ntt_constants.py

"""
Constants (Zq-roots of cyclotomic polynomials) for the NTT.
These were computed using scripts/generate_constants.sage.
"""

"""Roots of phi_4 = x^2 + 1."""
phi4_roots_Zq = [1479, 10810]


"""Roots of phi_8 = x^4 + 1"""
phi8_roots_Zq = [4043, 8246, 5146, 7143]


"""Roots of phi_16 = x^8 + 1"""
phi16_roots_Zq = [5736, 6553, 4134, 8155, 722, 11567, 1305, 10984]


"""Roots of phi_32 = x^16 + 1"""
phi32_roots_Zq = [1646, 10643, 1212, 11077, 5860, 6429, 3195, 9094, 2545, 9744, 3621, 8668, 3504, 8785, 3542, 8747]


"""Roots of phi_64 = x^32 + 1"""
phi64_roots_Zq = [4591, 7698, 5728, 6561, 5023, 7266, 5828, 6461, 4978, 7311, 1351, 10938, 3328, 8961, 5777, 6512, 2975, 9314, 563, 11726, 3006, 9283, 2744, 9545, 949, 11340, 2625, 9664, 4821, 7468, 2639, 9650]


"""Roots of phi_128 = x^64 + 1"""
phi128_roots_Zq = [1000, 11289, 4320, 7969, 3091, 9198, 81, 12208, 2963, 9326, 4896, 7393, 3051, 9238, 2366, 9923, 1853, 10436, 140, 12149, 4611, 7678, 726, 11563, 4255, 8034, 1177, 11112, 2768, 9521, 1635, 10654, 3712, 8577, 3135, 9154, 2747, 9542, 4846, 7443, 3553, 8736, 4805, 7484, 2294, 9995, 1062, 11227, 1326, 10963, 5086, 7203, 3014, 9275, 3201, 9088, 1170, 11119, 2319, 9970, 955, 11334, 790, 11499]


"""Roots of phi_256 = x^128 + 1"""
phi256_roots_Zq = [544, 11745, 5791, 6498, 339, 11950, 2468, 9821, 2842, 9447, 480, 11809, 9, 12280, 1022, 11267, 4278, 8011, 1673, 10616, 4989, 7300, 5331, 6958, 3584, 8705, 4177, 8112, 1381, 10908, 2525, 9764, 2396, 9893, 4452, 7837, 3296, 8993, 3949, 8340, 130, 12159, 4354, 7935, 5374, 6915, 2837, 9452, 5767, 6522, 827, 11462, 3748, 8541, 953, 11336, 5067, 7222, 2197, 10092, 118, 12171, 2476, 9813, 2548, 9741, 4231, 8058, 355, 11934, 3382, 8907, 3707, 8582, 1759, 10530, 3694, 8595, 5179, 7110, 5542, 6747, 145, 12144, 3637, 8652, 3459, 8830, 5911, 6378, 4890, 7399, 3932, 8357, 2731, 9558, 2089, 10200, 5092, 7197, 2881, 9408, 3284, 9005, 729, 11560, 3241, 9048, 3289, 9000, 2013, 10276, 5755, 6534, 4632, 7657, 1260, 11029, 4388, 7901, 334, 11955, 2426, 9863, 1696, 10593, 1428, 10861]


"""Roots of phi_512 = x^256 + 1"""
phi512_roots_Zq = [1663, 10626, 1777, 10512, 1426, 10863, 4654, 7635, 5291, 6998, 2704, 9585, 4938, 7351, 3636, 8653, 3915, 8374, 2166, 10123, 113, 12176, 4919, 7370, 3, 12286, 4437, 7852, 160, 12129, 3149, 9140, 4057, 8232, 3271, 9018, 1689, 10600, 3364, 8925, 4372, 7917, 2174, 10115, 4414, 7875, 2847, 9442, 2645, 9644, 4053, 8236, 2305, 9984, 5042, 7247, 5195, 7094, 2780, 9509, 1484, 10805, 4895, 7394, 3016, 9273, 243, 12046, 3000, 9289, 671, 11618, 3136, 9153, 5191, 7098, 2399, 9890, 3400, 8889, 2178, 10111, 1544, 10745, 420, 11869, 5559, 6730, 476, 11813, 3531, 8758, 3985, 8304, 4905, 7384, 5332, 6957, 3510, 8779, 2370, 9919, 2865, 9424, 2969, 9320, 3978, 8311, 2686, 9603, 3247, 9042, 4048, 8241, 2249, 10040, 1153, 11136, 2884, 9405, 5407, 6882, 3186, 9103, 1630, 10659, 2126, 10163, 2187, 10102, 2566, 9723, 2422, 9867, 6039, 6250, 2987, 9302, 6022, 6267, 2437, 9852, 3646, 8643, 875, 11414, 3780, 8509, 1607, 10682, 4976, 7313, 5011, 7278, 1002, 11287, 4284, 8005, 5088, 7201, 3248, 9041, 1207, 11082, 1168, 11121, 5277, 7012, 1065, 11224, 2143, 10146, 404, 11885, 4645, 7644, 1912, 10377, 1378, 10911, 435, 11854, 4337, 7952, 2381, 9908, 5444, 6845, 4096, 8193, 493, 11796, 545, 11744, 5019, 7270, 3704, 8585, 2678, 9611, 1537, 10752, 242, 12047, 4714, 7575, 4143, 8146, 27, 12262, 3066, 9223, 3763, 8526, 1440, 10849, 5084, 7205, 1632, 10657, 1017, 11272, 4885, 7404, 3778, 8511, 3833, 8456, 390, 11899, 773, 11516, 2401, 9888, 442, 11847, 5101, 7188, 1067, 11222, 2912, 9377, 5698, 6591, 354, 11935, 4861, 7428, 2859, 9430, 1045, 11244, 5012, 7277, 2481, 9808]


"""Roots of phi_1024 = x^512 + 1"""
phi1024_roots_Zq = [3957, 8332, 2839, 9450, 2127, 10162, 151, 12138, 431, 11858, 1579, 10710, 5906, 6383, 2505, 9784, 1323, 10966, 2766, 9523, 52, 12237, 3174, 9115, 6055, 6234, 3336, 8953, 677, 11612, 5874, 6415, 4169, 8120, 3127, 9162, 5241, 7048, 2920, 9369, 1010, 11279, 5468, 6821, 787, 11502, 3482, 8807, 1321, 10968, 192, 12097, 4912, 7377, 2049, 10240, 4698, 7591, 5057, 7232, 4780, 7509, 3445, 8844, 1956, 10333, 5009, 7280, 6008, 6281, 885, 11404, 3532, 8757, 1003, 11286, 58, 12231, 241, 12048, 975, 11314, 4212, 8077, 2844, 9445, 3438, 8851, 1105, 11184, 142, 12147, 5681, 6608, 3477, 8812, 2302, 9987, 605, 11684, 4213, 8076, 504, 11785, 5886, 6403, 4782, 7507, 5594, 6695, 3029, 9260, 421, 11868, 4080, 8209, 6068, 6221, 3602, 8687, 6077, 6212, 4624, 7665, 3263, 9026, 3600, 8689, 4948, 7341, 6137, 6152, 400, 11889, 1728, 10561, 5862, 6427, 6136, 6153, 5415, 6874, 3643, 8646, 56, 12233, 3199, 9090, 5206, 7083, 5529, 6760, 3565, 8724, 654, 11635, 1987, 10302, 1702, 10587, 3988, 8301, 468, 11821, 316, 11973, 382, 11907, 3710, 8579, 6093, 6196, 5446, 6843, 5339, 6950, 973, 11316, 1254, 11035, 1359, 10930, 5435, 6854, 2033, 10256, 3998, 8291, 3879, 8410, 1922, 10367, 3860, 8429, 5445, 6844, 4536, 7753, 1050, 11239, 3818, 8471, 6118, 6171, 1190, 11099, 2683, 9606, 3789, 8500, 147, 12142, 5456, 6833, 4449, 7840, 4749, 7540, 5537, 6752, 4789, 7500, 4467, 7822, 1018, 11271, 5925, 6364, 1041, 11248, 3514, 8775, 2344, 9945, 1278, 11011, 5574, 6715, 1973, 10316, 4324, 7965, 4916, 7373, 4075, 8214, 5315, 6974, 5079, 7210, 3262, 9027, 522, 11767, 2169, 10120, 1200, 11089, 5184, 7105, 2555, 9734, 6122, 6167, 5297, 6992, 6119, 6170, 3956, 8333, 1360, 10929, 1962, 10327, 1594, 10695, 5961, 6328, 5106, 7183, 4298, 7991, 3329, 8960, 168, 12121, 2692, 9597, 4049, 8240, 3728, 8561, 1159, 11130, 5990, 6299, 948, 11341, 1146, 11143, 1404, 10885, 325, 11964, 5766, 6523, 652, 11637, 295, 11994, 6099, 6190, 2919, 9370, 3762, 8527, 4016, 8273, 4077, 8212, 6065, 6224, 835, 11454, 3570, 8719, 4240, 8049, 4046, 8243, 709, 11580, 3150, 9139, 1319, 10970, 1058, 11231, 4079, 8210, 922, 11367, 441, 11848, 4322, 7967, 1958, 10331, 2078, 10211, 1112, 11177, 3834, 8455, 5257, 7032, 4433, 7856, 5919, 6370, 5486, 6803, 3054, 9235, 1747, 10542, 3123, 9166, 2948, 9341, 2503, 9786, 5782, 6507, 1566, 10723, 64, 12225, 3656, 8633, 2459, 9830, 683, 11606, 1293, 10996, 4737, 7552, 5429, 6860, 4774, 7515, 5908, 6381, 453, 11836, 418, 11871, 3772, 8517, 3991, 8298, 3969, 8320, 2767, 9522, 156, 12133, 2281, 10008, 5876, 6413, 5333, 6956, 2031, 10258, 3963, 8326, 576, 11713, 2447, 9842, 6142, 6147, 2051, 10238, 1954, 10335, 1805, 10484, 2882, 9407, 3529, 8760, 3434, 8855, 2908, 9381, 218, 12071, 3030, 9259, 4115, 8174, 1843, 10446, 2361, 9928, 3202, 9087, 4493, 7796, 2057, 10232, 5369, 6920, 1512, 10777, 350, 11939, 1815, 10474, 5383, 6906, 49, 12240, 1263, 11026, 5915, 6374, 1483, 10806, 1489, 10800, 2500, 9789, 5942, 6347, 1583, 10706, 1693, 10596, 3009, 9280, 174, 12115, 723, 11566, 2738, 9551, 5868, 6421, 5735, 6554, 2655, 9634, 3315, 8974, 426, 11863, 4754, 7535, 1858, 10431, 1975, 10314, 3757, 8532, 2925, 9364, 347, 11942]


"""Roots of phi_2048 = x^1024 + 1"""
phi2048_roots_Zq = [1826, 10463, 2926, 9363, 3171, 9118, 4489, 7800, 3238, 9051, 3708, 8581, 1136, 11153, 3449, 8840, 1092, 11197, 5209, 7080, 3359, 8930, 3205, 9084, 1928, 10361, 464, 11825, 4265, 8024, 3678, 8611, 3163, 9126, 4032, 8257, 4840, 7449, 6127, 6162, 2068, 10221, 1389, 10900, 4404, 7885, 346, 11943, 1526, 10763, 4222, 8067, 125, 12164, 540, 11749, 3368, 8921, 4227, 8062, 612, 11677, 4238, 8051, 1866, 10423, 5211, 7078, 4727, 7562, 1208, 11081, 3448, 8841, 343, 11946, 1908, 10381, 4538, 7751, 416, 11873, 814, 11475, 2450, 9839, 1705, 10584, 2164, 10125, 5416, 6873, 2110, 10179, 716, 11573, 2429, 9860, 4103, 8186, 1721, 10568, 1536, 10753, 1373, 10916, 2982, 9307, 3589, 8700, 717, 11572, 3278, 9011, 5993, 6296, 5412, 6877, 4209, 8080, 3515, 8774, 438, 11851, 5061, 7228, 1218, 11071, 2275, 10014, 2461, 9828, 5653, 6636, 4267, 8022, 3765, 8524, 1518, 10771, 4176, 8113, 5063, 7226, 3534, 8755, 3961, 8328, 4145, 8144, 1756, 10533, 5826, 6463, 2065, 10224, 4564, 7725, 3495, 8794, 3114, 9175, 2769, 9520, 5966, 6323, 212, 12077, 5596, 6693, 5987, 6302, 579, 11710, 3889, 8400, 1131, 11158, 1445, 10844, 4860, 7429, 1125, 11164, 5734, 6555, 1176, 11113, 1275, 11014, 5508, 6781, 5102, 7187, 412, 11877, 5845, 6444, 5588, 6701, 4963, 7326, 3744, 8545, 2528, 9761, 3056, 9233, 4505, 7784, 2257, 10032, 1417, 10872, 5676, 6613, 3087, 9202, 5835, 6454, 4883, 7406, 3975, 8314, 4781, 7508, 4924, 7365, 448, 11841, 1014, 11275, 3942, 8347, 5232, 7057, 1327, 10962, 3607, 8682, 5836, 6453, 4566, 7723, 68, 12221, 2260, 10029, 3200, 9089, 1535, 10754, 60, 12229, 2717, 9572, 3343, 8946, 4119, 8170, 2151, 10138, 1522, 10767, 20, 12269, 5002, 7287, 5163, 7126, 4608, 7681, 3654, 8635, 2894, 9395, 1314, 10975, 1744, 10545, 2455, 9834, 5690, 6599, 338, 11951, 3947, 8342, 4939, 7350, 5115, 7174, 2442, 9847, 1248, 11041, 3959, 8330, 5797, 6492, 2148, 10141, 5959, 6330, 1892, 10397, 3624, 8665, 5598, 6691, 3344, 8945, 1029, 11260, 1945, 10344, 5724, 6565, 1325, 10964, 923, 11366, 1038, 11251, 6085, 6204, 4167, 8122, 2231, 10058, 6092, 6197, 193, 12096, 2800, 9489, 1836, 10453, 425, 11864, 2185, 10104, 392, 11897, 375, 11914, 1620, 10669, 4578, 7711, 377, 11912, 2776, 9513, 1178, 11111, 3511, 8778, 5478, 6811, 3408, 8881, 1942, 10347, 1165, 11124, 2575, 9714, 1255, 11034, 506, 11783, 5784, 6505, 1392, 10897, 3276, 9013, 3338, 8951, 2212, 10077, 2674, 9615, 1236, 11053, 3017, 9272, 5246, 7043, 4475, 7814, 4705, 7584, 3121, 9168, 2600, 9689, 1057, 11232, 1226, 11063, 5518, 6771, 4739, 7550, 4251, 8038, 3028, 9261, 5216, 7073, 2360, 9929, 364, 11925, 2054, 10235, 2483, 9806, 3042, 9247, 1344, 10945, 463, 11826, 3407, 8882, 1468, 10821, 3981, 8308, 204, 12085, 5509, 6780, 5219, 7070, 1409, 10880, 2689, 9600, 4605, 7684, 4138, 8151, 180, 12109, 4499, 7790, 5672, 6617, 622, 11667, 1737, 10552, 5609, 6680, 636, 11653, 3982, 8307, 2947, 9342, 4335, 7954, 3393, 8896, 2291, 9998, 3375, 8914, 4235, 8054, 3825, 8464, 4913, 7376, 3528, 8761, 2900, 9389, 239, 12050, 994, 11295, 4554, 7735, 512, 11777, 4670, 7619, 5464, 6825, 4906, 7383, 406, 11883, 1687, 10602, 5268, 7021, 146, 12143, 5189, 7100, 6094, 6195, 1403, 10886, 1804, 10485, 1842, 10447, 3840, 8449, 72, 12217, 4113, 8176, 4352, 7937, 2828, 9461, 2712, 9577, 4834, 7455, 2643, 9646, 1095, 11194, 3045, 9244, 5781, 6508, 1241, 11048, 4378, 7911, 3451, 8838, 4094, 8195, 3020, 9269, 5673, 6616, 5406, 6883, 4665, 7624, 4770, 7519, 944, 11345, 3669, 8620, 5287, 7002, 1251, 11038, 5410, 6879, 5275, 7014, 1790, 10499, 1040, 11249, 2035, 10254, 1882, 10407, 6125, 6164, 3815, 8474, 1734, 10555, 1350, 10939, 5832, 6457, 3869, 8420, 4423, 7866, 1530, 10759, 1694, 10595, 2209, 10080, 1763, 10526, 3116, 9173, 189, 12100, 1279, 11010, 865, 11424, 5170, 7119, 2672, 9617, 2730, 9559, 5411, 6878, 2253, 10036, 1868, 10421, 4518, 7771, 3094, 9195, 1160, 11129, 4820, 7469, 4974, 7315, 4565, 7724, 5078, 7211, 1783, 10506, 2840, 9449, 2478, 9811, 4194, 8095, 3019, 9270, 5118, 7171, 502, 11787, 1901, 10388, 2602, 9687, 6063, 6226, 3793, 8496, 1573, 10716, 3846, 8443, 1030, 11259, 466, 11823, 3821, 8468, 1681, 10608, 5969, 6320, 4649, 7640, 2929, 9360, 6026, 6263, 2434, 9855, 791, 11498, 2827, 9462, 2873, 9416, 1120, 11169, 2535, 9754, 21, 12268, 5808, 6481, 170, 12119, 5650, 6639, 874, 11415, 2301, 9988, 648, 11641, 150, 12139, 2307, 9982, 4289, 8000, 3317, 8972, 2532, 9757, 3332, 8957, 139, 12150, 2940, 9349, 2046, 10243, 1481, 10808, 2957, 9332, 1701, 10588, 3466, 8823, 4697, 7592, 3578, 8711, 2626, 9663, 530, 11759, 778, 11511, 4504, 7785, 4390, 7899, 4218, 8071, 3758, 8531, 3454, 8835, 982, 11307, 2276, 10013, 2593, 9696, 879, 11410, 8, 12281, 457, 11832, 4301, 7988, 4523, 7766, 1849, 10440, 5776, 6513, 3268, 9021, 3795, 8494, 4719, 7570, 751, 11538, 910, 11379, 5900, 6389, 3065, 9224, 1506, 10783, 4483, 7806, 5703, 6586, 5043, 7246, 826, 11463, 1398, 10891, 3090, 9199, 5789, 6500, 3502, 8787, 5618, 6671, 1658, 10631, 4684, 7605, 3360, 8929, 63, 12226, 5135, 7154, 2373, 9916, 4987, 7302, 3670, 8619, 3808, 8481, 578, 11711, 5368, 6921, 450, 11839, 1944, 10345, 2622, 9667, 5386, 6903, 510, 11779, 4661, 7628, 1280, 11009, 614, 11675, 24, 12265, 1371, 10918, 5039, 7250, 5547, 6742, 904, 11385, 2485, 9804, 1927, 10362, 1015, 11274, 881, 11408, 365, 11924, 4510, 7779, 2637, 9652, 2946, 9343, 5461, 6828, 2334, 9955, 1223, 11066, 4411, 7878, 1590, 10699, 1802, 10487, 1555, 10734, 5103, 7186, 1891, 10398, 3469, 8820, 6138, 6151, 4443, 7846, 3418, 8871, 417, 11872, 2293, 9996, 4693, 7596, 2338, 9951, 3572, 8717, 1282, 11007, 2021, 10268, 2832, 9457, 3929, 8360, 1706, 10583, 3229, 9060, 4730, 7559, 3120, 9169, 6105, 6184, 6086, 6203, 5646, 6643, 3753, 8536, 3941, 8348, 3536, 8753, 5370, 6919, 7, 12282, 1936, 10353, 845, 11444, 3723, 8566, 3154, 9135, 5054, 7235, 3285, 9004, 4360, 7929, 769, 11520, 5526, 6763, 50, 12239, 216, 12073, 4153, 8136, 2213, 10076, 3805, 8484, 767, 11522, 2633, 9656, 1406, 10883, 5349, 6940, 2945, 9344, 3232, 9057, 293, 11996, 4855, 7434, 3769, 8520, 4099, 8190, 3944, 8345, 5530, 6759, 5604, 6685, 3480, 8809, 2171, 10118, 1265, 11024, 3007, 9282, 5207, 7082, 4050, 8239, 5202, 7087, 844, 11445, 4590, 7699, 5082, 7207, 980, 11309, 682, 11607, 567, 11722, 2941, 9348, 5289, 7000, 5662, 6627, 3221, 9068, 4273, 8016, 3837, 8452, 2595, 9694]


"""
For each table of roots, the following holds:
- The second half of the roots are the conjugates of the first half:
- The root at index (2 * i + 1) is the negation of the root at index (2 * i).
"""

"""A dictionary of all the roots."""
roots_dict_Zq = {2: phi4_roots_Zq,
                 4: phi8_roots_Zq,
                 8: phi16_roots_Zq,
                 16: phi32_roots_Zq,
                 32: phi64_roots_Zq,
                 64: phi128_roots_Zq,
                 128: phi256_roots_Zq,
                 256: phi512_roots_Zq,
                 512: phi1024_roots_Zq,
                 1024: phi2048_roots_Zq
                 }

"""The list of a^(-1) mod q, for a = 0, 1, ..., q - 1."""
inv_mod_q = [0, 1, 6145, 8193, 9217, 2458, 10241, 8778, 10753, 2731, 1229, 5586, 11265, 2836, 4389, 9012, 11521, 6506, 7510, 3234, 6759, 2926, 2793, 6946, 11777, 7865, 1418, 9103, 8339, 10594, 4506, 7532, 11905, 1862, 3253, 9129, 3755, 7307, 1617, 9138, 9524, 4496, 1463, 6859, 7541, 3004, 3473, 8367, 12033, 1254, 10077, 6265, 709, 8811, 10696, 3575, 10314, 1078, 5297, 10831, 2253, 7454, 3766, 9168, 12097, 3025, 931, 10088, 7771, 10508, 10709, 10212, 8022, 5892, 9798, 6718, 6953, 798, 4569, 10889, 4762, 11227, 2248, 4886, 6876, 3759, 9574, 11724, 9915, 5247, 1502, 9183, 7881, 6607, 10328, 10478, 12161, 6968, 627, 4717, 11183, 5962, 9277, 8829, 6499, 3043, 10550, 9992, 5348, 8343, 7932, 6532, 5157, 11854, 539, 3847, 8793, 3046, 11560, 2685, 7271, 1625, 3727, 5595, 1883, 1573, 4584, 6967, 12193, 10479, 7657, 1970, 6610, 462, 5044, 9194, 10030, 11392, 5254, 3448, 11499, 2789, 5106, 1375, 4011, 11950, 2946, 418, 4899, 10557, 3359, 1058, 9621, 10281, 399, 6422, 8429, 5714, 11589, 2937, 2381, 6259, 11758, 2111, 1124, 5288, 2443, 3385, 3438, 5890, 8024, 8552, 4787, 10229, 5862, 11657, 11102, 11803, 8768, 1785, 751, 10999, 10736, 6581, 10085, 6377, 9448, 3943, 5164, 3056, 5239, 3024, 12225, 9169, 3484, 9201, 6458, 1310, 8503, 4014, 11736, 7459, 2981, 3269, 10783, 3357, 10559, 7599, 9394, 294, 7666, 5300, 5275, 3404, 4996, 11203, 2674, 1076, 10316, 1964, 3966, 5227, 3266, 3582, 8723, 10432, 5927, 11098, 6414, 6225, 8068, 266, 10541, 8808, 1523, 6589, 5780, 7726, 7487, 7250, 9780, 6170, 6957, 11935, 8008, 10082, 8942, 4030, 7086, 5725, 6931, 11065, 2292, 3983, 9628, 1253, 12241, 8368, 11384, 4555, 9973, 3908, 985, 8364, 3305, 4220, 231, 1749, 2522, 868, 4597, 2222, 5015, 3061, 5696, 715, 2627, 8030, 1724, 10395, 11894, 656, 7539, 6861, 2553, 7589, 6832, 5909, 8150, 4720, 5975, 6419, 1473, 2894, 209, 4624, 8594, 9765, 11423, 11878, 7824, 4491, 529, 10180, 10955, 11322, 11285, 1361, 6344, 2943, 3211, 5453, 10359, 10640, 2857, 9207, 11939, 1163, 7613, 6549, 7335, 7427, 9274, 1636, 5879, 605, 7200, 2781, 562, 6462, 2644, 7314, 7366, 10370, 7837, 9391, 1719, 3209, 2945, 12144, 4012, 8505, 4276, 8957, 8538, 9475, 11259, 7083, 2931, 1162, 11973, 9208, 5551, 8007, 12046, 6958, 4384, 895, 7037, 5922, 6520, 817, 11644, 4638, 5368, 6094, 9435, 5592, 11187, 1865, 9333, 8281, 4724, 1845, 8116, 8717, 2582, 10268, 1528, 8625, 8764, 10515, 1512, 1861, 12257, 7533, 10729, 3493, 1742, 7961, 10745, 4023, 3229, 4753, 655, 12009, 10396, 11608, 2007, 154, 5868, 10818, 9874, 2470, 7635, 7161, 7779, 5133, 11536, 1292, 7823, 11990, 11424, 6814, 9944, 3435, 4697, 9342, 147, 7391, 3833, 9370, 2650, 5026, 8782, 10583, 1702, 4576, 2498, 8651, 11746, 1112, 1337, 11693, 538, 12176, 5158, 11361, 982, 8202, 1983, 8332, 8758, 9404, 1633, 5965, 1791, 3519, 10506, 7773, 5216, 8229, 9108, 4449, 5549, 9210, 3207, 1721, 9257, 3427, 4034, 5678, 133, 7246, 11415, 6237, 4404, 1421, 6906, 10219, 9439, 6001, 2890, 9561, 3863, 9469, 9888, 979, 3625, 2309, 4890, 3398, 3085, 10279, 9623, 8767, 12112, 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1442, 7061, 222, 8708, 9307, 203, 1507, 9723, 6306, 11080, 9350, 9910, 11520, 12274, 4390, 11442, 2514, 2708, 11791, 4971, 11462, 3408, 1926, 10887, 4571, 2197, 3104, 4410, 7955, 10438, 9241, 731, 1428, 6124, 5988, 10907, 5180, 2807, 11139, 8814, 3924, 264, 8070, 5994, 11468, 10057, 5647, 4877, 1243, 1710, 11069, 1987, 4903, 1908, 4063, 8616, 8110, 5669, 5634, 5440, 10910, 8375, 5073, 10878, 11340, 8077, 1037, 8537, 11946, 4277, 9742, 4794, 4240, 10676, 6763, 3651, 9386, 1589, 3394, 9282, 7699, 10070, 4029, 12043, 10083, 6583, 2168, 10239, 2460, 3841, 1821, 5498, 1505, 205, 1731, 150, 11232, 10044, 5450, 1268, 2422, 4733, 7729, 2241, 10388, 11585, 11381, 5800, 4151, 2135, 7463, 2334, 9548, 7944, 9164, 5819, 6439, 3224, 4989, 959, 9845, 167, 8852, 7594, 8397, 2774, 6130, 5918, 4170, 10699, 3342, 3008, 3644, 7398, 481, 9205, 2859, 9149, 6997, 7013, 213, 7294, 3857, 826, 3285, 10364, 6995, 9151, 5932, 10053, 10536, 6391, 572, 11282, 11667, 2534, 7801, 8316, 6755, 7708, 9529, 11270, 3031, 459, 8256, 9361, 9498, 7185, 8762, 8627, 2344, 415, 7593, 8903, 168, 6400, 10685, 6157, 6373, 5436, 7661, 10723, 2129, 7034, 139, 791, 7092, 8144, 4126, 936, 8080, 3596, 10920, 1070, 3799, 6498, 12186, 9278, 1679, 2115, 6070, 837, 2450, 3977, 8586, 4499, 4395, 7697, 9284, 46, 3923, 8986, 11140, 10695, 12236, 710, 1522, 12056, 10542, 3119, 194, 3089, 8309, 7926, 3717, 4202, 2574, 5055, 1559, 387, 10548, 3045, 12173, 3848, 6278, 10554, 4884, 2250, 1344, 4743, 3195, 1143, 10582, 11865, 5027, 10650, 10752, 12282, 10242, 7563, 10446, 2276, 10482, 6894, 10497, 447, 1784, 12111, 11804, 9624, 10514, 11909, 8626, 8857, 7186, 11011, 9403, 11847, 8333, 10522, 4378, 11406, 4167, 3259, 11570, 2962, 8578, 2058, 6429, 496, 7320, 4926, 6900, 3721, 5954, 4962, 10527, 11320, 10957, 7969, 5612, 9527, 7710, 2833, 3934, 4292, 5354, 8134, 6110, 7888, 3886, 10431, 12065, 3583, 1760, 971, 6234, 2581, 11914, 8117, 1592, 55, 1976, 2879, 11475, 4838, 9306, 9022, 223, 3567, 10530, 8676, 9592, 11155, 3038, 1849, 3050, 2748, 5580, 7056, 2479, 4208, 3455, 1370, 7620, 7833, 652, 1563, 8212, 2217, 8262, 8679, 1203, 8095, 5637, 1202, 8684, 8263, 9591, 8704, 10531, 8604, 7283, 5307, 3828, 3939, 6080, 1646, 6097, 926, 11309, 478, 9981, 11198, 4522, 9861, 10295, 5273, 5302, 6339, 4244, 6917, 9041, 11745, 11860, 2499, 10368, 7368, 1677, 9280, 3396, 4892, 10115, 6810, 1937, 7921, 5525, 3339, 2904, 4777, 9057, 659, 10968, 662, 2355, 5723, 7088, 2343, 8856, 8763, 11910, 1529, 10033, 11478, 9726, 4860, 3017, 4305, 8109, 8970, 4064, 6407, 10681, 4054, 5650, 4309, 9721, 1509, 2353, 664, 7282, 8674, 10532, 8196, 3782, 8015, 6331, 7145, 2087, 5657, 9764, 11993, 4625, 2267, 7939, 6794, 4620, 1461, 4498, 8821, 3978, 4365, 5667, 8112, 9462, 11242, 2057, 8749, 2963, 9906, 6032, 7165, 4362, 3488, 8088, 4071, 5388, 3547, 6336, 9513, 6161, 6321, 10663, 122, 6695, 1104, 6329, 8017, 7623, 11015, 9587, 4478, 4786, 12118, 8025, 4253, 8185, 7989, 10289, 9124, 10080, 8010, 2549, 8478, 7197, 2229, 9474, 11945, 8958, 1038, 3159, 36, 4983, 3199, 5412, 85, 2716, 1869, 8209, 10163, 9491, 4834, 62, 3122, 11503, 10975, 10858, 6283, 3789, 5283, 915, 1517, 9578, 2681, 5559, 9746, 9984, 4092, 3688, 4275, 11948, 4013, 12091, 1311, 6005, 3772, 7007, 4548, 2019, 10763, 7181, 10916, 11457, 6774, 11218, 3458, 5792, 10472, 10605, 3170, 1121, 1392, 9961, 11482, 1236, 10621, 7196, 8542, 2550, 2559, 9837, 8314, 7803, 7347, 10258, 11388, 2609, 2068, 2852, 6699, 11206, 10734, 11001, 6981, 3618, 8351, 1415, 3134, 4897, 420, 2920, 1301, 3918, 6492, 5978, 2340, 9828, 3353, 10469, 11432, 1250, 9176, 11749, 115, 3497, 6012, 4440, 1653, 1643, 3148, 6846, 7112, 4994, 3406, 11464, 5713, 12133, 6423, 2727, 474, 2821, 7809, 7505, 11771, 2996, 5676, 4036, 1727, 2739, 4347, 1824, 1240, 8329, 2596, 11107, 1489, 2632, 9835, 2561, 7431, 10109, 4400, 3564, 1859, 1514, 10254, 2025, 2773, 8901, 7595, 6681, 5351, 2924, 6761, 10678, 11687, 7219, 7948, 9886, 9471, 6645, 9570, 6887, 2315, 261, 11305, 4089, 9703, 600, 5072, 8964, 10911, 9336, 10987, 3836, 5798, 11383, 12032, 12242, 3474, 3304, 12026, 986, 10136, 6254, 1836, 4162, 1660, 1022, 9455, 3558, 7998, 2095, 1414, 8460, 3619, 6210, 11366, 2840, 187, 7126, 7931, 12180, 5349, 6683, 10593, 12261, 9104, 1788, 1629, 10850, 10521, 8757, 11848, 1984, 2595, 8413, 1241, 4879, 6974, 2043, 10324, 220, 7063, 1979, 7753, 10992, 4543, 6754, 8868, 7802, 8474, 9838, 3467, 3704, 7925, 8803, 3090, 9996, 253, 2662, 1067, 2636, 10603, 10474, 9045, 4931, 1050, 4947, 2656, 8206, 4002, 11105, 2598, 10706, 7870, 10418, 4082, 3995, 1185, 488, 7490, 5623, 4723, 11918, 9334, 10913, 144, 340, 3785, 199, 554, 6068, 2117, 4811, 5244, 5903, 6797, 1543, 391, 9061, 9590, 8678, 8685, 2218, 3346, 247, 5204, 9360, 8861, 460, 6612, 3870, 10563, 1896, 10217, 6908, 4960, 5956, 5146, 7436, 11092, 9115, 9881, 1017, 9260, 1945, 6777, 10903, 1607, 3677, 6640, 7414, 2187, 748, 9107, 11838, 5217, 10380, 3318, 3674, 5883, 9318, 7122, 1012, 5545, 4200, 3719, 6902, 4740, 6603, 576, 2216, 8687, 1564, 10162, 8527, 1870, 4001, 8295, 2657, 2530, 1982, 11850, 983, 3910, 2587, 2304, 3781, 8602, 10533, 9216, 12286, 6146, 7374, 7681, 4469, 878, 7229, 7988, 8549, 4254, 7204, 11137, 2809, 4851, 1199, 10334, 523, 5653, 1855, 6364, 7915, 11298, 9075, 11024, 6058, 4816, 2394, 1997, 2369, 4144, 3452, 11354, 6856, 1881, 5597, 7208, 5398, 11507, 10984, 1801, 8055, 11181, 4719, 12001, 5910, 2843, 9598, 9919, 4125, 8838, 7093, 4285, 6977, 10189, 6488, 3372, 10155, 11783, 6109, 8728, 5355, 7630, 6842, 3203, 9072, 10452, 3930, 10630, 9807, 7099, 882, 3536, 9031, 6370, 3392, 1591, 8716, 11915, 1846, 5051, 9461, 8582, 5668, 8969, 8617, 4306, 526, 5341, 514, 693, 2604, 2756, 2145, 5172, 1968, 7659, 5438, 5636, 8682, 1204, 11056, 1587, 9388, 6743, 4070, 8571, 3489, 9716, 4908, 9311, 7097, 9809, 3595, 8835, 937, 1036, 8960, 11341, 11732, 863, 5477, 10354, 5993, 8983, 265, 12059, 6226, 1714, 5583, 7609, 11594, 9687, 11449, 6021, 7876, 10616, 3110, 11180, 8153, 1802, 9884, 7950, 7171, 7494, 3336, 1614, 9505, 5949, 3634, 5373, 11030, 2746, 3052, 3193, 4745, 9667, 4263, 3739, 4105, 5086, 6927, 9255, 1723, 12012, 2628, 6045, 2621, 4252, 8551, 12119, 5891, 12217, 10213, 688, 7831, 7622, 8558, 6330, 8600, 3783, 342, 3333, 2548, 8544, 10081, 12045, 11936, 5552, 5195, 4147, 5313, 10248, 4766, 7080, 2094, 8354, 3559, 6936, 9367, 10990, 7755, 592, 975, 10288, 8548, 8186, 7230, 10961, 9271, 3671, 4181, 11764, 6638, 3679, 2569, 1622, 9231, 7052, 7603, 843, 10965, 10971, 2735, 5611, 8736, 10958, 2505, 6018, 9842, 7291, 1088, 10744, 11900, 1743, 4856, 2182, 11333, 10437, 8997, 4411, 1675, 7370, 7170, 8052, 9885, 8388, 7220, 7855, 9163, 8912, 9549, 3873, 10466, 6793, 8591, 2268, 7226, 5155, 6534, 2613, 6531, 12179, 8344, 7127, 10347, 5123, 3716, 8802, 8310, 3705, 6623, 5524, 8640, 1938, 2365, 4847, 2437, 11297, 8173, 6365, 5771, 1766, 3534, 884, 2556, 6864, 760, 5330, 356, 11395, 10790, 7737, 9452, 14, 3278, 848, 10003, 2803, 7789, 3470, 4593, 6199, 11515, 2179, 3885, 8726, 6111, 6051, 466, 10869, 3188, 6606, 12197, 9184, 3291, 4335, 10615, 8059, 6022, 11582, 10149, 5097, 10417, 8290, 10707, 10510, 3132, 1417, 12264, 11778, 6772, 11459, 7324, 10208, 5856, 11371, 2038, 9162, 7946, 7221, 2014, 11796, 4472, 6276, 3850, 10637, 9990, 10552, 6280, 6168, 9782, 6273, 3180, 453, 6741, 9390, 11955, 10371, 5841, 651, 8690, 7621, 8019, 689, 1408, 7807, 2823, 9753, 4490, 11989, 11879, 1293, 4607, 4100, 11412, 492, 4438, 6014, 9111, 4987, 3226, 2701, 3735, 7504, 8424, 2822, 7828, 1409, 951, 7346, 8473, 8315, 8869, 2535, 4464, 301, 11761, 6950, 6675, 2764, 41, 10827, 3702, 3469, 7895, 2804, 5473, 2347, 6873, 1694, 30, 4758, 2418, 5132, 11883, 7162, 10456, 11532, 765, 5215, 11840, 10507, 12221, 10089, 10742, 1090, 3628, 2429, 4952, 4864, 7627, 1227, 2733, 10973, 11505, 5400, 9976, 591, 7993, 10991, 8320, 1980, 2532, 11669, 11615, 11377, 1296, 3971, 5536, 4775, 2906, 5281, 3791, 10271, 921, 9451, 7902, 10791, 904, 259, 2317, 2392, 4818, 2240, 8923, 4734, 7486, 12052, 5781, 4781, 1160, 2933, 11490, 78, 1401, 3288, 10093, 6557, 6569, 10586, 427, 9792, 2832, 8733, 9528, 8866, 6756, 10715, 126, 5323, 10298, 5318, 7690, 10069, 8945, 9283, 8818, 4396, 6091, 6087, 11420, 270, 10068, 7701, 5319, 11664, 11325, 6573, 702, 910, 10995, 4468, 8190, 7375, 10399, 11119, 11018, 9300, 11743, 9043, 10476, 10330, 6384, 5494, 3700, 10829, 5299, 12079, 295, 3696, 10023, 10722, 8845, 5437, 8098, 1969, 12159, 10480, 2278, 2654, 4949, 644, 363, 6922, 7286, 6686, 6944, 2795, 11556, 10863, 11350, 11255, 9304, 4840, 9226, 6595, 9296, 7160, 11885, 2471, 10386, 2243, 6841, 8132, 5356, 1226, 7763, 4865, 10853, 11014, 8557, 8018, 7832, 8691, 1371, 834, 11613, 11671, 2411, 6548, 11971, 1164, 3155, 11593, 8064, 5584, 1231, 10704, 2600, 842, 7975, 7053, 1717, 9393, 12082, 10560, 9552, 6680, 8396, 8902, 8853, 416, 2948, 6831, 12004, 2554, 886, 763, 11534, 5135, 1841, 10015, 5813, 2641, 1829, 10403, 9428, 3142, 9424, 5489, 11661, 99, 1107, 4138, 289, 6315, 6665, 4007, 372, 10445, 8776, 10243, 5175, 7297, 2185, 7416, 9866, 3365, 4561, 4804, 11290, 7500, 2062, 5386, 4073, 5687, 10944, 3503, 9095, 4250, 2623, 3003, 12245, 6860, 12007, 657, 9059, 393, 11635, 10728, 11904, 12258, 4507, 9872, 10820, 1399, 80, 1063, 9160, 2040, 4288, 5210, 1482, 10931, 11158, 6102, 9773, 9583, 6752, 4545, 9384, 3653, 3233, 12271, 6507, 4565, 11130, 11770, 8423, 7810, 3736, 172, 2061, 7552, 11291, 5030, 11076, 2546, 3335, 8050, 7172, 4870, 5622, 8284, 489, 7249, 12051, 7727, 4735, 1000, 10338, 2150, 10119, 2052, 10171, 4018, 7046, 2132, 508, 6230, 4121, 9896, 4558, 10050, 6453, 1351, 2337, 637, 2871, 2333, 8915, 2136, 7379, 2980, 12088, 11737, 11554, 2797, 3765, 12228, 2254, 813, 3579, 2984, 4649, 3064, 5510, 1388, 1682, 9121, 9923, 4371, 9853, 9595, 9479, 4109, 11091, 8245, 5147, 10545, 4330, 10108, 8406, 2562, 3669, 9273, 11968, 7336, 4525, 4663, 1437, 1770, 11721, 5116, 4797, 6668, 9865, 7558, 2186, 8233, 6641, 3311, 11047, 3962, 5316, 10300, 7388, 1734, 3500, 10040, 83, 5414, 10597, 9979, 480, 8892, 3645, 2175, 10127, 5011, 9154, 3832, 11870, 148, 1733, 7407, 10301, 3316, 10382, 5101, 1280, 2572, 4204, 2979, 7461, 2137, 11606, 10398, 7680, 8191, 6147, 7023, 7169, 7952, 1676, 8648, 10369, 11957, 7315, 4968, 3545, 5390, 6541, 1284, 3243, 3990, 11240, 9464, 2538, 10262, 9518, 804, 1207, 2941, 6346, 10257, 8472, 7804, 952, 2090, 11238, 3992, 9634, 4636, 11646, 9859, 4524, 7426, 11969, 6550, 2616, 1128, 1797, 5380, 4041, 6334, 3549, 1763, 10207, 7861, 11460, 4973, 4925, 8745, 497, 3283, 828, 4967, 7365, 11958, 2645, 6805, 2639, 5815, 9503, 1616, 12252, 3756, 9091, 10837, 3177, 4475, 9064, 3382, 11331, 2184, 7560, 5176, 3856, 8884, 214, 1087, 7964, 9843, 961, 10591, 6685, 7649, 6923, 5306, 8673, 8605, 665, 7105, 2161, 4895, 3136, 6359, 10066, 272, 9229, 1624, 12169, 2686, 9770, 10167, 6722, 2975, 5555, 9638, 423, 3508, 1640, 997, 4791, 1214, 9903, 10028, 9196, 6690, 5083, 1154, 9779, 12050, 7488, 490, 11414, 11826, 134, 3096, 5711, 11466, 5996, 9249, 10442, 4175, 2829, 10375, 9714, 3491, 10731, 2503, 10960, 7987, 8187, 879, 5154, 7937, 2269, 1349, 6455, 2013, 7854, 7947, 8389, 11688, 3913, 3326, 1412, 2097, 2467, 5543, 1014, 1805, 5397, 8158, 5598, 5036, 11136, 8183, 4255, 5363, 2780, 11963, 606, 2228, 8541, 8479, 10622, 11604, 2139, 4417, 1873, 10185, 1906, 4905, 11010, 8761, 8858, 9499, 142, 10915, 8495, 10764, 5702, 5220, 2190, 10770, 2713, 567, 4869, 7493, 8051, 7951, 7371, 7024, 1941, 4361, 8574, 6033, 10455, 7778, 11884, 7636, 9297, 9870, 4509, 407, 754, 4705, 10449, 11301, 2155, 6117, 5334, 11493, 5504, 2086, 8598, 6332, 4043, 4854, 1745, 9172, 9762, 5659, 5188, 11409, 5062, 4353, 5756, 112, 436, 929, 3027, 10346, 7930, 8345, 188, 9234, 1011, 8222, 9319, 9612, 6444, 10143, 4189, 10322, 2045, 4728, 4993, 8434, 6847, 1381, 3300, 9483, 6818, 2160, 7280, 666, 609, 6629, 5152, 881, 8124, 9808, 8083, 9312, 6736, 4284, 8143, 8839, 792, 9826, 2342, 8629, 5724, 12041, 4031, 2930, 11942, 11260, 2093, 8000, 4767, 10808, 11551, 6504, 11523, 4515, 450, 4061, 1910, 6586, 5111, 10100, 11543, 7028, 2877, 1978, 8322, 221, 9024, 1443, 2869, 639, 2478, 8696, 5581, 1716, 7602, 7976, 9232, 190, 9266, 7032, 2131, 7477, 4019, 6387, 2373, 89, 10788, 11397, 3256, 5921, 11931, 896, 138, 8842, 2130, 7048, 9267, 11151, 2876, 7066, 11544, 2363, 1940, 7168, 7372, 6148, 6828, 6913, 11755, 6964, 1993, 3631, 6988, 212, 8886, 6998, 2489, 5573, 9382, 4547, 8499, 3773, 11375, 11617, 2913, 11164, 165, 9847, 2488, 7012, 8887, 9150, 8879, 10365, 11210, 58, 1459, 4622, 211, 7015, 3632, 5951, 2778, 5365, 5005, 3617, 8462, 11002, 9815, 10188, 8141, 4286, 2042, 8326, 4880, 1990, 4587, 4600, 626, 12192, 12162, 4585, 1992, 7018, 11756, 6261, 11401, 11528, 4383, 11934, 12047, 6171, 5140, 797, 12213, 6719, 6674, 7796, 11762, 4183, 11776, 12266, 2794, 7647, 6687, 2296, 108, 3947, 5607, 3895, 9366, 7996, 3560, 4156, 4660, 11064, 12039, 5726, 1355, 9254, 8033, 5087, 9510, 5305, 7285, 7650, 364, 6196, 6204, 9040, 8654, 4245, 1260, 11754, 7020, 6829, 2950, 10491, 4959, 8249, 10218, 11821, 1422, 10226, 4739, 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6121, 6009, 1737, 2299, 1652, 8439, 6013, 7817, 493, 10275, 5068, 4343, 3127, 10251, 918, 6433, 2081, 4965, 830, 5517, 511, 25, 10872, 9157, 1779, 1582, 3999, 1872, 7192, 2140, 707, 6267, 4230, 1674, 7954, 8998, 3105, 92, 5683, 9101, 1420, 11823, 6238, 6178, 3563, 8404, 10110, 774, 6090, 7696, 8819, 4500, 9486, 2286, 11441, 9011, 12275, 2837, 4552, 1499, 894, 11933, 6959, 11529, 5425, 9733, 11405, 8755, 10523, 6518, 5924, 4116, 992, 9852, 7442, 9924, 10351, 3649, 6765, 5666, 8584, 3979, 3487, 8573, 7166, 1942, 5162, 3945, 110, 5758, 9676, 5755, 7134, 5063, 10021, 3698, 5496, 1823, 8416, 2740, 3377, 3126, 4434, 5069, 3901, 2404, 4237, 5119, 4919, 10614, 7878, 3292, 1852, 956, 10107, 7433, 10546, 389, 1545, 11201, 4998, 2447, 6271, 9784, 1331, 3553, 6678, 9554, 1318, 1324, 11446, 4686, 5237, 3058, 10667, 9720, 8610, 5651, 525, 8108, 8618, 3018, 1328, 5059, 4103, 3741, 2001, 11314, 11697, 4534, 1299, 2922, 5353, 8730, 3935, 10195, 5209, 7523, 2041, 6976, 8142, 7094, 6737, 353, 244, 2208, 3745, 9741, 8956, 11947, 8506, 3689, 5959, 3731, 4667, 4458, 11601, 2076, 72, 6398, 170, 3738, 8037, 9668, 6244, 9661, 277, 10566, 3034, 5362, 7203, 8184, 8550, 8026, 2622, 7544, 9096, 9237, 9543, 1259, 6916, 8655, 6340, 2784, 10675, 8953, 4795, 5118, 4339, 2405, 10487, 4136, 1109, 9179, 1673, 4413, 6268, 840, 2602, 695, 4680, 6706, 10575, 6063, 230, 12024, 3306, 6296, 1935, 6812, 11426, 557, 948, 3329, 11253, 11352, 3454, 8694, 2480, 5192, 2978, 7381, 2573, 8800, 3718, 8219, 5546, 2901, 10702, 1233, 11085, 3607, 6653, 6851, 4630, 10321, 7117, 10144, 9533, 9685, 11596, 11775, 6948, 11763, 7983, 3672, 3320, 6621, 3707, 2828, 7238, 10443, 374, 3573, 10698, 8897, 5919, 3258, 8753, 11407, 5190, 2482, 1659, 8359, 1837, 3217, 9086, 5447, 4659, 6934, 3561, 6180, 506, 2134, 8917, 5801, 2100, 5312, 8004, 5196, 3451, 8164, 2370, 2691, 9446, 6379, 288, 7570, 1108, 4234, 10488, 1305, 782, 6891, 5081, 6692, 10408, 5433, 935, 8837, 8145, 9920, 10292, 9895, 7473, 6231, 1265, 3214, 991, 4374, 5925, 10434, 6636, 11766, 1955, 11090, 7438, 9480, 1152, 5085, 8035, 3740, 4301, 5060, 11411, 7820, 4608, 4915, 6143, 3, 3073, 1756, 3687, 8508, 9985, 9702, 8379, 11306, 439, 10307, 9759, 9632, 3994, 8288, 10419, 3762, 2127, 10725, 3602, 10073, 11713, 5686, 7549, 5387, 8570, 8089, 6744, 11277, 5167, 2971, 6406, 8615, 8971, 1909, 7072, 451, 3182, 11541, 10102, 4875, 5649, 8612, 10682, 1386, 5512, 10344, 3029, 11272, 2408, 3174, 1197, 4853, 7143, 6333, 7329, 5381, 2072, 10393, 1726, 8419, 5677, 11829, 3428, 2929, 7085, 12042, 8943, 10071, 3604, 3611, 2699, 3228, 11898, 10746, 5492, 6386, 7045, 7478, 10172, 6221, 11735, 12090, 8504, 11949, 12145, 1376, 2955, 371, 7566, 6666, 4799, 11801, 11104, 8294, 8207, 1871, 4419, 1583, 9691, 1184, 8287, 4083, 9633, 7342, 11239, 7358, 3244, 1815, 1686, 9653, 11222, 9627, 12036, 2293, 9199, 3486, 4364, 8585, 8822, 2451, 3815, 4487, 3421, 5535, 7746, 1297, 4536, 10310, 5226, 12069, 1965, 10246, 5315, 7410, 11048, 3876, 9694, 10305, 441, 3532, 1768, 1439, 10660, 10501, 3185, 28, 1696, 5606, 6940, 109, 4358, 5163, 12102, 9449, 923, 6079, 8670, 3829, 10875, 10194, 4291, 8731, 2834, 11267, 10629, 8127, 10453, 6035, 2153, 11303, 263, 8985, 8815, 47, 257, 906, 6491, 8453, 1302, 2953, 1378, 3325, 7217, 11689, 2586, 8200, 984, 12028, 9974, 5402, 2719, 5644, 2818, 2403, 4341, 5070, 602, 1611, 5528, 9365, 6938, 5608, 4694, 3388, 9516, 10264, 2035, 10775, 10430, 8725, 7889, 2180, 4858, 9728, 2454, 9657, 10800, 1182, 9693, 3960, 11049, 10465, 7942, 9550, 10562, 8253, 6613, 9293, 518, 4784, 4480, 9468, 11815, 9562, 5866, 156, 6576, 825, 8883, 7295, 5177, 5443, 9141, 10646, 10636, 7849, 6277, 8792, 12174, 540, 3113, 11039, 857, 1820, 8936, 2461, 9949, 6311, 5797, 8371, 10988, 9369, 11869, 7392, 9155, 10874, 3938, 8671, 5308, 1288, 1555, 1083, 5590, 9437, 10221, 9680, 901, 2031, 4942, 4486, 3975, 2452, 9730, 9739, 3747, 5093, 1668, 11053, 807, 2328, 10897, 11168, 9119, 1684, 1817, 6497, 8831, 1071, 5515, 832, 1373, 5108, 1526, 10270, 7741, 5282, 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6301, 6165, 10861, 11558, 3048, 1851, 4334, 7879, 9185, 10092, 7718, 1402, 10363, 8881, 827, 7318, 498, 9581, 9775, 847, 7899, 15, 769, 2379, 2939, 1209, 5983, 2566, 10782, 12086, 2982, 3581, 12067, 5228, 10847, 5766, 2882, 6527, 11569, 8752, 4168, 5920, 7039, 11398, 9128, 12255, 1863, 11189, 6084, 5371, 3636, 545, 4615, 1814, 3989, 7359, 1285, 2476, 641, 2432, 9416, 9958, 10713, 6758, 12270, 7511, 3654, 11631, 4752, 11897, 4024, 2700, 7813, 4988, 8908, 6440, 1949, 10141, 6446, 11640, 9085, 4160, 1838, 990, 4118, 1266, 5452, 11979, 2944, 11952, 1720, 11833, 9211, 648, 9071, 8130, 6843, 2768, 5411, 8532, 4984, 1453, 1142, 8785, 4744, 8040, 3053, 11280, 574, 6605, 7883, 10870, 27, 3951, 10502, 11540, 4059, 452, 7841, 6274, 4474, 7303, 10838, 1196, 4046, 2409, 11673, 1120, 8486, 10606, 4845, 2367, 1999, 3743, 2210, 6026, 890, 9035, 35, 8535, 1039, 580, 11592, 7611, 1165, 5745, 10671, 39, 2766, 6845, 8436, 1644, 6082, 11191, 942, 9423, 7576, 9429, 3401, 5293, 3411, 6358, 7277, 4896, 8458, 1416, 7867, 10511, 11225, 4764, 10250, 4433, 4344, 3378, 6471, 11502, 8522, 63, 193, 8806, 10543, 5149, 2528, 2659, 11038, 3845, 541, 11179, 8057, 10617, 6789, 10786, 91, 4409, 8999, 2198, 1549, 9190, 10739, 9188, 1551, 5710, 7244, 135, 2260, 5034, 5600, 9995, 8308, 8804, 195, 5832, 10278, 11807, 3399, 9431, 315, 351, 6739, 455, 9083, 11642, 819, 2234, 1755, 4095, 4, 9832, 10924, 11344, 1446, 11704, 6882, 5509, 7448, 4650, 5695, 12016, 5016, 10666, 4312, 5238, 12100, 5165, 11279, 3192, 8041, 2747, 8699, 1850, 3294, 11559, 12172, 8794, 10549, 12184, 6500, 6292, 5049, 1848, 8701, 11156, 10933, 5361, 4257, 10567, 458, 8863, 11271, 4049, 10345, 7129, 930, 12224, 12098, 5240, 5258, 1139, 1176, 1327, 4304, 8619, 4861, 322, 10654, 6326, 102, 3461, 10611, 3643, 8894, 3343, 4591, 3472, 12244, 7542, 2624, 5778, 6591, 11576, 2193, 5675, 8421, 11772, 5693, 4652, 5130, 2420, 1270, 4613, 547, 9442, 1033, 4648, 7450, 3580, 3268, 12087, 7460, 7380, 4205, 5193, 5554, 7266, 6723, 9565, 6405, 4066, 5168, 2678, 501, 613, 5465, 10026, 9905, 8577, 8750, 11571, 6514, 5507, 6884, 10423, 370, 4009, 1377, 3916, 1303, 10490, 6911, 6830, 7591, 417, 12143, 11951, 3210, 11980, 6345, 7350, 1208, 3274, 2380, 12130, 11590, 582, 11489, 7722, 1161, 11941, 7084, 4032, 3429, 2792, 12268, 6760, 8393, 5352, 4294, 1300, 8455, 421, 9640, 10132, 6174, 9671, 11163, 7003, 11618, 10841, 587, 6041, 6715, 5280, 7743, 4776, 8637, 3340, 10701, 4198, 5547, 4451, 335, 10571, 4689, 208, 11996, 1474, 1534, 9560, 11817, 6002, 1434, 1277, 3530, 443, 10657, 6526, 3262, 5767, 11474, 8712, 1977, 7065, 7029, 11152, 9856, 9051, 2332, 7465, 638, 7059, 1444, 11346, 9146, 4714, 6801, 1571, 1885, 4712, 9148, 8889, 9206, 11975, 10641, 6194, 366, 6698, 8467, 2069, 470, 6289, 11741, 9302, 11257, 9477, 9597, 8148, 5911, 186, 8347, 11367, 4551, 4388, 12276, 11266, 3933, 8732, 7711, 9793, 10374, 7237, 4176, 3708, 1048, 4933, 9752, 7827, 7808, 8425, 475, 2402, 3903, 5645, 10059, 3750, 345, 1031, 9444, 2693, 4850, 8181, 11138, 8988, 5181, 5472, 7788, 7896, 10004, 10692, 6184, 2125, 3764, 7456, 11555, 7646, 6945, 12267, 2927, 3430, 5105, 12148, 11500, 6473, 4980, 10674, 4242, 6341, 561, 11962, 7201, 5364, 6985, 5952, 3723, 6129, 8900, 8398, 2026, 4936, 11486, 5410, 3201, 6844, 3150, 40, 7794, 6676, 3555, 4580, 3424, 1020, 1662, 2144, 8102, 2605, 1477, 741, 2005, 11610, 6073, 5579, 8698, 3051, 8042, 11031, 6561, 10936, 9954, 3376, 4346, 8417, 1728, 4692, 5610, 7971, 10972, 7761, 1228, 12280, 10754, 9398, 473, 8427, 6424, 5565, 9316, 5885, 5991, 10356, 5643, 3905, 5403, 1868, 8529, 86, 566, 7175, 10771, 3776, 9609, 11790, 9008, 2515, 4773, 5538, 1168, 1273, 3734, 7812, 3227, 4025, 3612, 3586, 1135, 2435, 4849, 2811, 9445, 4142, 2371, 6389, 10538, 9769, 7270, 12170, 11561, 10008, 5558, 8512, 9579, 500, 2969, 5169, 5846, 1075, 12073, 11204, 6701, 1026, 1054, 11230, 152, 2009, 484, 3523, 1776, 1066, 8305, 254, 11037, 3115, 2529, 8205, 8296, 4948, 7654, 2279, 6733, 5025, 11867, 9371, 2158, 6820, 6804, 7313, 11959, 6463, 1828, 7580, 5814, 7311, 6806, 10602, 8303, 1068, 10922, 9834, 8409, 1490, 6537, 6044, 8029, 12013, 716, 5777, 3002, 7543, 4251, 8027, 6046, 6114, 9374, 1127, 7333, 6551, 6530, 7934, 6535, 1492, 2067, 8469, 11389, 1532, 1476, 2755, 8103, 694, 4227, 841, 7605, 10705, 8292, 11106, 8412, 8330, 1985, 11071, 10018, 10942, 5689, 10884, 2303, 8199, 3911, 11690, 5940, 10267, 11913, 8718, 6235, 11417, 777, 2165, 1913, 5054, 8799, 4203, 7382, 1281, 1621, 7979, 3680, 10781, 3271, 5984, 810, 3668, 7430, 8407, 9836, 8476, 2551, 6863, 7909, 885, 7588, 12005, 6862, 2558, 8477, 8543, 8011, 3334, 7496, 11077, 6729, 3779, 2306, 1093, 1495, 10261, 7355, 9465, 4463, 7800, 8870, 11668, 7751, 1981, 8204, 2658, 3116, 5150, 6631, 3694, 297, 867, 12021, 1750, 9602, 5020, 2123, 6186, 4772, 2707, 9009, 11443, 1179, 11134, 5038, 240, 6120, 4446, 6017, 7967, 10959, 7232, 10732, 11208, 10367, 8650, 11861, 4577, 9458, 1916, 6450, 5935, 6396, 74, 5572, 7011, 6999, 9848, 10633, 11295, 2439, 1658, 4164, 5191, 4207, 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