                0.0006263340564568615,
                1.67014297980912e-05,
                6.605212874576922e-05,
                8.939695228186476e-06,
                3.120192604471978e-05,
                3.5356250691324983e-05,
                4.5397857748103446e-05,
                3.1201915063805214e-05
            ],
            [
                3.1201926235527406e-05,
                1.4738988993532872e-05,
                5.1442238118931704e-05,
                2.4300246523773334e-05,
                6.9622570786798724e-06,
                1.892515049571424e-05,
                1.300712536203966e-05,
                1.1478768124992398e-05,
                6.962257909412379e-06,
                0.0006263341142785837
            ],
            [
                5.422217676866151e-06,
                1.4738980214280206e-05,
                1.6701417852987564e-05,
                1.147876402018431e-05,
                3.5356254855807646e-05,
                1.3709570432277435e-06,
                3.7266388394569345e-06,
                1.209865539274514e-06,
                2.1444945853375776e-05,
                5.422218322565793e-06
            ],
            [
                4.539787937568435e-05,
                8.481107150203266e-05,
                0.0001233945892022148,
                6.605212866984062e-05,
                7.484622706027895e-05,
                1.0129992182112188e-05,
                8.481105097531723e-05,
                3.535624216814385e-05,
                NaN,
                0.00012339458912680775
            ],
            [
                5.4222170259787e-06,
                NaN,
                7.889260701697028e-06,
                1.670142380876899e-05,
                1.4738980210258757e-05,
                2.7535700932494338e-05,
                0.8354835330070838,
                3.120192248986379e-05,
                2.5612822098455215e-06,
                0.9968273165492862
            ],
            [
                8.939698431942181e-06,
                0.001325022616243867,
                4.5397857795336036e-05,
                4.539789019426799e-05,
                4.006367783499403e-05,
                0.0001088968960910006,
                7.484624503872184e-05,
                2.430024362393472e-05,
                1.892515499637696e-05,
                1.8925141450398177e-05
            ],
            [
                0.00010889688182587557,
                0.0003799845982819624,
                NaN,
                0.999088948780274,
                NaN,
                0.00023050665558632872,
                0.0004305571825554353,
                1.5534983100765009e-06,
                NaN,
                NaN
            ],
            [
                0.0002611902447027239,
                1.4738987235622935e-05,
                2.4300234902055345e-05,
                0.00013982204009832413,
                8.481107119166687e-05,
                0.0001584362723822792,
                3.5356259102608094e-05,
                6.605214462205646e-05,
                0.0001233945593392299,
                3.5356254877415924e-05
            ],
            [
                6.96225541916544e-06,
                3.2887478884069663e-06,
                4.785096776133645e-06,
                1.0129992185060374e-05,
                1.0129995805359584e-05,
                1.0129990974903845e-05,
                0.00029595722977796354,
                3.1201922508819695e-05,
                6.144176798132662e-06,
                1.1478770861441461e-05
            ],
            [
                NaN,
                0.001169510347737247,
                3.120190759075595e-05,
                7.484624435641655e-05,
                NaN,
                3.120191504757351e-05,
                2.7535694288417536e-05,
                9.610240330734994e-05,
                0.0008040860619450949,
                NaN
            ],
            [
                1.0129995800789894e-05,
                1.0129988558423862e-05,
                5.422218965242531e-06,
                8.939698431942181e-06,
                NaN,
                1.0129987348120356e-05,
                1.4738981963234875e-05,
                5.42222090767305e-06,
                1.1478766755985128e-05,
                8.48110407610152e-05
            ],
            [
                4.006367778063115e-05,
                NaN,
                1.670141586454787e-05,
                2.5612819028684275e-06,
                1.994729244583164e-06,
                8.939695223535811e-06,
                2.144494582474442e-05,
                1.3007130014873483e-05,
                NaN,
                4.785096205651846e-06
            ],
            [
                2.2603242978007868e-06,
                4.4508499887035535e-07,
                4.4508526416286326e-07,
                4.450848927437622e-07,
                5.422218969306048e-06,
                5.422218969217281e-06,
                3.2887482810382622e-06,
                1.994729245822257e-06,
                1.5534977545102382e-06,
                3.726641060773727e-06
            ],
            [
                1.8925150489517924e-05,
                8.48110509642107e-05,
                0.00010889693480950339,
                8.481102077297355e-05,
                NaN,
                1.4738988994980593e-05,
                0.0007096703288438379,
                4.0063692112611227e-05,
                NaN,
                0.00017952805041042603
            ],
            [
                4.006369208491967e-05,
                3.120190756737323e-05,
                NaN,
                0.0002611902975507032,
                3.7266379500520703e-06,
                NaN,
                4.785092782597101e-06,
                2.1444945755155414e-05,
                2.430023781683279e-05,
                8.48110609650218e-05
            ],
            [
                0.8354835309589074,
                0.970687767658707,
                0.9999967112493665,
                0.9999910603068933,
                0.99999303774064,
                0.9999980052695652,
                0.9999921107355355,
                0.9324533069832974,
                0.999992110740252,
                0.9999756997511178
            ],
            [
                5.043473480643696e-07,
                5.71500310747347e-07,
                5.04347588540266e-07,
                1.3709568798420497e-06,
                1.0129990979215566e-05,
                9.422449308566668e-07,
                3.7266401722360055e-06,
                4.7850939065001245e-06,
                8.315283250082584e-07,
                2.260325375615501e-06
            ],
            [
                0.0002305067645898225,
                5.144220744545534e-05,
                0.0003353502225209584,
                0.00023050668241465121,
                0.0001398220565667444,
                0.0004878571673438422,
                1.1478769491598686e-05,
                0.00029595698611429986,
                4.539788471231027e-05,
                NaN
            ],
            [
                3.7266397280485686e-06,
                1.7603432131855856e-06,
                1.3709568799106278e-06,
                4.785095635296322e-06,
                1.553497939554384e-06,
                1.994729245519287e-06,
                3.7266392838544054e-06,
                1.4738988994498018e-05,
                2.9023116387069255e-06,
                1.760342793515064e-06
            ],
            [
                4.006369681113957e-05,
                7.889260696071684e-06,
                4.222834948542745e-06,
                6.605212847809689e-05,
                7.889265400583057e-06,
                2.144495348827454e-05,
                8.939699496489538e-06,
                5.8291258356863845e-05,
                1.3007133110746217e-05,
                7.484626206368391e-05
            ],
            [
                6.60521445946645e-05,
                1.4738987240475486e-05,
                7.889265405146477e-06,
                7.889262584809997e-06,
                2.1444950963097686e-05,
                8.93969950000193e-06,
                8.939698434966738e-06,
                7.889259763857458e-06,
                4.222834947851431e-06,
                9.61024034059329e-05
            ],
            [
                NaN,
                6.605216013792677e-05,
                0.00013982203943918052,
                6.962258735104638e-06,
                0.0001398220400027076,
                5.144223816721283e-05,
                NaN,
                0.999968798084945,
                2.7535697646567574e-05,
                0.00013982212338847295
            ],
            [
                2.5612831265630198e-06,
                5.4222215541571775e-06,
                2.4300240723831244e-05,
                1.1478770854029233e-05,
                3.120191136400031e-05,
                0.00043055716932854135,
                4.222834450820197e-06,
                3.726637951170554e-06,
                1.7603440517840551e-06,
                3.7266397280485686e-06
            ],
            [
                2.260325105981383e-06,
                1.1478773596283455e-05,
                NaN,
                NaN,
                7.338209804506587e-07,
                NaN,
                NaN,
                2.2603234891147668e-06,
                4.222833947282995e-06,
                NaN
            ],
            [
                2.561282515783711e-06,
                6.962256248606003e-06,
                1.0677031245710902e-06,
                3.5356254916002164e-05,
                4.222834451254188e-06,
                NaN,
                4.785096205347206e-06,
                5.715003788749385e-07,
                4.78509506499309e-06,
                1.994729959160889e-06
            ],
            [
                1.3709570432052998e-06,
                4.22283293835759e-06,
                6.96225541407444e-06,
                2.5612834318583854e-06,
                1.4738978446451746e-05,
                1.994729721265813e-06,
                3.120191870958057e-05,
                2.5612828208879873e-06,
                8.939694164159978e-06,
                1.6701419838268058e-05
            ],
            [
                NaN,
                7.484623575490519e-05,
                2.753570420970657e-05,
                5.144220740391114e-05,
                NaN,
                0.0001584362539523188,
                0.0008040858897047036,
                0.0002611904276643889,
                NaN,
                6.605213662504366e-05
            ],
            [
                NaN,
                2.1444943285915917e-05,
                2.5612815998141903e-06,
                1.7603432131375548e-06,
                NaN,
                1.3007126912826352e-05,
                2.561281599914358e-06,
                2.430023493052066e-05,
                1.8925152742706337e-05,
                6.962259569117366e-06
            ],
            [
                9.422445938557184e-07,
                5.043474682784511e-07,
                9.422443692176231e-07,
                3.726638395493353e-06,
                3.288750241374845e-06,
                4.45085104982401e-07,
                1.0677027425913395e-06,
                3.0590219043949756e-07,
                8.315284240372801e-07,
                5.715003107655392e-07
            ],
            [
                3.5356259136692605e-05,
                6.144173134868593e-06,
                2.753569108453202e-05,
                1.8925143707303306e-05,
                1.7603425833860538e-06,
                1.892515500388139e-05,
                5.144221362094481e-05,
                1.2098656834195822e-06,
                2.4300252245746546e-05,
                1.760344052650207e-06
            ],
            [
                1.4738985483879434e-05,
                3.120191506868607e-05,
                0.000430556981033228,
                8.93969416907082e-06,
                0.00026119024581227305,
                8.481104126512805e-05,
                9.610244928336962e-05,
                1.3007126910294786e-05,
                4.5397857772875786e-05,
                3.5356267545276676e-05
            ],
            [
                1.0129990973871981e-05,
                1.0129994585694721e-05,
                6.962253755294928e-06,
                7.889260698453844e-06,
                4.785096775842062e-06,
                4.785093923516432e-06,
                8.939694163769713e-06,
                1.1478765387416494e-05,
                1.670142579763494e-05,
                4.222835456227946e-06
            ],
            [
                3.120190762537599e-05,
                NaN,
                0.00013982202258422746,
                4.0063701593909114e-05,
                1.0129987352284668e-05,
                0.00017952798425088865,
                0.00013982202109708564,
                2.7535704192176552e-05,
                2.7535697622726747e-05,
                5.8291286239325165e-05
            ],
            [
                4.006369210678142e-05,
                NaN,
                1.670142778941753e-05,
                5.422221549955578e-06,
                2.5612822101436936e-06,
                7.484620928658632e-05,
                3.535626746861868e-05,
                7.484625381503078e-05,
                NaN,
                2.4300240679453632e-05
            ],
            [
                2.1444958628814052e-05,
                1.8925141464512013e-05,
                1.8925145978942173e-05,
                1.6701419731029486e-05,
                1.8925152750692706e-05,
                1.8925154974965226e-05,
                1.6701417835367632e-05,
                2.4300234910365097e-05,
                1.9947294834796172e-06,
                2.1444950938445074e-05
            ],
            [
                2.5612819043220148e-06,
                NaN,
                8.939694163379449e-06,
                NaN,
                1.3007123803043302e-05,
                1.473898547706978e-05,
                4.222832436779288e-06,
                3.288747888478753e-06,
                6.962255417544426e-06,
                1.370957533534567e-06
            ],
            [
                1.1478764013398468e-05,
                2.430025227845516e-05,
                0.99937366593254,
                5.422219613511613e-06,
                5.144222579863794e-05,
                0.9998766054403034,
                1.3007125359034903e-05,
                0.9990889489039336,
                0.7772998508568416,
                0.9999038976080801
            ],
            [
                1.0129988562164371e-05,
                1.5534979397394734e-06,
                1.3709572067181944e-06,
                8.93969736929749e-06,
                2.260325105870372e-06,
                2.26032348933062e-06,
                8.939698432690187e-06,
                3.726639728262097e-06,
                1.5534975693792215e-06,
                1.2098652507847127e-06
            ],
            [
                1.0129995790839764e-05,
                7.889264458825275e-06,
                1.892514371900746e-05,
                1.1478764016780948e-05,
                1.3007134647006878e-05,
                2.1444948395559206e-05,
                6.144172402765906e-06,
                1.892515048889829e-05,
                4.539785775107612e-05,
                3.5356250660713247e-05
            ],
            [
                3.9278610659491504e-07,
                5.043474081831035e-07,
                1.3709572067680694e-06,
                1.9947304347098384e-06,
                1.067702869636298e-06,
                6.14417313533799e-06,
                1.760344052632596e-06,
                4.222835457794923e-06,
                6.475948753847607e-07,
                3.927862470790036e-07
            ],
            [
                8.315278293687262e-07,
                1.670142582300158e-05,
                2.9023133689924295e-06,
                1.209866116170145e-06,
                8.939693106987645e-06,
                1.0129988562422337e-05,
                1.670142781025767e-05,
                6.962259568889411e-06,
                5.422217030362759e-06,
                1.5534973840786793e-06
            ],
            [
                8.481102108148808e-05,
                1.1478773597390071e-05,
                0.0003799844836325963,
                2.4300252293748645e-05,
                5.8291265503797524e-05,
                3.53562506560829e-05,
                7.889261642578988e-06,
                2.1444945851269378e-05,
                2.14449432697669e-05,
                5.1442195174572826e-05
            ],
            [
                1.3007130007042183e-05,
                0.00010889686829120017,
                1.0129993392342568e-05,
                6.605214453603606e-05,
                5.829129298251882e-05,
                1.6701429796754513e-05,
                0.00010889692203379031,
                6.605214462205646e-05,
                7.889266337834933e-06,
                3.120190386019117e-05
            ],
            [
                9.422450428801213e-07,
                5.4222209035996685e-06,
                7.889264460461219e-06,
                1.7603440522163308e-06,
                5.4222202609325635e-06,
                2.9023133679867307e-06,
                NaN,
                2.9023109446375753e-06,
                2.1444958623509054e-05,
                NaN
            ],
            [
                3.5356259116499136e-05,
                0.00015843621589601344,
                0.0001795280291695786,
                0.0002611902068488645,
                8.481106140311264e-05,
                0.00023050665873194936,
                0.00023050668541271647,
                9.610239143125221e-05,
                0.00013982207367803525,
                8.48110512764275e-05
            ],
            [
                3.535625067177463e-05,
                NaN,
                0.00013982212296328436,
                NaN,
                2.144495861750193e-05,
                9.610240313954919e-05,
                5.144220741701067e-05,
                NaN,
                0.0001795278990890328,
                0.8354835289107309
            ],
            [
                1.8925150486764003e-05,
                4.539785235863304e-05,
                7.484620016504614e-05,
                0.00020342702129569682,
                9.610241469123354e-05,
                9.610242627088607e-05,
                5.8291286290217195e-05,
                1.3007131561425676e-05,
                6.605215240858454e-05,
                8.481105126717208e-05
            ]
        ]
    }
]