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boringssl/crypto/newhope/precomp.c

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Import `newhope' (post-quantum key exchange). This derives from the reference implementation: Source: https://github.com/tpoeppelmann/newhope/tree/master/ref at bc06c1ac Paper: https://eprint.iacr.org/2015/1092 However, it does not interoperate, due to the replacement of SHAKE-128 with AES-CTR (for polynomial generation) and the replacement of SHA-3 with SHA-256 (for key whitening). Change-Id: I6a55507aea85331245e2fbd41bae5cc049fdca3c Reviewed-on: https://boringssl-review.googlesource.com/7690 Reviewed-by: Adam Langley <agl@google.com>
2016-04-18 19:30:19 +01:00
/* Copyright (c) 2016, Google Inc.
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
#include "internal.h"
uint16_t newhope_omegas_montgomery[PARAM_N / 2] = {
4075, 6974, 7373, 7965, 3262, 5079, 522, 2169, 6364, 1018, 1041,
8775, 2344, 11011, 5574, 1973, 4536, 1050, 6844, 3860, 3818, 6118,
2683, 1190, 4789, 7822, 7540, 6752, 5456, 4449, 3789, 12142, 11973,
382, 3988, 468, 6843, 5339, 6196, 3710, 11316, 1254, 5435, 10930,
3998, 10256, 10367, 3879, 11889, 1728, 6137, 4948, 5862, 6136, 3643,
6874, 8724, 654, 10302, 1702, 7083, 6760, 56, 3199, 9987, 605,
11785, 8076, 5594, 9260, 6403, 4782, 6212, 4624, 9026, 8689, 4080,
11868, 6221, 3602, 975, 8077, 8851, 9445, 5681, 3477, 1105, 142,
241, 12231, 1003, 3532, 5009, 1956, 6008, 11404, 7377, 2049, 10968,
12097, 7591, 5057, 3445, 4780, 2920, 7048, 3127, 8120, 11279, 6821,
11502, 8807, 12138, 2127, 2839, 3957, 431, 1579, 6383, 9784, 5874,
677, 3336, 6234, 2766, 1323, 9115, 12237, 2031, 6956, 6413, 2281,
3969, 3991, 12133, 9522, 4737, 10996, 4774, 5429, 11871, 3772, 453,
5908, 2882, 1805, 2051, 1954, 11713, 3963, 2447, 6142, 8174, 3030,
1843, 2361, 12071, 2908, 3529, 3434, 3202, 7796, 2057, 5369, 11939,
1512, 6906, 10474, 11026, 49, 10806, 5915, 1489, 9789, 5942, 10706,
10431, 7535, 426, 8974, 3757, 10314, 9364, 347, 5868, 9551, 9634,
6554, 10596, 9280, 11566, 174, 2948, 2503, 6507, 10723, 11606, 2459,
64, 3656, 8455, 5257, 5919, 7856, 1747, 9166, 5486, 9235, 6065,
835, 3570, 4240, 11580, 4046, 10970, 9139, 1058, 8210, 11848, 922,
7967, 1958, 10211, 1112, 3728, 4049, 11130, 5990, 1404, 325, 948,
11143, 6190, 295, 11637, 5766, 8212, 8273, 2919, 8527, 6119, 6992,
8333, 1360, 2555, 6167, 1200, 7105, 7991, 3329, 9597, 12121, 5106,
5961, 10695, 10327, 3051, 9923, 4896, 9326, 81, 3091, 1000, 7969,
4611, 726, 1853, 12149, 4255, 11112, 2768, 10654, 1062, 2294, 3553,
4805, 2747, 4846, 8577, 9154, 1170, 2319, 790, 11334, 9275, 9088,
1326, 5086, 9094, 6429, 11077, 10643, 3504, 3542, 8668, 9744, 1479,
1, 8246, 7143, 11567, 10984, 4134, 5736, 4978, 10938, 5777, 8961,
4591, 5728, 6461, 5023, 9650, 7468, 949, 9664, 2975, 11726, 2744,
9283, 10092, 5067, 12171, 2476, 3748, 11336, 6522, 827, 9452, 5374,
12159, 7935, 3296, 3949, 9893, 4452, 10908, 2525, 3584, 8112, 8011,
10616, 4989, 6958, 11809, 9447, 12280, 1022, 11950, 9821, 11745, 5791,
5092, 2089, 9005, 2881, 3289, 2013, 9048, 729, 7901, 1260, 5755,
4632, 11955, 2426, 10593, 1428, 4890, 5911, 3932, 9558, 8830, 3637,
5542, 145, 5179, 8595, 3707, 10530, 355, 3382, 4231, 9741, 1207,
9041, 7012, 1168, 10146, 11224, 4645, 11885, 10911, 10377, 435, 7952,
4096, 493, 9908, 6845, 6039, 2422, 2187, 9723, 8643, 9852, 9302,
6022, 7278, 1002, 4284, 5088, 1607, 7313, 875, 8509, 9430, 1045,
2481, 5012, 7428, 354, 6591, 9377, 11847, 2401, 1067, 7188, 11516,
390, 8511, 8456, 7270, 545, 8585, 9611, 12047, 1537, 4143, 4714,
4885, 1017, 5084, 1632, 3066, 27, 1440, 8526, 9273, 12046, 11618,
9289, 3400, 9890, 3136, 7098, 8758, 11813, 7384, 3985, 11869, 6730,
10745, 10111, 2249, 4048, 2884, 11136, 2126, 1630, 9103, 5407, 2686,
9042, 2969, 8311, 9424, 9919, 8779, 5332, 10626, 1777, 4654, 10863,
7351, 3636, 9585, 5291, 8374, 2166, 4919, 12176, 9140, 12129, 7852,
12286, 4895, 10805, 2780, 5195, 2305, 7247, 9644, 4053, 10600, 3364,
3271, 4057, 4414, 9442, 7917, 2174};
uint16_t newhope_omegas_inv_montgomery[PARAM_N / 2] = {
4075, 5315, 4324, 4916, 10120, 11767, 7210, 9027, 10316, 6715, 1278,
9945, 3514, 11248, 11271, 5925, 147, 8500, 7840, 6833, 5537, 4749,
4467, 7500, 11099, 9606, 6171, 8471, 8429, 5445, 11239, 7753, 9090,
12233, 5529, 5206, 10587, 1987, 11635, 3565, 5415, 8646, 6153, 6427,
7341, 6152, 10561, 400, 8410, 1922, 2033, 8291, 1359, 6854, 11035,
973, 8579, 6093, 6950, 5446, 11821, 8301, 11907, 316, 52, 3174,
10966, 9523, 6055, 8953, 11612, 6415, 2505, 5906, 10710, 11858, 8332,
9450, 10162, 151, 3482, 787, 5468, 1010, 4169, 9162, 5241, 9369,
7509, 8844, 7232, 4698, 192, 1321, 10240, 4912, 885, 6281, 10333,
7280, 8757, 11286, 58, 12048, 12147, 11184, 8812, 6608, 2844, 3438,
4212, 11314, 8687, 6068, 421, 8209, 3600, 3263, 7665, 6077, 7507,
5886, 3029, 6695, 4213, 504, 11684, 2302, 1962, 1594, 6328, 7183,
168, 2692, 8960, 4298, 5184, 11089, 6122, 9734, 10929, 3956, 5297,
6170, 3762, 9370, 4016, 4077, 6523, 652, 11994, 6099, 1146, 11341,
11964, 10885, 6299, 1159, 8240, 8561, 11177, 2078, 10331, 4322, 11367,
441, 4079, 11231, 3150, 1319, 8243, 709, 8049, 8719, 11454, 6224,
3054, 6803, 3123, 10542, 4433, 6370, 7032, 3834, 8633, 12225, 9830,
683, 1566, 5782, 9786, 9341, 12115, 723, 3009, 1693, 5735, 2655,
2738, 6421, 11942, 2925, 1975, 8532, 3315, 11863, 4754, 1858, 1583,
6347, 2500, 10800, 6374, 1483, 12240, 1263, 1815, 5383, 10777, 350,
6920, 10232, 4493, 9087, 8855, 8760, 9381, 218, 9928, 10446, 9259,
4115, 6147, 9842, 8326, 576, 10335, 10238, 10484, 9407, 6381, 11836,
8517, 418, 6860, 7515, 1293, 7552, 2767, 156, 8298, 8320, 10008,
5876, 5333, 10258, 10115, 4372, 2847, 7875, 8232, 9018, 8925, 1689,
8236, 2645, 5042, 9984, 7094, 9509, 1484, 7394, 3, 4437, 160,
3149, 113, 7370, 10123, 3915, 6998, 2704, 8653, 4938, 1426, 7635,
10512, 1663, 6957, 3510, 2370, 2865, 3978, 9320, 3247, 9603, 6882,
3186, 10659, 10163, 1153, 9405, 8241, 10040, 2178, 1544, 5559, 420,
8304, 4905, 476, 3531, 5191, 9153, 2399, 8889, 3000, 671, 243,
3016, 3763, 10849, 12262, 9223, 10657, 7205, 11272, 7404, 7575, 8146,
10752, 242, 2678, 3704, 11744, 5019, 3833, 3778, 11899, 773, 5101,
11222, 9888, 442, 2912, 5698, 11935, 4861, 7277, 9808, 11244, 2859,
3780, 11414, 4976, 10682, 7201, 8005, 11287, 5011, 6267, 2987, 2437,
3646, 2566, 10102, 9867, 6250, 5444, 2381, 11796, 8193, 4337, 11854,
1912, 1378, 404, 7644, 1065, 2143, 11121, 5277, 3248, 11082, 2548,
8058, 8907, 11934, 1759, 8582, 3694, 7110, 12144, 6747, 8652, 3459,
2731, 8357, 6378, 7399, 10861, 1696, 9863, 334, 7657, 6534, 11029,
4388, 11560, 3241, 10276, 9000, 9408, 3284, 10200, 7197, 6498, 544,
2468, 339, 11267, 9, 2842, 480, 5331, 7300, 1673, 4278, 4177,
8705, 9764, 1381, 7837, 2396, 8340, 8993, 4354, 130, 6915, 2837,
11462, 5767, 953, 8541, 9813, 118, 7222, 2197, 3006, 9545, 563,
9314, 2625, 11340, 4821, 2639, 7266, 5828, 6561, 7698, 3328, 6512,
1351, 7311, 6553, 8155, 1305, 722, 5146, 4043, 12288, 10810, 2545,
3621, 8747, 8785, 1646, 1212, 5860, 3195, 7203, 10963, 3201, 3014,
955, 11499, 9970, 11119, 3135, 3712, 7443, 9542, 7484, 8736, 9995,
11227, 1635, 9521, 1177, 8034, 140, 10436, 11563, 7678, 4320, 11289,
9198, 12208, 2963, 7393, 2366, 9238};
uint16_t newhope_psis_bitrev_montgomery[PARAM_N] = {
4075, 6974, 7373, 7965, 3262, 5079, 522, 2169, 6364, 1018, 1041,
8775, 2344, 11011, 5574, 1973, 4536, 1050, 6844, 3860, 3818, 6118,
2683, 1190, 4789, 7822, 7540, 6752, 5456, 4449, 3789, 12142, 11973,
382, 3988, 468, 6843, 5339, 6196, 3710, 11316, 1254, 5435, 10930,
3998, 10256, 10367, 3879, 11889, 1728, 6137, 4948, 5862, 6136, 3643,
6874, 8724, 654, 10302, 1702, 7083, 6760, 56, 3199, 9987, 605,
11785, 8076, 5594, 9260, 6403, 4782, 6212, 4624, 9026, 8689, 4080,
11868, 6221, 3602, 975, 8077, 8851, 9445, 5681, 3477, 1105, 142,
241, 12231, 1003, 3532, 5009, 1956, 6008, 11404, 7377, 2049, 10968,
12097, 7591, 5057, 3445, 4780, 2920, 7048, 3127, 8120, 11279, 6821,
11502, 8807, 12138, 2127, 2839, 3957, 431, 1579, 6383, 9784, 5874,
677, 3336, 6234, 2766, 1323, 9115, 12237, 2031, 6956, 6413, 2281,
3969, 3991, 12133, 9522, 4737, 10996, 4774, 5429, 11871, 3772, 453,
5908, 2882, 1805, 2051, 1954, 11713, 3963, 2447, 6142, 8174, 3030,
1843, 2361, 12071, 2908, 3529, 3434, 3202, 7796, 2057, 5369, 11939,
1512, 6906, 10474, 11026, 49, 10806, 5915, 1489, 9789, 5942, 10706,
10431, 7535, 426, 8974, 3757, 10314, 9364, 347, 5868, 9551, 9634,
6554, 10596, 9280, 11566, 174, 2948, 2503, 6507, 10723, 11606, 2459,
64, 3656, 8455, 5257, 5919, 7856, 1747, 9166, 5486, 9235, 6065,
835, 3570, 4240, 11580, 4046, 10970, 9139, 1058, 8210, 11848, 922,
7967, 1958, 10211, 1112, 3728, 4049, 11130, 5990, 1404, 325, 948,
11143, 6190, 295, 11637, 5766, 8212, 8273, 2919, 8527, 6119, 6992,
8333, 1360, 2555, 6167, 1200, 7105, 7991, 3329, 9597, 12121, 5106,
5961, 10695, 10327, 3051, 9923, 4896, 9326, 81, 3091, 1000, 7969,
4611, 726, 1853, 12149, 4255, 11112, 2768, 10654, 1062, 2294, 3553,
4805, 2747, 4846, 8577, 9154, 1170, 2319, 790, 11334, 9275, 9088,
1326, 5086, 9094, 6429, 11077, 10643, 3504, 3542, 8668, 9744, 1479,
1, 8246, 7143, 11567, 10984, 4134, 5736, 4978, 10938, 5777, 8961,
4591, 5728, 6461, 5023, 9650, 7468, 949, 9664, 2975, 11726, 2744,
9283, 10092, 5067, 12171, 2476, 3748, 11336, 6522, 827, 9452, 5374,
12159, 7935, 3296, 3949, 9893, 4452, 10908, 2525, 3584, 8112, 8011,
10616, 4989, 6958, 11809, 9447, 12280, 1022, 11950, 9821, 11745, 5791,
5092, 2089, 9005, 2881, 3289, 2013, 9048, 729, 7901, 1260, 5755,
4632, 11955, 2426, 10593, 1428, 4890, 5911, 3932, 9558, 8830, 3637,
5542, 145, 5179, 8595, 3707, 10530, 355, 3382, 4231, 9741, 1207,
9041, 7012, 1168, 10146, 11224, 4645, 11885, 10911, 10377, 435, 7952,
4096, 493, 9908, 6845, 6039, 2422, 2187, 9723, 8643, 9852, 9302,
6022, 7278, 1002, 4284, 5088, 1607, 7313, 875, 8509, 9430, 1045,
2481, 5012, 7428, 354, 6591, 9377, 11847, 2401, 1067, 7188, 11516,
390, 8511, 8456, 7270, 545, 8585, 9611, 12047, 1537, 4143, 4714,
4885, 1017, 5084, 1632, 3066, 27, 1440, 8526, 9273, 12046, 11618,
9289, 3400, 9890, 3136, 7098, 8758, 11813, 7384, 3985, 11869, 6730,
10745, 10111, 2249, 4048, 2884, 11136, 2126, 1630, 9103, 5407, 2686,
9042, 2969, 8311, 9424, 9919, 8779, 5332, 10626, 1777, 4654, 10863,
7351, 3636, 9585, 5291, 8374, 2166, 4919, 12176, 9140, 12129, 7852,
12286, 4895, 10805, 2780, 5195, 2305, 7247, 9644, 4053, 10600, 3364,
3271, 4057, 4414, 9442, 7917, 2174, 3947, 11951, 2455, 6599, 10545,
10975, 3654, 2894, 7681, 7126, 7287, 12269, 4119, 3343, 2151, 1522,
7174, 7350, 11041, 2442, 2148, 5959, 6492, 8330, 8945, 5598, 3624,
10397, 1325, 6565, 1945, 11260, 10077, 2674, 3338, 3276, 11034, 506,
6505, 1392, 5478, 8778, 1178, 2776, 3408, 10347, 11124, 2575, 9489,
12096, 6092, 10058, 4167, 6085, 923, 11251, 11912, 4578, 10669, 11914,
425, 10453, 392, 10104, 8464, 4235, 8761, 7376, 2291, 3375, 7954,
8896, 6617, 7790, 1737, 11667, 3982, 9342, 6680, 636, 6825, 7383,
512, 4670, 2900, 12050, 7735, 994, 1687, 11883, 7021, 146, 10485,
1403, 5189, 6094, 2483, 2054, 3042, 10945, 3981, 10821, 11826, 8882,
8151, 180, 9600, 7684, 5219, 10880, 6780, 204, 11232, 2600, 7584,
3121, 3017, 11053, 7814, 7043, 4251, 4739, 11063, 6771, 7073, 9261,
2360, 11925, 1928, 11825, 8024, 3678, 3205, 3359, 11197, 5209, 8581,
3238, 8840, 1136, 9363, 1826, 3171, 4489, 7885, 346, 2068, 1389,
8257, 3163, 4840, 6127, 8062, 8921, 612, 4238, 10763, 8067, 125,
11749, 10125, 5416, 2110, 716, 9839, 10584, 11475, 11873, 3448, 343,
1908, 4538, 10423, 7078, 4727, 1208, 11572, 3589, 2982, 1373, 1721,
10753, 4103, 2429, 4209, 5412, 5993, 9011, 438, 3515, 7228, 1218,
8347, 5232, 8682, 1327, 7508, 4924, 448, 1014, 10029, 12221, 4566,
5836, 12229, 2717, 1535, 3200, 5588, 5845, 412, 5102, 7326, 3744,
3056, 2528, 7406, 8314, 9202, 6454, 6613, 1417, 10032, 7784, 1518,
3765, 4176, 5063, 9828, 2275, 6636, 4267, 6463, 2065, 7725, 3495,
8328, 8755, 8144, 10533, 5966, 12077, 9175, 9520, 5596, 6302, 8400,
579, 6781, 11014, 5734, 11113, 11164, 4860, 1131, 10844, 9068, 8016,
9694, 3837, 567, 9348, 7000, 6627, 7699, 5082, 682, 11309, 5207,
4050, 7087, 844, 7434, 3769, 293, 9057, 6940, 9344, 10883, 2633,
8190, 3944, 5530, 5604, 3480, 2171, 9282, 11024, 2213, 8136, 3805,
767, 12239, 216, 11520, 6763, 10353, 7, 8566, 845, 7235, 3154,
4360, 3285, 10268, 2832, 3572, 1282, 7559, 3229, 8360, 10583, 6105,
3120, 6643, 6203, 8536, 8348, 6919, 3536, 9199, 10891, 11463, 5043,
1658, 5618, 8787, 5789, 4719, 751, 11379, 6389, 10783, 3065, 7806,
6586, 2622, 5386, 510, 7628, 6921, 578, 10345, 11839, 8929, 4684,
12226, 7154, 9916, 7302, 8481, 3670, 11066, 2334, 1590, 7878, 10734,
1802, 1891, 5103, 6151, 8820, 3418, 7846, 9951, 4693, 417, 9996,
9652, 4510, 2946, 5461, 365, 881, 1927, 1015, 11675, 11009, 1371,
12265, 2485, 11385, 5039, 6742, 8449, 1842, 12217, 8176, 9577, 4834,
7937, 9461, 2643, 11194, 3045, 6508, 4094, 3451, 7911, 11048, 5406,
4665, 3020, 6616, 11345, 7519, 3669, 5287, 1790, 7014, 5410, 11038,
11249, 2035, 6125, 10407, 4565, 7315, 5078, 10506, 2840, 2478, 9270,
4194, 9195, 4518, 7469, 1160, 6878, 2730, 10421, 10036, 1734, 3815,
10939, 5832, 10595, 10759, 4423, 8420, 9617, 7119, 11010, 11424, 9173,
189, 10080, 10526, 3466, 10588, 7592, 3578, 11511, 7785, 9663, 530,
12150, 8957, 2532, 3317, 9349, 10243, 1481, 9332, 3454, 3758, 7899,
4218, 2593, 11410, 2276, 982, 6513, 1849, 8494, 9021, 4523, 7988,
8, 457, 648, 150, 8000, 2307, 2301, 874, 5650, 170, 9462,
2873, 9855, 11498, 2535, 11169, 5808, 12268, 9687, 1901, 7171, 11787,
3846, 1573, 6063, 3793, 466, 11259, 10608, 3821, 6320, 4649, 6263,
2929};
uint16_t newhope_psis_inv_montgomery[PARAM_N] = {
256, 10570, 1510, 7238, 1034, 7170, 6291, 7921, 11665, 3422, 4000,
2327, 2088, 5565, 795, 10647, 1521, 5484, 2539, 7385, 1055, 7173,
8047, 11683, 1669, 1994, 3796, 5809, 4341, 9398, 11876, 12230, 10525,
12037, 12253, 3506, 4012, 9351, 4847, 2448, 7372, 9831, 3160, 2207,
5582, 2553, 7387, 6322, 9681, 1383, 10731, 1533, 219, 5298, 4268,
7632, 6357, 9686, 8406, 4712, 9451, 10128, 4958, 5975, 11387, 8649,
11769, 6948, 11526, 12180, 1740, 10782, 6807, 2728, 7412, 4570, 4164,
4106, 11120, 12122, 8754, 11784, 3439, 5758, 11356, 6889, 9762, 11928,
1704, 1999, 10819, 12079, 12259, 7018, 11536, 1648, 1991, 2040, 2047,
2048, 10826, 12080, 8748, 8272, 8204, 1172, 1923, 7297, 2798, 7422,
6327, 4415, 7653, 6360, 11442, 12168, 7005, 8023, 9924, 8440, 8228,
2931, 7441, 1063, 3663, 5790, 9605, 10150, 1450, 8985, 11817, 10466,
10273, 12001, 3470, 7518, 1074, 1909, 7295, 9820, 4914, 702, 5367,
7789, 8135, 9940, 1420, 3714, 11064, 12114, 12264, 1752, 5517, 9566,
11900, 1700, 3754, 5803, 829, 1874, 7290, 2797, 10933, 5073, 7747,
8129, 6428, 6185, 11417, 1631, 233, 5300, 9535, 10140, 11982, 8734,
8270, 2937, 10953, 8587, 8249, 2934, 9197, 4825, 5956, 4362, 9401,
1343, 3703, 529, 10609, 12049, 6988, 6265, 895, 3639, 4031, 4087,
4095, 585, 10617, 8539, 4731, 4187, 9376, 3095, 9220, 10095, 10220,
1460, 10742, 12068, 1724, 5513, 11321, 6884, 2739, 5658, 6075, 4379,
11159, 10372, 8504, 4726, 9453, 3106, 7466, 11600, 10435, 8513, 9994,
8450, 9985, 3182, 10988, 8592, 2983, 9204, 4826, 2445, 5616, 6069,
867, 3635, 5786, 11360, 5134, 2489, 10889, 12089, 1727, 7269, 2794,
9177, 1311, 5454, 9557, 6632, 2703, 9164, 10087, 1441, 3717, 531,
3587, 2268, 324, 5313, 759, 1864, 5533, 2546, 7386, 9833, 8427,
4715, 11207, 1601, 7251, 4547, 11183, 12131, 1733, 10781, 10318, 1474,
10744, 5046, 4232, 11138, 10369, 6748, 964, 7160, 4534, 7670, 8118,
8182, 4680, 11202, 6867, 981, 8918, 1274, 182, 26, 7026, 8026,
11680, 12202, 10521, 1503, 7237, 4545, 5916, 9623, 8397, 11733, 10454,
3249, 9242, 6587, 941, 1890, 270, 10572, 6777, 9746, 6659, 6218,
6155, 6146, 878, 1881, 7291, 11575, 12187, 1741, 7271, 8061, 11685,
6936, 4502, 9421, 4857, 4205, 7623, 1089, 10689, 1527, 8996, 10063,
11971, 10488, 6765, 2722, 3900, 9335, 11867, 6962, 11528, 5158, 4248,
4118, 5855, 2592, 5637, 6072, 2623, 7397, 8079, 9932, 4930, 5971,
853, 3633, 519, 8852, 11798, 3441, 11025, 1575, 225, 8810, 11792,
12218, 3501, 9278, 3081, 9218, 4828, 7712, 8124, 11694, 12204, 3499,
4011, 573, 3593, 5780, 7848, 9899, 10192, 1456, 208, 7052, 2763,
7417, 11593, 10434, 12024, 8740, 11782, 10461, 3250, 5731, 7841, 9898,
1414, 202, 3540, 7528, 2831, 2160, 10842, 5060, 4234, 4116, 588,
84, 12, 7024, 2759, 9172, 6577, 11473, 1639, 9012, 3043, 7457,
6332, 11438, 1634, 1989, 9062, 11828, 8712, 11778, 12216, 10523, 6770,
9745, 10170, 4964, 9487, 6622, 946, 8913, 6540, 6201, 4397, 9406,
8366, 9973, 8447, 8229, 11709, 8695, 10020, 3187, 5722, 2573, 10901,
6824, 4486, 4152, 9371, 8361, 2950, 2177, 311, 1800, 9035, 8313,
11721, 3430, 490, 70, 10, 1757, 251, 3547, 7529, 11609, 3414,
7510, 4584, 4166, 9373, 1339, 5458, 7802, 11648, 1664, 7260, 9815,
10180, 6721, 9738, 10169, 8475, 8233, 9954, 1422, 8981, 1283, 5450,
11312, 1616, 3742, 11068, 10359, 4991, 713, 3613, 9294, 8350, 4704,
672, 96, 7036, 9783, 11931, 3460, 5761, 823, 10651, 12055, 10500,
1500, 5481, 783, 3623, 11051, 8601, 8251, 8201, 11705, 10450, 5004,
4226, 7626, 2845, 2162, 3820, 7568, 9859, 3164, 452, 10598, 1514,
5483, 6050, 6131, 4387, 7649, 8115, 6426, 918, 8909, 8295, 1185,
5436, 11310, 8638, 1234, 5443, 11311, 5127, 2488, 2111, 10835, 5059,
7745, 2862, 3920, 560, 80, 1767, 2008, 3798, 11076, 6849, 2734,
10924, 12094, 8750, 1250, 10712, 6797, 971, 7161, 1023, 8924, 4786,
7706, 4612, 4170, 7618, 6355, 4419, 5898, 11376, 10403, 10264, 6733,
4473, 639, 5358, 2521, 9138, 3061, 5704, 4326, 618, 5355, 765,
5376, 768, 7132, 4530, 9425, 3102, 9221, 6584, 11474, 10417, 10266,
12000, 6981, 6264, 4406, 2385, 7363, 4563, 4163, 7617, 9866, 3165,
9230, 11852, 10471, 5007, 5982, 11388, 5138, 734, 3616, 11050, 12112,
6997, 11533, 12181, 10518, 12036, 3475, 2252, 7344, 9827, 4915, 9480,
6621, 4457, 7659, 9872, 6677, 4465, 4149, 7615, 4599, 657, 3605,
515, 10607, 6782, 4480, 640, 1847, 3775, 5806, 2585, 5636, 9583,
1369, 10729, 8555, 10000, 11962, 5220, 7768, 8132, 8184, 9947, 1421,
203, 29, 8782, 11788, 1684, 10774, 10317, 4985, 9490, 8378, 4708,
11206, 5112, 5997, 7879, 11659, 12199, 8765, 10030, 4944, 5973, 6120,
6141, 6144, 7900, 11662, 1666, 238, 34, 3516, 5769, 9602, 8394,
9977, 6692, 956, 10670, 6791, 9748, 11926, 8726, 11780, 5194, 742,
106, 8793, 10034, 3189, 10989, 5081, 4237, 5872, 4350, 2377, 10873,
6820, 6241, 11425, 10410, 10265, 3222, 5727, 9596, 4882, 2453, 2106,
3812, 11078, 12116, 5242, 4260, 11142, 8614, 11764, 12214, 5256, 4262,
4120, 11122, 5100, 11262, 5120, 2487, 5622, 9581, 8391, 8221, 2930,
10952, 12098, 6995, 6266, 9673, 4893, 699, 3611, 4027, 5842, 11368,
1624, 232, 8811, 8281, 1183, 169, 8802, 3013, 2186, 5579, 797,
3625, 4029, 11109, 1587, 7249, 11569, 8675, 6506, 2685, 10917, 12093,
12261, 12285, 1755, 7273, 1039, 1904, 272, 3550, 9285, 3082, 5707,
6082, 4380, 7648, 11626, 5172, 4250, 9385, 8363, 8217, 4685, 5936,
848, 8899, 6538, 934, 1889, 3781, 9318, 10109, 10222, 6727, 961,
5404, 772, 5377, 9546, 8386, 1198, 8949, 3034, 2189, 7335, 4559,
5918, 2601, 10905, 5069, 9502, 3113, 7467, 8089, 11689, 5181, 9518,
8382, 2953, 3933, 4073, 4093, 7607, 8109, 2914, 5683, 4323, 11151,
1593, 10761, 6804, 972, 3650, 2277, 5592, 4310, 7638, 9869, 4921,
703, 1856, 9043, 4803, 9464, 1352, 8971, 11815, 5199, 7765, 6376,
4422, 7654, 2849, 407, 8836, 6529, 7955, 2892, 9191, 1313, 10721,
12065, 12257, 1751, 9028, 8312, 2943, 2176, 3822, 546, 78, 8789,
11789, 10462, 12028, 6985, 4509, 9422, 1346, 5459, 4291, 613, 10621,
6784, 9747, 3148, 7472, 2823, 5670, 810, 7138, 8042, 4660, 7688,
6365, 6176, 6149, 2634, 5643, 9584, 10147, 11983, 5223, 9524, 11894,
10477, 8519, 1217, 3685, 2282, 326, 10580, 3267, 7489, 4581, 2410,
5611, 11335, 6886, 8006, 8166, 11700, 3427, 11023, 8597, 10006, 3185,
455, 65, 5276, 7776, 4622, 5927, 7869, 9902, 11948, 5218, 2501,
5624, 2559, 10899, 1557, 1978, 10816, 10323, 8497, 4725, 675, 1852,
10798, 12076, 10503, 3256, 9243, 3076, 2195, 10847, 12083, 10504, 12034,
10497};
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