1 // -*- C++ -*- 2 /** 3 * @brief Sobol' sequence directions 4 * 5 * Copyright 2005-2021 Airbus-EDF-IMACS-ONERA-Phimeca 6 * 7 * This library is free software: you can redistribute it and/or modify 8 * it under the terms of the GNU Lesser General Public License as published by 9 * the Free Software Foundation, either version 3 of the License, or 10 * (at your option) any later version. 11 * 12 * This library is distributed in the hope that it will be useful, 13 * but WITHOUT ANY WARRANTY; without even the implied warranty of 14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 * GNU Lesser General Public License for more details. 16 * 17 * You should have received a copy of the GNU Lesser General Public License 18 * along with this library. If not, see <http://www.gnu.org/licenses/>. 19 * 20 * The directions and primitive polynomials are based on the scilab lowdisc module: 21 * https://atoms.scilab.org/toolboxes/lowdisc 22 * which is covered by the LGPL license 23 */ 24 25 const UnsignedInteger SobolSequence::MaximumDimension = 1111; 26 const UnsignedInteger SobolSequence::MaximumInitialDegree = 13; 27 28 const UnsignedInteger SobolSequence::InitialBase[MaximumDimension * MaximumInitialDegree] = 29 { 30 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33 1, 3, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34 1, 1, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35 1, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36 1, 1, 3, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37 1, 3, 3, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 38 1, 3, 7, 13, 3, 0, 0, 0, 0, 0, 0, 0, 0, 39 1, 1, 5, 11, 27, 0, 0, 0, 0, 0, 0, 0, 0, 40 1, 3, 5, 1, 15, 0, 0, 0, 0, 0, 0, 0, 0, 41 1, 1, 7, 3, 29, 0, 0, 0, 0, 0, 0, 0, 0, 42 1, 3, 7, 7, 21, 0, 0, 0, 0, 0, 0, 0, 0, 43 1, 1, 1, 9, 23, 37, 0, 0, 0, 0, 0, 0, 0, 44 1, 3, 3, 5, 19, 33, 0, 0, 0, 0, 0, 0, 0, 45 1, 1, 3, 13, 11, 7, 0, 0, 0, 0, 0, 0, 0, 46 1, 1, 7, 13, 25, 5, 0, 0, 0, 0, 0, 0, 0, 47 1, 3, 5, 11, 7, 11, 0, 0, 0, 0, 0, 0, 0, 48 1, 1, 1, 3, 13, 39, 0, 0, 0, 0, 0, 0, 0, 49 1, 3, 1, 15, 17, 63, 13, 0, 0, 0, 0, 0, 0, 50 1, 1, 5, 5, 1, 59, 33, 0, 0, 0, 0, 0, 0, 51 1, 3, 3, 3, 25, 17, 115, 0, 0, 0, 0, 0, 0, 52 1, 1, 7, 15, 29, 15, 41, 0, 0, 0, 0, 0, 0, 53 1, 3, 1, 7, 3, 23, 79, 0, 0, 0, 0, 0, 0, 54 1, 3, 7, 9, 31, 29, 17, 0, 0, 0, 0, 0, 0, 55 1, 1, 5, 13, 11, 3, 29, 0, 0, 0, 0, 0, 0, 56 1, 1, 1, 9, 5, 21, 119, 0, 0, 0, 0, 0, 0, 57 1, 1, 3, 1, 23, 13, 75, 0, 0, 0, 0, 0, 0, 58 1, 3, 7, 11, 27, 31, 73, 0, 0, 0, 0, 0, 0, 59 1, 1, 7, 7, 19, 25, 105, 0, 0, 0, 0, 0, 0, 60 1, 3, 1, 5, 21, 9, 7, 0, 0, 0, 0, 0, 0, 61 1, 1, 1, 15, 5, 49, 59, 0, 0, 0, 0, 0, 0, 62 1, 3, 1, 1, 1, 33, 65, 0, 0, 0, 0, 0, 0, 63 1, 3, 5, 15, 17, 19, 21, 0, 0, 0, 0, 0, 0, 64 1, 1, 7, 11, 13, 29, 3, 0, 0, 0, 0, 0, 0, 65 1, 3, 7, 5, 7, 11, 113, 0, 0, 0, 0, 0, 0, 66 1, 1, 5, 11, 15, 19, 61, 0, 0, 0, 0, 0, 0, 67 1, 1, 1, 1, 9, 27, 89, 7, 0, 0, 0, 0, 0, 68 1, 1, 3, 7, 31, 15, 45, 23, 0, 0, 0, 0, 0, 69 1, 3, 3, 9, 25, 25, 107, 39, 0, 0, 0, 0, 0, 70 1, 1, 7, 7, 3, 63, 21, 217, 0, 0, 0, 0, 0, 71 1, 3, 5, 7, 5, 55, 71, 141, 0, 0, 0, 0, 0, 72 1, 1, 5, 1, 23, 17, 79, 27, 0, 0, 0, 0, 0, 73 1, 1, 5, 15, 7, 63, 19, 53, 0, 0, 0, 0, 0, 74 1, 1, 3, 15, 3, 49, 71, 181, 0, 0, 0, 0, 0, 75 1, 3, 3, 15, 17, 19, 61, 169, 0, 0, 0, 0, 0, 76 1, 3, 3, 13, 23, 41, 41, 35, 0, 0, 0, 0, 0, 77 1, 1, 1, 3, 3, 59, 57, 15, 0, 0, 0, 0, 0, 78 1, 3, 1, 3, 3, 3, 121, 207, 0, 0, 0, 0, 0, 79 1, 3, 5, 15, 21, 57, 87, 45, 0, 0, 0, 0, 0, 80 1, 1, 1, 5, 25, 33, 119, 247, 0, 0, 0, 0, 0, 81 1, 1, 1, 9, 25, 49, 55, 185, 0, 0, 0, 0, 0, 82 1, 3, 5, 7, 23, 53, 85, 117, 0, 0, 0, 0, 0, 83 1, 3, 3, 13, 11, 57, 121, 41, 235, 0, 0, 0, 0, 84 1, 1, 3, 3, 19, 57, 119, 81, 307, 0, 0, 0, 0, 85 1, 3, 3, 7, 3, 39, 11, 223, 495, 0, 0, 0, 0, 86 1, 3, 3, 5, 11, 21, 23, 151, 417, 0, 0, 0, 0, 87 1, 3, 1, 11, 31, 7, 61, 81, 57, 0, 0, 0, 0, 88 1, 1, 3, 9, 7, 53, 11, 189, 151, 0, 0, 0, 0, 89 1, 3, 7, 1, 9, 9, 35, 61, 19, 0, 0, 0, 0, 90 1, 1, 5, 9, 5, 55, 33, 95, 119, 0, 0, 0, 0, 91 1, 3, 7, 1, 17, 15, 43, 185, 375, 0, 0, 0, 0, 92 1, 1, 3, 5, 23, 59, 107, 23, 451, 0, 0, 0, 0, 93 1, 1, 7, 7, 17, 19, 113, 73, 55, 0, 0, 0, 0, 94 1, 3, 1, 13, 17, 49, 101, 113, 449, 0, 0, 0, 0, 95 1, 3, 3, 9, 25, 31, 29, 239, 501, 0, 0, 0, 0, 96 1, 1, 3, 9, 13, 3, 87, 85, 53, 0, 0, 0, 0, 97 1, 1, 5, 1, 11, 39, 119, 9, 185, 0, 0, 0, 0, 98 1, 1, 1, 7, 31, 5, 97, 201, 317, 0, 0, 0, 0, 99 1, 1, 3, 3, 27, 5, 29, 83, 17, 0, 0, 0, 0, 100 1, 3, 5, 5, 19, 41, 17, 53, 21, 0, 0, 0, 0, 101 1, 1, 5, 1, 17, 9, 89, 183, 487, 0, 0, 0, 0, 102 1, 1, 7, 11, 23, 19, 5, 203, 13, 0, 0, 0, 0, 103 1, 3, 7, 11, 7, 9, 127, 91, 347, 0, 0, 0, 0, 104 1, 1, 7, 13, 5, 57, 89, 149, 393, 0, 0, 0, 0, 105 1, 1, 1, 7, 11, 25, 119, 101, 15, 0, 0, 0, 0, 106 1, 1, 1, 7, 19, 1, 117, 13, 391, 0, 0, 0, 0, 107 1, 3, 3, 9, 19, 15, 103, 111, 307, 0, 0, 0, 0, 108 1, 3, 3, 9, 7, 51, 105, 239, 189, 0, 0, 0, 0, 109 1, 1, 1, 1, 13, 11, 41, 3, 381, 0, 0, 0, 0, 110 1, 3, 1, 1, 21, 19, 83, 205, 71, 0, 0, 0, 0, 111 1, 3, 5, 3, 21, 61, 25, 253, 163, 0, 0, 0, 0, 112 1, 1, 1, 9, 7, 53, 41, 247, 99, 0, 0, 0, 0, 113 1, 3, 5, 15, 9, 29, 55, 121, 467, 0, 0, 0, 0, 114 1, 3, 7, 1, 11, 19, 69, 189, 167, 0, 0, 0, 0, 115 1, 3, 5, 5, 1, 11, 117, 169, 433, 0, 0, 0, 0, 116 1, 1, 1, 13, 5, 9, 49, 179, 337, 0, 0, 0, 0, 117 1, 3, 7, 1, 21, 21, 127, 197, 257, 0, 0, 0, 0, 118 1, 3, 5, 9, 11, 19, 29, 175, 179, 0, 0, 0, 0, 119 1, 3, 3, 9, 13, 43, 1, 217, 47, 0, 0, 0, 0, 120 1, 1, 3, 9, 25, 13, 99, 249, 385, 0, 0, 0, 0, 121 1, 3, 1, 9, 9, 13, 53, 195, 23, 0, 0, 0, 0, 122 1, 3, 5, 9, 7, 41, 83, 95, 117, 0, 0, 0, 0, 123 1, 1, 7, 13, 7, 25, 15, 63, 369, 0, 0, 0, 0, 124 1, 3, 1, 11, 27, 31, 31, 19, 425, 0, 0, 0, 0, 125 1, 3, 7, 3, 15, 9, 73, 7, 207, 0, 0, 0, 0, 126 1, 3, 5, 5, 25, 11, 115, 5, 433, 0, 0, 0, 0, 127 1, 1, 1, 11, 15, 19, 35, 75, 301, 0, 0, 0, 0, 128 1, 3, 7, 11, 21, 5, 21, 217, 147, 0, 0, 0, 0, 129 1, 1, 3, 13, 17, 53, 89, 245, 333, 0, 0, 0, 0, 130 1, 3, 1, 5, 19, 37, 5, 111, 85, 0, 0, 0, 0, 131 1, 1, 7, 3, 19, 7, 1, 189, 221, 519, 0, 0, 0, 132 1, 1, 1, 15, 21, 51, 91, 165, 423, 307, 0, 0, 0, 133 1, 3, 7, 1, 5, 45, 53, 169, 49, 931, 0, 0, 0, 134 1, 3, 3, 11, 11, 7, 35, 141, 3, 1023, 0, 0, 0, 135 1, 1, 3, 11, 3, 7, 95, 221, 43, 517, 0, 0, 0, 136 1, 3, 5, 7, 5, 61, 83, 249, 229, 771, 0, 0, 0, 137 1, 3, 7, 13, 29, 23, 19, 159, 227, 151, 0, 0, 0, 138 1, 1, 3, 15, 31, 45, 85, 253, 201, 1023, 0, 0, 0, 139 1, 1, 3, 11, 29, 7, 55, 207, 383, 539, 0, 0, 0, 140 1, 1, 5, 13, 5, 59, 51, 249, 281, 725, 0, 0, 0, 141 1, 3, 1, 9, 5, 41, 101, 219, 229, 45, 0, 0, 0, 142 1, 3, 3, 11, 1, 1, 33, 23, 207, 927, 0, 0, 0, 143 1, 1, 3, 15, 31, 29, 41, 49, 21, 707, 0, 0, 0, 144 1, 3, 1, 15, 27, 61, 55, 127, 343, 29, 0, 0, 0, 145 1, 3, 3, 13, 11, 37, 45, 237, 251, 125, 0, 0, 0, 146 1, 1, 5, 3, 13, 27, 95, 5, 397, 371, 0, 0, 0, 147 1, 3, 1, 15, 1, 47, 61, 25, 173, 275, 0, 0, 0, 148 1, 1, 3, 7, 3, 15, 27, 177, 507, 279, 0, 0, 0, 149 1, 1, 3, 9, 7, 31, 37, 37, 421, 817, 0, 0, 0, 150 1, 3, 3, 11, 11, 35, 89, 103, 443, 389, 0, 0, 0, 151 1, 3, 7, 13, 7, 31, 75, 65, 399, 453, 0, 0, 0, 152 1, 3, 1, 11, 3, 17, 57, 167, 53, 989, 0, 0, 0, 153 1, 1, 1, 9, 23, 51, 61, 81, 345, 1015, 0, 0, 0, 154 1, 1, 7, 9, 13, 13, 15, 87, 77, 29, 0, 0, 0, 155 1, 1, 3, 5, 31, 25, 117, 119, 385, 169, 0, 0, 0, 156 1, 3, 1, 13, 17, 45, 15, 45, 317, 743, 0, 0, 0, 157 1, 1, 3, 9, 1, 5, 21, 79, 155, 99, 0, 0, 0, 158 1, 1, 7, 1, 27, 5, 27, 143, 187, 923, 0, 0, 0, 159 1, 3, 5, 13, 11, 33, 25, 57, 269, 981, 0, 0, 0, 160 1, 1, 5, 7, 25, 39, 27, 79, 501, 181, 0, 0, 0, 161 1, 1, 7, 7, 1, 5, 123, 187, 19, 693, 0, 0, 0, 162 1, 3, 5, 7, 23, 47, 39, 143, 169, 309, 0, 0, 0, 163 1, 3, 5, 7, 29, 29, 109, 183, 235, 227, 0, 0, 0, 164 1, 1, 3, 7, 17, 35, 93, 75, 415, 111, 0, 0, 0, 165 1, 3, 1, 5, 25, 47, 51, 97, 61, 219, 0, 0, 0, 166 1, 1, 3, 9, 7, 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3, 9, 9, 39, 107, 197, 385, 385, 991, 3991, 569, 565 1, 3, 7, 15, 7, 5, 37, 15, 289, 261, 1997, 575, 1021, 566 1, 3, 1, 13, 11, 19, 81, 97, 363, 345, 841, 1877, 2077, 567 1, 1, 5, 15, 15, 61, 67, 197, 331, 297, 459, 1009, 5945, 568 1, 1, 5, 9, 19, 61, 29, 139, 265, 199, 221, 3929, 1833, 569 1, 3, 1, 13, 15, 57, 115, 203, 407, 385, 327, 473, 2631, 570 1, 3, 1, 1, 27, 59, 119, 63, 37, 617, 1595, 3009, 4851, 571 1, 1, 3, 11, 17, 21, 75, 33, 433, 25, 1881, 2595, 6371, 572 1, 3, 1, 7, 11, 59, 73, 251, 315, 515, 1269, 3249, 833, 573 1, 3, 3, 11, 11, 61, 99, 217, 343, 275, 1007, 675, 7987, 574 1, 1, 3, 3, 31, 57, 103, 199, 63, 849, 129, 3593, 331, 575 1, 3, 7, 13, 13, 25, 7, 199, 51, 401, 1413, 2453, 1899, 576 1, 3, 1, 5, 25, 55, 57, 99, 185, 471, 475, 1567, 8093, 577 1, 1, 7, 1, 25, 27, 45, 249, 71, 377, 1105, 973, 6719, 578 1, 1, 3, 7, 9, 31, 61, 33, 27, 661, 791, 595, 6903, 579 1, 3, 1, 15, 7, 41, 95, 229, 267, 535, 1983, 1335, 5903, 580 1, 1, 7, 3, 13, 33, 49, 177, 503, 505, 1359, 1715, 5657, 581 1, 3, 3, 13, 29, 63, 101, 13, 239, 939, 503, 589, 5007, 582 1, 3, 1, 7, 19, 19, 101, 209, 293, 465, 691, 85, 2689, 583 1, 1, 7, 13, 5, 57, 35, 147, 245, 225, 659, 2265, 6637, 584 1, 1, 3, 13, 19, 35, 47, 97, 281, 929, 691, 3069, 2675, 585 1, 3, 5, 11, 31, 13, 119, 31, 297, 219, 343, 461, 1645, 586 1, 1, 3, 3, 25, 63, 39, 125, 75, 955, 1375, 1659, 1819, 587 1, 3, 5, 5, 13, 35, 67, 177, 461, 659, 1919, 2627, 689, 588 1, 1, 7, 3, 25, 17, 31, 137, 371, 441, 263, 1307, 6709, 589 1, 3, 3, 13, 15, 11, 103, 187, 129, 117, 1373, 1731, 7717, 590 1, 1, 3, 11, 5, 11, 7, 11, 189, 527, 603, 1501, 6295, 591 1, 1, 3, 9, 9, 49, 61, 91, 189, 427, 1383, 1699, 7013, 592 1, 3, 5, 9, 29, 41, 127, 223, 339, 515, 297, 3545, 7695, 593 1, 3, 1, 3, 31, 55, 87, 29, 287, 287, 781, 3803, 3705, 594 1, 1, 7, 11, 9, 5, 3, 169, 111, 191, 145, 2157, 7069, 595 1, 1, 7, 11, 29, 45, 35, 231, 111, 33, 285, 453, 2621, 596 1, 1, 1, 7, 27, 17, 29, 59, 379, 389, 767, 2813, 3631, 597 1, 3, 3, 9, 25, 35, 73, 31, 93, 197, 1739, 2047, 6571, 598 1, 3, 1, 13, 27, 5, 95, 163, 27, 825, 1715, 2999, 6259, 599 1, 1, 3, 11, 11, 31, 103, 41, 185, 63, 715, 3841, 7261, 600 1, 3, 7, 7, 17, 31, 71, 57, 347, 417, 317, 2361, 3397, 601 1, 1, 7, 15, 5, 37, 75, 87, 337, 949, 1333, 1079, 7645, 602 1, 1, 1, 13, 17, 17, 51, 247, 247, 35, 85, 573, 1115, 603 1, 3, 3, 7, 3, 45, 87, 25, 507, 571, 831, 69, 4753, 604 1, 3, 7, 5, 23, 51, 57, 127, 161, 9, 1615, 1363, 2047, 605 1, 1, 3, 3, 15, 1, 97, 101, 231, 131, 81, 1597, 7579, 606 1, 1, 1, 1, 9, 39, 11, 207, 43, 609, 1667, 3427, 2271, 607 1, 3, 5, 5, 9, 49, 105, 187, 499, 439, 1467, 2899, 5403, 608 1, 1, 3, 15, 17, 55, 87, 73, 73, 95, 1457, 2771, 4911, 609 1, 3, 1, 15, 17, 19, 41, 61, 327, 19, 1453, 1327, 7629, 610 1, 1, 1, 3, 31, 41, 73, 105, 263, 569, 1825, 1117, 4225, 611 1, 1, 1, 11, 11, 13, 109, 27, 331, 893, 109, 1523, 1209, 612 1, 1, 5, 1, 19, 5, 69, 91, 249, 451, 387, 3521, 6955, 613 1, 1, 3, 7, 25, 51, 35, 171, 493, 397, 1207, 2393, 6951, 614 1, 1, 3, 3, 13, 5, 121, 243, 37, 971, 2039, 2537, 1829, 615 1, 3, 7, 15, 23, 49, 39, 33, 25, 801, 213, 1979, 5579, 616 1, 1, 1, 11, 15, 1, 111, 3, 115, 125, 1351, 3179, 5231, 617 1, 1, 5, 5, 25, 21, 1, 1, 3, 471, 1329, 683, 1783, 618 1, 1, 3, 5, 21, 13, 77, 21, 167, 187, 1173, 2453, 4285, 619 1, 1, 5, 3, 31, 17, 39, 229, 197, 257, 57, 453, 7425, 620 1, 3, 1, 5, 19, 59, 47, 93, 127, 67, 1769, 1227, 599, 621 1, 1, 3, 5, 3, 51, 53, 71, 357, 949, 951, 779, 5785, 622 1, 3, 1, 1, 11, 11, 91, 61, 497, 621, 183, 671, 3275, 623 1, 1, 3, 15, 25, 3, 3, 37, 103, 453, 23, 3483, 5643, 624 1, 1, 1, 5, 7, 61, 17, 183, 125, 411, 451, 2135, 2263, 625 1, 3, 5, 1, 15, 1, 51, 65, 191, 621, 1155, 3139, 657, 626 1, 3, 7, 5, 19, 33, 83, 211, 165, 955, 1551, 3381, 6769, 627 1, 1, 7, 3, 7, 37, 39, 53, 55, 309, 2037, 3945, 6261, 628 1, 1, 1, 7, 5, 33, 125, 11, 101, 783, 811, 57, 1251, 629 1, 3, 1, 5, 3, 61, 85, 151, 95, 893, 635, 1541, 3249, 630 1, 1, 5, 11, 13, 25, 111, 165, 79, 597, 1671, 3405, 4447, 631 1, 3, 3, 3, 13, 27, 21, 47, 351, 377, 1451, 3381, 4111, 632 1, 1, 1, 13, 1, 59, 69, 5, 341, 753, 863, 2371, 3991, 633 1, 3, 5, 9, 23, 7, 85, 129, 43, 145, 1499, 2879, 1215, 634 1, 3, 1, 13, 5, 49, 29, 79, 125, 637, 1673, 1985, 131, 635 1, 3, 1, 15, 25, 13, 55, 101, 135, 941, 363, 987, 4397, 636 1, 1, 7, 5, 11, 63, 11, 147, 173, 593, 1029, 3017, 3487, 637 1, 3, 7, 3, 25, 3, 117, 169, 289, 317, 1077, 3031, 7585, 638 1, 3, 3, 5, 15, 33, 1, 181, 373, 555, 1525, 3839, 5565, 639 1, 3, 5, 9, 13, 3, 47, 19, 133, 375, 277, 1401, 7199, 640 1, 1, 5, 5, 21, 15, 17, 95, 421, 575, 1023, 3749, 3573, 641 1, 1, 1, 3, 11, 9, 65, 77, 241, 175, 655, 2977, 7105, 642 1, 3, 7, 11, 23, 13, 63, 139, 281, 403, 665, 681, 7409, 643 1, 3, 1, 1, 29, 35, 47, 197, 213, 571, 1869, 1175, 1671, 644 1, 3, 5, 13, 5, 39, 117, 219, 177, 555, 1255, 1519, 949, 645 1, 1, 1, 9, 17, 11, 17, 97, 363, 109, 965, 3355, 3889, 646 1, 1, 1, 15, 27, 59, 115, 239, 151, 377, 277, 907, 5971, 647 1, 1, 3, 3, 9, 59, 51, 183, 227, 931, 1601, 117, 3333, 648 1, 1, 1, 5, 19, 1, 25, 143, 145, 499, 329, 771, 225, 649 1, 3, 5, 11, 15, 57, 33, 9, 363, 649, 1603, 3741, 3647, 650 1, 1, 7, 9, 5, 11, 123, 13, 239, 653, 1901, 3337, 5403, 651 1, 3, 5, 1, 29, 5, 123, 209, 431, 329, 395, 1743, 3409, 652 1, 1, 7, 3, 23, 57, 83, 23, 81, 279, 65, 1227, 7459, 653 1, 3, 7, 15, 19, 13, 51, 215, 397, 271, 1307, 3335, 6879, 654 1, 1, 1, 9, 1, 31, 113, 53, 241, 647, 2029, 2755, 5789, 655 1, 1, 5, 9, 27, 13, 95, 137, 67, 721, 21, 1909, 6567, 656 1, 3, 1, 9, 3, 11, 121, 203, 291, 665, 1321, 3603, 5581, 657 1, 3, 1, 11, 23, 55, 51, 19, 255, 429, 543, 2397, 4919, 658 1, 1, 3, 7, 21, 45, 91, 151, 405, 957, 1569, 653, 1927, 659 1, 1, 5, 5, 19, 9, 109, 171, 421, 803, 1185, 87, 4407, 660 1, 1, 1, 13, 27, 55, 43, 133, 399, 767, 1905, 2025, 8085, 661 1, 3, 5, 1, 11, 55, 55, 219, 75, 425, 1701, 2617, 4691, 662 1, 3, 5, 15, 17, 19, 35, 231, 399, 477, 413, 3257, 611, 663 1, 1, 3, 3, 13, 25, 55, 3, 105, 995, 2041, 287, 3005, 664 1, 3, 1, 13, 27, 41, 87, 15, 329, 105, 1697, 3051, 591, 665 1, 1, 3, 9, 11, 23, 33, 253, 41, 495, 725, 3809, 753, 666 1, 3, 1, 13, 31, 45, 37, 225, 425, 575, 1417, 897, 589, 667 1, 1, 5, 5, 23, 29, 5, 33, 7, 687, 1847, 2215, 171, 668 1, 1, 5, 1, 5, 63, 3, 111, 283, 385, 411, 63, 5729, 669 1, 1, 3, 5, 9, 59, 45, 183, 375, 227, 211, 2043, 5891, 670 1, 1, 3, 1, 21, 27, 21, 213, 475, 923, 915, 1757, 1033, 671 1, 1, 3, 13, 31, 39, 105, 169, 427, 563, 1891, 3671, 3049, 672 1, 1, 3, 13, 29, 21, 127, 119, 277, 723, 17, 297, 6567, 673 1, 3, 1, 7, 11, 37, 35, 111, 209, 481, 1877, 3131, 5257, 674 1, 1, 1, 7, 21, 7, 17, 15, 411, 717, 1699, 1305, 8003, 675 1, 3, 3, 1, 17, 61, 35, 201, 3, 111, 687, 293, 1757, 676 1, 3, 1, 9, 15, 49, 37, 123, 137, 633, 1089, 3865, 4489, 677 1, 1, 3, 5, 7, 35, 97, 121, 195, 113, 1973, 3173, 4923, 678 1, 3, 5, 11, 15, 39, 97, 225, 289, 369, 1809, 3397, 6379, 679 1, 3, 5, 9, 7, 9, 21, 113, 509, 955, 851, 2269, 5171, 680 1, 3, 7, 11, 9, 29, 77, 113, 121, 253, 1495, 3673, 1757, 681 1, 1, 5, 13, 21, 7, 123, 225, 55, 321, 1257, 717, 689, 682 1, 3, 5, 3, 27, 25, 17, 161, 147, 409, 63, 3041, 3081, 683 1, 1, 7, 15, 25, 23, 89, 165, 275, 909, 1323, 3341, 1389, 684 1, 1, 5, 15, 29, 57, 53, 1, 251, 367, 1307, 3595, 4113, 685 1, 3, 7, 13, 11, 5, 105, 139, 19, 33, 609, 3819, 455, 686 1, 3, 1, 15, 3, 19, 75, 55, 129, 967, 881, 2871, 2761, 687 1, 1, 3, 7, 21, 15, 25, 3, 285, 453, 1543, 3973, 847, 688 1, 1, 7, 5, 13, 33, 125, 93, 415, 863, 177, 1129, 7575, 689 1, 3, 7, 7, 23, 49, 13, 217, 487, 449, 617, 513, 5829, 690 1, 3, 3, 9, 19, 37, 47, 193, 491, 539, 1505, 871, 633, 691 1, 1, 5, 7, 27, 25, 21, 97, 193, 781, 1747, 1485, 6629, 692 1, 1, 5, 9, 17, 17, 125, 29, 219, 911, 1537, 3977, 1103, 693 1, 1, 7, 9, 29, 45, 23, 69, 403, 113, 925, 2473, 7635, 694 1, 3, 5, 9, 25, 29, 55, 231, 23, 7, 183, 1171, 803, 695 1, 1, 5, 11, 17, 15, 63, 161, 97, 219, 77, 1143, 6175, 696 1, 3, 3, 9, 9, 25, 61, 93, 65, 725, 1723, 3063, 6587, 697 1, 3, 3, 3, 1, 3, 5, 69, 285, 1015, 1877, 3547, 2711, 698 1, 1, 3, 11, 19, 3, 17, 143, 75, 971, 1703, 2183, 3879, 699 1, 1, 1, 15, 23, 49, 93, 137, 21, 1021, 397, 3993, 67, 700 1, 3, 7, 13, 5, 11, 57, 9, 373, 525, 459, 133, 1179, 701 1, 1, 1, 13, 23, 39, 121, 87, 261, 785, 521, 2529, 4761, 702 1, 1, 5, 5, 1, 15, 69, 183, 339, 873, 257, 2699, 7281, 703 1, 3, 5, 9, 17, 19, 73, 113, 239, 191, 1177, 233, 1557, 704 1, 1, 5, 15, 17, 57, 93, 183, 495, 893, 389, 2355, 3379, 705 1, 3, 3, 1, 13, 39, 121, 73, 415, 297, 1947, 231, 2459, 706 1, 1, 3, 1, 27, 15, 105, 215, 333, 507, 1553, 3241, 4273, 707 1, 1, 5, 9, 23, 11, 75, 137, 107, 215, 1583, 611, 4127, 708 1, 1, 1, 5, 7, 3, 91, 89, 435, 21, 1831, 1309, 7147, 709 1, 3, 3, 13, 7, 57, 67, 251, 297, 153, 261, 3829, 35, 710 1, 3, 1, 3, 11, 31, 95, 163, 213, 645, 485, 1839, 3549, 711 1, 3, 3, 13, 13, 55, 75, 41, 149, 913, 289, 1495, 395, 712 1, 3, 3, 15, 17, 61, 9, 227, 463, 755, 1281, 301, 3735, 713 1, 1, 3, 3, 13, 19, 69, 145, 199, 371, 1543, 1169, 5787, 714 1, 1, 7, 1, 11, 5, 97, 57, 323, 881, 1591, 1613, 4179, 715 1, 3, 1, 3, 21, 41, 99, 81, 45, 113, 1123, 2673, 5889, 716 1, 3, 7, 11, 13, 35, 93, 57, 19, 903, 573, 243, 5057, 717 1, 1, 7, 13, 23, 59, 11, 11, 301, 225, 821, 3601, 7473, 718 1, 1, 3, 1, 1, 61, 53, 135, 121, 49, 1065, 3669, 4713, 719 1, 1, 7, 15, 27, 39, 19, 145, 499, 587, 1933, 2813, 2133, 720 1, 1, 1, 9, 13, 41, 73, 161, 187, 201, 1373, 2671, 2897, 721 1, 3, 1, 9, 9, 53, 5, 175, 229, 927, 2005, 2679, 1841, 722 1, 1, 5, 3, 7, 53, 33, 159, 63, 429, 905, 3463, 2125, 723 1, 1, 7, 1, 1, 63, 79, 25, 425, 599, 207, 2477, 1029, 724 1, 3, 1, 9, 27, 31, 107, 55, 99, 513, 173, 1795, 1695, 725 1, 3, 7, 1, 29, 9, 65, 167, 281, 97, 1573, 617, 6523, 726 1, 3, 1, 9, 5, 59, 69, 157, 35, 319, 1597, 2317, 1143, 727 1, 1, 7, 1, 13, 13, 79, 211, 125, 331, 573, 1855, 5105, 728 1, 1, 7, 13, 25, 35, 125, 97, 349, 833, 1883, 1057, 7133, 729 1, 3, 1, 11, 21, 55, 25, 247, 87, 325, 1795, 1703, 3351, 730 1, 3, 3, 15, 3, 41, 93, 249, 101, 887, 1499, 1761, 2775, 731 1, 1, 7, 7, 31, 49, 55, 23, 59, 139, 1743, 2515, 3971, 732 1, 3, 5, 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867 1, 3, 5, 11, 13, 19, 31, 155, 491, 699, 1027, 3673, 1955, 868 1, 3, 5, 3, 13, 57, 3, 41, 489, 767, 1563, 2693, 2881, 869 1, 3, 7, 13, 5, 13, 103, 9, 439, 917, 859, 3925, 5167, 870 1, 1, 1, 15, 19, 63, 61, 95, 385, 9, 215, 1541, 6451, 871 1, 3, 5, 3, 5, 43, 71, 123, 487, 107, 1673, 1871, 4211, 872 1, 1, 5, 5, 17, 19, 35, 65, 177, 341, 1919, 2285, 179, 873 1, 3, 1, 3, 9, 7, 7, 117, 393, 587, 1633, 847, 5573, 874 1, 1, 5, 5, 11, 13, 119, 249, 33, 903, 779, 4035, 7879, 875 1, 1, 5, 7, 11, 37, 29, 85, 71, 965, 411, 1101, 3387, 876 1, 3, 3, 3, 29, 33, 45, 169, 375, 599, 1845, 2029, 7759, 877 1, 1, 1, 9, 27, 19, 49, 129, 443, 507, 1477, 855, 5455, 878 1, 3, 3, 9, 23, 15, 111, 241, 129, 843, 1489, 2733, 7157, 879 1, 3, 1, 5, 19, 63, 41, 173, 407, 739, 447, 2503, 1891, 880 1, 1, 7, 1, 17, 51, 109, 251, 395, 579, 1545, 121, 5683, 881 1, 3, 3, 7, 25, 11, 59, 225, 127, 397, 351, 2855, 5689, 882 1, 1, 1, 11, 13, 49, 125, 147, 65, 397, 1989, 1069, 6535, 883 1, 3, 3, 9, 1, 23, 13, 165, 333, 325, 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185, 163, 421, 285, 2959, 2431, 935 1, 3, 3, 11, 3, 25, 9, 35, 503, 517, 697, 2925, 5235, 936 1, 3, 7, 3, 19, 33, 53, 133, 99, 971, 163, 3861, 4739, 937 1, 1, 1, 3, 25, 17, 113, 123, 499, 499, 981, 2043, 7703, 938 1, 3, 7, 7, 19, 57, 97, 185, 251, 435, 153, 3887, 7223, 939 1, 1, 1, 1, 27, 29, 73, 27, 239, 769, 1515, 351, 6525, 940 1, 1, 1, 9, 9, 27, 89, 55, 81, 75, 47, 2865, 5891, 941 1, 1, 5, 7, 27, 23, 79, 245, 167, 203, 1553, 369, 5605, 942 1, 1, 1, 15, 13, 47, 49, 61, 391, 793, 599, 1377, 4433, 943 1, 3, 7, 9, 15, 41, 61, 75, 255, 985, 225, 2639, 3533, 944 1, 1, 5, 9, 29, 29, 105, 205, 317, 343, 1147, 1261, 5267, 945 1, 3, 3, 3, 23, 19, 13, 213, 363, 955, 381, 3625, 5125, 946 1, 1, 7, 11, 13, 47, 99, 169, 359, 735, 135, 3279, 5037, 947 1, 1, 3, 15, 25, 41, 53, 163, 395, 523, 821, 2201, 225, 948 1, 3, 5, 7, 25, 25, 71, 63, 419, 659, 1965, 2949, 6717, 949 1, 1, 3, 1, 17, 5, 7, 55, 307, 703, 609, 3049, 1121, 950 1, 3, 1, 3, 19, 51, 87, 49, 251, 303, 1033, 449, 5741, 951 1, 1, 1, 1, 17, 43, 21, 83, 267, 421, 983, 1297, 2013, 952 1, 3, 5, 1, 15, 39, 101, 195, 171, 951, 503, 897, 4327, 953 1, 3, 5, 1, 27, 29, 5, 51, 461, 405, 1117, 1891, 4839, 954 1, 3, 1, 9, 3, 7, 71, 31, 183, 631, 327, 411, 569, 955 1, 3, 7, 1, 25, 31, 31, 41, 465, 825, 453, 2773, 5227, 956 1, 3, 7, 5, 17, 45, 123, 15, 165, 735, 2005, 749, 7677, 957 1, 3, 3, 15, 27, 51, 121, 203, 163, 433, 1257, 2753, 4315, 958 1, 1, 7, 15, 3, 49, 121, 41, 293, 841, 343, 1825, 2391, 959 1, 3, 3, 7, 27, 55, 73, 63, 477, 485, 1649, 853, 5551, 960 1, 3, 7, 5, 31, 17, 79, 127, 223, 49, 1199, 2775, 859, 961 1, 3, 1, 5, 23, 43, 115, 161, 403, 749, 599, 3547, 3627, 962 1, 3, 5, 7, 13, 49, 13, 5, 389, 107, 1877, 3923, 6377, 963 1, 1, 1, 9, 31, 45, 39, 143, 97, 669, 569, 3923, 3903, 964 1, 3, 5, 7, 11, 9, 101, 7, 335, 211, 695, 987, 4311, 965 1, 3, 3, 15, 15, 29, 19, 199, 357, 497, 1587, 3723, 6527, 966 1, 1, 7, 13, 7, 3, 37, 251, 297, 143, 1475, 2189, 7573, 967 1, 3, 3, 13, 21, 5, 51, 95, 19, 99, 187, 3877, 4905, 968 1, 3, 5, 11, 19, 47, 83, 75, 469, 57, 973, 3577, 7731, 969 1, 3, 7, 1, 27, 9, 97, 101, 501, 277, 233, 297, 1909, 970 1, 3, 7, 9, 19, 15, 55, 15, 249, 969, 511, 2763, 1555, 971 1, 3, 7, 11, 21, 19, 81, 43, 85, 107, 51, 1845, 3279, 972 1, 1, 3, 1, 29, 51, 91, 237, 213, 397, 1083, 3083, 1949, 973 1, 1, 3, 13, 7, 45, 127, 197, 311, 563, 665, 2951, 1887, 974 1, 1, 1, 1, 31, 57, 105, 117, 265, 551, 1321, 483, 6675, 975 1, 1, 1, 7, 13, 63, 89, 167, 379, 447, 531, 2169, 5509, 976 1, 3, 5, 15, 9, 9, 63, 155, 297, 381, 1875, 3985, 2033, 977 1, 3, 5, 15, 9, 21, 47, 21, 283, 187, 1939, 245, 5473, 978 1, 3, 3, 5, 7, 59, 49, 83, 393, 57, 859, 3655, 3539, 979 1, 1, 7, 5, 21, 3, 75, 205, 449, 405, 1507, 3441, 5033, 980 1, 3, 1, 1, 13, 9, 37, 255, 463, 731, 1979, 1023, 5935, 981 1, 3, 1, 11, 11, 13, 77, 49, 289, 769, 1203, 235, 6095, 982 1, 1, 1, 3, 9, 45, 15, 101, 159, 923, 1965, 835, 4761, 983 1, 1, 3, 9, 11, 23, 49, 213, 289, 955, 737, 3693, 1771, 984 1, 3, 5, 11, 29, 15, 107, 237, 499, 915, 921, 3585, 1271, 985 1, 3, 3, 9, 19, 31, 23, 135, 407, 737, 1565, 327, 1717, 986 1, 1, 1, 9, 11, 21, 23, 135, 129, 595, 1943, 1003, 4415, 987 1, 1, 1, 9, 19, 15, 35, 21, 137, 341, 819, 543, 5083, 988 1, 3, 3, 1, 21, 51, 19, 73, 221, 253, 223, 3059, 6277, 989 1, 3, 3, 9, 5, 35, 69, 93, 43, 823, 365, 2637, 3147, 990 1, 1, 7, 3, 29, 9, 17, 115, 89, 197, 167, 2923, 7695, 991 1, 3, 5, 5, 13, 11, 59, 7, 403, 321, 1705, 87, 2461, 992 1, 1, 1, 15, 7, 61, 63, 85, 271, 315, 413, 3617, 4783, 993 1, 1, 1, 1, 19, 23, 73, 223, 75, 181, 1577, 1031, 4539, 994 1, 3, 3, 1, 19, 53, 29, 237, 83, 885, 745, 1043, 5833, 995 1, 1, 7, 9, 27, 29, 125, 79, 445, 497, 1573, 903, 5583, 996 1, 3, 1, 7, 23, 51, 61, 89, 453, 159, 655, 2913, 651, 997 1, 3, 5, 3, 31, 45, 65, 5, 389, 571, 1633, 2177, 1419, 998 1, 3, 7, 3, 1, 31, 95, 57, 149, 981, 1003, 2641, 2605, 999 1, 3, 3, 1, 27, 29, 101, 239, 143, 899, 91, 3279, 5511, 1000 1, 3, 7, 9, 21, 5, 81, 67, 423, 785, 1123, 389, 3913, 1001 1, 1, 5, 9, 7, 35, 57, 65, 499, 947, 477, 2009, 5795, 1002 1, 3, 5, 11, 3, 29, 69, 201, 317, 217, 1741, 525, 2333, 1003 1, 1, 7, 9, 7, 53, 83, 155, 445, 217, 1663, 4085, 2329, 1004 1, 1, 3, 9, 11, 35, 37, 71, 157, 135, 35, 3299, 4431, 1005 1, 3, 5, 13, 23, 17, 11, 85, 137, 753, 715, 987, 3725, 1006 1, 3, 3, 13, 13, 59, 37, 195, 453, 623, 37, 2409, 6069, 1007 1, 3, 1, 3, 29, 55, 95, 89, 163, 565, 1513, 813, 2699, 1008 1, 3, 5, 13, 11, 27, 1, 181, 87, 717, 815, 2683, 7055, 1009 1, 1, 3, 11, 31, 51, 73, 119, 23, 903, 941, 373, 6879, 1010 1, 3, 1, 13, 19, 59, 27, 135, 391, 581, 1379, 2695, 1017, 1011 1, 1, 1, 5, 1, 27, 29, 147, 119, 955, 263, 3775, 3121, 1012 1, 1, 7, 1, 5, 47, 57, 237, 427, 621, 1831, 2375, 2547, 1013 1, 3, 5, 5, 5, 15, 7, 173, 323, 361, 1735, 1119, 4603, 1014 1, 3, 1, 5, 11, 29, 65, 41, 173, 869, 1111, 2791, 2385, 1015 1, 3, 7, 9, 5, 37, 83, 155, 89, 87, 1449, 223, 6915, 1016 1, 3, 3, 9, 3, 7, 99, 67, 259, 943, 353, 325, 6103, 1017 1, 3, 7, 3, 27, 49, 69, 113, 377, 907, 1941, 587, 5669, 1018 1, 3, 5, 13, 5, 55, 19, 111, 511, 853, 1655, 1379, 7833, 1019 1, 1, 1, 13, 7, 5, 103, 21, 249, 353, 1349, 2877, 2001, 1020 1, 1, 7, 9, 11, 19, 43, 183, 31, 335, 877, 2867, 4287, 1021 1, 3, 1, 15, 31, 45, 95, 23, 363, 197, 285, 3793, 6619, 1022 1, 1, 7, 9, 1, 29, 25, 103, 229, 771, 1723, 655, 955, 1023 1, 3, 7, 11, 27, 19, 19, 207, 353, 433, 125, 831, 2761, 1024 1, 1, 1, 7, 31, 57, 103, 253, 329, 743, 1753, 3425, 5711, 1025 1, 1, 1, 11, 31, 33, 41, 69, 493, 195, 985, 1663, 6291, 1026 1, 3, 7, 9, 23, 53, 125, 219, 427, 91, 723, 1681, 3415, 1027 1, 1, 1, 13, 5, 45, 97, 205, 57, 1023, 175, 2657, 3909, 1028 1, 1, 5, 9, 21, 21, 71, 195, 205, 63, 439, 1865, 2841, 1029 1, 1, 5, 1, 27, 9, 105, 43, 389, 301, 791, 3943, 5627, 1030 1, 1, 1, 15, 9, 3, 83, 197, 91, 647, 1051, 2977, 4939, 1031 1, 3, 1, 9, 25, 35, 83, 229, 83, 205, 1261, 1979, 7671, 1032 1, 3, 7, 7, 3, 29, 61, 139, 13, 485, 717, 2271, 6059, 1033 1, 1, 5, 7, 15, 43, 39, 177, 219, 927, 1555, 3247, 6275, 1034 1, 1, 7, 1, 19, 31, 9, 129, 439, 1003, 1757, 1267, 6517, 1035 1, 3, 1, 7, 1, 39, 45, 69, 45, 987, 1777, 1747, 1931, 1036 1, 1, 5, 9, 19, 3, 117, 97, 35, 359, 577, 811, 4583, 1037 1, 1, 3, 9, 9, 45, 63, 201, 371, 577, 1583, 159, 7301, 1038 1, 1, 5, 15, 5, 1, 31, 163, 441, 147, 1957, 429, 1267, 1039 1, 3, 3, 1, 25, 41, 5, 189, 17, 141, 873, 2001, 7509, 1040 1, 1, 3, 11, 21, 29, 117, 11, 267, 1017, 331, 1195, 1435, 1041 1, 3, 7, 1, 15, 5, 67, 99, 501, 701, 1163, 3065, 2169, 1042 1, 1, 1, 13, 25, 59, 125, 91, 53, 273, 313, 553, 6939, 1043 1, 1, 5, 13, 29, 41, 41, 253, 25, 89, 1, 1499, 3515, 1044 1, 3, 1, 15, 15, 33, 117, 239, 333, 589, 1963, 3529, 2985, 1045 1, 3, 1, 9, 21, 35, 43, 91, 17, 487, 963, 1081, 2787, 1046 1, 1, 5, 13, 11, 27, 77, 145, 201, 859, 1905, 2877, 2123, 1047 1, 3, 5, 7, 19, 19, 97, 19, 475, 343, 821, 3077, 1969, 1048 1, 1, 3, 15, 15, 13, 15, 179, 257, 91, 1677, 845, 3307, 1049 1, 1, 3, 3, 3, 25, 29, 231, 417, 847, 185, 1793, 353, 1050 1, 3, 7, 9, 7, 27, 5, 121, 345, 341, 709, 2409, 4359, 1051 1, 3, 5, 3, 13, 43, 59, 7, 381, 173, 545, 3995, 7059, 1052 1, 3, 5, 1, 11, 33, 25, 225, 377, 287, 1723, 2559, 5273, 1053 1, 3, 1, 13, 25, 35, 63, 237, 55, 1003, 215, 4081, 5873, 1054 1, 3, 1, 7, 17, 17, 87, 125, 403, 289, 1885, 1195, 6657, 1055 1, 1, 1, 5, 1, 17, 39, 191, 77, 639, 1249, 2955, 6765, 1056 1, 3, 3, 9, 5, 23, 39, 119, 389, 983, 583, 1117, 6229, 1057 1, 1, 1, 3, 31, 7, 77, 59, 347, 685, 1803, 1409, 3179, 1058 1, 1, 5, 1, 13, 35, 85, 175, 363, 697, 839, 785, 1583, 1059 1, 1, 7, 7, 29, 15, 37, 237, 211, 35, 885, 287, 6237, 1060 1, 3, 7, 1, 23, 61, 81, 131, 413, 701, 485, 1521, 2155, 1061 1, 1, 1, 1, 9, 61, 73, 79, 419, 645, 413, 1607, 371, 1062 1, 1, 7, 13, 5, 53, 89, 43, 5, 911, 1767, 85, 273, 1063 1, 1, 5, 3, 29, 5, 29, 45, 167, 501, 425, 3055, 7491, 1064 1, 3, 7, 3, 7, 15, 125, 205, 219, 705, 129, 3123, 3309, 1065 1, 1, 3, 11, 17, 23, 109, 199, 201, 873, 1035, 2533, 6805, 1066 1, 1, 7, 1, 27, 11, 21, 251, 285, 763, 329, 2329, 3015, 1067 1, 3, 3, 7, 7, 13, 23, 153, 425, 745, 1263, 3477, 6831, 1068 1, 1, 1, 13, 17, 43, 119, 207, 11, 657, 1881, 799, 7819, 1069 1, 3, 3, 15, 31, 55, 105, 37, 77, 559, 1779, 3683, 713, 1070 1, 3, 7, 15, 9, 47, 43, 179, 269, 699, 1565, 3715, 4747, 1071 1, 3, 3, 5, 31, 25, 93, 113, 489, 315, 359, 337, 3935, 1072 1, 3, 1, 7, 9, 43, 97, 255, 281, 347, 367, 3139, 4109, 1073 1, 3, 5, 13, 9, 15, 15, 107, 403, 429, 453, 3311, 1311, 1074 1, 1, 5, 13, 7, 57, 125, 217, 79, 197, 707, 431, 709, 1075 1, 1, 3, 15, 21, 45, 29, 61, 425, 165, 1419, 3511, 3089, 1076 1, 1, 5, 11, 3, 1, 51, 7, 125, 955, 831, 2299, 7059, 1077 1, 3, 1, 13, 3, 49, 69, 181, 81, 859, 1889, 365, 4247, 1078 1, 3, 3, 1, 3, 63, 37, 247, 331, 167, 887, 2941, 2989, 1079 1, 3, 5, 13, 9, 57, 45, 31, 437, 303, 1871, 3067, 1509, 1080 1, 3, 5, 13, 11, 15, 31, 13, 271, 833, 1869, 1331, 4919, 1081 1, 1, 5, 3, 21, 31, 75, 113, 397, 531, 747, 1081, 1841, 1082 1, 3, 1, 9, 11, 31, 109, 145, 299, 473, 223, 1097, 3045, 1083 1, 3, 1, 15, 31, 7, 119, 107, 475, 635, 1547, 2853, 3821, 1084 1, 3, 7, 15, 9, 53, 53, 233, 271, 641, 1799, 2299, 6929, 1085 1, 3, 7, 11, 25, 27, 5, 233, 249, 195, 433, 495, 4655, 1086 1, 1, 1, 15, 5, 15, 101, 43, 413, 589, 1441, 1745, 1333, 1087 1, 1, 5, 9, 1, 47, 125, 79, 233, 821, 553, 749, 6429, 1088 1, 3, 5, 15, 31, 23, 121, 23, 261, 205, 2021, 3819, 6649, 1089 1, 3, 1, 1, 13, 7, 35, 169, 495, 3, 1303, 619, 2131, 1090 1, 3, 3, 13, 29, 29, 29, 137, 171, 635, 1505, 1059, 5265, 1091 1, 1, 5, 15, 9, 53, 7, 129, 69, 371, 1735, 3559, 1051, 1092 1, 3, 1, 1, 29, 47, 63, 183, 27, 891, 1619, 183, 261, 1093 1, 1, 5, 1, 1, 9, 17, 53, 409, 249, 1065, 3743, 8057, 1094 1, 1, 3, 5, 11, 53, 63, 91, 21, 123, 1161, 723, 3379, 1095 1, 3, 5, 11, 19, 3, 13, 55, 421, 77, 2047, 949, 2179, 1096 1, 3, 3, 5, 7, 25, 69, 103, 367, 623, 347, 3501, 1993, 1097 1, 1, 3, 1, 27, 55, 15, 223, 81, 993, 867, 733, 5655, 1098 1, 3, 7, 11, 13, 45, 105, 87, 483, 401, 881, 2599, 3063, 1099 1, 3, 5, 11, 31, 63, 51, 177, 255, 525, 1447, 3983, 6381, 1100 1, 1, 7, 5, 7, 21, 127, 157, 15, 427, 329, 3961, 3587, 1101 1, 1, 3, 3, 31, 17, 105, 79, 219, 71, 781, 911, 7417, 1102 1, 1, 7, 9, 7, 23, 9, 213, 365, 655, 1065, 1899, 1579, 1103 1, 1, 3, 1, 25, 31, 57, 139, 497, 951, 219, 985, 1541, 1104 1, 1, 1, 3, 23, 27, 95, 183, 181, 357, 589, 2493, 2107, 1105 1, 3, 3, 5, 21, 27, 59, 231, 75, 851, 645, 1795, 5085, 1106 1, 1, 7, 13, 29, 43, 109, 205, 431, 899, 1257, 653, 2873, 1107 1, 1, 7, 9, 11, 63, 35, 143, 99, 535, 1833, 157, 6141, 1108 1, 3, 3, 7, 11, 55, 49, 129, 325, 493, 749, 433, 955, 1109 1, 3, 3, 7, 13, 63, 23, 243, 407, 323, 1841, 2361, 3537, 1110 1, 1, 1, 1, 11, 45, 33, 205, 229, 1003, 1733, 3093, 2157, 1111 1, 1, 1, 9, 27, 51, 107, 93, 281, 343, 1179, 3119, 841, 1112 1, 1, 3, 9, 1, 15, 55, 59, 63, 515, 1191, 3679, 1999, 1113 1, 3, 3, 15, 23, 27, 33, 15, 83, 859, 1025, 2367, 1465, 1114 1, 1, 3, 7, 31, 5, 57, 89, 493, 1017, 1639, 1701, 5171, 1115 1, 1, 3, 5, 21, 37, 79, 9, 5, 5, 1955, 1445, 5651, 1116 1, 3, 3, 5, 23, 43, 73, 11, 113, 423, 1423, 1321, 1535, 1117 1, 3, 5, 15, 21, 11, 69, 47, 15, 315, 1685, 2397, 7235, 1118 1, 1, 5, 13, 19, 27, 59, 133, 271, 1011, 1711, 1241, 4349, 1119 1, 3, 3, 9, 31, 5, 107, 227, 37, 703, 493, 3305, 1263, 1120 1, 3, 3, 7, 5, 27, 55, 75, 87, 41, 549, 3985, 1453, 1121 1, 3, 3, 13, 31, 59, 11, 9, 451, 777, 783, 2349, 1005, 1122 1, 3, 1, 3, 25, 21, 63, 91, 299, 163, 1653, 4067, 6893, 1123 1, 3, 3, 13, 25, 7, 95, 19, 83, 95, 397, 3805, 2919, 1124 1, 3, 5, 11, 19, 39, 103, 171, 451, 831, 895, 3073, 1947, 1125 1, 3, 7, 13, 17, 27, 23, 163, 311, 79, 233, 2837, 1635, 1126 1, 3, 7, 7, 11, 63, 125, 79, 441, 975, 759, 1567, 3963, 1127 1, 1, 1, 9, 25, 35, 91, 7, 47, 235, 1505, 3783, 397, 1128 1, 1, 5, 13, 7, 47, 31, 103, 455, 633, 677, 451, 969, 1129 1, 3, 7, 13, 13, 55, 91, 5, 47, 723, 1449, 2441, 4569, 1130 1, 3, 3, 13, 1, 17, 51, 119, 253, 297, 1573, 1181, 655, 1131 1, 1, 7, 15, 29, 17, 65, 155, 13, 589, 1297, 487, 6737, 1132 1, 1, 1, 9, 17, 17, 61, 75, 109, 317, 1821, 543, 2995, 1133 1, 3, 1, 5, 23, 3, 75, 11, 369, 679, 1691, 1201, 7235, 1134 1, 1, 3, 5, 15, 19, 69, 71, 347, 981, 791, 3735, 7713, 1135 1, 3, 5, 3, 7, 21, 107, 95, 11, 195, 289, 2517, 973, 1136 1, 3, 7, 3, 29, 13, 65, 17, 409, 399, 1187, 733, 4821, 1137 1, 3, 5, 3, 17, 49, 101, 13, 275, 1003, 867, 1535, 2377, 1138 1, 3, 3, 1, 13, 61, 59, 243, 63, 121, 1535, 2175, 1673, 1139 1, 3, 3, 3, 3, 39, 35, 207, 441, 501, 575, 3613, 1, 1140 1, 1, 3, 15, 17, 15, 15, 187, 15, 155, 183, 3019, 6541 1141 } ; 1142 1143 const Unsigned64BitsInteger SobolSequence::PrimitivePolynomial[MaximumDimension] = 1144 { 1145 1, 3, 7, 11, 13, 19, 25, 37, 1146 59, 47, 61, 55, 41, 67, 97, 91, 1147 109, 103, 115, 131, 193, 137, 145, 143, 1148 241, 157, 185, 167, 229, 171, 213, 191, 1149 253, 203, 211, 239, 247, 285, 369, 299, 1150 301, 333, 351, 355, 357, 361, 391, 397, 1151 425, 451, 463, 487, 501, 529, 539, 545, 1152 557, 563, 601, 607, 617, 623, 631, 637, 1153 647, 661, 675, 677, 687, 695, 701, 719, 1154 721, 731, 757, 761, 787, 789, 799, 803, 1155 817, 827, 847, 859, 865, 875, 877, 883, 1156 895, 901, 911, 949, 953, 967, 971, 973, 1157 981, 985, 995, 1001, 1019, 1033, 1051, 1063, 1158 1069, 1125, 1135, 1153, 1163, 1221, 1239, 1255, 1159 1267, 1279, 1293, 1305, 1315, 1329, 1341, 1347, 1160 1367, 1387, 1413, 1423, 1431, 1441, 1479, 1509, 1161 1527, 1531, 1555, 1557, 1573, 1591, 1603, 1615, 1162 1627, 1657, 1663, 1673, 1717, 1729, 1747, 1759, 1163 1789, 1815, 1821, 1825, 1849, 1863, 1869, 1877, 1164 1881, 1891, 1917, 1933, 1939, 1969, 2011, 2035, 1165 2041, 2053, 2071, 2091, 2093, 2119, 2147, 2149, 1166 2161, 2171, 2189, 2197, 2207, 2217, 2225, 2255, 1167 2257, 2273, 2279, 2283, 2293, 2317, 2323, 2341, 1168 2345, 2363, 2365, 2373, 2377, 2385, 2395, 2419, 1169 2421, 2431, 2435, 2447, 2475, 2477, 2489, 2503, 1170 2521, 2533, 2551, 2561, 2567, 2579, 2581, 2601, 1171 2633, 2657, 2669, 2681, 2687, 2693, 2705, 2717, 1172 2727, 2731, 2739, 2741, 2773, 2783, 2793, 2799, 1173 2801, 2811, 2819, 2825, 2833, 2867, 2879, 2881, 1174 2891, 2905, 2911, 2917, 2927, 2941, 2951, 2955, 1175 2963, 2965, 2991, 2999, 3005, 3017, 3035, 3037, 1176 3047, 3053, 3083, 3085, 3097, 3103, 3159, 3169, 1177 3179, 3187, 3205, 3209, 3223, 3227, 3229, 3251, 1178 3263, 3271, 3277, 3283, 3285, 3299, 3305, 3319, 1179 3331, 3343, 3357, 3367, 3373, 3393, 3399, 3413, 1180 3417, 3427, 3439, 3441, 3475, 3487, 3497, 3515, 1181 3517, 3529, 3543, 3547, 3553, 3559, 3573, 3589, 1182 3613, 3617, 3623, 3627, 3635, 3641, 3655, 3659, 1183 3669, 3679, 3697, 3707, 3709, 3713, 3731, 3743, 1184 3747, 3771, 3791, 3805, 3827, 3833, 3851, 3865, 1185 3889, 3895, 3933, 3947, 3949, 3957, 3971, 3985, 1186 3991, 3995, 4007, 4013, 4021, 4045, 4051, 4069, 1187 4073, 4179, 4201, 4219, 4221, 4249, 4305, 4331, 1188 4359, 4383, 4387, 4411, 4431, 4439, 4449, 4459, 1189 4485, 4531, 4569, 4575, 4621, 4663, 4669, 4711, 1190 4723, 4735, 4793, 4801, 4811, 4879, 4893, 4897, 1191 4921, 4927, 4941, 4977, 5017, 5027, 5033, 5127, 1192 5169, 5175, 5199, 5213, 5223, 5237, 5287, 5293, 1193 5331, 5391, 5405, 5453, 5523, 5573, 5591, 5597, 1194 5611, 5641, 5703, 5717, 5721, 5797, 5821, 5909, 1195 5913, 5955, 5957, 6005, 6025, 6061, 6067, 6079, 1196 6081, 6231, 6237, 6289, 6295, 6329, 6383, 6427, 1197 6453, 6465, 6501, 6523, 6539, 6577, 6589, 6601, 1198 6607, 6631, 6683, 6699, 6707, 6761, 6795, 6865, 1199 6881, 6901, 6923, 6931, 6943, 6999, 7057, 7079, 1200 7103, 7105, 7123, 7173, 7185, 7191, 7207, 7245, 1201 7303, 7327, 7333, 7355, 7365, 7369, 7375, 7411, 1202 7431, 7459, 7491, 7505, 7515, 7541, 7557, 7561, 1203 7701, 7705, 7727, 7749, 7761, 7783, 7795, 7823, 1204 7907, 7953, 7963, 7975, 8049, 8089, 8123, 8125, 1205 8137, 8219, 8231, 8245, 8275, 8293, 8303, 8331, 1206 8333, 8351, 8357, 8367, 8379, 8381, 8387, 8393, 1207 8417, 8435, 8461, 8469, 8489, 8495, 8507, 8515, 1208 8551, 8555, 8569, 8585, 8599, 8605, 8639, 8641, 1209 8647, 8653, 8671, 8675, 8689, 8699, 8729, 8741, 1210 8759, 8765, 8771, 8795, 8797, 8825, 8831, 8841, 1211 8855, 8859, 8883, 8895, 8909, 8943, 8951, 8955, 1212 8965, 8999, 9003, 9031, 9045, 9049, 9071, 9073, 1213 9085, 9095, 9101, 9109, 9123, 9129, 9137, 9143, 1214 9147, 9185, 9197, 9209, 9227, 9235, 9247, 9253, 1215 9257, 9277, 9297, 9303, 9313, 9325, 9343, 9347, 1216 9371, 9373, 9397, 9407, 9409, 9415, 9419, 9443, 1217 9481, 9495, 9501, 9505, 9517, 9529, 9555, 9557, 1218 9571, 9585, 9591, 9607, 9611, 9621, 9625, 9631, 1219 9647, 9661, 9669, 9679, 9687, 9707, 9731, 9733, 1220 9745, 9773, 9791, 9803, 9811, 9817, 9833, 9847, 1221 9851, 9863, 9875, 9881, 9905, 9911, 9917, 9923, 1222 9963, 9973, 10003, 10025, 10043, 10063, 10071, 10077, 1223 10091, 10099, 10105, 10115, 10129, 10145, 10169, 10183, 1224 10187, 10207, 10223, 10225, 10247, 10265, 10271, 10275, 1225 10289, 10299, 10301, 10309, 10343, 10357, 10373, 10411, 1226 10413, 10431, 10445, 10453, 10463, 10467, 10473, 10491, 1227 10505, 10511, 10513, 10523, 10539, 10549, 10559, 10561, 1228 10571, 10581, 10615, 10621, 10625, 10643, 10655, 10671, 1229 10679, 10685, 10691, 10711, 10739, 10741, 10755, 10767, 1230 10781, 10785, 10803, 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