[90] | 1 | #include <stdio.h> |
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[89] | 2 | #include <math.h> |
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[90] | 3 | #include <malloc.h> |
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[91] | 4 | #include <omp.h> |
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| 5 | |
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[89] | 6 | #define ROTATE(a,i,j,k,l) g=a[i][j];h=a[k][l];a[i][j]=g-s*(h+g*tau);\ |
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| 7 | a[k][l]=h+s*(g-h*tau); |
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| 8 | |
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| 9 | /* |
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| 10 | Computes all eigenvalues and eigenvectors of a real symmetric matrix a[1..n][1..n]. On |
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| 11 | output, elements of a above the diagonal are destroyed. d[1..n] returns the eigenvalues of a. |
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| 12 | v[1..n][1..n] is a matrix whose columns contain, on output, the normalized eigenvectors of |
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| 13 | a. nrot returns the number of Jacobi rotations that were required. |
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| 14 | */ |
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| 15 | void jacobi(float **a, int n, float d[], float **v, int *nrot) |
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| 16 | { |
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| 17 | int j,iq,ip,i; |
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[90] | 18 | float tresh,theta,tau,sm,s,h,g,c,*b,*z; |
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| 19 | float t; |
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| 20 | b = (float *) malloc(n * sizeof(float)); |
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| 21 | z = (float *) malloc(n * sizeof(float)); |
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[89] | 22 | |
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[91] | 23 | int nthreads, tid; |
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| 24 | |
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| 25 | /* Fork a team of threads giving them their own copies of variables */ |
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| 26 | #pragma omp parallel private(nthreads, tid) |
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| 27 | { |
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| 28 | |
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| 29 | /* Obtain thread number */ |
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| 30 | tid = omp_get_thread_num(); |
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| 31 | printf("Hello World from thread = %d\n", tid); |
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| 32 | |
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| 33 | /* Only master thread does this */ |
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| 34 | if (tid == 0) |
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| 35 | { |
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| 36 | nthreads = omp_get_num_threads(); |
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| 37 | printf("Number of threads = %d\n", nthreads); |
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| 38 | } |
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| 39 | |
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| 40 | } /* All threads join master thread and disband */ |
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[90] | 41 | |
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| 42 | for (ip=0;ip<n;ip++) { // Initialize to the identity matrix. |
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| 43 | for (iq=0;iq<n;iq++) |
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| 44 | v[ip][iq]=0.0; |
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| 45 | v[ip][ip]=1.0; |
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[89] | 46 | } |
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[90] | 47 | for (ip=0;ip<n;ip++) { // Initialize b and d to the diagonal of a. |
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| 48 | b[ip]=d[ip]=a[ip][ip]; |
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| 49 | z[ip]=0.0; // This vector will accumulate terms of the form t*a[pq] as in equation (11.1.14). |
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[89] | 50 | } |
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| 51 | |
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| 52 | *nrot=0; |
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| 53 | for (i=1;i<=50;i++) { |
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| 54 | sm=0.0; |
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[90] | 55 | for (ip=0;ip<n-1;ip++) { // Sum off-diagonal elements. |
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[89] | 56 | for (iq=ip+1;iq<n;iq++) |
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| 57 | sm += fabs(a[ip][iq]); |
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| 58 | } |
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[90] | 59 | if (sm == 0.0) { // The normal return, which relies on quadratic convergence to machine underflow. |
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| 60 | free(z); |
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| 61 | free(b); |
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[89] | 62 | return; |
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| 63 | } |
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| 64 | if (i < 4) |
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[90] | 65 | tresh=0.2*sm/(n*n); // ...on the first three sweeps. |
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[89] | 66 | else |
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[90] | 67 | tresh=0.0; // ...thereafter. |
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[89] | 68 | for (ip=0;ip<n-1;ip++) { |
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| 69 | for (iq=ip+1;iq<n;iq++) { |
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| 70 | g=100.0*fabs(a[ip][iq]); |
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[90] | 71 | if (i > 4 && (float)(fabs(d[ip])+g) == (float)fabs(d[ip]) // After four sweeps, skip the rotation if the off-diagonal element is small. |
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[89] | 72 | && (float)(fabs(d[iq])+g) == (float)fabs(d[iq])) |
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| 73 | a[ip][iq]=0.0; |
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| 74 | else if (fabs(a[ip][iq]) > tresh) { |
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| 75 | h=d[iq]-d[ip]; |
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| 76 | if ((float)(fabs(h)+g) == (float)fabs(h)) |
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[90] | 77 | t=(a[ip][iq])/h; // t = 1/(2*theta) |
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[89] | 78 | else { |
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[90] | 79 | theta=0.5*h/(a[ip][iq]); |
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[89] | 80 | t=1.0/(fabs(theta)+sqrt(1.0+theta*theta)); |
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| 81 | if (theta < 0.0) t = -t; |
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| 82 | } |
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| 83 | |
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| 84 | c=1.0/sqrt(1+t*t); |
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| 85 | s=t*c; |
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| 86 | tau=s/(1.0+c); |
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| 87 | h=t*a[ip][iq]; |
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| 88 | z[ip] -= h; |
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| 89 | z[iq] += h; |
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| 90 | d[ip] -= h; |
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| 91 | d[iq] += h; |
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| 92 | a[ip][iq]=0.0; |
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| 93 | |
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[92] | 94 | for (j=0;j<=ip-1;j++) { // Case of rotations 1 <= j < p. |
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[89] | 95 | ROTATE(a,j,ip,j,iq) |
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[90] | 96 | } |
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[92] | 97 | for (j=ip+1;j<=iq-1;j++) { // Case of rotations p < j < q. |
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[89] | 98 | ROTATE(a,ip,j,j,iq) |
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| 99 | } |
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[90] | 100 | for (j=iq+1;j<n;j++) { // Case of rotations q < j <= n. |
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[89] | 101 | ROTATE(a,ip,j,iq,j) |
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| 102 | } |
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| 103 | for (j=0;j<n;j++) { |
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| 104 | ROTATE(v,j,ip,j,iq) |
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| 105 | } |
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| 106 | |
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| 107 | ++(*nrot); |
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| 108 | } |
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| 109 | } |
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| 110 | } |
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| 111 | |
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| 112 | for (ip=0;ip<n;ip++) { |
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| 113 | b[ip] += z[ip]; |
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[90] | 114 | d[ip]=b[ip]; // Update d with the sum of t*a[pq], |
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| 115 | z[ip]=0.0; // and reinitialize z. |
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[89] | 116 | } |
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| 117 | } |
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| 118 | |
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| 119 | printf("Too many iterations in routine jacobi\n"); |
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[90] | 120 | } |
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| 121 | |
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[91] | 122 | int main(int argc, char * argv[]) |
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[90] | 123 | { |
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| 124 | int n, i, j; |
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| 125 | float *d; |
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| 126 | float **a; |
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| 127 | float **v; |
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| 128 | int nrot = 0; |
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[91] | 129 | |
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| 130 | char * filename = argv[1]; |
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| 131 | FILE * f = fopen(filename, "r"); |
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[90] | 132 | fscanf(f,"%d", &n); |
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| 133 | |
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| 134 | a = (float **)malloc(n * sizeof(float*)); |
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| 135 | for(i = 0; i < n; i++) |
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| 136 | a[i] = (float *)malloc(n * sizeof(float)); |
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| 137 | |
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| 138 | v = (float **)malloc(n * sizeof(float*)); |
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| 139 | for(i = 0; i < n; i++) |
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| 140 | v[i] = (float *)malloc(n * sizeof(float)); |
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| 141 | |
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| 142 | d = (float *)malloc(n * sizeof(float)); |
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| 143 | |
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| 144 | for(i = 0; i < n; i++) |
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| 145 | for(j = 0; j < n; j++) |
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| 146 | fscanf(f,"%f", &a[i][j]); |
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| 147 | for(i = 0; i < n; i++) |
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| 148 | { |
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| 149 | for(j = 0; j < n; j++) |
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| 150 | printf("%f ", a[i][j]); |
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| 151 | printf("\n"); |
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| 152 | } |
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| 153 | |
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| 154 | jacobi(a, n, d, v, &nrot); |
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| 155 | |
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| 156 | printf("v:\n"); |
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| 157 | for(i = 0; i < n; i++) |
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| 158 | { |
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| 159 | for(j = 0; j < n; j++) |
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| 160 | printf("%f ", v[i][j]); |
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| 161 | printf("\n"); |
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| 162 | } |
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| 163 | |
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| 164 | printf("d:\n"); |
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| 165 | for(i = 0; i < n; i++) |
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| 166 | { |
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| 167 | printf("%f ", d[i]); |
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| 168 | } |
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[91] | 169 | printf("\n"); |
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[90] | 170 | |
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| 171 | return 0; |
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| 172 | } |
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| 173 | |
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