paths.cpp

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#include <string>
#include "paths.h"
 
const std::string skills_1 = R"(
X = [(-1.194,0.010),(-1.194,0.010),(-1.194,0.010),(-1.193,0.010),(-1.193,0.010),(-1.192,0.010),(-1.191,0.010),(-1.190,0.010),(-1.189,0.010),(-1.187,0.010),(-1.186,0.010),(-1.184,0.010),(-1.182,0.010),(-1.180,0.011),(-1.178,0.011),(-1.176,0.011),(-1.174,0.011),(-1.171,0.011),(-1.168,0.011),(-1.166,0.011),(-1.163,0.011),(-1.159,0.012),(-1.156,0.012),(-1.153,0.012),(-1.149,0.012),(-1.145,0.013),(-1.141,0.013),(-1.137,0.013),(-1.133,0.014),(-1.129,0.014),(-1.124,0.014),(-1.120,0.015),(-1.115,0.015),(-1.110,0.016),(-1.105,0.016),(-1.100,0.017),(-1.094,0.017),(-1.089,0.018),(-1.083,0.019),(-1.077,0.019),(-1.071,0.020),(-1.065,0.021),(-1.059,0.022),(-1.053,0.023),(-1.046,0.024),(-1.040,0.025),(-1.033,0.026),(-1.026,0.027),(-1.019,0.028),(-1.011,0.029),(-1.004,0.030),(-0.996,0.032),(-0.989,0.033),(-0.981,0.035),(-0.973,0.036),(-0.965,0.038),(-0.957,0.039),(-0.948,0.041),(-0.940,0.043),(-0.931,0.045),(-0.922,0.047),(-0.913,0.049),(-0.905,0.051),(-0.896,0.053),(-0.887,0.055),(-0.878,0.058),(-0.869,0.060),(-0.860,0.062),(-0.851,0.065),(-0.842,0.067),(-0.834,0.070),(-0.825,0.072),(-0.816,0.075),(-0.808,0.078),(-0.799,0.080),(-0.790,0.083),(-0.782,0.086),(-0.773,0.089),(-0.765,0.092),(-0.756,0.095),(-0.748,0.098),(-0.739,0.101),(-0.731,0.104),(-0.722,0.107),(-0.714,0.110),(-0.706,0.114),(-0.698,0.117),(-0.690,0.120),(-0.681,0.124),(-0.673,0.127),(-0.666,0.131),(-0.658,0.135),(-0.650,0.138),(-0.642,0.142),(-0.634,0.146),(-0.627,0.150),(-0.619,0.154),(-0.612,0.158),(-0.604,0.162),(-0.597,0.166),(-0.590,0.170),(-0.583,0.174),(-0.576,0.178),(-0.569,0.183),(-0.563,0.187),(-0.556,0.192),(-0.549,0.196),(-0.543,0.201),(-0.537,0.205),(-0.531,0.210),(-0.525,0.215),(-0.519,0.219),(-0.514,0.224),(-0.508,0.229),(-0.503,0.234),(-0.498,0.239),(-0.493,0.244),(-0.489,0.249),(-0.484,0.253),(-0.480,0.258),(-0.476,0.263),(-0.472,0.268),(-0.468,0.273),(-0.465,0.278),(-0.462,0.283),(-0.459,0.288),(-0.456,0.293),(-0.453,0.298),(-0.451,0.303),(-0.449,0.308),(-0.446,0.313),(-0.445,0.318),(-0.443,0.323),(-0.442,0.328),(-0.440,0.333),(-0.439,0.338),(-0.438,0.343),(-0.437,0.348),(-0.437,0.352),(-0.437,0.357),(-0.436,0.362),(-0.436,0.367),(-0.436,0.372),(-0.437,0.377),(-0.437,0.382),(-0.438,0.387),(-0.439,0.392),(-0.440,0.396),(-0.441,0.401),(-0.442,0.406),(-0.444,0.411),(-0.446,0.416),(-0.447,0.422),(-0.450,0.427),(-0.452,0.432),(-0.454,0.436),(-0.457,0.441),(-0.459,0.445),(-0.461,0.450),(-0.464,0.454),(-0.466,0.458),(-0.469,0.461),(-0.471,0.465),(-0.474,0.468),(-0.476,0.471),(-0.478,0.475),(-0.481,0.477),(-0.483,0.480),(-0.485,0.483),(-0.487,0.485),(-0.489,0.488),(-0.491,0.490),(-0.493,0.492),(-0.495,0.494),(-0.496,0.496),(-0.498,0.498),(-0.499,0.499),(-0.501,0.501),(-0.502,0.502),(-0.503,0.503),(-0.505,0.504),(-0.506,0.505),(-0.506,0.506),(-0.507,0.507),(-0.508,0.508)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.585),(0.400,0.600),(0.410,0.615),(0.420,0.630),(0.430,0.645),(0.440,0.660),(0.450,0.675),(0.460,0.690),(0.470,0.705),(0.480,0.720),(0.490,0.735),(0.500,0.750),(0.510,0.765),(0.520,0.780),(0.530,0.795),(0.540,0.810),(0.550,0.825),(0.560,0.840),(0.570,0.855),(0.580,0.870),(0.590,0.885),(0.600,0.900),(0.610,0.915),(0.620,0.918),(0.630,0.918),(0.640,0.917),(0.650,0.917),(0.660,0.916),(0.670,0.915),(0.680,0.915),(0.690,0.914),(0.700,0.913),(0.710,0.912),(0.720,0.911),(0.730,0.910),(0.740,0.908),(0.750,0.907),(0.760,0.906),(0.770,0.904),(0.780,0.902),(0.790,0.901),(0.800,0.899),(0.810,0.897),(0.820,0.895),(0.830,0.893),(0.840,0.890),(0.850,0.888),(0.860,0.885),(0.870,0.882),(0.880,0.879),(0.890,0.876),(0.900,0.873),(0.910,0.869),(0.920,0.866),(0.930,0.862),(0.940,0.858),(0.950,0.853),(0.960,0.849),(0.970,0.844),(0.980,0.839),(0.990,0.833),(1.000,0.828),(1.010,0.822),(1.020,0.815),(1.030,0.809),(1.040,0.802),(1.050,0.794),(1.060,0.786),(1.070,0.778),(1.080,0.770),(1.090,0.761),(1.100,0.752),(1.110,0.742),(1.120,0.733),(1.130,0.722),(1.140,0.712),(1.150,0.701),(1.160,0.690),(1.170,0.678),(1.180,0.667),(1.190,0.655),(1.200,0.643),(1.210,0.631),(1.220,0.620),(1.230,0.608),(1.240,0.596),(1.250,0.585),(1.260,0.574),(1.270,0.564),(1.280,0.554),(1.290,0.544),(1.300,0.535),(1.310,0.527),(1.320,0.519),(1.330,0.512),(1.340,0.506),(1.350,0.501),(1.360,0.496),(1.370,0.492),(1.380,0.490),(1.390,0.488),(1.400,0.487),(1.410,0.487),(1.420,0.487),(1.430,0.489),(1.440,0.492),(1.450,0.495),(1.460,0.499),(1.470,0.504),(1.480,0.510),(1.490,0.517),(1.500,0.525),(1.510,0.533),(1.520,0.541),(1.530,0.551),(1.540,0.550),(1.550,0.535),(1.560,0.520),(1.570,0.505),(1.580,0.490),(1.590,0.475),(1.600,0.460),(1.610,0.445),(1.620,0.430),(1.630,0.415),(1.640,0.400),(1.650,0.385),(1.660,0.370),(1.670,0.355),(1.680,0.340),(1.690,0.325),(1.700,0.310),(1.710,0.295),(1.720,0.280),(1.730,0.265),(1.740,0.250),(1.750,0.235),(1.760,0.220),(1.770,0.205),(1.780,0.190),(1.790,0.175),(1.800,0.160),(1.810,0.145),(1.820,0.130),(1.830,0.115),(1.840,0.100)]
A = [(0.000,0.000),(0.010,0.014),(0.020,0.028),(0.030,0.042),(0.040,0.056),(0.050,0.070),(0.060,0.083),(0.070,0.097),(0.080,0.110),(0.090,0.123),(0.100,0.136),(0.110,0.149),(0.120,0.161),(0.130,0.173),(0.140,0.185),(0.150,0.197),(0.160,0.208),(0.170,0.219),(0.180,0.230),(0.190,0.240),(0.200,0.250),(0.210,0.260),(0.220,0.270),(0.230,0.279),(0.240,0.288),(0.250,0.297),(0.260,0.305),(0.270,0.313),(0.280,0.321),(0.290,0.329),(0.300,0.336),(0.310,0.343),(0.320,0.351),(0.330,0.357),(0.340,0.364),(0.350,0.371),(0.360,0.377),(0.370,0.384),(0.380,0.390),(0.390,0.396),(0.400,0.402),(0.410,0.409),(0.420,0.415),(0.430,0.421),(0.440,0.427),(0.450,0.433),(0.460,0.440),(0.470,0.446),(0.480,0.453),(0.490,0.460),(0.500,0.467),(0.510,0.474),(0.520,0.481),(0.530,0.489),(0.540,0.497),(0.550,0.506),(0.560,0.515),(0.570,0.524),(0.580,0.534),(0.590,0.544),(0.600,0.555),(0.610,0.566),(0.620,0.571),(0.630,0.574),(0.640,0.577),(0.650,0.582),(0.660,0.586),(0.670,0.592),(0.680,0.597),(0.690,0.604),(0.700,0.610),(0.710,0.618),(0.720,0.626),(0.730,0.635),(0.740,0.644),(0.750,0.654),(0.760,0.665),(0.770,0.676),(0.780,0.688),(0.790,0.701),(0.800,0.715),(0.810,0.730),(0.820,0.745),(0.830,0.762),(0.840,0.779),(0.850,0.798),(0.860,0.817),(0.870,0.838),(0.880,0.860),(0.890,0.883),(0.900,0.908),(0.910,0.934),(0.920,0.961),(0.930,0.990),(0.940,1.021),(0.950,1.054),(0.960,1.088),(0.970,1.124),(0.980,1.162),(0.990,1.202),(1.000,1.245),(1.010,1.289),(1.020,1.336),(1.030,1.386),(1.040,1.438),(1.050,1.492),(1.060,1.550),(1.070,1.610),(1.080,1.672),(1.090,1.738),(1.100,1.806),(1.110,1.876),(1.120,1.950),(1.130,2.025),(1.140,2.103),(1.150,2.182),(1.160,2.264),(1.170,2.347),(1.180,2.430),(1.190,2.515),(1.200,2.599),(1.210,2.683),(1.220,2.766),(1.230,2.847),(1.240,2.927),(1.250,3.003),(1.260,3.077),(1.270,3.147),(1.280,3.212),(1.290,3.273),(1.300,3.329),(1.310,3.379),(1.320,3.424),(1.330,3.462),(1.340,3.495),(1.350,3.521),(1.360,3.540),(1.370,3.554),(1.380,3.561),(1.390,3.561),(1.400,3.555),(1.410,3.543),(1.420,3.525),(1.430,3.501),(1.440,3.471),(1.450,3.436),(1.460,3.395),(1.470,3.350),(1.480,3.299),(1.490,3.245),(1.500,3.186),(1.510,3.123),(1.520,3.056),(1.530,2.987),(1.540,2.860),(1.550,2.669),(1.560,2.489),(1.570,2.321),(1.580,2.165),(1.590,2.019),(1.600,1.883),(1.610,1.756),(1.620,1.638),(1.630,1.528),(1.640,1.426),(1.650,1.330),(1.660,1.241),(1.670,1.157),(1.680,1.078),(1.690,1.004),(1.700,0.935),(1.710,0.869),(1.720,0.807),(1.730,0.749),(1.740,0.693),(1.750,0.640),(1.760,0.589),(1.770,0.540),(1.780,0.494),(1.790,0.449),(1.800,0.405),(1.810,0.363),(1.820,0.323),(1.830,0.283),(1.840,0.244)]
)";
 
const std::string skills_2 = R"(
X = [(-0.310,0.338),(-0.310,0.338),(-0.310,0.338),(-0.310,0.339),(-0.311,0.339),(-0.311,0.340),(-0.312,0.341),(-0.312,0.342),(-0.313,0.343),(-0.314,0.344),(-0.314,0.345),(-0.315,0.346),(-0.316,0.348),(-0.317,0.349),(-0.318,0.351),(-0.320,0.353),(-0.321,0.355),(-0.322,0.357),(-0.324,0.360),(-0.325,0.362),(-0.327,0.365),(-0.329,0.367),(-0.330,0.370),(-0.332,0.373),(-0.334,0.376),(-0.336,0.379),(-0.338,0.382),(-0.340,0.386),(-0.343,0.389),(-0.345,0.393),(-0.347,0.397),(-0.350,0.401),(-0.352,0.405),(-0.355,0.409),(-0.358,0.414),(-0.360,0.418),(-0.363,0.423),(-0.366,0.427),(-0.369,0.432),(-0.372,0.437),(-0.375,0.442),(-0.379,0.447),(-0.382,0.453),(-0.385,0.458),(-0.389,0.464),(-0.392,0.470),(-0.396,0.476),(-0.400,0.482),(-0.403,0.488),(-0.407,0.494),(-0.411,0.500),(-0.415,0.507),(-0.419,0.513),(-0.424,0.520),(-0.428,0.527),(-0.432,0.534),(-0.437,0.541),(-0.441,0.548),(-0.446,0.556),(-0.450,0.563),(-0.455,0.571),(-0.460,0.579),(-0.465,0.587),(-0.470,0.595),(-0.475,0.603),(-0.480,0.611),(-0.486,0.619),(-0.491,0.627),(-0.496,0.636),(-0.502,0.644),(-0.507,0.652),(-0.512,0.660),(-0.518,0.668),(-0.523,0.677),(-0.528,0.685),(-0.534,0.693),(-0.539,0.701),(-0.544,0.709),(-0.550,0.717),(-0.555,0.725),(-0.560,0.733),(-0.566,0.741),(-0.571,0.749),(-0.577,0.757),(-0.582,0.765),(-0.588,0.773),(-0.593,0.781),(-0.599,0.789),(-0.604,0.797),(-0.610,0.804),(-0.615,0.812),(-0.621,0.820),(-0.627,0.828),(-0.632,0.836),(-0.638,0.843),(-0.643,0.851),(-0.649,0.859),(-0.655,0.866),(-0.660,0.874),(-0.666,0.881),(-0.672,0.889),(-0.678,0.896),(-0.683,0.904),(-0.689,0.911),(-0.695,0.919),(-0.701,0.926),(-0.707,0.933),(-0.713,0.941),(-0.719,0.948),(-0.725,0.955),(-0.731,0.962),(-0.737,0.970),(-0.743,0.977),(-0.749,0.984),(-0.755,0.991),(-0.761,0.998),(-0.767,1.005),(-0.773,1.012),(-0.779,1.018),(-0.785,1.025),(-0.792,1.032),(-0.798,1.039),(-0.804,1.045),(-0.810,1.052),(-0.817,1.058),(-0.823,1.065),(-0.829,1.071),(-0.836,1.077),(-0.842,1.084),(-0.849,1.090),(-0.855,1.096),(-0.862,1.102),(-0.868,1.108),(-0.875,1.114),(-0.881,1.120),(-0.888,1.126),(-0.894,1.131),(-0.901,1.137),(-0.908,1.142),(-0.915,1.148),(-0.921,1.153),(-0.928,1.159),(-0.935,1.164),(-0.942,1.169),(-0.948,1.174),(-0.955,1.179),(-0.962,1.183),(-0.969,1.188),(-0.976,1.193),(-0.983,1.197),(-0.990,1.201),(-0.997,1.206),(-1.004,1.210),(-1.011,1.214),(-1.018,1.218),(-1.025,1.221),(-1.032,1.225),(-1.039,1.229),(-1.046,1.232),(-1.053,1.235),(-1.060,1.238),(-1.067,1.241),(-1.074,1.244),(-1.081,1.247),(-1.088,1.249),(-1.095,1.252),(-1.102,1.254),(-1.109,1.256),(-1.116,1.258),(-1.123,1.260),(-1.130,1.261),(-1.137,1.263),(-1.144,1.264),(-1.151,1.266),(-1.158,1.267),(-1.165,1.268),(-1.172,1.268),(-1.179,1.269),(-1.186,1.269),(-1.192,1.270),(-1.199,1.270),(-1.204,1.270),(-1.204,1.270),(-1.211,1.270),(-1.218,1.270),(-1.225,1.270),(-1.233,1.270),(-1.240,1.270),(-1.248,1.270),(-1.256,1.270),(-1.264,1.270),(-1.272,1.270),(-1.281,1.270),(-1.289,1.270),(-1.298,1.270),(-1.307,1.270),(-1.316,1.270),(-1.325,1.270),(-1.334,1.270),(-1.343,1.270),(-1.353,1.270),(-1.362,1.270),(-1.372,1.270),(-1.382,1.270),(-1.391,1.270),(-1.400,1.270),(-1.409,1.270),(-1.418,1.270),(-1.427,1.270),(-1.436,1.270),(-1.444,1.270),(-1.453,1.270),(-1.461,1.270),(-1.469,1.270),(-1.477,1.270),(-1.484,1.270),(-1.492,1.270),(-1.500,1.270),(-1.507,1.270),(-1.514,1.270),(-1.521,1.270),(-1.528,1.270),(-1.534,1.270),(-1.541,1.270),(-1.547,1.270),(-1.553,1.270),(-1.560,1.270),(-1.565,1.270),(-1.571,1.270),(-1.577,1.270),(-1.582,1.270),(-1.588,1.270),(-1.593,1.270),(-1.598,1.270),(-1.603,1.270),(-1.607,1.270),(-1.612,1.270),(-1.616,1.270),(-1.620,1.270),(-1.625,1.270),(-1.628,1.270),(-1.632,1.270),(-1.636,1.270),(-1.639,1.270),(-1.643,1.270),(-1.646,1.270),(-1.649,1.270),(-1.652,1.270),(-1.654,1.270),(-1.657,1.270),(-1.659,1.270),(-1.662,1.270),(-1.664,1.270),(-1.666,1.270),(-1.667,1.270),(-1.669,1.270),(-1.670,1.270),(-1.672,1.270),(-1.673,1.270),(-1.674,1.270),(-1.675,1.270),(-1.675,1.270),(-1.676,1.270),(-1.676,1.270)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.585),(0.400,0.600),(0.410,0.615),(0.420,0.630),(0.430,0.645),(0.440,0.660),(0.450,0.675),(0.460,0.690),(0.470,0.705),(0.480,0.720),(0.490,0.735),(0.500,0.750),(0.510,0.765),(0.520,0.780),(0.530,0.795),(0.540,0.810),(0.550,0.825),(0.560,0.840),(0.570,0.855),(0.580,0.870),(0.590,0.885),(0.600,0.900),(0.610,0.915),(0.620,0.930),(0.630,0.945),(0.640,0.960),(0.650,0.975),(0.660,0.980),(0.670,0.979),(0.680,0.978),(0.690,0.977),(0.700,0.976),(0.710,0.976),(0.720,0.975),(0.730,0.974),(0.740,0.973),(0.750,0.972),(0.760,0.971),(0.770,0.970),(0.780,0.970),(0.790,0.969),(0.800,0.968),(0.810,0.967),(0.820,0.966),(0.830,0.965),(0.840,0.964),(0.850,0.963),(0.860,0.962),(0.870,0.962),(0.880,0.961),(0.890,0.960),(0.900,0.959),(0.910,0.958),(0.920,0.957),(0.930,0.956),(0.940,0.954),(0.950,0.953),(0.960,0.952),(0.970,0.951),(0.980,0.950),(0.990,0.949),(1.000,0.948),(1.010,0.946),(1.020,0.945),(1.030,0.944),(1.040,0.943),(1.050,0.941),(1.060,0.940),(1.070,0.938),(1.080,0.937),(1.090,0.935),(1.100,0.934),(1.110,0.932),(1.120,0.931),(1.130,0.929),(1.140,0.927),(1.150,0.926),(1.160,0.924),(1.170,0.922),(1.180,0.920),(1.190,0.918),(1.200,0.916),(1.210,0.914),(1.220,0.912),(1.230,0.910),(1.240,0.907),(1.250,0.905),(1.260,0.902),(1.270,0.900),(1.280,0.897),(1.290,0.895),(1.300,0.892),(1.310,0.889),(1.320,0.886),(1.330,0.883),(1.340,0.880),(1.350,0.877),(1.360,0.874),(1.370,0.870),(1.380,0.867),(1.390,0.864),(1.400,0.860),(1.410,0.856),(1.420,0.852),(1.430,0.848),(1.440,0.844),(1.450,0.840),(1.460,0.836),(1.470,0.832),(1.480,0.827),(1.490,0.823),(1.500,0.818),(1.510,0.813),(1.520,0.809),(1.530,0.804),(1.540,0.799),(1.550,0.794),(1.560,0.789),(1.570,0.784),(1.580,0.779),(1.590,0.774),(1.600,0.769),(1.610,0.763),(1.620,0.758),(1.630,0.753),(1.640,0.748),(1.650,0.743),(1.660,0.738),(1.670,0.733),(1.680,0.729),(1.690,0.724),(1.700,0.720),(1.710,0.715),(1.720,0.711),(1.730,0.707),(1.740,0.703),(1.750,0.700),(1.760,0.697),(1.770,0.694),(1.780,0.691),(1.790,0.688),(1.800,0.686),(1.810,0.684),(1.810,0.684),(1.820,0.699),(1.830,0.714),(1.840,0.729),(1.850,0.744),(1.860,0.759),(1.870,0.774),(1.880,0.789),(1.890,0.804),(1.900,0.819),(1.910,0.834),(1.920,0.849),(1.930,0.864),(1.940,0.879),(1.950,0.894),(1.960,0.909),(1.970,0.924),(1.980,0.939),(1.990,0.954),(2.000,0.969),(2.010,0.970),(2.020,0.955),(2.030,0.940),(2.040,0.924),(2.050,0.909),(2.060,0.894),(2.070,0.879),(2.080,0.864),(2.090,0.849),(2.100,0.834),(2.110,0.819),(2.120,0.803),(2.130,0.788),(2.140,0.773),(2.150,0.758),(2.160,0.743),(2.170,0.728),(2.180,0.712),(2.190,0.697),(2.200,0.682),(2.210,0.667),(2.220,0.652),(2.230,0.637),(2.240,0.621),(2.250,0.606),(2.260,0.591),(2.270,0.576),(2.280,0.561),(2.290,0.545),(2.300,0.530),(2.310,0.515),(2.320,0.500),(2.330,0.485),(2.340,0.469),(2.350,0.454),(2.360,0.439),(2.370,0.424),(2.380,0.408),(2.390,0.393),(2.400,0.378),(2.410,0.362),(2.420,0.347),(2.430,0.332),(2.440,0.316),(2.450,0.301),(2.460,0.286),(2.470,0.270),(2.480,0.255),(2.490,0.239),(2.500,0.224),(2.510,0.208),(2.520,0.193),(2.530,0.177),(2.540,0.161),(2.550,0.146),(2.560,0.130),(2.570,0.114),(2.580,0.098),(2.590,0.081),(2.600,0.064),(2.610,0.047),(2.620,0.028)]
A = [(0.000,-0.000),(0.010,-0.005),(0.020,-0.009),(0.030,-0.014),(0.040,-0.018),(0.050,-0.022),(0.060,-0.027),(0.070,-0.031),(0.080,-0.034),(0.090,-0.038),(0.100,-0.041),(0.110,-0.045),(0.120,-0.048),(0.130,-0.050),(0.140,-0.053),(0.150,-0.055),(0.160,-0.057),(0.170,-0.058),(0.180,-0.060),(0.190,-0.060),(0.200,-0.061),(0.210,-0.062),(0.220,-0.062),(0.230,-0.061),(0.240,-0.061),(0.250,-0.060),(0.260,-0.059),(0.270,-0.058),(0.280,-0.056),(0.290,-0.054),(0.300,-0.052),(0.310,-0.050),(0.320,-0.047),(0.330,-0.044),(0.340,-0.041),(0.350,-0.038),(0.360,-0.035),(0.370,-0.031),(0.380,-0.027),(0.390,-0.023),(0.400,-0.019),(0.410,-0.014),(0.420,-0.010),(0.430,-0.005),(0.440,-0.000),(0.450,0.005),(0.460,0.010),(0.470,0.015),(0.480,0.021),(0.490,0.026),(0.500,0.032),(0.510,0.038),(0.520,0.044),(0.530,0.050),(0.540,0.057),(0.550,0.063),(0.560,0.070),(0.570,0.077),(0.580,0.084),(0.590,0.091),(0.600,0.098),(0.610,0.106),(0.620,0.113),(0.630,0.121),(0.640,0.129),(0.650,0.138),(0.660,0.145),(0.670,0.151),(0.680,0.157),(0.690,0.163),(0.700,0.169),(0.710,0.175),(0.720,0.181),(0.730,0.187),(0.740,0.193),(0.750,0.199),(0.760,0.204),(0.770,0.210),(0.780,0.216),(0.790,0.223),(0.800,0.229),(0.810,0.235),(0.820,0.241),(0.830,0.247),(0.840,0.254),(0.850,0.260),(0.860,0.267),(0.870,0.273),(0.880,0.280),(0.890,0.287),(0.900,0.294),(0.910,0.301),(0.920,0.308),(0.930,0.315),(0.940,0.323),(0.950,0.331),(0.960,0.338),(0.970,0.346),(0.980,0.354),(0.990,0.363),(1.000,0.371),(1.010,0.380),(1.020,0.389),(1.030,0.398),(1.040,0.407),(1.050,0.417),(1.060,0.427),(1.070,0.437),(1.080,0.447),(1.090,0.458),(1.100,0.469),(1.110,0.480),(1.120,0.492),(1.130,0.504),(1.140,0.516),(1.150,0.529),(1.160,0.542),(1.170,0.555),(1.180,0.569),(1.190,0.583),(1.200,0.597),(1.210,0.612),(1.220,0.628),(1.230,0.644),(1.240,0.660),(1.250,0.677),(1.260,0.694),(1.270,0.712),(1.280,0.731),(1.290,0.750),(1.300,0.769),(1.310,0.790),(1.320,0.810),(1.330,0.832),(1.340,0.854),(1.350,0.877),(1.360,0.900),(1.370,0.924),(1.380,0.949),(1.390,0.974),(1.400,1.000),(1.410,1.027),(1.420,1.054),(1.430,1.083),(1.440,1.111),(1.450,1.141),(1.460,1.171),(1.470,1.202),(1.480,1.234),(1.490,1.266),(1.500,1.299),(1.510,1.332),(1.520,1.366),(1.530,1.400),(1.540,1.435),(1.550,1.470),(1.560,1.505),(1.570,1.541),(1.580,1.577),(1.590,1.613),(1.600,1.648),(1.610,1.684),(1.620,1.720),(1.630,1.755),(1.640,1.790),(1.650,1.824),(1.660,1.857),(1.670,1.890),(1.680,1.922),(1.690,1.953),(1.700,1.983),(1.710,2.011),(1.720,2.038),(1.730,2.064),(1.740,2.088),(1.750,2.110),(1.760,2.130),(1.770,2.149),(1.780,2.165),(1.790,2.180),(1.800,2.192),(1.810,2.198),(1.810,-0.000),(1.820,-0.000),(1.830,-0.000),(1.840,-0.000),(1.850,-0.000),(1.860,-0.000),(1.870,-0.000),(1.880,-0.000),(1.890,-0.000),(1.900,-0.000),(1.910,-0.000),(1.920,-0.000),(1.930,-0.000),(1.940,-0.000),(1.950,-0.000),(1.960,-0.000),(1.970,-0.000),(1.980,-0.000),(1.990,-0.000),(2.000,-0.000),(2.010,-0.000),(2.020,-0.000),(2.030,-0.000),(2.040,-0.000),(2.050,0.000),(2.060,0.000),(2.070,0.000),(2.080,0.000),(2.090,0.000),(2.100,0.000),(2.110,0.000),(2.120,0.000),(2.130,0.000),(2.140,0.000),(2.150,0.000),(2.160,0.000),(2.170,0.000),(2.180,0.000),(2.190,0.000),(2.200,0.000),(2.210,0.000),(2.220,0.000),(2.230,0.000),(2.240,0.000),(2.250,0.000),(2.260,0.000),(2.270,0.000),(2.280,0.000),(2.290,0.000),(2.300,0.000),(2.310,0.000),(2.320,0.000),(2.330,0.000),(2.340,0.000),(2.350,0.000),(2.360,0.000),(2.370,0.000),(2.380,0.000),(2.390,0.000),(2.400,0.000),(2.410,0.000),(2.420,0.000),(2.430,0.000),(2.440,0.000),(2.450,0.000),(2.460,0.000),(2.470,0.000),(2.480,0.000),(2.490,0.000),(2.500,0.000),(2.510,0.000),(2.520,0.000),(2.530,0.000),(2.540,0.000),(2.550,0.000),(2.560,0.000),(2.570,0.000),(2.580,0.000),(2.590,0.000),(2.600,0.000),(2.610,0.000),(2.620,0.000)]
)";
 
const std::string skills_3 = R"(
X = [(-1.524,1.181),(-1.524,1.181),(-1.524,1.181),(-1.523,1.181),(-1.522,1.181),(-1.522,1.181),(-1.521,1.181),(-1.520,1.181),(-1.519,1.181),(-1.517,1.181),(-1.516,1.181),(-1.514,1.181),(-1.512,1.181),(-1.510,1.181),(-1.508,1.181),(-1.506,1.181),(-1.504,1.181),(-1.501,1.181),(-1.498,1.182),(-1.496,1.182),(-1.493,1.182),(-1.489,1.182),(-1.486,1.182),(-1.483,1.183),(-1.479,1.183),(-1.475,1.183),(-1.471,1.184),(-1.467,1.184),(-1.463,1.185),(-1.459,1.185),(-1.455,1.186),(-1.450,1.187),(-1.445,1.188),(-1.440,1.189),(-1.435,1.190),(-1.430,1.191),(-1.425,1.193),(-1.420,1.194),(-1.414,1.196),(-1.409,1.198),(-1.404,1.200),(-1.399,1.203),(-1.394,1.205),(-1.390,1.207),(-1.385,1.210),(-1.381,1.212),(-1.377,1.215),(-1.373,1.218),(-1.369,1.221),(-1.365,1.224),(-1.362,1.228),(-1.358,1.231),(-1.355,1.235),(-1.351,1.238),(-1.348,1.242),(-1.345,1.247),(-1.342,1.251),(-1.338,1.256),(-1.335,1.260),(-1.332,1.265),(-1.329,1.271),(-1.326,1.276),(-1.323,1.282),(-1.320,1.287),(-1.317,1.293),(-1.314,1.300),(-1.311,1.306),(-1.308,1.312),(-1.304,1.319),(-1.301,1.325),(-1.298,1.332),(-1.294,1.339),(-1.290,1.346),(-1.287,1.353),(-1.283,1.359),(-1.279,1.366),(-1.275,1.372),(-1.271,1.378),(-1.267,1.384),(-1.263,1.389),(-1.259,1.395),(-1.255,1.400),(-1.251,1.405),(-1.246,1.410),(-1.242,1.415),(-1.237,1.420),(-1.232,1.424),(-1.227,1.429),(-1.222,1.433),(-1.217,1.438),(-1.212,1.442),(-1.207,1.446),(-1.201,1.450),(-1.196,1.455),(-1.190,1.459),(-1.184,1.462),(-1.178,1.466),(-1.172,1.470),(-1.166,1.474),(-1.159,1.477),(-1.153,1.481),(-1.146,1.484),(-1.139,1.487),(-1.132,1.491),(-1.125,1.494),(-1.118,1.497),(-1.111,1.500),(-1.104,1.503),(-1.096,1.506),(-1.088,1.509),(-1.081,1.511),(-1.073,1.514),(-1.065,1.517),(-1.057,1.519),(-1.049,1.522),(-1.041,1.524),(-1.033,1.526),(-1.025,1.528),(-1.016,1.531),(-1.008,1.533),(-1.000,1.535),(-0.991,1.537),(-0.983,1.538),(-0.974,1.540),(-0.965,1.542),(-0.957,1.544),(-0.948,1.545),(-0.939,1.547),(-0.930,1.548),(-0.921,1.550),(-0.912,1.551),(-0.903,1.553),(-0.894,1.554),(-0.885,1.555),(-0.876,1.556),(-0.867,1.558),(-0.858,1.559),(-0.849,1.560),(-0.840,1.561),(-0.830,1.562),(-0.821,1.563),(-0.812,1.564),(-0.803,1.565),(-0.793,1.565),(-0.784,1.566),(-0.775,1.567),(-0.765,1.568),(-0.756,1.568),(-0.746,1.569),(-0.737,1.569),(-0.728,1.570),(-0.718,1.571),(-0.709,1.571),(-0.699,1.572),(-0.690,1.572),(-0.680,1.572),(-0.671,1.573),(-0.661,1.573),(-0.651,1.573),(-0.642,1.574),(-0.632,1.574),(-0.623,1.574),(-0.613,1.574),(-0.604,1.574),(-0.594,1.575),(-0.584,1.575),(-0.575,1.575),(-0.565,1.575),(-0.555,1.575),(-0.546,1.575),(-0.541,1.575),(-0.541,1.575),(-0.531,1.575),(-0.521,1.575),(-0.511,1.575),(-0.501,1.575),(-0.491,1.575),(-0.481,1.575),(-0.471,1.575),(-0.461,1.575),(-0.451,1.575),(-0.441,1.575),(-0.431,1.575),(-0.421,1.575),(-0.411,1.575),(-0.401,1.575),(-0.391,1.575),(-0.381,1.575),(-0.371,1.575),(-0.361,1.575),(-0.351,1.575),(-0.341,1.575),(-0.331,1.575),(-0.321,1.575),(-0.311,1.575),(-0.301,1.575),(-0.291,1.575),(-0.281,1.575),(-0.271,1.575),(-0.261,1.575),(-0.251,1.575),(-0.241,1.575),(-0.231,1.575),(-0.221,1.575),(-0.211,1.575),(-0.201,1.575),(-0.191,1.575),(-0.181,1.575),(-0.171,1.575),(-0.161,1.575),(-0.151,1.575),(-0.141,1.575),(-0.131,1.575),(-0.121,1.575),(-0.111,1.575),(-0.101,1.575),(-0.091,1.575),(-0.081,1.575),(-0.071,1.575),(-0.061,1.575),(-0.051,1.575),(-0.041,1.575),(-0.031,1.575),(-0.021,1.575),(-0.011,1.575),(-0.001,1.575),(0.009,1.575),(0.019,1.575),(0.029,1.575),(0.039,1.575),(0.049,1.575),(0.059,1.575),(0.069,1.575),(0.079,1.575),(0.089,1.575),(0.099,1.575),(0.109,1.575),(0.119,1.575),(0.129,1.575),(0.139,1.575),(0.149,1.575),(0.159,1.575),(0.169,1.575),(0.179,1.575),(0.189,1.575),(0.199,1.575),(0.209,1.575),(0.219,1.575),(0.229,1.575),(0.239,1.575),(0.249,1.575),(0.259,1.575),(0.269,1.575),(0.279,1.575),(0.289,1.575),(0.299,1.575),(0.309,1.575),(0.319,1.575),(0.329,1.575),(0.339,1.575),(0.349,1.575),(0.359,1.575),(0.369,1.575),(0.379,1.575),(0.389,1.575),(0.399,1.575),(0.409,1.575),(0.419,1.575),(0.429,1.575),(0.439,1.575),(0.449,1.575),(0.459,1.575),(0.469,1.575),(0.479,1.575),(0.489,1.575),(0.499,1.575),(0.509,1.575),(0.519,1.575),(0.529,1.575),(0.539,1.575),(0.549,1.575),(0.559,1.575),(0.569,1.575),(0.579,1.575),(0.589,1.575),(0.599,1.575),(0.609,1.575),(0.611,1.575),(0.611,1.575),(0.621,1.575),(0.631,1.575),(0.641,1.575),(0.651,1.575),(0.661,1.575),(0.671,1.575),(0.681,1.575),(0.691,1.575),(0.701,1.575),(0.710,1.575),(0.720,1.575),(0.730,1.575),(0.740,1.575),(0.750,1.575),(0.759,1.575),(0.769,1.575),(0.779,1.574),(0.788,1.574),(0.798,1.574),(0.807,1.574),(0.817,1.574),(0.826,1.573),(0.836,1.573),(0.845,1.573),(0.855,1.572),(0.864,1.572),(0.873,1.571),(0.883,1.571),(0.892,1.570),(0.901,1.570),(0.910,1.569),(0.919,1.568),(0.928,1.568),(0.937,1.567),(0.946,1.566),(0.954,1.565),(0.963,1.564),(0.972,1.563),(0.980,1.562),(0.989,1.560),(0.997,1.559),(1.005,1.558),(1.014,1.556),(1.022,1.554),(1.030,1.553),(1.037,1.551),(1.045,1.549),(1.053,1.547),(1.060,1.545),(1.068,1.543),(1.075,1.541),(1.082,1.539),(1.089,1.536),(1.096,1.534),(1.103,1.531),(1.109,1.528),(1.115,1.526),(1.122,1.523),(1.128,1.520),(1.134,1.517),(1.139,1.513),(1.145,1.510),(1.150,1.507),(1.156,1.503),(1.161,1.500),(1.166,1.496),(1.170,1.492),(1.175,1.489),(1.179,1.485),(1.184,1.481),(1.188,1.477),(1.192,1.472),(1.196,1.468),(1.199,1.464),(1.203,1.459),(1.206,1.455),(1.210,1.450),(1.213,1.445),(1.216,1.441),(1.219,1.436),(1.221,1.431),(1.224,1.425),(1.227,1.420),(1.229,1.415),(1.231,1.409),(1.233,1.404),(1.235,1.398),(1.237,1.392),(1.239,1.386),(1.240,1.380),(1.242,1.374),(1.243,1.368),(1.244,1.361),(1.245,1.355),(1.245,1.355),(1.243,1.349),(1.241,1.342),(1.238,1.336),(1.236,1.330),(1.233,1.324),(1.230,1.318),(1.227,1.313),(1.224,1.307),(1.221,1.302),(1.218,1.297),(1.215,1.292),(1.211,1.287),(1.208,1.282),(1.204,1.277),(1.200,1.273),(1.197,1.268),(1.193,1.264),(1.189,1.260),(1.184,1.256),(1.180,1.252),(1.176,1.248),(1.171,1.245),(1.166,1.241),(1.161,1.238),(1.156,1.234),(1.151,1.231),(1.146,1.228),(1.141,1.225),(1.135,1.222),(1.130,1.219),(1.124,1.216),(1.118,1.214),(1.112,1.211),(1.106,1.209),(1.099,1.207),(1.093,1.204),(1.086,1.202),(1.079,1.200),(1.072,1.199),(1.065,1.197),(1.058,1.195),(1.051,1.194),(1.043,1.192),(1.036,1.191),(1.028,1.189),(1.020,1.188),(1.012,1.187),(1.004,1.186),(0.996,1.185),(0.987,1.185),(0.979,1.184),(0.970,1.183),(0.962,1.183),(0.953,1.182),(0.945,1.182),(0.936,1.181),(0.928,1.181),(0.920,1.181),(0.912,1.180),(0.904,1.180),(0.897,1.180),(0.889,1.180),(0.882,1.180),(0.875,1.180),(0.868,1.180),(0.861,1.180),(0.854,1.180),(0.847,1.180),(0.841,1.180),(0.835,1.180),(0.829,1.180),(0.823,1.180),(0.817,1.180),(0.811,1.180),(0.806,1.180),(0.800,1.180),(0.795,1.180),(0.790,1.180),(0.785,1.180),(0.780,1.181),(0.776,1.181),(0.771,1.181),(0.767,1.181),(0.763,1.181),(0.759,1.181),(0.755,1.181),(0.751,1.181),(0.747,1.181),(0.744,1.181),(0.741,1.181),(0.738,1.181),(0.735,1.181),(0.732,1.181),(0.729,1.181),(0.727,1.181),(0.724,1.181),(0.722,1.181),(0.720,1.181),(0.718,1.181),(0.716,1.181),(0.715,1.181),(0.713,1.181),(0.712,1.181),(0.711,1.181)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.566),(0.400,0.552),(0.410,0.539),(0.420,0.528),(0.430,0.517),(0.440,0.508),(0.450,0.501),(0.460,0.495),(0.470,0.491),(0.480,0.489),(0.490,0.488),(0.500,0.490),(0.510,0.494),(0.520,0.500),(0.530,0.508),(0.540,0.519),(0.550,0.533),(0.560,0.548),(0.570,0.563),(0.580,0.578),(0.590,0.593),(0.600,0.608),(0.610,0.623),(0.620,0.638),(0.630,0.653),(0.640,0.668),(0.650,0.683),(0.660,0.698),(0.670,0.713),(0.680,0.728),(0.690,0.743),(0.700,0.758),(0.710,0.773),(0.720,0.788),(0.730,0.776),(0.740,0.761),(0.750,0.746),(0.760,0.731),(0.770,0.716),(0.780,0.701),(0.790,0.686),(0.800,0.676),(0.810,0.671),(0.820,0.668),(0.830,0.665),(0.840,0.664),(0.850,0.664),(0.860,0.666),(0.870,0.668),(0.880,0.670),(0.890,0.674),(0.900,0.678),(0.910,0.683),(0.920,0.688),(0.930,0.694),(0.940,0.700),(0.950,0.706),(0.960,0.713),(0.970,0.720),(0.980,0.727),(0.990,0.735),(1.000,0.742),(1.010,0.749),(1.020,0.757),(1.030,0.764),(1.040,0.771),(1.050,0.779),(1.060,0.786),(1.070,0.793),(1.080,0.800),(1.090,0.806),(1.100,0.813),(1.110,0.819),(1.120,0.825),(1.130,0.831),(1.140,0.837),(1.150,0.843),(1.160,0.848),(1.170,0.853),(1.180,0.858),(1.190,0.863),(1.200,0.868),(1.210,0.872),(1.220,0.876),(1.230,0.880),(1.240,0.884),(1.250,0.888),(1.260,0.892),(1.270,0.895),(1.280,0.899),(1.290,0.902),(1.300,0.905),(1.310,0.908),(1.320,0.911),(1.330,0.913),(1.340,0.916),(1.350,0.918),(1.360,0.921),(1.370,0.923),(1.380,0.925),(1.390,0.927),(1.400,0.929),(1.410,0.931),(1.420,0.933),(1.430,0.935),(1.440,0.937),(1.450,0.938),(1.460,0.940),(1.470,0.942),(1.480,0.943),(1.490,0.944),(1.500,0.946),(1.510,0.947),(1.520,0.948),(1.530,0.950),(1.540,0.951),(1.550,0.952),(1.560,0.953),(1.570,0.954),(1.580,0.955),(1.590,0.956),(1.600,0.957),(1.610,0.958),(1.620,0.959),(1.630,0.960),(1.640,0.961),(1.650,0.962),(1.660,0.962),(1.670,0.963),(1.680,0.964),(1.690,0.965),(1.700,0.965),(1.700,0.965),(1.710,0.980),(1.720,0.995),(1.730,1.000),(1.740,1.000),(1.750,1.000),(1.760,1.000),(1.770,1.000),(1.780,1.000),(1.790,1.000),(1.800,1.000),(1.810,1.000),(1.820,1.000),(1.830,1.000),(1.840,1.000),(1.850,1.000),(1.860,1.000),(1.870,1.000),(1.880,1.000),(1.890,1.000),(1.900,1.000),(1.910,1.000),(1.920,1.000),(1.930,1.000),(1.940,1.000),(1.950,1.000),(1.960,1.000),(1.970,1.000),(1.980,1.000),(1.990,1.000),(2.000,1.000),(2.010,1.000),(2.020,1.000),(2.030,1.000),(2.040,1.000),(2.050,1.000),(2.060,1.000),(2.070,1.000),(2.080,1.000),(2.090,1.000),(2.100,1.000),(2.110,1.000),(2.120,1.000),(2.130,1.000),(2.140,1.000),(2.150,1.000),(2.160,1.000),(2.170,1.000),(2.180,1.000),(2.190,1.000),(2.200,1.000),(2.210,1.000),(2.220,1.000),(2.230,1.000),(2.240,1.000),(2.250,1.000),(2.260,1.000),(2.270,1.000),(2.280,1.000),(2.290,1.000),(2.300,1.000),(2.310,1.000),(2.320,1.000),(2.330,1.000),(2.340,1.000),(2.350,1.000),(2.360,1.000),(2.370,1.000),(2.380,1.000),(2.390,1.000),(2.400,1.000),(2.410,1.000),(2.420,1.000),(2.430,1.000),(2.440,1.000),(2.450,1.000),(2.460,1.000),(2.470,1.000),(2.480,1.000),(2.490,1.000),(2.500,1.000),(2.510,1.000),(2.520,1.000),(2.530,1.000),(2.540,1.000),(2.550,1.000),(2.560,1.000),(2.570,1.000),(2.580,1.000),(2.590,1.000),(2.600,1.000),(2.610,1.000),(2.620,1.000),(2.630,1.000),(2.640,1.000),(2.650,1.000),(2.660,1.000),(2.670,1.000),(2.680,1.000),(2.690,1.000),(2.700,1.000),(2.710,1.000),(2.720,1.000),(2.730,1.000),(2.740,1.000),(2.750,1.000),(2.760,1.000),(2.770,1.000),(2.780,1.000),(2.790,1.000),(2.800,1.000),(2.810,1.000),(2.820,1.000),(2.830,1.000),(2.840,1.000),(2.850,1.000),(2.860,1.000),(2.860,1.000),(2.870,0.992),(2.880,0.994),(2.890,0.996),(2.900,0.999),(2.910,0.999),(2.920,0.997),(2.930,0.994),(2.940,0.992),(2.950,0.989),(2.960,0.987),(2.970,0.984),(2.980,0.981),(2.990,0.978),(3.000,0.976),(3.010,0.973),(3.020,0.970),(3.030,0.967),(3.040,0.963),(3.050,0.960),(3.060,0.957),(3.070,0.953),(3.080,0.950),(3.090,0.946),(3.100,0.942),(3.110,0.938),(3.120,0.934),(3.130,0.929),(3.140,0.925),(3.150,0.920),(3.160,0.915),(3.170,0.910),(3.180,0.905),(3.190,0.900),(3.200,0.894),(3.210,0.888),(3.220,0.882),(3.230,0.875),(3.240,0.869),(3.250,0.862),(3.260,0.855),(3.270,0.847),(3.280,0.839),(3.290,0.831),(3.300,0.823),(3.310,0.815),(3.320,0.806),(3.330,0.797),(3.340,0.787),(3.350,0.778),(3.360,0.768),(3.370,0.758),(3.380,0.748),(3.390,0.737),(3.400,0.727),(3.410,0.717),(3.420,0.706),(3.430,0.696),(3.440,0.685),(3.450,0.675),(3.460,0.665),(3.470,0.655),(3.480,0.646),(3.490,0.637),(3.500,0.628),(3.510,0.620),(3.520,0.612),(3.530,0.605),(3.540,0.598),(3.550,0.592),(3.560,0.586),(3.570,0.582),(3.580,0.578),(3.590,0.574),(3.600,0.572),(3.610,0.570),(3.620,0.569),(3.630,0.569),(3.640,0.569),(3.650,0.571),(3.660,0.573),(3.670,0.575),(3.680,0.579),(3.690,0.583),(3.700,0.587),(3.710,0.593),(3.720,0.599),(3.730,0.605),(3.740,0.612),(3.750,0.620),(3.760,0.628),(3.770,0.636),(3.780,0.644),(3.790,0.653),(3.800,0.662),(3.800,0.662),(3.810,0.677),(3.820,0.672),(3.830,0.663),(3.840,0.654),(3.850,0.646),(3.860,0.638),(3.870,0.630),(3.880,0.623),(3.890,0.616),(3.900,0.610),(3.910,0.604),(3.920,0.599),(3.930,0.595),(3.940,0.591),(3.950,0.588),(3.960,0.586),(3.970,0.584),(3.980,0.583),(3.990,0.583),(4.000,0.584),(4.010,0.585),(4.020,0.588),(4.030,0.591),(4.040,0.594),(4.050,0.599),(4.060,0.604),(4.070,0.610),(4.080,0.616),(4.090,0.623),(4.100,0.631),(4.110,0.639),(4.120,0.648),(4.130,0.657),(4.140,0.667),(4.150,0.677),(4.160,0.687),(4.170,0.697),(4.180,0.708),(4.190,0.719),(4.200,0.730),(4.210,0.741),(4.220,0.751),(4.230,0.762),(4.240,0.773),(4.250,0.784),(4.260,0.795),(4.270,0.805),(4.280,0.815),(4.290,0.825),(4.300,0.835),(4.310,0.845),(4.320,0.854),(4.330,0.863),(4.340,0.867),(4.350,0.852),(4.360,0.837),(4.370,0.822),(4.380,0.807),(4.390,0.792),(4.400,0.777),(4.410,0.762),(4.420,0.747),(4.430,0.732),(4.440,0.717),(4.450,0.702),(4.460,0.687),(4.470,0.672),(4.480,0.657),(4.490,0.642),(4.500,0.627),(4.510,0.612),(4.520,0.597),(4.530,0.582),(4.540,0.567),(4.550,0.552),(4.560,0.537),(4.570,0.522),(4.580,0.507),(4.590,0.492),(4.600,0.477),(4.610,0.462),(4.620,0.447),(4.630,0.432),(4.640,0.417),(4.650,0.402),(4.660,0.387),(4.670,0.372),(4.680,0.357),(4.690,0.342),(4.700,0.327),(4.710,0.312),(4.720,0.297),(4.730,0.282),(4.740,0.267),(4.750,0.252),(4.760,0.237),(4.770,0.222),(4.780,0.207),(4.790,0.192),(4.800,0.177),(4.810,0.162),(4.820,0.147),(4.830,0.132),(4.840,0.117)]
A = [(0.000,0.000),(0.010,0.025),(0.020,0.050),(0.030,0.075),(0.040,0.101),(0.050,0.127),(0.060,0.154),(0.070,0.181),(0.080,0.209),(0.090,0.238),(0.100,0.268),(0.110,0.300),(0.120,0.332),(0.130,0.367),(0.140,0.403),(0.150,0.441),(0.160,0.482),(0.170,0.525),(0.180,0.570),(0.190,0.619),(0.200,0.672),(0.210,0.728),(0.220,0.789),(0.230,0.855),(0.240,0.926),(0.250,1.004),(0.260,1.088),(0.270,1.181),(0.280,1.282),(0.290,1.392),(0.300,1.514),(0.310,1.648),(0.320,1.795),(0.330,1.957),(0.340,2.134),(0.350,2.329),(0.360,2.543),(0.370,2.774),(0.380,3.024),(0.390,3.178),(0.400,3.266),(0.410,3.343),(0.420,3.410),(0.430,3.464),(0.440,3.507),(0.450,3.536),(0.460,3.553),(0.470,3.555),(0.480,3.543),(0.490,3.517),(0.500,3.477),(0.510,3.420),(0.520,3.348),(0.530,3.260),(0.540,3.154),(0.550,3.030),(0.560,2.880),(0.570,2.696),(0.580,2.484),(0.590,2.246),(0.600,1.987),(0.610,1.712),(0.620,1.424),(0.630,1.127),(0.640,0.823),(0.650,0.516),(0.660,0.207),(0.670,-0.101),(0.680,-0.408),(0.690,-0.710),(0.700,-1.007),(0.710,-1.297),(0.720,-1.577),(0.730,-1.775),(0.740,-1.932),(0.750,-2.056),(0.760,-2.149),(0.770,-2.215),(0.780,-2.257),(0.790,-2.276),(0.800,-2.294),(0.810,-2.314),(0.820,-2.324),(0.830,-2.327),(0.840,-2.322),(0.850,-2.311),(0.860,-2.294),(0.870,-2.272),(0.880,-2.246),(0.890,-2.215),(0.900,-2.181),(0.910,-2.143),(0.920,-2.102),(0.930,-2.059),(0.940,-2.014),(0.950,-1.967),(0.960,-1.919),(0.970,-1.870),(0.980,-1.820),(0.990,-1.769),(1.000,-1.719),(1.010,-1.668),(1.020,-1.618),(1.030,-1.568),(1.040,-1.518),(1.050,-1.470),(1.060,-1.422),(1.070,-1.375),(1.080,-1.330),(1.090,-1.285),(1.100,-1.242),(1.110,-1.200),(1.120,-1.160),(1.130,-1.120),(1.140,-1.082),(1.150,-1.046),(1.160,-1.010),(1.170,-0.976),(1.180,-0.943),(1.190,-0.912),(1.200,-0.881),(1.210,-0.852),(1.220,-0.824),(1.230,-0.797),(1.240,-0.771),(1.250,-0.746),(1.260,-0.722),(1.270,-0.700),(1.280,-0.678),(1.290,-0.657),(1.300,-0.636),(1.310,-0.617),(1.320,-0.599),(1.330,-0.581),(1.340,-0.564),(1.350,-0.547),(1.360,-0.531),(1.370,-0.516),(1.380,-0.502),(1.390,-0.488),(1.400,-0.474),(1.410,-0.461),(1.420,-0.449),(1.430,-0.437),(1.440,-0.426),(1.450,-0.414),(1.460,-0.404),(1.470,-0.394),(1.480,-0.384),(1.490,-0.374),(1.500,-0.365),(1.510,-0.356),(1.520,-0.348),(1.530,-0.339),(1.540,-0.331),(1.550,-0.324),(1.560,-0.316),(1.570,-0.309),(1.580,-0.302),(1.590,-0.296),(1.600,-0.289),(1.610,-0.283),(1.620,-0.277),(1.630,-0.271),(1.640,-0.265),(1.650,-0.260),(1.660,-0.254),(1.670,-0.249),(1.680,-0.244),(1.690,-0.239),(1.700,-0.237),(1.700,0.000),(1.710,0.000),(1.720,0.000),(1.730,0.000),(1.740,0.000),(1.750,0.000),(1.760,0.000),(1.770,0.000),(1.780,0.000),(1.790,0.000),(1.800,0.000),(1.810,0.000),(1.820,0.000),(1.830,0.000),(1.840,0.000),(1.850,0.000),(1.860,0.000),(1.870,0.000),(1.880,0.000),(1.890,0.000),(1.900,0.000),(1.910,0.000),(1.920,0.000),(1.930,0.000),(1.940,0.000),(1.950,0.000),(1.960,0.000),(1.970,0.000),(1.980,0.000),(1.990,0.000),(2.000,0.000),(2.010,0.000),(2.020,0.000),(2.030,0.000),(2.040,0.000),(2.050,0.000),(2.060,0.000),(2.070,0.000),(2.080,0.000),(2.090,0.000),(2.100,0.000),(2.110,0.000),(2.120,0.000),(2.130,0.000),(2.140,0.000),(2.150,0.000),(2.160,0.000),(2.170,0.000),(2.180,0.000),(2.190,0.000),(2.200,0.000),(2.210,0.000),(2.220,0.000),(2.230,0.000),(2.240,0.000),(2.250,0.000),(2.260,0.000),(2.270,0.000),(2.280,0.000),(2.290,0.000),(2.300,0.000),(2.310,0.000),(2.320,0.000),(2.330,0.000),(2.340,0.000),(2.350,0.000),(2.360,0.000),(2.370,0.000),(2.380,0.000),(2.390,0.000),(2.400,0.000),(2.410,0.000),(2.420,0.000),(2.430,0.000),(2.440,0.000),(2.450,0.000),(2.460,0.000),(2.470,0.000),(2.480,0.000),(2.490,0.000),(2.500,0.000),(2.510,0.000),(2.520,0.000),(2.530,0.000),(2.540,0.000),(2.550,0.000),(2.560,0.000),(2.570,0.000),(2.580,0.000),(2.590,0.000),(2.600,0.000),(2.610,0.000),(2.620,0.000),(2.630,0.000),(2.640,0.000),(2.650,0.000),(2.660,0.000),(2.670,0.000),(2.680,0.000),(2.690,0.000),(2.700,0.000),(2.710,0.000),(2.720,0.000),(2.730,0.000),(2.740,0.000),(2.750,0.000),(2.760,0.000),(2.770,0.000),(2.780,0.000),(2.790,0.000),(2.800,0.000),(2.810,0.000),(2.820,0.000),(2.830,0.000),(2.840,0.000),(2.850,0.000),(2.860,0.000),(2.860,0.056),(2.870,0.041),(2.880,0.025),(2.890,0.010),(2.900,-0.007),(2.910,-0.023),(2.920,-0.040),(2.930,-0.057),(2.940,-0.075),(2.950,-0.093),(2.960,-0.111),(2.970,-0.130),(2.980,-0.149),(2.990,-0.169),(3.000,-0.189),(3.010,-0.210),(3.020,-0.232),(3.030,-0.254),(3.040,-0.277),(3.050,-0.300),(3.060,-0.325),(3.070,-0.350),(3.080,-0.376),(3.090,-0.403),(3.100,-0.431),(3.110,-0.460),(3.120,-0.491),(3.130,-0.522),(3.140,-0.555),(3.150,-0.589),(3.160,-0.624),(3.170,-0.661),(3.180,-0.699),(3.190,-0.739),(3.200,-0.780),(3.210,-0.824),(3.220,-0.869),(3.230,-0.915),(3.240,-0.964),(3.250,-1.015),(3.260,-1.067),(3.270,-1.122),(3.280,-1.178),(3.290,-1.237),(3.300,-1.297),(3.310,-1.360),(3.320,-1.424),(3.330,-1.490),(3.340,-1.558),(3.350,-1.628),(3.360,-1.698),(3.370,-1.770),(3.380,-1.843),(3.390,-1.917),(3.400,-1.991),(3.410,-2.065),(3.420,-2.138),(3.430,-2.211),(3.440,-2.283),(3.450,-2.354),(3.460,-2.422),(3.470,-2.488),(3.480,-2.551),(3.490,-2.612),(3.500,-2.669),(3.510,-2.721),(3.520,-2.770),(3.530,-2.815),(3.540,-2.854),(3.550,-2.889),(3.560,-2.919),(3.570,-2.943),(3.580,-2.962),(3.590,-2.976),(3.600,-2.985),(3.610,-2.988),(3.620,-2.986),(3.630,-2.979),(3.640,-2.966),(3.650,-2.949),(3.660,-2.927),(3.670,-2.900),(3.680,-2.869),(3.690,-2.833),(3.700,-2.794),(3.710,-2.751),(3.720,-2.704),(3.730,-2.654),(3.740,-2.601),(3.750,-2.546),(3.760,-2.488),(3.770,-2.429),(3.780,-2.368),(3.790,-2.305),(3.800,-2.248),(3.800,-2.150),(3.810,-2.292),(3.820,-2.366),(3.830,-2.427),(3.840,-2.485),(3.850,-2.540),(3.860,-2.593),(3.870,-2.642),(3.880,-2.688),(3.890,-2.729),(3.900,-2.766),(3.910,-2.799),(3.920,-2.827),(3.930,-2.849),(3.940,-2.867),(3.950,-2.879),(3.960,-2.887),(3.970,-2.888),(3.980,-2.885),(3.990,-2.876),(4.000,-2.862),(4.010,-2.843),(4.020,-2.819),(4.030,-2.790),(4.040,-2.756),(4.050,-2.718),(4.060,-2.675),(4.070,-2.628),(4.080,-2.577),(4.090,-2.522),(4.100,-2.465),(4.110,-2.404),(4.120,-2.340),(4.130,-2.274),(4.140,-2.206),(4.150,-2.136),(4.160,-2.064),(4.170,-1.992),(4.180,-1.918),(4.190,-1.844),(4.200,-1.770),(4.210,-1.695),(4.220,-1.621),(4.230,-1.548),(4.240,-1.475),(4.250,-1.403),(4.260,-1.332),(4.270,-1.262),(4.280,-1.194),(4.290,-1.127),(4.300,-1.062),(4.310,-0.998),(4.320,-0.936),(4.330,-0.875),(4.340,-0.812),(4.350,-0.736),(4.360,-0.667),(4.370,-0.604),(4.380,-0.546),(4.390,-0.492),(4.400,-0.443),(4.410,-0.398),(4.420,-0.356),(4.430,-0.318),(4.440,-0.282),(4.450,-0.250),(4.460,-0.220),(4.470,-0.192),(4.480,-0.166),(4.490,-0.143),(4.500,-0.121),(4.510,-0.101),(4.520,-0.083),(4.530,-0.066),(4.540,-0.051),(4.550,-0.037),(4.560,-0.024),(4.570,-0.013),(4.580,-0.002),(4.590,0.007),(4.600,0.016),(4.610,0.024),(4.620,0.030),(4.630,0.036),(4.640,0.041),(4.650,0.045),(4.660,0.049),(4.670,0.052),(4.680,0.055),(4.690,0.056),(4.700,0.058),(4.710,0.058),(4.720,0.058),(4.730,0.058),(4.740,0.058),(4.750,0.056),(4.760,0.055),(4.770,0.053),(4.780,0.051),(4.790,0.049),(4.800,0.046),(4.810,0.043),(4.820,0.040),(4.830,0.036),(4.840,0.032)]
)";
 
const std::string skills_4 = R"(
X = [(0.711,1.207),(0.711,1.207),(0.711,1.207),(0.712,1.207),(0.712,1.207),(0.713,1.207),(0.714,1.207),(0.715,1.207),(0.716,1.207),(0.718,1.207),(0.719,1.207),(0.721,1.207),(0.723,1.207),(0.725,1.207),(0.727,1.207),(0.729,1.207),(0.731,1.207),(0.734,1.207),(0.737,1.207),(0.739,1.207),(0.742,1.207),(0.746,1.207),(0.749,1.206),(0.752,1.206),(0.756,1.206),(0.760,1.206),(0.764,1.206),(0.768,1.206),(0.772,1.206),(0.776,1.205),(0.781,1.205),(0.785,1.205),(0.790,1.204),(0.795,1.204),(0.800,1.204),(0.805,1.203),(0.811,1.203),(0.816,1.202),(0.822,1.202),(0.828,1.201),(0.834,1.200),(0.840,1.200),(0.846,1.199),(0.852,1.198),(0.859,1.197),(0.866,1.196),(0.872,1.195),(0.879,1.194),(0.886,1.192),(0.894,1.191),(0.901,1.189),(0.907,1.188),(0.914,1.186),(0.921,1.184),(0.928,1.182),(0.934,1.180),(0.941,1.178),(0.947,1.176),(0.953,1.174),(0.959,1.172),(0.965,1.169),(0.971,1.167),(0.977,1.165),(0.982,1.162),(0.988,1.159),(0.993,1.157),(0.998,1.154),(1.003,1.151),(1.008,1.148),(1.013,1.145),(1.018,1.142),(1.022,1.139),(1.027,1.135),(1.031,1.132),(1.035,1.129),(1.039,1.125),(1.043,1.122),(1.047,1.118),(1.050,1.115),(1.054,1.111),(1.057,1.107),(1.060,1.103),(1.064,1.099),(1.067,1.095),(1.069,1.091),(1.072,1.087),(1.075,1.083),(1.077,1.079),(1.080,1.075),(1.082,1.070),(1.084,1.066),(1.086,1.061),(1.088,1.056),(1.090,1.052),(1.092,1.047),(1.093,1.042),(1.095,1.037),(1.096,1.032),(1.097,1.027),(1.098,1.022),(1.099,1.016),(1.100,1.011),(1.101,1.005),(1.102,1.000),(1.102,0.994),(1.102,0.988),(1.103,0.982),(1.103,0.976),(1.103,0.970),(1.103,0.964),(1.103,0.958),(1.102,0.951),(1.102,0.945),(1.101,0.939),(1.101,0.932),(1.100,0.925),(1.099,0.919),(1.098,0.912),(1.097,0.905),(1.096,0.898),(1.094,0.891),(1.093,0.884),(1.091,0.877),(1.090,0.870),(1.088,0.863),(1.086,0.856),(1.084,0.849),(1.082,0.841),(1.080,0.834),(1.078,0.827),(1.076,0.819),(1.073,0.812),(1.071,0.805),(1.068,0.797),(1.066,0.790),(1.063,0.782),(1.061,0.775),(1.058,0.767),(1.055,0.759),(1.052,0.752),(1.049,0.744),(1.046,0.737),(1.043,0.729),(1.040,0.721),(1.037,0.714),(1.034,0.706),(1.030,0.698),(1.027,0.691),(1.024,0.683),(1.020,0.675),(1.017,0.667),(1.014,0.660),(1.010,0.652),(1.007,0.644),(1.003,0.636),(0.999,0.628),(0.996,0.620),(0.992,0.613),(0.989,0.605),(0.985,0.597),(0.981,0.589),(0.978,0.581),(0.974,0.573),(0.970,0.565),(0.966,0.557),(0.962,0.549),(0.959,0.541),(0.955,0.533),(0.951,0.525),(0.947,0.517),(0.943,0.509),(0.939,0.501),(0.936,0.493),(0.932,0.485),(0.928,0.477),(0.924,0.469),(0.920,0.461),(0.917,0.453),(0.913,0.445),(0.909,0.437),(0.905,0.429),(0.902,0.421),(0.898,0.413),(0.894,0.405),(0.891,0.397),(0.887,0.389),(0.884,0.382),(0.880,0.374),(0.877,0.366),(0.873,0.358),(0.870,0.350),(0.867,0.342),(0.863,0.335),(0.860,0.327),(0.857,0.319),(0.854,0.311),(0.850,0.304),(0.847,0.296),(0.844,0.288),(0.841,0.281),(0.838,0.273),(0.836,0.265),(0.833,0.258),(0.830,0.250),(0.828,0.242),(0.825,0.235),(0.822,0.227),(0.820,0.220),(0.818,0.212),(0.815,0.205),(0.813,0.197),(0.811,0.190),(0.809,0.183),(0.807,0.175),(0.806,0.168),(0.804,0.161),(0.802,0.154),(0.801,0.147),(0.799,0.140),(0.798,0.133),(0.797,0.126),(0.796,0.119),(0.795,0.112),(0.794,0.105),(0.794,0.099),(0.793,0.092),(0.793,0.086),(0.793,0.079),(0.793,0.073),(0.793,0.067),(0.793,0.061),(0.793,0.055),(0.793,0.049),(0.794,0.043),(0.795,0.037),(0.795,0.032),(0.796,0.026),(0.797,0.021),(0.798,0.015),(0.800,0.010),(0.801,0.005),(0.803,0.000),(0.804,-0.005),(0.806,-0.010),(0.808,-0.014),(0.810,-0.019),(0.812,-0.023),(0.814,-0.028),(0.817,-0.032),(0.819,-0.036),(0.822,-0.040),(0.824,-0.044),(0.827,-0.048),(0.830,-0.052),(0.833,-0.056),(0.836,-0.060),(0.839,-0.063),(0.843,-0.067),(0.846,-0.070),(0.850,-0.074),(0.854,-0.077),(0.858,-0.080),(0.861,-0.084),(0.866,-0.087),(0.870,-0.090),(0.874,-0.093),(0.879,-0.096),(0.883,-0.099),(0.888,-0.101),(0.893,-0.104),(0.898,-0.107),(0.903,-0.109),(0.908,-0.112),(0.914,-0.114),(0.919,-0.116),(0.925,-0.119),(0.931,-0.121),(0.937,-0.123),(0.943,-0.125),(0.949,-0.127),(0.955,-0.129),(0.962,-0.131),(0.968,-0.132),(0.975,-0.134),(0.981,-0.136),(0.988,-0.137),(0.995,-0.139),(1.002,-0.140),(1.009,-0.141),(1.015,-0.142),(1.022,-0.143),(1.028,-0.144),(1.034,-0.145),(1.040,-0.146),(1.046,-0.146),(1.052,-0.147),(1.057,-0.148),(1.063,-0.148),(1.068,-0.149),(1.073,-0.149),(1.078,-0.149),(1.083,-0.150),(1.088,-0.150),(1.092,-0.150),(1.097,-0.151),(1.101,-0.151),(1.105,-0.151),(1.109,-0.151),(1.113,-0.151),(1.117,-0.151),(1.120,-0.151),(1.123,-0.152),(1.127,-0.152),(1.130,-0.152),(1.132,-0.152),(1.135,-0.152),(1.138,-0.152),(1.140,-0.152),(1.142,-0.152),(1.144,-0.152),(1.146,-0.152),(1.148,-0.152),(1.149,-0.152),(1.151,-0.152),(1.152,-0.152),(1.153,-0.152),(1.154,-0.152),(1.154,-0.152),(1.155,-0.152),(1.155,-0.152)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.585),(0.400,0.600),(0.410,0.615),(0.420,0.630),(0.430,0.645),(0.440,0.660),(0.450,0.675),(0.460,0.690),(0.470,0.705),(0.480,0.720),(0.490,0.721),(0.500,0.715),(0.510,0.708),(0.520,0.702),(0.530,0.695),(0.540,0.687),(0.550,0.680),(0.560,0.673),(0.570,0.665),(0.580,0.657),(0.590,0.649),(0.600,0.641),(0.610,0.633),(0.620,0.625),(0.630,0.617),(0.640,0.608),(0.650,0.600),(0.660,0.592),(0.670,0.584),(0.680,0.576),(0.690,0.568),(0.700,0.561),(0.710,0.554),(0.720,0.547),(0.730,0.540),(0.740,0.533),(0.750,0.527),(0.760,0.522),(0.770,0.517),(0.780,0.512),(0.790,0.508),(0.800,0.504),(0.810,0.501),(0.820,0.498),(0.830,0.496),(0.840,0.495),(0.850,0.494),(0.860,0.493),(0.870,0.493),(0.880,0.494),(0.890,0.496),(0.900,0.497),(0.910,0.500),(0.920,0.503),(0.930,0.506),(0.940,0.510),(0.950,0.515),(0.960,0.520),(0.970,0.525),(0.980,0.531),(0.990,0.537),(1.000,0.544),(1.010,0.551),(1.020,0.558),(1.030,0.566),(1.040,0.574),(1.050,0.582),(1.060,0.590),(1.070,0.598),(1.080,0.607),(1.090,0.615),(1.100,0.624),(1.110,0.632),(1.120,0.641),(1.130,0.649),(1.140,0.658),(1.150,0.666),(1.160,0.674),(1.170,0.682),(1.180,0.690),(1.190,0.698),(1.200,0.706),(1.210,0.713),(1.220,0.720),(1.230,0.727),(1.240,0.734),(1.250,0.740),(1.260,0.747),(1.270,0.753),(1.280,0.759),(1.290,0.765),(1.300,0.770),(1.310,0.776),(1.320,0.781),(1.330,0.786),(1.340,0.791),(1.350,0.795),(1.360,0.800),(1.370,0.804),(1.380,0.809),(1.390,0.813),(1.400,0.817),(1.410,0.820),(1.420,0.824),(1.430,0.828),(1.440,0.831),(1.450,0.834),(1.460,0.838),(1.470,0.841),(1.480,0.844),(1.490,0.847),(1.500,0.850),(1.510,0.853),(1.520,0.855),(1.530,0.858),(1.540,0.861),(1.550,0.863),(1.560,0.866),(1.570,0.869),(1.580,0.871),(1.590,0.874),(1.600,0.876),(1.610,0.878),(1.620,0.881),(1.630,0.883),(1.640,0.885),(1.650,0.888),(1.660,0.890),(1.670,0.893),(1.680,0.895),(1.690,0.897),(1.700,0.900),(1.710,0.898),(1.720,0.896),(1.730,0.893),(1.740,0.891),(1.750,0.889),(1.760,0.886),(1.770,0.884),(1.780,0.881),(1.790,0.879),(1.800,0.876),(1.810,0.874),(1.820,0.871),(1.830,0.869),(1.840,0.866),(1.850,0.864),(1.860,0.861),(1.870,0.858),(1.880,0.855),(1.890,0.852),(1.900,0.849),(1.910,0.846),(1.920,0.843),(1.930,0.840),(1.940,0.837),(1.950,0.833),(1.960,0.830),(1.970,0.826),(1.980,0.822),(1.990,0.818),(2.000,0.814),(2.010,0.810),(2.020,0.806),(2.030,0.801),(2.040,0.796),(2.050,0.791),(2.060,0.786),(2.070,0.781),(2.080,0.775),(2.090,0.770),(2.100,0.764),(2.110,0.758),(2.120,0.751),(2.130,0.745),(2.140,0.738),(2.150,0.731),(2.160,0.723),(2.170,0.716),(2.180,0.708),(2.190,0.700),(2.200,0.692),(2.210,0.683),(2.220,0.674),(2.230,0.666),(2.240,0.656),(2.250,0.647),(2.260,0.638),(2.270,0.629),(2.280,0.619),(2.290,0.610),(2.300,0.600),(2.310,0.591),(2.320,0.582),(2.330,0.573),(2.340,0.564),(2.350,0.555),(2.360,0.547),(2.370,0.539),(2.380,0.531),(2.390,0.524),(2.400,0.518),(2.410,0.511),(2.420,0.506),(2.430,0.500),(2.440,0.496),(2.450,0.492),(2.460,0.488),(2.470,0.485),(2.480,0.483),(2.490,0.481),(2.500,0.480),(2.510,0.480),(2.520,0.480),(2.530,0.481),(2.540,0.483),(2.550,0.485),(2.560,0.487),(2.570,0.491),(2.580,0.494),(2.590,0.499),(2.600,0.503),(2.610,0.509),(2.620,0.515),(2.630,0.521),(2.640,0.527),(2.650,0.534),(2.660,0.541),(2.670,0.549),(2.680,0.557),(2.690,0.565),(2.700,0.573),(2.710,0.581),(2.720,0.590),(2.730,0.598),(2.740,0.607),(2.750,0.615),(2.760,0.624),(2.770,0.632),(2.780,0.641),(2.790,0.649),(2.800,0.657),(2.810,0.665),(2.820,0.673),(2.830,0.681),(2.840,0.688),(2.850,0.696),(2.860,0.697),(2.870,0.682),(2.880,0.666),(2.890,0.651),(2.900,0.636),(2.910,0.621),(2.920,0.606),(2.930,0.590),(2.940,0.575),(2.950,0.560),(2.960,0.545),(2.970,0.530),(2.980,0.514),(2.990,0.499),(3.000,0.484),(3.010,0.469),(3.020,0.454),(3.030,0.438),(3.040,0.423),(3.050,0.408),(3.060,0.392),(3.070,0.377),(3.080,0.362),(3.090,0.346),(3.100,0.331),(3.110,0.316),(3.120,0.300),(3.130,0.285),(3.140,0.270),(3.150,0.254),(3.160,0.239),(3.170,0.223),(3.180,0.208),(3.190,0.192),(3.200,0.176),(3.210,0.161),(3.220,0.145),(3.230,0.129),(3.240,0.113),(3.250,0.097),(3.260,0.081),(3.270,0.064),(3.280,0.046),(3.290,0.028)]
A = [(0.000,-0.000),(0.010,-0.011),(0.020,-0.022),(0.030,-0.033),(0.040,-0.044),(0.050,-0.055),(0.060,-0.066),(0.070,-0.077),(0.080,-0.089),(0.090,-0.101),(0.100,-0.112),(0.110,-0.124),(0.120,-0.137),(0.130,-0.149),(0.140,-0.162),(0.150,-0.175),(0.160,-0.189),(0.170,-0.203),(0.180,-0.217),(0.190,-0.232),(0.200,-0.248),(0.210,-0.263),(0.220,-0.280),(0.230,-0.297),(0.240,-0.315),(0.250,-0.334),(0.260,-0.353),(0.270,-0.373),(0.280,-0.394),(0.290,-0.417),(0.300,-0.440),(0.310,-0.465),(0.320,-0.491),(0.330,-0.518),(0.340,-0.547),(0.350,-0.578),(0.360,-0.611),(0.370,-0.645),(0.380,-0.682),(0.390,-0.722),(0.400,-0.764),(0.410,-0.809),(0.420,-0.857),(0.430,-0.909),(0.440,-0.965),(0.450,-1.025),(0.460,-1.090),(0.470,-1.161),(0.480,-1.237),(0.490,-1.294),(0.500,-1.340),(0.510,-1.387),(0.520,-1.436),(0.530,-1.486),(0.540,-1.538),(0.550,-1.591),(0.560,-1.645),(0.570,-1.701),(0.580,-1.757),(0.590,-1.814),(0.600,-1.871),(0.610,-1.929),(0.620,-1.987),(0.630,-2.045),(0.640,-2.103),(0.650,-2.161),(0.660,-2.217),(0.670,-2.273),(0.680,-2.327),(0.690,-2.379),(0.700,-2.430),(0.710,-2.478),(0.720,-2.524),(0.730,-2.568),(0.740,-2.608),(0.750,-2.645),(0.760,-2.679),(0.770,-2.710),(0.780,-2.737),(0.790,-2.760),(0.800,-2.780),(0.810,-2.795),(0.820,-2.807),(0.830,-2.814),(0.840,-2.818),(0.850,-2.817),(0.860,-2.813),(0.870,-2.805),(0.880,-2.793),(0.890,-2.777),(0.900,-2.757),(0.910,-2.734),(0.920,-2.707),(0.930,-2.677),(0.940,-2.643),(0.950,-2.607),(0.960,-2.568),(0.970,-2.526),(0.980,-2.481),(0.990,-2.434),(1.000,-2.386),(1.010,-2.335),(1.020,-2.282),(1.030,-2.228),(1.040,-2.173),(1.050,-2.117),(1.060,-2.060),(1.070,-2.002),(1.080,-1.944),(1.090,-1.886),(1.100,-1.828),(1.110,-1.770),(1.120,-1.712),(1.130,-1.655),(1.140,-1.599),(1.150,-1.543),(1.160,-1.489),(1.170,-1.435),(1.180,-1.383),(1.190,-1.332),(1.200,-1.282),(1.210,-1.233),(1.220,-1.185),(1.230,-1.139),(1.240,-1.095),(1.250,-1.051),(1.260,-1.009),(1.270,-0.969),(1.280,-0.929),(1.290,-0.891),(1.300,-0.855),(1.310,-0.819),(1.320,-0.785),(1.330,-0.752),(1.340,-0.720),(1.350,-0.689),(1.360,-0.659),(1.370,-0.630),(1.380,-0.602),(1.390,-0.575),(1.400,-0.549),(1.410,-0.524),(1.420,-0.499),(1.430,-0.475),(1.440,-0.452),(1.450,-0.430),(1.460,-0.408),(1.470,-0.387),(1.480,-0.366),(1.490,-0.346),(1.500,-0.326),(1.510,-0.307),(1.520,-0.288),(1.530,-0.270),(1.540,-0.252),(1.550,-0.234),(1.560,-0.217),(1.570,-0.200),(1.580,-0.183),(1.590,-0.166),(1.600,-0.149),(1.610,-0.133),(1.620,-0.117),(1.630,-0.100),(1.640,-0.084),(1.650,-0.068),(1.660,-0.052),(1.670,-0.036),(1.680,-0.019),(1.690,-0.003),(1.700,0.014),(1.710,0.030),(1.720,0.047),(1.730,0.063),(1.740,0.080),(1.750,0.096),(1.760,0.113),(1.770,0.130),(1.780,0.147),(1.790,0.164),(1.800,0.181),(1.810,0.198),(1.820,0.216),(1.830,0.234),(1.840,0.253),(1.850,0.272),(1.860,0.291),(1.870,0.310),(1.880,0.331),(1.890,0.351),(1.900,0.373),(1.910,0.395),(1.920,0.417),(1.930,0.440),(1.940,0.464),(1.950,0.489),(1.960,0.515),(1.970,0.541),(1.980,0.569),(1.990,0.597),(2.000,0.627),(2.010,0.658),(2.020,0.689),(2.030,0.723),(2.040,0.757),(2.050,0.793),(2.060,0.830),(2.070,0.868),(2.080,0.908),(2.090,0.950),(2.100,0.993),(2.110,1.038),(2.120,1.085),(2.130,1.133),(2.140,1.184),(2.150,1.235),(2.160,1.289),(2.170,1.344),(2.180,1.401),(2.190,1.460),(2.200,1.520),(2.210,1.582),(2.220,1.645),(2.230,1.709),(2.240,1.774),(2.250,1.840),(2.260,1.906),(2.270,1.973),(2.280,2.039),(2.290,2.106),(2.300,2.172),(2.310,2.237),(2.320,2.300),(2.330,2.362),(2.340,2.422),(2.350,2.480),(2.360,2.535),(2.370,2.587),(2.380,2.636),(2.390,2.682),(2.400,2.724),(2.410,2.762),(2.420,2.796),(2.430,2.826),(2.440,2.851),(2.450,2.872),(2.460,2.888),(2.470,2.901),(2.480,2.908),(2.490,2.911),(2.500,2.910),(2.510,2.904),(2.520,2.895),(2.530,2.881),(2.540,2.863),(2.550,2.841),(2.560,2.816),(2.570,2.786),(2.580,2.754),(2.590,2.718),(2.600,2.680),(2.610,2.638),(2.620,2.594),(2.630,2.548),(2.640,2.499),(2.650,2.449),(2.660,2.397),(2.670,2.343),(2.680,2.288),(2.690,2.232),(2.700,2.175),(2.710,2.118),(2.720,2.060),(2.730,2.002),(2.740,1.944),(2.750,1.886),(2.760,1.829),(2.770,1.772),(2.780,1.716),(2.790,1.660),(2.800,1.606),(2.810,1.552),(2.820,1.500),(2.830,1.449),(2.840,1.399),(2.850,1.350),(2.860,1.292),(2.870,1.210),(2.880,1.134),(2.890,1.064),(2.900,0.999),(2.910,0.939),(2.920,0.884),(2.930,0.832),(2.940,0.784),(2.950,0.739),(2.960,0.697),(2.970,0.658),(2.980,0.621),(2.990,0.586),(3.000,0.553),(3.010,0.523),(3.020,0.494),(3.030,0.466),(3.040,0.440),(3.050,0.416),(3.060,0.392),(3.070,0.370),(3.080,0.348),(3.090,0.328),(3.100,0.308),(3.110,0.289),(3.120,0.271),(3.130,0.254),(3.140,0.237),(3.150,0.221),(3.160,0.205),(3.170,0.190),(3.180,0.175),(3.190,0.160),(3.200,0.146),(3.210,0.132),(3.220,0.118),(3.230,0.105),(3.240,0.091),(3.250,0.078),(3.260,0.064),(3.270,0.051),(3.280,0.037),(3.290,0.022)]
)";
 
const std::string skills_5 = R"(
X = [(1.171000,0.002000),(1.170850,0.001999),(1.170550,0.001998),(1.170100,0.001997),(1.169501,0.001995),(1.168751,0.001993),(1.167851,0.001992),(1.166801,0.001991),(1.165601,0.001991),(1.164251,0.001993),(1.162751,0.001997),(1.161101,0.002003),(1.159301,0.002012),(1.157351,0.002026),(1.155251,0.002044),(1.153001,0.002067),(1.150601,0.002097),(1.148052,0.002134),(1.145352,0.002179),(1.142502,0.002234),(1.139503,0.002299),(1.136354,0.002376),(1.133055,0.002465),(1.129607,0.002569),(1.126009,0.002688),(1.122262,0.002825),(1.118365,0.002979),(1.114319,0.003154),(1.110123,0.003351),(1.105779,0.003570),(1.101286,0.003815),(1.096645,0.004087),(1.091855,0.004388),(1.086916,0.004720),(1.081830,0.005084),(1.076596,0.005484),(1.071213,0.005921),(1.065684,0.006398),(1.060008,0.006917),(1.054185,0.007480),(1.048216,0.008090),(1.042101,0.008750),(1.035842,0.009462),(1.029437,0.010229),(1.022889,0.011054),(1.016198,0.011940),(1.009363,0.012890),(1.002387,0.013907),(0.995270,0.014994),(0.988012,0.016156),(0.980615,0.017394),(0.973080,0.018714),(0.965407,0.020118),(0.957599,0.021611),(0.949655,0.023196),(0.941579,0.024877),(0.933370,0.026659),(0.925031,0.028546),(0.916564,0.030542),(0.907970,0.032652),(0.899251,0.034881),(0.890409,0.037234),(0.881447,0.039715),(0.872367,0.042331),(0.863293,0.045048),(0.854265,0.047858),(0.845285,0.050760),(0.836355,0.053754),(0.827476,0.056841),(0.818651,0.060020),(0.809882,0.063293),(0.801170,0.066658),(0.792519,0.070117),(0.783930,0.073669),(0.775405,0.077315),(0.766948,0.081054),(0.758561,0.084887),(0.750246,0.088813),(0.742005,0.092832),(0.733842,0.096945),(0.725760,0.101151),(0.717761,0.105449),(0.709848,0.109841),(0.702025,0.114324),(0.694293,0.118900),(0.686657,0.123567),(0.679120,0.128325),(0.671685,0.133173),(0.664356,0.138110),(0.657135,0.143136),(0.650026,0.148250),(0.643034,0.153451),(0.636161,0.158738),(0.629412,0.164109),(0.622790,0.169563),(0.616298,0.175098),(0.609941,0.180714),(0.603721,0.186409),(0.597644,0.192180),(0.591713,0.198026),(0.585931,0.203944),(0.580302,0.209933),(0.574830,0.215990),(0.569518,0.222112),(0.564370,0.228298),(0.559390,0.234543),(0.554579,0.240847),(0.549942,0.247206),(0.545481,0.253616),(0.541199,0.260076),(0.537099,0.266581),(0.533183,0.273129),(0.529454,0.279717),(0.525913,0.286342),(0.522563,0.293000),(0.519404,0.299689),(0.516439,0.306405),(0.513668,0.313146),(0.511092,0.319909),(0.508713,0.326692),(0.506531,0.333491),(0.504546,0.340304),(0.502759,0.347129),(0.501170,0.353963),(0.499779,0.360805),(0.498586,0.367653),(0.497591,0.374505),(0.496794,0.381359),(0.496194,0.388214),(0.495792,0.395068),(0.495587,0.401921),(0.495579,0.408770),(0.495768,0.415615),(0.496153,0.422454),(0.496735,0.429287),(0.497513,0.436113),(0.498488,0.442929),(0.499658,0.449736),(0.501024,0.456532),(0.502586,0.463317),(0.504340,0.470074),(0.506233,0.476635),(0.508250,0.483001),(0.510376,0.489172),(0.512597,0.495147),(0.514898,0.500929),(0.517267,0.506519),(0.519691,0.511919),(0.522158,0.517132),(0.524658,0.522160),(0.527179,0.527007),(0.529712,0.531674),(0.532248,0.536166),(0.534778,0.540485),(0.537294,0.544635),(0.539789,0.548619),(0.542256,0.552441),(0.544687,0.556102),(0.547078,0.559608),(0.549423,0.562959),(0.551715,0.566160),(0.553950,0.569213),(0.556125,0.572121),(0.558233,0.574886),(0.560272,0.577512),(0.562237,0.579999),(0.564126,0.582351),(0.565935,0.584570),(0.567661,0.586657),(0.569301,0.588615),(0.570853,0.590445),(0.572314,0.592148),(0.573682,0.593727),(0.574955,0.595181),(0.576131,0.596513),(0.577208,0.597723),(0.578184,0.598812),(0.579057,0.599780),(0.579826,0.600627),(0.580487,0.601353),(0.581040,0.601957),(0.581481,0.602437),(0.581806,0.602790),(0.582000,0.603000)]
L = [(0.000000,0.000000),(0.010000,0.015000),(0.020000,0.030000),(0.030000,0.045000),(0.040000,0.060000),(0.050000,0.075000),(0.060000,0.090000),(0.070000,0.105000),(0.080000,0.120000),(0.090000,0.135000),(0.100000,0.150000),(0.110000,0.165000),(0.120000,0.180000),(0.130000,0.195000),(0.140000,0.210000),(0.150000,0.225000),(0.160000,0.240000),(0.170000,0.255000),(0.180000,0.270000),(0.190000,0.285000),(0.200000,0.300000),(0.210000,0.315000),(0.220000,0.330000),(0.230000,0.345000),(0.240000,0.360000),(0.250000,0.375000),(0.260000,0.390000),(0.270000,0.405000),(0.280000,0.420000),(0.290000,0.435000),(0.300000,0.450000),(0.310000,0.465000),(0.320000,0.480000),(0.330000,0.495000),(0.340000,0.510000),(0.350000,0.525000),(0.360000,0.540000),(0.370000,0.555000),(0.380000,0.570000),(0.390000,0.585000),(0.400000,0.600000),(0.410000,0.615000),(0.420000,0.630000),(0.430000,0.645000),(0.440000,0.660000),(0.450000,0.675000),(0.460000,0.690000),(0.470000,0.705000),(0.480000,0.720000),(0.490000,0.735000),(0.500000,0.750000),(0.510000,0.765000),(0.520000,0.779999),(0.530000,0.794999),(0.540000,0.809999),(0.550000,0.824999),(0.560000,0.839999),(0.570000,0.854999),(0.580000,0.869999),(0.590000,0.884999),(0.600000,0.899999),(0.610000,0.914999),(0.620000,0.929999),(0.630000,0.944999),(0.640000,0.947214),(0.650000,0.945510),(0.660000,0.943745),(0.670000,0.941917),(0.680000,0.940023),(0.690000,0.938061),(0.700000,0.936028),(0.710000,0.933920),(0.720000,0.931736),(0.730000,0.929471),(0.740000,0.927124),(0.750000,0.924691),(0.760000,0.922168),(0.770000,0.919554),(0.780000,0.916843),(0.790000,0.914034),(0.800000,0.911122),(0.810000,0.908105),(0.820000,0.904979),(0.830000,0.901742),(0.839999,0.898389),(0.849999,0.894917),(0.859999,0.891325),(0.869999,0.887609),(0.879999,0.883766),(0.889999,0.879795),(0.899999,0.875693),(0.909999,0.871460),(0.919999,0.867092),(0.929999,0.862591),(0.939999,0.857956),(0.949999,0.853188),(0.959999,0.848287),(0.969999,0.843257),(0.979999,0.838099),(0.989999,0.832818),(0.999999,0.827420),(1.009999,0.821909),(1.019999,0.816295),(1.029999,0.810585),(1.039999,0.804789),(1.049999,0.798920),(1.059999,0.792990),(1.069999,0.787013),(1.079999,0.781006),(1.089999,0.774985),(1.099999,0.768971),(1.109999,0.762982),(1.119999,0.757040),(1.129999,0.751168),(1.139999,0.745389),(1.149999,0.739728),(1.159999,0.734210),(1.169999,0.728859),(1.179999,0.723703),(1.189999,0.718766),(1.199999,0.714074),(1.209999,0.709652),(1.219999,0.705524),(1.229999,0.701713),(1.239999,0.698241),(1.249999,0.695128),(1.259999,0.692394),(1.269999,0.690055),(1.279999,0.688127),(1.289999,0.686623),(1.299999,0.685553),(1.309999,0.684926),(1.319999,0.684749),(1.329999,0.685024),(1.339999,0.685753),(1.349999,0.686935),(1.359999,0.688567),(1.369999,0.690641),(1.379999,0.693150),(1.389999,0.696082),(1.399999,0.697984),(1.409999,0.682819),(1.419999,0.667650),(1.429999,0.652477),(1.439999,0.637299),(1.449999,0.622117),(1.459999,0.606931),(1.469999,0.591738),(1.479999,0.576541),(1.489999,0.561341),(1.499999,0.546132),(1.509999,0.530920),(1.519999,0.515702),(1.529999,0.500477),(1.539999,0.485246),(1.549999,0.470007),(1.559999,0.454759),(1.569999,0.439504),(1.579999,0.424239),(1.589999,0.408963),(1.599999,0.393678),(1.609999,0.378381),(1.619999,0.363072),(1.629999,0.347748),(1.639999,0.332410),(1.649999,0.317056),(1.659999,0.301684),(1.669999,0.286292),(1.679999,0.270876),(1.689999,0.255436),(1.699999,0.239968),(1.709999,0.224467),(1.719999,0.208929),(1.729999,0.193349),(1.739999,0.177718),(1.749999,0.162025),(1.759999,0.146257),(1.769999,0.130399),(1.779999,0.114419),(1.789999,0.098281),(1.799999,0.081922),(1.809999,0.065223),(1.819999,0.047924),(1.829999,0.029315)]
A = [(0.000000,-0.000000),(0.010000,-0.012688),(0.020000,-0.025381),(0.030000,-0.038082),(0.040000,-0.050796),(0.050000,-0.063525),(0.060000,-0.076273),(0.070000,-0.089044),(0.080000,-0.101842),(0.090000,-0.114671),(0.100000,-0.127533),(0.110000,-0.140435),(0.120000,-0.153378),(0.130000,-0.166368),(0.140000,-0.179409),(0.150000,-0.192505),(0.160000,-0.205660),(0.170000,-0.218879),(0.180000,-0.232166),(0.190000,-0.245528),(0.200000,-0.258967),(0.210000,-0.272491),(0.220000,-0.286104),(0.230000,-0.299811),(0.240000,-0.313619),(0.250000,-0.327534),(0.260000,-0.341562),(0.270000,-0.355710),(0.280000,-0.369985),(0.290000,-0.384394),(0.300000,-0.398945),(0.310000,-0.413646),(0.320000,-0.428506),(0.330000,-0.443534),(0.340000,-0.458739),(0.350000,-0.474131),(0.360000,-0.489723),(0.370000,-0.505523),(0.380000,-0.521546),(0.390000,-0.537804),(0.400000,-0.554310),(0.410000,-0.571079),(0.420000,-0.588126),(0.430000,-0.605470),(0.440000,-0.623126),(0.450000,-0.641115),(0.460000,-0.659457),(0.470000,-0.678174),(0.480000,-0.697290),(0.490000,-0.716829),(0.500000,-0.736820),(0.510000,-0.757292),(0.520000,-0.778276),(0.530000,-0.799807),(0.540000,-0.821923),(0.550000,-0.844662),(0.560000,-0.868070),(0.570000,-0.892192),(0.580000,-0.917080),(0.590000,-0.942790),(0.600000,-0.969382),(0.610000,-0.996924),(0.620000,-1.025486),(0.630000,-1.055147),(0.640000,-1.071342),(0.650000,-1.083652),(0.660000,-1.096407),(0.670000,-1.109624),(0.680000,-1.123321),(0.690000,-1.137518),(0.700000,-1.152235),(0.710000,-1.167493),(0.720000,-1.183311),(0.730000,-1.199714),(0.740000,-1.216720),(0.750000,-1.234355),(0.760000,-1.252639),(0.770000,-1.271598),(0.780000,-1.291253),(0.790000,-1.311630),(0.800000,-1.332750),(0.810000,-1.354637),(0.820000,-1.377315),(0.830000,-1.400806),(0.839999,-1.425131),(0.849999,-1.450314),(0.859999,-1.476371),(0.869999,-1.503323),(0.879999,-1.531184),(0.889999,-1.559970),(0.899999,-1.589691),(0.909999,-1.620357),(0.919999,-1.651969),(0.929999,-1.684532),(0.939999,-1.718035),(0.949999,-1.752475),(0.959999,-1.787835),(0.969999,-1.824090),(0.979999,-1.861216),(0.989999,-1.899170),(0.999999,-1.937908),(1.009999,-1.977376),(1.019999,-2.017508),(1.029999,-2.058228),(1.039999,-2.099450),(1.049999,-2.141079),(1.059999,-2.183014),(1.069999,-2.225128),(1.079999,-2.267298),(1.089999,-2.309378),(1.099999,-2.351225),(1.109999,-2.392677),(1.119999,-2.433567),(1.129999,-2.473723),(1.139999,-2.512966),(1.149999,-2.551110),(1.159999,-2.587971),(1.169999,-2.623365),(1.179999,-2.657106),(1.189999,-2.689012),(1.199999,-2.718907),(1.209999,-2.746624),(1.219999,-2.772002),(1.229999,-2.794891),(1.239999,-2.815158),(1.249999,-2.832677),(1.259999,-2.847341),(1.269999,-2.859058),(1.279999,-2.867753),(1.289999,-2.873366),(1.299999,-2.875858),(1.309999,-2.875204),(1.319999,-2.871400),(1.329999,-2.864456),(1.339999,-2.854402),(1.349999,-2.841283),(1.359999,-2.825161),(1.369999,-2.806112),(1.379999,-2.784227),(1.389999,-2.759611),(1.399999,-2.726836),(1.409999,-2.625845),(1.419999,-2.524985),(1.429999,-2.424867),(1.439999,-2.326006),(1.449999,-2.228825),(1.459999,-2.133667),(1.469999,-2.040797),(1.479999,-1.950429),(1.489999,-1.862695),(1.499999,-1.777686),(1.509999,-1.695460),(1.519999,-1.616021),(1.529999,-1.539348),(1.539999,-1.465404),(1.549999,-1.394123),(1.559999,-1.325428),(1.569999,-1.259234),(1.579999,-1.195442),(1.589999,-1.133952),(1.599999,-1.074655),(1.609999,-1.017443),(1.619999,-0.962205),(1.629999,-0.908832),(1.639999,-0.857213),(1.649999,-0.807243),(1.659999,-0.758814),(1.669999,-0.711820),(1.679999,-0.666158),(1.689999,-0.621731),(1.699999,-0.578438),(1.709999,-0.536181),(1.719999,-0.494864),(1.729999,-0.454393),(1.739999,-0.414665),(1.749999,-0.375580),(1.759999,-0.337031),(1.769999,-0.298907),(1.779999,-0.261067),(1.789999,-0.223358),(1.799999,-0.185565),(1.809999,-0.147349),(1.819999,-0.108059),(1.829999,-0.066024)]
)";
 
const std::string skills_6 = R"(
X = [(0.381,0.381),(0.381,0.381),(0.381,0.381),(0.382,0.382),(0.382,0.382),(0.383,0.383),(0.383,0.383),(0.384,0.384),(0.385,0.385),(0.386,0.386),(0.387,0.387),(0.388,0.388),(0.389,0.389),(0.391,0.391),(0.392,0.392),(0.394,0.394),(0.395,0.395),(0.397,0.397),(0.399,0.399),(0.401,0.401),(0.403,0.403),(0.406,0.405),(0.408,0.408),(0.410,0.410),(0.413,0.413),(0.416,0.415),(0.419,0.418),(0.422,0.421),(0.425,0.424),(0.428,0.427),(0.431,0.430),(0.434,0.433),(0.438,0.436),(0.442,0.439),(0.445,0.443),(0.449,0.446),(0.453,0.450),(0.457,0.454),(0.461,0.458),(0.466,0.462),(0.470,0.466),(0.475,0.470),(0.480,0.474),(0.485,0.478),(0.490,0.482),(0.495,0.487),(0.500,0.491),(0.506,0.495),(0.511,0.500),(0.517,0.505),(0.523,0.509),(0.529,0.514),(0.535,0.519),(0.541,0.523),(0.548,0.528),(0.555,0.533),(0.562,0.538),(0.569,0.542),(0.576,0.547),(0.583,0.552),(0.591,0.556),(0.599,0.561),(0.607,0.565),(0.615,0.569),(0.623,0.573),(0.630,0.577),(0.638,0.580),(0.645,0.583),(0.653,0.586),(0.660,0.588),(0.667,0.590),(0.674,0.592),(0.681,0.594),(0.688,0.595),(0.694,0.596),(0.701,0.597),(0.707,0.597),(0.713,0.597),(0.720,0.597),(0.726,0.597),(0.731,0.596),(0.737,0.595),(0.743,0.594),(0.748,0.593),(0.754,0.591),(0.759,0.590),(0.765,0.588),(0.770,0.585),(0.775,0.583),(0.780,0.580),(0.785,0.577),(0.791,0.574),(0.796,0.570),(0.801,0.567),(0.806,0.562),(0.811,0.558),(0.815,0.553),(0.820,0.549),(0.825,0.543),(0.830,0.538),(0.834,0.532),(0.839,0.526),(0.843,0.520),(0.848,0.514),(0.852,0.507),(0.856,0.500),(0.860,0.493),(0.865,0.486),(0.869,0.478),(0.872,0.470),(0.876,0.462),(0.880,0.454),(0.884,0.446),(0.887,0.437),(0.891,0.429),(0.894,0.420),(0.898,0.411),(0.901,0.401),(0.904,0.392),(0.908,0.382),(0.911,0.372),(0.914,0.362),(0.917,0.352),(0.920,0.342),(0.923,0.332),(0.926,0.321),(0.928,0.311),(0.930,0.304),(0.930,0.304),(0.934,0.294),(0.938,0.283),(0.941,0.273),(0.945,0.262),(0.949,0.251),(0.953,0.240),(0.957,0.229),(0.961,0.218),(0.965,0.207),(0.969,0.195),(0.973,0.184),(0.977,0.173),(0.981,0.162),(0.984,0.151),(0.988,0.140),(0.992,0.129),(0.996,0.118),(0.999,0.107),(1.003,0.096),(1.007,0.085),(1.010,0.074),(1.014,0.063),(1.017,0.052),(1.021,0.040),(1.024,0.029),(1.028,0.018),(1.031,0.007),(1.035,-0.004),(1.038,-0.015),(1.041,-0.026),(1.045,-0.037),(1.048,-0.048),(1.051,-0.059),(1.054,-0.071),(1.058,-0.082),(1.061,-0.093),(1.064,-0.104),(1.067,-0.115),(1.070,-0.126),(1.073,-0.138),(1.076,-0.149),(1.079,-0.160),(1.082,-0.171),(1.085,-0.182),(1.087,-0.194),(1.090,-0.205),(1.093,-0.216),(1.096,-0.227),(1.098,-0.239),(1.101,-0.250),(1.104,-0.261),(1.106,-0.272),(1.109,-0.284),(1.111,-0.295),(1.114,-0.306),(1.116,-0.318),(1.119,-0.329),(1.121,-0.340),(1.124,-0.351),(1.126,-0.363),(1.128,-0.374),(1.130,-0.386),(1.133,-0.397),(1.135,-0.408),(1.137,-0.420),(1.139,-0.431),(1.141,-0.442),(1.143,-0.454),(1.145,-0.465),(1.148,-0.477),(1.149,-0.488),(1.151,-0.500),(1.153,-0.511),(1.155,-0.522),(1.157,-0.534),(1.159,-0.545),(1.161,-0.557),(1.163,-0.568),(1.164,-0.580),(1.166,-0.591),(1.168,-0.603),(1.169,-0.614),(1.171,-0.626),(1.172,-0.637),(1.174,-0.649),(1.176,-0.660),(1.177,-0.672),(1.179,-0.683),(1.180,-0.695),(1.181,-0.706),(1.183,-0.718),(1.184,-0.730),(1.185,-0.741),(1.187,-0.753),(1.188,-0.764),(1.189,-0.776),(1.190,-0.788),(1.192,-0.799),(1.193,-0.811),(1.194,-0.822),(1.195,-0.834),(1.196,-0.846),(1.197,-0.857),(1.198,-0.869),(1.199,-0.880),(1.200,-0.892),(1.201,-0.904),(1.202,-0.915),(1.203,-0.927),(1.204,-0.938),(1.205,-0.950),(1.205,-0.961),(1.206,-0.972),(1.207,-0.983),(1.208,-0.994),(1.208,-1.004),(1.209,-1.015),(1.209,-1.025),(1.210,-1.035),(1.211,-1.046),(1.211,-1.055),(1.212,-1.065),(1.212,-1.075),(1.212,-1.084),(1.213,-1.093),(1.213,-1.103),(1.214,-1.112),(1.214,-1.120),(1.214,-1.129),(1.215,-1.138),(1.215,-1.146),(1.215,-1.154),(1.216,-1.162),(1.216,-1.170),(1.216,-1.178),(1.216,-1.186),(1.217,-1.193),(1.217,-1.200),(1.217,-1.208),(1.217,-1.215),(1.217,-1.221),(1.217,-1.228),(1.218,-1.235),(1.218,-1.241),(1.218,-1.247),(1.218,-1.254),(1.218,-1.260),(1.218,-1.265),(1.218,-1.271),(1.218,-1.277),(1.218,-1.282),(1.218,-1.287),(1.219,-1.292),(1.219,-1.297),(1.219,-1.302),(1.219,-1.306),(1.219,-1.311),(1.219,-1.315),(1.219,-1.319),(1.219,-1.323),(1.219,-1.327),(1.219,-1.331),(1.219,-1.334),(1.219,-1.338),(1.219,-1.341),(1.219,-1.344),(1.219,-1.347),(1.219,-1.349),(1.219,-1.352),(1.219,-1.355),(1.219,-1.357),(1.219,-1.359),(1.219,-1.361),(1.219,-1.363),(1.219,-1.364),(1.219,-1.366),(1.219,-1.367),(1.219,-1.368),(1.219,-1.370),(1.219,-1.370),(1.219,-1.371),(1.219,-1.372),(1.219,-1.372),(1.219,-1.372)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.585),(0.400,0.600),(0.410,0.615),(0.420,0.630),(0.430,0.645),(0.440,0.660),(0.450,0.675),(0.460,0.690),(0.470,0.705),(0.480,0.720),(0.490,0.735),(0.500,0.750),(0.510,0.765),(0.520,0.780),(0.530,0.795),(0.540,0.810),(0.550,0.825),(0.560,0.840),(0.570,0.855),(0.580,0.870),(0.590,0.885),(0.600,0.900),(0.610,0.915),(0.620,0.902),(0.630,0.884),(0.640,0.866),(0.650,0.846),(0.660,0.826),(0.670,0.806),(0.680,0.786),(0.690,0.765),(0.700,0.745),(0.710,0.725),(0.720,0.705),(0.730,0.686),(0.740,0.668),(0.750,0.651),(0.760,0.636),(0.770,0.622),(0.780,0.609),(0.790,0.598),(0.800,0.589),(0.810,0.581),(0.820,0.575),(0.830,0.571),(0.840,0.569),(0.850,0.569),(0.860,0.571),(0.870,0.574),(0.880,0.579),(0.890,0.586),(0.900,0.595),(0.910,0.605),(0.920,0.617),(0.930,0.630),(0.940,0.645),(0.950,0.660),(0.960,0.675),(0.970,0.690),(0.980,0.705),(0.990,0.720),(1.000,0.735),(1.010,0.750),(1.020,0.765),(1.030,0.780),(1.040,0.795),(1.050,0.810),(1.060,0.825),(1.070,0.840),(1.080,0.855),(1.090,0.870),(1.100,0.885),(1.110,0.900),(1.120,0.915),(1.130,0.930),(1.140,0.945),(1.150,0.960),(1.160,0.975),(1.170,0.990),(1.180,1.005),(1.190,1.020),(1.200,1.035),(1.210,1.045),(1.220,1.052),(1.230,1.060),(1.240,1.066),(1.250,1.073),(1.260,1.079),(1.270,1.084),(1.270,1.084),(1.280,1.099),(1.290,1.114),(1.300,1.129),(1.310,1.144),(1.320,1.159),(1.330,1.174),(1.340,1.181),(1.350,1.180),(1.360,1.178),(1.370,1.176),(1.380,1.175),(1.390,1.173),(1.400,1.172),(1.410,1.171),(1.420,1.170),(1.430,1.169),(1.440,1.168),(1.450,1.167),(1.460,1.166),(1.470,1.165),(1.480,1.164),(1.490,1.164),(1.500,1.163),(1.510,1.162),(1.520,1.162),(1.530,1.161),(1.540,1.161),(1.550,1.160),(1.560,1.160),(1.570,1.160),(1.580,1.159),(1.590,1.159),(1.600,1.159),(1.610,1.158),(1.620,1.158),(1.630,1.158),(1.640,1.158),(1.650,1.158),(1.660,1.157),(1.670,1.157),(1.680,1.157),(1.690,1.157),(1.700,1.157),(1.710,1.157),(1.720,1.157),(1.730,1.157),(1.740,1.157),(1.750,1.157),(1.760,1.157),(1.770,1.157),(1.780,1.157),(1.790,1.157),(1.800,1.157),(1.810,1.157),(1.820,1.157),(1.830,1.158),(1.840,1.158),(1.850,1.158),(1.860,1.158),(1.870,1.158),(1.880,1.158),(1.890,1.158),(1.900,1.158),(1.910,1.159),(1.920,1.159),(1.930,1.159),(1.940,1.159),(1.950,1.159),(1.960,1.159),(1.970,1.160),(1.980,1.160),(1.990,1.160),(2.000,1.160),(2.010,1.160),(2.020,1.161),(2.030,1.161),(2.040,1.161),(2.050,1.161),(2.060,1.161),(2.070,1.162),(2.080,1.162),(2.090,1.162),(2.100,1.162),(2.110,1.162),(2.120,1.163),(2.130,1.163),(2.140,1.163),(2.150,1.163),(2.160,1.163),(2.170,1.164),(2.180,1.164),(2.190,1.164),(2.200,1.164),(2.210,1.164),(2.220,1.165),(2.230,1.165),(2.240,1.165),(2.250,1.165),(2.260,1.165),(2.270,1.166),(2.280,1.166),(2.290,1.166),(2.300,1.166),(2.310,1.167),(2.320,1.167),(2.330,1.167),(2.340,1.167),(2.350,1.167),(2.360,1.168),(2.370,1.156),(2.380,1.141),(2.390,1.126),(2.400,1.111),(2.410,1.096),(2.420,1.081),(2.430,1.065),(2.440,1.050),(2.450,1.035),(2.460,1.020),(2.470,1.005),(2.480,0.990),(2.490,0.975),(2.500,0.960),(2.510,0.945),(2.520,0.929),(2.530,0.914),(2.540,0.899),(2.550,0.884),(2.560,0.869),(2.570,0.854),(2.580,0.839),(2.590,0.823),(2.600,0.808),(2.610,0.793),(2.620,0.778),(2.630,0.763),(2.640,0.748),(2.650,0.733),(2.660,0.717),(2.670,0.702),(2.680,0.687),(2.690,0.672),(2.700,0.657),(2.710,0.642),(2.720,0.626),(2.730,0.611),(2.740,0.596),(2.750,0.581),(2.760,0.566),(2.770,0.550),(2.780,0.535),(2.790,0.520),(2.800,0.505),(2.810,0.490),(2.820,0.474),(2.830,0.459),(2.840,0.444),(2.850,0.429),(2.860,0.413),(2.870,0.398),(2.880,0.383),(2.890,0.367),(2.900,0.352),(2.910,0.337),(2.920,0.321),(2.930,0.306),(2.940,0.291),(2.950,0.275),(2.960,0.260),(2.970,0.244),(2.980,0.229),(2.990,0.213),(3.000,0.198),(3.010,0.182),(3.020,0.166),(3.030,0.151),(3.040,0.135),(3.050,0.119),(3.060,0.103),(3.070,0.087),(3.080,0.070),(3.090,0.053),(3.100,0.035),(3.110,0.013)]
A = [(0.000,-0.000),(0.010,-0.005),(0.020,-0.010),(0.030,-0.016),(0.040,-0.021),(0.050,-0.026),(0.060,-0.032),(0.070,-0.037),(0.080,-0.043),(0.090,-0.049),(0.100,-0.055),(0.110,-0.061),(0.120,-0.067),(0.130,-0.073),(0.140,-0.080),(0.150,-0.087),(0.160,-0.094),(0.170,-0.101),(0.180,-0.109),(0.190,-0.117),(0.200,-0.125),(0.210,-0.134),(0.220,-0.143),(0.230,-0.152),(0.240,-0.162),(0.250,-0.172),(0.260,-0.183),(0.270,-0.195),(0.280,-0.207),(0.290,-0.220),(0.300,-0.234),(0.310,-0.248),(0.320,-0.264),(0.330,-0.280),(0.340,-0.297),(0.350,-0.316),(0.360,-0.336),(0.370,-0.357),(0.380,-0.379),(0.390,-0.403),(0.400,-0.429),(0.410,-0.457),(0.420,-0.487),(0.430,-0.519),(0.440,-0.554),(0.450,-0.592),(0.460,-0.633),(0.470,-0.677),(0.480,-0.726),(0.490,-0.779),(0.500,-0.837),(0.510,-0.901),(0.520,-0.971),(0.530,-1.048),(0.540,-1.134),(0.550,-1.229),(0.560,-1.334),(0.570,-1.452),(0.580,-1.584),(0.590,-1.733),(0.600,-1.900),(0.610,-2.089),(0.620,-2.230),(0.630,-2.365),(0.640,-2.505),(0.650,-2.649),(0.660,-2.795),(0.670,-2.943),(0.680,-3.092),(0.690,-3.238),(0.700,-3.382),(0.710,-3.522),(0.720,-3.655),(0.730,-3.780),(0.740,-3.896),(0.750,-4.001),(0.760,-4.095),(0.770,-4.176),(0.780,-4.245),(0.790,-4.299),(0.800,-4.340),(0.810,-4.367),(0.820,-4.381),(0.830,-4.382),(0.840,-4.369),(0.850,-4.344),(0.860,-4.306),(0.870,-4.257),(0.880,-4.198),(0.890,-4.127),(0.900,-4.047),(0.910,-3.959),(0.920,-3.862),(0.930,-3.757),(0.940,-3.646),(0.950,-3.527),(0.960,-3.398),(0.970,-3.263),(0.980,-3.126),(0.990,-2.987),(1.000,-2.849),(1.010,-2.713),(1.020,-2.581),(1.030,-2.454),(1.040,-2.331),(1.050,-2.214),(1.060,-2.102),(1.070,-1.997),(1.080,-1.897),(1.090,-1.802),(1.100,-1.713),(1.110,-1.629),(1.120,-1.550),(1.130,-1.476),(1.140,-1.406),(1.150,-1.340),(1.160,-1.278),(1.170,-1.220),(1.180,-1.165),(1.190,-1.114),(1.200,-1.065),(1.210,-1.015),(1.220,-0.966),(1.230,-0.920),(1.240,-0.877),(1.250,-0.836),(1.260,-0.798),(1.270,-0.776),(1.270,-0.036),(1.280,-0.052),(1.290,-0.068),(1.300,-0.083),(1.310,-0.098),(1.320,-0.113),(1.330,-0.128),(1.340,-0.142),(1.350,-0.153),(1.360,-0.164),(1.370,-0.175),(1.380,-0.184),(1.390,-0.193),(1.400,-0.202),(1.410,-0.210),(1.420,-0.217),(1.430,-0.224),(1.440,-0.231),(1.450,-0.237),(1.460,-0.242),(1.470,-0.247),(1.480,-0.252),(1.490,-0.257),(1.500,-0.261),(1.510,-0.265),(1.520,-0.269),(1.530,-0.272),(1.540,-0.275),(1.550,-0.278),(1.560,-0.280),(1.570,-0.283),(1.580,-0.285),(1.590,-0.287),(1.600,-0.289),(1.610,-0.290),(1.620,-0.292),(1.630,-0.293),(1.640,-0.294),(1.650,-0.295),(1.660,-0.296),(1.670,-0.296),(1.680,-0.297),(1.690,-0.297),(1.700,-0.297),(1.710,-0.298),(1.720,-0.298),(1.730,-0.298),(1.740,-0.298),(1.750,-0.297),(1.760,-0.297),(1.770,-0.297),(1.780,-0.296),(1.790,-0.296),(1.800,-0.295),(1.810,-0.295),(1.820,-0.294),(1.830,-0.293),(1.840,-0.292),(1.850,-0.292),(1.860,-0.291),(1.870,-0.290),(1.880,-0.289),(1.890,-0.288),(1.900,-0.287),(1.910,-0.286),(1.920,-0.284),(1.930,-0.283),(1.940,-0.282),(1.950,-0.281),(1.960,-0.280),(1.970,-0.278),(1.980,-0.277),(1.990,-0.276),(2.000,-0.275),(2.010,-0.273),(2.020,-0.272),(2.030,-0.271),(2.040,-0.269),(2.050,-0.268),(2.060,-0.266),(2.070,-0.265),(2.080,-0.264),(2.090,-0.262),(2.100,-0.261),(2.110,-0.259),(2.120,-0.258),(2.130,-0.256),(2.140,-0.255),(2.150,-0.253),(2.160,-0.252),(2.170,-0.250),(2.180,-0.249),(2.190,-0.248),(2.200,-0.246),(2.210,-0.245),(2.220,-0.243),(2.230,-0.242),(2.240,-0.240),(2.250,-0.239),(2.260,-0.237),(2.270,-0.236),(2.280,-0.234),(2.290,-0.233),(2.300,-0.232),(2.310,-0.230),(2.320,-0.229),(2.330,-0.227),(2.340,-0.226),(2.350,-0.224),(2.360,-0.223),(2.370,-0.219),(2.380,-0.215),(2.390,-0.211),(2.400,-0.207),(2.410,-0.203),(2.420,-0.199),(2.430,-0.195),(2.440,-0.191),(2.450,-0.187),(2.460,-0.183),(2.470,-0.180),(2.480,-0.176),(2.490,-0.172),(2.500,-0.169),(2.510,-0.165),(2.520,-0.162),(2.530,-0.158),(2.540,-0.155),(2.550,-0.152),(2.560,-0.148),(2.570,-0.145),(2.580,-0.142),(2.590,-0.139),(2.600,-0.135),(2.610,-0.132),(2.620,-0.129),(2.630,-0.126),(2.640,-0.123),(2.650,-0.120),(2.660,-0.117),(2.670,-0.114),(2.680,-0.111),(2.690,-0.108),(2.700,-0.106),(2.710,-0.103),(2.720,-0.100),(2.730,-0.097),(2.740,-0.095),(2.750,-0.092),(2.760,-0.089),(2.770,-0.087),(2.780,-0.084),(2.790,-0.081),(2.800,-0.079),(2.810,-0.076),(2.820,-0.074),(2.830,-0.071),(2.840,-0.068),(2.850,-0.066),(2.860,-0.063),(2.870,-0.061),(2.880,-0.059),(2.890,-0.056),(2.900,-0.054),(2.910,-0.051),(2.920,-0.049),(2.930,-0.046),(2.940,-0.044),(2.950,-0.042),(2.960,-0.039),(2.970,-0.037),(2.980,-0.034),(2.990,-0.032),(3.000,-0.030),(3.010,-0.027),(3.020,-0.025),(3.030,-0.023),(3.040,-0.020),(3.050,-0.018),(3.060,-0.015),(3.070,-0.013),(3.080,-0.010),(3.090,-0.008),(3.100,-0.005),(3.110,-0.002)]
)";
 
const std::string skills_7 = R"(
X = 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1.563),(-0.980,-1.562),(-0.989,-1.560),(-0.997,-1.559),(-1.005,-1.558),(-1.014,-1.556),(-1.022,-1.554),(-1.030,-1.553),(-1.037,-1.551),(-1.045,-1.549),(-1.053,-1.547),(-1.060,-1.545),(-1.068,-1.543),(-1.075,-1.541),(-1.082,-1.539),(-1.089,-1.536),(-1.096,-1.534),(-1.103,-1.531),(-1.109,-1.528),(-1.115,-1.526),(-1.122,-1.523),(-1.128,-1.520),(-1.134,-1.517),(-1.139,-1.513),(-1.145,-1.510),(-1.150,-1.507),(-1.156,-1.503),(-1.161,-1.500),(-1.166,-1.496),(-1.170,-1.492),(-1.175,-1.489),(-1.179,-1.485),(-1.184,-1.481),(-1.188,-1.477),(-1.192,-1.472),(-1.196,-1.468),(-1.199,-1.464),(-1.203,-1.459),(-1.206,-1.455),(-1.210,-1.450),(-1.213,-1.445),(-1.216,-1.441),(-1.219,-1.436),(-1.221,-1.431),(-1.224,-1.425),(-1.227,-1.420),(-1.229,-1.415),(-1.231,-1.409),(-1.233,-1.404),(-1.235,-1.398),(-1.237,-1.392),(-1.239,-1.386),(-1.240,-1.380),(-1.242,-1.374),(-1.243,-1.368),(-1.244,-1.361),(-1.245,-1.355),(-1.245,-1.355),(-1.244,-1.349),(-1.243,-1.342),(-1.242,-1.336),(-1.241,-1.330),(-1.239,-1.325),(-1.238,-1.319),(-1.236,-1.314),(-1.234,-1.309),(-1.231,-1.304),(-1.229,-1.300),(-1.227,-1.295),(-1.224,-1.291),(-1.222,-1.287),(-1.219,-1.283),(-1.216,-1.280),(-1.213,-1.276),(-1.210,-1.272),(-1.207,-1.269),(-1.203,-1.265),(-1.199,-1.262),(-1.196,-1.259),(-1.192,-1.255),(-1.187,-1.252),(-1.183,-1.249),(-1.178,-1.246),(-1.174,-1.243),(-1.169,-1.240),(-1.164,-1.238),(-1.158,-1.235),(-1.153,-1.232),(-1.147,-1.230),(-1.141,-1.227),(-1.135,-1.225),(-1.129,-1.223),(-1.122,-1.221),(-1.115,-1.219),(-1.109,-1.217),(-1.102,-1.215),(-1.094,-1.213),(-1.087,-1.211),(-1.080,-1.210),(-1.072,-1.208),(-1.064,-1.207),(-1.056,-1.205),(-1.048,-1.204),(-1.040,-1.203),(-1.032,-1.202),(-1.024,-1.201),(-1.015,-1.200),(-1.007,-1.199),(-0.998,-1.198),(-0.989,-1.198),(-0.981,-1.197),(-0.972,-1.197),(-0.963,-1.196),(-0.954,-1.196),(-0.946,-1.195),(-0.937,-1.195),(-0.929,-1.195),(-0.921,-1.194),(-0.913,-1.194),(-0.905,-1.194),(-0.898,-1.194),(-0.890,-1.194),(-0.883,-1.194),(-0.875,-1.194),(-0.868,-1.194),(-0.862,-1.193),(-0.855,-1.193),(-0.848,-1.193),(-0.842,-1.193),(-0.835,-1.193),(-0.829,-1.193),(-0.823,-1.193),(-0.817,-1.193),(-0.812,-1.194),(-0.806,-1.194),(-0.801,-1.194),(-0.796,-1.194),(-0.791,-1.194),(-0.786,-1.194),(-0.781,-1.194),(-0.776,-1.194),(-0.772,-1.194),(-0.767,-1.194),(-0.763,-1.194),(-0.759,-1.194),(-0.755,-1.194),(-0.751,-1.194),(-0.748,-1.194),(-0.744,-1.194),(-0.741,-1.194),(-0.738,-1.194),(-0.735,-1.194),(-0.732,-1.194),(-0.729,-1.194),(-0.727,-1.194),(-0.724,-1.194),(-0.722,-1.194),(-0.720,-1.194),(-0.718,-1.194),(-0.716,-1.194),(-0.715,-1.194),(-0.713,-1.194),(-0.712,-1.194),(-0.711,-1.194)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.566),(0.400,0.552),(0.410,0.539),(0.420,0.528),(0.430,0.517),(0.440,0.508),(0.450,0.501),(0.460,0.495),(0.470,0.491),(0.480,0.489),(0.490,0.488),(0.500,0.490),(0.510,0.494),(0.520,0.500),(0.530,0.508),(0.540,0.519),(0.550,0.533),(0.560,0.548),(0.570,0.563),(0.580,0.578),(0.590,0.593),(0.600,0.608),(0.610,0.623),(0.620,0.638),(0.630,0.653),(0.640,0.668),(0.650,0.683),(0.660,0.698),(0.670,0.713),(0.680,0.728),(0.690,0.743),(0.700,0.758),(0.710,0.773),(0.720,0.788),(0.730,0.776),(0.740,0.761),(0.750,0.746),(0.760,0.731),(0.770,0.716),(0.780,0.701),(0.790,0.686),(0.800,0.676),(0.810,0.671),(0.820,0.668),(0.830,0.665),(0.840,0.664),(0.850,0.664),(0.860,0.666),(0.870,0.668),(0.880,0.670),(0.890,0.674),(0.900,0.678),(0.910,0.683),(0.920,0.688),(0.930,0.694),(0.940,0.700),(0.950,0.706),(0.960,0.713),(0.970,0.720),(0.980,0.727),(0.990,0.735),(1.000,0.742),(1.010,0.749),(1.020,0.757),(1.030,0.764),(1.040,0.771),(1.050,0.779),(1.060,0.786),(1.070,0.793),(1.080,0.800),(1.090,0.806),(1.100,0.813),(1.110,0.819),(1.120,0.825),(1.130,0.831),(1.140,0.837),(1.150,0.843),(1.160,0.848),(1.170,0.853),(1.180,0.858),(1.190,0.863),(1.200,0.868),(1.210,0.872),(1.220,0.876),(1.230,0.880),(1.240,0.884),(1.250,0.888),(1.260,0.892),(1.270,0.895),(1.280,0.899),(1.290,0.902),(1.300,0.905),(1.310,0.908),(1.320,0.911),(1.330,0.913),(1.340,0.916),(1.350,0.918),(1.360,0.921),(1.370,0.923),(1.380,0.925),(1.390,0.927),(1.400,0.929),(1.410,0.931),(1.420,0.933),(1.430,0.935),(1.440,0.937),(1.450,0.938),(1.460,0.940),(1.470,0.942),(1.480,0.943),(1.490,0.944),(1.500,0.946),(1.510,0.947),(1.520,0.948),(1.530,0.950),(1.540,0.951),(1.550,0.952),(1.560,0.953),(1.570,0.954),(1.580,0.955),(1.590,0.956),(1.600,0.957),(1.610,0.958),(1.620,0.959),(1.630,0.960),(1.640,0.961),(1.650,0.962),(1.660,0.962),(1.670,0.963),(1.680,0.964),(1.690,0.965),(1.700,0.965),(1.700,0.965),(1.710,0.980),(1.720,0.995),(1.730,1.000),(1.740,1.000),(1.750,1.000),(1.760,1.000),(1.770,1.000),(1.780,1.000),(1.790,1.000),(1.800,1.000),(1.810,1.000),(1.820,1.000),(1.830,1.000),(1.840,1.000),(1.850,1.000),(1.860,1.000),(1.870,1.000),(1.880,1.000),(1.890,1.000),(1.900,1.000),(1.910,1.000),(1.920,1.000),(1.930,1.000),(1.940,1.000),(1.950,1.000),(1.960,1.000),(1.970,1.000),(1.980,1.000),(1.990,1.000),(2.000,1.000),(2.010,1.000),(2.020,1.000),(2.030,1.000),(2.040,1.000),(2.050,1.000),(2.060,1.000),(2.070,1.000),(2.080,1.000),(2.090,1.000),(2.100,1.000),(2.110,1.000),(2.120,1.000),(2.130,1.000),(2.140,1.000),(2.150,1.000),(2.160,1.000),(2.170,1.000),(2.180,1.000),(2.190,1.000),(2.200,1.000),(2.210,1.000),(2.220,1.000),(2.230,1.000),(2.240,1.000),(2.250,1.000),(2.260,1.000),(2.270,1.000),(2.280,1.000),(2.290,1.000),(2.300,1.000),(2.310,1.000),(2.320,1.000),(2.330,1.000),(2.340,1.000),(2.350,1.000),(2.360,1.000),(2.370,1.000),(2.380,1.000),(2.390,1.000),(2.400,1.000),(2.410,1.000),(2.420,1.000),(2.430,1.000),(2.440,1.000),(2.450,1.000),(2.460,1.000),(2.470,1.000),(2.480,1.000),(2.490,1.000),(2.500,1.000),(2.510,1.000),(2.520,1.000),(2.530,1.000),(2.540,1.000),(2.550,1.000),(2.560,1.000),(2.570,1.000),(2.580,1.000),(2.590,1.000),(2.600,1.000),(2.610,1.000),(2.620,1.000),(2.630,1.000),(2.640,1.000),(2.650,1.000),(2.660,1.000),(2.670,1.000),(2.680,1.000),(2.690,1.000),(2.700,1.000),(2.710,1.000),(2.720,1.000),(2.730,1.000),(2.740,1.000),(2.750,1.000),(2.760,1.000),(2.770,1.000),(2.780,1.000),(2.790,1.000),(2.800,1.000),(2.810,1.000),(2.820,1.000),(2.830,1.000),(2.840,1.000),(2.850,1.000),(2.860,1.000),(2.860,1.000),(2.870,0.992),(2.880,0.994),(2.890,0.996),(2.900,0.999),(2.910,0.999),(2.920,0.997),(2.930,0.994),(2.940,0.992),(2.950,0.989),(2.960,0.987),(2.970,0.984),(2.980,0.981),(2.990,0.978),(3.000,0.976),(3.010,0.973),(3.020,0.970),(3.030,0.967),(3.040,0.963),(3.050,0.960),(3.060,0.957),(3.070,0.953),(3.080,0.950),(3.090,0.946),(3.100,0.942),(3.110,0.938),(3.120,0.934),(3.130,0.929),(3.140,0.925),(3.150,0.920),(3.160,0.915),(3.170,0.910),(3.180,0.905),(3.190,0.900),(3.200,0.894),(3.210,0.888),(3.220,0.882),(3.230,0.875),(3.240,0.869),(3.250,0.862),(3.260,0.855),(3.270,0.847),(3.280,0.839),(3.290,0.831),(3.300,0.823),(3.310,0.815),(3.320,0.806),(3.330,0.797),(3.340,0.787),(3.350,0.778),(3.360,0.768),(3.370,0.758),(3.380,0.748),(3.390,0.737),(3.400,0.727),(3.410,0.717),(3.420,0.706),(3.430,0.696),(3.440,0.685),(3.450,0.675),(3.460,0.665),(3.470,0.655),(3.480,0.646),(3.490,0.637),(3.500,0.628),(3.510,0.620),(3.520,0.612),(3.530,0.605),(3.540,0.598),(3.550,0.592),(3.560,0.586),(3.570,0.582),(3.580,0.578),(3.590,0.574),(3.600,0.572),(3.610,0.570),(3.620,0.569),(3.630,0.569),(3.640,0.569),(3.650,0.571),(3.660,0.573),(3.670,0.575),(3.680,0.579),(3.690,0.583),(3.700,0.587),(3.710,0.593),(3.720,0.599),(3.730,0.605),(3.740,0.612),(3.750,0.620),(3.760,0.628),(3.770,0.636),(3.780,0.644),(3.790,0.653),(3.800,0.662),(3.800,0.662),(3.810,0.647),(3.820,0.632),(3.830,0.617),(3.840,0.602),(3.850,0.587),(3.860,0.572),(3.870,0.557),(3.880,0.542),(3.890,0.527),(3.900,0.512),(3.910,0.497),(3.920,0.482),(3.930,0.472),(3.940,0.473),(3.950,0.474),(3.960,0.477),(3.970,0.481),(3.980,0.486),(3.990,0.492),(4.000,0.499),(4.010,0.507),(4.020,0.516),(4.030,0.525),(4.040,0.536),(4.050,0.547),(4.060,0.559),(4.070,0.571),(4.080,0.584),(4.090,0.598),(4.100,0.612),(4.110,0.626),(4.120,0.640),(4.130,0.655),(4.140,0.669),(4.150,0.683),(4.160,0.697),(4.170,0.711),(4.180,0.725),(4.190,0.738),(4.200,0.751),(4.210,0.764),(4.220,0.776),(4.230,0.788),(4.240,0.799),(4.250,0.810),(4.260,0.821),(4.270,0.831),(4.280,0.840),(4.290,0.849),(4.300,0.858),(4.310,0.866),(4.320,0.874),(4.330,0.882),(4.340,0.889),(4.350,0.884),(4.360,0.869),(4.370,0.854),(4.380,0.839),(4.390,0.824),(4.400,0.809),(4.410,0.794),(4.420,0.779),(4.430,0.764),(4.440,0.749),(4.450,0.734),(4.460,0.719),(4.470,0.704),(4.480,0.689),(4.490,0.674),(4.500,0.659),(4.510,0.644),(4.520,0.629),(4.530,0.614),(4.540,0.599),(4.550,0.584),(4.560,0.569),(4.570,0.554),(4.580,0.539),(4.590,0.524),(4.600,0.509),(4.610,0.494),(4.620,0.479),(4.630,0.464),(4.640,0.449),(4.650,0.434),(4.660,0.419),(4.670,0.404),(4.680,0.389),(4.690,0.374),(4.700,0.359),(4.710,0.344),(4.720,0.329),(4.730,0.314),(4.740,0.299),(4.750,0.284),(4.760,0.269),(4.770,0.254),(4.780,0.239),(4.790,0.224),(4.800,0.209),(4.810,0.194),(4.820,0.179),(4.830,0.164),(4.840,0.149),(4.850,0.134),(4.860,0.119)]
A = [(0.000,0.000),(0.010,0.025),(0.020,0.050),(0.030,0.075),(0.040,0.101),(0.050,0.127),(0.060,0.154),(0.070,0.181),(0.080,0.209),(0.090,0.238),(0.100,0.268),(0.110,0.300),(0.120,0.332),(0.130,0.367),(0.140,0.403),(0.150,0.441),(0.160,0.482),(0.170,0.525),(0.180,0.570),(0.190,0.619),(0.200,0.672),(0.210,0.728),(0.220,0.789),(0.230,0.855),(0.240,0.926),(0.250,1.004),(0.260,1.088),(0.270,1.181),(0.280,1.282),(0.290,1.392),(0.300,1.514),(0.310,1.648),(0.320,1.795),(0.330,1.957),(0.340,2.134),(0.350,2.329),(0.360,2.543),(0.370,2.774),(0.380,3.024),(0.390,3.178),(0.400,3.266),(0.410,3.343),(0.420,3.410),(0.430,3.464),(0.440,3.507),(0.450,3.536),(0.460,3.553),(0.470,3.555),(0.480,3.543),(0.490,3.517),(0.500,3.477),(0.510,3.420),(0.520,3.348),(0.530,3.260),(0.540,3.154),(0.550,3.030),(0.560,2.880),(0.570,2.696),(0.580,2.484),(0.590,2.246),(0.600,1.987),(0.610,1.712),(0.620,1.424),(0.630,1.127),(0.640,0.823),(0.650,0.516),(0.660,0.207),(0.670,-0.101),(0.680,-0.408),(0.690,-0.710),(0.700,-1.007),(0.710,-1.297),(0.720,-1.577),(0.730,-1.775),(0.740,-1.932),(0.750,-2.056),(0.760,-2.149),(0.770,-2.215),(0.780,-2.257),(0.790,-2.276),(0.800,-2.294),(0.810,-2.314),(0.820,-2.324),(0.830,-2.327),(0.840,-2.322),(0.850,-2.311),(0.860,-2.294),(0.870,-2.272),(0.880,-2.246),(0.890,-2.215),(0.900,-2.181),(0.910,-2.143),(0.920,-2.102),(0.930,-2.059),(0.940,-2.014),(0.950,-1.967),(0.960,-1.919),(0.970,-1.870),(0.980,-1.820),(0.990,-1.769),(1.000,-1.719),(1.010,-1.668),(1.020,-1.618),(1.030,-1.568),(1.040,-1.518),(1.050,-1.470),(1.060,-1.422),(1.070,-1.375),(1.080,-1.330),(1.090,-1.285),(1.100,-1.242),(1.110,-1.200),(1.120,-1.160),(1.130,-1.120),(1.140,-1.082),(1.150,-1.046),(1.160,-1.010),(1.170,-0.976),(1.180,-0.943),(1.190,-0.912),(1.200,-0.881),(1.210,-0.852),(1.220,-0.824),(1.230,-0.797),(1.240,-0.771),(1.250,-0.746),(1.260,-0.722),(1.270,-0.700),(1.280,-0.678),(1.290,-0.657),(1.300,-0.636),(1.310,-0.617),(1.320,-0.599),(1.330,-0.581),(1.340,-0.564),(1.350,-0.547),(1.360,-0.531),(1.370,-0.516),(1.380,-0.502),(1.390,-0.488),(1.400,-0.474),(1.410,-0.461),(1.420,-0.449),(1.430,-0.437),(1.440,-0.426),(1.450,-0.414),(1.460,-0.404),(1.470,-0.394),(1.480,-0.384),(1.490,-0.374),(1.500,-0.365),(1.510,-0.356),(1.520,-0.348),(1.530,-0.339),(1.540,-0.331),(1.550,-0.324),(1.560,-0.316),(1.570,-0.309),(1.580,-0.302),(1.590,-0.296),(1.600,-0.289),(1.610,-0.283),(1.620,-0.277),(1.630,-0.271),(1.640,-0.265),(1.650,-0.260),(1.660,-0.254),(1.670,-0.249),(1.680,-0.244),(1.690,-0.239),(1.700,-0.237),(1.700,-0.000),(1.710,-0.000),(1.720,-0.000),(1.730,-0.000),(1.740,-0.000),(1.750,-0.000),(1.760,-0.000),(1.770,-0.000),(1.780,-0.000),(1.790,-0.000),(1.800,-0.000),(1.810,-0.000),(1.820,-0.000),(1.830,-0.000),(1.840,-0.000),(1.850,-0.000),(1.860,-0.000),(1.870,-0.000),(1.880,-0.000),(1.890,-0.000),(1.900,-0.000),(1.910,-0.000),(1.920,-0.000),(1.930,-0.000),(1.940,-0.000),(1.950,-0.000),(1.960,-0.000),(1.970,-0.000),(1.980,-0.000),(1.990,-0.000),(2.000,-0.000),(2.010,-0.000),(2.020,-0.000),(2.030,-0.000),(2.040,-0.000),(2.050,-0.000),(2.060,-0.000),(2.070,-0.000),(2.080,-0.000),(2.090,-0.000),(2.100,-0.000),(2.110,-0.000),(2.120,-0.000),(2.130,-0.000),(2.140,-0.000),(2.150,-0.000),(2.160,-0.000),(2.170,-0.000),(2.180,-0.000),(2.190,-0.000),(2.200,-0.000),(2.210,-0.000),(2.220,-0.000),(2.230,-0.000),(2.240,-0.000),(2.250,-0.000),(2.260,-0.000),(2.270,-0.000),(2.280,-0.000),(2.290,-0.000),(2.300,-0.000),(2.310,-0.000),(2.320,-0.000),(2.330,-0.000),(2.340,-0.000),(2.350,-0.000),(2.360,-0.000),(2.370,-0.000),(2.380,-0.000),(2.390,-0.000),(2.400,-0.000),(2.410,-0.000),(2.420,-0.000),(2.430,-0.000),(2.440,-0.000),(2.450,-0.000),(2.460,-0.000),(2.470,-0.000),(2.480,-0.000),(2.490,-0.000),(2.500,-0.000),(2.510,-0.000),(2.520,-0.000),(2.530,-0.000),(2.540,-0.000),(2.550,-0.000),(2.560,-0.000),(2.570,-0.000),(2.580,-0.000),(2.590,-0.000),(2.600,-0.000),(2.610,-0.000),(2.620,-0.000),(2.630,-0.000),(2.640,-0.000),(2.650,-0.000),(2.660,-0.000),(2.670,-0.000),(2.680,-0.000),(2.690,-0.000),(2.700,-0.000),(2.710,-0.000),(2.720,-0.000),(2.730,0.000),(2.740,0.000),(2.750,0.000),(2.760,0.000),(2.770,0.000),(2.780,0.000),(2.790,0.000),(2.800,0.000),(2.810,0.000),(2.820,0.000),(2.830,0.000),(2.840,0.000),(2.850,0.000),(2.860,0.000),(2.860,0.056),(2.870,0.041),(2.880,0.025),(2.890,0.010),(2.900,-0.007),(2.910,-0.023),(2.920,-0.040),(2.930,-0.057),(2.940,-0.075),(2.950,-0.093),(2.960,-0.111),(2.970,-0.130),(2.980,-0.149),(2.990,-0.169),(3.000,-0.189),(3.010,-0.210),(3.020,-0.232),(3.030,-0.254),(3.040,-0.277),(3.050,-0.300),(3.060,-0.325),(3.070,-0.350),(3.080,-0.376),(3.090,-0.403),(3.100,-0.431),(3.110,-0.460),(3.120,-0.491),(3.130,-0.522),(3.140,-0.555),(3.150,-0.589),(3.160,-0.624),(3.170,-0.661),(3.180,-0.699),(3.190,-0.739),(3.200,-0.780),(3.210,-0.824),(3.220,-0.869),(3.230,-0.915),(3.240,-0.964),(3.250,-1.015),(3.260,-1.067),(3.270,-1.122),(3.280,-1.178),(3.290,-1.237),(3.300,-1.297),(3.310,-1.360),(3.320,-1.424),(3.330,-1.490),(3.340,-1.558),(3.350,-1.628),(3.360,-1.698),(3.370,-1.770),(3.380,-1.843),(3.390,-1.917),(3.400,-1.991),(3.410,-2.065),(3.420,-2.138),(3.430,-2.211),(3.440,-2.283),(3.450,-2.354),(3.460,-2.422),(3.470,-2.488),(3.480,-2.551),(3.490,-2.612),(3.500,-2.669),(3.510,-2.721),(3.520,-2.770),(3.530,-2.815),(3.540,-2.854),(3.550,-2.889),(3.560,-2.919),(3.570,-2.943),(3.580,-2.962),(3.590,-2.976),(3.600,-2.985),(3.610,-2.988),(3.620,-2.986),(3.630,-2.979),(3.640,-2.966),(3.650,-2.949),(3.660,-2.927),(3.670,-2.900),(3.680,-2.869),(3.690,-2.833),(3.700,-2.794),(3.710,-2.751),(3.720,-2.704),(3.730,-2.654),(3.740,-2.601),(3.750,-2.546),(3.760,-2.488),(3.770,-2.429),(3.780,-2.368),(3.790,-2.305),(3.800,-2.248),(3.800,-3.601),(3.810,-3.720),(3.820,-3.827),(3.830,-3.919),(3.840,-3.991),(3.850,-4.043),(3.860,-4.072),(3.870,-4.075),(3.880,-4.054),(3.890,-4.008),(3.900,-3.939),(3.910,-3.847),(3.920,-3.737),(3.930,-3.645),(3.940,-3.625),(3.950,-3.597),(3.960,-3.563),(3.970,-3.521),(3.980,-3.474),(3.990,-3.420),(4.000,-3.360),(4.010,-3.295),(4.020,-3.225),(4.030,-3.150),(4.040,-3.071),(4.050,-2.988),(4.060,-2.902),(4.070,-2.812),(4.080,-2.720),(4.090,-2.627),(4.100,-2.531),(4.110,-2.435),(4.120,-2.339),(4.130,-2.243),(4.140,-2.147),(4.150,-2.053),(4.160,-1.960),(4.170,-1.868),(4.180,-1.779),(4.190,-1.692),(4.200,-1.607),(4.210,-1.525),(4.220,-1.446),(4.230,-1.370),(4.240,-1.297),(4.250,-1.226),(4.260,-1.159),(4.270,-1.094),(4.280,-1.032),(4.290,-0.973),(4.300,-0.916),(4.310,-0.861),(4.320,-0.809),(4.330,-0.759),(4.340,-0.712),(4.350,-0.657),(4.360,-0.601),(4.370,-0.549),(4.380,-0.502),(4.390,-0.458),(4.400,-0.418),(4.410,-0.381),(4.420,-0.347),(4.430,-0.315),(4.440,-0.286),(4.450,-0.259),(4.460,-0.233),(4.470,-0.210),(4.480,-0.188),(4.490,-0.168),(4.500,-0.149),(4.510,-0.132),(4.520,-0.115),(4.530,-0.100),(4.540,-0.086),(4.550,-0.073),(4.560,-0.061),(4.570,-0.050),(4.580,-0.039),(4.590,-0.030),(4.600,-0.021),(4.610,-0.013),(4.620,-0.006),(4.630,0.001),(4.640,0.007),(4.650,0.013),(4.660,0.018),(4.670,0.022),(4.680,0.026),(4.690,0.029),(4.700,0.032),(4.710,0.034),(4.720,0.036),(4.730,0.037),(4.740,0.038),(4.750,0.039),(4.760,0.039),(4.770,0.039),(4.780,0.038),(4.790,0.037),(4.800,0.036),(4.810,0.035),(4.820,0.033),(4.830,0.031),(4.840,0.029),(4.850,0.027),(4.860,0.024)]
)";
 
const std::string skills_8 = R"(
X = [(-0.762,-1.201),(-0.762,-1.201),(-0.762,-1.201),(-0.763,-1.201),(-0.763,-1.201),(-0.764,-1.201),(-0.765,-1.201),(-0.766,-1.201),(-0.767,-1.201),(-0.769,-1.201),(-0.770,-1.201),(-0.772,-1.201),(-0.774,-1.201),(-0.776,-1.201),(-0.778,-1.201),(-0.780,-1.200),(-0.782,-1.200),(-0.785,-1.200),(-0.788,-1.200),(-0.790,-1.200),(-0.793,-1.199),(-0.797,-1.199),(-0.800,-1.199),(-0.803,-1.198),(-0.807,-1.198),(-0.811,-1.198),(-0.814,-1.197),(-0.818,-1.196),(-0.823,-1.196),(-0.827,-1.195),(-0.831,-1.194),(-0.836,-1.193),(-0.841,-1.192),(-0.845,-1.191),(-0.850,-1.190),(-0.856,-1.189),(-0.861,-1.188),(-0.866,-1.186),(-0.872,-1.185),(-0.877,-1.183),(-0.883,-1.182),(-0.889,-1.180),(-0.895,-1.178),(-0.901,-1.176),(-0.907,-1.174),(-0.914,-1.172),(-0.920,-1.170),(-0.927,-1.167),(-0.934,-1.165),(-0.941,-1.162),(-0.948,-1.159),(-0.955,-1.156),(-0.962,-1.153),(-0.969,-1.150),(-0.977,-1.147),(-0.984,-1.144),(-0.992,-1.140),(-0.999,-1.136),(-1.007,-1.133),(-1.015,-1.129),(-1.023,-1.125),(-1.031,-1.121),(-1.039,-1.117),(-1.046,-1.113),(-1.054,-1.108),(-1.062,-1.104),(-1.070,-1.100),(-1.077,-1.095),(-1.085,-1.091),(-1.093,-1.086),(-1.100,-1.082),(-1.108,-1.077),(-1.116,-1.072),(-1.123,-1.067),(-1.131,-1.062),(-1.138,-1.057),(-1.146,-1.052),(-1.153,-1.047),(-1.161,-1.042),(-1.168,-1.037),(-1.176,-1.032),(-1.183,-1.027),(-1.190,-1.021),(-1.198,-1.016),(-1.205,-1.011),(-1.212,-1.005),(-1.219,-1.000),(-1.227,-0.994),(-1.234,-0.988),(-1.241,-0.983),(-1.248,-0.977),(-1.255,-0.971),(-1.262,-0.966),(-1.269,-0.960),(-1.276,-0.954),(-1.283,-0.948),(-1.290,-0.942),(-1.297,-0.936),(-1.304,-0.930),(-1.310,-0.924),(-1.317,-0.918),(-1.324,-0.912),(-1.331,-0.905),(-1.337,-0.899),(-1.344,-0.893),(-1.350,-0.887),(-1.357,-0.880),(-1.363,-0.874),(-1.370,-0.867),(-1.376,-0.861),(-1.382,-0.854),(-1.388,-0.848),(-1.395,-0.841),(-1.401,-0.835),(-1.407,-0.828),(-1.413,-0.821),(-1.419,-0.815),(-1.425,-0.808),(-1.431,-0.801),(-1.437,-0.794),(-1.442,-0.788),(-1.448,-0.781),(-1.454,-0.774),(-1.459,-0.767),(-1.465,-0.760),(-1.470,-0.753),(-1.476,-0.746),(-1.481,-0.739),(-1.486,-0.732),(-1.491,-0.725),(-1.496,-0.718),(-1.501,-0.710),(-1.506,-0.703),(-1.511,-0.696),(-1.516,-0.689),(-1.521,-0.682),(-1.525,-0.674),(-1.530,-0.667),(-1.534,-0.660),(-1.538,-0.652),(-1.543,-0.645),(-1.547,-0.638),(-1.551,-0.631),(-1.554,-0.623),(-1.558,-0.616),(-1.562,-0.610),(-1.565,-0.603),(-1.568,-0.596),(-1.571,-0.589),(-1.574,-0.583),(-1.577,-0.576),(-1.580,-0.570),(-1.582,-0.564),(-1.585,-0.558),(-1.587,-0.552),(-1.589,-0.546),(-1.591,-0.540),(-1.593,-0.534),(-1.595,-0.529),(-1.596,-0.523),(-1.598,-0.518),(-1.599,-0.513),(-1.601,-0.508),(-1.602,-0.503),(-1.603,-0.498),(-1.604,-0.494),(-1.605,-0.489),(-1.606,-0.485),(-1.607,-0.481),(-1.608,-0.477),(-1.608,-0.473),(-1.609,-0.469),(-1.610,-0.465),(-1.610,-0.462),(-1.611,-0.458),(-1.611,-0.455),(-1.611,-0.452),(-1.612,-0.449),(-1.612,-0.446),(-1.612,-0.444),(-1.612,-0.441),(-1.612,-0.439),(-1.613,-0.437),(-1.613,-0.435),(-1.613,-0.433),(-1.613,-0.432),(-1.613,-0.430),(-1.613,-0.429),(-1.613,-0.428),(-1.613,-0.427),(-1.613,-0.426),(-1.613,-0.425),(-1.613,-0.424),(-1.613,-0.424),(-1.613,-0.424)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.585),(0.400,0.600),(0.410,0.615),(0.420,0.630),(0.430,0.645),(0.440,0.660),(0.450,0.675),(0.460,0.690),(0.470,0.705),(0.480,0.720),(0.490,0.735),(0.500,0.750),(0.510,0.765),(0.520,0.780),(0.530,0.795),(0.540,0.810),(0.550,0.825),(0.560,0.840),(0.570,0.855),(0.580,0.870),(0.590,0.873),(0.600,0.876),(0.610,0.878),(0.620,0.880),(0.630,0.883),(0.640,0.885),(0.650,0.887),(0.660,0.889),(0.670,0.890),(0.680,0.892),(0.690,0.894),(0.700,0.895),(0.710,0.897),(0.720,0.898),(0.730,0.899),(0.740,0.900),(0.750,0.902),(0.760,0.903),(0.770,0.904),(0.780,0.904),(0.790,0.905),(0.800,0.906),(0.810,0.907),(0.820,0.907),(0.830,0.908),(0.840,0.909),(0.850,0.909),(0.860,0.909),(0.870,0.910),(0.880,0.910),(0.890,0.910),(0.900,0.911),(0.910,0.911),(0.920,0.911),(0.930,0.911),(0.940,0.911),(0.950,0.911),(0.960,0.911),(0.970,0.911),(0.980,0.911),(0.990,0.911),(1.000,0.910),(1.010,0.910),(1.020,0.910),(1.030,0.909),(1.040,0.909),(1.050,0.908),(1.060,0.908),(1.070,0.907),(1.080,0.906),(1.090,0.906),(1.100,0.905),(1.110,0.904),(1.120,0.903),(1.130,0.902),(1.140,0.901),(1.150,0.900),(1.160,0.899),(1.170,0.898),(1.180,0.897),(1.190,0.895),(1.200,0.894),(1.210,0.892),(1.220,0.891),(1.230,0.889),(1.240,0.887),(1.250,0.886),(1.260,0.884),(1.270,0.882),(1.280,0.880),(1.290,0.877),(1.300,0.875),(1.310,0.873),(1.320,0.870),(1.330,0.868),(1.340,0.865),(1.350,0.862),(1.360,0.859),(1.370,0.856),(1.380,0.853),(1.390,0.850),(1.400,0.846),(1.410,0.839),(1.420,0.824),(1.430,0.808),(1.440,0.793),(1.450,0.778),(1.460,0.763),(1.470,0.748),(1.480,0.733),(1.490,0.718),(1.500,0.702),(1.510,0.687),(1.520,0.672),(1.530,0.657),(1.540,0.642),(1.550,0.627),(1.560,0.611),(1.570,0.596),(1.580,0.581),(1.590,0.566),(1.600,0.551),(1.610,0.535),(1.620,0.520),(1.630,0.505),(1.640,0.490),(1.650,0.474),(1.660,0.459),(1.670,0.444),(1.680,0.429),(1.690,0.413),(1.700,0.398),(1.710,0.383),(1.720,0.368),(1.730,0.352),(1.740,0.337),(1.750,0.322),(1.760,0.306),(1.770,0.291),(1.780,0.275),(1.790,0.260),(1.800,0.245),(1.810,0.229),(1.820,0.213),(1.830,0.198),(1.840,0.182),(1.850,0.167),(1.860,0.151),(1.870,0.135),(1.880,0.119),(1.890,0.103),(1.900,0.087),(1.910,0.070),(1.920,0.053),(1.930,0.035),(1.940,0.013)]
A = [(0.000,-0.000),(0.010,-0.049),(0.020,-0.098),(0.030,-0.146),(0.040,-0.194),(0.050,-0.241),(0.060,-0.288),(0.070,-0.333),(0.080,-0.378),(0.090,-0.421),(0.100,-0.464),(0.110,-0.505),(0.120,-0.544),(0.130,-0.582),(0.140,-0.619),(0.150,-0.654),(0.160,-0.687),(0.170,-0.718),(0.180,-0.748),(0.190,-0.776),(0.200,-0.802),(0.210,-0.826),(0.220,-0.848),(0.230,-0.868),(0.240,-0.887),(0.250,-0.904),(0.260,-0.919),(0.270,-0.932),(0.280,-0.944),(0.290,-0.954),(0.300,-0.962),(0.310,-0.969),(0.320,-0.975),(0.330,-0.980),(0.340,-0.983),(0.350,-0.985),(0.360,-0.986),(0.370,-0.986),(0.380,-0.985),(0.390,-0.983),(0.400,-0.981),(0.410,-0.977),(0.420,-0.974),(0.430,-0.969),(0.440,-0.964),(0.450,-0.959),(0.460,-0.953),(0.470,-0.947),(0.480,-0.941),(0.490,-0.935),(0.500,-0.928),(0.510,-0.922),(0.520,-0.915),(0.530,-0.908),(0.540,-0.902),(0.550,-0.895),(0.560,-0.889),(0.570,-0.882),(0.580,-0.876),(0.590,-0.859),(0.600,-0.842),(0.610,-0.826),(0.620,-0.811),(0.630,-0.796),(0.640,-0.783),(0.650,-0.770),(0.660,-0.757),(0.670,-0.746),(0.680,-0.735),(0.690,-0.724),(0.700,-0.715),(0.710,-0.705),(0.720,-0.697),(0.730,-0.689),(0.740,-0.681),(0.750,-0.674),(0.760,-0.667),(0.770,-0.661),(0.780,-0.655),(0.790,-0.650),(0.800,-0.645),(0.810,-0.640),(0.820,-0.636),(0.830,-0.632),(0.840,-0.629),(0.850,-0.626),(0.860,-0.624),(0.870,-0.621),(0.880,-0.619),(0.890,-0.618),(0.900,-0.617),(0.910,-0.616),(0.920,-0.615),(0.930,-0.615),(0.940,-0.615),(0.950,-0.616),(0.960,-0.617),(0.970,-0.618),(0.980,-0.619),(0.990,-0.621),(1.000,-0.623),(1.010,-0.626),(1.020,-0.629),(1.030,-0.632),(1.040,-0.636),(1.050,-0.639),(1.060,-0.644),(1.070,-0.648),(1.080,-0.653),(1.090,-0.659),(1.100,-0.665),(1.110,-0.671),(1.120,-0.678),(1.130,-0.685),(1.140,-0.692),(1.150,-0.700),(1.160,-0.708),(1.170,-0.717),(1.180,-0.727),(1.190,-0.736),(1.200,-0.747),(1.210,-0.758),(1.220,-0.769),(1.230,-0.781),(1.240,-0.794),(1.250,-0.807),(1.260,-0.821),(1.270,-0.835),(1.280,-0.850),(1.290,-0.866),(1.300,-0.883),(1.310,-0.900),(1.320,-0.918),(1.330,-0.937),(1.340,-0.957),(1.350,-0.977),(1.360,-0.998),(1.370,-1.021),(1.380,-1.044),(1.390,-1.068),(1.400,-1.093),(1.410,-1.114),(1.420,-1.125),(1.430,-1.136),(1.440,-1.146),(1.450,-1.157),(1.460,-1.167),(1.470,-1.176),(1.480,-1.185),(1.490,-1.194),(1.500,-1.202),(1.510,-1.209),(1.520,-1.215),(1.530,-1.221),(1.540,-1.225),(1.550,-1.228),(1.560,-1.231),(1.570,-1.232),(1.580,-1.231),(1.590,-1.230),(1.600,-1.226),(1.610,-1.222),(1.620,-1.215),(1.630,-1.207),(1.640,-1.197),(1.650,-1.186),(1.660,-1.172),(1.670,-1.157),(1.680,-1.139),(1.690,-1.120),(1.700,-1.098),(1.710,-1.075),(1.720,-1.050),(1.730,-1.022),(1.740,-0.993),(1.750,-0.962),(1.760,-0.929),(1.770,-0.894),(1.780,-0.857),(1.790,-0.818),(1.800,-0.778),(1.810,-0.736),(1.820,-0.693),(1.830,-0.648),(1.840,-0.601),(1.850,-0.554),(1.860,-0.505),(1.870,-0.454),(1.880,-0.403),(1.890,-0.350),(1.900,-0.296),(1.910,-0.240),(1.920,-0.182),(1.930,-0.120),(1.940,-0.046)]
)";
 
const std::string left_1 = R"(
X = [(0.599,1.549),(0.599,1.549),(0.599,1.549),(0.600,1.549),(0.600,1.549),(0.601,1.549),(0.602,1.549),(0.603,1.549),(0.604,1.549),(0.606,1.549),(0.607,1.549),(0.609,1.549),(0.611,1.549),(0.613,1.549),(0.615,1.549),(0.617,1.549),(0.619,1.549),(0.622,1.549),(0.625,1.549),(0.627,1.549),(0.630,1.549),(0.634,1.549),(0.637,1.549),(0.640,1.549),(0.644,1.550),(0.648,1.550),(0.652,1.550),(0.656,1.550),(0.660,1.550),(0.664,1.550),(0.669,1.550),(0.673,1.550),(0.678,1.551),(0.683,1.551),(0.688,1.551),(0.693,1.551),(0.699,1.551),(0.704,1.551),(0.710,1.552),(0.716,1.552),(0.722,1.552),(0.728,1.552),(0.734,1.553),(0.741,1.553),(0.747,1.553),(0.754,1.553),(0.761,1.554),(0.768,1.554),(0.775,1.554),(0.783,1.555),(0.790,1.555),(0.798,1.555),(0.806,1.556),(0.814,1.556),(0.822,1.556),(0.830,1.557),(0.838,1.557),(0.847,1.557),(0.855,1.557),(0.864,1.558),(0.873,1.558),(0.882,1.558),(0.892,1.558),(0.901,1.559),(0.911,1.559),(0.920,1.559),(0.930,1.559),(0.939,1.559),(0.949,1.559),(0.958,1.559),(0.968,1.559),(0.977,1.559),(0.986,1.559),(0.996,1.559),(1.005,1.558),(1.014,1.558),(1.023,1.558),(1.032,1.557),(1.041,1.557),(1.050,1.557),(1.059,1.556),(1.068,1.555),(1.077,1.555),(1.085,1.554),(1.094,1.553),(1.103,1.552),(1.111,1.551),(1.120,1.550),(1.128,1.549),(1.136,1.548),(1.144,1.546),(1.152,1.545),(1.160,1.543),(1.168,1.542),(1.175,1.540),(1.183,1.538),(1.190,1.536),(1.197,1.534),(1.204,1.532),(1.211,1.530),(1.218,1.528),(1.224,1.526),(1.230,1.523),(1.236,1.521),(1.242,1.518),(1.248,1.515),(1.253,1.512),(1.258,1.510),(1.263,1.507),(1.268,1.503),(1.272,1.500),(1.276,1.497),(1.280,1.494),(1.284,1.491),(1.288,1.487),(1.291,1.484),(1.294,1.481),(1.297,1.477),(1.300,1.474),(1.302,1.470),(1.305,1.467),(1.307,1.463),(1.309,1.459),(1.311,1.455),(1.312,1.452),(1.314,1.448),(1.315,1.444),(1.317,1.440),(1.318,1.436),(1.319,1.431),(1.320,1.427),(1.320,1.423),(1.321,1.418),(1.321,1.414),(1.321,1.414),(1.320,1.409),(1.320,1.404),(1.319,1.399),(1.319,1.394),(1.318,1.389),(1.318,1.383),(1.317,1.377),(1.316,1.372),(1.315,1.366),(1.315,1.360),(1.314,1.353),(1.313,1.347),(1.312,1.340),(1.311,1.334),(1.309,1.327),(1.308,1.320),(1.307,1.313),(1.305,1.306),(1.303,1.299),(1.301,1.292),(1.299,1.286),(1.297,1.280),(1.295,1.274),(1.292,1.268),(1.289,1.263),(1.287,1.257),(1.283,1.252),(1.280,1.248),(1.277,1.243),(1.273,1.239),(1.269,1.236),(1.265,1.232),(1.262,1.229),(1.258,1.227),(1.254,1.224),(1.250,1.222),(1.246,1.220),(1.242,1.218),(1.238,1.216),(1.233,1.215),(1.229,1.213),(1.224,1.212),(1.219,1.210),(1.214,1.209),(1.209,1.208),(1.203,1.207),(1.197,1.206),(1.192,1.205),(1.186,1.204),(1.180,1.203),(1.173,1.203),(1.167,1.202),(1.160,1.202),(1.153,1.201),(1.146,1.201),(1.139,1.201),(1.132,1.201),(1.125,1.200),(1.117,1.200),(1.110,1.200),(1.102,1.200),(1.094,1.200),(1.086,1.200),(1.077,1.200),(1.069,1.200),(1.060,1.200),(1.052,1.200),(1.043,1.201),(1.034,1.201),(1.025,1.201),(1.015,1.201),(1.006,1.201),(0.996,1.202),(0.986,1.202),(0.977,1.202),(0.967,1.202),(0.958,1.203),(0.948,1.203),(0.939,1.203),(0.930,1.203),(0.921,1.203),(0.913,1.204),(0.904,1.204),(0.896,1.204),(0.888,1.204),(0.880,1.204),(0.872,1.205),(0.864,1.205),(0.856,1.205),(0.849,1.205),(0.842,1.205),(0.834,1.205),(0.827,1.206),(0.821,1.206),(0.814,1.206),(0.807,1.206),(0.801,1.206),(0.795,1.206),(0.789,1.206),(0.783,1.206),(0.777,1.206),(0.771,1.206),(0.766,1.206),(0.760,1.207),(0.755,1.207),(0.750,1.207),(0.745,1.207),(0.740,1.207),(0.736,1.207),(0.731,1.207),(0.727,1.207),(0.723,1.207),(0.719,1.207),(0.715,1.207),(0.711,1.207),(0.708,1.207),(0.704,1.207),(0.701,1.207),(0.698,1.207),(0.695,1.207),(0.692,1.207),(0.689,1.207),(0.687,1.207),(0.685,1.207),(0.682,1.207),(0.680,1.207),(0.678,1.207),(0.677,1.207),(0.675,1.207),(0.674,1.207),(0.672,1.207),(0.672,1.207)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.585),(0.400,0.600),(0.410,0.615),(0.420,0.630),(0.430,0.645),(0.440,0.660),(0.450,0.675),(0.460,0.690),(0.470,0.705),(0.480,0.720),(0.490,0.735),(0.500,0.750),(0.510,0.765),(0.520,0.780),(0.530,0.795),(0.540,0.810),(0.550,0.825),(0.560,0.840),(0.570,0.855),(0.580,0.870),(0.590,0.885),(0.600,0.900),(0.610,0.915),(0.620,0.930),(0.630,0.945),(0.640,0.957),(0.650,0.954),(0.660,0.951),(0.670,0.948),(0.680,0.945),(0.690,0.942),(0.700,0.938),(0.710,0.935),(0.720,0.931),(0.730,0.927),(0.740,0.923),(0.750,0.919),(0.760,0.914),(0.770,0.910),(0.780,0.905),(0.790,0.900),(0.800,0.894),(0.810,0.889),(0.820,0.883),(0.830,0.877),(0.840,0.870),(0.850,0.863),(0.860,0.855),(0.870,0.847),(0.880,0.839),(0.890,0.830),(0.900,0.821),(0.910,0.811),(0.920,0.801),(0.930,0.790),(0.940,0.778),(0.950,0.766),(0.960,0.753),(0.970,0.740),(0.980,0.726),(0.990,0.711),(1.000,0.696),(1.010,0.681),(1.020,0.666),(1.030,0.651),(1.040,0.636),(1.050,0.621),(1.060,0.606),(1.070,0.591),(1.080,0.576),(1.090,0.561),(1.100,0.546),(1.110,0.531),(1.120,0.516),(1.130,0.501),(1.140,0.486),(1.150,0.471),(1.160,0.457),(1.170,0.448),(1.180,0.440),(1.190,0.433),(1.200,0.428),(1.210,0.424),(1.220,0.421),(1.230,0.419),(1.240,0.418),(1.250,0.419),(1.260,0.421),(1.270,0.424),(1.280,0.428),(1.290,0.433),(1.300,0.440),(1.310,0.448),(1.320,0.456),(1.330,0.466),(1.330,0.466),(1.340,0.481),(1.350,0.496),(1.360,0.511),(1.370,0.526),(1.380,0.541),(1.390,0.556),(1.400,0.571),(1.410,0.586),(1.420,0.601),(1.430,0.616),(1.440,0.631),(1.450,0.646),(1.460,0.661),(1.470,0.676),(1.480,0.691),(1.490,0.706),(1.500,0.721),(1.510,0.720),(1.520,0.705),(1.530,0.690),(1.540,0.675),(1.550,0.660),(1.560,0.645),(1.570,0.630),(1.580,0.615),(1.590,0.600),(1.600,0.585),(1.610,0.570),(1.620,0.555),(1.630,0.540),(1.640,0.525),(1.650,0.510),(1.660,0.495),(1.670,0.480),(1.680,0.465),(1.690,0.450),(1.700,0.435),(1.710,0.438),(1.720,0.453),(1.730,0.468),(1.740,0.483),(1.750,0.498),(1.760,0.513),(1.770,0.528),(1.780,0.543),(1.790,0.558),(1.800,0.573),(1.810,0.588),(1.820,0.603),(1.830,0.618),(1.840,0.633),(1.850,0.648),(1.860,0.663),(1.870,0.678),(1.880,0.693),(1.890,0.708),(1.900,0.723),(1.910,0.738),(1.920,0.753),(1.930,0.768),(1.940,0.783),(1.950,0.798),(1.960,0.813),(1.970,0.828),(1.980,0.843),(1.990,0.858),(2.000,0.873),(2.010,0.888),(2.020,0.903),(2.030,0.918),(2.040,0.933),(2.050,0.948),(2.060,0.963),(2.070,0.978),(2.080,0.971),(2.090,0.956),(2.100,0.941),(2.110,0.926),(2.120,0.911),(2.130,0.896),(2.140,0.881),(2.150,0.866),(2.160,0.851),(2.170,0.836),(2.180,0.821),(2.190,0.806),(2.200,0.791),(2.210,0.776),(2.220,0.761),(2.230,0.746),(2.240,0.731),(2.250,0.716),(2.260,0.701),(2.270,0.686),(2.280,0.671),(2.290,0.656),(2.300,0.641),(2.310,0.626),(2.320,0.611),(2.330,0.596),(2.340,0.581),(2.350,0.566),(2.360,0.551),(2.370,0.536),(2.380,0.521),(2.390,0.506),(2.400,0.491),(2.410,0.476),(2.420,0.461),(2.430,0.446),(2.440,0.431),(2.450,0.416),(2.460,0.401),(2.470,0.386),(2.480,0.371),(2.490,0.356),(2.500,0.341),(2.510,0.326),(2.520,0.311),(2.530,0.296),(2.540,0.281),(2.550,0.266),(2.560,0.251),(2.570,0.236),(2.580,0.221),(2.590,0.206),(2.600,0.191),(2.610,0.176),(2.620,0.161),(2.630,0.146),(2.640,0.131),(2.650,0.116)]
A = [(0.000,0.000),(0.010,0.010),(0.020,0.020),(0.030,0.030),(0.040,0.040),(0.050,0.049),(0.060,0.058),(0.070,0.067),(0.080,0.076),(0.090,0.084),(0.100,0.091),(0.110,0.098),(0.120,0.105),(0.130,0.111),(0.140,0.116),(0.150,0.121),(0.160,0.125),(0.170,0.128),(0.180,0.131),(0.190,0.133),(0.200,0.135),(0.210,0.136),(0.220,0.136),(0.230,0.136),(0.240,0.135),(0.250,0.134),(0.260,0.132),(0.270,0.130),(0.280,0.127),(0.290,0.123),(0.300,0.119),(0.310,0.114),(0.320,0.110),(0.330,0.104),(0.340,0.098),(0.350,0.092),(0.360,0.085),(0.370,0.078),(0.380,0.070),(0.390,0.062),(0.400,0.054),(0.410,0.045),(0.420,0.036),(0.430,0.026),(0.440,0.016),(0.450,0.005),(0.460,-0.005),(0.470,-0.017),(0.480,-0.029),(0.490,-0.041),(0.500,-0.054),(0.510,-0.068),(0.520,-0.082),(0.530,-0.097),(0.540,-0.112),(0.550,-0.128),(0.560,-0.145),(0.570,-0.163),(0.580,-0.181),(0.590,-0.201),(0.600,-0.222),(0.610,-0.244),(0.620,-0.267),(0.630,-0.292),(0.640,-0.317),(0.650,-0.339),(0.660,-0.360),(0.670,-0.383),(0.680,-0.406),(0.690,-0.430),(0.700,-0.455),(0.710,-0.480),(0.720,-0.507),(0.730,-0.535),(0.740,-0.565),(0.750,-0.596),(0.760,-0.628),(0.770,-0.662),(0.780,-0.697),(0.790,-0.735),(0.800,-0.775),(0.810,-0.817),(0.820,-0.861),(0.830,-0.908),(0.840,-0.957),(0.850,-1.010),(0.860,-1.066),(0.870,-1.125),(0.880,-1.187),(0.890,-1.254),(0.900,-1.324),(0.910,-1.398),(0.920,-1.477),(0.930,-1.560),(0.940,-1.647),(0.950,-1.739),(0.960,-1.835),(0.970,-1.936),(0.980,-2.041),(0.990,-2.150),(1.000,-2.262),(1.010,-2.379),(1.020,-2.501),(1.030,-2.626),(1.040,-2.754),(1.050,-2.885),(1.060,-3.016),(1.070,-3.146),(1.080,-3.274),(1.090,-3.396),(1.100,-3.511),(1.110,-3.615),(1.120,-3.707),(1.130,-3.783),(1.140,-3.840),(1.150,-3.876),(1.160,-3.898),(1.170,-3.944),(1.180,-3.982),(1.190,-4.009),(1.200,-4.028),(1.210,-4.038),(1.220,-4.039),(1.230,-4.031),(1.240,-4.016),(1.250,-3.992),(1.260,-3.960),(1.270,-3.920),(1.280,-3.874),(1.290,-3.820),(1.300,-3.760),(1.310,-3.693),(1.320,-3.620),(1.330,-3.560),(1.330,-0.119),(1.340,-0.142),(1.350,-0.169),(1.360,-0.200),(1.370,-0.236),(1.380,-0.277),(1.390,-0.325),(1.400,-0.381),(1.410,-0.446),(1.420,-0.522),(1.430,-0.612),(1.440,-0.717),(1.450,-0.842),(1.460,-0.990),(1.470,-1.167),(1.480,-1.378),(1.490,-1.633),(1.500,-1.942),(1.510,-2.259),(1.520,-2.569),(1.530,-2.912),(1.540,-3.286),(1.550,-3.688),(1.560,-4.110),(1.570,-4.541),(1.580,-4.962),(1.590,-5.349),(1.600,-5.677),(1.610,-5.917),(1.620,-6.048),(1.630,-6.057),(1.640,-5.944),(1.650,-5.723),(1.660,-5.417),(1.670,-5.054),(1.680,-4.659),(1.690,-4.254),(1.700,-3.858),(1.710,-3.623),(1.720,-3.465),(1.730,-3.286),(1.740,-3.095),(1.750,-2.897),(1.760,-2.697),(1.770,-2.500),(1.780,-2.308),(1.790,-2.124),(1.800,-1.949),(1.810,-1.785),(1.820,-1.631),(1.830,-1.488),(1.840,-1.356),(1.850,-1.233),(1.860,-1.121),(1.870,-1.017),(1.880,-0.921),(1.890,-0.833),(1.900,-0.752),(1.910,-0.678),(1.920,-0.610),(1.930,-0.548),(1.940,-0.490),(1.950,-0.437),(1.960,-0.389),(1.970,-0.344),(1.980,-0.303),(1.990,-0.265),(2.000,-0.230),(2.010,-0.197),(2.020,-0.167),(2.030,-0.140),(2.040,-0.114),(2.050,-0.091),(2.060,-0.069),(2.070,-0.049),(2.080,-0.030),(2.090,-0.014),(2.100,0.000),(2.110,0.012),(2.120,0.023),(2.130,0.031),(2.140,0.039),(2.150,0.045),(2.160,0.051),(2.170,0.055),(2.180,0.059),(2.190,0.062),(2.200,0.064),(2.210,0.066),(2.220,0.068),(2.230,0.069),(2.240,0.070),(2.250,0.070),(2.260,0.071),(2.270,0.071),(2.280,0.070),(2.290,0.070),(2.300,0.070),(2.310,0.069),(2.320,0.068),(2.330,0.067),(2.340,0.066),(2.350,0.065),(2.360,0.064),(2.370,0.062),(2.380,0.061),(2.390,0.060),(2.400,0.058),(2.410,0.057),(2.420,0.055),(2.430,0.053),(2.440,0.052),(2.450,0.050),(2.460,0.048),(2.470,0.047),(2.480,0.045),(2.490,0.043),(2.500,0.042),(2.510,0.040),(2.520,0.038),(2.530,0.036),(2.540,0.034),(2.550,0.033),(2.560,0.031),(2.570,0.029),(2.580,0.027),(2.590,0.025),(2.600,0.023),(2.610,0.022),(2.620,0.020),(2.630,0.018),(2.640,0.016),(2.650,0.014)]
)";
 
const std::string left_2 = R"(
X = [(-1.219,1.207),(-1.219,1.207),(-1.219,1.207),(-1.218,1.207),(-1.218,1.208),(-1.217,1.208),(-1.216,1.209),(-1.215,1.209),(-1.214,1.210),(-1.213,1.211),(-1.212,1.211),(-1.211,1.212),(-1.209,1.213),(-1.207,1.214),(-1.206,1.215),(-1.204,1.217),(-1.202,1.218),(-1.200,1.219),(-1.197,1.221),(-1.195,1.222),(-1.192,1.224),(-1.190,1.225),(-1.187,1.227),(-1.184,1.229),(-1.181,1.231),(-1.178,1.233),(-1.174,1.235),(-1.171,1.237),(-1.167,1.239),(-1.164,1.242),(-1.160,1.244),(-1.156,1.247),(-1.152,1.249),(-1.148,1.252),(-1.143,1.254),(-1.139,1.257),(-1.134,1.260),(-1.130,1.263),(-1.125,1.266),(-1.120,1.269),(-1.115,1.272),(-1.110,1.275),(-1.104,1.279),(-1.099,1.282),(-1.093,1.286),(-1.087,1.289),(-1.081,1.293),(-1.075,1.296),(-1.069,1.300),(-1.063,1.304),(-1.056,1.308),(-1.050,1.312),(-1.043,1.316),(-1.036,1.320),(-1.029,1.324),(-1.022,1.328),(-1.015,1.332),(-1.007,1.336),(-1.000,1.341),(-0.992,1.345),(-0.984,1.349),(-0.976,1.354),(-0.968,1.358),(-0.960,1.362),(-0.952,1.366),(-0.944,1.371),(-0.936,1.375),(-0.928,1.379),(-0.920,1.382),(-0.912,1.386),(-0.904,1.390),(-0.896,1.394),(-0.888,1.397),(-0.880,1.401),(-0.872,1.404),(-0.864,1.407),(-0.856,1.410),(-0.848,1.413),(-0.840,1.416),(-0.832,1.419),(-0.824,1.422),(-0.816,1.425),(-0.808,1.427),(-0.800,1.430),(-0.792,1.432),(-0.784,1.435),(-0.776,1.437),(-0.768,1.439),(-0.760,1.441),(-0.752,1.443),(-0.743,1.445),(-0.735,1.447),(-0.727,1.449),(-0.718,1.451),(-0.710,1.452),(-0.701,1.454),(-0.693,1.455),(-0.684,1.457),(-0.676,1.458),(-0.667,1.459),(-0.658,1.460),(-0.650,1.461),(-0.641,1.462),(-0.633,1.463),(-0.625,1.464),(-0.617,1.465),(-0.609,1.466),(-0.602,1.466),(-0.594,1.467),(-0.587,1.468),(-0.579,1.468),(-0.572,1.469),(-0.565,1.469),(-0.558,1.469),(-0.552,1.470),(-0.545,1.470),(-0.539,1.470),(-0.533,1.471),(-0.527,1.471),(-0.521,1.471),(-0.515,1.471),(-0.509,1.472),(-0.504,1.472),(-0.498,1.472),(-0.493,1.472),(-0.488,1.472),(-0.483,1.472),(-0.479,1.472),(-0.474,1.472),(-0.470,1.473),(-0.465,1.473),(-0.461,1.473),(-0.457,1.473),(-0.453,1.473),(-0.450,1.473),(-0.446,1.473),(-0.443,1.473),(-0.440,1.473),(-0.437,1.473),(-0.434,1.473),(-0.431,1.473),(-0.428,1.473),(-0.426,1.473),(-0.423,1.473),(-0.421,1.473),(-0.419,1.473),(-0.417,1.473),(-0.416,1.473),(-0.414,1.473),(-0.413,1.473),(-0.411,1.473),(-0.411,1.473)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.585),(0.400,0.600),(0.410,0.615),(0.420,0.630),(0.430,0.645),(0.440,0.660),(0.450,0.675),(0.460,0.690),(0.470,0.705),(0.480,0.720),(0.490,0.735),(0.500,0.750),(0.510,0.765),(0.520,0.780),(0.530,0.795),(0.540,0.810),(0.550,0.825),(0.560,0.840),(0.570,0.855),(0.580,0.870),(0.590,0.885),(0.600,0.900),(0.610,0.915),(0.620,0.918),(0.630,0.913),(0.640,0.908),(0.650,0.904),(0.660,0.899),(0.670,0.894),(0.680,0.889),(0.690,0.885),(0.700,0.880),(0.710,0.876),(0.720,0.871),(0.730,0.867),(0.740,0.863),(0.750,0.860),(0.760,0.856),(0.770,0.853),(0.780,0.851),(0.790,0.848),(0.800,0.846),(0.810,0.845),(0.820,0.843),(0.830,0.842),(0.840,0.842),(0.850,0.842),(0.860,0.842),(0.870,0.843),(0.880,0.844),(0.890,0.845),(0.900,0.847),(0.910,0.849),(0.920,0.851),(0.930,0.854),(0.940,0.857),(0.950,0.860),(0.960,0.863),(0.970,0.867),(0.980,0.870),(0.990,0.874),(1.000,0.878),(1.010,0.863),(1.020,0.848),(1.030,0.833),(1.040,0.818),(1.050,0.803),(1.060,0.788),(1.070,0.773),(1.080,0.758),(1.090,0.743),(1.100,0.728),(1.110,0.713),(1.120,0.698),(1.130,0.683),(1.140,0.668),(1.150,0.653),(1.160,0.638),(1.170,0.623),(1.180,0.608),(1.190,0.593),(1.200,0.578),(1.210,0.563),(1.220,0.548),(1.230,0.533),(1.240,0.518),(1.250,0.503),(1.260,0.488),(1.270,0.473),(1.280,0.458),(1.290,0.443),(1.300,0.428),(1.310,0.413),(1.320,0.398),(1.330,0.383),(1.340,0.368),(1.350,0.353),(1.360,0.338),(1.370,0.323),(1.380,0.308),(1.390,0.293),(1.400,0.278),(1.410,0.263),(1.420,0.248),(1.430,0.233),(1.440,0.218),(1.450,0.203),(1.460,0.188),(1.470,0.173),(1.480,0.158),(1.490,0.143),(1.500,0.128),(1.510,0.113)]
A = [(0.000,-0.000),(0.010,-0.000),(0.020,-0.000),(0.030,-0.001),(0.040,-0.001),(0.050,-0.001),(0.060,-0.001),(0.070,-0.002),(0.080,-0.002),(0.090,-0.002),(0.100,-0.003),(0.110,-0.003),(0.120,-0.004),(0.130,-0.005),(0.140,-0.005),(0.150,-0.006),(0.160,-0.007),(0.170,-0.008),(0.180,-0.009),(0.190,-0.010),(0.200,-0.012),(0.210,-0.013),(0.220,-0.015),(0.230,-0.017),(0.240,-0.019),(0.250,-0.021),(0.260,-0.023),(0.270,-0.026),(0.280,-0.029),(0.290,-0.032),(0.300,-0.036),(0.310,-0.039),(0.320,-0.044),(0.330,-0.048),(0.340,-0.053),(0.350,-0.059),(0.360,-0.065),(0.370,-0.071),(0.380,-0.078),(0.390,-0.086),(0.400,-0.094),(0.410,-0.103),(0.420,-0.113),(0.430,-0.123),(0.440,-0.135),(0.450,-0.147),(0.460,-0.161),(0.470,-0.176),(0.480,-0.192),(0.490,-0.209),(0.500,-0.228),(0.510,-0.249),(0.520,-0.271),(0.530,-0.295),(0.540,-0.321),(0.550,-0.349),(0.560,-0.379),(0.570,-0.411),(0.580,-0.446),(0.590,-0.484),(0.600,-0.524),(0.610,-0.568),(0.620,-0.605),(0.630,-0.638),(0.640,-0.671),(0.650,-0.705),(0.660,-0.738),(0.670,-0.771),(0.680,-0.803),(0.690,-0.835),(0.700,-0.866),(0.710,-0.896),(0.720,-0.924),(0.730,-0.950),(0.740,-0.975),(0.750,-0.998),(0.760,-1.019),(0.770,-1.037),(0.780,-1.053),(0.790,-1.067),(0.800,-1.078),(0.810,-1.086),(0.820,-1.092),(0.830,-1.095),(0.840,-1.095),(0.850,-1.092),(0.860,-1.087),(0.870,-1.079),(0.880,-1.069),(0.890,-1.057),(0.900,-1.043),(0.910,-1.026),(0.920,-1.008),(0.930,-0.987),(0.940,-0.966),(0.950,-0.943),(0.960,-0.919),(0.970,-0.894),(0.980,-0.868),(0.990,-0.841),(1.000,-0.814),(1.010,-0.770),(1.020,-0.728),(1.030,-0.688),(1.040,-0.650),(1.050,-0.614),(1.060,-0.579),(1.070,-0.546),(1.080,-0.515),(1.090,-0.486),(1.100,-0.458),(1.110,-0.432),(1.120,-0.408),(1.130,-0.384),(1.140,-0.363),(1.150,-0.342),(1.160,-0.323),(1.170,-0.304),(1.180,-0.287),(1.190,-0.271),(1.200,-0.256),(1.210,-0.241),(1.220,-0.228),(1.230,-0.215),(1.240,-0.203),(1.250,-0.192),(1.260,-0.181),(1.270,-0.171),(1.280,-0.161),(1.290,-0.152),(1.300,-0.143),(1.310,-0.135),(1.320,-0.127),(1.330,-0.120),(1.340,-0.112),(1.350,-0.106),(1.360,-0.099),(1.370,-0.093),(1.380,-0.087),(1.390,-0.082),(1.400,-0.076),(1.410,-0.071),(1.420,-0.066),(1.430,-0.061),(1.440,-0.056),(1.450,-0.052),(1.460,-0.048),(1.470,-0.043),(1.480,-0.039),(1.490,-0.035),(1.500,-0.031),(1.510,-0.028)]
)";
 
const std::string left_3 = R"(
X = [(-0.330,0.330),(-0.330,0.330),(-0.330,0.330),(-0.331,0.331),(-0.331,0.331),(-0.332,0.332),(-0.332,0.332),(-0.333,0.333),(-0.334,0.334),(-0.335,0.335),(-0.336,0.336),(-0.337,0.337),(-0.338,0.338),(-0.340,0.340),(-0.341,0.341),(-0.343,0.343),(-0.344,0.345),(-0.346,0.346),(-0.348,0.348),(-0.350,0.351),(-0.352,0.353),(-0.354,0.355),(-0.356,0.358),(-0.358,0.360),(-0.361,0.363),(-0.363,0.366),(-0.366,0.369),(-0.369,0.372),(-0.371,0.375),(-0.374,0.378),(-0.377,0.382),(-0.380,0.385),(-0.383,0.389),(-0.386,0.393),(-0.389,0.397),(-0.393,0.401),(-0.396,0.405),(-0.399,0.409),(-0.403,0.414),(-0.406,0.418),(-0.410,0.423),(-0.414,0.428),(-0.418,0.433),(-0.421,0.438),(-0.425,0.444),(-0.429,0.449),(-0.433,0.455),(-0.437,0.461),(-0.441,0.466),(-0.446,0.472),(-0.450,0.479),(-0.454,0.485),(-0.459,0.491),(-0.463,0.498),(-0.468,0.505),(-0.472,0.512),(-0.477,0.519),(-0.482,0.526),(-0.486,0.533),(-0.491,0.540),(-0.496,0.548),(-0.501,0.556),(-0.506,0.563),(-0.511,0.571),(-0.516,0.579),(-0.522,0.588),(-0.527,0.596),(-0.532,0.604),(-0.538,0.613),(-0.543,0.621),(-0.549,0.629),(-0.554,0.637),(-0.559,0.646),(-0.565,0.654),(-0.570,0.662),(-0.575,0.670),(-0.581,0.678),(-0.586,0.686),(-0.591,0.694),(-0.597,0.702),(-0.602,0.709),(-0.607,0.717),(-0.613,0.725),(-0.618,0.733),(-0.623,0.740),(-0.629,0.748),(-0.634,0.755),(-0.640,0.763),(-0.645,0.770),(-0.651,0.778),(-0.656,0.785),(-0.662,0.792),(-0.667,0.799),(-0.673,0.806),(-0.679,0.814),(-0.684,0.821),(-0.690,0.828),(-0.696,0.834),(-0.702,0.841),(-0.708,0.848),(-0.713,0.855),(-0.719,0.861),(-0.725,0.868),(-0.731,0.875),(-0.737,0.881),(-0.743,0.888),(-0.749,0.894),(-0.755,0.900),(-0.762,0.906),(-0.768,0.913),(-0.774,0.919),(-0.780,0.925),(-0.787,0.931),(-0.793,0.937),(-0.800,0.942),(-0.806,0.948),(-0.813,0.954),(-0.819,0.960),(-0.826,0.965),(-0.832,0.971),(-0.839,0.976),(-0.846,0.981),(-0.853,0.987),(-0.859,0.992),(-0.866,0.997),(-0.873,1.002),(-0.880,1.007),(-0.887,1.012),(-0.894,1.017),(-0.901,1.021),(-0.908,1.026),(-0.916,1.031),(-0.923,1.035),(-0.930,1.040),(-0.937,1.044),(-0.945,1.048),(-0.952,1.053),(-0.960,1.057),(-0.967,1.061),(-0.975,1.065),(-0.982,1.069),(-0.990,1.073),(-0.998,1.077),(-1.005,1.080),(-1.013,1.084),(-1.021,1.088),(-1.029,1.091),(-1.037,1.095),(-1.045,1.098),(-1.053,1.101),(-1.061,1.105),(-1.069,1.108),(-1.077,1.111),(-1.085,1.114),(-1.093,1.117),(-1.101,1.120),(-1.109,1.122),(-1.118,1.125),(-1.126,1.128),(-1.134,1.130),(-1.143,1.133),(-1.151,1.135),(-1.159,1.138),(-1.168,1.140),(-1.176,1.142),(-1.185,1.144),(-1.193,1.146),(-1.202,1.148),(-1.211,1.150),(-1.219,1.152),(-1.228,1.154),(-1.237,1.156),(-1.245,1.158),(-1.254,1.159),(-1.263,1.161),(-1.271,1.162),(-1.280,1.164),(-1.288,1.165),(-1.296,1.166),(-1.304,1.167),(-1.312,1.168),(-1.319,1.169),(-1.327,1.170),(-1.334,1.171),(-1.342,1.172),(-1.349,1.173),(-1.356,1.174),(-1.363,1.174),(-1.369,1.175),(-1.376,1.175),(-1.382,1.176),(-1.388,1.176),(-1.394,1.177),(-1.400,1.177),(-1.406,1.178),(-1.412,1.178),(-1.417,1.178),(-1.423,1.179),(-1.428,1.179),(-1.433,1.179),(-1.438,1.179),(-1.443,1.180),(-1.447,1.180),(-1.452,1.180),(-1.456,1.180),(-1.460,1.180),(-1.464,1.180),(-1.468,1.180),(-1.472,1.181),(-1.475,1.181),(-1.479,1.181),(-1.482,1.181),(-1.485,1.181),(-1.488,1.181),(-1.491,1.181),(-1.493,1.181),(-1.496,1.181),(-1.498,1.181),(-1.500,1.181),(-1.502,1.181),(-1.504,1.181),(-1.506,1.181),(-1.508,1.181),(-1.509,1.181),(-1.510,1.181),(-1.511,1.181)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.585),(0.400,0.600),(0.410,0.615),(0.420,0.630),(0.430,0.645),(0.440,0.660),(0.450,0.675),(0.460,0.690),(0.470,0.705),(0.480,0.720),(0.490,0.735),(0.500,0.750),(0.510,0.765),(0.520,0.780),(0.530,0.795),(0.540,0.810),(0.550,0.825),(0.560,0.840),(0.570,0.855),(0.580,0.870),(0.590,0.885),(0.600,0.900),(0.610,0.915),(0.620,0.930),(0.630,0.945),(0.640,0.960),(0.650,0.975),(0.660,0.990),(0.670,0.997),(0.680,0.993),(0.690,0.988),(0.700,0.984),(0.710,0.980),(0.720,0.976),(0.730,0.972),(0.740,0.968),(0.750,0.965),(0.760,0.961),(0.770,0.957),(0.780,0.954),(0.790,0.950),(0.800,0.947),(0.810,0.944),(0.820,0.941),(0.830,0.937),(0.840,0.934),(0.850,0.931),(0.860,0.928),(0.870,0.926),(0.880,0.923),(0.890,0.920),(0.900,0.917),(0.910,0.914),(0.920,0.912),(0.930,0.909),(0.940,0.907),(0.950,0.904),(0.960,0.902),(0.970,0.899),(0.980,0.897),(0.990,0.895),(1.000,0.892),(1.010,0.890),(1.020,0.888),(1.030,0.886),(1.040,0.884),(1.050,0.882),(1.060,0.880),(1.070,0.879),(1.080,0.877),(1.090,0.875),(1.100,0.873),(1.110,0.872),(1.120,0.870),(1.130,0.869),(1.140,0.868),(1.150,0.866),(1.160,0.865),(1.170,0.864),(1.180,0.863),(1.190,0.862),(1.200,0.861),(1.210,0.860),(1.220,0.859),(1.230,0.858),(1.240,0.858),(1.250,0.857),(1.260,0.856),(1.270,0.856),(1.280,0.856),(1.290,0.855),(1.300,0.855),(1.310,0.855),(1.320,0.855),(1.330,0.855),(1.340,0.855),(1.350,0.855),(1.360,0.855),(1.370,0.855),(1.380,0.855),(1.390,0.856),(1.400,0.856),(1.410,0.856),(1.420,0.857),(1.430,0.857),(1.440,0.858),(1.450,0.859),(1.460,0.859),(1.470,0.860),(1.480,0.861),(1.490,0.862),(1.500,0.862),(1.510,0.863),(1.520,0.864),(1.530,0.865),(1.540,0.866),(1.550,0.867),(1.560,0.868),(1.570,0.869),(1.580,0.871),(1.590,0.872),(1.600,0.873),(1.610,0.874),(1.620,0.875),(1.630,0.876),(1.640,0.878),(1.650,0.879),(1.660,0.880),(1.670,0.881),(1.680,0.883),(1.690,0.884),(1.700,0.885),(1.710,0.886),(1.720,0.888),(1.730,0.889),(1.740,0.880),(1.750,0.865),(1.760,0.850),(1.770,0.835),(1.780,0.820),(1.790,0.805),(1.800,0.790),(1.810,0.775),(1.820,0.760),(1.830,0.745),(1.840,0.730),(1.850,0.715),(1.860,0.700),(1.870,0.685),(1.880,0.670),(1.890,0.655),(1.900,0.640),(1.910,0.625),(1.920,0.610),(1.930,0.595),(1.940,0.580),(1.950,0.565),(1.960,0.550),(1.970,0.535),(1.980,0.520),(1.990,0.505),(2.000,0.490),(2.010,0.475),(2.020,0.460),(2.030,0.445),(2.040,0.430),(2.050,0.415),(2.060,0.400),(2.070,0.385),(2.080,0.370),(2.090,0.355),(2.100,0.340),(2.110,0.325),(2.120,0.310),(2.130,0.295),(2.140,0.280),(2.150,0.265),(2.160,0.250),(2.170,0.235),(2.180,0.220),(2.190,0.205),(2.200,0.190),(2.210,0.175),(2.220,0.160),(2.230,0.145),(2.240,0.130),(2.250,0.115)]
A = [(0.000,-0.000),(0.010,-0.022),(0.020,-0.044),(0.030,-0.066),(0.040,-0.088),(0.050,-0.109),(0.060,-0.131),(0.070,-0.152),(0.080,-0.173),(0.090,-0.193),(0.100,-0.213),(0.110,-0.233),(0.120,-0.252),(0.130,-0.271),(0.140,-0.290),(0.150,-0.307),(0.160,-0.325),(0.170,-0.341),(0.180,-0.357),(0.190,-0.372),(0.200,-0.387),(0.210,-0.400),(0.220,-0.413),(0.230,-0.425),(0.240,-0.436),(0.250,-0.446),(0.260,-0.456),(0.270,-0.464),(0.280,-0.472),(0.290,-0.478),(0.300,-0.483),(0.310,-0.488),(0.320,-0.491),(0.330,-0.493),(0.340,-0.495),(0.350,-0.495),(0.360,-0.494),(0.370,-0.492),(0.380,-0.489),(0.390,-0.484),(0.400,-0.479),(0.410,-0.473),(0.420,-0.465),(0.430,-0.456),(0.440,-0.447),(0.450,-0.436),(0.460,-0.424),(0.470,-0.411),(0.480,-0.397),(0.490,-0.382),(0.500,-0.366),(0.510,-0.349),(0.520,-0.331),(0.530,-0.312),(0.540,-0.293),(0.550,-0.272),(0.560,-0.250),(0.570,-0.227),(0.580,-0.203),(0.590,-0.179),(0.600,-0.153),(0.610,-0.127),(0.620,-0.099),(0.630,-0.071),(0.640,-0.042),(0.650,-0.012),(0.660,0.019),(0.670,0.051),(0.680,0.081),(0.690,0.110),(0.700,0.139),(0.710,0.167),(0.720,0.194),(0.730,0.220),(0.740,0.246),(0.750,0.272),(0.760,0.296),(0.770,0.320),(0.780,0.344),(0.790,0.367),(0.800,0.390),(0.810,0.412),(0.820,0.434),(0.830,0.456),(0.840,0.477),(0.850,0.497),(0.860,0.517),(0.870,0.537),(0.880,0.557),(0.890,0.576),(0.900,0.594),(0.910,0.613),(0.920,0.631),(0.930,0.648),(0.940,0.665),(0.950,0.682),(0.960,0.699),(0.970,0.715),(0.980,0.731),(0.990,0.746),(1.000,0.761),(1.010,0.776),(1.020,0.790),(1.030,0.804),(1.040,0.817),(1.050,0.830),(1.060,0.842),(1.070,0.855),(1.080,0.866),(1.090,0.877),(1.100,0.888),(1.110,0.899),(1.120,0.909),(1.130,0.918),(1.140,0.927),(1.150,0.935),(1.160,0.943),(1.170,0.951),(1.180,0.958),(1.190,0.965),(1.200,0.971),(1.210,0.976),(1.220,0.982),(1.230,0.986),(1.240,0.990),(1.250,0.994),(1.260,0.997),(1.270,1.000),(1.280,1.002),(1.290,1.004),(1.300,1.005),(1.310,1.006),(1.320,1.006),(1.330,1.006),(1.340,1.006),(1.350,1.005),(1.360,1.004),(1.370,1.002),(1.380,1.000),(1.390,0.997),(1.400,0.994),(1.410,0.991),(1.420,0.987),(1.430,0.983),(1.440,0.978),(1.450,0.973),(1.460,0.968),(1.470,0.963),(1.480,0.957),(1.490,0.951),(1.500,0.945),(1.510,0.939),(1.520,0.932),(1.530,0.925),(1.540,0.918),(1.550,0.911),(1.560,0.903),(1.570,0.895),(1.580,0.887),(1.590,0.879),(1.600,0.871),(1.610,0.863),(1.620,0.855),(1.630,0.846),(1.640,0.837),(1.650,0.829),(1.660,0.820),(1.670,0.811),(1.680,0.802),(1.690,0.794),(1.700,0.785),(1.710,0.776),(1.720,0.767),(1.730,0.758),(1.740,0.741),(1.750,0.718),(1.760,0.697),(1.770,0.676),(1.780,0.655),(1.790,0.636),(1.800,0.616),(1.810,0.597),(1.820,0.579),(1.830,0.561),(1.840,0.543),(1.850,0.526),(1.860,0.509),(1.870,0.493),(1.880,0.477),(1.890,0.462),(1.900,0.446),(1.910,0.432),(1.920,0.417),(1.930,0.403),(1.940,0.389),(1.950,0.376),(1.960,0.363),(1.970,0.350),(1.980,0.337),(1.990,0.325),(2.000,0.313),(2.010,0.301),(2.020,0.289),(2.030,0.278),(2.040,0.267),(2.050,0.256),(2.060,0.245),(2.070,0.234),(2.080,0.224),(2.090,0.213),(2.100,0.203),(2.110,0.193),(2.120,0.183),(2.130,0.174),(2.140,0.164),(2.150,0.155),(2.160,0.145),(2.170,0.136),(2.180,0.127),(2.190,0.118),(2.200,0.109),(2.210,0.100),(2.220,0.091),(2.230,0.083),(2.240,0.074),(2.250,0.065)]
)";
 
const std::string right_1 = R"(
X = [(-1.194,-1.207),(-1.194,-1.207),(-1.194,-1.207),(-1.193,-1.206),(-1.193,-1.206),(-1.193,-1.205),(-1.192,-1.205),(-1.191,-1.204),(-1.191,-1.203),(-1.190,-1.202),(-1.189,-1.201),(-1.188,-1.199),(-1.187,-1.198),(-1.186,-1.196),(-1.184,-1.195),(-1.183,-1.193),(-1.181,-1.191),(-1.180,-1.189),(-1.178,-1.187),(-1.176,-1.185),(-1.174,-1.182),(-1.172,-1.180),(-1.170,-1.177),(-1.168,-1.175),(-1.166,-1.172),(-1.164,-1.169),(-1.161,-1.166),(-1.159,-1.163),(-1.156,-1.160),(-1.153,-1.156),(-1.150,-1.153),(-1.147,-1.149),(-1.144,-1.145),(-1.141,-1.142),(-1.138,-1.138),(-1.134,-1.134),(-1.131,-1.130),(-1.127,-1.126),(-1.123,-1.121),(-1.119,-1.117),(-1.115,-1.112),(-1.111,-1.108),(-1.107,-1.103),(-1.103,-1.098),(-1.098,-1.094),(-1.094,-1.089),(-1.089,-1.084),(-1.084,-1.079),(-1.079,-1.074),(-1.073,-1.069),(-1.068,-1.063),(-1.062,-1.058),(-1.057,-1.053),(-1.051,-1.047),(-1.045,-1.042),(-1.039,-1.037),(-1.032,-1.032),(-1.026,-1.027),(-1.020,-1.022),(-1.014,-1.017),(-1.008,-1.013),(-1.001,-1.008),(-0.995,-1.004),(-0.989,-1.000),(-0.982,-0.996),(-0.976,-0.992),(-0.969,-0.988),(-0.963,-0.984),(-0.956,-0.980),(-0.949,-0.977),(-0.942,-0.974),(-0.936,-0.970),(-0.929,-0.967),(-0.922,-0.964),(-0.915,-0.961),(-0.908,-0.958),(-0.900,-0.955),(-0.893,-0.953),(-0.886,-0.950),(-0.878,-0.948),(-0.871,-0.945),(-0.863,-0.943),(-0.855,-0.941),(-0.848,-0.939),(-0.840,-0.936),(-0.832,-0.935),(-0.824,-0.933),(-0.816,-0.931),(-0.807,-0.929),(-0.799,-0.927),(-0.791,-0.926),(-0.782,-0.924),(-0.774,-0.923),(-0.765,-0.922),(-0.757,-0.920),(-0.748,-0.919),(-0.739,-0.918),(-0.730,-0.917),(-0.722,-0.916),(-0.713,-0.915),(-0.704,-0.914),(-0.695,-0.913),(-0.685,-0.912),(-0.676,-0.911),(-0.667,-0.911),(-0.658,-0.910),(-0.649,-0.909),(-0.639,-0.909),(-0.630,-0.908),(-0.621,-0.908),(-0.612,-0.907),(-0.603,-0.907),(-0.595,-0.906),(-0.586,-0.906),(-0.578,-0.905),(-0.570,-0.905),(-0.562,-0.905),(-0.554,-0.905),(-0.546,-0.904),(-0.539,-0.904),(-0.531,-0.904),(-0.524,-0.904),(-0.517,-0.904),(-0.510,-0.903),(-0.503,-0.903),(-0.496,-0.903),(-0.490,-0.903),(-0.483,-0.903),(-0.477,-0.903),(-0.471,-0.903),(-0.465,-0.903),(-0.459,-0.903),(-0.454,-0.903),(-0.448,-0.902),(-0.443,-0.902),(-0.438,-0.902),(-0.433,-0.902),(-0.428,-0.902),(-0.423,-0.902),(-0.419,-0.902),(-0.414,-0.902),(-0.410,-0.902),(-0.406,-0.902),(-0.402,-0.902),(-0.398,-0.902),(-0.394,-0.902),(-0.391,-0.902),(-0.388,-0.902),(-0.384,-0.902),(-0.381,-0.902),(-0.378,-0.902),(-0.376,-0.902),(-0.373,-0.902),(-0.370,-0.902),(-0.368,-0.902),(-0.366,-0.902),(-0.364,-0.902),(-0.362,-0.902),(-0.360,-0.902),(-0.359,-0.902),(-0.357,-0.902),(-0.356,-0.902)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.585),(0.400,0.600),(0.410,0.615),(0.420,0.630),(0.430,0.645),(0.440,0.660),(0.450,0.675),(0.460,0.690),(0.470,0.705),(0.480,0.720),(0.490,0.735),(0.500,0.750),(0.510,0.765),(0.520,0.780),(0.530,0.795),(0.540,0.810),(0.550,0.804),(0.560,0.798),(0.570,0.792),(0.580,0.787),(0.590,0.781),(0.600,0.776),(0.610,0.772),(0.620,0.768),(0.630,0.765),(0.640,0.762),(0.650,0.760),(0.660,0.758),(0.670,0.757),(0.680,0.756),(0.690,0.756),(0.700,0.757),(0.710,0.758),(0.720,0.760),(0.730,0.762),(0.740,0.765),(0.750,0.768),(0.760,0.772),(0.770,0.776),(0.780,0.780),(0.790,0.785),(0.800,0.790),(0.810,0.796),(0.820,0.801),(0.830,0.807),(0.840,0.813),(0.850,0.819),(0.860,0.825),(0.870,0.831),(0.880,0.838),(0.890,0.844),(0.900,0.850),(0.910,0.856),(0.920,0.862),(0.930,0.868),(0.940,0.874),(0.950,0.879),(0.960,0.885),(0.970,0.890),(0.980,0.895),(0.990,0.900),(1.000,0.905),(1.010,0.909),(1.020,0.914),(1.030,0.918),(1.040,0.922),(1.050,0.926),(1.060,0.930),(1.070,0.933),(1.080,0.922),(1.090,0.907),(1.100,0.892),(1.110,0.877),(1.120,0.862),(1.130,0.847),(1.140,0.832),(1.150,0.817),(1.160,0.802),(1.170,0.787),(1.180,0.772),(1.190,0.757),(1.200,0.742),(1.210,0.727),(1.220,0.712),(1.230,0.697),(1.240,0.682),(1.250,0.667),(1.260,0.652),(1.270,0.637),(1.280,0.622),(1.290,0.607),(1.300,0.592),(1.310,0.577),(1.320,0.562),(1.330,0.547),(1.340,0.532),(1.350,0.517),(1.360,0.502),(1.370,0.487),(1.380,0.472),(1.390,0.457),(1.400,0.442),(1.410,0.427),(1.420,0.412),(1.430,0.397),(1.440,0.382),(1.450,0.367),(1.460,0.352),(1.470,0.337),(1.480,0.322),(1.490,0.307),(1.500,0.292),(1.510,0.277),(1.520,0.262),(1.530,0.247),(1.540,0.232),(1.550,0.217),(1.560,0.202),(1.570,0.187),(1.580,0.172),(1.590,0.157),(1.600,0.142),(1.610,0.127)]
A = [(0.000,-0.000),(0.010,-0.004),(0.020,-0.009),(0.030,-0.013),(0.040,-0.018),(0.050,-0.023),(0.060,-0.027),(0.070,-0.032),(0.080,-0.037),(0.090,-0.043),(0.100,-0.048),(0.110,-0.054),(0.120,-0.060),(0.130,-0.066),(0.140,-0.073),(0.150,-0.080),(0.160,-0.087),(0.170,-0.095),(0.180,-0.103),(0.190,-0.111),(0.200,-0.121),(0.210,-0.131),(0.220,-0.141),(0.230,-0.152),(0.240,-0.164),(0.250,-0.177),(0.260,-0.191),(0.270,-0.205),(0.280,-0.221),(0.290,-0.238),(0.300,-0.256),(0.310,-0.275),(0.320,-0.296),(0.330,-0.318),(0.340,-0.342),(0.350,-0.367),(0.360,-0.395),(0.370,-0.424),(0.380,-0.456),(0.390,-0.489),(0.400,-0.526),(0.410,-0.565),(0.420,-0.607),(0.430,-0.651),(0.440,-0.699),(0.450,-0.750),(0.460,-0.804),(0.470,-0.862),(0.480,-0.923),(0.490,-0.988),(0.500,-1.057),(0.510,-1.129),(0.520,-1.204),(0.530,-1.282),(0.540,-1.363),(0.550,-1.408),(0.560,-1.450),(0.570,-1.488),(0.580,-1.524),(0.590,-1.557),(0.600,-1.587),(0.610,-1.613),(0.620,-1.635),(0.630,-1.653),(0.640,-1.668),(0.650,-1.678),(0.660,-1.685),(0.670,-1.687),(0.680,-1.686),(0.690,-1.680),(0.700,-1.671),(0.710,-1.658),(0.720,-1.641),(0.730,-1.621),(0.740,-1.598),(0.750,-1.572),(0.760,-1.543),(0.770,-1.512),(0.780,-1.478),(0.790,-1.442),(0.800,-1.405),(0.810,-1.366),(0.820,-1.326),(0.830,-1.285),(0.840,-1.243),(0.850,-1.201),(0.860,-1.159),(0.870,-1.116),(0.880,-1.074),(0.890,-1.032),(0.900,-0.990),(0.910,-0.949),(0.920,-0.909),(0.930,-0.870),(0.940,-0.831),(0.950,-0.794),(0.960,-0.757),(0.970,-0.722),(0.980,-0.688),(0.990,-0.655),(1.000,-0.624),(1.010,-0.593),(1.020,-0.564),(1.030,-0.536),(1.040,-0.510),(1.050,-0.484),(1.060,-0.459),(1.070,-0.436),(1.080,-0.408),(1.090,-0.380),(1.100,-0.354),(1.110,-0.330),(1.120,-0.309),(1.130,-0.288),(1.140,-0.270),(1.150,-0.252),(1.160,-0.236),(1.170,-0.221),(1.180,-0.207),(1.190,-0.194),(1.200,-0.182),(1.210,-0.171),(1.220,-0.161),(1.230,-0.151),(1.240,-0.142),(1.250,-0.133),(1.260,-0.125),(1.270,-0.118),(1.280,-0.111),(1.290,-0.104),(1.300,-0.098),(1.310,-0.093),(1.320,-0.087),(1.330,-0.082),(1.340,-0.077),(1.350,-0.073),(1.360,-0.069),(1.370,-0.065),(1.380,-0.061),(1.390,-0.057),(1.400,-0.054),(1.410,-0.051),(1.420,-0.048),(1.430,-0.045),(1.440,-0.042),(1.450,-0.040),(1.460,-0.037),(1.470,-0.035),(1.480,-0.033),(1.490,-0.031),(1.500,-0.028),(1.510,-0.027),(1.520,-0.025),(1.530,-0.023),(1.540,-0.021),(1.550,-0.020),(1.560,-0.018),(1.570,-0.016),(1.580,-0.015),(1.590,-0.014),(1.600,-0.012),(1.610,-0.011)]
)";
 
// TEST THIS!!!!!
const std::string awp_1 = R"(
X = [(-0.940,-1.207),(-0.940,-1.207),(-0.940,-1.207),(-0.940,-1.206),(-0.939,-1.206),(-0.939,-1.205),(-0.939,-1.204),(-0.938,-1.203),(-0.938,-1.202),(-0.937,-1.201),(-0.937,-1.199),(-0.936,-1.198),(-0.935,-1.196),(-0.934,-1.195),(-0.933,-1.193),(-0.932,-1.191),(-0.931,-1.188),(-0.930,-1.186),(-0.929,-1.184),(-0.928,-1.181),(-0.927,-1.178),(-0.925,-1.176),(-0.924,-1.173),(-0.922,-1.170),(-0.921,-1.166),(-0.919,-1.163),(-0.917,-1.159),(-0.916,-1.156),(-0.914,-1.152),(-0.912,-1.148),(-0.910,-1.144),(-0.907,-1.140),(-0.905,-1.136),(-0.903,-1.132),(-0.900,-1.127),(-0.898,-1.122),(-0.895,-1.118),(-0.893,-1.113),(-0.890,-1.108),(-0.887,-1.103),(-0.884,-1.098),(-0.881,-1.092),(-0.878,-1.087),(-0.874,-1.081),(-0.871,-1.076),(-0.868,-1.070),(-0.864,-1.064),(-0.860,-1.058),(-0.856,-1.052),(-0.852,-1.046),(-0.848,-1.039),(-0.844,-1.033),(-0.840,-1.026),(-0.836,-1.020),(-0.831,-1.013),(-0.826,-1.006),(-0.822,-0.999),(-0.817,-0.992),(-0.812,-0.985),(-0.807,-0.978),(-0.801,-0.971),(-0.796,-0.963),(-0.790,-0.956),(-0.785,-0.948),(-0.779,-0.940),(-0.773,-0.933),(-0.767,-0.925),(-0.761,-0.917),(-0.755,-0.909),(-0.748,-0.901),(-0.742,-0.892),(-0.735,-0.884),(-0.729,-0.875),(-0.722,-0.867),(-0.715,-0.858),(-0.708,-0.849),(-0.701,-0.840),(-0.694,-0.831),(-0.687,-0.822),(-0.680,-0.813),(-0.672,-0.803),(-0.665,-0.793),(-0.658,-0.784),(-0.651,-0.774),(-0.644,-0.765),(-0.638,-0.755),(-0.631,-0.746),(-0.625,-0.737),(-0.619,-0.727),(-0.614,-0.718),(-0.608,-0.709),(-0.603,-0.700),(-0.598,-0.690),(-0.593,-0.681),(-0.589,-0.672),(-0.585,-0.663),(-0.581,-0.654),(-0.578,-0.645),(-0.575,-0.636),(-0.572,-0.627),(-0.569,-0.618),(-0.567,-0.609),(-0.565,-0.601),(-0.563,-0.592),(-0.562,-0.583),(-0.561,-0.575),(-0.560,-0.566),(-0.559,-0.559),(-0.559,-0.559),(-0.558,-0.550),(-0.558,-0.541),(-0.557,-0.532),(-0.557,-0.522),(-0.556,-0.513),(-0.555,-0.503),(-0.555,-0.493),(-0.554,-0.483),(-0.554,-0.473),(-0.553,-0.463),(-0.552,-0.452),(-0.552,-0.442),(-0.551,-0.431),(-0.551,-0.420),(-0.550,-0.409),(-0.549,-0.398),(-0.549,-0.387),(-0.548,-0.375),(-0.548,-0.364),(-0.547,-0.352),(-0.547,-0.340),(-0.546,-0.328),(-0.545,-0.315),(-0.545,-0.303),(-0.544,-0.291),(-0.544,-0.278),(-0.543,-0.265),(-0.542,-0.252),(-0.542,-0.239),(-0.541,-0.226),(-0.541,-0.213),(-0.540,-0.200),(-0.540,-0.188),(-0.539,-0.175),(-0.538,-0.162),(-0.538,-0.149),(-0.537,-0.136),(-0.537,-0.123),(-0.536,-0.110),(-0.536,-0.097),(-0.535,-0.084),(-0.535,-0.071),(-0.534,-0.058),(-0.534,-0.046),(-0.534,-0.033),(-0.533,-0.020),(-0.533,-0.007),(-0.532,0.006),(-0.532,0.019),(-0.531,0.032),(-0.531,0.045),(-0.531,0.058),(-0.530,0.071),(-0.530,0.083),(-0.529,0.096),(-0.529,0.109),(-0.529,0.122),(-0.528,0.135),(-0.528,0.148),(-0.528,0.161),(-0.527,0.174),(-0.527,0.186),(-0.527,0.199),(-0.526,0.212),(-0.526,0.225),(-0.526,0.238),(-0.526,0.251),(-0.526,0.264),(-0.525,0.276),(-0.525,0.289),(-0.525,0.302),(-0.525,0.315),(-0.525,0.327),(-0.525,0.340),(-0.524,0.353),(-0.524,0.366),(-0.524,0.378),(-0.524,0.391),(-0.524,0.404),(-0.524,0.416),(-0.525,0.429),(-0.525,0.441),(-0.525,0.454),(-0.525,0.466),(-0.525,0.479),(-0.526,0.491),(-0.526,0.503),(-0.527,0.515),(-0.527,0.527),(-0.528,0.539),(-0.529,0.550),(-0.530,0.561),(-0.531,0.573),(-0.533,0.584),(-0.533,0.584),(-0.533,0.584),(-0.532,0.595),(-0.533,0.605),(-0.535,0.616),(-0.538,0.625),(-0.542,0.635),(-0.545,0.644),(-0.549,0.653),(-0.553,0.662),(-0.558,0.671),(-0.562,0.680),(-0.567,0.689),(-0.572,0.698),(-0.577,0.707),(-0.583,0.716),(-0.589,0.725),(-0.594,0.735),(-0.600,0.744),(-0.606,0.753),(-0.613,0.763),(-0.619,0.772),(-0.626,0.782),(-0.633,0.791),(-0.640,0.801),(-0.647,0.810),(-0.654,0.820),(-0.661,0.829),(-0.668,0.839),(-0.676,0.848),(-0.683,0.857),(-0.691,0.867),(-0.698,0.876),(-0.706,0.885),(-0.714,0.894),(-0.721,0.903),(-0.729,0.912),(-0.737,0.921),(-0.745,0.930),(-0.753,0.939),(-0.761,0.948),(-0.769,0.957),(-0.778,0.965),(-0.786,0.974),(-0.794,0.982),(-0.802,0.990),(-0.810,0.998),(-0.818,1.006),(-0.826,1.014),(-0.834,1.022),(-0.842,1.029),(-0.850,1.036),(-0.858,1.043),(-0.866,1.050),(-0.873,1.057),(-0.881,1.063),(-0.889,1.070),(-0.896,1.076),(-0.904,1.082),(-0.911,1.088),(-0.918,1.094),(-0.926,1.099),(-0.933,1.105),(-0.940,1.110),(-0.947,1.115),(-0.954,1.120),(-0.961,1.125),(-0.968,1.130),(-0.974,1.134),(-0.981,1.138),(-0.988,1.143),(-0.994,1.147),(-1.001,1.151),(-1.007,1.154),(-1.013,1.158),(-1.019,1.161),(-1.026,1.165),(-1.032,1.168),(-1.037,1.171),(-1.043,1.174),(-1.049,1.176),(-1.055,1.179),(-1.060,1.181),(-1.065,1.184),(-1.071,1.186),(-1.076,1.188),(-1.081,1.190),(-1.086,1.191),(-1.091,1.193),(-1.095,1.195),(-1.100,1.196),(-1.105,1.197),(-1.109,1.199),(-1.113,1.200),(-1.117,1.201),(-1.121,1.202),(-1.125,1.202),(-1.129,1.203),(-1.132,1.204),(-1.136,1.204),(-1.139,1.205),(-1.142,1.205),(-1.145,1.206),(-1.148,1.206),(-1.151,1.206),(-1.153,1.206),(-1.156,1.207),(-1.158,1.207),(-1.160,1.207),(-1.162,1.207),(-1.164,1.207),(-1.165,1.207),(-1.167,1.207),(-1.168,1.207)]
L = [(0.000,0.000),(0.010,0.015),(0.020,0.030),(0.030,0.045),(0.040,0.060),(0.050,0.075),(0.060,0.090),(0.070,0.105),(0.080,0.120),(0.090,0.135),(0.100,0.150),(0.110,0.165),(0.120,0.180),(0.130,0.195),(0.140,0.210),(0.150,0.225),(0.160,0.240),(0.170,0.255),(0.180,0.270),(0.190,0.285),(0.200,0.300),(0.210,0.315),(0.220,0.330),(0.230,0.345),(0.240,0.360),(0.250,0.375),(0.260,0.390),(0.270,0.405),(0.280,0.420),(0.290,0.435),(0.300,0.450),(0.310,0.465),(0.320,0.480),(0.330,0.495),(0.340,0.510),(0.350,0.525),(0.360,0.540),(0.370,0.555),(0.380,0.570),(0.390,0.585),(0.400,0.600),(0.410,0.615),(0.420,0.630),(0.430,0.645),(0.440,0.660),(0.450,0.675),(0.460,0.690),(0.470,0.705),(0.480,0.720),(0.490,0.735),(0.500,0.750),(0.510,0.765),(0.520,0.780),(0.530,0.795),(0.540,0.810),(0.550,0.825),(0.560,0.840),(0.570,0.855),(0.580,0.870),(0.590,0.885),(0.600,0.900),(0.610,0.915),(0.620,0.930),(0.630,0.945),(0.640,0.960),(0.650,0.975),(0.660,0.990),(0.670,1.005),(0.680,1.020),(0.690,1.035),(0.700,1.050),(0.710,1.065),(0.720,1.080),(0.730,1.095),(0.740,1.110),(0.750,1.125),(0.760,1.140),(0.770,1.155),(0.780,1.170),(0.790,1.185),(0.800,1.200),(0.810,1.208),(0.820,1.193),(0.830,1.178),(0.840,1.163),(0.850,1.148),(0.860,1.133),(0.870,1.118),(0.880,1.103),(0.890,1.088),(0.900,1.073),(0.910,1.058),(0.920,1.043),(0.930,1.028),(0.940,1.013),(0.950,0.998),(0.960,0.983),(0.970,0.968),(0.980,0.953),(0.990,0.938),(1.000,0.923),(1.010,0.908),(1.020,0.893),(1.030,0.884),(1.040,0.881),(1.050,0.880),(1.060,0.879),(1.070,0.880),(1.070,0.880),(1.080,0.895),(1.090,0.910),(1.100,0.925),(1.110,0.940),(1.120,0.955),(1.130,0.970),(1.140,0.985),(1.150,1.000),(1.160,1.015),(1.170,1.030),(1.180,1.045),(1.190,1.060),(1.200,1.075),(1.210,1.090),(1.220,1.105),(1.230,1.120),(1.240,1.135),(1.250,1.150),(1.260,1.165),(1.270,1.180),(1.280,1.195),(1.290,1.210),(1.300,1.225),(1.310,1.240),(1.320,1.255),(1.330,1.270),(1.340,1.285),(1.350,1.292),(1.360,1.292),(1.370,1.292),(1.380,1.292),(1.390,1.292),(1.400,1.292),(1.410,1.292),(1.420,1.292),(1.430,1.292),(1.440,1.292),(1.450,1.292),(1.460,1.292),(1.470,1.292),(1.480,1.292),(1.490,1.292),(1.500,1.292),(1.510,1.292),(1.520,1.291),(1.530,1.291),(1.540,1.291),(1.550,1.291),(1.560,1.291),(1.570,1.291),(1.580,1.290),(1.590,1.290),(1.600,1.290),(1.610,1.290),(1.620,1.289),(1.630,1.289),(1.640,1.289),(1.650,1.288),(1.660,1.288),(1.670,1.288),(1.680,1.287),(1.690,1.287),(1.700,1.286),(1.710,1.286),(1.720,1.285),(1.730,1.284),(1.740,1.284),(1.750,1.283),(1.760,1.282),(1.770,1.281),(1.780,1.280),(1.790,1.279),(1.800,1.277),(1.810,1.276),(1.820,1.274),(1.830,1.272),(1.840,1.270),(1.850,1.268),(1.860,1.265),(1.870,1.262),(1.880,1.258),(1.890,1.254),(1.900,1.249),(1.910,1.243),(1.920,1.235),(1.930,1.226),(1.940,1.214),(1.950,1.199),(1.960,1.184),(1.970,1.169),(1.980,1.154),(1.990,1.139),(2.000,1.124),(2.010,1.109),(2.020,1.094),(2.020,1.094),(2.030,1.079),(2.040,1.064),(2.050,1.049),(2.060,1.034),(2.070,1.019),(2.080,1.004),(2.090,0.989),(2.100,0.974),(2.110,0.986),(2.120,1.001),(2.130,1.016),(2.140,1.031),(2.150,1.046),(2.160,1.061),(2.170,1.076),(2.180,1.091),(2.190,1.106),(2.200,1.121),(2.210,1.136),(2.220,1.151),(2.230,1.166),(2.240,1.173),(2.250,1.177),(2.260,1.181),(2.270,1.184),(2.280,1.187),(2.290,1.189),(2.300,1.191),(2.310,1.193),(2.320,1.195),(2.330,1.196),(2.340,1.196),(2.350,1.197),(2.360,1.197),(2.370,1.197),(2.380,1.197),(2.390,1.197),(2.400,1.196),(2.410,1.196),(2.420,1.195),(2.430,1.194),(2.440,1.187),(2.450,1.172),(2.460,1.157),(2.470,1.142),(2.480,1.127),(2.490,1.112),(2.500,1.097),(2.510,1.082),(2.520,1.067),(2.530,1.052),(2.540,1.037),(2.550,1.022),(2.560,1.007),(2.570,0.992),(2.580,0.977),(2.590,0.962),(2.600,0.947),(2.610,0.932),(2.620,0.917),(2.630,0.902),(2.640,0.887),(2.650,0.872),(2.660,0.857),(2.670,0.842),(2.680,0.827),(2.690,0.812),(2.700,0.797),(2.710,0.782),(2.720,0.767),(2.730,0.752),(2.740,0.737),(2.750,0.722),(2.760,0.707),(2.770,0.692),(2.780,0.677),(2.790,0.662),(2.800,0.647),(2.810,0.632),(2.820,0.617),(2.830,0.602),(2.840,0.587),(2.850,0.572),(2.860,0.557),(2.870,0.542),(2.880,0.527),(2.890,0.512),(2.900,0.497),(2.910,0.482),(2.920,0.467),(2.930,0.452),(2.940,0.437),(2.950,0.422),(2.960,0.407),(2.970,0.392),(2.980,0.377),(2.990,0.362),(3.000,0.347),(3.010,0.332),(3.020,0.317),(3.030,0.302),(3.040,0.287),(3.050,0.272),(3.060,0.257),(3.070,0.242),(3.080,0.227),(3.090,0.212),(3.100,0.197),(3.110,0.182),(3.120,0.167),(3.130,0.152),(3.140,0.137)]
A = [(0.000,-0.000),(0.010,-0.012),(0.020,-0.024),(0.030,-0.037),(0.040,-0.049),(0.050,-0.061),(0.060,-0.073),(0.070,-0.086),(0.080,-0.098),(0.090,-0.110),(0.100,-0.123),(0.110,-0.135),(0.120,-0.147),(0.130,-0.159),(0.140,-0.172),(0.150,-0.184),(0.160,-0.196),(0.170,-0.208),(0.180,-0.221),(0.190,-0.233),(0.200,-0.245),(0.210,-0.257),(0.220,-0.269),(0.230,-0.282),(0.240,-0.294),(0.250,-0.306),(0.260,-0.318),(0.270,-0.329),(0.280,-0.341),(0.290,-0.353),(0.300,-0.364),(0.310,-0.376),(0.320,-0.387),(0.330,-0.398),(0.340,-0.409),(0.350,-0.420),(0.360,-0.430),(0.370,-0.440),(0.380,-0.450),(0.390,-0.460),(0.400,-0.469),(0.410,-0.478),(0.420,-0.486),(0.430,-0.494),(0.440,-0.501),(0.450,-0.508),(0.460,-0.514),(0.470,-0.519),(0.480,-0.524),(0.490,-0.528),(0.500,-0.531),(0.510,-0.532),(0.520,-0.533),(0.530,-0.533),(0.540,-0.531),(0.550,-0.528),(0.560,-0.523),(0.570,-0.517),(0.580,-0.509),(0.590,-0.499),(0.600,-0.487),(0.610,-0.473),(0.620,-0.456),(0.630,-0.437),(0.640,-0.415),(0.650,-0.389),(0.660,-0.361),(0.670,-0.328),(0.680,-0.292),(0.690,-0.251),(0.700,-0.206),(0.710,-0.155),(0.720,-0.099),(0.730,-0.036),(0.740,0.033),(0.750,0.110),(0.760,0.195),(0.770,0.289),(0.780,0.393),(0.790,0.508),(0.800,0.635),(0.810,0.769),(0.820,0.895),(0.830,1.024),(0.840,1.156),(0.850,1.292),(0.860,1.429),(0.870,1.567),(0.880,1.707),(0.890,1.845),(0.900,1.982),(0.910,2.115),(0.920,2.244),(0.930,2.366),(0.940,2.480),(0.950,2.583),(0.960,2.675),(0.970,2.753),(0.980,2.816),(0.990,2.863),(1.000,2.894),(1.010,2.908),(1.020,2.905),(1.030,2.909),(1.040,2.915),(1.050,2.913),(1.060,2.901),(1.070,2.886),(1.070,0.300),(1.080,0.242),(1.090,0.202),(1.100,0.173),(1.110,0.151),(1.120,0.134),(1.130,0.121),(1.140,0.110),(1.150,0.101),(1.160,0.094),(1.170,0.088),(1.180,0.083),(1.190,0.079),(1.200,0.075),(1.210,0.072),(1.220,0.069),(1.230,0.067),(1.240,0.065),(1.250,0.063),(1.260,0.061),(1.270,0.060),(1.280,0.059),(1.290,0.058),(1.300,0.058),(1.310,0.057),(1.320,0.057),(1.330,0.056),(1.340,0.056),(1.350,0.056),(1.360,0.055),(1.370,0.055),(1.380,0.055),(1.390,0.054),(1.400,0.054),(1.410,0.054),(1.420,0.054),(1.430,0.055),(1.440,0.055),(1.450,0.055),(1.460,0.056),(1.470,0.056),(1.480,0.057),(1.490,0.057),(1.500,0.058),(1.510,0.059),(1.520,0.060),(1.530,0.061),(1.540,0.062),(1.550,0.063),(1.560,0.065),(1.570,0.066),(1.580,0.068),(1.590,0.069),(1.600,0.071),(1.610,0.073),(1.620,0.075),(1.630,0.078),(1.640,0.080),(1.650,0.083),(1.660,0.086),(1.670,0.089),(1.680,0.092),(1.690,0.096),(1.700,0.100),(1.710,0.104),(1.720,0.109),(1.730,0.114),(1.740,0.119),(1.750,0.125),(1.760,0.132),(1.770,0.139),(1.780,0.148),(1.790,0.157),(1.800,0.167),(1.810,0.178),(1.820,0.191),(1.830,0.206),(1.840,0.223),(1.850,0.242),(1.860,0.264),(1.870,0.290),(1.880,0.320),(1.890,0.356),(1.900,0.400),(1.910,0.453),(1.920,0.519),(1.930,0.601),(1.940,0.708),(1.950,0.848),(1.960,1.042),(1.970,1.327),(1.980,1.770),(1.990,2.535),(2.000,4.070),(2.010,8.142),(2.020,8.331),(2.020,38.785),(2.030,18.952),(2.040,10.904),(2.050,7.150),(2.060,5.120),(2.070,3.896),(2.080,3.097),(2.090,2.545),(2.100,2.145),(2.110,1.890),(2.120,1.694),(2.130,1.536),(2.140,1.407),(2.150,1.300),(2.160,1.211),(2.170,1.137),(2.180,1.074),(2.190,1.021),(2.200,0.975),(2.210,0.937),(2.220,0.904),(2.230,0.877),(2.240,0.847),(2.250,0.821),(2.260,0.799),(2.270,0.780),(2.280,0.764),(2.290,0.750),(2.300,0.738),(2.310,0.729),(2.320,0.722),(2.330,0.717),(2.340,0.713),(2.350,0.711),(2.360,0.710),(2.370,0.711),(2.380,0.714),(2.390,0.718),(2.400,0.723),(2.410,0.730),(2.420,0.738),(2.430,0.747),(2.440,0.754),(2.450,0.757),(2.460,0.761),(2.470,0.766),(2.480,0.772),(2.490,0.779),(2.500,0.787),(2.510,0.796),(2.520,0.806),(2.530,0.816),(2.540,0.827),(2.550,0.839),(2.560,0.852),(2.570,0.865),(2.580,0.879),(2.590,0.894),(2.600,0.910),(2.610,0.926),(2.620,0.943),(2.630,0.961),(2.640,0.980),(2.650,0.999),(2.660,1.019),(2.670,1.039),(2.680,1.060),(2.690,1.082),(2.700,1.104),(2.710,1.127),(2.720,1.150),(2.730,1.174),(2.740,1.197),(2.750,1.222),(2.760,1.246),(2.770,1.270),(2.780,1.295),(2.790,1.319),(2.800,1.343),(2.810,1.367),(2.820,1.390),(2.830,1.412),(2.840,1.434),(2.850,1.454),(2.860,1.473),(2.870,1.490),(2.880,1.506),(2.890,1.520),(2.900,1.532),(2.910,1.541),(2.920,1.547),(2.930,1.551),(2.940,1.551),(2.950,1.548),(2.960,1.541),(2.970,1.531),(2.980,1.517),(2.990,1.499),(3.000,1.476),(3.010,1.450),(3.020,1.419),(3.030,1.384),(3.040,1.345),(3.050,1.301),(3.060,1.254),(3.070,1.203),(3.080,1.147),(3.090,1.088),(3.100,1.026),(3.110,0.960),(3.120,0.892),(3.130,0.820),(3.140,0.745)]
)";