paths.cpp

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#include <string>
#include <vector>
#include "paths.h"
 
const std::string skills_1 = R"(
X = [(-1.501000,1.194000),(-1.500750,1.193995),(-1.500251,1.193985),(-1.499501,1.193972),(-1.498501,1.193956),(-1.497251,1.193939),(-1.495751,1.193924),(-1.494001,1.193913),(-1.492001,1.193909),(-1.489751,1.193917),(-1.487251,1.193940),(-1.484502,1.193984),(-1.481503,1.194052),(-1.478254,1.194152),(-1.474757,1.194289),(-1.471011,1.194470),(-1.467018,1.194704),(-1.462778,1.194998),(-1.458293,1.195361),(-1.453564,1.195803),(-1.448592,1.196333),(-1.443380,1.196963),(-1.437930,1.197704),(-1.432246,1.198567),(-1.426330,1.199565),(-1.420187,1.200710),(-1.413820,1.202016),(-1.407234,1.203496),(-1.400436,1.205164),(-1.393431,1.207032),(-1.386226,1.209114),(-1.378828,1.211423),(-1.371244,1.213970),(-1.363483,1.216766),(-1.355552,1.219823),(-1.347458,1.223148),(-1.339211,1.226750),(-1.330816,1.230634),(-1.322281,1.234805),(-1.313611,1.239265),(-1.304812,1.244016),(-1.295887,1.249056),(-1.286839,1.254384),(-1.277669,1.259994),(-1.268377,1.265881),(-1.258961,1.272038),(-1.249418,1.278455),(-1.239744,1.285123),(-1.229932,1.292032),(-1.219975,1.299167),(-1.209864,1.306517),(-1.199590,1.314067),(-1.189142,1.321803),(-1.178509,1.329708),(-1.167678,1.337767),(-1.156636,1.345961),(-1.145371,1.354274),(-1.133870,1.362687),(-1.122369,1.371000),(-1.110948,1.379138),(-1.099585,1.387103),(-1.088259,1.394895),(-1.076954,1.402515),(-1.065655,1.409966),(-1.054349,1.417247),(-1.043027,1.424359),(-1.031677,1.431304),(-1.020293,1.438081),(-1.008866,1.444692),(-0.997391,1.451137),(-0.985862,1.457417),(-0.974275,1.463533),(-0.962626,1.469486),(-0.950910,1.475275),(-0.939127,1.480902),(-0.927274,1.486367),(-0.915348,1.491672),(-0.903349,1.496818),(-0.891276,1.501804),(-0.879128,1.506633),(-0.866904,1.511305),(-0.854606,1.515822),(-0.842234,1.520183),(-0.829787,1.524392),(-0.817268,1.528448),(-0.804676,1.532353),(-0.792013,1.536109),(-0.779280,1.539718),(-0.766479,1.543179),(-0.753611,1.546496),(-0.740677,1.549670),(-0.727680,1.552703),(-0.714723,1.555573),(-0.701983,1.558251),(-0.689464,1.560747),(-0.677169,1.563070),(-0.665100,1.565232),(-0.653261,1.567240),(-0.641655,1.569103),(-0.630283,1.570829),(-0.619148,1.572427),(-0.608250,1.573905),(-0.597594,1.575268),(-0.587178,1.576525),(-0.577006,1.577682),(-0.567078,1.578745),(-0.557396,1.579719),(-0.547960,1.580611),(-0.538772,1.581427),(-0.529832,1.582170),(-0.521141,1.582846),(-0.512699,1.583459),(-0.504508,1.584015),(-0.496568,1.584516),(-0.488880,1.584967),(-0.481443,1.585372),(-0.474259,1.585734),(-0.467327,1.586057),(-0.460649,1.586343),(-0.454225,1.586596),(-0.448055,1.586818),(-0.442139,1.587013),(-0.436477,1.587182),(-0.431071,1.587328),(-0.425921,1.587454),(-0.421027,1.587561),(-0.416389,1.587652),(-0.412009,1.587727),(-0.407886,1.587790),(-0.404020,1.587841),(-0.400413,1.587882),(-0.397066,1.587915),(-0.393979,1.587940),(-0.391152,1.587960),(-0.388588,1.587974),(-0.386287,1.587984),(-0.384252,1.587991),(-0.382483,1.587995),(-0.380986,1.587998),(-0.379764,1.587999),(-0.378825,1.588000),(-0.378183,1.588000),(-0.378000,1.588000)]
L = [(0.000000,0.000000),(0.010000,0.025000),(0.020000,0.050000),(0.030000,0.075000),(0.040000,0.100000),(0.050000,0.125000),(0.060000,0.150000),(0.070000,0.175000),(0.080000,0.200000),(0.090000,0.225000),(0.100000,0.250000),(0.110000,0.275000),(0.120000,0.300000),(0.130000,0.325000),(0.140000,0.350000),(0.150000,0.375000),(0.160000,0.400000),(0.170000,0.425000),(0.180000,0.450000),(0.190000,0.475000),(0.200000,0.500000),(0.210000,0.525000),(0.220000,0.550000),(0.230000,0.575000),(0.240000,0.600000),(0.250000,0.625000),(0.260000,0.650000),(0.270000,0.675000),(0.280000,0.700000),(0.290000,0.725000),(0.300000,0.750000),(0.310000,0.775000),(0.320000,0.800000),(0.330000,0.825000),(0.340000,0.850000),(0.350000,0.875000),(0.360000,0.900000),(0.370000,0.925000),(0.380000,0.950000),(0.390000,0.975000),(0.400000,1.000000),(0.410000,1.025000),(0.420000,1.050000),(0.430000,1.075000),(0.440000,1.100000),(0.450000,1.125000),(0.460000,1.149999),(0.470000,1.174999),(0.480000,1.199999),(0.490000,1.224999),(0.500000,1.249999),(0.510000,1.274999),(0.520000,1.299999),(0.530000,1.324999),(0.540000,1.349999),(0.550000,1.374999),(0.560000,1.399999),(0.570000,1.424999),(0.580000,1.419067),(0.590000,1.402370),(0.600000,1.387675),(0.610000,1.374742),(0.620000,1.363371),(0.630000,1.353396),(0.640000,1.344673),(0.650000,1.337081),(0.660000,1.330515),(0.670000,1.324883),(0.680000,1.320105),(0.690000,1.316107),(0.700000,1.312825),(0.710000,1.310199),(0.720000,1.308177),(0.730000,1.306709),(0.740000,1.305749),(0.750000,1.305254),(0.760000,1.305186),(0.770000,1.305506),(0.780000,1.306180),(0.790000,1.307174),(0.800000,1.308460),(0.810000,1.310006),(0.820000,1.311786),(0.830000,1.313775),(0.839999,1.315948),(0.849999,1.318282),(0.859999,1.320757),(0.869999,1.323354),(0.879999,1.326053),(0.889999,1.328838),(0.899999,1.331694),(0.909999,1.334606),(0.919999,1.327007),(0.929999,1.301767),(0.939999,1.276523),(0.949999,1.251273),(0.959999,1.226018),(0.969999,1.200758),(0.979999,1.175492),(0.989999,1.150220),(0.999999,1.124943),(1.009999,1.099659),(1.019999,1.074368),(1.029999,1.049070),(1.039999,1.023764),(1.049999,0.998451),(1.059999,0.973130),(1.069999,0.947800),(1.079999,0.922462),(1.089999,0.897114),(1.099999,0.871755),(1.109999,0.846385),(1.119999,0.821005),(1.129999,0.795612),(1.139999,0.770207),(1.149999,0.744787),(1.159999,0.719352),(1.169999,0.693902),(1.179999,0.668434),(1.189999,0.642948),(1.199999,0.617442),(1.209999,0.591913),(1.219999,0.566362),(1.229999,0.540780),(1.239999,0.515171),(1.249999,0.489531),(1.259999,0.463857),(1.269999,0.438144),(1.279999,0.412386),(1.289999,0.386578),(1.299999,0.360711),(1.309999,0.334780),(1.319999,0.308769),(1.329999,0.282666),(1.339999,0.256450),(1.349999,0.230095),(1.359999,0.203564),(1.369999,0.176804),(1.379999,0.149730),(1.389999,0.122200),(1.399999,0.093929),(1.409999,0.064233),(1.419999,0.030238)]
A = [(0.000000,0.000000),(0.010000,0.058592),(0.020000,0.117400),(0.030000,0.176585),(0.040000,0.236306),(0.050000,0.296720),(0.060000,0.357982),(0.070000,0.420240),(0.080000,0.483638),(0.090000,0.548312),(0.100000,0.614385),(0.110000,0.681968),(0.120000,0.751155),(0.130000,0.822015),(0.140000,0.894592),(0.150000,0.968894),(0.160000,1.044885),(0.170000,1.122481),(0.180000,1.201536),(0.190000,1.281833),(0.200000,1.363069),(0.210000,1.444849),(0.220000,1.526670),(0.230000,1.607912),(0.240000,1.687831),(0.250000,1.765552),(0.260000,1.840068),(0.270000,1.910252),(0.280000,1.974866),(0.290000,2.032586),(0.300000,2.082038),(0.310000,2.121839),(0.320000,2.150647),(0.330000,2.167221),(0.340000,2.170477),(0.350000,2.159543),(0.360000,2.133806),(0.370000,2.092953),(0.380000,2.036981),(0.390000,1.966208),(0.400000,1.881247),(0.410000,1.782980),(0.420000,1.672506),(0.430000,1.551094),(0.440000,1.420123),(0.450000,1.281028),(0.460000,1.135253),(0.470000,0.984209),(0.480000,0.829248),(0.490000,0.671636),(0.500000,0.512549),(0.510000,0.353062),(0.520000,0.194161),(0.530000,0.036743),(0.540000,-0.118370),(0.550000,-0.270421),(0.560000,-0.418709),(0.570000,-0.562576),(0.580000,-0.683863),(0.590000,-0.785772),(0.600000,-0.875220),(0.610000,-0.953660),(0.620000,-1.022306),(0.630000,-1.082184),(0.640000,-1.134166),(0.650000,-1.179001),(0.660000,-1.217347),(0.670000,-1.249781),(0.680000,-1.276815),(0.690000,-1.298907),(0.700000,-1.316473),(0.710000,-1.329889),(0.720000,-1.339503),(0.730000,-1.345635),(0.740000,-1.348581),(0.750000,-1.348616),(0.760000,-1.346000),(0.770000,-1.340974),(0.780000,-1.333763),(0.790000,-1.324580),(0.800000,-1.313626),(0.810000,-1.301087),(0.820000,-1.287139),(0.830000,-1.271946),(0.839999,-1.255662),(0.849999,-1.238430),(0.859999,-1.220384),(0.869999,-1.201647),(0.879999,-1.182335),(0.889999,-1.162552),(0.899999,-1.142397),(0.909999,-1.121959),(0.919999,-1.092811),(0.929999,-1.050123),(0.939999,-1.008765),(0.949999,-0.968756),(0.959999,-0.930103),(0.969999,-0.892797),(0.979999,-0.856820),(0.989999,-0.822145),(0.999999,-0.788737),(1.009999,-0.756561),(1.019999,-0.725575),(1.029999,-0.695734),(1.039999,-0.666995),(1.049999,-0.639313),(1.059999,-0.612640),(1.069999,-0.586933),(1.079999,-0.562146),(1.089999,-0.538233),(1.099999,-0.515153),(1.109999,-0.492864),(1.119999,-0.471325),(1.129999,-0.450497),(1.139999,-0.430342),(1.149999,-0.410823),(1.159999,-0.391906),(1.169999,-0.373555),(1.179999,-0.355740),(1.189999,-0.338429),(1.199999,-0.321590),(1.209999,-0.305196),(1.219999,-0.289219),(1.229999,-0.273628),(1.239999,-0.258403),(1.249999,-0.243516),(1.259999,-0.228943),(1.269999,-0.214660),(1.279999,-0.200643),(1.289999,-0.186868),(1.299999,-0.173312),(1.309999,-0.159953),(1.319999,-0.146765),(1.329999,-0.133724),(1.339999,-0.120804),(1.349999,-0.107974),(1.359999,-0.095201),(1.369999,-0.082443),(1.379999,-0.069645),(1.389999,-0.056724),(1.399999,-0.043533),(1.409999,-0.029738),(1.419999,-0.013995)]
)";
 
const std::string skills_2 = R"(
X = [(0.711000,1.194000),(0.711250,1.194004),(0.711750,1.194013),(0.712500,1.194024),(0.713500,1.194037),(0.714750,1.194051),(0.716250,1.194062),(0.718000,1.194070),(0.720000,1.194069),(0.722250,1.194059),(0.724749,1.194035),(0.727499,1.193993),(0.730498,1.193930),(0.733747,1.193841),(0.737245,1.193722),(0.740992,1.193569),(0.744987,1.193376),(0.749231,1.193139),(0.753722,1.192852),(0.758459,1.192512),(0.763443,1.192112),(0.768673,1.191648),(0.774147,1.191114),(0.779865,1.190505),(0.785826,1.189816),(0.792028,1.189042),(0.798471,1.188177),(0.805153,1.187217),(0.812072,1.186156),(0.819228,1.184988),(0.826618,1.183710),(0.834241,1.182314),(0.842096,1.180797),(0.850181,1.179154),(0.858494,1.177378),(0.867032,1.175465),(0.875794,1.173409),(0.884778,1.171206),(0.893981,1.168850),(0.903401,1.166336),(0.913036,1.163658),(0.922883,1.160812),(0.932939,1.157790),(0.943201,1.154589),(0.953667,1.151203),(0.964332,1.147625),(0.975195,1.143850),(0.986251,1.139873),(0.997497,1.135686),(1.008929,1.131284),(1.020542,1.126660),(1.032333,1.121809),(1.044297,1.116722),(1.056428,1.111394),(1.068520,1.105911),(1.080548,1.100283),(1.092508,1.094512),(1.104397,1.088600),(1.116212,1.082547),(1.127949,1.076356),(1.139605,1.070027),(1.151177,1.063562),(1.162661,1.056961),(1.174054,1.050226),(1.185353,1.043357),(1.196555,1.036356),(1.207657,1.029224),(1.218654,1.021960),(1.229544,1.014567),(1.240323,1.007044),(1.250989,0.999394),(1.261536,0.991616),(1.271963,0.983711),(1.282266,0.975681),(1.292440,0.967526),(1.302483,0.959247),(1.312391,0.950845),(1.322160,0.942321),(1.331787,0.933676),(1.341268,0.924911),(1.350599,0.916026),(1.359778,0.907024),(1.368799,0.897905),(1.377660,0.888671),(1.386357,0.879322),(1.394887,0.869860),(1.403246,0.860287),(1.411429,0.850604),(1.419435,0.840812),(1.427259,0.830914),(1.434898,0.820909),(1.442348,0.810802),(1.449607,0.800592),(1.456672,0.790282),(1.463538,0.779875),(1.470203,0.769371),(1.476665,0.758772),(1.482919,0.748082),(1.488965,0.737302),(1.494799,0.726433),(1.500382,0.715551),(1.505652,0.704794),(1.510618,0.694171),(1.515288,0.683691),(1.519673,0.673363),(1.523781,0.663194),(1.527623,0.653191),(1.531209,0.643363),(1.534549,0.633716),(1.537653,0.624257),(1.540531,0.614991),(1.543194,0.605925),(1.545652,0.597064),(1.547915,0.588413),(1.549994,0.579976),(1.551897,0.571759),(1.553636,0.563764),(1.555219,0.555996),(1.556656,0.548459),(1.557956,0.541154),(1.559129,0.534086),(1.560182,0.527257),(1.561124,0.520668),(1.561964,0.514323),(1.562709,0.508223),(1.563367,0.502370),(1.563945,0.496765),(1.564450,0.491409),(1.564888,0.486305),(1.565267,0.481454),(1.565591,0.476855),(1.565866,0.472512),(1.566098,0.468423),(1.566291,0.464592),(1.566451,0.461017),(1.566582,0.457701),(1.566687,0.454645),(1.566771,0.451849),(1.566836,0.449314),(1.566886,0.447044),(1.566924,0.445038),(1.566951,0.443301),(1.566971,0.441835),(1.566985,0.440644),(1.566994,0.439737),(1.566999,0.439130),(1.567000,0.439000)]
L = [(0.000000,0.000000),(0.010000,0.025000),(0.020000,0.050000),(0.030000,0.075000),(0.040000,0.100000),(0.050000,0.125000),(0.060000,0.150000),(0.070000,0.175000),(0.080000,0.200000),(0.090000,0.225000),(0.100000,0.250000),(0.110000,0.275000),(0.120000,0.300000),(0.130000,0.325000),(0.140000,0.350000),(0.150000,0.375000),(0.160000,0.400000),(0.170000,0.425000),(0.180000,0.450000),(0.190000,0.475000),(0.200000,0.500000),(0.210000,0.525000),(0.220000,0.550000),(0.230000,0.575000),(0.240000,0.600000),(0.250000,0.625000),(0.260000,0.650000),(0.270000,0.675000),(0.280000,0.700000),(0.290000,0.725000),(0.300000,0.750000),(0.310000,0.775000),(0.320000,0.800000),(0.330000,0.825000),(0.340000,0.850000),(0.350000,0.875000),(0.360000,0.900000),(0.370000,0.925000),(0.380000,0.950000),(0.390000,0.975000),(0.400000,1.000000),(0.410000,1.025000),(0.420000,1.050000),(0.430000,1.075000),(0.440000,1.100000),(0.450000,1.125000),(0.460000,1.149999),(0.470000,1.174999),(0.480000,1.199999),(0.490000,1.224999),(0.500000,1.249999),(0.510000,1.274999),(0.520000,1.299999),(0.530000,1.324999),(0.540000,1.327731),(0.550000,1.327933),(0.560000,1.327948),(0.570000,1.327787),(0.580000,1.327457),(0.590000,1.326966),(0.600000,1.326321),(0.610000,1.325528),(0.620000,1.324593),(0.630000,1.323521),(0.640000,1.322317),(0.650000,1.320986),(0.660000,1.319531),(0.670000,1.317958),(0.680000,1.316269),(0.690000,1.314469),(0.700000,1.312562),(0.710000,1.310551),(0.720000,1.308440),(0.730000,1.306234),(0.740000,1.303935),(0.750000,1.301547),(0.760000,1.299076),(0.770000,1.296526),(0.780000,1.293900),(0.790000,1.291206),(0.800000,1.288446),(0.810000,1.285628),(0.820000,1.282756),(0.830000,1.279838),(0.839999,1.276880),(0.849999,1.273889),(0.859999,1.270872),(0.869999,1.267838),(0.879999,1.264794),(0.889999,1.261750),(0.899999,1.258714),(0.909999,1.255696),(0.919999,1.252706),(0.929999,1.249754),(0.939999,1.246851),(0.949999,1.244006),(0.959999,1.241231),(0.969999,1.238537),(0.979999,1.235935),(0.989999,1.233436),(0.999999,1.223145),(1.009999,1.197884),(1.019999,1.172618),(1.029999,1.147345),(1.039999,1.122067),(1.049999,1.096782),(1.059999,1.071491),(1.069999,1.046192),(1.079999,1.020886),(1.089999,0.995572),(1.099999,0.970251),(1.109999,0.944920),(1.119999,0.919581),(1.129999,0.894231),(1.139999,0.868871),(1.149999,0.843501),(1.159999,0.818119),(1.169999,0.792724),(1.179999,0.767317),(1.189999,0.741896),(1.199999,0.716459),(1.209999,0.691007),(1.219999,0.665538),(1.229999,0.640050),(1.239999,0.614542),(1.249999,0.589012),(1.259999,0.563458),(1.269999,0.537877),(1.279999,0.512268),(1.289999,0.486626),(1.299999,0.460948),(1.309999,0.435231),(1.319999,0.409468),(1.329999,0.383654),(1.339999,0.357782),(1.349999,0.331842),(1.359999,0.305823),(1.369999,0.279707),(1.379999,0.253475),(1.389999,0.227102),(1.399999,0.200551),(1.409999,0.173762),(1.419999,0.146647),(1.429999,0.119055),(1.439999,0.090671),(1.449999,0.060717),(1.459999,0.025501)]
A = [(0.000000,0.000000),(0.010000,-0.057520),(0.020000,-0.114611),(0.030000,-0.170958),(0.040000,-0.226262),(0.050000,-0.280243),(0.060000,-0.332642),(0.070000,-0.383231),(0.080000,-0.431809),(0.090000,-0.478211),(0.100000,-0.522301),(0.110000,-0.563982),(0.120000,-0.603187),(0.130000,-0.639882),(0.140000,-0.674065),(0.150000,-0.705761),(0.160000,-0.735020),(0.170000,-0.761916),(0.180000,-0.786541),(0.190000,-0.809004),(0.200000,-0.829428),(0.210000,-0.847944),(0.220000,-0.864693),(0.230000,-0.879819),(0.240000,-0.893466),(0.250000,-0.905786),(0.260000,-0.916926),(0.270000,-0.927031),(0.280000,-0.936242),(0.290000,-0.944696),(0.300000,-0.952524),(0.310000,-0.959853),(0.320000,-0.966803),(0.330000,-0.973489),(0.340000,-0.980022),(0.350000,-0.986505),(0.360000,-0.993036),(0.370000,-0.999709),(0.380000,-1.006613),(0.390000,-1.013834),(0.400000,-1.021451),(0.410000,-1.029545),(0.420000,-1.038190),(0.430000,-1.047459),(0.440000,-1.057424),(0.450000,-1.068156),(0.460000,-1.079723),(0.470000,-1.092196),(0.480000,-1.105645),(0.490000,-1.120138),(0.500000,-1.135748),(0.510000,-1.152550),(0.520000,-1.170617),(0.530000,-1.190028),(0.540000,-1.190905),(0.550000,-1.190965),(0.560000,-1.192241),(0.570000,-1.194677),(0.580000,-1.198222),(0.590000,-1.202829),(0.600000,-1.208455),(0.610000,-1.215063),(0.620000,-1.222615),(0.630000,-1.231079),(0.640000,-1.240425),(0.650000,-1.250621),(0.660000,-1.261640),(0.670000,-1.273455),(0.680000,-1.286040),(0.690000,-1.299369),(0.700000,-1.313416),(0.710000,-1.328155),(0.720000,-1.343558),(0.730000,-1.359600),(0.740000,-1.376252),(0.750000,-1.393483),(0.760000,-1.411263),(0.770000,-1.429559),(0.780000,-1.448336),(0.790000,-1.467557),(0.800000,-1.487184),(0.810000,-1.507174),(0.820000,-1.527483),(0.830000,-1.548063),(0.839999,-1.568866),(0.849999,-1.589837),(0.859999,-1.610923),(0.869999,-1.632063),(0.879999,-1.653197),(0.889999,-1.674260),(0.899999,-1.695186),(0.909999,-1.715905),(0.919999,-1.736345),(0.929999,-1.756435),(0.939999,-1.776097),(0.949999,-1.795257),(0.959999,-1.813837),(0.969999,-1.831760),(0.979999,-1.848949),(0.989999,-1.865327),(0.999999,-1.868619),(1.009999,-1.847139),(1.019999,-1.823568),(1.029999,-1.797976),(1.039999,-1.770443),(1.049999,-1.741061),(1.059999,-1.709933),(1.069999,-1.677169),(1.079999,-1.642884),(1.089999,-1.607200),(1.099999,-1.570239),(1.109999,-1.532125),(1.119999,-1.492983),(1.129999,-1.452932),(1.139999,-1.412090),(1.149999,-1.370572),(1.159999,-1.328486),(1.169999,-1.285933),(1.179999,-1.243011),(1.189999,-1.199807),(1.199999,-1.156402),(1.209999,-1.112870),(1.219999,-1.069279),(1.229999,-1.025683),(1.239999,-0.982137),(1.249999,-0.938685),(1.259999,-0.895360),(1.269999,-0.852195),(1.279999,-0.809211),(1.289999,-0.766425),(1.299999,-0.723850),(1.309999,-0.681490),(1.319999,-0.639342),(1.329999,-0.597400),(1.339999,-0.555652),(1.349999,-0.514077),(1.359999,-0.472652),(1.369999,-0.431337),(1.379999,-0.390090),(1.389999,-0.348855),(1.399999,-0.307557),(1.409999,-0.266087),(1.419999,-0.224286),(1.429999,-0.181900),(1.439999,-0.138426),(1.449999,-0.092647),(1.459999,-0.038907)]
)";
 
const std::string skills_3 = R"(
X = [(1.588000,-0.452000),(1.588000,-0.452250),(1.587999,-0.452750),(1.587996,-0.453500),(1.587989,-0.454500),(1.587976,-0.455750),(1.587952,-0.457249),(1.587916,-0.458999),(1.587860,-0.460998),(1.587782,-0.463247),(1.587674,-0.465744),(1.587530,-0.468490),(1.587343,-0.471485),(1.587106,-0.474726),(1.586809,-0.478213),(1.586444,-0.481945),(1.586002,-0.485921),(1.585473,-0.490138),(1.584845,-0.494594),(1.584109,-0.499286),(1.583252,-0.504212),(1.582264,-0.509368),(1.581133,-0.514751),(1.579847,-0.520355),(1.578395,-0.526176),(1.576764,-0.532210),(1.574945,-0.538450),(1.572926,-0.544891),(1.570696,-0.551526),(1.568247,-0.558350),(1.565568,-0.565355),(1.562653,-0.572536),(1.559493,-0.579885),(1.556081,-0.587396),(1.552414,-0.595064),(1.548486,-0.602883),(1.544293,-0.610847),(1.539834,-0.618951),(1.535107,-0.627191),(1.530112,-0.635564),(1.524850,-0.644067),(1.519321,-0.652698),(1.513528,-0.661455),(1.507474,-0.670339),(1.501164,-0.679349),(1.494602,-0.688487),(1.487794,-0.697755),(1.480746,-0.707157),(1.473466,-0.716697),(1.465961,-0.726379),(1.458240,-0.736209),(1.450312,-0.746195),(1.442188,-0.756344),(1.433880,-0.766666),(1.425399,-0.777169),(1.416758,-0.787865),(1.407973,-0.798765),(1.399214,-0.809687),(1.390497,-0.820642),(1.381836,-0.831642),(1.373245,-0.842696),(1.364799,-0.853737),(1.356579,-0.864680),(1.348617,-0.875500),(1.340920,-0.886200),(1.333493,-0.896783),(1.326341,-0.907249),(1.319469,-0.917599),(1.312879,-0.927832),(1.306573,-0.937945),(1.300552,-0.947938),(1.294815,-0.957805),(1.289362,-0.967543),(1.284191,-0.977146),(1.279298,-0.986611),(1.274681,-0.995931),(1.270333,-1.005100),(1.266250,-1.014114),(1.262426,-1.022965),(1.258853,-1.031646),(1.255524,-1.040153),(1.252430,-1.048478),(1.249564,-1.056616),(1.246915,-1.064560),(1.244475,-1.072305),(1.242234,-1.079845),(1.240183,-1.087176),(1.238310,-1.094291),(1.236606,-1.101187),(1.235061,-1.107860),(1.233665,-1.114305),(1.232409,-1.120518),(1.231282,-1.126497),(1.230276,-1.132238),(1.229380,-1.137739),(1.228587,-1.142997),(1.227887,-1.148010),(1.227273,-1.152775),(1.226737,-1.157291),(1.226272,-1.161556),(1.225869,-1.165569),(1.225524,-1.169328),(1.225229,-1.172831),(1.224979,-1.176078),(1.224769,-1.179066),(1.224594,-1.181795),(1.224448,-1.184263),(1.224330,-1.186467),(1.224233,-1.188407),(1.224157,-1.190078),(1.224097,-1.191478),(1.224052,-1.192600),(1.224021,-1.193437),(1.224001,-1.193967),(1.224000,-1.194000)]
L = [(0.000000,0.000000),(0.010000,0.025000),(0.020000,0.050000),(0.030000,0.075000),(0.040000,0.100000),(0.050000,0.125000),(0.060000,0.150000),(0.070000,0.175000),(0.080000,0.200000),(0.090000,0.225000),(0.100000,0.250000),(0.110000,0.275000),(0.120000,0.300000),(0.130000,0.325000),(0.140000,0.350000),(0.150000,0.375000),(0.160000,0.400000),(0.170000,0.425000),(0.180000,0.450000),(0.190000,0.475000),(0.200000,0.500000),(0.210000,0.525000),(0.220000,0.550000),(0.230000,0.575000),(0.240000,0.600000),(0.250000,0.625000),(0.260000,0.650000),(0.270000,0.675000),(0.280000,0.700000),(0.290000,0.725000),(0.300000,0.750000),(0.310000,0.775000),(0.320000,0.800000),(0.330000,0.825000),(0.340000,0.850000),(0.350000,0.875000),(0.360000,0.900000),(0.370000,0.925000),(0.380000,0.950000),(0.390000,0.975000),(0.400000,1.000000),(0.410000,1.025000),(0.420000,1.050000),(0.430000,1.075000),(0.440000,1.100000),(0.450000,1.125000),(0.460000,1.149999),(0.470000,1.174999),(0.480000,1.199999),(0.490000,1.224999),(0.500000,1.249999),(0.510000,1.274999),(0.520000,1.299999),(0.530000,1.324999),(0.540000,1.349999),(0.550000,1.374999),(0.560000,1.399999),(0.570000,1.399999),(0.580000,1.399999),(0.590000,1.399999),(0.600000,1.399999),(0.610000,1.390143),(0.620000,1.368572),(0.630000,1.343339),(0.640000,1.318102),(0.650000,1.292860),(0.660000,1.267613),(0.670000,1.242361),(0.680000,1.217104),(0.690000,1.191841),(0.700000,1.166573),(0.710000,1.141298),(0.720000,1.116016),(0.730000,1.090728),(0.740000,1.065434),(0.750000,1.040134),(0.760000,1.014826),(0.770000,0.989510),(0.780000,0.964186),(0.790000,0.938853),(0.800000,0.913512),(0.810000,0.888160),(0.820000,0.862798),(0.830000,0.837424),(0.839999,0.812040),(0.849999,0.786643),(0.859999,0.761232),(0.869999,0.735808),(0.879999,0.710368),(0.889999,0.684912),(0.899999,0.659438),(0.909999,0.633946),(0.919999,0.608432),(0.929999,0.582896),(0.939999,0.557337),(0.949999,0.531749),(0.959999,0.506132),(0.969999,0.480482),(0.979999,0.454796),(0.989999,0.429068),(0.999999,0.403294),(1.009999,0.377467),(1.019999,0.351579),(1.029999,0.325621),(1.039999,0.299580),(1.049999,0.273439),(1.059999,0.247178),(1.069999,0.220766),(1.079999,0.194162),(1.089999,0.167306),(1.099999,0.140094),(1.109999,0.112346),(1.119999,0.083691),(1.129999,0.053089),(1.139999,0.012791)]
A = [(0.000000,0.000000),(0.010000,-0.086139),(0.020000,-0.172348),(0.030000,-0.258674),(0.040000,-0.345152),(0.050000,-0.431808),(0.060000,-0.518645),(0.070000,-0.605646),(0.080000,-0.692768),(0.090000,-0.779934),(0.100000,-0.867033),(0.110000,-0.953910),(0.120000,-1.040368),(0.130000,-1.126158),(0.140000,-1.210979),(0.150000,-1.294472),(0.160000,-1.376226),(0.170000,-1.455771),(0.180000,-1.532583),(0.190000,-1.606089),(0.200000,-1.675677),(0.210000,-1.740700),(0.220000,-1.800495),(0.230000,-1.854396),(0.240000,-1.901752),(0.250000,-1.941946),(0.260000,-1.974415),(0.270000,-1.998668),(0.280000,-2.014306),(0.290000,-2.021032),(0.300000,-2.018669),(0.310000,-2.007153),(0.320000,-1.986548),(0.330000,-1.957032),(0.340000,-1.918887),(0.350000,-1.872490),(0.360000,-1.818292),(0.370000,-1.756801),(0.380000,-1.688560),(0.390000,-1.614126),(0.400000,-1.534053),(0.410000,-1.448876),(0.420000,-1.359094),(0.430000,-1.265156),(0.440000,-1.167457),(0.450000,-1.066328),(0.460000,-0.962031),(0.470000,-0.854756),(0.480000,-0.744617),(0.490000,-0.631672),(0.500000,-0.515900),(0.510000,-0.397211),(0.520000,-0.275452),(0.530000,-0.150412),(0.540000,-0.021820),(0.550000,0.110642),(0.560000,0.247338),(0.570000,0.379513),(0.580000,0.509694),(0.590000,0.638340),(0.600000,0.765845),(0.610000,0.885370),(0.620000,0.992173),(0.630000,1.089674),(0.640000,1.180442),(0.650000,1.264634),(0.660000,1.342343),(0.670000,1.413607),(0.680000,1.478428),(0.690000,1.536783),(0.700000,1.588634),(0.710000,1.633943),(0.720000,1.672681),(0.730000,1.704831),(0.740000,1.730422),(0.750000,1.749501),(0.760000,1.762157),(0.770000,1.768523),(0.780000,1.768771),(0.790000,1.763117),(0.800000,1.751816),(0.810000,1.735157),(0.820000,1.713461),(0.830000,1.687073),(0.839999,1.656356),(0.849999,1.621684),(0.859999,1.583437),(0.869999,1.541990),(0.879999,1.497714),(0.889999,1.450968),(0.899999,1.402091),(0.909999,1.351406),(0.919999,1.299207),(0.929999,1.245772),(0.939999,1.191348),(0.949999,1.136151),(0.959999,1.080380),(0.969999,1.024202),(0.979999,0.967762),(0.989999,0.911175),(0.999999,0.854539),(1.009999,0.797928),(1.019999,0.741390),(1.029999,0.684958),(1.039999,0.628641),(1.049999,0.572428),(1.059999,0.516283),(1.069999,0.460144),(1.079999,0.403915),(1.089999,0.347450),(1.099999,0.290510),(1.109999,0.232689),(1.119999,0.173181),(1.129999,0.109792),(1.139999,0.026452)]
)";
 
const std::string skills_4 = R"(
X = [(1.501000,-1.194000),(1.500750,-1.193995),(1.500251,-1.193985),(1.499501,-1.193972),(1.498501,-1.193956),(1.497251,-1.193939),(1.495751,-1.193924),(1.494001,-1.193913),(1.492001,-1.193909),(1.489751,-1.193917),(1.487251,-1.193940),(1.484502,-1.193984),(1.481503,-1.194052),(1.478254,-1.194152),(1.474757,-1.194289),(1.471011,-1.194470),(1.467018,-1.194704),(1.462778,-1.194998),(1.458293,-1.195361),(1.453564,-1.195803),(1.448592,-1.196333),(1.443380,-1.196963),(1.437930,-1.197704),(1.432246,-1.198567),(1.426330,-1.199565),(1.420187,-1.200710),(1.413820,-1.202016),(1.407234,-1.203496),(1.400436,-1.205164),(1.393431,-1.207032),(1.386226,-1.209114),(1.378828,-1.211423),(1.371244,-1.213970),(1.363483,-1.216766),(1.355552,-1.219823),(1.347458,-1.223148),(1.339211,-1.226750),(1.330816,-1.230634),(1.322281,-1.234805),(1.313611,-1.239265),(1.304812,-1.244016),(1.295887,-1.249056),(1.286839,-1.254384),(1.277669,-1.259994),(1.268377,-1.265881),(1.258961,-1.272038),(1.249418,-1.278455),(1.239744,-1.285123),(1.229932,-1.292032),(1.219975,-1.299167),(1.209864,-1.306517),(1.199590,-1.314067),(1.189142,-1.321803),(1.178509,-1.329708),(1.167678,-1.337767),(1.156636,-1.345961),(1.145371,-1.354274),(1.133870,-1.362687),(1.122369,-1.371000),(1.110948,-1.379138),(1.099585,-1.387103),(1.088259,-1.394895),(1.076954,-1.402515),(1.065655,-1.409966),(1.054349,-1.417247),(1.043027,-1.424359),(1.031677,-1.431304),(1.020293,-1.438081),(1.008866,-1.444692),(0.997391,-1.451137),(0.985862,-1.457417),(0.974275,-1.463533),(0.962626,-1.469486),(0.950910,-1.475275),(0.939127,-1.480902),(0.927274,-1.486367),(0.915348,-1.491672),(0.903349,-1.496818),(0.891276,-1.501804),(0.879128,-1.506633),(0.866904,-1.511305),(0.854606,-1.515822),(0.842234,-1.520183),(0.829787,-1.524392),(0.817268,-1.528448),(0.804676,-1.532353),(0.792013,-1.536109),(0.779280,-1.539718),(0.766479,-1.543179),(0.753611,-1.546496),(0.740677,-1.549670),(0.727680,-1.552703),(0.714723,-1.555573),(0.701983,-1.558251),(0.689464,-1.560747),(0.677169,-1.563070),(0.665100,-1.565232),(0.653261,-1.567240),(0.641655,-1.569103),(0.630283,-1.570829),(0.619148,-1.572427),(0.608250,-1.573905),(0.597594,-1.575268),(0.587178,-1.576525),(0.577006,-1.577682),(0.567078,-1.578745),(0.557396,-1.579719),(0.547960,-1.580611),(0.538772,-1.581427),(0.529832,-1.582170),(0.521141,-1.582846),(0.512699,-1.583459),(0.504508,-1.584015),(0.496568,-1.584516),(0.488880,-1.584967),(0.481443,-1.585372),(0.474259,-1.585734),(0.467327,-1.586057),(0.460649,-1.586343),(0.454225,-1.586596),(0.448055,-1.586818),(0.442139,-1.587013),(0.436477,-1.587182),(0.431071,-1.587328),(0.425921,-1.587454),(0.421027,-1.587561),(0.416389,-1.587652),(0.412009,-1.587727),(0.407886,-1.587790),(0.404020,-1.587841),(0.400413,-1.587882),(0.397066,-1.587915),(0.393979,-1.587940),(0.391152,-1.587960),(0.388588,-1.587974),(0.386287,-1.587984),(0.384252,-1.587991),(0.382483,-1.587995),(0.380986,-1.587998),(0.379764,-1.587999),(0.378825,-1.588000),(0.378183,-1.588000),(0.378000,-1.588000)]
L = [(0.000000,0.000000),(0.010000,0.025000),(0.020000,0.050000),(0.030000,0.075000),(0.040000,0.100000),(0.050000,0.125000),(0.060000,0.150000),(0.070000,0.175000),(0.080000,0.200000),(0.090000,0.225000),(0.100000,0.250000),(0.110000,0.275000),(0.120000,0.300000),(0.130000,0.325000),(0.140000,0.350000),(0.150000,0.375000),(0.160000,0.400000),(0.170000,0.425000),(0.180000,0.450000),(0.190000,0.475000),(0.200000,0.500000),(0.210000,0.525000),(0.220000,0.550000),(0.230000,0.575000),(0.240000,0.600000),(0.250000,0.625000),(0.260000,0.650000),(0.270000,0.675000),(0.280000,0.700000),(0.290000,0.725000),(0.300000,0.750000),(0.310000,0.775000),(0.320000,0.800000),(0.330000,0.825000),(0.340000,0.850000),(0.350000,0.875000),(0.360000,0.900000),(0.370000,0.925000),(0.380000,0.950000),(0.390000,0.975000),(0.400000,1.000000),(0.410000,1.025000),(0.420000,1.050000),(0.430000,1.075000),(0.440000,1.100000),(0.450000,1.125000),(0.460000,1.149999),(0.470000,1.174999),(0.480000,1.199999),(0.490000,1.224999),(0.500000,1.249999),(0.510000,1.274999),(0.520000,1.299999),(0.530000,1.324999),(0.540000,1.349999),(0.550000,1.374999),(0.560000,1.399999),(0.570000,1.424999),(0.580000,1.419067),(0.590000,1.402370),(0.600000,1.387675),(0.610000,1.374742),(0.620000,1.363371),(0.630000,1.353396),(0.640000,1.344673),(0.650000,1.337081),(0.660000,1.330515),(0.670000,1.324883),(0.680000,1.320105),(0.690000,1.316107),(0.700000,1.312825),(0.710000,1.310199),(0.720000,1.308177),(0.730000,1.306709),(0.740000,1.305749),(0.750000,1.305254),(0.760000,1.305186),(0.770000,1.305506),(0.780000,1.306180),(0.790000,1.307174),(0.800000,1.308460),(0.810000,1.310006),(0.820000,1.311786),(0.830000,1.313775),(0.839999,1.315948),(0.849999,1.318282),(0.859999,1.320757),(0.869999,1.323354),(0.879999,1.326053),(0.889999,1.328838),(0.899999,1.331694),(0.909999,1.334606),(0.919999,1.327007),(0.929999,1.301767),(0.939999,1.276523),(0.949999,1.251273),(0.959999,1.226018),(0.969999,1.200758),(0.979999,1.175492),(0.989999,1.150220),(0.999999,1.124943),(1.009999,1.099659),(1.019999,1.074368),(1.029999,1.049070),(1.039999,1.023764),(1.049999,0.998451),(1.059999,0.973130),(1.069999,0.947800),(1.079999,0.922462),(1.089999,0.897114),(1.099999,0.871755),(1.109999,0.846385),(1.119999,0.821005),(1.129999,0.795612),(1.139999,0.770207),(1.149999,0.744787),(1.159999,0.719352),(1.169999,0.693902),(1.179999,0.668434),(1.189999,0.642948),(1.199999,0.617442),(1.209999,0.591913),(1.219999,0.566362),(1.229999,0.540780),(1.239999,0.515171),(1.249999,0.489531),(1.259999,0.463857),(1.269999,0.438144),(1.279999,0.412386),(1.289999,0.386578),(1.299999,0.360711),(1.309999,0.334780),(1.319999,0.308769),(1.329999,0.282666),(1.339999,0.256450),(1.349999,0.230095),(1.359999,0.203564),(1.369999,0.176804),(1.379999,0.149730),(1.389999,0.122200),(1.399999,0.093929),(1.409999,0.064233),(1.419999,0.030238)]
A = [(0.000000,0.000000),(0.010000,0.058592),(0.020000,0.117400),(0.030000,0.176585),(0.040000,0.236306),(0.050000,0.296720),(0.060000,0.357982),(0.070000,0.420240),(0.080000,0.483638),(0.090000,0.548312),(0.100000,0.614385),(0.110000,0.681968),(0.120000,0.751155),(0.130000,0.822015),(0.140000,0.894592),(0.150000,0.968894),(0.160000,1.044885),(0.170000,1.122481),(0.180000,1.201536),(0.190000,1.281833),(0.200000,1.363069),(0.210000,1.444849),(0.220000,1.526670),(0.230000,1.607912),(0.240000,1.687831),(0.250000,1.765552),(0.260000,1.840068),(0.270000,1.910252),(0.280000,1.974866),(0.290000,2.032586),(0.300000,2.082038),(0.310000,2.121839),(0.320000,2.150647),(0.330000,2.167221),(0.340000,2.170477),(0.350000,2.159543),(0.360000,2.133806),(0.370000,2.092953),(0.380000,2.036981),(0.390000,1.966208),(0.400000,1.881247),(0.410000,1.782980),(0.420000,1.672506),(0.430000,1.551094),(0.440000,1.420123),(0.450000,1.281028),(0.460000,1.135253),(0.470000,0.984209),(0.480000,0.829248),(0.490000,0.671636),(0.500000,0.512549),(0.510000,0.353062),(0.520000,0.194161),(0.530000,0.036743),(0.540000,-0.118370),(0.550000,-0.270421),(0.560000,-0.418709),(0.570000,-0.562576),(0.580000,-0.683863),(0.590000,-0.785772),(0.600000,-0.875220),(0.610000,-0.953660),(0.620000,-1.022306),(0.630000,-1.082184),(0.640000,-1.134166),(0.650000,-1.179001),(0.660000,-1.217347),(0.670000,-1.249781),(0.680000,-1.276815),(0.690000,-1.298907),(0.700000,-1.316473),(0.710000,-1.329889),(0.720000,-1.339503),(0.730000,-1.345635),(0.740000,-1.348581),(0.750000,-1.348616),(0.760000,-1.346000),(0.770000,-1.340974),(0.780000,-1.333763),(0.790000,-1.324580),(0.800000,-1.313626),(0.810000,-1.301087),(0.820000,-1.287139),(0.830000,-1.271946),(0.839999,-1.255662),(0.849999,-1.238430),(0.859999,-1.220384),(0.869999,-1.201647),(0.879999,-1.182335),(0.889999,-1.162552),(0.899999,-1.142397),(0.909999,-1.121959),(0.919999,-1.092811),(0.929999,-1.050123),(0.939999,-1.008765),(0.949999,-0.968756),(0.959999,-0.930103),(0.969999,-0.892797),(0.979999,-0.856820),(0.989999,-0.822145),(0.999999,-0.788737),(1.009999,-0.756561),(1.019999,-0.725575),(1.029999,-0.695734),(1.039999,-0.666995),(1.049999,-0.639313),(1.059999,-0.612640),(1.069999,-0.586933),(1.079999,-0.562146),(1.089999,-0.538233),(1.099999,-0.515153),(1.109999,-0.492864),(1.119999,-0.471325),(1.129999,-0.450497),(1.139999,-0.430342),(1.149999,-0.410823),(1.159999,-0.391906),(1.169999,-0.373555),(1.179999,-0.355740),(1.189999,-0.338429),(1.199999,-0.321590),(1.209999,-0.305196),(1.219999,-0.289219),(1.229999,-0.273628),(1.239999,-0.258403),(1.249999,-0.243516),(1.259999,-0.228943),(1.269999,-0.214660),(1.279999,-0.200643),(1.289999,-0.186868),(1.299999,-0.173312),(1.309999,-0.159953),(1.319999,-0.146765),(1.329999,-0.133724),(1.339999,-0.120804),(1.349999,-0.107974),(1.359999,-0.095201),(1.369999,-0.082443),(1.379999,-0.069645),(1.389999,-0.056724),(1.399999,-0.043533),(1.409999,-0.029738),(1.419999,-0.013995)]
)";
 
const std::string skills_5 = R"(
X = [(-0.762000,-1.575000),(-0.762250,-1.575010),(-0.762749,-1.575031),(-0.763498,-1.575062),(-0.764497,-1.575103),(-0.765746,-1.575152),(-0.767245,-1.575209),(-0.768994,-1.575273),(-0.770993,-1.575344),(-0.773242,-1.575418),(-0.775740,-1.575496),(-0.778489,-1.575574),(-0.781488,-1.575652),(-0.784737,-1.575726),(-0.788236,-1.575795),(-0.791985,-1.575855),(-0.795984,-1.575903),(-0.800234,-1.575936),(-0.804734,-1.575951),(-0.809484,-1.575942),(-0.814484,-1.575906),(-0.819734,-1.575836),(-0.825233,-1.575729),(-0.830980,-1.575576),(-0.836977,-1.575373),(-0.843221,-1.575110),(-0.849713,-1.574780),(-0.856451,-1.574374),(-0.863433,-1.573881),(-0.870659,-1.573291),(-0.878126,-1.572590),(-0.885832,-1.571764),(-0.893774,-1.570800),(-0.901947,-1.569678),(-0.910347,-1.568380),(-0.918968,-1.566885),(-0.927803,-1.565169),(-0.936841,-1.563205),(-0.946073,-1.560965),(-0.955483,-1.558416),(-0.965055,-1.555522),(-0.974531,-1.552330),(-0.983895,-1.548823),(-0.993044,-1.545021),(-1.001870,-1.540966),(-1.010377,-1.536657),(-1.018571,-1.532094),(-1.026460,-1.527276),(-1.034056,-1.522201),(-1.041371,-1.516864),(-1.048417,-1.511260),(-1.055209,-1.505380),(-1.061751,-1.499223),(-1.068036,-1.492805),(-1.074058,-1.486139),(-1.079817,-1.479244),(-1.085314,-1.472139),(-1.090555,-1.464842),(-1.095547,-1.457373),(-1.100300,-1.449750),(-1.104826,-1.441990),(-1.109138,-1.434108),(-1.113250,-1.426120),(-1.117176,-1.418039),(-1.120931,-1.409877),(-1.124529,-1.401645),(-1.127985,-1.393352),(-1.131313,-1.385006),(-1.134891,-1.375638),(-1.138258,-1.366460),(-1.141438,-1.357485),(-1.144451,-1.348719),(-1.147315,-1.340171),(-1.150046,-1.331846),(-1.152657,-1.323748),(-1.155158,-1.315882),(-1.157559,-1.308251),(-1.159867,-1.300858),(-1.162088,-1.293704),(-1.164228,-1.286791),(-1.166290,-1.280120),(-1.168277,-1.273694),(-1.170192,-1.267512),(-1.172037,-1.261576),(-1.173811,-1.255886),(-1.175517,-1.250442),(-1.177155,-1.245244),(-1.178723,-1.240294),(-1.180223,-1.235591),(-1.181652,-1.231135),(-1.183011,-1.226926),(-1.184299,-1.222965),(-1.185513,-1.219252),(-1.186654,-1.215786),(-1.187719,-1.212568),(-1.188708,-1.209599),(-1.189619,-1.206879),(-1.190450,-1.204408),(-1.191201,-1.202187),(-1.191870,-1.200219),(-1.192455,-1.198503),(-1.192954,-1.197044),(-1.193365,-1.195844),(-1.193686,-1.194911),(-1.193912,-1.194255),(-1.194000,-1.194000)]
L = [(0.000000,0.000000),(0.010000,0.025000),(0.020000,0.050000),(0.030000,0.075000),(0.040000,0.100000),(0.050000,0.125000),(0.060000,0.150000),(0.070000,0.175000),(0.080000,0.200000),(0.090000,0.225000),(0.100000,0.250000),(0.110000,0.275000),(0.120000,0.300000),(0.130000,0.325000),(0.140000,0.350000),(0.150000,0.375000),(0.160000,0.400000),(0.170000,0.425000),(0.180000,0.450000),(0.190000,0.475000),(0.200000,0.500000),(0.210000,0.525000),(0.220000,0.550000),(0.230000,0.575000),(0.240000,0.600000),(0.250000,0.625000),(0.260000,0.650000),(0.270000,0.675000),(0.280000,0.700000),(0.290000,0.725000),(0.300000,0.750000),(0.310000,0.775000),(0.320000,0.800000),(0.330000,0.825000),(0.340000,0.850000),(0.350000,0.875000),(0.360000,0.900000),(0.370000,0.925000),(0.380000,0.950000),(0.390000,0.975000),(0.400000,1.000000),(0.410000,1.000000),(0.420000,1.000000),(0.430000,0.990747),(0.440000,0.971369),(0.450000,0.953656),(0.460000,0.937932),(0.470000,0.924496),(0.480000,0.913615),(0.490000,0.905517),(0.500000,0.900390),(0.510000,0.898385),(0.520000,0.898385),(0.530000,0.898385),(0.540000,0.898385),(0.550000,0.898385),(0.560000,0.898385),(0.570000,0.898385),(0.580000,0.898385),(0.590000,0.898385),(0.600000,0.898385),(0.610000,0.898385),(0.620000,0.898385),(0.630000,0.898385),(0.640000,0.898385),(0.650000,0.898385),(0.660000,0.898385),(0.670000,0.898385),(0.680000,1.002725),(0.690000,0.977405),(0.700000,0.952077),(0.710000,0.926740),(0.720000,0.901393),(0.730000,0.876036),(0.740000,0.850669),(0.750000,0.825291),(0.760000,0.799900),(0.770000,0.774496),(0.780000,0.749079),(0.790000,0.723647),(0.800000,0.698199),(0.810000,0.672734),(0.820000,0.647251),(0.830000,0.621748),(0.839999,0.596224),(0.849999,0.570677),(0.859999,0.545103),(0.869999,0.519502),(0.879999,0.493869),(0.889999,0.468203),(0.899999,0.442498),(0.909999,0.416750),(0.919999,0.390952),(0.929999,0.365098),(0.939999,0.339179),(0.949999,0.313184),(0.959999,0.287097),(0.969999,0.260902),(0.979999,0.234575),(0.989999,0.208079),(0.999999,0.181363),(1.009999,0.154352),(1.019999,0.126912),(1.029999,0.098791),(1.039999,0.069443),(1.049999,0.036763)]
A = [(0.000000,0.000000),(0.010000,-0.021516),(0.020000,-0.043145),(0.030000,-0.064974),(0.040000,-0.087091),(0.050000,-0.109586),(0.060000,-0.132555),(0.070000,-0.156095),(0.080000,-0.180312),(0.090000,-0.205317),(0.100000,-0.231229),(0.110000,-0.258177),(0.120000,-0.286299),(0.130000,-0.315747),(0.140000,-0.346687),(0.150000,-0.379300),(0.160000,-0.413791),(0.170000,-0.450381),(0.180000,-0.489318),(0.190000,-0.530881),(0.200000,-0.575379),(0.210000,-0.623159),(0.220000,-0.674615),(0.230000,-0.730187),(0.240000,-0.790373),(0.250000,-0.855738),(0.260000,-0.926920),(0.270000,-1.004641),(0.280000,-1.089721),(0.290000,-1.183084),(0.300000,-1.285773),(0.310000,-1.398962),(0.320000,-1.523958),(0.330000,-1.662209),(0.340000,-1.815292),(0.350000,-1.984895),(0.360000,-2.172763),(0.370000,-2.380606),(0.380000,-2.609993),(0.390000,-2.862090),(0.400000,-3.137347),(0.410000,-3.345989),(0.420000,-3.558074),(0.430000,-3.732295),(0.440000,-3.852156),(0.450000,-3.955978),(0.460000,-4.041655),(0.470000,-4.107427),(0.480000,-4.151941),(0.490000,-4.174255),(0.500000,-4.173797),(0.510000,-4.150355),(0.520000,-4.098535),(0.530000,-4.010369),(0.540000,-3.888837),(0.550000,-3.738239),(0.560000,-3.563809),(0.570000,-3.371151),(0.580000,-3.165840),(0.590000,-2.953067),(0.600000,-2.737389),(0.610000,-2.522618),(0.620000,-2.311778),(0.630000,-2.107193),(0.640000,-1.910468),(0.650000,-1.722667),(0.660000,-1.544405),(0.670000,-1.375938),(0.680000,-1.338752),(0.690000,-1.130228),(0.700000,-0.946206),(0.710000,-0.784092),(0.720000,-0.641497),(0.730000,-0.516259),(0.740000,-0.406446),(0.750000,-0.310341),(0.760000,-0.226430),(0.770000,-0.153376),(0.780000,-0.090006),(0.790000,-0.035286),(0.800000,0.011695),(0.810000,0.051741),(0.820000,0.085563),(0.830000,0.113790),(0.839999,0.136983),(0.849999,0.155640),(0.859999,0.170206),(0.869999,0.181080),(0.879999,0.188619),(0.889999,0.193147),(0.899999,0.194953),(0.909999,0.194300),(0.919999,0.191426),(0.929999,0.186548),(0.939999,0.179861),(0.949999,0.171542),(0.959999,0.161754),(0.969999,0.150643),(0.979999,0.138341),(0.989999,0.124961),(0.999999,0.110601),(1.009999,0.095335),(1.019999,0.079194),(1.029999,0.062131),(1.039999,0.043912),(1.049999,0.023296)]
)";
 
const std::string skills_6 = R"(
X = [(-1.501000,-1.194000),(-1.500750,-1.194006),(-1.500251,-1.194018),(-1.499501,-1.194035),(-1.498501,-1.194057),(-1.497251,-1.194082),(-1.495752,-1.194109),(-1.494002,-1.194137),(-1.492002,-1.194164),(-1.489752,-1.194187),(-1.487252,-1.194204),(-1.484502,-1.194213),(-1.481502,-1.194210),(-1.478252,-1.194191),(-1.474753,-1.194154),(-1.471003,-1.194092),(-1.467004,-1.194003),(-1.462756,-1.193880),(-1.458259,-1.193718),(-1.453513,-1.193511),(-1.448520,-1.193252),(-1.443280,-1.192933),(-1.437793,-1.192547),(-1.432062,-1.192084),(-1.426087,-1.191536),(-1.419870,-1.190891),(-1.413414,-1.190139),(-1.406721,-1.189267),(-1.399794,-1.188261),(-1.392636,-1.187109),(-1.385252,-1.185793),(-1.377648,-1.184297),(-1.369830,-1.182604),(-1.361804,-1.180693),(-1.353580,-1.178543),(-1.345169,-1.176134),(-1.336582,-1.173440),(-1.327833,-1.170439),(-1.318938,-1.167103),(-1.309916,-1.163406),(-1.300789,-1.159322),(-1.291687,-1.154877),(-1.282822,-1.150163),(-1.274195,-1.145181),(-1.265802,-1.139929),(-1.257642,-1.134409),(-1.249712,-1.128618),(-1.242009,-1.122556),(-1.234529,-1.116222),(-1.227269,-1.109613),(-1.220227,-1.102728),(-1.213399,-1.095566),(-1.206783,-1.088123),(-1.200376,-1.080400),(-1.194177,-1.072394),(-1.188184,-1.064106),(-1.182396,-1.055535),(-1.176811,-1.046683),(-1.171429,-1.037551),(-1.166249,-1.028141),(-1.161269,-1.018459),(-1.156490,-1.008508),(-1.151908,-0.998294),(-1.147524,-0.987824),(-1.143336,-0.977106),(-1.139340,-0.966146),(-1.135534,-0.954954),(-1.131916,-0.943538),(-1.128482,-0.931910),(-1.125227,-0.920077),(-1.122149,-0.908050),(-1.119241,-0.895839),(-1.116500,-0.883454),(-1.113921,-0.870904),(-1.111497,-0.858198),(-1.109223,-0.845345),(-1.107095,-0.832355),(-1.105105,-0.819234),(-1.103249,-0.805992),(-1.101520,-0.792635),(-1.099914,-0.779171),(-1.098423,-0.765607),(-1.097044,-0.751948),(-1.095769,-0.738201),(-1.094595,-0.724370),(-1.093515,-0.710462),(-1.092524,-0.696479),(-1.091618,-0.682428),(-1.090792,-0.668312),(-1.090040,-0.654135),(-1.089359,-0.639900),(-1.088744,-0.625611),(-1.088191,-0.611270),(-1.087696,-0.596881),(-1.087255,-0.582446),(-1.086863,-0.567967),(-1.086518,-0.553447),(-1.086216,-0.538887),(-1.085953,-0.524291),(-1.085726,-0.509658),(-1.085532,-0.494991),(-1.085368,-0.480292),(-1.085231,-0.465561),(-1.085118,-0.450801),(-1.085027,-0.436013),(-1.084954,-0.421252),(-1.084898,-0.406743),(-1.084856,-0.392485),(-1.084825,-0.378479),(-1.084803,-0.364725),(-1.084786,-0.351223),(-1.084774,-0.337973),(-1.084765,-0.324974),(-1.084758,-0.312228),(-1.084750,-0.299734),(-1.084741,-0.287492),(-1.084730,-0.275503),(-1.084716,-0.263766),(-1.084699,-0.252281),(-1.084678,-0.241048),(-1.084653,-0.230069),(-1.084623,-0.219342),(-1.084588,-0.208868),(-1.084548,-0.198647),(-1.084503,-0.188679),(-1.084453,-0.178964),(-1.084398,-0.169502),(-1.084339,-0.160293),(-1.084274,-0.151338),(-1.084206,-0.142637),(-1.084134,-0.134190),(-1.084057,-0.125996),(-1.083978,-0.118057),(-1.083895,-0.110371),(-1.083809,-0.102940),(-1.083722,-0.095763),(-1.083632,-0.088841),(-1.083542,-0.082174),(-1.083450,-0.075761),(-1.083357,-0.069603),(-1.083265,-0.063701),(-1.083172,-0.058054),(-1.083081,-0.052665),(-1.082991,-0.047531),(-1.082902,-0.042653),(-1.082815,-0.038033),(-1.082731,-0.033671),(-1.082650,-0.029566),(-1.082572,-0.025720),(-1.082497,-0.022132),(-1.082426,-0.018804),(-1.082360,-0.015737),(-1.082298,-0.012931),(-1.082241,-0.010387),(-1.082189,-0.008107),(-1.082143,-0.006093),(-1.082103,-0.004347),(-1.082068,-0.002872),(-1.082040,-0.001673),(-1.082018,-0.000758),(-1.082003,-0.000142),(-1.082000,0.000000)]
L = [(0.000000,0.000000),(0.010000,0.025000),(0.020000,0.050000),(0.030000,0.075000),(0.040000,0.100000),(0.050000,0.125000),(0.060000,0.150000),(0.070000,0.175000),(0.080000,0.200000),(0.090000,0.225000),(0.100000,0.250000),(0.110000,0.275000),(0.120000,0.300000),(0.130000,0.325000),(0.140000,0.350000),(0.150000,0.375000),(0.160000,0.400000),(0.170000,0.425000),(0.180000,0.450000),(0.190000,0.475000),(0.200000,0.500000),(0.210000,0.525000),(0.220000,0.550000),(0.230000,0.575000),(0.240000,0.600000),(0.250000,0.625000),(0.260000,0.650000),(0.270000,0.675000),(0.280000,0.700000),(0.290000,0.725000),(0.300000,0.750000),(0.310000,0.775000),(0.320000,0.800000),(0.330000,0.825000),(0.340000,0.850000),(0.350000,0.875000),(0.360000,0.900000),(0.370000,0.925000),(0.380000,0.950000),(0.390000,0.975000),(0.400000,1.000000),(0.410000,1.013053),(0.420000,1.004058),(0.430000,0.996364),(0.440000,0.990069),(0.450000,0.985254),(0.460000,0.981982),(0.470000,0.980296),(0.480000,0.980223),(0.490000,0.981766),(0.500000,0.984912),(0.510000,0.989625),(0.520000,0.995853),(0.530000,1.003526),(0.540000,1.012557),(0.550000,1.022844),(0.560000,1.034273),(0.570000,1.046719),(0.580000,1.060049),(0.590000,1.074125),(0.600000,1.088807),(0.610000,1.103953),(0.620000,1.119429),(0.630000,1.135103),(0.640000,1.150851),(0.650000,1.166562),(0.660000,1.182134),(0.670000,1.197477),(0.680000,1.212513),(0.690000,1.227180),(0.700000,1.241424),(0.710000,1.255206),(0.720000,1.268493),(0.730000,1.281266),(0.740000,1.293513),(0.750000,1.305229),(0.760000,1.316415),(0.770000,1.327077),(0.780000,1.337227),(0.790000,1.346877),(0.800000,1.356045),(0.810000,1.364748),(0.820000,1.373005),(0.830000,1.380837),(0.839999,1.388263),(0.849999,1.395306),(0.859999,1.401984),(0.869999,1.408318),(0.879999,1.414326),(0.889999,1.420028),(0.899999,1.425442),(0.909999,1.430583),(0.919999,1.435469),(0.929999,1.440114),(0.939999,1.444534),(0.949999,1.448742),(0.959999,1.452750),(0.969999,1.456571),(0.979999,1.460216),(0.989999,1.463696),(0.999999,1.467021),(1.009999,1.470201),(1.019999,1.473242),(1.029999,1.476155),(1.039999,1.478947),(1.049999,1.476184),(1.059999,1.450969),(1.069999,1.425750),(1.079999,1.400526),(1.089999,1.375299),(1.099999,1.350068),(1.109999,1.324832),(1.119999,1.299592),(1.129999,1.274347),(1.139999,1.249097),(1.149999,1.223841),(1.159999,1.198581),(1.169999,1.173315),(1.179999,1.148043),(1.189999,1.122764),(1.199999,1.097479),(1.209999,1.072188),(1.219999,1.046889),(1.229999,1.021583),(1.239999,0.996269),(1.249999,0.970947),(1.259999,0.945617),(1.269999,0.920277),(1.279999,0.894928),(1.289999,0.869569),(1.299999,0.844200),(1.309999,0.818818),(1.319999,0.793425),(1.329999,0.768018),(1.339999,0.742597),(1.349999,0.717162),(1.359999,0.691711),(1.369999,0.666242),(1.379999,0.640755),(1.389999,0.615243),(1.399999,0.589711),(1.409999,0.564154),(1.419999,0.538572),(1.429999,0.512962),(1.439999,0.487318),(1.449999,0.461640),(1.459999,0.435923),(1.469999,0.410160),(1.479999,0.384347),(1.489999,0.358475),(1.499999,0.332537),(1.509999,0.306519),(1.519999,0.280406),(1.529999,0.254181),(1.539999,0.227813),(1.549999,0.201267),(1.559999,0.174486),(1.569999,0.147379),(1.579999,0.119798),(1.589999,0.091444),(1.599999,0.061536),(1.609999,0.026621)]
A = [(0.000000,0.000000),(0.010000,0.033939),(0.020000,0.068032),(0.030000,0.102395),(0.040000,0.137148),(0.050000,0.172412),(0.060000,0.208312),(0.070000,0.244978),(0.080000,0.282546),(0.090000,0.321157),(0.100000,0.360962),(0.110000,0.402117),(0.120000,0.444792),(0.130000,0.489166),(0.140000,0.535430),(0.150000,0.583791),(0.160000,0.634467),(0.170000,0.687696),(0.180000,0.743733),(0.190000,0.802851),(0.200000,0.865347),(0.210000,0.931534),(0.220000,1.001751),(0.230000,1.076359),(0.240000,1.155738),(0.250000,1.240291),(0.260000,1.330436),(0.270000,1.426602),(0.280000,1.529223),(0.290000,1.638725),(0.300000,1.755508),(0.310000,1.879930),(0.320000,2.012273),(0.330000,2.152709),(0.340000,2.301253),(0.350000,2.457702),(0.360000,2.621574),(0.370000,2.792027),(0.380000,2.967772),(0.390000,3.147003),(0.400000,3.327315),(0.410000,3.463770),(0.420000,3.513194),(0.430000,3.552294),(0.440000,3.580596),(0.450000,3.597783),(0.460000,3.603683),(0.470000,3.598276),(0.480000,3.581684),(0.490000,3.554164),(0.500000,3.516099),(0.510000,3.467986),(0.520000,3.410421),(0.530000,3.344091),(0.540000,3.269755),(0.550000,3.188236),(0.560000,3.100397),(0.570000,3.007136),(0.580000,2.909364),(0.590000,2.807987),(0.600000,2.703904),(0.610000,2.597973),(0.620000,2.491020),(0.630000,2.383808),(0.640000,2.277042),(0.650000,2.171354),(0.660000,2.067301),(0.670000,1.965365),(0.680000,1.865947),(0.690000,1.769380),(0.700000,1.675915),(0.710000,1.585754),(0.720000,1.499027),(0.730000,1.415812),(0.740000,1.336144),(0.750000,1.260018),(0.760000,1.187390),(0.770000,1.118194),(0.780000,1.052352),(0.790000,0.989751),(0.800000,0.930276),(0.810000,0.873802),(0.820000,0.820197),(0.830000,0.769327),(0.839999,0.721059),(0.849999,0.675256),(0.859999,0.631790),(0.869999,0.590531),(0.879999,0.551357),(0.889999,0.514148),(0.899999,0.478791),(0.909999,0.445177),(0.919999,0.413203),(0.929999,0.382771),(0.939999,0.353790),(0.949999,0.326172),(0.959999,0.299835),(0.969999,0.274703),(0.979999,0.250703),(0.989999,0.227767),(0.999999,0.205832),(1.009999,0.184839),(1.019999,0.164731),(1.029999,0.145458),(1.039999,0.126970),(1.049999,0.108885),(1.059999,0.090536),(1.069999,0.073710),(1.079999,0.058284),(1.089999,0.044146),(1.099999,0.031193),(1.109999,0.019337),(1.119999,0.008495),(1.129999,-0.001407),(1.139999,-0.010436),(1.149999,-0.018654),(1.159999,-0.026115),(1.169999,-0.032871),(1.179999,-0.038968),(1.189999,-0.044449),(1.199999,-0.049353),(1.209999,-0.053716),(1.219999,-0.057572),(1.229999,-0.060950),(1.239999,-0.063879),(1.249999,-0.066386),(1.259999,-0.068495),(1.269999,-0.070228),(1.279999,-0.071608),(1.289999,-0.072654),(1.299999,-0.073384),(1.309999,-0.073817),(1.319999,-0.073967),(1.329999,-0.073851),(1.339999,-0.073484),(1.349999,-0.072878),(1.359999,-0.072047),(1.369999,-0.071003),(1.379999,-0.069758),(1.389999,-0.068322),(1.399999,-0.066706),(1.409999,-0.064920),(1.419999,-0.062974),(1.429999,-0.060877),(1.439999,-0.058636),(1.449999,-0.056261),(1.459999,-0.053759),(1.469999,-0.051138),(1.479999,-0.048405),(1.489999,-0.045566),(1.499999,-0.042628),(1.509999,-0.039596),(1.519999,-0.036476),(1.529999,-0.033271),(1.539999,-0.029985),(1.549999,-0.026620),(1.559999,-0.023174),(1.569999,-0.019642),(1.579999,-0.016012),(1.589999,-0.012248),(1.599999,-0.008254),(1.609999,-0.003572)]
)";
 
const std::string skills_test = R"(
X = [(-0.924000,0.924000),(-0.923857,0.923795),(-0.923573,0.923384),(-0.923145,0.922768),(-0.922577,0.921946),(-0.921867,0.920916),(-0.921018,0.919680),(-0.920030,0.918236),(-0.918905,0.916582),(-0.917644,0.914719),(-0.916249,0.912644),(-0.914722,0.910357),(-0.913067,0.907855),(-0.911284,0.905138),(-0.909378,0.902203),(-0.907351,0.899049),(-0.905207,0.895672),(-0.902950,0.892071),(-0.900584,0.888243),(-0.898114,0.884186),(-0.895546,0.879896),(-0.892885,0.875370),(-0.890138,0.870605),(-0.887312,0.865598),(-0.884414,0.860344),(-0.881453,0.854840),(-0.878438,0.849081),(-0.875380,0.843064),(-0.872290,0.836783),(-0.869181,0.830233),(-0.866065,0.823411),(-0.862959,0.816312),(-0.859878,0.808929),(-0.856840,0.801259),(-0.853866,0.793297),(-0.850977,0.785038),(-0.848197,0.776478),(-0.845551,0.767615),(-0.843066,0.758446),(-0.840773,0.748970),(-0.838702,0.739187),(-0.836888,0.729099),(-0.835383,0.718861),(-0.834224,0.708660),(-0.833412,0.698493),(-0.832944,0.688354),(-0.832819,0.678236),(-0.833037,0.668132),(-0.833597,0.658031),(-0.834497,0.647924),(-0.835738,0.637800),(-0.837320,0.627647),(-0.839242,0.617453),(-0.841506,0.607204),(-0.844110,0.596888),(-0.847056,0.586488),(-0.850344,0.575991),(-0.853972,0.565379),(-0.857938,0.554636),(-0.862237,0.543753),(-0.866855,0.532730),(-0.871776,0.521564),(-0.876979,0.510251),(-0.882444,0.498785),(-0.888144,0.487155),(-0.894054,0.475350),(-0.900141,0.463355),(-0.906372,0.451153),(-0.912710,0.438725),(-0.919114,0.426050),(-0.925342,0.413510),(-0.931267,0.401278),(-0.936881,0.389309),(-0.942179,0.377568),(-0.947154,0.366022),(-0.951802,0.354646),(-0.956122,0.343417),(-0.960109,0.332316),(-0.963764,0.321324),(-0.967086,0.310426),(-0.970076,0.299607),(-0.972734,0.288854),(-0.975060,0.278156),(-0.977056,0.267501),(-0.978724,0.256878),(-0.980065,0.246277),(-0.981079,0.235689),(-0.981769,0.225105),(-0.982135,0.214518),(-0.982178,0.203921),(-0.981899,0.193308),(-0.981299,0.182672),(-0.980379,0.172010),(-0.979140,0.161319),(-0.977583,0.150595),(-0.975709,0.139836),(-0.973521,0.129044),(-0.971021,0.118217),(-0.968212,0.107356),(-0.965097,0.096464),(-0.961681,0.085541),(-0.957967,0.074592),(-0.953961,0.063618),(-0.949669,0.052625),(-0.945096,0.041616),(-0.940251,0.030595),(-0.935140,0.019567),(-0.929770,0.008535),(-0.924150,-0.002496),(-0.918287,-0.013522),(-0.912190,-0.024539),(-0.905868,-0.035543),(-0.899327,-0.046532),(-0.892577,-0.057501),(-0.885626,-0.068447),(-0.878482,-0.079369),(-0.871153,-0.090263),(-0.863646,-0.101128),(-0.855969,-0.111962),(-0.848128,-0.122763),(-0.840132,-0.133529),(-0.831986,-0.144261),(-0.823696,-0.154956),(-0.815270,-0.165614),(-0.806712,-0.176234),(-0.802000,-0.182000),(-0.802000,-0.182000),(-0.796797,-0.194148),(-0.791793,-0.206266),(-0.786999,-0.218350),(-0.782425,-0.230394),(-0.778082,-0.242391),(-0.773980,-0.254334),(-0.770130,-0.266216),(-0.766541,-0.278029),(-0.763226,-0.289765),(-0.760192,-0.301416),(-0.757449,-0.312974),(-0.755006,-0.324432),(-0.752870,-0.335781),(-0.751047,-0.347015),(-0.749545,-0.358129),(-0.748366,-0.369117),(-0.747514,-0.379976),(-0.746993,-0.390706),(-0.746802,-0.401305),(-0.746944,-0.411776),(-0.747419,-0.422123),(-0.748227,-0.432351),(-0.749368,-0.442470),(-0.750842,-0.452488),(-0.752649,-0.462417),(-0.754792,-0.472269),(-0.757271,-0.482059),(-0.760088,-0.491802),(-0.763247,-0.501513),(-0.766751,-0.511209),(-0.770605,-0.520909),(-0.774811,-0.530628),(-0.779374,-0.540383),(-0.784296,-0.550194),(-0.789580,-0.560076),(-0.795225,-0.570045),(-0.801218,-0.580100),(-0.807547,-0.590245),(-0.814194,-0.600483),(-0.821141,-0.610821),(-0.828371,-0.621271),(-0.835862,-0.631843),(-0.843595,-0.642550),(-0.851546,-0.653406),(-0.859695,-0.664428),(-0.868017,-0.675631),(-0.876436,-0.686957),(-0.884683,-0.698095),(-0.892743,-0.709057),(-0.900601,-0.719855),(-0.908244,-0.730495),(-0.915665,-0.740983),(-0.922856,-0.751323),(-0.929814,-0.761517),(-0.936536,-0.771565),(-0.943020,-0.781468),(-0.949266,-0.791223),(-0.955276,-0.800828),(-0.961053,-0.810281),(-0.966598,-0.819578),(-0.971916,-0.828715),(-0.977010,-0.837690),(-0.981886,-0.846496),(-0.986548,-0.855130),(-0.991003,-0.863589),(-0.995255,-0.871868),(-0.999310,-0.879962),(-1.003175,-0.887868),(-1.006854,-0.895582),(-1.010355,-0.903100),(-1.013683,-0.910418),(-1.016844,-0.917534),(-1.019843,-0.924442),(-1.022687,-0.931141),(-1.025381,-0.937628),(-1.027930,-0.943899),(-1.030339,-0.949952),(-1.032614,-0.955784),(-1.034759,-0.961393),(-1.036778,-0.966776),(-1.038677,-0.971931),(-1.040459,-0.976857),(-1.042129,-0.981551),(-1.043690,-0.986012),(-1.045145,-0.990237),(-1.046499,-0.994225),(-1.047753,-0.997974),(-1.048912,-1.001483),(-1.049977,-1.004749),(-1.050952,-1.007772),(-1.051838,-1.010549),(-1.052637,-1.013080),(-1.053351,-1.015361),(-1.053981,-1.017391),(-1.054529,-1.019168),(-1.054994,-1.020687),(-1.055378,-1.021946),(-1.055679,-1.022937),(-1.055894,-1.023651),(-1.056000,-1.024000)]
L = [(0.000000,0.000000),(0.010000,0.025000),(0.020000,0.050000),(0.030000,0.075000),(0.040000,0.100000),(0.050000,0.125000),(0.060000,0.150000),(0.070000,0.175000),(0.080000,0.200000),(0.090000,0.225000),(0.100000,0.250000),(0.110000,0.275000),(0.120000,0.300000),(0.130000,0.325000),(0.140000,0.350000),(0.150000,0.375000),(0.160000,0.400000),(0.170000,0.425000),(0.180000,0.450000),(0.190000,0.475000),(0.200000,0.500000),(0.210000,0.525000),(0.220000,0.550000),(0.230000,0.575000),(0.240000,0.600000),(0.250000,0.625000),(0.260000,0.650000),(0.270000,0.675000),(0.280000,0.700000),(0.290000,0.725000),(0.300000,0.750000),(0.310000,0.775000),(0.320000,0.800000),(0.330000,0.825000),(0.340000,0.850000),(0.350000,0.875000),(0.360000,0.900000),(0.370000,0.925000),(0.380000,0.950000),(0.390000,0.975000),(0.400000,1.000000),(0.410000,1.025000),(0.420000,1.034918),(0.430000,1.026677),(0.440000,1.019999),(0.450000,1.015033),(0.460000,1.011914),(0.470000,1.010761),(0.480000,1.011676),(0.490000,1.014742),(0.500000,1.020029),(0.510000,1.027584),(0.520000,1.037442),(0.530000,1.049621),(0.540000,1.064126),(0.550000,1.080948),(0.560000,1.100075),(0.570000,1.121487),(0.580000,1.145169),(0.590000,1.170169),(0.600000,1.195168),(0.610000,1.220168),(0.620000,1.245168),(0.630000,1.270168),(0.640000,1.295168),(0.650000,1.320168),(0.660000,1.345168),(0.670000,1.370168),(0.680000,1.395168),(0.690000,1.420168),(0.700000,1.400239),(0.710000,1.359342),(0.720000,1.322229),(0.730000,1.288396),(0.740000,1.257478),(0.750000,1.229208),(0.760000,1.203401),(0.770000,1.179923),(0.780000,1.158683),(0.790000,1.139615),(0.800000,1.122672),(0.810000,1.107817),(0.820000,1.095018),(0.830000,1.084243),(0.839999,1.075453),(0.849999,1.068607),(0.859999,1.063651),(0.869999,1.060526),(0.879999,1.059162),(0.889999,1.059477),(0.899999,1.061380),(0.909999,1.064772),(0.919999,1.069545),(0.929999,1.075582),(0.939999,1.082763),(0.949999,1.090961),(0.959999,1.100049),(0.969999,1.109895),(0.979999,1.120375),(0.989999,1.131362),(0.999999,1.142738),(1.009999,1.154389),(1.019999,1.166209),(1.029999,1.178101),(1.039999,1.189978),(1.049999,1.201764),(1.059999,1.213390),(1.069999,1.224799),(1.079999,1.235943),(1.089999,1.246784),(1.099999,1.257292),(1.109999,1.267444),(1.119999,1.277223),(1.129999,1.286620),(1.139999,1.295631),(1.149999,1.304255),(1.159999,1.312494),(1.169999,1.320357),(1.179999,1.327850),(1.189999,1.334985),(1.199999,1.341774),(1.209999,1.348229),(1.219999,1.354365),(1.229999,1.360193),(1.239999,1.365730),(1.249999,1.370989),(1.249999,1.370989),(1.259999,1.321521),(1.269999,1.311115),(1.279999,1.300055),(1.289999,1.288324),(1.299999,1.275909),(1.309999,1.262811),(1.319999,1.249039),(1.329999,1.234617),(1.339999,1.219584),(1.349999,1.204003),(1.359999,1.187951),(1.369999,1.171535),(1.379999,1.154882),(1.389999,1.138147),(1.399999,1.121506),(1.409999,1.105159),(1.419999,1.089323),(1.429999,1.074229),(1.439999,1.060119),(1.449999,1.047236),(1.459999,1.035821),(1.469999,1.026107),(1.479999,1.018310),(1.489999,1.012631),(1.499999,1.009247),(1.509999,1.008310),(1.519999,1.009945),(1.529999,1.014249),(1.539999,1.021287),(1.549999,1.031095),(1.559999,1.043676),(1.569999,1.059000),(1.579999,1.077003),(1.589999,1.097589),(1.599999,1.120624),(1.609999,1.145624),(1.619999,1.170624),(1.629999,1.195624),(1.639999,1.220623),(1.649999,1.245623),(1.659999,1.270623),(1.669999,1.295623),(1.679999,1.320623),(1.689999,1.345623),(1.699999,1.370623),(1.709999,1.395623),(1.719999,1.411210),(1.729999,1.385985),(1.739999,1.360755),(1.749999,1.335521),(1.759999,1.310283),(1.769999,1.285040),(1.779999,1.259792),(1.789999,1.234539),(1.799999,1.209280),(1.809999,1.184016),(1.819999,1.158747),(1.829999,1.133471),(1.839999,1.108189),(1.849999,1.082900),(1.859999,1.057604),(1.869999,1.032300),(1.879999,1.006987),(1.889999,0.981669),(1.899999,0.956342),(1.909999,0.931007),(1.919999,0.905662),(1.929999,0.880307),(1.939999,0.854941),(1.949998,0.829565),(1.959998,0.804177),(1.969998,0.778776),(1.979998,0.753361),(1.989998,0.727932),(1.999998,0.702488),(2.009999,0.677026),(2.019999,0.651547),(2.029999,0.626047),(2.039999,0.600527),(2.049999,0.574984),(2.059999,0.549415),(2.069999,0.523819),(2.079998,0.498192),(2.089998,0.472527),(2.099998,0.446825),(2.109998,0.421081),(2.119998,0.395290),(2.129998,0.369445),(2.139998,0.343536),(2.149998,0.317552),(2.159998,0.291482),(2.169998,0.265307),(2.179998,0.239003),(2.189998,0.212539),(2.199998,0.185865),(2.209998,0.158910),(2.219998,0.131553),(2.229998,0.103580),(2.239998,0.074501),(2.249998,0.042711)]
A = [(0.000000,-0.000000),(0.010000,-0.030304),(0.020000,-0.060743),(0.030000,-0.091421),(0.040000,-0.122442),(0.050000,-0.153913),(0.060000,-0.185946),(0.070000,-0.218654),(0.080000,-0.252158),(0.090000,-0.286584),(0.100000,-0.322063),(0.110000,-0.358737),(0.120000,-0.396755),(0.130000,-0.436277),(0.140000,-0.477474),(0.150000,-0.520530),(0.160000,-0.565644),(0.170000,-0.613030),(0.180000,-0.662918),(0.190000,-0.715557),(0.200000,-0.771217),(0.210000,-0.830187),(0.220000,-0.892780),(0.230000,-0.959333),(0.240000,-1.030204),(0.250000,-1.105775),(0.260000,-1.186448),(0.270000,-1.272643),(0.280000,-1.364792),(0.290000,-1.463329),(0.300000,-1.568680),(0.310000,-1.681233),(0.320000,-1.801339),(0.330000,-1.929253),(0.340000,-2.065099),(0.350000,-2.208813),(0.360000,-2.360070),(0.370000,-2.518205),(0.380000,-2.682111),(0.390000,-2.850132),(0.400000,-3.019962),(0.410000,-3.188541),(0.420000,-3.302744),(0.430000,-3.344420),(0.440000,-3.373466),(0.450000,-3.389045),(0.460000,-3.390479),(0.470000,-3.377228),(0.480000,-3.348903),(0.490000,-3.305244),(0.500000,-3.246119),(0.510000,-3.171498),(0.520000,-3.081443),(0.530000,-2.976090),(0.540000,-2.855627),(0.550000,-2.720236),(0.560000,-2.570117),(0.570000,-2.405427),(0.580000,-2.226251),(0.590000,-2.031117),(0.600000,-1.818905),(0.610000,-1.591168),(0.620000,-1.349203),(0.630000,-1.093999),(0.640000,-0.826203),(0.650000,-0.546119),(0.660000,-0.253740),(0.670000,0.051189),(0.680000,0.369083),(0.690000,0.700397),(0.700000,1.002962),(0.710000,1.265107),(0.720000,1.503227),(0.730000,1.720069),(0.740000,1.917585),(0.750000,2.097151),(0.760000,2.259725),(0.770000,2.405982),(0.780000,2.536403),(0.790000,2.651363),(0.800000,2.751175),(0.810000,2.836139),(0.820000,2.906561),(0.830000,2.962820),(0.839999,3.005329),(0.849999,3.034570),(0.859999,3.051092),(0.869999,3.055506),(0.879999,3.048491),(0.889999,3.030776),(0.899999,3.003143),(0.909999,2.966406),(0.919999,2.921420),(0.929999,2.869052),(0.939999,2.810179),(0.949999,2.745677),(0.959999,2.676429),(0.969999,2.603265),(0.979999,2.527004),(0.989999,2.448424),(0.999999,2.368249),(1.009999,2.287157),(1.019999,2.205760),(1.029999,2.124615),(1.039999,2.044209),(1.049999,1.964967),(1.059999,1.887256),(1.069999,1.811375),(1.079999,1.737571),(1.089999,1.666034),(1.099999,1.596910),(1.109999,1.530301),(1.119999,1.466271),(1.129999,1.404846),(1.139999,1.346033),(1.149999,1.289806),(1.159999,1.236125),(1.169999,1.184934),(1.179999,1.136162),(1.189999,1.089732),(1.199999,1.045559),(1.209999,1.003552),(1.219999,0.963623),(1.229999,0.925676),(1.239999,0.889616),(1.249999,0.872249),(1.249999,-1.281714),(1.259999,-1.317879),(1.269999,-1.395835),(1.279999,-1.478613),(1.289999,-1.566296),(1.299999,-1.658901),(1.309999,-1.756360),(1.319999,-1.858500),(1.329999,-1.965022),(1.339999,-2.075473),(1.349999,-2.189253),(1.359999,-2.305565),(1.369999,-2.423424),(1.379999,-2.541654),(1.389999,-2.658890),(1.399999,-2.773605),(1.409999,-2.884124),(1.419999,-2.988689),(1.429999,-3.085477),(1.439999,-3.172683),(1.449999,-3.248552),(1.459999,-3.311448),(1.469999,-3.359891),(1.479999,-3.392592),(1.489999,-3.408490),(1.499999,-3.406747),(1.509999,-3.386771),(1.519999,-3.348206),(1.529999,-3.290914),(1.539999,-3.214981),(1.549999,-3.120698),(1.559999,-3.008524),(1.569999,-2.879125),(1.579999,-2.733332),(1.589999,-2.572143),(1.599999,-2.396706),(1.609999,-2.207768),(1.619999,-2.004373),(1.629999,-1.790139),(1.639999,-1.568468),(1.649999,-1.342457),(1.659999,-1.114811),(1.669999,-0.887837),(1.679999,-0.663453),(1.689999,-0.443274),(1.699999,-0.228569),(1.709999,-0.020380),(1.719999,0.177975),(1.729999,0.349485),(1.739999,0.496469),(1.749999,0.621566),(1.759999,0.727152),(1.769999,0.815360),(1.779999,0.888101),(1.789999,0.947090),(1.799999,0.993870),(1.809999,1.029825),(1.819999,1.056208),(1.829999,1.074145),(1.839999,1.084652),(1.849999,1.088648),(1.859999,1.086957),(1.869999,1.080324),(1.879999,1.069413),(1.889999,1.054829),(1.899999,1.037105),(1.909999,1.016715),(1.919999,0.994084),(1.929999,0.969586),(1.939999,0.943550),(1.949998,0.916267),(1.959998,0.887990),(1.969998,0.858937),(1.979998,0.829299),(1.989998,0.799241),(1.999998,0.768900),(2.009999,0.738396),(2.019999,0.707827),(2.029999,0.677277),(2.039999,0.646813),(2.049999,0.616488),(2.059999,0.586346),(2.069999,0.556419),(2.079998,0.526729),(2.089998,0.497288),(2.099998,0.468108),(2.109998,0.439191),(2.119998,0.410532),(2.129998,0.382120),(2.139998,0.353939),(2.149998,0.325967),(2.159998,0.298179),(2.169998,0.270542),(2.179998,0.243012),(2.189998,0.215540),(2.199998,0.188055),(2.209998,0.160463),(2.219998,0.132618),(2.229998,0.104282),(2.239998,0.074935),(2.249998,0.042939)]
)";
 
const std::string left_1 = R"(
X = [(-0.559000,0.559000),(-0.558804,0.559155),(-0.558412,0.559465),(-0.557824,0.559931),(-0.557040,0.560552),(-0.556063,0.561332),(-0.554892,0.562269),(-0.553528,0.563366),(-0.551973,0.564623),(-0.550228,0.566044),(-0.548294,0.567628),(-0.546173,0.569378),(-0.543866,0.571296),(-0.541376,0.573384),(-0.538702,0.575645),(-0.535849,0.578079),(-0.532817,0.580688),(-0.529608,0.583476),(-0.526225,0.586444),(-0.522669,0.589594),(-0.518943,0.592928),(-0.515049,0.596449),(-0.510987,0.600158),(-0.506762,0.604058),(-0.502375,0.608151),(-0.497828,0.612439),(-0.493123,0.616924),(-0.488263,0.621608),(-0.483250,0.626494),(-0.478087,0.631584),(-0.472776,0.636879),(-0.467320,0.642383),(-0.461722,0.648098),(-0.455984,0.654026),(-0.450109,0.660169),(-0.444100,0.666530),(-0.437962,0.673111),(-0.431696,0.679915),(-0.425306,0.686946),(-0.418797,0.694204),(-0.412171,0.701696),(-0.405434,0.709421),(-0.398590,0.717385),(-0.391644,0.725589),(-0.384760,0.733846),(-0.377938,0.742154),(-0.371181,0.750515),(-0.364489,0.758928),(-0.357864,0.767394),(-0.351307,0.775912),(-0.344820,0.784484),(-0.338404,0.793110),(-0.332062,0.801790),(-0.325796,0.810524),(-0.319608,0.819314),(-0.313501,0.828161),(-0.307477,0.837065),(-0.301541,0.846027),(-0.295694,0.855048),(-0.289941,0.864129),(-0.284285,0.873271),(-0.278731,0.882475),(-0.273284,0.891742),(-0.267948,0.901074),(-0.262795,0.910352),(-0.257879,0.919473),(-0.253198,0.928432),(-0.248750,0.937227),(-0.244532,0.945852),(-0.240540,0.954305),(-0.236770,0.962582),(-0.233219,0.970679),(-0.229883,0.978593),(-0.226757,0.986318),(-0.223837,0.993853),(-0.221118,1.001191),(-0.218594,1.008331),(-0.216260,1.015266),(-0.214111,1.021995),(-0.212139,1.028512),(-0.210338,1.034813),(-0.208700,1.040896),(-0.207220,1.046756),(-0.205889,1.052390),(-0.204699,1.057793),(-0.203642,1.062963),(-0.202710,1.067896),(-0.201894,1.072590),(-0.201186,1.077041),(-0.200576,1.081247),(-0.200057,1.085206),(-0.199620,1.088914),(-0.199255,1.092369),(-0.198956,1.095570),(-0.198714,1.098515),(-0.198521,1.101201),(-0.198370,1.103626),(-0.198254,1.105789),(-0.198167,1.107686),(-0.198104,1.109315),(-0.198059,1.110672),(-0.198029,1.111751),(-0.198010,1.112541),(-0.198000,1.113000)]
L = [(0.000000,0.000000),(0.010000,0.025000),(0.020000,0.050000),(0.030000,0.075000),(0.040000,0.100000),(0.050000,0.125000),(0.060000,0.150000),(0.070000,0.175000),(0.080000,0.200000),(0.090000,0.225000),(0.100000,0.250000),(0.110000,0.275000),(0.120000,0.300000),(0.130000,0.325000),(0.140000,0.350000),(0.150000,0.375000),(0.160000,0.400000),(0.170000,0.425000),(0.180000,0.450000),(0.190000,0.475000),(0.200000,0.500000),(0.210000,0.525000),(0.220000,0.550000),(0.230000,0.575000),(0.240000,0.600000),(0.250000,0.625000),(0.260000,0.650000),(0.270000,0.675000),(0.280000,0.700000),(0.290000,0.725000),(0.300000,0.750000),(0.310000,0.775000),(0.320000,0.800000),(0.330000,0.825000),(0.340000,0.850000),(0.350000,0.875000),(0.360000,0.900000),(0.370000,0.925000),(0.380000,0.950000),(0.390000,0.975000),(0.400000,1.000000),(0.410000,1.025000),(0.420000,1.050000),(0.430000,1.075000),(0.440000,1.075000),(0.450000,1.075000),(0.460000,1.075000),(0.470000,1.075000),(0.480000,1.075000),(0.490000,1.075000),(0.500000,1.075000),(0.510000,1.075000),(0.520000,1.075000),(0.530000,1.075000),(0.540000,1.075000),(0.550000,1.075000),(0.560000,1.075000),(0.570000,1.075000),(0.580000,1.075000),(0.590000,1.075000),(0.600000,1.075000),(0.610000,1.075000),(0.620000,1.075000),(0.630000,1.075000),(0.640000,1.061439),(0.650000,1.036139),(0.660000,1.010830),(0.670000,0.985513),(0.680000,0.960187),(0.690000,0.934853),(0.700000,0.909510),(0.710000,0.884156),(0.720000,0.858792),(0.730000,0.833418),(0.740000,0.808031),(0.750000,0.782632),(0.760000,0.757219),(0.770000,0.731792),(0.780000,0.706350),(0.790000,0.680891),(0.800000,0.655415),(0.810000,0.629919),(0.820000,0.604402),(0.830000,0.578862),(0.839999,0.553297),(0.849999,0.527705),(0.859999,0.502083),(0.869999,0.476428),(0.879999,0.450736),(0.889999,0.425001),(0.899999,0.399220),(0.909999,0.373384),(0.919999,0.347486),(0.929999,0.321516),(0.939999,0.295462),(0.949999,0.269305),(0.959999,0.243023),(0.969999,0.216587),(0.979999,0.189949),(0.989999,0.163045),(0.999999,0.135764),(1.009999,0.107906),(1.019999,0.079052),(1.029999,0.047926)]
A = [(0.000000,0.000000),(0.010000,0.039397),(0.020000,0.078300),(0.030000,0.116355),(0.040000,0.153240),(0.050000,0.188670),(0.060000,0.222409),(0.070000,0.254268),(0.080000,0.284113),(0.090000,0.311863),(0.100000,0.337485),(0.110000,0.360991),(0.120000,0.382434),(0.130000,0.401901),(0.140000,0.419502),(0.150000,0.435375),(0.160000,0.449670),(0.170000,0.462545),(0.180000,0.474163),(0.190000,0.484690),(0.200000,0.494289),(0.210000,0.503118),(0.220000,0.511330),(0.230000,0.519073),(0.240000,0.526485),(0.250000,0.533698),(0.260000,0.540836),(0.270000,0.548018),(0.280000,0.555355),(0.290000,0.562953),(0.300000,0.570916),(0.310000,0.579341),(0.320000,0.588327),(0.330000,0.597968),(0.340000,0.608362),(0.350000,0.619606),(0.360000,0.631802),(0.370000,0.645055),(0.380000,0.659476),(0.390000,0.675186),(0.400000,0.692311),(0.410000,0.710994),(0.420000,0.731390),(0.430000,0.753669),(0.440000,0.760171),(0.450000,0.768280),(0.460000,0.777985),(0.470000,0.789287),(0.480000,0.802206),(0.490000,0.816772),(0.500000,0.833031),(0.510000,0.851041),(0.520000,0.870876),(0.530000,0.892622),(0.540000,0.916386),(0.550000,0.942285),(0.560000,0.970458),(0.570000,1.001062),(0.580000,1.034273),(0.590000,1.070293),(0.600000,1.109349),(0.610000,1.151697),(0.620000,1.197623),(0.630000,1.247452),(0.640000,1.284424),(0.650000,1.308266),(0.660000,1.332434),(0.670000,1.356766),(0.680000,1.381078),(0.690000,1.405173),(0.700000,1.428830),(0.710000,1.451812),(0.720000,1.473858),(0.730000,1.494691),(0.740000,1.514009),(0.750000,1.531497),(0.760000,1.546818),(0.770000,1.559622),(0.780000,1.569550),(0.790000,1.576235),(0.800000,1.579309),(0.810000,1.578405),(0.820000,1.573172),(0.830000,1.563270),(0.839999,1.548387),(0.849999,1.528240),(0.859999,1.502582),(0.869999,1.471212),(0.879999,1.433973),(0.889999,1.390760),(0.899999,1.341526),(0.909999,1.286273),(0.919999,1.225060),(0.929999,1.157993),(0.939999,1.085230),(0.949999,1.006960),(0.959999,0.923396),(0.969999,0.834773),(0.979999,0.741295),(0.989999,0.643131),(0.999999,0.540290),(1.009999,0.432456),(1.019999,0.318450),(1.029999,0.193638)]
)";
 
const std::string left_2 = R"(
X = [(-0.198000,1.113000),(-0.198023,1.112751),(-0.198069,1.112254),(-0.198140,1.111507),(-0.198239,1.110512),(-0.198368,1.109269),(-0.198531,1.107778),(-0.198732,1.106039),(-0.198978,1.104054),(-0.199275,1.101824),(-0.199628,1.099349),(-0.200047,1.096631),(-0.200541,1.093672),(-0.201118,1.090474),(-0.201790,1.087039),(-0.202568,1.083371),(-0.203464,1.079472),(-0.204492,1.075349),(-0.205665,1.071006),(-0.207000,1.066448),(-0.208510,1.061682),(-0.210214,1.056716),(-0.212128,1.051560),(-0.214268,1.046224),(-0.216654,1.040718),(-0.219301,1.035057),(-0.222230,1.029254),(-0.225455,1.023325),(-0.228995,1.017287),(-0.232865,1.011156),(-0.237081,1.004954),(-0.241656,0.998699),(-0.246602,0.992411),(-0.251930,0.986113),(-0.257650,0.979826),(-0.263768,0.973571),(-0.270289,0.967369),(-0.277218,0.961242),(-0.284556,0.955209),(-0.292304,0.949291),(-0.300365,0.943571),(-0.308722,0.938062),(-0.317368,0.932768),(-0.326294,0.927694),(-0.335490,0.922846),(-0.344945,0.918228),(-0.354648,0.913843),(-0.364589,0.909695),(-0.374753,0.905787),(-0.385131,0.902122),(-0.395708,0.898701),(-0.406473,0.895527),(-0.417413,0.892600),(-0.428515,0.889922),(-0.439768,0.887491),(-0.451158,0.885310),(-0.462675,0.883376),(-0.474306,0.881691),(-0.486041,0.880253),(-0.497870,0.879060),(-0.509779,0.878112),(-0.521760,0.877408),(-0.533803,0.876947),(-0.545897,0.876726),(-0.558033,0.876745),(-0.570203,0.877002),(-0.582398,0.877495),(-0.594608,0.878223),(-0.606826,0.879184),(-0.619043,0.880378),(-0.631251,0.881802),(-0.643442,0.883456),(-0.655609,0.885337),(-0.667743,0.887445),(-0.679838,0.889778),(-0.691886,0.892336),(-0.703879,0.895116),(-0.715811,0.898117),(-0.727673,0.901339),(-0.739458,0.904780),(-0.751159,0.908440),(-0.762769,0.912315),(-0.774280,0.916407),(-0.785685,0.920712),(-0.796977,0.925231),(-0.808148,0.929961),(-0.819192,0.934901),(-0.830099,0.940049),(-0.840865,0.945405),(-0.851481,0.950966),(-0.861940,0.956731),(-0.872234,0.962698),(-0.882356,0.968863),(-0.892299,0.975226),(-0.902057,0.981784),(-0.911613,0.988529),(-0.920809,0.995341),(-0.929647,1.002207),(-0.938130,1.009113),(-0.946261,1.016045),(-0.954044,1.022991),(-0.961485,1.029937),(-0.968589,1.036869),(-0.975360,1.043775),(-0.981806,1.050642),(-0.987934,1.057457),(-0.993751,1.064209),(-0.999264,1.070885),(-1.004483,1.077474),(-1.009414,1.083963),(-1.014068,1.090343),(-1.018452,1.096603),(-1.022576,1.102732),(-1.026451,1.108722),(-1.030084,1.114563),(-1.033486,1.120247),(-1.036667,1.125766),(-1.039635,1.131111),(-1.042400,1.136277),(-1.044972,1.141255),(-1.047358,1.146041),(-1.049569,1.150627),(-1.051613,1.155009),(-1.053497,1.159182),(-1.055230,1.163140),(-1.056820,1.166880),(-1.058272,1.170398),(-1.059595,1.173689),(-1.060794,1.176750),(-1.061875,1.179577),(-1.062843,1.182168),(-1.063703,1.184520),(-1.064460,1.186628),(-1.065117,1.188489),(-1.065677,1.190101),(-1.066143,1.191458),(-1.066515,1.192554),(-1.066793,1.193382),(-1.066974,1.193923),(-1.067000,1.194000)]
L = [(0.000000,0.000000),(0.010000,0.025000),(0.020000,0.050000),(0.030000,0.075000),(0.040000,0.100000),(0.050000,0.125000),(0.060000,0.150000),(0.070000,0.175000),(0.080000,0.200000),(0.090000,0.225000),(0.100000,0.250000),(0.110000,0.275000),(0.120000,0.300000),(0.130000,0.325000),(0.140000,0.350000),(0.150000,0.375000),(0.160000,0.400000),(0.170000,0.425000),(0.180000,0.450000),(0.190000,0.475000),(0.200000,0.500000),(0.210000,0.525000),(0.220000,0.550000),(0.230000,0.575000),(0.240000,0.600000),(0.250000,0.625000),(0.260000,0.650000),(0.270000,0.675000),(0.280000,0.700000),(0.290000,0.725000),(0.300000,0.750000),(0.310000,0.775000),(0.320000,0.800000),(0.330000,0.825000),(0.340000,0.850000),(0.350000,0.875000),(0.360000,0.900000),(0.370000,0.925000),(0.380000,0.950000),(0.390000,0.975000),(0.400000,0.988461),(0.410000,1.001058),(0.420000,1.013849),(0.430000,1.026724),(0.440000,1.039579),(0.450000,1.052319),(0.460000,1.064861),(0.470000,1.077129),(0.480000,1.089061),(0.490000,1.100602),(0.500000,1.111708),(0.510000,1.122345),(0.520000,1.132486),(0.530000,1.142114),(0.540000,1.151214),(0.550000,1.159783),(0.560000,1.167816),(0.570000,1.175318),(0.580000,1.182294),(0.590000,1.188752),(0.600000,1.194702),(0.610000,1.200156),(0.620000,1.205127),(0.630000,1.209627),(0.640000,1.213670),(0.650000,1.217270),(0.660000,1.220439),(0.670000,1.223191),(0.680000,1.225538),(0.690000,1.227493),(0.700000,1.229066),(0.710000,1.230268),(0.720000,1.231111),(0.730000,1.231603),(0.740000,1.231753),(0.750000,1.231570),(0.760000,1.231063),(0.770000,1.230239),(0.780000,1.229105),(0.790000,1.227670),(0.800000,1.225940),(0.810000,1.223923),(0.820000,1.221626),(0.830000,1.219056),(0.839999,1.216223),(0.849999,1.213133),(0.859999,1.209798),(0.869999,1.206226),(0.879999,1.202429),(0.889999,1.198418),(0.899999,1.194207),(0.909999,1.189811),(0.919999,1.185244),(0.929999,1.180525),(0.939999,1.175673),(0.949999,1.169715),(0.959999,1.144442),(0.969999,1.119163),(0.979999,1.093877),(0.989999,1.068584),(0.999999,1.043285),(1.009999,1.017978),(1.019999,0.992663),(1.029999,0.967340),(1.039999,0.942008),(1.049999,0.916669),(1.059999,0.891320),(1.069999,0.865959),(1.079999,0.840587),(1.089999,0.815201),(1.099999,0.789805),(1.109999,0.764396),(1.119999,0.738973),(1.129999,0.713535),(1.139999,0.688081),(1.149999,0.662610),(1.159999,0.637120),(1.169999,0.611609),(1.179999,0.586076),(1.189999,0.560519),(1.199999,0.534935),(1.209999,0.509323),(1.219999,0.483676),(1.229999,0.457995),(1.239999,0.432273),(1.249999,0.406505),(1.259999,0.380686),(1.269999,0.354806),(1.279999,0.328858),(1.289999,0.302827),(1.299999,0.276701),(1.309999,0.250457),(1.319999,0.224066),(1.329999,0.197488),(1.339999,0.170670),(1.349999,0.143510),(1.359999,0.115842),(1.369999,0.087329),(1.379999,0.057100),(1.389999,0.020132)]
A = [(0.000000,0.000000),(0.010000,-0.100553),(0.020000,-0.201459),(0.030000,-0.302981),(0.040000,-0.405375),(0.050000,-0.508893),(0.060000,-0.613776),(0.070000,-0.720254),(0.080000,-0.828539),(0.090000,-0.938823),(0.100000,-1.051270),(0.110000,-1.166011),(0.120000,-1.283137),(0.130000,-1.402688),(0.140000,-1.524643),(0.150000,-1.648909),(0.160000,-1.775310),(0.170000,-1.903570),(0.180000,-2.033309),(0.190000,-2.164022),(0.200000,-2.295073),(0.210000,-2.425688),(0.220000,-2.554951),(0.230000,-2.681813),(0.240000,-2.805098),(0.250000,-2.923531),(0.260000,-3.035766),(0.270000,-3.140431),(0.280000,-3.236175),(0.290000,-3.321726),(0.300000,-3.395953),(0.310000,-3.457922),(0.320000,-3.506948),(0.330000,-3.542634),(0.340000,-3.564892),(0.350000,-3.573956),(0.360000,-3.570359),(0.370000,-3.554907),(0.380000,-3.528636),(0.390000,-3.492759),(0.400000,-3.410324),(0.410000,-3.322782),(0.420000,-3.235037),(0.430000,-3.147724),(0.440000,-3.061422),(0.450000,-2.976649),(0.460000,-2.893859),(0.470000,-2.813443),(0.480000,-2.735731),(0.490000,-2.660989),(0.500000,-2.589433),(0.510000,-2.521226),(0.520000,-2.456483),(0.530000,-2.395281),(0.540000,-2.337659),(0.550000,-2.283628),(0.560000,-2.233171),(0.570000,-2.186253),(0.580000,-2.142822),(0.590000,-2.102809),(0.600000,-2.066149),(0.610000,-2.032756),(0.620000,-2.002546),(0.630000,-1.975435),(0.640000,-1.951333),(0.650000,-1.930157),(0.660000,-1.911821),(0.670000,-1.896244),(0.680000,-1.883350),(0.690000,-1.873063),(0.700000,-1.865314),(0.710000,-1.860034),(0.720000,-1.857161),(0.730000,-1.856637),(0.740000,-1.858403),(0.750000,-1.862406),(0.760000,-1.868595),(0.770000,-1.876919),(0.780000,-1.887329),(0.790000,-1.899778),(0.800000,-1.914215),(0.810000,-1.930590),(0.820000,-1.948851),(0.830000,-1.968944),(0.839999,-1.990808),(0.849999,-2.014378),(0.859999,-2.039586),(0.869999,-2.066353),(0.879999,-2.094599),(0.889999,-2.124227),(0.899999,-2.155133),(0.909999,-2.187204),(0.919999,-2.220313),(0.929999,-2.254324),(0.939999,-2.289086),(0.949999,-2.322424),(0.959999,-2.316381),(0.969999,-2.308290),(0.979999,-2.297919),(0.989999,-2.285052),(0.999999,-2.269509),(1.009999,-2.251139),(1.019999,-2.229817),(1.029999,-2.205460),(1.039999,-2.178009),(1.049999,-2.147452),(1.059999,-2.113796),(1.069999,-2.077083),(1.079999,-2.037387),(1.089999,-1.994803),(1.099999,-1.949465),(1.109999,-1.901510),(1.119999,-1.851099),(1.129999,-1.798404),(1.139999,-1.743605),(1.149999,-1.686885),(1.159999,-1.628434),(1.169999,-1.568436),(1.179999,-1.507069),(1.189999,-1.444507),(1.199999,-1.380914),(1.209999,-1.316440),(1.219999,-1.251221),(1.229999,-1.185387),(1.239999,-1.119045),(1.249999,-1.052288),(1.259999,-0.985197),(1.269999,-0.917829),(1.279999,-0.850228),(1.289999,-0.782418),(1.299999,-0.714406),(1.309999,-0.646168),(1.319999,-0.577654),(1.329999,-0.508774),(1.339999,-0.439392),(1.349999,-0.369252),(1.359999,-0.297914),(1.369999,-0.224500),(1.379999,-0.146750),(1.389999,-0.051740)]
)";
 
const std::string left_3 = R"(
X = [(-0.711000,1.194000),(-0.711100,1.194002),(-0.711300,1.194007),(-0.711600,1.194014),(-0.711999,1.194024),(-0.712499,1.194037),(-0.713099,1.194052),(-0.713798,1.194070),(-0.714598,1.194092),(-0.715498,1.194116),(-0.716497,1.194145),(-0.717597,1.194177),(-0.718796,1.194214),(-0.720096,1.194255),(-0.721495,1.194300),(-0.722994,1.194352),(-0.724593,1.194409),(-0.726292,1.194472),(-0.728090,1.194542),(-0.729989,1.194619),(-0.731987,1.194703),(-0.734085,1.194796),(-0.736283,1.194898),(-0.738580,1.195010),(-0.740977,1.195132),(-0.743473,1.195264),(-0.746069,1.195409),(-0.748764,1.195566),(-0.751558,1.195736),(-0.754452,1.195921),(-0.757444,1.196120),(-0.760537,1.196336),(-0.763728,1.196569),(-0.767018,1.196820),(-0.770408,1.197090),(-0.773896,1.197380),(-0.777482,1.197691),(-0.781167,1.198026),(-0.784950,1.198384),(-0.788831,1.198767),(-0.792810,1.199177),(-0.796887,1.199615),(-0.801061,1.200083),(-0.805332,1.200581),(-0.809699,1.201113),(-0.814164,1.201678),(-0.818724,1.202280),(-0.823380,1.202919),(-0.828132,1.203599),(-0.832979,1.204320),(-0.837920,1.205086),(-0.842955,1.205897),(-0.848083,1.206757),(-0.853305,1.207667),(-0.858618,1.208630),(-0.864023,1.209650),(-0.869518,1.210727),(-0.875103,1.211866),(-0.880777,1.213070),(-0.886538,1.214340),(-0.892386,1.215682),(-0.898319,1.217098),(-0.904337,1.218591),(-0.910436,1.220167),(-0.916616,1.221828),(-0.922876,1.223580),(-0.929088,1.225390),(-0.935247,1.227257),(-0.941349,1.229181),(-0.947392,1.231162),(-0.953372,1.233201),(-0.959287,1.235297),(-0.965133,1.237449),(-0.970907,1.239659),(-0.976605,1.241924),(-0.982223,1.244246),(-0.987758,1.246622),(-0.993206,1.249053),(-0.998561,1.251536),(-1.003820,1.254072),(-1.008978,1.256659),(-1.014031,1.259296),(-1.018973,1.261979),(-1.023801,1.264708),(-1.028508,1.267480),(-1.033090,1.270293),(-1.037541,1.273143),(-1.041858,1.276028),(-1.046035,1.278944),(-1.050068,1.281888),(-1.053952,1.284854),(-1.057684,1.287840),(-1.061259,1.290840),(-1.064675,1.293850),(-1.067930,1.296865),(-1.071020,1.299881),(-1.073947,1.302892),(-1.076707,1.305895),(-1.079303,1.308884),(-1.081734,1.311855),(-1.084003,1.314803),(-1.086111,1.317727),(-1.088062,1.320621),(-1.089860,1.323484),(-1.091507,1.326312),(-1.093009,1.329105),(-1.094370,1.331860),(-1.095595,1.334578),(-1.096690,1.337258),(-1.097658,1.339900),(-1.098506,1.342506),(-1.099236,1.345075),(-1.099855,1.347610),(-1.100366,1.350112),(-1.100772,1.352584),(-1.101077,1.355027),(-1.101284,1.357444),(-1.101395,1.359837),(-1.101412,1.362208),(-1.101337,1.364562),(-1.101170,1.366899),(-1.100913,1.369224),(-1.100564,1.371538),(-1.100124,1.373844),(-1.099591,1.376145),(-1.098964,1.378443),(-1.098242,1.380741),(-1.097421,1.383040),(-1.096499,1.385343),(-1.095472,1.387650),(-1.094337,1.389965),(-1.093091,1.392289),(-1.091728,1.394621),(-1.090243,1.396965),(-1.088633,1.399318),(-1.086893,1.401681),(-1.085017,1.404055),(-1.083002,1.406437),(-1.080842,1.408827),(-1.078536,1.411219),(-1.076086,1.413608),(-1.073490,1.415990),(-1.070751,1.418359),(-1.067868,1.420711),(-1.064845,1.423043),(-1.061682,1.425352),(-1.058382,1.427634),(-1.054947,1.429887),(-1.051378,1.432108),(-1.047678,1.434295),(-1.043849,1.436447),(-1.039891,1.438562),(-1.035807,1.440639),(-1.031599,1.442677),(-1.027267,1.444676),(-1.022562,1.446741),(-1.017725,1.448759),(-1.012760,1.450729),(-1.007672,1.452648),(-1.002466,1.454515),(-0.997145,1.456330),(-0.991714,1.458091),(-0.986178,1.459799),(-0.980539,1.461452),(-0.974802,1.463051),(-0.968971,1.464594),(-0.963050,1.466083),(-0.957041,1.467517),(-0.950949,1.468897),(-0.944777,1.470223),(-0.938528,1.471494),(-0.932204,1.472712),(-0.925810,1.473876),(-0.919398,1.474980),(-0.913066,1.476009),(-0.906817,1.476968),(-0.900653,1.477862),(-0.894575,1.478694),(-0.888585,1.479468),(-0.882682,1.480187),(-0.876870,1.480855),(-0.871148,1.481475),(-0.865517,1.482049),(-0.859980,1.482580),(-0.854536,1.483071),(-0.849186,1.483524),(-0.843932,1.483942),(-0.838774,1.484325),(-0.833712,1.484677),(-0.828747,1.484999),(-0.823880,1.485294),(-0.819112,1.485562),(-0.814442,1.485805),(-0.809872,1.486025),(-0.805401,1.486224),(-0.801031,1.486402),(-0.796761,1.486562),(-0.792592,1.486704),(-0.788523,1.486829),(-0.784557,1.486939),(-0.780691,1.487035),(-0.776928,1.487117),(-0.773267,1.487188),(-0.769708,1.487247),(-0.766252,1.487296),(-0.762897,1.487335),(-0.759646,1.487366),(-0.756497,1.487389),(-0.753452,1.487405),(-0.750511,1.487414),(-0.747673,1.487417),(-0.744938,1.487415),(-0.742308,1.487409),(-0.739781,1.487399),(-0.737358,1.487385),(-0.735040,1.487369),(-0.732825,1.487350),(-0.730715,1.487328),(-0.728710,1.487306),(-0.726810,1.487282),(-0.725014,1.487258),(-0.723324,1.487233),(-0.721738,1.487208),(-0.720258,1.487184),(-0.718884,1.487159),(-0.717616,1.487136),(-0.716455,1.487114),(-0.715400,1.487094),(-0.714453,1.487074),(-0.713614,1.487057),(-0.712883,1.487041),(-0.712263,1.487028),(-0.711755,1.487017),(-0.711363,1.487008),(-0.711091,1.487002),(-0.711000,1.487000)]
L = [(0.000000,0.000000),(0.010000,0.010000),(0.020000,0.020000),(0.030000,0.030000),(0.040000,0.040000),(0.050000,0.050000),(0.060000,0.060000),(0.070000,0.070000),(0.080000,0.080000),(0.090000,0.090000),(0.100000,0.100000),(0.110000,0.110000),(0.120000,0.120000),(0.130000,0.130000),(0.140000,0.140000),(0.150000,0.150000),(0.160000,0.160000),(0.170000,0.170000),(0.180000,0.180000),(0.190000,0.190000),(0.200000,0.200000),(0.210000,0.210000),(0.220000,0.220000),(0.230000,0.230000),(0.240000,0.240000),(0.250000,0.250000),(0.260000,0.260000),(0.270000,0.270000),(0.280000,0.280000),(0.290000,0.290000),(0.300000,0.300000),(0.310000,0.310000),(0.320000,0.320000),(0.330000,0.330000),(0.340000,0.340000),(0.350000,0.350000),(0.360000,0.360000),(0.370000,0.370000),(0.380000,0.380000),(0.390000,0.390000),(0.400000,0.400000),(0.410000,0.410000),(0.420000,0.420000),(0.430000,0.430000),(0.440000,0.440000),(0.450000,0.450000),(0.460000,0.460000),(0.470000,0.470000),(0.480000,0.480000),(0.490000,0.490000),(0.500000,0.500000),(0.510000,0.510000),(0.520000,0.520000),(0.530000,0.530000),(0.540000,0.540000),(0.550000,0.550000),(0.560000,0.560000),(0.570000,0.570000),(0.580000,0.580000),(0.590000,0.590000),(0.600000,0.600000),(0.610000,0.610000),(0.620000,0.620000),(0.630000,0.630000),(0.640000,0.640000),(0.650000,0.650000),(0.660000,0.647108),(0.670000,0.643567),(0.680000,0.639849),(0.690000,0.635944),(0.700000,0.631841),(0.710000,0.627527),(0.720000,0.622990),(0.730000,0.618219),(0.740000,0.613198),(0.750000,0.607915),(0.760000,0.602355),(0.770000,0.596505),(0.780000,0.590350),(0.790000,0.583876),(0.800000,0.577069),(0.810000,0.569917),(0.820000,0.562407),(0.830000,0.554530),(0.839999,0.546276),(0.849999,0.537640),(0.859999,0.528619),(0.869999,0.519213),(0.879999,0.509427),(0.889999,0.499272),(0.899999,0.488762),(0.909999,0.477919),(0.919999,0.466771),(0.929999,0.455354),(0.939999,0.443708),(0.949999,0.431880),(0.959999,0.419925),(0.969999,0.407901),(0.979999,0.395873),(0.989999,0.383906),(0.999999,0.372069),(1.009999,0.360429),(1.019999,0.349054),(1.029999,0.338005),(1.039999,0.327343),(1.049999,0.317120),(1.059999,0.307384),(1.069999,0.298174),(1.079999,0.289528),(1.089999,0.281468),(1.099999,0.274016),(1.109999,0.267187),(1.119999,0.260992),(1.129999,0.255436),(1.139999,0.250523),(1.149999,0.246249),(1.159999,0.242615),(1.169999,0.239616),(1.179999,0.237249),(1.189999,0.235511),(1.199999,0.234396),(1.209999,0.233904),(1.219999,0.234032),(1.229999,0.234779),(1.239999,0.236145),(1.249999,0.238133),(1.259999,0.240745),(1.269999,0.243983),(1.279999,0.247850),(1.289999,0.252351),(1.299999,0.257486),(1.309999,0.263257),(1.319999,0.269664),(1.329999,0.276704),(1.339999,0.284372),(1.349999,0.292652),(1.359999,0.301531),(1.369999,0.310987),(1.379999,0.320987),(1.389999,0.330987),(1.399999,0.340987),(1.409999,0.350987),(1.419999,0.360987),(1.429999,0.370987),(1.439999,0.380987),(1.449999,0.390987),(1.459999,0.400987),(1.469999,0.410987),(1.479999,0.420987),(1.489999,0.430987),(1.499999,0.440987),(1.509999,0.450987),(1.519999,0.460987),(1.529999,0.470987),(1.539999,0.480987),(1.549999,0.518604),(1.559999,0.529458),(1.569999,0.539937),(1.579999,0.550031),(1.589999,0.559734),(1.599999,0.569041),(1.609999,0.577956),(1.619999,0.586484),(1.629999,0.594631),(1.639999,0.602407),(1.649999,0.609823),(1.659999,0.616891),(1.669999,0.623624),(1.679999,0.630035),(1.689999,0.636139),(1.699999,0.641949),(1.709999,0.647479),(1.719999,0.652742),(1.729999,0.652697),(1.739999,0.642620),(1.749999,0.632541),(1.759999,0.622460),(1.769999,0.612379),(1.779999,0.602296),(1.789999,0.592211),(1.799999,0.582125),(1.809999,0.572038),(1.819999,0.561949),(1.829999,0.551858),(1.839999,0.541766),(1.849999,0.531672),(1.859999,0.521576),(1.869999,0.511478),(1.879999,0.501378),(1.889999,0.491276),(1.899999,0.481172),(1.909999,0.471066),(1.919999,0.460958),(1.929999,0.450847),(1.939999,0.440734),(1.949998,0.430618),(1.959998,0.420499),(1.969998,0.410377),(1.979998,0.400252),(1.989998,0.390124),(1.999998,0.379992),(2.009999,0.369857),(2.019999,0.359718),(2.029999,0.349575),(2.039999,0.339427),(2.049999,0.329276),(2.059999,0.319116),(2.069999,0.308951),(2.079998,0.298781),(2.089998,0.288605),(2.099998,0.278424),(2.109998,0.268235),(2.119998,0.258039),(2.129998,0.247836),(2.139998,0.237623),(2.149998,0.227402),(2.159998,0.217170),(2.169998,0.206927),(2.179998,0.196671),(2.189998,0.186402),(2.199998,0.176117),(2.209998,0.165815),(2.219998,0.155492),(2.229998,0.145148),(2.239998,0.134776),(2.249998,0.124375),(2.259998,0.113935),(2.269998,0.103454),(2.279998,0.092917),(2.289998,0.082311),(2.299998,0.071614),(2.309998,0.060788),(2.319998,0.049784),(2.329998,0.038500),(2.339998,0.026684),(2.349998,0.013350)]
A = [(0.000000,0.000000),(0.010000,-0.009123),(0.020000,-0.018252),(0.030000,-0.027393),(0.040000,-0.036550),(0.050000,-0.045728),(0.060000,-0.054931),(0.070000,-0.064166),(0.080000,-0.073436),(0.090000,-0.082748),(0.100000,-0.092106),(0.110000,-0.101516),(0.120000,-0.110983),(0.130000,-0.120514),(0.140000,-0.130113),(0.150000,-0.139788),(0.160000,-0.149543),(0.170000,-0.159386),(0.180000,-0.169324),(0.190000,-0.179362),(0.200000,-0.189510),(0.210000,-0.199773),(0.220000,-0.210160),(0.230000,-0.220680),(0.240000,-0.231341),(0.250000,-0.242152),(0.260000,-0.253122),(0.270000,-0.264263),(0.280000,-0.275584),(0.290000,-0.287097),(0.300000,-0.298815),(0.310000,-0.310749),(0.320000,-0.322914),(0.330000,-0.335324),(0.340000,-0.347995),(0.350000,-0.360943),(0.360000,-0.374185),(0.370000,-0.387742),(0.380000,-0.401632),(0.390000,-0.415878),(0.400000,-0.430505),(0.410000,-0.445536),(0.420000,-0.461000),(0.430000,-0.476927),(0.440000,-0.493349),(0.450000,-0.510301),(0.460000,-0.527822),(0.470000,-0.545954),(0.480000,-0.564743),(0.490000,-0.584238),(0.500000,-0.604495),(0.510000,-0.625575),(0.520000,-0.647544),(0.530000,-0.670477),(0.540000,-0.694455),(0.550000,-0.719570),(0.560000,-0.745922),(0.570000,-0.773626),(0.580000,-0.802807),(0.590000,-0.833608),(0.600000,-0.866190),(0.610000,-0.900732),(0.620000,-0.937442),(0.630000,-0.976552),(0.640000,-1.018328),(0.650000,-1.063077),(0.660000,-1.088820),(0.670000,-1.115038),(0.680000,-1.142602),(0.690000,-1.171595),(0.700000,-1.202103),(0.710000,-1.234220),(0.720000,-1.268043),(0.730000,-1.303671),(0.740000,-1.341210),(0.750000,-1.380767),(0.760000,-1.422450),(0.770000,-1.466374),(0.780000,-1.512646),(0.790000,-1.561376),(0.800000,-1.612671),(0.810000,-1.666626),(0.820000,-1.723333),(0.830000,-1.782865),(0.839999,-1.845281),(0.849999,-1.910618),(0.859999,-1.978880),(0.869999,-2.050044),(0.879999,-2.124050),(0.889999,-2.200787),(0.899999,-2.280097),(0.909999,-2.361774),(0.919999,-2.445524),(0.929999,-2.531062),(0.939999,-2.617991),(0.949999,-2.705866),(0.959999,-2.794199),(0.969999,-2.882455),(0.979999,-2.970071),(0.989999,-3.056471),(0.999999,-3.141064),(1.009999,-3.223272),(1.019999,-3.302560),(1.029999,-3.378403),(1.039999,-3.450350),(1.049999,-3.518010),(1.059999,-3.581031),(1.069999,-3.639126),(1.079999,-3.692173),(1.089999,-3.739993),(1.099999,-3.782505),(1.109999,-3.819690),(1.119999,-3.851578),(1.129999,-3.878197),(1.139999,-3.899705),(1.149999,-3.916135),(1.159999,-3.927639),(1.169999,-3.934342),(1.179999,-3.936363),(1.189999,-3.933840),(1.199999,-3.926885),(1.209999,-3.915616),(1.219999,-3.900133),(1.229999,-3.880534),(1.239999,-3.856890),(1.249999,-3.829290),(1.259999,-3.797790),(1.269999,-3.762453),(1.279999,-3.723339),(1.289999,-3.680502),(1.299999,-3.633995),(1.309999,-3.583873),(1.319999,-3.530207),(1.329999,-3.473050),(1.339999,-3.412599),(1.349999,-3.348898),(1.359999,-3.282123),(1.369999,-3.212445),(1.379999,-3.140034),(1.389999,-3.060693),(1.399999,-2.976067),(1.409999,-2.887684),(1.419999,-2.796907),(1.429999,-2.704953),(1.439999,-2.612860),(1.449999,-2.521485),(1.459999,-2.431540),(1.469999,-2.343580),(1.479999,-2.258034),(1.489999,-2.175217),(1.499999,-2.095300),(1.509999,-2.018437),(1.519999,-1.944695),(1.529999,-1.874088),(1.539999,-1.806592),(1.549999,-1.834362),(1.559999,-1.765269),(1.569999,-1.698580),(1.579999,-1.634346),(1.589999,-1.572596),(1.599999,-1.513329),(1.609999,-1.456516),(1.619999,-1.402134),(1.629999,-1.350127),(1.639999,-1.300438),(1.649999,-1.252998),(1.659999,-1.207732),(1.669999,-1.164559),(1.679999,-1.123396),(1.689999,-1.084160),(1.699999,-1.046767),(1.709999,-1.011132),(1.719999,-0.977174),(1.729999,-0.937848),(1.739999,-0.887843),(1.749999,-0.841703),(1.759999,-0.799013),(1.769999,-0.759413),(1.779999,-0.722589),(1.789999,-0.688267),(1.799999,-0.656205),(1.809999,-0.626191),(1.819999,-0.598040),(1.829999,-0.571582),(1.839999,-0.546671),(1.849999,-0.523174),(1.859999,-0.500972),(1.869999,-0.479961),(1.879999,-0.460043),(1.889999,-0.441134),(1.899999,-0.423155),(1.909999,-0.406035),(1.919999,-0.389711),(1.929999,-0.374125),(1.939999,-0.359222),(1.949998,-0.344954),(1.959998,-0.331278),(1.969998,-0.318151),(1.979998,-0.305537),(1.989998,-0.293400),(1.999998,-0.281710),(2.009999,-0.270436),(2.019999,-0.259552),(2.029999,-0.249032),(2.039999,-0.238852),(2.049999,-0.228990),(2.059999,-0.219424),(2.069999,-0.210138),(2.079998,-0.201114),(2.089998,-0.192335),(2.099998,-0.183785),(2.109998,-0.175450),(2.119998,-0.167315),(2.129998,-0.159368),(2.139998,-0.151595),(2.149998,-0.143985),(2.159998,-0.136527),(2.169998,-0.129209),(2.179998,-0.122021),(2.189998,-0.114953),(2.199998,-0.107996),(2.209998,-0.101139),(2.219998,-0.094373),(2.229998,-0.087688),(2.239998,-0.081075),(2.249998,-0.074525),(2.259998,-0.068025),(2.269998,-0.061567),(2.279998,-0.055135),(2.289998,-0.048716),(2.299998,-0.042291),(2.309998,-0.035829),(2.319998,-0.029298),(2.329998,-0.022630),(2.339998,-0.015672),(2.349998,-0.007838)]
)";
 
const std::string awp_1 = R"(
X = [(-1.283000,-0.762000),(-1.283000,-0.762250),(-1.283000,-0.762750),(-1.283000,-0.763499),(-1.282999,-0.764499),(-1.282998,-0.765749),(-1.282995,-0.767249),(-1.282992,-0.768999),(-1.282987,-0.770999),(-1.282979,-0.773249),(-1.282969,-0.775749),(-1.282956,-0.778499),(-1.282940,-0.781499),(-1.282919,-0.784749),(-1.282894,-0.788249),(-1.282864,-0.791998),(-1.282827,-0.795998),(-1.282786,-0.800248),(-1.282738,-0.804747),(-1.282684,-0.809497),(-1.282623,-0.814496),(-1.282556,-0.819744),(-1.282483,-0.825244),(-1.282404,-0.830993),(-1.282320,-0.836993),(-1.282233,-0.843242),(-1.282143,-0.849741),(-1.282052,-0.856491),(-1.281962,-0.863490),(-1.281877,-0.870740),(-1.281800,-0.878238),(-1.281734,-0.885987),(-1.281685,-0.893987),(-1.281658,-0.902236),(-1.281662,-0.910736),(-1.281703,-0.919486),(-1.281793,-0.928485),(-1.281942,-0.937734),(-1.282166,-0.947231),(-1.282479,-0.956976),(-1.282902,-0.966967),(-1.283457,-0.977202),(-1.284171,-0.987677),(-1.285075,-0.998389),(-1.286210,-1.009330),(-1.287617,-1.020491),(-1.289317,-1.031646),(-1.291269,-1.042367),(-1.293477,-1.052638),(-1.295943,-1.062448),(-1.298664,-1.071791),(-1.301636,-1.080667),(-1.304855,-1.089082),(-1.308315,-1.097044),(-1.312011,-1.104570),(-1.315938,-1.111678),(-1.320096,-1.118390),(-1.324484,-1.124727),(-1.329106,-1.130713),(-1.333968,-1.136368),(-1.339079,-1.141714),(-1.344449,-1.146769),(-1.350093,-1.151548),(-1.356025,-1.156063),(-1.362262,-1.160324),(-1.368819,-1.164339),(-1.375714,-1.168109),(-1.382961,-1.171636),(-1.390393,-1.174846),(-1.397716,-1.177652),(-1.404899,-1.180097),(-1.411917,-1.182223),(-1.418750,-1.184065),(-1.425383,-1.185657),(-1.431804,-1.187029),(-1.438003,-1.188208),(-1.443973,-1.189217),(-1.449707,-1.190077),(-1.455201,-1.190807),(-1.460450,-1.191424),(-1.465453,-1.191941),(-1.470206,-1.192373),(-1.474707,-1.192729),(-1.478955,-1.193022),(-1.482949,-1.193259),(-1.486687,-1.193449),(-1.490167,-1.193600),(-1.493390,-1.193717),(-1.496353,-1.193806),(-1.499056,-1.193872),(-1.501497,-1.193919),(-1.503675,-1.193952),(-1.505587,-1.193974),(-1.507231,-1.193987),(-1.508602,-1.193995),(-1.509696,-1.193999),(-1.510502,-1.194000),(-1.511000,-1.194000)]
L = [(0.000000,0.000000),(0.010000,0.025000),(0.020000,0.050000),(0.030000,0.075000),(0.040000,0.100000),(0.050000,0.125000),(0.060000,0.150000),(0.070000,0.175000),(0.080000,0.200000),(0.090000,0.225000),(0.100000,0.250000),(0.110000,0.275000),(0.120000,0.300000),(0.130000,0.325000),(0.140000,0.350000),(0.150000,0.375000),(0.160000,0.400000),(0.170000,0.425000),(0.180000,0.450000),(0.190000,0.475000),(0.200000,0.500000),(0.210000,0.525000),(0.220000,0.550000),(0.230000,0.575000),(0.240000,0.600000),(0.250000,0.625000),(0.260000,0.650000),(0.270000,0.675000),(0.280000,0.700000),(0.290000,0.725000),(0.300000,0.750000),(0.310000,0.775000),(0.320000,0.800000),(0.330000,0.825000),(0.340000,0.850000),(0.350000,0.875000),(0.360000,0.900000),(0.370000,0.925000),(0.380000,0.950000),(0.390000,0.975000),(0.400000,1.000000),(0.410000,1.025000),(0.420000,1.050000),(0.430000,1.075000),(0.440000,1.100000),(0.450000,1.125000),(0.460000,1.128411),(0.470000,1.089740),(0.480000,1.050613),(0.490000,1.011570),(0.500000,0.973202),(0.510000,0.936130),(0.520000,0.900964),(0.530000,0.868273),(0.540000,0.838556),(0.550000,0.812230),(0.560000,0.789610),(0.570000,0.770929),(0.580000,0.756333),(0.590000,0.745900),(0.600000,0.739647),(0.610000,0.737547),(0.620000,0.739533),(0.630000,0.745502),(0.640000,0.755317),(0.650000,0.768803),(0.660000,0.785740),(0.670000,0.805861),(0.680000,0.809528),(0.690000,0.784130),(0.700000,0.758718),(0.710000,0.733292),(0.720000,0.707850),(0.730000,0.682393),(0.740000,0.656917),(0.750000,0.631423),(0.760000,0.605907),(0.770000,0.580369),(0.780000,0.554806),(0.790000,0.529216),(0.800000,0.503597),(0.810000,0.477944),(0.820000,0.452256),(0.830000,0.426526),(0.839999,0.400750),(0.849999,0.374920),(0.859999,0.349028),(0.869999,0.323066),(0.879999,0.297020),(0.889999,0.270871),(0.899999,0.244600),(0.909999,0.218173),(0.919999,0.191552),(0.929999,0.164666),(0.939999,0.137410),(0.949999,0.109594),(0.959999,0.080814),(0.969999,0.049930)]
A = [(0.000000,0.000000),(0.010000,0.008502),(0.020000,0.016914),(0.030000,0.025166),(0.040000,0.033188),(0.050000,0.040909),(0.060000,0.048258),(0.070000,0.055158),(0.080000,0.061532),(0.090000,0.067300),(0.100000,0.072377),(0.110000,0.076673),(0.120000,0.080095),(0.130000,0.082543),(0.140000,0.083910),(0.150000,0.084080),(0.160000,0.082930),(0.170000,0.080324),(0.180000,0.076117),(0.190000,0.070147),(0.200000,0.062237),(0.210000,0.052190),(0.220000,0.039785),(0.230000,0.024777),(0.240000,0.006893),(0.250000,-0.014181),(0.260000,-0.038798),(0.270000,-0.067361),(0.280000,-0.100335),(0.290000,-0.138253),(0.300000,-0.181732),(0.310000,-0.231498),(0.320000,-0.288396),(0.330000,-0.353421),(0.340000,-0.427750),(0.350000,-0.512783),(0.360000,-0.610188),(0.370000,-0.721973),(0.380000,-0.850553),(0.390000,-0.998851),(0.400000,-1.170417),(0.410000,-1.369562),(0.420000,-1.601527),(0.430000,-1.872664),(0.440000,-2.190616),(0.450000,-2.564438),(0.460000,-2.940683),(0.470000,-3.226600),(0.480000,-3.511514),(0.490000,-3.790373),(0.500000,-4.057803),(0.510000,-4.308506),(0.520000,-4.537597),(0.530000,-4.740908),(0.540000,-4.915202),(0.550000,-5.058342),(0.560000,-5.169082),(0.570000,-5.247163),(0.580000,-5.293054),(0.590000,-5.307821),(0.600000,-5.292889),(0.610000,-5.249979),(0.620000,-5.180974),(0.630000,-5.087863),(0.640000,-4.972718),(0.650000,-4.837686),(0.660000,-4.685003),(0.670000,-4.517013),(0.680000,-4.242128),(0.690000,-3.835209),(0.700000,-3.462727),(0.710000,-3.125282),(0.720000,-2.821591),(0.730000,-2.549326),(0.740000,-2.305669),(0.750000,-2.087664),(0.760000,-1.892435),(0.770000,-1.717305),(0.780000,-1.559825),(0.790000,-1.417808),(0.800000,-1.289322),(0.810000,-1.172660),(0.820000,-1.066334),(0.830000,-0.969035),(0.839999,-0.879618),(0.849999,-0.797077),(0.859999,-0.720530),(0.869999,-0.649195),(0.879999,-0.582373),(0.889999,-0.519433),(0.899999,-0.459806),(0.909999,-0.402957),(0.919999,-0.348383),(0.929999,-0.295567),(0.939999,-0.243963),(0.949999,-0.192894),(0.959999,-0.141333),(0.969999,-0.086977)]
)";