= R"(
P = {(-0.701, -1.219, 3.142),(-0.701, -1.219, 3.142),(-0.701, -1.219, 3.141),(-0.702, -1.219, 3.141),(-0.702, -1.219, 3.141),(-0.703, -1.219, 3.140),(-0.704, -1.219, 3.140),(-0.705, -1.219, 3.139),(-0.706, -1.219, 3.139),(-0.708, -1.219, 3.138),(-0.709, -1.219, 3.137),(-0.711, -1.219, 3.136),(-0.713, -1.219, 3.135),(-0.715, -1.219, 3.134),(-0.717, -1.219, 3.133),(-0.719, -1.219, 3.132),(-0.721, -1.219, 3.131),(-0.724, -1.219, 3.129),(-0.727, -1.219, 3.128),(-0.729, -1.219, 3.126),(-0.732, -1.219, 3.125),(-0.736, -1.219, 3.123),(-0.739, -1.219, 3.121),(-0.742, -1.219, 3.119),(-0.746, -1.218, 3.117),(-0.750, -1.218, 3.115),(-0.754, -1.218, 3.113),(-0.758, -1.218, 3.110),(-0.762, -1.218, 3.108),(-0.766, -1.218, 3.105),(-0.771, -1.218, 3.103),(-0.775, -1.217, 3.100),(-0.780, -1.217, 3.097),(-0.785, -1.217, 3.094),(-0.790, -1.217, 3.091),(-0.795, -1.217, 3.088),(-0.801, -1.216, 3.085),(-0.806, -1.216, 3.081),(-0.812, -1.216, 3.078),(-0.818, -1.215, 3.074),(-0.824, -1.215, 3.070),(-0.830, -1.214, 3.066),(-0.836, -1.214, 3.062),(-0.843, -1.213, 3.058),(-0.849, -1.213, 3.054),(-0.856, -1.212, 3.049),(-0.863, -1.211, 3.044),(-0.870, -1.211, 3.040),(-0.877, -1.210, 3.035),(-0.884, -1.209, 3.029),(-0.892, -1.208, 3.024),(-0.899, -1.207, 3.018),(-0.907, -1.206, 3.013),(-0.915, -1.205, 3.007),(-0.923, -1.204, 3.001),(-0.931, -1.203, 2.995),(-0.940, -1.202, 2.988),(-0.948, -1.201, 2.981),(-0.957, -1.199, 2.974),(-0.965, -1.198, 2.967),(-0.974, -1.196, 2.960),(-0.983, -1.194, 2.952),(-0.992, -1.193, 2.944),(-1.002, -1.191, 2.936),(-1.011, -1.189, 2.928),(-1.020, -1.187, 2.919),(-1.030, -1.184, 2.910),(-1.040, -1.182, 2.901),(-1.050, -1.179, 2.892),(-1.060, -1.177, 2.882),(-1.070, -1.174, 2.872),(-1.080, -1.171, 2.861),(-1.091, -1.168, 2.850),(-1.101, -1.165, 2.839),(-1.112, -1.162, 2.827),(-1.122, -1.158, 2.816),(-1.133, -1.154, 2.803),(-1.144, -1.150, 2.790),(-1.155, -1.146, 2.777),(-1.166, -1.142, 2.764),(-1.176, -1.138, 2.751),(-1.187, -1.133, 2.737),(-1.198, -1.129, 2.723),(-1.208, -1.124, 2.709),(-1.218, -1.119, 2.695),(-1.229, -1.114, 2.680),(-1.239, -1.109, 2.665),(-1.249, -1.104, 2.650),(-1.259, -1.098, 2.635),(-1.269, -1.093, 2.620),(-1.278, -1.087, 2.604),(-1.288, -1.081, 2.589),(-1.297, -1.075, 2.573),(-1.307, -1.069, 2.557),(-1.316, -1.063, 2.541),(-1.325, -1.056, 2.524),(-1.334, -1.050, 2.508),(-1.343, -1.043, 2.491),(-1.352, -1.037, 2.475),(-1.361, -1.030, 2.458),(-1.369, -1.023, 2.441),(-1.377, -1.015, 2.424),(-1.386, -1.008, 2.406),(-1.394, -1.001, 2.389),(-1.402, -0.993, 2.372),(-1.410, -0.985, 2.355),(-1.417, -0.977, 2.337),(-1.425, -0.969, 2.320),(-1.432, -0.961, 2.302),(-1.440, -0.953, 2.285),(-1.447, -0.945, 2.267),(-1.454, -0.936, 2.250),(-1.460, -0.928, 2.233),(-1.467, -0.919, 2.215),(-1.474, -0.910, 2.198),(-1.480, -0.901, 2.180),(-1.486, -0.892, 2.163),(-1.492, -0.883, 2.146),(-1.498, -0.874, 2.129),(-1.504, -0.864, 2.112),(-1.510, -0.855, 2.095),(-1.515, -0.845, 2.078),(-1.520, -0.835, 2.062),(-1.526, -0.825, 2.045),(-1.531, -0.815, 2.029),(-1.535, -0.806, 2.013),(-1.540, -0.796, 1.997),(-1.544, -0.786, 1.982),(-1.548, -0.776, 1.967),(-1.552, -0.766, 1.953),(-1.556, -0.757, 1.938),(-1.560, -0.747, 1.925),(-1.563, -0.738, 1.911),(-1.566, -0.729, 1.898),(-1.569, -0.720, 1.886),(-1.572, -0.711, 1.874),(-1.575, -0.702, 1.862),(-1.578, -0.693, 1.850),(-1.580, -0.684, 1.839),(-1.582, -0.675, 1.828),(-1.585, -0.667, 1.817),(-1.587, -0.658, 1.807),(-1.589, -0.650, 1.797),(-1.590, -0.642, 1.787),(-1.592, -0.634, 1.778),(-1.594, -0.626, 1.769),(-1.595, -0.618, 1.760),(-1.597, -0.611, 1.752),(-1.598, -0.603, 1.743),(-1.599, -0.596, 1.735),(-1.600, -0.589, 1.727),(-1.602, -0.582, 1.720),(-1.603, -0.575, 1.713),(-1.604, -0.568, 1.706),(-1.604, -0.562, 1.699),(-1.605, -0.555, 1.692),(-1.606, -0.549, 1.686),(-1.607, -0.543, 1.680),(-1.607, -0.536, 1.674),(-1.608, -0.531, 1.668),(-1.608, -0.525, 1.662),(-1.609, -0.519, 1.657),(-1.609, -0.514, 1.652),(-1.610, -0.508, 1.647),(-1.610, -0.503, 1.642),(-1.611, -0.498, 1.637),(-1.611, -0.493, 1.633),(-1.611, -0.489, 1.628),(-1.611, -0.484, 1.624),(-1.612, -0.480, 1.620),(-1.612, -0.475, 1.616),(-1.612, -0.471, 1.613),(-1.612, -0.467, 1.609),(-1.612, -0.463, 1.606),(-1.612, -0.460, 1.603),(-1.613, -0.456, 1.600),(-1.613, -0.453, 1.597),(-1.613, -0.450, 1.594),(-1.613, -0.447, 1.591),(-1.613, -0.444, 1.589),(-1.613, -0.441, 1.586),(-1.613, -0.438, 1.584),(-1.613, -0.436, 1.582),(-1.613, -0.433, 1.580),(-1.613, -0.431, 1.578),(-1.613, -0.429, 1.577),(-1.613, -0.427, 1.575),(-1.613, -0.426, 1.574),(-1.613, -0.424, 1.572),(-1.613, -0.423, 1.571),(-1.613, -0.422, 1.571)};
V = {(0.000, -0.000),(0.015, -0.008),(0.030, -0.016),(0.045, -0.024),(0.060, -0.032),(0.075, -0.040),(0.090, -0.048),(0.105, -0.056),(0.120, -0.064),(0.135, -0.072),(0.150, -0.080),(0.165, -0.088),(0.180, -0.096),(0.195, -0.105),(0.210, -0.113),(0.225, -0.122),(0.240, -0.130),(0.255, -0.139),(0.270, -0.148),(0.285, -0.157),(0.300, -0.166),(0.315, -0.175),(0.330, -0.184),(0.345, -0.194),(0.360, -0.203),(0.375, -0.213),(0.390, -0.223),(0.405, -0.233),(0.420, -0.243),(0.435, -0.253),(0.450, -0.264),(0.465, -0.275),(0.480, -0.286),(0.495, -0.297),(0.510, -0.309),(0.525, -0.321),(0.540, -0.333),(0.555, -0.345),(0.570, -0.358),(0.585, -0.370),(0.600, -0.384),(0.615, -0.397),(0.630, -0.411),(0.645, -0.425),(0.660, -0.440),(0.675, -0.455),(0.690, -0.471),(0.705, -0.487),(0.720, -0.503),(0.735, -0.520),(0.750, -0.537),(0.765, -0.555),(0.780, -0.573),(0.795, -0.592),(0.810, -0.612),(0.825, -0.632),(0.840, -0.653),(0.855, -0.674),(0.870, -0.696),(0.885, -0.719),(0.900, -0.743),(0.915, -0.767),(0.930, -0.792),(0.945, -0.818),(0.960, -0.845),(0.975, -0.873),(0.990, -0.902),(1.005, -0.931),(1.020, -0.962),(1.035, -0.994),(1.050, -1.026),(1.065, -1.060),(1.080, -1.095),(1.095, -1.131),(1.110, -1.168),(1.125, -1.206),(1.140, -1.245),(1.155, -1.286),(1.163, -1.319),(1.160, -1.341),(1.157, -1.362),(1.154, -1.383),(1.151, -1.404),(1.148, -1.425),(1.145, -1.445),(1.142, -1.465),(1.139, -1.485),(1.136, -1.505),(1.133, -1.524),(1.130, -1.542),(1.128, -1.561),(1.125, -1.578),(1.123, -1.595),(1.120, -1.611),(1.118, -1.627),(1.115, -1.642),(1.113, -1.656),(1.111, -1.669),(1.109, -1.681),(1.108, -1.692),(1.106, -1.702),(1.104, -1.712),(1.103, -1.720),(1.102, -1.727),(1.101, -1.733),(1.100, -1.738),(1.099, -1.742),(1.098, -1.745),(1.098, -1.747),(1.098, -1.747),(1.098, -1.746),(1.098, -1.745),(1.098, -1.742),(1.098, -1.738),(1.099, -1.732),(1.100, -1.726),(1.100, -1.719),(1.101, -1.711),(1.103, -1.701),(1.104, -1.691),(1.105, -1.680),(1.107, -1.668),(1.109, -1.655),(1.110, -1.642),(1.112, -1.627),(1.103, -1.596),(1.088, -1.557),(1.073, -1.517),(1.058, -1.478),(1.043, -1.439),(1.028, -1.401),(1.013, -1.363),(0.998, -1.326),(0.983, -1.290),(0.968, -1.254),(0.953, -1.218),(0.938, -1.184),(0.923, -1.150),(0.908, -1.116),(0.893, -1.084),(0.878, -1.052),(0.863, -1.021),(0.848, -0.991),(0.833, -0.961),(0.818, -0.932),(0.803, -0.904),(0.788, -0.877),(0.773, -0.850),(0.758, -0.824),(0.743, -0.798),(0.728, -0.773),(0.713, -0.749),(0.698, -0.725),(0.683, -0.702),(0.668, -0.680),(0.653, -0.658),(0.638, -0.636),(0.623, -0.615),(0.608, -0.595),(0.593, -0.575),(0.578, -0.555),(0.563, -0.536),(0.548, -0.517),(0.533, -0.499),(0.518, -0.481),(0.503, -0.464),(0.488, -0.446),(0.473, -0.429),(0.458, -0.413),(0.443, -0.397),(0.428, -0.381),(0.413, -0.365),(0.398, -0.350),(0.383, -0.334),(0.368, -0.320),(0.353, -0.305),(0.338, -0.290),(0.323, -0.276),(0.308, -0.262),(0.293, -0.248),(0.278, -0.235),(0.263, -0.221),(0.248, -0.208),(0.233, -0.194),(0.218, -0.181),(0.203, -0.168),(0.188, -0.155),(0.173, -0.143),(0.158, -0.130),(0.143, -0.117),(0.128, -0.105)};
const std::string test_u = R"(
P = {(0.000, 0.000, 1.571),(0.000, 0.000, 1.571),(0.000, 0.000, 1.571),(0.000, 0.001, 1.571),(0.000, 0.002, 1.570),(0.000, 0.002, 1.570),(0.000, 0.003, 1.570),(0.000, 0.004, 1.570),(0.000, 0.005, 1.569),(0.000, 0.007, 1.569),(0.000, 0.008, 1.568),(0.000, 0.010, 1.568),(0.000, 0.012, 1.567),(0.000, 0.014, 1.567),(0.000, 0.016, 1.566),(0.000, 0.018, 1.565),(0.000, 0.020, 1.565),(0.000, 0.023, 1.564),(0.000, 0.026, 1.563),(0.000, 0.029, 1.562),(0.000, 0.032, 1.561),(0.000, 0.035, 1.560),(0.000, 0.038, 1.559),(0.000, 0.041, 1.558),(0.000, 0.045, 1.557),(0.000, 0.049, 1.556),(0.000, 0.053, 1.555),(0.000, 0.057, 1.553),(0.001, 0.061, 1.552),(0.001, 0.065, 1.551),(0.001, 0.070, 1.549),(0.001, 0.074, 1.548),(0.001, 0.079, 1.546),(0.001, 0.084, 1.544),(0.001, 0.089, 1.543),(0.001, 0.095, 1.541),(0.002, 0.100, 1.539),(0.002, 0.105, 1.537),(0.002, 0.111, 1.535),(0.002, 0.117, 1.533),(0.002, 0.123, 1.531),(0.003, 0.129, 1.529),(0.003, 0.135, 1.527),(0.003, 0.142, 1.525),(0.003, 0.148, 1.523),(0.004, 0.155, 1.520),(0.004, 0.162, 1.518),(0.005, 0.169, 1.515),(0.005, 0.176, 1.513),(0.005, 0.184, 1.510),(0.006, 0.191, 1.507),(0.006, 0.199, 1.504),(0.007, 0.207, 1.502),(0.007, 0.214, 1.499),(0.008, 0.223, 1.496),(0.009, 0.231, 1.492),(0.009, 0.239, 1.489),(0.010, 0.248, 1.486),(0.011, 0.256, 1.482),(0.012, 0.265, 1.479),(0.012, 0.274, 1.475),(0.013, 0.283, 1.472),(0.014, 0.292, 1.468),(0.015, 0.302, 1.464),(0.016, 0.311, 1.460),(0.017, 0.321, 1.456),(0.018, 0.330, 1.452),(0.020, 0.339, 1.448),(0.021, 0.349, 1.443),(0.022, 0.358, 1.439),(0.023, 0.367, 1.435),(0.025, 0.377, 1.431),(0.026, 0.386, 1.426),(0.027, 0.395, 1.422),(0.029, 0.404, 1.417),(0.030, 0.414, 1.413),(0.032, 0.423, 1.408),(0.033, 0.432, 1.404),(0.035, 0.441, 1.399),(0.036, 0.450, 1.394),(0.038, 0.460, 1.389),(0.040, 0.469, 1.384),(0.041, 0.478, 1.379),(0.043, 0.487, 1.374),(0.045, 0.496, 1.369),(0.047, 0.505, 1.364),(0.049, 0.514, 1.359),(0.051, 0.523, 1.353),(0.053, 0.532, 1.348),(0.055, 0.541, 1.343),(0.057, 0.550, 1.337),(0.059, 0.559, 1.331),(0.061, 0.568, 1.326),(0.064, 0.577, 1.320),(0.066, 0.586, 1.314),(0.068, 0.594, 1.308),(0.071, 0.603, 1.302),(0.073, 0.612, 1.295),(0.076, 0.621, 1.289),(0.078, 0.630, 1.283),(0.081, 0.638, 1.276),(0.083, 0.647, 1.270),(0.086, 0.655, 1.263),(0.089, 0.664, 1.256),(0.092, 0.673, 1.249),(0.095, 0.681, 1.242),(0.097, 0.690, 1.235),(0.100, 0.698, 1.227),(0.104, 0.706, 1.220),(0.107, 0.715, 1.212),(0.110, 0.723, 1.204),(0.113, 0.731, 1.196),(0.116, 0.740, 1.188),(0.120, 0.748, 1.180),(0.123, 0.756, 1.171),(0.126, 0.764, 1.163),(0.130, 0.772, 1.154),(0.133, 0.780, 1.145),(0.137, 0.788, 1.136),(0.141, 0.796, 1.127),(0.145, 0.803, 1.117),(0.148, 0.811, 1.108),(0.152, 0.819, 1.098),(0.156, 0.826, 1.087),(0.160, 0.834, 1.077),(0.164, 0.841, 1.067),(0.168, 0.849, 1.056),(0.173, 0.856, 1.045),(0.177, 0.863, 1.033),(0.181, 0.870, 1.022),(0.185, 0.878, 1.010),(0.190, 0.884, 0.998),(0.194, 0.891, 0.985),(0.199, 0.898, 0.973),(0.204, 0.905, 0.960),(0.208, 0.911, 0.946),(0.213, 0.918, 0.933),(0.218, 0.924, 0.919),(0.223, 0.931, 0.905),(0.228, 0.937, 0.890),(0.233, 0.943, 0.875),(0.238, 0.949, 0.860),(0.243, 0.955, 0.844),(0.248, 0.961, 0.828),(0.253, 0.966, 0.812),(0.259, 0.972, 0.795),(0.264, 0.977, 0.778),(0.269, 0.982, 0.760),(0.275, 0.987, 0.742),(0.280, 0.992, 0.723),(0.286, 0.997, 0.705),(0.291, 1.002, 0.685),(0.297, 1.006, 0.666),(0.303, 1.010, 0.645),(0.308, 1.015, 0.625),(0.314, 1.019, 0.604),(0.320, 1.023, 0.582),(0.326, 1.026, 0.561),(0.331, 1.030, 0.538),(0.337, 1.033, 0.516),(0.343, 1.037, 0.493),(0.349, 1.040, 0.469),(0.355, 1.043, 0.445),(0.361, 1.045, 0.421),(0.367, 1.048, 0.397),(0.373, 1.050, 0.372),(0.379, 1.053, 0.347),(0.385, 1.055, 0.321),(0.391, 1.056, 0.295),(0.397, 1.058, 0.269),(0.403, 1.060, 0.243),(0.409, 1.061, 0.216),(0.415, 1.062, 0.190),(0.421, 1.064, 0.163),(0.427, 1.064, 0.136),(0.433, 1.065, 0.108),(0.439, 1.066, 0.081),(0.445, 1.066, 0.054),(0.451, 1.066, 0.026),(0.457, 1.066, -0.001),(0.463, 1.066, -0.028),(0.469, 1.066, -0.056),(0.475, 1.066, -0.083),(0.481, 1.065, -0.110),(0.487, 1.064, -0.137),(0.493, 1.063, -0.164),(0.499, 1.062, -0.191),(0.505, 1.061, -0.218),(0.511, 1.060, -0.244),(0.517, 1.058, -0.270),(0.523, 1.056, -0.296),(0.529, 1.055, -0.322),(0.535, 1.052, -0.347),(0.541, 1.050, -0.372),(0.547, 1.048, -0.397),(0.553, 1.045, -0.421),(0.559, 1.043, -0.445),(0.565, 1.040, -0.469),(0.571, 1.037, -0.492),(0.577, 1.033, -0.515),(0.582, 1.030, -0.537),(0.588, 1.026, -0.560),(0.594, 1.023, -0.581),(0.600, 1.019, -0.602),(0.605, 1.015, -0.623),(0.611, 1.011, -0.644),(0.617, 1.006, -0.664),(0.622, 1.002, -0.683),(0.628, 0.997, -0.702),(0.633, 0.993, -0.721),(0.639, 0.988, -0.740),(0.644, 0.983, -0.758),(0.649, 0.978, -0.775),(0.655, 0.972, -0.792),(0.660, 0.967, -0.809),(0.665, 0.961, -0.825),(0.670, 0.956, -0.841),(0.675, 0.950, -0.857),(0.680, 0.944, -0.872),(0.685, 0.938, -0.887),(0.690, 0.932, -0.902),(0.695, 0.926, -0.916),(0.700, 0.919, -0.930),(0.705, 0.913, -0.944),(0.709, 0.906, -0.957),(0.714, 0.900, -0.970),(0.719, 0.893, -0.983),(0.723, 0.886, -0.995),(0.727, 0.879, -1.007),(0.732, 0.872, -1.019),(0.736, 0.865, -1.030),(0.740, 0.858, -1.042),(0.745, 0.851, -1.053),(0.749, 0.843, -1.064),(0.753, 0.836, -1.074),(0.757, 0.828, -1.085),(0.761, 0.821, -1.095),(0.765, 0.813, -1.105),(0.768, 0.806, -1.115),(0.772, 0.798, -1.124),(0.776, 0.790, -1.133),(0.779, 0.782, -1.143),(0.783, 0.774, -1.152),(0.787, 0.766, -1.160),(0.790, 0.758, -1.169),(0.793, 0.750, -1.177),(0.797, 0.742, -1.186),(0.800, 0.734, -1.194),(0.803, 0.726, -1.202),(0.806, 0.717, -1.210),(0.810, 0.709, -1.217),(0.813, 0.701, -1.225),(0.816, 0.692, -1.232),(0.819, 0.684, -1.239),(0.821, 0.675, -1.247),(0.824, 0.667, -1.254),(0.827, 0.658, -1.261),(0.830, 0.650, -1.267),(0.832, 0.641, -1.274),(0.835, 0.632, -1.281),(0.838, 0.624, -1.287),(0.840, 0.615, -1.293),(0.843, 0.606, -1.300),(0.845, 0.597, -1.306),(0.847, 0.589, -1.312),(0.850, 0.580, 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)"