[becded3] | 1 | static double |
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| 2 | stacked_disks_kernel( |
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[2a0b2b1] | 3 | double qab, |
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| 4 | double qc, |
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[edf1e8b] | 5 | double halfheight, |
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| 6 | double thick_layer, |
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| 7 | double radius, |
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[19f996b] | 8 | int n_stacking, |
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[edf1e8b] | 9 | double sigma_dnn, |
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| 10 | double core_sld, |
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| 11 | double layer_sld, |
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| 12 | double solvent_sld, |
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| 13 | double d) |
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[66d119f] | 14 | |
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| 15 | { |
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[3ac4e1b] | 16 | // q is the q-value for the calculation (1/A) |
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| 17 | // radius is the core radius of the cylinder (A) |
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| 18 | // *_sld are the respective SLD's |
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| 19 | // halfheight is the *Half* CORE-LENGTH of the cylinder = L (A) |
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| 20 | // zi is the dummy variable for the integration (x in Feigin's notation) |
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| 21 | |
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[2a0b2b1] | 22 | const double besarg1 = radius*qab; |
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| 23 | //const double besarg2 = radius*qab; |
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[3ac4e1b] | 24 | |
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[2a0b2b1] | 25 | const double sinarg1 = halfheight*qc; |
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| 26 | const double sinarg2 = (halfheight+thick_layer)*qc; |
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[3ac4e1b] | 27 | |
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[592343f] | 28 | const double be1 = sas_2J1x_x(besarg1); |
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[6c3e266] | 29 | //const double be2 = sas_2J1x_x(besarg2); |
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[3ac4e1b] | 30 | const double be2 = be1; |
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[1e7b0db0] | 31 | const double si1 = sas_sinx_x(sinarg1); |
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| 32 | const double si2 = sas_sinx_x(sinarg2); |
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[3ac4e1b] | 33 | |
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| 34 | const double dr1 = core_sld - solvent_sld; |
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| 35 | const double dr2 = layer_sld - solvent_sld; |
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| 36 | const double area = M_PI*radius*radius; |
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| 37 | const double totald = 2.0*(thick_layer + halfheight); |
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| 38 | |
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| 39 | const double t1 = area * (2.0*halfheight) * dr1 * si1 * be1; |
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| 40 | const double t2 = area * dr2 * (totald*si2 - 2.0*halfheight*si1) * be2; |
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| 41 | |
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| 42 | double pq = square(t1 + t2); |
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| 43 | |
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| 44 | // loop for the structure factor S(q) |
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[2a0b2b1] | 45 | double qd_cos_alpha = d*qc; |
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[98ce141] | 46 | //d*cos_alpha is the projection of d onto q (in other words the component |
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| 47 | //of d that is parallel to q. |
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[3ac4e1b] | 48 | double debye_arg = -0.5*square(qd_cos_alpha*sigma_dnn); |
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| 49 | double sq=0.0; |
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| 50 | for (int kk=1; kk<n_stacking; kk++) { |
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| 51 | sq += (n_stacking-kk) * cos(qd_cos_alpha*kk) * exp(debye_arg*kk); |
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| 52 | } |
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| 53 | // end of loop for S(q) |
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| 54 | sq = 1.0 + 2.0*sq/n_stacking; |
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| 55 | |
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[98ce141] | 56 | return pq * sq * n_stacking; |
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| 57 | // volume normalization should be per disk not per stack but form_volume |
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| 58 | // is per stack so correct here for now. Could change form_volume but |
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| 59 | // if one ever wants to use P*S we need the ER based on the total volume |
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[66d119f] | 60 | } |
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| 61 | |
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| 62 | |
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[becded3] | 63 | static double |
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| 64 | stacked_disks_1d( |
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[edf1e8b] | 65 | double q, |
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| 66 | double thick_core, |
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| 67 | double thick_layer, |
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| 68 | double radius, |
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[19f996b] | 69 | int n_stacking, |
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[edf1e8b] | 70 | double sigma_dnn, |
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| 71 | double core_sld, |
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| 72 | double layer_sld, |
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| 73 | double solvent_sld) |
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[66d119f] | 74 | { |
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[3ac4e1b] | 75 | /* StackedDiscsX : calculates the form factor of a stacked "tactoid" of core shell disks |
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[66d119f] | 76 | like clay platelets that are not exfoliated |
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| 77 | */ |
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[3ac4e1b] | 78 | double summ = 0.0; //initialize integral |
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| 79 | |
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| 80 | double d = 2.0*thick_layer+thick_core; |
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| 81 | double halfheight = 0.5*thick_core; |
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| 82 | |
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[74768cb] | 83 | for(int i=0; i<GAUSS_N; i++) { |
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| 84 | double zi = (GAUSS_Z[i] + 1.0)*M_PI_4; |
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[3ac4e1b] | 85 | double sin_alpha, cos_alpha; // slots to hold sincos function output |
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| 86 | SINCOS(zi, sin_alpha, cos_alpha); |
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[2a0b2b1] | 87 | double yyy = stacked_disks_kernel(q*sin_alpha, q*cos_alpha, |
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[edf1e8b] | 88 | halfheight, |
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| 89 | thick_layer, |
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[3ac4e1b] | 90 | radius, |
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[edf1e8b] | 91 | n_stacking, |
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| 92 | sigma_dnn, |
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[3ac4e1b] | 93 | core_sld, |
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| 94 | layer_sld, |
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| 95 | solvent_sld, |
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[edf1e8b] | 96 | d); |
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[74768cb] | 97 | summ += GAUSS_W[i] * yyy * sin_alpha; |
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[3ac4e1b] | 98 | } |
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| 99 | |
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| 100 | double answer = M_PI_4*summ; |
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| 101 | |
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| 102 | //Convert to [cm-1] |
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| 103 | return 1.0e-4*answer; |
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[66d119f] | 104 | } |
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| 105 | |
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[becded3] | 106 | static double |
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| 107 | form_volume( |
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[edf1e8b] | 108 | double thick_core, |
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| 109 | double thick_layer, |
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| 110 | double radius, |
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| 111 | double fp_n_stacking) |
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| 112 | { |
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| 113 | int n_stacking = (int)(fp_n_stacking + 0.5); |
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[6831fa0] | 114 | double d = 2.0 * thick_layer + thick_core; |
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| 115 | return M_PI * radius * radius * d * n_stacking; |
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[66d119f] | 116 | } |
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| 117 | |
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[becded3] | 118 | static double |
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| 119 | Iq( |
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[edf1e8b] | 120 | double q, |
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| 121 | double thick_core, |
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| 122 | double thick_layer, |
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| 123 | double radius, |
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| 124 | double fp_n_stacking, |
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| 125 | double sigma_dnn, |
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| 126 | double core_sld, |
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| 127 | double layer_sld, |
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| 128 | double solvent_sld) |
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[66d119f] | 129 | { |
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[edf1e8b] | 130 | int n_stacking = (int)(fp_n_stacking + 0.5); |
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| 131 | return stacked_disks_1d(q, |
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[a807206] | 132 | thick_core, |
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| 133 | thick_layer, |
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[66d119f] | 134 | radius, |
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| 135 | n_stacking, |
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[a807206] | 136 | sigma_dnn, |
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[66d119f] | 137 | core_sld, |
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| 138 | layer_sld, |
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| 139 | solvent_sld); |
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| 140 | } |
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[6831fa0] | 141 | |
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| 142 | |
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[becded3] | 143 | static double |
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[108e70e] | 144 | Iqac(double qab, double qc, |
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[edf1e8b] | 145 | double thick_core, |
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| 146 | double thick_layer, |
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| 147 | double radius, |
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| 148 | double fp_n_stacking, |
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| 149 | double sigma_dnn, |
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| 150 | double core_sld, |
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| 151 | double layer_sld, |
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[becded3] | 152 | double solvent_sld) |
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[6831fa0] | 153 | { |
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[b34fc77] | 154 | int n_stacking = (int)(fp_n_stacking + 0.5); |
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[6831fa0] | 155 | double d = 2.0 * thick_layer + thick_core; |
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| 156 | double halfheight = 0.5*thick_core; |
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[2a0b2b1] | 157 | double answer = stacked_disks_kernel(qab, qc, |
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[edf1e8b] | 158 | halfheight, |
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| 159 | thick_layer, |
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[6831fa0] | 160 | radius, |
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[edf1e8b] | 161 | n_stacking, |
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| 162 | sigma_dnn, |
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[6831fa0] | 163 | core_sld, |
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| 164 | layer_sld, |
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| 165 | solvent_sld, |
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[edf1e8b] | 166 | d); |
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[6831fa0] | 167 | |
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| 168 | //convert to [cm-1] |
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| 169 | answer *= 1.0e-4; |
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| 170 | |
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| 171 | return answer; |
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| 172 | } |
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| 173 | |
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