/* 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};