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2 | #include <cmath>
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3 | #include <iostream>
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4 | #include <iomanip>
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5 |
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6 | #include "bnctides.h"
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7 |
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8 | using namespace std;
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9 |
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10 | // Auxiliary Functions
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11 | ///////////////////////////////////////////////////////////////////////////
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12 | namespace {
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13 |
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14 | static const double RHO_DEG = 180.0 / M_PI;
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15 | static const double RHO_SEC = 3600.0 * RHO_DEG;
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16 | static const double MJD_J2000 = 51544.5;
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17 |
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18 | double Frac (double x) { return x-floor(x); };
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19 | double Modulo (double x, double y) { return y*Frac(x/y); }
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20 |
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21 | Matrix rotX(double Angle) {
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22 | const double C = cos(Angle);
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23 | const double S = sin(Angle);
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24 | Matrix UU(3,3);
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25 | UU[0][0] = 1.0; UU[0][1] = 0.0; UU[0][2] = 0.0;
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26 | UU[1][0] = 0.0; UU[1][1] = +C; UU[1][2] = +S;
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27 | UU[2][0] = 0.0; UU[2][1] = -S; UU[2][2] = +C;
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28 | return UU;
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29 | }
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30 |
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31 | Matrix rotY(double Angle) {
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32 | const double C = cos(Angle);
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33 | const double S = sin(Angle);
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34 | Matrix UU(3,3);
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35 | UU[0][0] = +C; UU[0][1] = 0.0; UU[0][2] = -S;
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36 | UU[1][0] = 0.0; UU[1][1] = 1.0; UU[1][2] = 0.0;
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37 | UU[2][0] = +S; UU[2][1] = 0.0; UU[2][2] = +C;
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38 | return UU;
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39 | }
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40 |
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41 | Matrix rotZ(double Angle) {
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42 | const double C = cos(Angle);
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43 | const double S = sin(Angle);
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44 | Matrix UU(3,3);
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45 | UU[0][0] = +C; UU[0][1] = +S; UU[0][2] = 0.0;
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46 | UU[1][0] = -S; UU[1][1] = +C; UU[1][2] = 0.0;
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47 | UU[2][0] = 0.0; UU[2][1] = 0.0; UU[2][2] = 1.0;
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48 | return UU;
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49 | }
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50 | }
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51 |
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52 | // Greenwich Mean Sidereal Time
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53 | ///////////////////////////////////////////////////////////////////////////
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54 | double GMST(double Mjd_UT1) {
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55 |
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56 | const double Secs = 86400.0;
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57 |
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58 | double Mjd_0 = floor(Mjd_UT1);
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59 | double UT1 = Secs*(Mjd_UT1-Mjd_0);
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60 | double T_0 = (Mjd_0 -MJD_J2000)/36525.0;
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61 | double T = (Mjd_UT1-MJD_J2000)/36525.0;
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62 |
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63 | double gmst = 24110.54841 + 8640184.812866*T_0 + 1.002737909350795*UT1
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64 | + (0.093104-6.2e-6*T)*T*T;
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65 |
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66 | return 2.0*M_PI*Frac(gmst/Secs);
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67 | }
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68 |
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69 | // Nutation Matrix
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70 | ///////////////////////////////////////////////////////////////////////////
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71 | Matrix NutMatrix(double Mjd_TT) {
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72 |
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73 | const double T = (Mjd_TT-MJD_J2000)/36525.0;
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74 |
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75 | double ls = 2.0*M_PI*Frac(0.993133+ 99.997306*T);
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76 | double D = 2.0*M_PI*Frac(0.827362+1236.853087*T);
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77 | double F = 2.0*M_PI*Frac(0.259089+1342.227826*T);
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78 | double N = 2.0*M_PI*Frac(0.347346- 5.372447*T);
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79 |
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80 | double dpsi = ( -17.200*sin(N) - 1.319*sin(2*(F-D+N)) - 0.227*sin(2*(F+N))
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81 | + 0.206*sin(2*N) + 0.143*sin(ls) ) / RHO_SEC;
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82 | double deps = ( + 9.203*cos(N) + 0.574*cos(2*(F-D+N)) + 0.098*cos(2*(F+N))
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83 | - 0.090*cos(2*N) ) / RHO_SEC;
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84 |
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85 | double eps = 0.4090928-2.2696E-4*T;
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86 |
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87 | return rotX(-eps-deps)*rotZ(-dpsi)*rotX(+eps);
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88 | }
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89 |
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90 | // Precession Matrix
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91 | ///////////////////////////////////////////////////////////////////////////
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92 | Matrix PrecMatrix (double Mjd_1, double Mjd_2) {
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93 |
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94 | const double T = (Mjd_1-MJD_J2000)/36525.0;
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95 | const double dT = (Mjd_2-Mjd_1)/36525.0;
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96 |
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97 | double zeta = ( (2306.2181+(1.39656-0.000139*T)*T)+
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98 | ((0.30188-0.000344*T)+0.017998*dT)*dT )*dT/RHO_SEC;
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99 | double z = zeta + ( (0.79280+0.000411*T)+0.000205*dT)*dT*dT/RHO_SEC;
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100 | double theta = ( (2004.3109-(0.85330+0.000217*T)*T)-
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101 | ((0.42665+0.000217*T)+0.041833*dT)*dT )*dT/RHO_SEC;
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102 |
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103 | return rotZ(-z) * rotY(theta) * rotZ(-zeta);
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104 | }
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105 |
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106 | // Sun's position
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107 | ///////////////////////////////////////////////////////////////////////////
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108 | ColumnVector Sun(double Mjd_TT) {
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109 |
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110 | const double eps = 23.43929111/RHO_DEG;
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111 | const double T = (Mjd_TT-MJD_J2000)/36525.0;
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112 |
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113 | double M = 2.0*M_PI * Frac ( 0.9931267 + 99.9973583*T);
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114 | double L = 2.0*M_PI * Frac ( 0.7859444 + M/2.0*M_PI +
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115 | (6892.0*sin(M)+72.0*sin(2.0*M)) / 1296.0e3);
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116 | double r = 149.619e9 - 2.499e9*cos(M) - 0.021e9*cos(2*M);
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117 |
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118 | ColumnVector r_Sun(3);
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119 | r_Sun << r*cos(L) << r*sin(L) << 0.0; r_Sun = rotX(-eps) * r_Sun;
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120 |
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121 | return rotZ(GMST(Mjd_TT))
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122 | * NutMatrix(Mjd_TT)
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123 | * PrecMatrix(MJD_J2000, Mjd_TT)
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124 | * r_Sun;
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125 | }
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126 |
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127 | // Moon's position
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128 | ///////////////////////////////////////////////////////////////////////////
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129 | ColumnVector Moon(double Mjd_TT) {
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130 |
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131 | const double eps = 23.43929111/RHO_DEG;
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132 | const double T = (Mjd_TT-MJD_J2000)/36525.0;
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133 |
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134 | double L_0 = Frac ( 0.606433 + 1336.851344*T );
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135 | double l = 2.0*M_PI*Frac ( 0.374897 + 1325.552410*T );
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136 | double lp = 2.0*M_PI*Frac ( 0.993133 + 99.997361*T );
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137 | double D = 2.0*M_PI*Frac ( 0.827361 + 1236.853086*T );
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138 | double F = 2.0*M_PI*Frac ( 0.259086 + 1342.227825*T );
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139 |
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140 | double dL = +22640*sin(l) - 4586*sin(l-2*D) + 2370*sin(2*D) + 769*sin(2*l)
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141 | -668*sin(lp) - 412*sin(2*F) - 212*sin(2*l-2*D)- 206*sin(l+lp-2*D)
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142 | +192*sin(l+2*D) - 165*sin(lp-2*D) - 125*sin(D) - 110*sin(l+lp)
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143 | +148*sin(l-lp) - 55*sin(2*F-2*D);
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144 |
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145 | double L = 2.0*M_PI * Frac( L_0 + dL/1296.0e3 );
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146 |
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147 | double S = F + (dL+412*sin(2*F)+541*sin(lp)) / RHO_SEC;
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148 | double h = F-2*D;
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149 | double N = -526*sin(h) + 44*sin(l+h) - 31*sin(-l+h) - 23*sin(lp+h)
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150 | +11*sin(-lp+h) - 25*sin(-2*l+F) + 21*sin(-l+F);
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151 |
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152 | double B = ( 18520.0*sin(S) + N ) / RHO_SEC;
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153 |
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154 | double cosB = cos(B);
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155 |
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156 | double R = 385000e3 - 20905e3*cos(l) - 3699e3*cos(2*D-l) - 2956e3*cos(2*D)
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157 | -570e3*cos(2*l) + 246e3*cos(2*l-2*D) - 205e3*cos(lp-2*D)
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158 | -171e3*cos(l+2*D) - 152e3*cos(l+lp-2*D);
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159 |
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160 | ColumnVector r_Moon(3);
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161 | r_Moon << R*cos(L)*cosB << R*sin(L)*cosB << R*sin(B);
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162 | r_Moon = rotX(-eps) * r_Moon;
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163 |
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164 | return rotZ(GMST(Mjd_TT))
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165 | * NutMatrix(Mjd_TT)
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166 | * PrecMatrix(MJD_J2000, Mjd_TT)
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167 | * r_Moon;
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168 | }
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