#include <array>
// constexpr std::array<double, 73> coeffs0 = {
// 0.00766925, -0.0152275, 0.000983599, -2.35601e-05, 0.0168686, -0.000402097,
// -1.23509e-05, 0.00304878, -0.00340812, 7.57372e-05, 0.0374575, 0.00152225,
// -3.16092e-05, -0.0182843, 0.00155329, -6.26147e-05, 0.00306138, 0.000619179,
// 5.35856e-05, -0.0297402, -0.000781041, -2.56154e-05, 0.0653388, 0.000568441,
// -1.98927e-05, -0.0510004, -0.000132666, 7.88617e-05, 0.00514666, 0.000112344,
// -3.38687e-05, 0.00312502, -0.000377664, -1.23875e-05, 0.0179219, -0.00102039,
// -2.87833e-05, -0.0572452, 0.000576139, 0.000102372, 0.010822, 0.0013362,
// 5.22881e-05, 0.0506703, -0.001513, -0.000220544, -0.0495059, 0.00137524,
// 0.000178251, 0.00482799, -0.00132573, -1.66445e-05, 0.007311, 0.00117387,
// -2.342e-05, -0.00292137, 0.00121374, -4.14102e-05, 0.0123776, -0.00174378,
// 9.87679e-06, -0.0542158, -0.000289026, 6.54544e-05, -0.0273884, 0.00197059,
// -6.18012e-05, 0.0105729, 0.00487263, -8.35412e-05, 1.05961, -0.00631764,
// 8.79278e-05,
// };
// constexpr std::array<double, 73> coeffs1 = {
// -0.0660465, -0.0523863, 0.00290234, -6.23062e-05, 0.0279323, -0.00143928, 1.73708e-06,
// 0.0141463, -0.005198, 0.00016202, 0.0780376, 0.00232198, -9.72459e-05,
// -0.0117064, 0.00263476, -0.000140647, -0.0189935, -5.90258e-05, 0.000143234, -0.0711243,
// -0.000468948, 3.09947e-05, 0.114186, -0.000111775, -0.00010362, -0.0354674, 0.00202552,
// 6.7354e-05, -0.0370191, -0.00161064, 2.4727e-05, 0.0286061, 0.000336308, -4.90408e-05,
// 0.0419965, -0.00197436, -2.92422e-05, -0.099989, 0.000189314, 9.84368e-05, 8.32877e-06,
// 0.00101646, 0.000104693, 0.0617418, 0.00130221, -0.000305534, -0.0498766, -0.000118494,
// 0.000218671, -0.0212647, -0.000491674, 8.94399e-05, 0.0236246, 0.000679779,
// -0.000143165, 0.0275308, 0.0013992, -1.25276e-05, 0.0196942, -0.00182278, -1.17582e-05,
// -0.0791713, -0.00126338, 9.73349e-05, -0.0220166, 0.0032494, -8.13857e-05, -0.0384851,
// 0.00864635, -0.000203234, 1.10878, -0.0113024, 0.000203164,
// };
// constexpr std::array<double, 73> coeffs2 = {
// -0.159233, -0.0778349, 0.00463196, -9.9843e-05, 0.00638828, -0.00197854, 1.88567e-05,
// 0.00192733, -0.00619822, 0.000189395, 0.111196, 0.000803877, -4.31455e-05, -0.0105218,
// 0.00370532, -0.000155689, 0.0404681, 0.000687006, 6.61611e-05, -0.103385, -0.000299858,
// 7.78533e-05, 0.105869, 6.02967e-05, -7.85276e-05, -0.0371411, 0.00179115, 2.57414e-05,
// -0.0202491, -0.000842176, 4.49825e-05, 0.0207288, -5.3584e-06, -5.38268e-05, 0.0521417,
// -0.00273558, -7.37968e-05, -0.0989728, 0.00027777, 0.000150667, -0.0351368, 0.000914818,
// 0.000122424, 0.0717416, 0.00143801, -0.000319664, -0.028557, -5.4664e-05, 0.000176168,
// -0.0774796, -0.000296889, 0.00014111, 0.0500274, 0.00130991, -0.000120924, 0.0332956,
// 0.00257536, -5.51853e-05, 0.0944641, -0.00294156, -9.16695e-05, -0.0728534, -0.00243153,
// 0.000205147, -0.08279, 0.0045601, -9.55065e-05, -0.0290182, 0.00976638, -0.000329404,
// 1.09715, -0.0138122, 0.000293621,
// };
// constexpr std::array<double, 73> coeffs3 = {
// -0.282158, -0.0696095, 0.00339944, -7.94632e-05, -0.014656, -0.000814109,
// -2.8753e-05, -0.0829653, -0.00661034, 0.000282699, 0.147478, 0.000676931,
// -7.01854e-05, 0.0747956, 0.00460475, -0.000238705, 0.0211699, 0.000456073, 8.84238e-05,
// -0.13225, -0.00124869, 0.00021389, 0.130225, 0.00120772, -0.000132048, -0.0303239,
// 0.00227197, -7.86832e-05, -0.00260217, -0.00127373, 7.17083e-05, -0.027095, 0.00156907,
// -5.65716e-05, 0.109969, -0.00462967, -5.0313e-05, -0.141695, 0.000339583, 0.000157553,
// -0.0456829, 0.00291742, 0.000140348, 0.102027, -0.00104496, -0.00038681, -0.0772817,
// 0.000190304, 0.000308533, -0.0831058, 0.000619507, 0.000101607, 0.0920874, 0.00305422,
// -0.000206923, 0.0770148, -5.64646e-05, 1.70059e-05, 0.119889, -0.00266125, -0.000162711,
// -0.0582026, -0.00289234, 0.000210363, -0.126028, 0.00679545, -7.28566e-05, -0.0781218,
// 0.0089482, -0.000307205, 1.1104, -0.0149193, 0.000260931,
// };
// constexpr std::array<double, 73> coeffs4 = {
// -0.385888, -0.0684688, 0.0027519, -6.53062e-05, -0.0532685, 0.000852822,
// -6.53579e-05, -0.0833564, -0.00894833, 0.00035945, 0.0787293, 0.00217242,
// -8.48793e-05, 0.0898204, 0.00494615, -0.00028147, 0.102182, 0.000594155, 7.25099e-05,
// -0.0943494, -0.00251974, 0.000260518, 0.138982, 0.0013727, -0.000150805, -0.122199,
// 0.00407552, 9.75668e-06, 0.0832472, -0.00101584, -0.000128874, -0.0803602, 0.000723537,
// 0.000100428, 0.121549, -0.00427706, -7.56763e-05, -0.139427, 0.00101135, 0.000198254,
// -0.0235968, 0.002117, 2.84707e-05, 0.0572549, -0.0015671, -0.000200535, -0.0634509,
// 0.000781027, 0.000159382, -0.0925803, 0.00135629, 9.60912e-05, 0.133475, 0.00333472,
// -0.000209912, 0.12694, -0.00215413, 8.79664e-05, 0.145015, -0.00228078, -0.000192411,
// -0.0716851, -0.00243203, 0.000126594, -0.0988659, 0.00589692, -5.54681e-05, -0.127094,
// 0.0128553, -0.000399106, 1.0559, -0.0188179, 0.000393127,
// };
// constexpr std::array<double, 73> coeffs5 = {
// -0.46506, -0.0586907, 0.00132253, -4.53477e-05, -0.042409, 0.00287138,
// -0.000143297, -0.0973444, -0.00851252, 0.000375566, 0.000459652, 0.000484058,
// -1.48065e-05, 0.0314459, 0.0037391, -0.000244219, 0.152505, 0.00117272, 8.07798e-05,
// 0.00915874, -0.000274203, 0.00014601, 0.0886509, -0.000814426, -2.47952e-05, -0.121128,
// 0.00761951, -7.37067e-05, 0.0773576, -0.00356234, -9.67506e-05, -0.0660973, 0.00100002,
// 0.00011193, 0.139157, -0.00384951, -0.000198069, -0.116295, 0.0019349, 0.000259189,
// -0.0546106, 0.00036712, 2.36302e-05, 0.019563, -0.00114166, -0.000122497, -0.0430367,
// 0.00161671, 0.000109029, -0.0402775, 0.00184552, 5.86724e-05, 0.220533, 0.00324397,
// -0.000229226, 0.0793501, -0.0053041, 0.000213201, 0.11471, 0.000956578, -0.000213552,
// -0.0556105, -0.00287486, 0.000106274, -0.0513184, 0.00714198, -0.000190013, -0.106074,
// 0.0122207, -0.000363314, 0.93374, -0.020158, 0.000447021,
// };
// constexpr std::array<double, 73> coeffs6 = {
// -0.525526, -0.0724773, 0.000148522, -4.79879e-05, -0.0383199, 0.00365391, -0.000132362,
// -0.087597, -0.00717153, 0.000364359, -0.0293866, -0.0013004, -2.02765e-05, -0.0296842,
// 0.00526655, -0.000224975, 0.143921, -0.00252698, 0.000109647, 0.0836788, 0.00324218,
// 0.000109069, 0.0544878, -0.00285698, 0.000109001, -0.103565, 0.0103274, -0.000230855,
// 0.114653, -0.00517161, -5.38674e-05, -0.0793052, 0.00176543, 0.000131211, 0.142502,
// -0.00212922, -0.000248802, -0.0976414, -0.000699901, 0.000245839, -0.0953563, 0.000119718,
// 9.35412e-05, 0.00043999, 0.00135412, -0.000126349, -0.0086474, 0.000806402, 0.000143736,
// 0.126062, 0.0018905, -0.000176986, 0.151144, 0.00184759, -8.1935e-05, 0.0212118,
// -0.00434886, 0.000292262, 0.104912, 0.00117061, -0.00022459, -0.00610418, -0.00216656,
// 3.40687e-05, -0.0413439, 0.00649343, -0.000188027, -0.0894272, 0.0131026, -0.000386172,
// 0.84533, -0.0217109, 0.000469793,
// };
// constexpr std::array<double, 73> coeffs7 = {
// -0.633589, -0.0658289, -0.000244531, -7.00149e-05, -0.019621, 0.00484468,
// -0.000136132, -0.0984868, -0.00922368, 0.000449105, -0.0416755, -0.000188331,
// -6.33007e-05, -0.0561148, 0.00804612, -0.000296994, 0.114408, -0.00632052, 0.000210889,
// 0.0639793, 0.00213261, 4.05895e-05, 0.0602189, -0.00188264, 0.000201156, -0.115787,
// 0.01185, -0.000221628, 0.191699, -0.00396191, -0.000177934, -0.116619, 0.000732679,
// 0.000207608, 0.170775, -0.00304258, -0.000298362, -0.0879719, -0.000950724, 0.00024087,
// -0.101429, 0.00056935, 0.000152442, 0.0122781, 0.00306445, -0.0001561, 0.0634574,
// 0.000573269, 7.78119e-05, 0.181017, 0.00161008, -0.000215533, 0.0559691, 0.00153896,
// -1.3166e-05, -0.00795821, -0.00450346, 0.000346559, 0.14575, 0.00162777, -0.000252211,
// -0.0473803, -0.00090856, 5.87936e-05, 0.0243375, 0.00559234, -0.000232322, -0.11863,
// 0.0138848, -0.00037664, 0.801012, -0.0238063, 0.000468061,
// };
// constexpr std::array<double, 73> coeffs8 = {
// -0.726605, -0.0955604, -0.00062043, -6.17374e-05, -0.0156778, 0.00581542,
// -0.000138782, -0.0656898, -0.00928287, 0.000425549, -0.0457586, 0.000497694,
// -6.96689e-05, -0.0902655, 0.00702086, -0.000259051, 0.116809, -0.00686549,
// 0.000241154, 0.0736266, 0.00131242, -5.90614e-05, -0.0114263, -0.0044023,
// 0.000265126, -0.0574285, 0.0145486, -0.000238415, 0.203171, -0.00278737,
// -0.000194126, -0.136213, -0.000466055, 0.000257898, 0.212159, -0.00140743,
// -0.000385131, -0.0946765, -0.0017821, 0.000277827, -0.112356, 0.00178981,
// 0.000262862, 0.0817634, 0.00383957, -0.000248703, 0.0620299, 0.000197015,
// 5.27358e-05, 0.229014, 0.000610261, -0.000287512, -0.050794, 0.00180371,
// 0.000118202, 0.0177192, -0.00547718, 0.000353153, 0.124094, 0.00269125,
// -0.000224985, -0.0423416, -0.000233209, 3.19159e-05, 0.0494855, 0.0062734,
// -0.000283506, -0.0908049, 0.0122724, -0.000339173, 0.736591, -0.0240808,
// 0.000448602,
// };
// constexpr std::array<double, 73> coeffs9 = {
// -0.810086, -0.0784208, -0.000775006, -7.08006e-05, -0.041122, 0.00655653,
// -0.000171176, -0.0149588, -0.0107369, 0.000446826, -0.117483, 0.000944377,
// -1.76855e-05, -0.076214, 0.00939985, -0.00034963, 0.124092, -0.0102122,
// 0.000356311, 0.0558894, 0.00260939, -0.000131136, -0.032602, -0.00682393,
// 0.000285506, -0.0302991, 0.015352, -0.000247062, 0.207471, -0.00208218,
// -0.00022558, -0.159028, 0.000353279, 0.000329158, 0.26385, -0.00369733,
// -0.000402215, -0.112318, 0.00103473, 0.000214975, -0.11044, 0.00218066,
// 0.000344431, 0.11368, 0.0039149, -0.000329535, 0.0797381, 0.000315781,
// 0.000107519, 0.225746, -0.000942574, -0.000364835, -0.111084, 0.00345116,
// 0.000262185, 0.0698713, -0.00733177, 0.000300302, 0.109315, 0.00406603,
// -0.000232152, -0.060813, -0.000517889, 7.59956e-05, 0.057497, 0.00658956,
// -0.000287847, -0.0639832, 0.013884, -0.000420062, 0.689174, -0.0258611,
// 0.000476182,
// };
// constexpr std::array<double, 73> coeffs10 = {
// -0.905451, -0.0620926, -0.00140601, -7.89076e-05, -0.0666362, 0.00703395,
// -0.000139023, 0.035458, -0.0103143, 0.000370719, -0.157153, -0.000113349, 4.4546e-05,
// -0.0683334, 0.0108939, -0.0003691, 0.0727486, -0.0110365, 0.000404426, 0.0946822,
// 0.00321509, -0.00021939, -0.0510535, -0.00850332, 0.000327262, 0.032021, 0.0149411,
// -0.000308556, 0.127698, -0.0010127, -0.000198873, -0.140662, -0.000271593,
// 0.00037994, 0.300537, -0.00338427, -0.000448074, -0.130726, 0.0004628, 0.00022798,
// -0.107391, 0.00435878, 0.000397438, 0.136625, 0.00416413, -0.000362611, 0.1035,
// -0.000268459, 4.44048e-05, 0.222274, -0.00129316, -0.000370993, -0.152862, 0.00315919,
// 0.000343944, 0.104278, -0.00697675, 0.000262785, 0.107738, 0.00340461, -0.000199289,
// -0.0588311, 0.000776607, 5.2795e-05, -0.00296248, 0.00644316, -0.000219184,
// -0.00185655, 0.0151465, -0.000523986, 0.648694, -0.0276708, 0.000523509,
// };
// constexpr std::array<double, 73> coeffs11 = {
// -0.991743, -0.0250385, -0.00157808, -0.000122033, -0.0836214, 0.00597695,
// -7.79421e-05, 0.00958369, -0.00852214, 0.000338588, -0.14841, -0.00197136,
// 0.000104224, -0.0726166, 0.0133226, -0.000432772, 0.0510559, -0.0117227, 0.000418028,
// 0.118969, 0.00272181, -0.000258616, -0.0832931, -0.00910047, 0.000422102, 0.0509364,
// 0.014764, -0.000363426, 0.130695, -0.000323092, -0.000231584, -0.169126, -0.00153075,
// 0.00049807, 0.358308, -0.00302922, -0.000560802, -0.154834, 0.00123517, 0.000291464,
// -0.10321, 0.0039686, 0.000388845, 0.159834, 0.0046293, -0.000429312, 0.0882609,
// 0.000268662, 0.000146947, 0.26756, -0.00206309, -0.000554544, -0.203089, 0.00304674,
// 0.000543682, 0.108214, -0.00575747, 0.00019946, 0.104434, 0.00311171, -0.000189347,
// -0.0135981, -0.000184924, 5.27834e-05, -0.0611654, 0.0065887, -0.000190481,
// 0.00983708, 0.0177139, -0.00059873, 0.642704, -0.0296153, 0.000545273,
// };
//constexpr std::array<double, 49> coeffs0 = {
// 0.022543, -0.027511, 0.000763997, 0.0188262, -0.000812318, 0.0246511, -0.00196012,
// 0.0283525, 0.0010092, -0.0406867, 0.000943607, 0.0270802, 0.000760175, -0.0391367,
// -0.00119283, 0.0559696, 0.000604626, -0.0223533, 0.000160252, -0.00997814, 0.000301821,
// -0.00158171, -0.000369651, 0.0117059, -0.0010222, -0.0256329, -0.000151605, 0.028227,
// 0.00136561, -0.0218874, -0.000726999, 0.0090311, 0.00175633, -0.0058602, -0.00150267,
// 0.00265082, 0.000855115, -0.0113589, 0.000690687, 0.00767067, -0.00126208, -0.0215403,
// 6.57858e-05, -0.0538931, 0.00144812, -0.0227491, 0.00367035, 1.09384, -0.00502064,
//};
//constexpr std::array<double, 49> coeffs1 = {
// -0.0500304, -0.0784427, 0.00202029, 0.0411009, -0.00186865, 0.0603755, -0.00217621,
// 0.0451726, 0.00101282, -0.0660611, 0.00142127, 0.0464325, 0.000306635, -0.0574079,
// -0.00053684, 0.0695427, -0.000326564, -0.0113549, 0.00237425, -0.0339125, -0.00138881,
// 0.013226, 0.000159835, 0.0362954, -0.0015377, -0.069686, -0.000884425, 0.0300344,
// 0.00103416, -0.033275, 0.00211227, 0.0178704, 0.000955992, 0.00912139, -0.00132735,
// -0.0307867, 0.000549752, 0.0406642, 0.000459768, -0.00414775, -0.000796374, -0.0261993,
// -0.000931731, -0.058446, 0.00262958, -0.116415, 0.00574709, 1.18428, -0.00834257,
//};
//constexpr std::array<double, 49> coeffs2 = {
// -0.150097, -0.116103, 0.00306139, 0.0229186, -0.00211907, 0.0599114, -0.0028016,
// 0.102021, -6.34075e-05, -0.067882, 0.00239128, 0.0722326, 0.00052537, -0.0694839,
// -0.000413285, 0.0725807, -7.47365e-05, -0.0345742, 0.00245164, -0.00926546, -0.000712676,
// 0.00705657, -0.000513209, 0.0284724, -0.00196225, -0.0491966, -0.00097664, -0.00354554,
// 0.000802629, -0.0260696, 0.00243778, 0.0268306, 0.00144086, -0.0308298, -0.00121841,
// 0.00718923, 0.000879702, 0.0353923, 0.00140721, 0.0246155, -0.00144312, 0.0385046,
// -0.00194237, -0.131574, 0.00405098, -0.155622, 0.00514051, 1.20493, -0.00947374,
//};
//constexpr std::array<double, 49> coeffs3 = {
// -0.279483, -0.094669, 0.00187516, -0.0172078, -0.00176599, 0.00894394, -0.00178365,
// 0.123346, -0.000455721, -0.00873991, 0.00234544, 0.0596367, 0.000384451, -0.0428982,
// -0.000473398, 0.0814407, 0.00052421, -0.0783028, 0.00353215, 0.0167051, -0.00113409,
// -0.0330728, 0.000360751, 0.092818, -0.00353024, -0.0910229, -0.00110632, -0.00699513,
// 0.00267313, -0.0132511, 0.000198426, 0.0155017, 0.0018565, -0.0511911, -0.000588625,
// 0.0179016, 0.00282692, 0.113183, -0.0012731, 0.0196715, -0.0011316, 0.0524384,
// -0.00230951, -0.16287, 0.00625441, -0.200868, 0.00475429, 1.20895, -0.0111146,
//};
//constexpr std::array<double, 49> coeffs4 = {
// -0.414289, -0.0845413, 0.0011929, -0.0631948, -0.00100482, 0.0314292, -0.00278693,
// 0.0436246, 0.00106998, -0.0138298, 0.0023791, 0.140755, 0.000117639, 0.0170829,
// -0.00154347, 0.0765569, 0.000898132, -0.134036, 0.00506675, 0.0245579, -0.000209007,
// -0.0263345, -0.00138769, 0.0932441, -0.00296536, -0.0713507, -0.000615718, -0.0252293,
// 0.00233984, 0.00506986, -0.000574096, -0.0177222, 0.0022801, -0.0675111, 0.000590347,
// 0.0597137, 0.00317227, 0.195544, -0.00360039, 0.0318466, -0.000437166, -0.000149131,
// -0.00212426, -0.128385, 0.00547392, -0.283101, 0.00723913, 1.20255, -0.0133058,
//};
//constexpr std::array<double, 49> coeffs5 = {
// -0.501131, -0.0580507, -0.000170051, -0.0908313, 0.000106478, 0.0225907, -0.00205818,
// -0.00252855, -1.26793e-05, -0.061109, 0.00146843, 0.186964, 0.00118814, 0.0831361,
// -0.000128191, 0.0754824, -0.00126375, -0.163387, 0.00871604, 0.0317954, -0.00291277,
// -0.00577566, -0.00139647, 0.0616295, -0.00183708, -0.0268776, 0.000384035, -0.0580559,
// 0.000361168, -0.00617749, -0.00021801, -0.00773913, 0.00261673, -0.0319237, 0.00138098,
// 0.139652, 0.00345682, 0.194596, -0.00664415, -0.00504429, 0.00240272, 0.014665,
// -0.00249736, -0.144766, 0.00577362, -0.251718, 0.00710117, 1.10538, -0.0141407,
//};
//constexpr std::array<double, 49> coeffs6 = {
// -0.569774, -0.0609769, -0.00176361, -0.0929124, 0.00135238, 0.0257322, -0.000638331,
// -0.0322718, -0.00192054, -0.113575, 0.00268671, 0.181068, -0.00188113, 0.146672,
// 0.00330486, 0.0960851, -0.00315203, -0.205336, 0.0113162, 0.0836048, -0.00453817,
// -0.00586502, -0.00117951, 0.0369521, 0.000327893, -0.0109597, -0.00188863, -0.0692645,
// -0.000562149, -0.0320856, 0.00282961, 0.0497573, 0.000354106, 0.043471, 0.00263981,
// 0.129673, 0.00227374, 0.157985, -0.00546917, -0.0107492, 0.00204358, 0.0294212,
// -0.00170326, -0.130394, 0.00509656, -0.252522, 0.00797526, 1.03104, -0.0155983,
//};
//constexpr std::array<double, 49> coeffs7 = {
// -0.688881, -0.0583025, -0.00265298, -0.0766917, 0.00250482, 0.0386964, -0.0011438,
// -0.0525033, -0.00171064, -0.171245, 0.00467799, 0.187613, -0.00468498, 0.100255,
// 0.0020417, 0.137173, -0.00170604, -0.208889, 0.0122847, 0.111285, -0.00301769,
// -0.0147914, -0.00269399, 0.0486051, -0.000151161, -0.00368428, -0.00220378, -0.0556776,
// -0.000169065, -0.0349085, 0.00452972, 0.109979, -0.000458162, 0.0866734, 0.00271676,
// 0.0546868, 0.00237794, 0.147106, -0.00551774, 0.020073, 0.00215743, 0.000133408,
// -0.000218561, -0.0802195, 0.0038282, -0.286176, 0.00913567, 0.98971, -0.0178617,
//};
//constexpr std::array<double, 49> coeffs8 = {
// -0.76317, -0.081431, -0.00301226, -0.0766555, 0.0036348, 0.0591248, -0.00136179,
// -0.0535517, -0.00120719, -0.194276, 0.00384713, 0.199264, -0.00472985, 0.0724088,
// 0.000576196, 0.0901514, -0.00396949, -0.154477, 0.0148655, 0.116832, -0.00165977,
// -0.01689, -0.00411904, 0.0612447, 0.00162672, -0.00191459, -0.00279223, -0.0249055,
// 0.000222174, -0.00367628, 0.00596667, 0.109785, -0.00144756, 0.105767, 0.0025404,
// -0.00407924, 0.00248553, 0.168845, -0.00659624, 0.0178384, 0.00268908, -0.00952315,
// 0.000686289, -0.0725688, 0.00411358, -0.251061, 0.00826029, 0.923033, -0.0185071,
//};
//constexpr std::array<double, 49> coeffs9 = {
// -0.822531, -0.0712378, -0.00313101, -0.108902, 0.00380999, 0.111512, -0.0021371,
// -0.0945075, -0.000532056, -0.224572, 0.00542104, 0.260602, -0.00747028, 0.0183687,
// 0.00171695, 0.0808101, -0.00637411, -0.132876, 0.0156997, 0.108437, -0.000795661,
// -0.0127316, -0.00358653, 0.107174, -0.0006072, -0.0426276, 0.000399772, 0.00723423,
// 7.06816e-05, -0.00312098, 0.00637031, 0.151212, -0.00163771, 0.072658, 0.00162029,
// -0.00982919, 0.00372867, 0.197455, -0.00864862, -0.00013303, 0.00382212, -0.00845755,
// 0.000809484, -0.0621978, 0.00447161, -0.262596, 0.00901561, 0.889328, -0.0198217,
//};
//constexpr std::array<double, 49> coeffs10 = {
// -0.909713, -0.0548256, -0.00403347, -0.127377, 0.00503493, 0.133105, -0.00281644,
// -0.104179, -0.000981371, -0.235574, 0.00703771, 0.236287, -0.00811245, 0.0186884,
// 0.00191514, 0.0826825, -0.00796688, -0.0967704, 0.0154384, 0.0393416, 0.000396565,
// 0.0243417, -0.004513, 0.128051, -0.000226333, -0.0579554, 3.35462e-06, 0.0286993,
// 0.0018972, 0.0045047, 0.0069718, 0.159399, -0.00261737, 0.0659868, 0.0016418,
// -0.0181462, 0.00322013, 0.211427, -0.00823299, 0.012687, 0.00316808, -0.0176033,
// 0.00193481, -0.0885832, 0.00501, -0.242723, 0.0089834, 0.865588, -0.0209022,
//};
//constexpr std::array<double, 49> coeffs11 = {
// -0.982919, -0.0312033, -0.00492114, -0.122954, 0.00496899, 0.0907386, -0.00124363,
// -0.0659749, -0.00236144, -0.267646, 0.00878218, 0.221023, -0.00873823, 0.0246664,
// 0.00119215, 0.0917497, -0.00825055, -0.103667, 0.0154737, 0.0302442, 0.00118764,
// 0.0414964, -0.00638103, 0.143632, 0.000462449, -0.0610465, 0.000741319, 0.0346026,
// 0.0013265, -0.00076253, 0.00811984, 0.185666, -0.00297452, 0.0379137, 0.00193336,
// 0.014719, 0.00261795, 0.186014, -0.00729897, 0.0148214, 0.00277203, 0.025097,
// 0.00122791, -0.131459, 0.00548501, -0.26672, 0.0107603, 0.872948, -0.022576,
//};
constexpr std::array<double, 325> coeffs0 = {0.0192062,-0.0185192,0.0257993,0.0119561,-0.0229226,0.00140825,0.0306359,-0.0430086,0.0582909,-0.0157608,-0.0257299,0.0272466,0.0416862,-0.105623,0.0284596,0.0114961,0.00972879,-0.017979,0.0171265,-0.0528794,0.0283911,-0.020313,-0.0444713,-0.03119,1.10785,0.00608935,-0.0290731,0.0131128,0.00989818,-0.00389008,0.00261744,-0.032802,0.0299196,-0.00734099,-0.021134,0.0297238,-0.0150827,0.0219274,0.0102967,-0.0144799,-0.0342574,0.0128628,0.0292916,0.0114733,-0.0325169,-0.0130085,0.0275742,-0.0094596,0.0041191,0.0253606,-0.0282587,0.016149,-0.026188,-0.00560515,0.0260305,0.0106024,-0.0244225,0.0400686,-0.050116,0.0247905,0.0211444,-0.0461396,0.020427,0.0327708,-0.0338642,0.0107382,-0.0340288,0.0285748,0.0400071,-0.0769416,0.0365497,-0.00404113,0.0197403,-0.025747,0.0205178,0.00262411,0.00258957,-0.0471779,0.0452578,-0.043941,0.0407137,-0.0130537,-0.0336246,0.0135199,-0.0306457,0.0301334,0.034818,-0.0543979,0.0434526,-0.00268,-0.00748029,0.0312329,-0.0361898,-0.00204454,-0.00489839,0.0177563,-0.0230074,0.0175449,0.0317539,-0.041933,0.0488237,-0.0710616,0.0253319,-0.00611991,0.0604851,-0.0262686,0.0014128,-0.0224069,0.023109,-0.0687476,0.0720247,-0.0706239,0.0376675,-0.0238275,0.0317591,-0.00177353,0.0128114,-0.038833,-0.0106588,0.034366,-0.0179772,0.0671385,-0.0427222,-0.00551207,0.000198384,0.0044452,0.0135947,-0.0154217,-0.0303438,0.0754837,-0.0842888,0.0593669,-0.0360651,0.0568196,-0.0440451,0.010643,-0.0167143,0.0199945,-0.0333819,0.0311437,-0.0493225,0.0362697,0.00646682,-0.0747225,0.0902413,-0.0865059,0.0631187,0.00953441,-0.0212906,0.0452059,-0.0682263,0.0454407,-0.0553256,0.0470578,0.0174936,0.00450283,0.00222522,-0.0683299,0.0788578,-0.0162993,-0.0253373,0.0532016,-0.0741466,0.0875537,-0.0863921,0.0353312,-0.00347929,-0.0170561,0.0601226,-0.0604794,0.0668511,-0.030847,-0.0130572,0.0135963,0.041415,-0.0858474,0.048025,0.0134275,-0.0454634,0.0709275,-0.0635011,0.0443248,-0.0245032,0.000620258,-0.0296584,0.0706701,-0.0424451,-0.028505,0.00351254,-0.00603171,-0.0150121,0.0629454,-0.0689079,0.0164908,0.0549745,-0.0541637,-0.014031,0.0263551,-0.00614791,0.0259214,-0.0126217,-0.042179,0.0483527,-0.0338271,0.0363884,0.010681,-0.0358995,0.0588149,-0.0202001,-0.0184919,-0.0103826,0.0304017,-0.0450025,0.0458894,-0.0299858,0.0148806,-0.0400495,0.0771377,0.0138473,-0.0571949,0.00687124,-0.0333006,0.052276,-0.0204222,0.00147442,-0.00648247,0.0353086,-0.0462828,-0.00243768,0.0294997,0.0483413,-0.109606,0.023216,0.0273407,0.00971219,-0.0565648,-0.00103877,0.0203947,0.0746366,-0.0943063,0.0427226,0.0168936,0.00909723,-0.0784736,0.0817664,-0.0123028,-0.028509,0.0142771,0.0450902,-0.0754188,-0.0156305,0.0646095,-0.0274168,-0.0120048,-0.0280474,0.0171899,-0.00865466,-0.0044118,0.0329288,-0.0370728,0.0954514,-0.0651606,-0.00694297,0.0336043,-0.0120215,0.000859073,0.026569,-0.0330528,0.016591,-0.0101738,-0.020018,0.0202293,0.000684159,-0.026401,-0.00943008,0.0327873,0.0151717,0.0119935,-0.0162152,-0.0102081,-0.0014354,0.0234851,-0.018633,0.0326313,0.0185208,-0.0750749,-0.0114043,-0.0199927,0.0526551,-0.00979218,0.0194067,-0.0205133,-0.0605627,0.10077,-0.0192788,0.0431592,-0.0469592,-0.00908924,0.0170069,0.0125425,-0.0429587,0.0267874,-0.0291859,0.0202775,-0.00528012,0.00806371,-0.0183288,0.00252239,0.0138707,-0.00473322,-0.00450738,0.0281287,-0.016968,0.0110628,-0.0193033,-0.0270501,0.0777006,-0.0352521,0.0011031,-0.04057,-0.00145859,0.031659,0.0134934,0.00268986,-0.0205979,};
constexpr std::array<double, 325> coeffs1 = {-0.047022,-0.0695284,0.0404465,0.0668447,-0.0230988,-0.0293616,0.0347121,-0.0306401,0.0566708,-0.0133579,-0.033486,0.0466477,0.0642257,-0.119174,0.0327077,-0.0401439,0.0155706,0.01171,-0.00863252,-0.0538101,0.0522898,-0.0268347,-0.0493969,-0.128626,1.20933,0.0055623,-0.0332582,0.0499464,-0.0456225,0.0362716,0.0167423,-0.0946163,0.0396743,0.0202402,0.00707692,-0.0300946,-0.0188158,0.0639196,-0.0114702,0.00585979,-0.0576526,0.0150315,0.0563322,-0.0200659,-0.00146217,-0.0117031,-0.000790942,-0.027587,0.0364536,0.0346257,-0.0822218,0.0758485,-0.0533876,-0.0421987,0.115826,-0.00629097,-0.0599781,0.0106282,-0.00593892,0.0468391,-0.0544153,0.0505687,-0.0262839,0.060266,-0.0702335,-0.00484594,0.0173042,-0.0317782,0.0258705,0.00149129,0.0279849,-0.0326619,0.0350779,-0.0367955,0.00504081,0.0341035,-0.0289218,-0.0410005,0.0594966,-0.0551381,0.0571869,-0.00709407,-0.0279256,-0.0607407,-0.000722255,0.0345805,0.0424355,-0.0359708,0.0254136,0.0248184,0.00604884,-0.0485923,0.0501854,-0.0451448,-0.0058945,0.0446636,-0.0434448,0.0164058,0.0202066,-0.0343758,0.0736837,-0.0983914,0.0344381,0.00797868,0.0738163,-0.0784693,0.0198548,0.0173581,-0.0306872,-0.0484561,0.0535735,-0.0467807,0.071008,-0.149892,0.120299,-0.0185432,0.024824,-0.0501962,0.0128977,0.0326702,-0.0341228,0.0884149,-0.0734269,0.0189196,-0.0373008,0.0604049,-0.0117952,-0.0193067,-0.0297294,0.0561567,-0.0343767,-0.000436279,0.00629743,0.0726321,-0.073406,0.00310064,-0.0123274,0.0597906,-0.0709299,0.0289219,-0.0293679,0.00149715,0.00393442,-0.0379392,0.100015,-0.10849,0.0340309,0.0583464,-0.0522752,0.039578,-0.0179832,-0.0475877,0.0344144,0.0186331,0.041002,-0.0707877,0.016053,-0.0378187,0.0549883,0.0218555,-0.065784,0.0652188,-0.101417,0.133109,-0.0673604,-0.0359172,0.0748859,-0.0957886,0.065187,0.0211839,0.0638212,-0.0693766,-0.000535996,0.0235925,0.0204695,-0.0809625,0.0536919,0.0345564,-0.0546894,0.0534953,-0.0648907,0.038533,0.0141216,-0.0459615,0.0295221,0.0512616,-0.0360802,-0.135545,0.0829272,-0.000710524,-0.00201367,0.0305183,-0.0495912,0.0247515,0.0438684,-0.0503014,-0.0338044,0.0358349,0.0136732,0.0323231,-0.0635777,-0.0152437,0.0254543,0.037951,-0.00877849,-0.015624,0.0508576,0.00760502,-0.0285518,-0.017315,0.0131482,0.0531819,-0.0767811,0.0119144,0.00435618,0.0700296,-0.118892,0.0519546,0.0685766,-0.0726346,-0.0291988,-0.0343434,0.0870696,-0.0493557,0.00700304,-0.0340112,0.0711729,-0.0204681,-0.0430637,-0.0156626,0.1533,-0.118818,-0.053248,0.0712638,0.0290006,-0.0896386,0.0684246,-0.00232573,0.0235836,-0.0663841,0.00168021,0.079916,0.00799254,-0.141901,0.152677,-0.0827066,0.00300945,0.0273573,0.00311395,-0.0799338,0.0349662,0.013092,0.0463354,-0.0922197,-0.0125299,0.0562551,-0.0742413,0.0917601,-0.0165741,-0.0507764,0.122082,-0.0524964,0.034286,-0.0458812,0.0155306,0.0476146,-0.04451,0.0174254,0.0012702,-0.0245418,-0.0164791,-0.00344172,-0.0173553,0.00259805,0.00212184,-0.0509726,0.0937081,-0.0327763,0.0284493,-0.0115681,0.0106805,-0.00665155,0.0226296,-0.0157242,0.0886457,-0.103172,-0.016218,-0.0367556,0.0554193,0.0166123,-0.0415605,0.0396054,-0.0955984,0.0803634,0.00344382,0.0432866,-0.0420873,0.00790374,-0.0196993,0.0484639,-0.0271073,0.0490643,-0.096323,0.0481674,0.00604307,-0.00393182,-0.0399945,-0.0180939,0.0644683,-0.0231454,-0.0138573,0.0395261,-0.0127816,0.00390316,-0.00934712,-0.016125,0.0572356,-0.0199363,-0.0129745,-0.0346831,0.0226972,0.000430455,-0.0336765,0.0712218,-0.0410281,};
constexpr std::array<double, 325> coeffs2 = {-0.146414,-0.119215,0.0496369,0.0669968,0.012497,-0.0206188,0.050756,-0.0403237,0.0222918,0.0224411,-0.0454153,0.0639322,0.0856614,-0.109462,-0.0423396,-0.00978454,0.0208585,-0.0126645,0.00557887,-0.0245708,0.0439237,0.032557,-0.112761,-0.200732,1.26666,0.00564954,-0.0356392,0.0539093,-0.0534535,0.0533545,-0.0163311,-0.0467078,0.0290657,-0.0350848,0.0203543,-0.0163581,-0.0106158,0.119487,-0.0889308,0.0616476,-0.0862988,0.0111735,0.0660094,-0.0518553,0.0251142,-0.0261929,-0.0317476,0.07891,-0.023634,0.0474728,-0.0956662,0.0686436,-0.0931804,0.0302424,0.0621832,-0.0150868,0.0280331,-0.0540969,0.0184314,0.0436952,-0.154715,0.160704,-0.0608154,0.0489511,-0.0508478,0.0108451,-0.00586586,0.00311824,-0.0126722,0.0917454,-0.0916401,0.006639,0.0410757,-0.0388904,0.0403554,-0.0367092,-0.0047668,-0.0421288,0.0878063,-0.00967592,-0.0593894,0.0410631,-0.00100731,-0.0613363,-0.0525809,0.0677062,0.0277638,-0.0448057,0.0701858,-0.0256849,0.0573051,-0.0636909,0.0411635,-0.0463761,0.0130222,0.0161593,-0.0188791,0.0217562,0.0593039,-0.153197,0.0670847,0.0392585,-0.0680543,0.0428938,0.0610161,-0.0450519,0.00274943,0.0194291,-0.0273118,-0.0554554,0.0539368,-0.060754,0.0440954,-0.150148,0.151814,-0.0196079,0.0635974,-0.0957527,-0.0193774,0.109829,-0.0289316,0.0417049,-0.0560078,0.0155609,-0.0283506,0.0183868,0.059448,-0.0448405,-0.0614249,0.108132,-0.136733,0.0818637,0.0178584,0.0732399,-0.087352,-0.0254102,0.0113779,0.0926519,-0.09592,0.0513168,-0.0596276,0.0462698,-0.0297679,-0.0833285,0.181019,-0.209155,0.0881543,0.0941409,-0.118187,0.115952,-0.080591,-0.0729243,0.0934019,-0.00116617,0.049156,-0.0850577,0.0173968,-0.0849164,0.0723262,0.0308442,-0.0583685,0.100457,-0.146612,0.198222,-0.105217,-0.0741902,0.105914,-0.110564,0.126597,-0.002756,0.0221262,-0.0481291,-0.0235427,0.035558,0.0790211,-0.0851271,0.0400287,0.0651215,-0.130224,0.0752301,-0.067571,0.0321526,0.045557,-0.0456189,0.0663772,-0.0621938,0.0170623,-0.101643,0.0618508,0.00436763,-0.0366265,0.0708897,-0.0865055,0.00574687,0.108412,-0.0493777,-0.0981174,0.118614,-0.0345324,-0.00712783,-0.0409377,0.0628955,-0.00697903,-0.0424334,0.0380354,-0.00711123,0.0260127,-0.00813264,-0.00055226,-0.0204464,-0.0135744,0.112948,-0.161375,0.0664307,0.0537457,-0.00857793,-0.145849,0.0947179,0.124592,-0.110243,-0.0304736,-0.0102063,0.0525637,-0.0372182,0.025526,-0.0565972,0.0785502,-0.0235168,-0.100977,0.0653262,0.194015,-0.191713,-0.0931787,0.109744,0.0447591,-0.1045,0.0730993,-0.0206843,0.0253065,-0.0488348,-0.00496429,0.120682,-0.0126541,-0.255164,0.240289,0.0377725,-0.109118,0.0440801,0.00308068,-0.10636,0.0793535,-0.0112866,0.0366801,-0.0927835,-0.0631134,0.190527,-0.148262,-0.0228045,0.0933139,-0.0669871,0.148003,-0.089054,0.0529365,-0.045051,0.029658,0.0230291,-0.058556,0.0622434,0.00757997,-0.0474009,-0.0248566,0.0363628,-0.0290405,0.00954644,-0.0259119,0.0494008,0.0179318,-0.0775113,0.0903411,-0.0359454,-0.0166279,0.00488655,0.0342088,-0.0245325,0.0690377,-0.0930636,0.0234625,-0.0906773,0.0893158,0.0242165,-0.0778273,0.0802378,-0.128407,0.12111,-0.0188967,0.0378108,-0.0464791,0.0225291,-0.0421245,0.0449599,-0.0162244,0.0345841,-0.0547407,0.0206985,0.0089657,0.0175153,-0.0788944,0.0267484,0.058132,-0.0366633,-0.0446768,0.094955,-0.0231571,-0.0505451,0.0587173,-0.0333603,0.00741325,-0.00218367,-0.000187178,0.0112942,0.0337775,-0.0733225,-0.0347287,0.0826626,-0.0324922,};
constexpr std::array<double, 325> coeffs3 = {-0.272067,-0.109525,0.0316225,0.0224498,0.0290788,0.0511171,0.0122411,-0.026461,0.0383032,0.013337,-0.0311393,0.000163594,0.177901,-0.181886,-0.0506404,0.0155467,0.0548923,-0.0349556,-0.0199554,0.0449288,0.0445514,0.0398469,-0.167551,-0.251483,1.30508,0.0124192,-0.0363248,0.0410704,-0.0534799,0.036618,0.0182846,-0.0568142,0.024007,-0.0661153,0.0399295,-0.0270242,0.0211315,0.086278,-0.0683412,0.0806856,-0.124621,0.0237978,0.0877658,-0.0627045,-0.00587577,-0.00530643,-0.00201968,0.0544734,-0.0242026,0.0320805,-0.0706258,0.099654,-0.0882695,-0.0134418,0.0696705,-0.00655777,0.0354773,-0.0568586,0.0208407,-0.00264067,-0.0948446,0.204239,-0.145881,0.0754641,-0.0407323,-0.0344749,0.0275046,-0.00307893,0.0345357,0.0253405,-0.0700736,0.00468402,0.0334351,-0.0597962,0.0425416,-0.0312754,0.0209167,-0.0712441,0.103214,-0.0141447,-0.0462409,0.0419487,-0.0325745,-0.0819565,-0.0105145,0.0718045,0.00870871,-0.0368486,0.0646947,0.0241231,-0.0346371,0.0294612,-0.0123758,-0.0244406,0.0248318,-0.0190444,-0.00212867,-0.0109555,0.100848,-0.162485,0.0622571,0.0330519,-0.0421914,0.0612616,-0.0266592,0.0105484,-0.012058,0.0395454,-0.0534232,-0.0251607,0.0275498,-0.00829876,-0.031645,-0.0784859,0.103861,0.0141107,0.0355542,-0.0744703,-0.0299565,0.101598,-0.0307324,0.0768889,-0.109829,0.000931924,0.0137405,0.0160295,0.0771669,-0.0735136,-0.0112195,0.0600253,-0.129038,0.0129365,0.0749307,0.112171,-0.115443,-0.0136429,-0.019049,0.113003,-0.116509,0.0811641,-0.0953374,0.0735944,0.017323,-0.11589,0.158938,-0.223488,0.112673,0.0536041,-0.101951,0.132536,0.0156161,-0.158148,0.0272675,0.059787,0.0644891,-0.108384,0.08632,-0.168237,0.0932484,0.063087,-0.131983,0.146391,-0.129566,0.167121,-0.0954074,-0.0454857,0.117442,-0.154224,0.0668386,0.0691793,-0.000550197,-0.0295687,-0.0335567,0.021874,0.135142,-0.124171,0.0376814,0.13024,-0.182356,0.0802514,-0.0464797,-0.000207333,0.0711235,-0.0496392,0.0335655,-0.0522514,0.0026604,-0.047794,0.0352599,-0.0131257,-0.00777538,0.0712252,-0.0849307,-0.0243074,0.165418,-0.124491,-0.0358973,0.105933,-0.0630145,-0.0500305,0.077061,0.0190329,0.0337935,-0.105436,0.0532057,-0.0378345,0.0786188,-0.0647136,0.00739603,0.00477411,-0.0177641,0.102653,-0.142661,0.0489,0.0845845,-0.037837,-0.143658,0.0650676,0.179898,-0.132312,-0.0489211,0.01859,0.0373833,-0.054234,0.0563759,-0.0619066,0.0318709,0.0142288,-0.111839,0.093575,0.167309,-0.213064,-0.0567222,0.0955245,0.0500022,-0.119235,0.0670264,0.00322201,-0.0256658,-0.00668,0.0254899,0.122702,-0.0818742,-0.203876,0.236541,-0.0136809,-0.0662682,0.0479605,0.0403681,-0.162388,0.1053,0.0356152,-0.024276,-0.0959619,-0.0395357,0.200903,-0.141166,-0.0305965,0.0770937,-0.121566,0.248146,-0.116493,0.02912,-0.0450506,0.062537,0.0229988,-0.110473,0.0787446,0.0339847,-0.060986,-0.056393,0.0477096,-0.0286218,0.00444603,-0.0627291,0.0615886,0.0812788,-0.0760608,0.0381529,-0.0228517,0.00232582,-0.0419325,0.0802603,0.00140403,0.0135842,-0.0818478,-0.0279338,-0.0158728,0.0732701,0.049127,-0.127427,0.105099,-0.0855179,0.0826842,0.0158492,-0.0010735,-0.0462457,0.0373701,-0.0678262,0.0434541,-0.0152303,0.0533705,-0.0701324,0.0406065,-0.00278407,0.0360805,-0.0734835,0.0221067,0.0186217,-0.0144567,-0.0631988,0.0948558,-0.0599582,0.0581905,0.0030542,-0.0262165,0.0103124,-0.03481,0.0242613,0.0349661,-0.00552591,-0.0633065,-0.0312046,0.0944252,-0.0436622,};
constexpr std::array<double, 325> coeffs4 = {-0.413934,-0.0950796,-0.0318826,0.0473926,-0.00169514,0.0776216,0.050826,0.00667466,-9.04158e-05,-0.0350474,-0.00439406,0.00119688,0.209912,-0.201634,-0.031598,0.0361648,0.0286477,-0.0380491,-0.00983718,0.0494237,0.0974777,0.000439586,-0.10139,-0.345783,1.29598,0.0169609,-0.0613049,0.0679289,-0.060502,0.0462958,0.0253244,-0.0851322,0.0169425,-0.0162223,-0.0354064,0.0242371,-0.00219923,0.0920466,-0.0742802,0.116738,-0.156936,0.0304456,0.109694,-0.0772615,0.013362,-0.0550962,0.0224903,0.0401243,-0.00971371,0.0541275,-0.0847549,0.0916962,-0.064943,-0.0539486,0.113923,0.00652767,-0.0430657,0.00826258,-0.0190814,0.0109659,-0.0937298,0.233818,-0.207628,0.105732,-0.0355611,-0.0827246,0.0835828,-0.0148702,0.0393768,0.0380702,-0.0627175,-0.01997,0.0244482,-0.0676075,0.0425794,-0.0127319,-0.0277458,-0.0475886,0.115239,-0.00932142,-0.0695354,0.0673413,0.0205386,-0.128089,-0.0543514,0.145642,-0.0583307,0.0114598,0.0516801,-0.0362157,0.0669936,-0.0465216,0.0294407,-0.035216,0.046475,-0.0741718,0.00194852,0.0511156,0.077063,-0.131421,0.0374362,0.0496296,-0.0588889,-0.0116861,0.00719102,0.100692,-0.130122,0.112309,-0.0782716,-0.00619764,0.0201316,-0.0198596,0.0114425,-0.0825747,0.0719711,0.0441736,0.0211582,-0.112585,-0.0103768,0.0497358,0.0544455,0.0326095,-0.0458915,-0.088225,0.0407576,-0.00114195,0.133569,-0.109589,0.00677562,0.0271862,-0.0636442,0.000880941,0.0162831,0.0814809,-0.0646331,-0.0129676,-0.0094268,0.134697,-0.113483,0.0238825,-0.0266774,-0.0131852,0.121066,-0.153677,0.181595,-0.2489,0.1176,0.0331598,-0.0979306,0.15707,-0.0774559,-0.0743221,0.0156344,0.0738023,0.0908094,-0.17523,0.105971,-0.172781,0.0732966,0.0820674,-0.0980507,0.109894,-0.124222,0.133589,-0.0400414,-0.0507171,0.113345,-0.243097,0.158572,0.0293747,0.0365018,-0.0521871,-0.03122,0.0513583,0.157342,-0.165355,0.0132454,0.155497,-0.178002,0.0441585,0.0216362,-0.040987,0.0813938,-0.0442114,0.0762469,-0.0735066,-0.0155722,-0.1372,0.117892,-0.0368737,-0.0241723,0.132113,-0.0399292,-0.102805,0.203238,-0.119102,-0.0751299,0.10428,-0.0513033,-0.100319,0.11051,0.0214064,0.0670399,-0.0350715,-0.027641,-0.0245655,0.0558479,-0.0728007,-0.00437747,0.0346095,-0.0109665,0.0839929,-0.126933,0.00939399,0.153916,-0.053163,-0.16536,0.0318719,0.14011,-0.0678805,-0.0590372,0.0123279,0.0871973,-0.134422,0.0689229,0.0112938,-0.0188282,0.0382191,-0.142412,0.0927577,0.190209,-0.203365,-0.0374679,0.0640189,0.0432712,-0.134238,0.109368,0.0579543,-0.156509,0.0723412,0.0148876,0.156664,-0.103213,-0.227653,0.223306,0.0680469,-0.128307,0.0576612,0.0193056,-0.214705,0.179021,0.0265511,-0.0192971,-0.150383,-0.0171565,0.178441,-0.0490264,-0.155402,0.145067,-0.109441,0.235027,-0.0853261,-0.0439047,-0.00967744,0.0940733,0.0175132,-0.0543932,-0.031278,0.0839008,-0.0675873,-0.0562357,0.0219004,0.0493271,-0.0439314,-0.0688951,0.0740122,0.0498764,-0.0683677,0.0259284,-0.00786069,-0.00245634,-0.0466613,0.0893816,0.0193001,-0.0285989,-0.051152,0.0235626,0.0234185,-0.00283029,0.0269215,-0.115253,0.11696,-0.0878821,0.0752039,0.0221657,-0.0456131,-0.00837952,0.0363314,-0.071341,0.044843,0.0251292,-0.0288301,-0.0527982,0.0705343,-0.0332377,0.0833168,-0.145834,0.0800204,0.0013607,-0.00736743,-0.0751922,0.102093,-0.0489639,0.0787452,-0.0273357,-0.0265242,0.0333189,-0.0399529,0.017703,0.0195141,0.017707,-0.0841511,-0.0441601,0.111076,-0.0438864,};
constexpr std::array<double, 325> coeffs5 = {-0.503555,-0.0978156,-0.0545519,0.0726777,-0.0732984,0.126906,0.0544892,0.0260063,-0.0159909,-0.0489496,0.0211428,-0.0173115,0.190789,-0.111264,-0.0909178,0.0984149,-0.0101337,-0.0424345,0.0557448,0.0339207,0.0766107,0.0139872,-0.116047,-0.306519,1.21421,0.0298161,-0.0778131,0.0642121,-0.0724902,0.0762435,-0.0119149,-0.0604128,-0.0151153,0.0199765,-0.0485977,0.0251634,0.0131559,0.0831054,-0.0518362,0.0879231,-0.147189,0.0124919,0.121762,-0.0858809,0.0175275,-0.0790933,0.0488815,0.0158723,0.00759845,0.0367124,-0.0456331,0.119811,-0.0858899,-0.0414191,0.101545,0.0298768,-0.0563126,-0.0189037,-0.00117518,-0.0713379,-0.00413484,0.260284,-0.26094,0.108532,0.0196896,-0.153909,0.123678,-0.0114054,0.0148246,0.0380875,-0.0317476,-0.0311747,0.00773738,-0.078054,0.0550872,-0.0318423,-0.028469,-0.000120967,0.0565802,0.0498823,-0.112338,0.104714,-0.0566869,-0.157587,0.094626,0.0591952,-0.064668,0.056472,0.0287253,-0.0605223,0.160158,-0.137999,0.101615,-0.0822106,0.0441945,-0.111241,0.0583061,0.0469016,0.0272035,-0.12043,0.0692537,0.063699,-0.0304595,-0.0528047,-0.0122195,0.0482581,-0.0418942,0.0355325,-0.0276691,0.00510975,0.0238038,-0.0941466,0.10378,-0.160993,0.11417,0.0421617,0.032067,-0.0974644,-0.0176905,0.0854138,-0.0472096,0.124702,-0.0394615,-0.0603386,-0.0367076,0.0359471,0.0538548,0.0702623,-0.138034,0.0650138,-0.0667877,0.0317508,0.00893271,0.0644215,-0.0797569,-0.0275982,-0.00484098,0.147026,-0.136471,0.114216,-0.171329,0.0312931,0.0813628,-0.0307401,0.147415,-0.227849,-0.0200213,0.168196,-0.19603,0.231648,-0.0686043,-0.136942,0.044479,0.0773106,0.0678546,-0.145631,0.107969,-0.221168,0.143964,-0.00718167,0.00416995,0.0287279,-0.119523,0.1916,-0.0768139,-0.0232452,0.129074,-0.297172,0.139142,0.0706221,0.0204578,-0.0355976,-0.0647024,0.0778765,0.157701,-0.145602,0.0419472,0.111516,-0.128107,-0.00535804,0.00154108,0.000410449,0.0409506,-0.0144525,0.0317634,-0.0616963,0.00670067,-0.125438,0.110302,-0.0429013,-0.0145653,0.170535,-0.0897794,-0.128675,0.200219,-0.0541368,-0.0873166,0.103904,-0.0981908,-0.0907357,0.163996,0.00332089,0.0792472,-0.0712896,-0.0178194,-0.0417916,0.0452031,-0.0137873,0.00756066,0.00559063,-0.0426415,0.111621,-0.164656,0.0738964,0.150153,-0.0471722,-0.205649,0.0106462,0.192202,-0.0866076,-0.0914956,-0.014532,0.127181,-0.115681,0.0486384,-0.00367432,0.0337187,-0.0506071,-0.0859635,0.0281764,0.298067,-0.226635,-0.0771708,0.0705763,0.0610165,-0.176982,0.152335,0.0312559,-0.143372,0.0654035,0.0677047,0.110099,-0.0983659,-0.262651,0.239315,0.0874485,-0.121697,0.0764487,-0.0277837,-0.148406,0.158161,-0.00966929,-0.00923793,-0.164222,0.0348618,0.165543,-0.0523023,-0.18269,0.151171,-0.117103,0.226046,-0.0682279,-0.00430516,-0.0531637,0.139701,-0.0148147,-0.0842447,-0.0371236,0.107121,-0.0559467,-0.0623926,0.00202004,0.0571526,0.00609522,-0.0672183,0.0163198,0.114535,-0.0764732,0.0170103,-0.0425712,0.00475271,-0.0639996,0.0825634,-0.00739862,0.0370015,-0.129893,0.0671197,0.0562293,-0.0127905,0.0124751,-0.077209,0.0989449,-0.108677,0.167242,-0.0221906,-0.0872698,0.0150922,-0.00603074,-0.0373079,0.0810789,-0.0579349,0.00340205,-0.0567289,0.0966171,-0.0566684,0.0966106,-0.128626,0.025873,0.063085,-0.0414926,-0.0934291,0.107253,-0.0024839,0.0164603,0.00440978,-0.00760517,-0.01441,-0.0146807,0.0104551,0.0453182,0.0443964,-0.126488,-0.0697701,0.13181,-0.0413264,};
constexpr std::array<double, 325> coeffs6 = {-0.587049,-0.0841871,-0.0845563,0.0769176,-0.159157,0.189789,0.08314,0.0415505,-0.0637416,-0.017378,0.0156873,0.00830265,0.142953,-0.0734416,-0.057994,0.03676,0.0336375,-0.0197551,0.0784181,-0.0127993,0.13972,-0.0755076,-0.0591393,-0.323413,1.17406,0.0246653,-0.059864,0.0856858,-0.0807418,0.0320406,0.0535121,-0.0976321,-0.00953242,0.0347885,-0.0520691,0.00513098,0.0343973,0.0710307,-0.0698759,0.0611451,-0.0897932,-0.0208746,0.143587,-0.0325362,-0.0482325,-0.0902476,0.0788934,0.00448353,-0.00452072,0.0242725,-0.0965944,0.137527,0.0132726,-0.108452,0.103833,0.0276755,-0.0945174,0.00705641,0.00590991,-0.0726957,0.0199494,0.235175,-0.200951,0.0250611,0.0906399,-0.198243,0.096845,-0.00474684,0.0395904,0.0101606,0.0426135,-0.0659601,0.0220154,-0.0288274,-0.0463929,0.000106726,-0.0164175,0.0323269,0.00737948,0.0509573,-0.0768144,0.103111,-0.101309,-0.106437,0.0836964,0.0454587,-0.0782269,0.0698663,0.0494619,-0.118546,0.219264,-0.110368,0.00556447,-0.0231088,0.00348683,-0.0816165,0.0378579,0.0792398,-0.0333076,-0.0486827,0.06291,0.036282,-0.0669233,-0.0071243,-0.0170128,0.0335892,-0.0176153,0.00561382,-0.0174206,-0.0326087,0.157739,-0.205915,0.0995333,-0.129767,0.107998,0.0545544,0.0273095,-0.11618,-0.013757,0.114935,-0.0768824,0.141689,-0.00323075,-0.0999054,-0.0495637,0.065391,0.0233678,0.136633,-0.193538,0.0671432,-0.0301673,0.0341411,-0.00586296,0.0516192,-0.0866596,-0.0403932,0.0163,0.182311,-0.166665,0.117102,-0.199228,0.0371762,0.113951,-0.0810295,0.141542,-0.13227,-0.117133,0.255452,-0.249885,0.175573,0.0596444,-0.191297,0.0788091,0.0252409,0.0708336,-0.170931,0.103658,-0.204119,0.157449,0.0234473,-0.0679644,0.103938,-0.11994,0.0988386,-0.0276776,-0.06789,0.218151,-0.305271,0.0132365,0.152773,-0.0539518,0.0407779,-0.0522241,0.0502989,0.179879,-0.133301,-0.0304201,0.163878,-0.115271,-0.0686292,0.0636604,-0.0259633,0.0780009,-0.0938439,0.057881,-0.0320828,-0.0724718,-0.053773,0.113545,-0.0281894,-0.0393833,0.171633,-0.0555945,-0.117272,0.153691,-0.0220202,-0.109594,0.126911,-0.0897157,-0.0860962,0.150201,0.013705,0.107946,-0.0799858,-0.0446127,-0.0391938,0.0425491,-0.0290873,0.0082264,0.0162061,-0.0241594,0.109816,-0.178767,0.0224424,0.198019,-0.0625562,-0.240382,0.0861652,0.13569,-0.0619066,-0.0995688,-0.0161532,0.113084,-0.0401109,-0.0231104,0.0116544,0.0254113,-0.0643594,-0.0177868,-0.00549194,0.36214,-0.332405,-0.02878,0.0540245,0.0719109,-0.182997,0.0789973,0.120598,-0.161948,0.0812354,0.085351,0.0476788,-0.0672131,-0.33539,0.311938,0.108305,-0.152363,0.0966271,-0.0118952,-0.213096,0.189177,-0.0405661,0.0385921,-0.211701,0.0292926,0.243202,-0.125393,-0.170308,0.166333,-0.150341,0.314673,-0.135986,0.0784419,-0.139676,0.209079,-0.0314004,-0.108305,0.00196735,0.0957485,-0.0749846,-0.112991,0.0592401,0.0218057,0.0868071,-0.135002,0.0566505,0.0665935,-0.0504303,-0.0418523,0.0103493,-0.0070556,-0.0302039,-0.0118866,0.0412356,0.0318881,-0.103762,0.0567414,0.109494,-0.0582297,-0.0497272,0.0330971,0.0641831,-0.105562,0.202142,-0.0625923,-0.146884,0.0767745,-0.0295781,-0.0335583,0.0815986,-0.0991406,0.032731,-0.0123106,0.060265,-0.0495491,0.104727,-0.150555,0.0592959,0.0361296,-0.0421471,-0.0998683,0.140405,-0.0551809,0.0328072,0.0108425,-0.0152168,-0.0107965,-0.0321412,0.0418482,0.0549531,0.0973731,-0.186985,-0.0843055,0.134335,-0.0341741,};
constexpr std::array<double, 325> coeffs7 = {-0.661012,-0.0871182,-0.0962688,0.108353,-0.215144,0.194409,0.110989,-0.0117985,-0.0124627,-0.0411149,0.0329884,-0.0326842,0.192918,-0.0313674,-0.0982518,0.0354252,0.0368854,0.0725879,0.0309862,-0.0100527,0.157527,-0.0894906,-0.0812301,-0.351167,1.16618,0.0248338,-0.0368378,0.0857901,-0.0896023,-0.012162,0.0783457,-0.0910053,0.0281145,0.000866044,-0.0158505,-0.0253538,0.0314879,0.0440281,-0.056842,0.121883,-0.158666,-0.0095855,0.119505,-0.0046185,-0.0178903,-0.122048,0.076076,0.0109423,-0.0123243,-0.0191732,-0.0855617,0.18112,0.0455208,-0.137207,0.0968971,0.0111252,-0.0952732,-0.0122271,0.0863544,-0.123298,0.0319376,0.238039,-0.250861,0.075768,0.0850697,-0.183171,0.0797357,-0.0718778,0.111922,0.00860323,0.0327906,-0.0452426,0.0164502,-0.0304606,-0.0359578,0.00205577,-0.026447,0.0512441,0.00231834,0.0177862,-0.115267,0.137784,-0.0148955,-0.154639,0.031367,0.1142,-0.107677,0.0519382,0.0891897,-0.114571,0.169118,-0.0998798,0.0708901,-0.0759281,-0.0249121,-0.0513367,0.0195929,0.09204,-0.0555741,-0.033541,0.0677145,0.0439013,-0.0202763,-0.119787,-0.00244395,0.101594,-0.0603804,0.0275671,0.00451493,-0.0821858,0.181826,-0.19539,0.0895423,-0.166415,0.145701,0.0211165,0.101242,-0.141819,-0.0517352,0.118617,0.00333594,0.103826,-0.0475531,-0.125215,0.0421412,0.0235729,0.0233257,0.152725,-0.206375,0.0509571,0.0152149,0.0462712,-0.0252061,0.00392055,-0.0595703,-0.068095,0.0123718,0.190536,-0.111883,-0.00802113,-0.0677186,-0.0139542,0.172365,-0.139022,0.103844,-0.0860133,-0.143085,0.263897,-0.236807,0.184748,0.0283696,-0.151152,0.0480327,0.0134394,0.0897496,-0.192698,0.115933,-0.180172,0.0537756,0.0773954,-0.0237266,0.0617671,-0.0555824,0.0274305,0.0253632,-0.0759109,0.208543,-0.360542,0.0250589,0.170921,-0.026534,0.0356441,-0.00942739,-0.0379585,0.243883,-0.142146,-0.0341928,0.103293,-0.018437,-0.125758,0.0752209,-0.0689894,0.116991,-0.0876303,0.0558263,-0.0111441,-0.105102,-0.0199927,0.0862075,-0.0257463,-0.00814874,0.169539,-0.0590761,-0.0686553,0.0675963,0.0179944,-0.0995398,0.123223,-0.104289,-0.0768326,0.138749,0.0383394,0.106383,-0.0803749,-0.0471311,-0.0807604,0.0459707,0.000106717,-0.0152252,0.0338756,-0.0348914,0.126008,-0.18372,0.0143162,0.211881,-0.0536852,-0.292383,0.1108,0.10992,-0.0268246,-0.0935746,-0.0196077,0.0798016,0.00553608,-0.0368083,0.0120295,-0.00779873,-0.0351476,-0.0328098,0.0180594,0.405579,-0.404773,0.0151744,0.0199748,0.0595995,-0.144819,0.0613475,0.128628,-0.19924,0.170617,0.0201339,0.0477444,-0.0787824,-0.373042,0.366679,0.0913498,-0.134754,0.0838351,-0.0127677,-0.195752,0.22952,-0.0926838,0.0467633,-0.23874,0.0269914,0.300786,-0.134855,-0.185567,0.168532,-0.153829,0.263398,-0.128005,0.0888311,-0.10246,0.231529,-0.0408293,-0.170771,0.0422782,0.101581,-0.0988112,-0.080542,0.0502933,-0.00190685,0.089752,-0.10728,0.0366542,0.0825484,-0.104801,-0.0302325,0.0554518,-0.0298044,0.0142401,-0.0363013,0.031302,0.0348801,-0.0763843,0.0688046,0.0909621,-0.0711566,-0.0796809,0.080719,0.0432141,-0.0494212,0.157962,-0.0602837,-0.128793,0.0486077,-0.0447884,-0.0349349,0.0570002,-0.0872254,0.0269273,-0.0349826,0.10258,-0.0413102,0.0880523,-0.147548,0.084138,0.0306887,-0.0558163,-0.0849591,0.138593,-0.0891572,0.0461256,0.0171185,-0.00634997,0.00129165,-0.016826,-0.000787435,0.0334468,0.114586,-0.160145,-0.109383,0.160018,-0.0485587,};
constexpr std::array<double, 325> coeffs8 = {-0.719153,-0.125725,-0.0841929,0.129306,-0.258452,0.190103,0.134641,-0.00274504,-0.0506068,0.0304901,-0.00527607,-0.0328351,0.193363,0.0126611,-0.104437,0.0720698,-0.00456528,0.11153,0.0164821,-0.00843412,0.135436,-0.121447,-0.0661729,-0.277003,1.08523,0.0269182,-0.0220592,0.0763634,-0.0866092,-0.0518776,0.161336,-0.149339,0.0379671,0.0230462,-0.05038,-0.0411096,0.0760155,-0.0279371,-0.0214262,0.123102,-0.13651,-0.0195485,0.104281,0.0204193,-0.00358091,-0.139831,0.0326434,0.0668342,-0.033968,-0.0478483,-0.0689495,0.202049,0.0762544,-0.182533,0.0768306,0.0317467,-0.0807122,-0.0027474,0.119295,-0.195789,0.108758,0.197906,-0.236075,0.0130289,0.144128,-0.177062,0.0441884,-0.0985577,0.147991,0.0388608,0.00426998,-0.0372884,0.00896878,-0.0309753,-0.00614864,-0.050921,0.0204157,0.0658969,-0.0471024,0.0348153,-0.130728,0.166014,-0.015467,-0.171128,0.0231189,0.182394,-0.153877,0.0270535,0.112007,-0.112936,0.181013,-0.106383,0.0103333,-0.0247328,-0.0566984,-0.0219694,0.0244361,0.143136,-0.0837755,-0.0878373,0.0997319,0.0944395,-0.0963269,-0.0598889,-0.0421519,0.117112,-0.0847347,0.0525163,0.0229187,-0.138179,0.215856,-0.207651,0.045899,-0.0705087,0.102857,-0.0229412,0.134301,-0.160873,-0.0954336,0.219186,-0.0223222,0.0199003,0.0589304,-0.206471,0.0680736,0.0505627,-0.00187272,0.104927,-0.151919,0.0887008,0.0333615,-0.0191805,0.0256922,-0.0158357,-0.0653111,-0.056811,-0.04373,0.23299,-0.138732,-0.0195079,-0.032804,-0.0161372,0.124703,-0.0410557,-0.00894173,-0.016799,-0.135178,0.239706,-0.244831,0.139324,0.106998,-0.11908,-0.0438987,0.0307055,0.131597,-0.25085,0.140228,-0.155679,0.0248311,0.052313,0.0534335,-0.00203336,-0.0237518,0.0110389,0.0310694,-0.0754704,0.217052,-0.324865,-0.0486166,0.125418,0.0440439,0.0399843,0.0239589,-0.0514479,0.240888,-0.123745,-0.0635495,0.09412,0.0111529,-0.137537,0.0600103,-0.0244101,0.0633352,-0.0627305,0.0102121,0.0250044,-0.069931,-0.0589473,0.0891901,-0.0416668,-0.0207213,0.162814,0.00772399,-0.0709757,0.0292493,0.0554548,-0.112757,0.062849,-0.0572319,-0.0874439,0.171519,0.0267342,0.101394,-0.00814061,-0.127305,-0.0749062,0.0524812,-0.0412428,0.00692509,0.0197293,-0.0529015,0.162389,-0.172145,0.0283954,0.198309,-0.110197,-0.244126,0.0999835,0.0553889,0.0384279,-0.095575,-0.00779849,0.0392842,0.0756967,-0.0412226,-0.0114319,-0.02112,-0.0499672,-0.055171,0.0925102,0.385544,-0.415163,0.0422704,-0.00393939,0.0512238,-0.107864,0.0166346,0.161864,-0.23053,0.209964,-0.012394,0.109215,-0.13754,-0.374334,0.361416,0.0536403,-0.0841687,0.069484,-0.0163097,-0.185108,0.249309,-0.128499,0.0724914,-0.269835,0.0831853,0.240569,-0.104552,-0.158877,0.1361,-0.135889,0.201163,-0.105713,0.109335,-0.131539,0.250793,-0.059899,-0.149154,0.0737469,0.0242542,-0.0599499,-0.0684165,0.0555612,0.000787855,0.0985862,-0.0898352,0.0263719,0.0871386,-0.175411,0.0535264,0.0398337,-0.0380502,0.0158184,-0.0380867,-0.000719074,0.0503008,-0.0847981,0.0911069,0.105877,-0.0992969,-0.0992529,0.137963,0.0175895,-0.0821548,0.208369,-0.0402072,-0.151007,0.0328149,-0.0647762,-0.0214998,0.095109,-0.14239,-0.00186045,-0.0121064,0.116909,-0.0386786,0.0503241,-0.0886447,0.0735529,0.000294428,-0.0380707,-0.0686999,0.113524,-0.0790192,0.0626772,-0.00260313,0.000759848,-0.0181559,-0.0307131,0.0243605,0.0436529,0.134271,-0.1652,-0.121565,0.155016,-0.0496857,};
constexpr std::array<double, 325> coeffs9 = {-0.781781,-0.120344,-0.12456,0.193799,-0.312863,0.201664,0.169607,-0.0455999,-0.0173589,-0.036002,0.0399209,-0.0443053,0.234917,-0.00405044,-0.0653944,0.0106791,0.0556388,0.114751,-0.017132,0.0043353,0.155544,-0.14248,-0.0791502,-0.287553,1.07693,0.0231159,0.00701504,0.0620968,-0.0871315,-0.0699955,0.195994,-0.172118,0.0753217,-0.008362,-0.0609569,-0.0396008,0.145708,-0.137167,0.00442224,0.159824,-0.163248,-0.0204605,0.112095,0.0480844,-0.0296124,-0.115412,-0.00211189,0.0914425,-0.0517633,-0.0821634,-0.0456431,0.205132,0.0924141,-0.187117,0.0750492,-0.0028255,-0.0523824,0.0251649,0.105476,-0.260181,0.203147,0.139931,-0.188865,-0.0233044,0.17801,-0.18467,-0.0349889,-0.0228006,0.111833,0.062766,-0.0222042,-0.00738058,0.00199142,-0.0222964,-0.0124839,-0.0772815,0.0396388,0.0906294,-0.0442375,0.0064048,-0.0996167,0.122658,0.0191895,-0.154609,-0.0403915,0.244871,-0.200976,0.027146,0.16872,-0.179223,0.197197,-0.0933519,0.0363835,-0.052341,-0.0717778,-0.00974529,0.0257592,0.164223,-0.113213,-0.0824882,0.0862483,0.101653,-0.0306904,-0.129199,-0.0481708,0.134936,-0.0705263,0.0472676,0.00435859,-0.117999,0.215166,-0.189975,0.00396385,-0.0767346,0.132297,-0.0162483,0.120191,-0.182632,-0.0809212,0.226908,-0.0070583,-0.00338485,0.017925,-0.154813,0.0749921,0.0636219,-0.0739391,0.157478,-0.13792,0.0616015,0.0412503,-0.00664792,0.0486631,-0.0556511,-0.0601714,-0.0535204,-0.0335043,0.247984,-0.135229,-0.0596856,-0.0244435,0.0112653,0.120983,-0.0319422,-0.0710244,0.0420879,-0.179092,0.257919,-0.213889,0.0945972,0.0990442,-0.0996063,-0.00909819,-0.00696102,0.125131,-0.287731,0.139687,-0.0865081,-0.0289235,0.0603708,0.0976181,-0.021012,-0.0465519,0.0390136,0.0399038,-0.108328,0.20877,-0.252671,-0.086185,0.109466,0.00575873,0.091094,0.0485915,-0.0876086,0.23893,-0.054673,-0.121055,0.0362936,0.038951,-0.124006,0.0693933,-0.0347517,0.0999276,-0.0886357,0.0217574,0.0129401,-0.0477312,-0.0114937,0.00527094,-0.0289239,-0.0414894,0.145937,0.0778968,-0.125732,0.0277501,0.130548,-0.196307,0.108424,-0.0813977,-0.0856032,0.128582,0.0696583,0.0838249,-0.0641386,-0.0473684,-0.067541,0.0433072,-0.0723544,0.065448,-0.00737359,-0.0766878,0.195419,-0.195676,0.0456687,0.20573,-0.134095,-0.248895,0.12604,0.0608777,0.0219466,-0.104128,-0.00304637,0.057562,0.13495,-0.108182,-0.0128227,-0.0340338,-0.0474219,-0.0498547,0.14126,0.326945,-0.392144,0.0906832,-0.0560816,0.0386036,-0.107593,0.00879305,0.19754,-0.212049,0.184466,-0.0045705,0.127977,-0.192259,-0.328781,0.343453,-0.00641012,-0.0288022,0.0689564,-0.0455132,-0.154026,0.232805,-0.103243,0.0372893,-0.284552,0.109781,0.264223,-0.149019,-0.102646,0.10964,-0.134129,0.159755,-0.0734387,0.105658,-0.151356,0.301462,-0.048903,-0.191261,0.0634217,0.0360902,-0.050267,-0.0509378,0.0111525,0.0410225,0.0774062,-0.0972854,0.0298453,0.0775542,-0.12303,0.0266421,0.0322968,-0.0125381,-0.0228494,0.00268501,-0.0370919,0.0322729,-0.0426341,0.073879,0.096319,-0.0897633,-0.0967067,0.135434,0.0107626,-0.0455935,0.184622,-0.0328936,-0.15369,0.023411,-0.047279,-0.024022,0.0586954,-0.149744,0.0158615,0.00251392,0.112633,-0.0361419,0.0450124,-0.0738892,0.0289504,-0.0333847,0.0147554,-0.0515713,0.0933379,-0.0369799,0.0598705,-0.0295857,0.0231605,-0.0434685,-0.00261835,-0.00503146,0.0162076,0.161531,-0.132901,-0.131399,0.151574,-0.0572444,};
constexpr std::array<double, 325> coeffs10 = {-0.852558,-0.0895251,-0.171691,0.195723,-0.289596,0.164875,0.1892,-0.0460988,-0.0296559,0.00623262,-0.0380753,0.00717352,0.24315,0.0344797,-0.11862,0.0477692,0.0424696,0.106408,0.0168804,-0.0238422,0.172477,-0.118924,-0.137123,-0.282108,1.07601,0.0215956,-0.00551481,0.0843273,-0.0759454,-0.0959254,0.209365,-0.170219,0.101959,-0.022663,-0.0778119,-0.0699304,0.1824,-0.162642,0.0217879,0.179213,-0.19515,-0.00609745,0.111394,0.0617621,-0.0185409,-0.152904,0.0219573,0.0730196,-0.0498218,-0.0764848,-0.0638931,0.217029,0.11595,-0.22987,0.0877788,-0.0409224,-0.0143014,0.0390504,0.171974,-0.348866,0.212267,0.144291,-0.216426,0.0305885,0.154203,-0.168554,-0.0736608,-0.037599,0.178161,0.00634364,-0.0070684,0.0168076,0.008009,-0.0473471,-0.0196216,-0.0139662,-0.00779192,0.115305,-0.0647543,0.0212229,-0.150963,0.16002,0.0764142,-0.225047,-0.00579187,0.230698,-0.20325,0.00136777,0.201276,-0.200854,0.175919,-0.0588419,0.0574666,-0.0851972,-0.0899542,0.0463454,-0.0306219,0.21291,-0.105518,-0.12206,0.0807224,0.105052,0.0101332,-0.15622,-0.040883,0.115589,-0.077752,0.0808752,0.00576094,-0.134265,0.25655,-0.215476,0.00811336,-0.112368,0.157868,-0.0387831,0.133074,-0.198176,-0.0984273,0.242704,-0.00704875,0.0610782,-0.0344425,-0.214419,0.132296,0.0803387,-0.0902888,0.127974,-0.108178,0.0599424,0.0220379,0.0271827,0.0306372,-0.0462865,-0.0689146,-0.0581325,-0.00530801,0.225058,-0.0712024,-0.0950608,-0.104046,0.0603545,0.170018,-0.0700409,-0.087384,0.10154,-0.227729,0.27091,-0.200266,0.0790154,0.0824979,-0.0712503,-0.0201344,-0.00912857,0.0996542,-0.278312,0.107005,-0.0377536,-0.000393939,0.0251278,0.0857549,0.0249185,-0.0610052,-0.0158498,0.089968,-0.116349,0.180938,-0.195972,-0.106935,0.0628299,0.0638799,0.069924,0.0698817,-0.111742,0.241743,-0.0836108,-0.0960039,0.00808948,0.0601516,-0.123964,0.0607092,-0.00912558,0.042907,-0.0221422,-0.0231975,0.0390863,-0.0173149,-0.0831531,0.0348397,-0.0223841,-0.0629077,0.155957,0.073312,-0.0479922,-0.0847743,0.187972,-0.180587,0.0690929,-0.0506154,-0.111956,0.146015,0.0379463,0.10031,-0.0330083,-0.0698413,-0.0671678,0.0583448,-0.0423017,0.00988469,0.0217838,-0.109716,0.213544,-0.184646,0.0755429,0.145234,-0.149039,-0.201907,0.105161,0.0811797,0.00688188,-0.11182,-0.0139931,0.0310715,0.242069,-0.175278,0.000309232,-0.0501347,-0.0683482,0.0175584,0.144878,0.258292,-0.338295,0.0274326,-0.011521,0.0170848,-0.0635557,-0.0352569,0.218011,-0.238647,0.245882,-0.0277432,0.0999817,-0.209095,-0.268924,0.306176,0.0488787,-0.0768238,0.07493,-0.0970236,-0.109761,0.25752,-0.187129,0.0839461,-0.278635,0.125111,0.25225,-0.179798,-0.0818417,0.113482,-0.11359,0.130204,-0.0887272,0.131839,-0.170319,0.321906,-0.0598446,-0.169557,0.06111,0.0198096,-0.0381787,-0.0250788,-0.0179763,0.0895887,-0.00351856,-0.0560448,0.0117792,0.08045,-0.117085,0.0319434,0.0220292,0.00341512,-0.0497125,0.0621776,-0.112871,0.0778811,-0.0526723,0.0690046,0.069468,-0.0641313,-0.115869,0.160503,0.0443237,-0.0746552,0.154955,0.0182634,-0.157531,0.01578,-0.0426469,-0.0664679,0.0807525,-0.123494,-0.021591,0.027974,0.0878436,-0.0192664,0.0510536,-0.103082,0.031227,-0.073705,0.0689156,-0.0703687,0.117905,-0.0342951,0.0674812,-0.0427623,0.0161343,-0.014541,0.016779,-0.042199,-0.0174294,0.158352,-0.0881854,-0.128398,0.146335,-0.0675371,};
constexpr std::array<double, 325> coeffs11 = {-0.921193,-0.0663553,-0.149836,0.113118,-0.252579,0.154431,0.178999,-0.0243799,-0.052648,0.0258759,-0.0190118,-0.0522888,0.341293,-0.0383017,-0.0673508,0.0479428,0.0112802,0.136506,-0.0109855,-0.00097481,0.174913,-0.0709798,-0.226524,-0.292011,1.09505,0.0227304,0.00861221,0.0805316,-0.0728496,-0.133565,0.230276,-0.173445,0.142365,-0.0498715,-0.0914562,-0.075182,0.190421,-0.15385,-0.0240574,0.208779,-0.161829,-0.0252454,0.130335,0.0190566,-0.00793954,-0.154274,0.0536782,0.047919,-0.0482138,-0.106043,-0.0270829,0.212291,0.149395,-0.254031,0.101684,-0.0892771,0.0156811,0.0437484,0.173693,-0.331833,0.199886,0.153003,-0.253489,0.0391938,0.147843,-0.139168,-0.0838762,-0.0161054,0.161642,-0.0233055,0.040608,-0.00379437,-0.00991234,-0.0576419,0.0107026,-0.00910216,-0.0389324,0.152514,-0.118276,0.0837359,-0.189695,0.101516,0.100646,-0.128131,-0.0618204,0.238174,-0.217076,-0.0211402,0.260957,-0.267868,0.222726,-0.0843989,0.0543235,-0.0685311,-0.08643,0.0189797,-0.000477943,0.185084,-0.0977252,-0.0606351,-0.00777716,0.18774,0.0159046,-0.154021,-0.125272,0.201342,-0.162021,0.147724,-0.0293496,-0.131063,0.269165,-0.241223,0.0193768,-0.118041,0.172059,-0.0240636,0.0947918,-0.151357,-0.138604,0.216649,0.0398735,0.0461934,0.00988721,-0.278425,0.133425,0.111019,-0.0910564,0.106387,-0.0834441,0.0170592,0.0898259,0.00462959,0.0340476,-0.0496853,-0.087762,-0.0533257,-0.011592,0.239362,-0.0441737,-0.124859,-0.147205,0.0256149,0.256951,-0.05545,-0.156553,0.148354,-0.230885,0.261692,-0.178854,0.0736224,0.0569941,-0.0526189,-0.0200722,-0.0163772,0.0992984,-0.294064,0.0994287,-0.0182167,0.0265682,0.0371217,0.0568014,0.00466434,-0.0509387,0.0104862,0.063813,-0.13327,0.228671,-0.267061,-0.0507296,0.0602709,0.0276926,0.104596,0.0853905,-0.134745,0.236168,-0.0632121,-0.109388,-0.028257,0.129028,-0.142636,0.0403909,-0.0250361,0.0981912,-0.0742717,0.0233996,0.025245,-0.0527204,-0.045815,0.0150047,-0.00677392,-0.0542196,0.11568,0.0648636,-0.00610998,-0.138904,0.211461,-0.165195,0.0619034,-0.0365911,-0.137844,0.147025,0.0499615,0.144395,-0.0735119,-0.0686614,-0.0775982,0.0748133,-0.0138053,-0.00386236,-0.0092438,-0.0829689,0.212681,-0.121546,-0.0303651,0.203451,-0.18214,-0.171157,0.062044,0.116155,-0.00415596,-0.118799,-0.0263743,0.04135,0.274639,-0.195157,-0.00843792,-0.098282,-0.0177878,0.0200631,0.142134,0.197486,-0.295938,0.0481145,-0.0164149,0.0384009,-0.0999568,-0.0193483,0.216774,-0.285169,0.288724,-0.0259669,0.109995,-0.23218,-0.211387,0.267411,0.0118522,-0.0509375,0.0924584,-0.134249,-0.0738503,0.252245,-0.18835,0.0687956,-0.283343,0.133384,0.226909,-0.15228,-0.0522689,0.0859249,-0.0857076,0.0501532,-0.00891057,0.109146,-0.173101,0.317535,-0.0379671,-0.204508,0.0977084,0.0152457,-0.050549,0.00250582,-0.0503801,0.116335,-0.0117849,-0.0388157,-0.0110389,0.140029,-0.184026,-0.00336356,0.0715643,-0.00211403,-0.0524604,0.0577402,-0.140635,0.114286,-0.0667142,0.0760093,0.0895684,-0.08739,-0.129856,0.187163,0.0409712,-0.0746805,0.117466,0.043398,-0.153392,0.0198873,-0.0345996,-0.0990012,0.0998033,-0.109452,-0.0391538,0.0237209,0.090306,0.0109887,0.0253246,-0.108542,0.0276882,-0.076779,0.0735205,-0.0771387,0.133176,-0.0185071,0.067999,-0.0562989,0.0124229,-0.023663,0.0364426,-0.0544566,-0.0235236,0.15231,-0.0594304,-0.136698,0.154461,-0.0792525,};
#include <functional>
#include <iostream>
constexpr std::array<std::reference_wrapper<std::array<double, 325> const>, 12> all_coeffs = {
coeffs0, coeffs1, coeffs2, coeffs3, coeffs4, coeffs5,
coeffs6, coeffs7, coeffs8, coeffs9, coeffs10, coeffs11};
double estimate_using(std::array<double, 24> const& vals, std::array<double, 325> const& coeffs) {
double r = coeffs[0];
for (int i = 0; i < 24; ++i) {
r += coeffs[1 + i] * vals[i];
}
int cur = 25;
for (int i = 0; i < 24; ++i) {
for (int j = i; j < 24; ++j) {
r += coeffs[cur++] * vals[i] * vals[j];
}
}
return r;
}
constexpr bool submission = true;
int main() {
int n;
std::cin >> n;
double mean_diff = 0;
for (int i = 0; i < n; ++i) {
// Read input
std::array<double, 24> vals;
for (auto& x: vals) {
double v;
std::cin >> v;
x = v;
}
std::array<double, 12> extra;
if constexpr (!submission) {
// Read extra 12
for (auto& v: extra) {
double x;
std::cin >> x;
v = x;
}
}
// Calculate all
double diff = 0;
for (int i = 0; i < 12; ++i) {
double r = estimate_using(vals, all_coeffs[i]);
if constexpr (submission) {
std::cout << r << " ";
} else {
double error = extra[i] - r;
error *= error;
diff += error;
}
}
if constexpr (!submission) {
std::cout << "Error: " << diff / 12;
mean_diff += diff / 12;
}
std::cout << "\n";
}
std::cout << "Mean diff: " << mean_diff / n << "\n";
}
