Decapsulation -- ML-KEM-1024
dk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
c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

dk_pke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
ek_pke: A48407213AA1B0908F4B174F86D573FA04386498BE68398E8D720D278111D8B17303602A96E35F56FB25173C4F4A03CA2AC9BF79DCAB764BCE4410401E1013E6528CCC5113358577DA8375E02343108C2924D2551E5CC5A1B04DEF88324D854FC92C4ADF7C2301337E4520BFC365566F66092E367AE60612744653C1EB47F0820951A2A14C425909340D8727188EAA08E48678984876D0008DAE99015B3663FDCB725741530BC3895B11620CE3B417A320E18813B99C235AC06F55600F983882BFF00236107B5042545B6B775868AEFB79B595596902C69B9ECA3D358C61FEE036D218AC43BA3F52C06A8F881A7ED70386142CBAC5CC04FCC31E16277651CE2DCC5014F6BA5A915C1338834EF474B6715913BC7A4E593C688766ADD70698B37E06E53915F385388C25C4265E1CB44FE3D019D121AE4C32434F37B0A4CB69C7CC95707350C3493D0FB11CD4D09F29DC56C07BC8EB0BD0082B41442145663C21AB433467B95EC2478423C18BF2EC703EFBA28CDABD42B7B833150D6DA25EB00A8328902E2D089B55D69AAD9A94D818264C54B04D614D147A30ABFC03D9929D96BA7F81865DA353C454BA7AA7881AB974C1B8F0831E79C4418664E953A54DE93213697281341D37F508E8CBAE3D8185054567DEFC8E3BBCAA4247907C483B8F1B84B324C1A7CA8442DB6B7B128C8313BE1FE25791209B864A3E1A618D56D710D6F3BF559510167C464C6B9B8BC490B8E03925D03D0EEB5D78179428BB80D3FB148840709C41147A686FC9BCBDCDF7C7EA7C30FB640FF05B7539ABAB70892908E93CC9C347F8AC889E56468A135B99754738E15F4E677DF375BF1B43606A2C47380B10A0C14C28583C83311A2854B2A9931FD66086C10749F334577FD70B51B95060075199319B3F7CB5B237302C370A23175E4E013C56281BAFE2BE9F825A3066AB8BBA5793E21E7A48978CF60C091B1F80C0C23814A30F7760601ACEABB1215200940FFA152272096D458D00DD039F236B2727B588C62204E79C451681DFE410EEC42B74945AEC0313A391942AE1B122174DBE59AB1E390CD64941436C75A9323C69A641880870FBB280B3B37B3BD982B82955620B0783B82E8961A4043BC7F66C0EF25A5ED15326F8816E5EA4167EE8BF6666451D315B2C751441172C278300268261C78C6F0C46562779B3A1196F87835F79FCB7E0CBA15336CC83E156C5022887A80986B49C1B576594A23142624ABF524822418C6101905262806572494D3753C06281E7F17E0D796CD7767FDCE901FE1712A00A3D36EB423E29868846932A9431B8CA660FC1975E23A75B4A51DE1069D3A59F6EEB2A5CE72A8916B5E863476E6AC572929F2C29BC5627BA994163CED35AB7031C00490724555ACDE613AEB4C3E99981C62B5DC6A9B35BA79220243689E0594996857C045D67193D9E411B4FF39D0F8C3C0A70ADB72A7021E36D64FB294D932B24E1A2BC0BC41C4AA3B5EC3CF0E672DE140F484733FD82BF082934B540A635C44898E8AB8E0645705AA581718B4132C427927FAE75BF9616A5424C2020EBC5CFC1BC0ED1653AE5005A1754181620B7F06D716313033BB72A40647ADB2E667370F2C74FDB94420DA48DD1379DBA59AA22F857E231C5C083290066C548761BDF385F2F85817B212066D39F03B77F8EF41219E4BFB9C12E4FC98800571D223AA92A32C7A3C2A7CF9C995AE0A7B59391FE9A4F0D633BFB798C34B72BBA6A9F16C4132E88B570758BD551C91BD2ADEB53A72AC6AA03689DD64B035709A8AF468543CB1736DBC9C72B529E70596D18B19CA68E617A147C189D283A77688CAF94DA5A0E9B63181A40BBE7BD4168A24D274319A993BCEA8ABF505FE862129692B5BDE849F36AC92F7171E53859313604EAC10BE2786FF385B9C718154818772FA7B899C04EFD18A8019A79B6F64D5B9A2C55E784CB47CA294856689AA6A70CC27B6C20D4D1C729C409D0B925C40C30C0777815077749488B8DF0390695ABDB048C7CE1853602A54D153CF2A51617847B11E63C4C761966D5AD93350DBADA4A15C124BD808871993FC775B6E410C386590F730A8EC9475EEE915039E91B6FE425B90668C6AC5258B7AF103B9F5E230B719BBB09871DC1621517BA2A839C96AAA6440A875EAC90B298D61BD3F3AC89B405DB394232686A2BE0F3C75F15E64E61F070791EB4BB97B7019825F117C7D73A12
h: FD3DCC22D581B0E41B786374A461EA0D88DAA89B659F0DC82443423515B633B0
z: 05C958EC26561B6DB818F4B8CB2E28990E748417587FEC38A1284BBB4FF9E478

c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
c2: FEC1DB352C49583A7D817EAF62000888ECB0EBFFEF69FF8E590CFA25BEAB21605B635ABC2CA23680789725CF700F553C88352F31616154873D18B6C6EB519FC639B070FD67F86AAB62349DBFFA89F93051A7C7B7BD161FCD73672CEEF59A9BB7F571EABE2570C5BF31ECAA1F9CA7A9C6D31EA5FB7C979CDD2613897E7D1503FB0C19ADDCFB3A63E2185FC4101838DA66CCE2D3D9FFB47746C2003EDD86C2F8C3
u: [[3071, 1403, 2568, 1534, 2888, 2554, 884, 3019, 1058, 2038, 995, 871, 2394, 1510, 2544, 2102, 688, 50, 1824, 3032, 2676, 2706, 2637, 1257, 3209, 2845, 1052, 1172, 636, 530, 1795, 748, 1515, 288, 2643, 2601, 3062, 2962, 1265, 816, 388, 192, 2628, 1172, 974, 1500, 1814, 1302, 1482, 549, 2910, 1001, 1315, 870, 1851, 2329, 1079, 1717, 2973, 2064, 1648, 1338, 3028, 1539, 145, 242, 1749, 559, 2441, 1804, 2459, 50, 2614, 1892, 1190, 2546, 2409, 1361, 1715, 3220, 367, 637, 966, 683, 231, 375, 1577, 1222, 249, 1213, 1331, 600, 996, 232, 1284, 325, 3147, 2355, 640, 766, 20, 2276, 2554, 3123, 145, 2823, 2051, 2637, 2687, 2320, 5, 2552, 2386, 904, 2438, 1118, 3145, 2934, 57, 488, 2845, 2641, 2949, 180, 2454, 2680, 390, 535, 55, 3227, 1640, 2901, 566, 2388, 766, 2373, 1469, 444, 1304, 1544, 98, 70, 2845, 575, 322, 2056, 1843, 2346, 3184, 1016, 265, 673, 957, 571, 2767, 692, 2211, 1851, 1091, 2915, 502, 164, 1521, 2167, 2705, 1426, 966, 268, 1123, 1629, 3155, 1364, 1959, 783, 63, 2077, 553, 306, 3023, 1790, 437, 1105, 1757, 18, 1650, 3175, 3066, 923, 1913, 2003, 2755, 1086, 1952, 1946, 354, 1959, 418, 2789, 55, 1738, 2303, 450, 3114, 15, 2887, 1923, 2867, 2199, 1208, 2100, 309, 2432, 3084, 1564, 1887, 3158, 2685, 1239, 1242, 2120, 1375, 330, 1968, 1013, 3002, 2341, 1980, 2090, 3240, 925, 3010, 842, 2467, 753, 3188, 1128, 366, 2025, 1772, 2849, 3171, 964, 1213, 3028, 1349, 304, 567, 1148, 1916, 2237, 1087, 3041, 935, 1720, 1562, 140],
[606, 2207, 1164, 535, 1988, 2767, 2697, 3197, 1435, 2404, 89, 918, 2087, 1426, 2284, 2705, 2063, 618, 176, 1481, 2654, 1230, 3009, 1679, 1170, 210, 681, 3253, 117, 271, 1751, 2843, 2705, 1227, 3071, 444, 362, 1149, 1240, 1157, 1925, 1796, 268, 1965, 463, 2059, 712, 709, 3231, 1474, 1508, 1240, 1096, 1482, 1812, 2360, 795, 1204, 10, 3184, 2086, 2110, 1237, 2568, 2152, 1556, 2797, 2376, 606, 1973, 2380, 335, 2562, 845, 580, 2589, 85, 1955, 2393, 1271, 1320, 2177, 1335, 1388, 2064, 1460, 1226, 231, 884, 636, 2467, 1756, 2867, 2988, 1842, 2454, 172, 2736, 961, 3092, 1890, 1582, 2201, 1850, 759, 488, 1782, 327, 1400, 1517, 1252, 3061, 3171, 2484, 3215, 2380, 3246, 673, 301, 2373, 640, 1877, 1933, 1039, 2107, 2788, 728, 2183, 1398, 2781, 1603, 652, 2750, 1200, 562, 1161, 3327, 1612, 2775, 930, 751, 2672, 224, 1302, 1346, 1447, 3079, 806, 2258, 3129, 689, 2354, 392, 2292, 247, 3002, 2702, 2380, 1648, 712, 1003, 180, 725, 1691, 1461, 1599, 319, 104, 1159, 3175, 1671, 2567, 1326, 1998, 2760, 1048, 2581, 2, 1595, 2142, 2781, 514, 263, 1084, 2989, 1318, 858, 320, 822, 3183, 863, 1401, 1455, 1185, 358, 1239, 881, 2342, 2936, 2976, 1770, 1879, 1487, 1743, 1994, 1154, 1070, 2892, 346, 70, 3114, 1486, 1068, 34, 176, 2606, 1206, 2820, 2819, 268, 2754, 2747, 2541, 2043, 3264, 1162, 2037, 1824, 1520, 819, 2146, 1430, 2669, 2502, 2942, 627, 1700, 1013, 1352, 2367, 1682, 3210, 644, 1343, 3012, 2212, 3179, 2454, 2923, 65, 2952, 2557, 1973, 463, 1994, 2381],
[1769, 3266, 3045, 127, 262, 2121, 2316, 1681, 2310, 2910, 1416, 2105, 953, 229, 1318, 2671, 2033, 2342, 2063, 1270, 2885, 2750, 2832, 1396, 1458, 618, 154, 3149, 11, 714, 2289, 2997, 2389, 284, 2682, 215, 1442, 237, 310, 281, 2575, 1403, 735, 3002, 1318, 276, 1770, 2017, 1170, 2232, 2477, 720, 2498, 2068, 2674, 2294, 1092, 2012, 2581, 2347, 2684, 624, 2526, 1482, 2950, 3197, 1910, 743, 1169, 1634, 1515, 3040, 2747, 2298, 1091, 1484, 788, 1647, 2771, 2659, 3058, 671, 3189, 1782, 2653, 106, 72, 1123, 2394, 3152, 1860, 3062, 158, 1835, 1026, 1135, 2263, 3038, 2599, 2207, 780, 41, 1022, 1027, 2255, 2110, 2077, 2094, 2120, 2698, 597, 3041, 1499, 463, 1057, 85, 257, 413, 2996, 1588, 367, 2825, 2507, 2407, 1565, 2635, 2033, 1681, 2485, 1107, 650, 1707, 3293, 3010, 3212, 1565, 1148, 649, 1417, 2066, 42, 2742, 393, 2903, 2216, 3253, 640, 114, 1157, 85, 60, 2677, 358, 718, 2255, 428, 845, 3205, 268, 738, 2589, 1830, 2038, 2516, 2417, 2554, 1543, 2757, 2190, 961, 3067, 2658, 2086, 3132, 1739, 2633, 182, 1791, 930, 1437, 1946, 923, 2352, 2994, 291, 2511, 1554, 2328, 2341, 540, 1344, 1565, 1100, 1365, 3162, 2905, 380, 1655, 814, 2693, 16, 1715, 1013, 902, 569, 2284, 2329, 1325, 1570, 535, 2094, 992, 1320, 229, 884, 133, 2422, 98, 1858, 3244, 3279, 2695, 2667, 2266, 1157, 2549, 2437, 387, 805, 803, 944, 2866, 1279, 1856, 1460, 1916, 2121, 494, 1284, 1452, 1986, 2046, 1625, 3183, 2363, 31, 1538, 1861, 2739, 80, 2581, 1213, 2396, 2191, 931, 2915],
[1603, 907, 2780, 2897, 1440, 1196, 866, 2225, 1720, 2596, 1432, 1359, 2268, 2489, 548, 1928, 1364, 1925, 1850, 2866, 1073, 2029, 2971, 2937, 93, 1243, 2389, 1985, 1817, 3305, 1704, 2386, 125, 1365, 2575, 728, 450, 943, 1977, 793, 436, 3137, 2368, 811, 328, 28, 975, 2684, 509, 2572, 1130, 657, 2651, 3175, 2298, 2136, 1873, 1232, 1040, 2931, 953, 323, 1413, 3222, 579, 2159, 156, 2464, 146, 836, 1855, 1830, 3279, 3184, 2064, 3309, 2082, 1047, 1257, 2715, 783, 3111, 821, 2619, 161, 2911, 2020, 429, 1281, 1918, 580, 2285, 3103, 1504, 2903, 1567, 1492, 1947, 1903, 3136, 3253, 3144, 7, 1942, 458, 3048, 2680, 2890, 2211, 814, 623, 432, 1697, 65, 2915, 918, 746, 393, 1447, 1091, 2146, 1006, 813, 692, 987, 2204, 1951, 3119, 1437, 670, 1764, 2190, 2534, 247, 3110, 2500, 2363, 3009, 590, 2924, 2032, 2373, 2796, 3179, 444, 665, 1942, 2698, 788, 1383, 1109, 1577, 158, 1913, 2380, 3202, 891, 1299, 2313, 1837, 2651, 1035, 348, 2949, 341, 312, 1643, 1191, 416, 522, 2848, 1227, 1525, 2185, 1291, 2750, 2684, 3301, 1843, 1330, 983, 2276, 98, 3214, 957, 2386, 2653, 3212, 1765, 2882, 909, 585, 3035, 2211, 312, 465, 1721, 397, 2502, 2477, 336, 1110, 2682, 3041, 1211, 1274, 2963, 866, 692, 1960, 2355, 1417, 1439, 540, 2149, 2495, 1908, 478, 2211, 1782, 1923, 2141, 1795, 735, 1484, 3238, 2368, 73, 892, 896, 922, 180, 2550, 3254, 1785, 782, 3318, 3235, 2822, 3205, 1022, 3100, 914, 855, 2667, 3290, 3035, 1087, 1055, 1939, 1975, 770, 1305, 897, 2929, 2976]]
v: [3121, 1560, 1665, 2393, 3017, 2705, 1665, 520, 936, 208, 2289, 2081, 1977, 3121, 520, 1665, 3121, 2809, 1144, 520, 624, 0, 0, 104, 832, 416, 2809, 104, 2809, 2185, 3225, 3225, 1560, 1560, 2705, 3121, 1560, 728, 624, 1144, 1248, 1665, 3121, 1144, 208, 3225, 1456, 2185, 104, 104, 2497, 2289, 2185, 1769, 936, 1144, 2913, 520, 1144, 416, 1040, 2809, 0, 1665, 2497, 2809, 520, 1144, 1873, 728, 312, 1456, 1560, 832, 2185, 2497, 312, 416, 2289, 624, 1560, 936, 1248, 208, 2289, 1665, 1769, 1040, 728, 1248, 1560, 1665, 104, 2809, 2705, 2497, 1144, 1560, 2081, 3121, 936, 312, 728, 728, 1665, 520, 2913, 2705, 3225, 1977, 104, 3225, 1040, 2809, 1040, 520, 624, 2705, 2081, 1977, 3225, 2185, 3121, 1977, 2497, 2913, 312, 624, 1769, 2705, 936, 1560, 2913, 2809, 2289, 2393, 2289, 2497, 728, 2705, 2913, 2601, 3017, 1248, 1248, 1769, 2809, 1144, 1560, 1352, 1456, 1977, 2393, 1352, 3017, 312, 728, 2185, 2809, 2393, 520, 104, 2913, 1040, 2913, 3225, 624, 624, 1248, 2393, 1040, 3225, 104, 1456, 3121, 2081, 936, 2185, 1769, 728, 1352, 1560, 2081, 2081, 2809, 728, 3225, 1456, 936, 1456, 2289, 2809, 624, 2601, 416, 1873, 832, 3225, 2185, 1560, 2185, 2497, 0, 2289, 1560, 624, 416, 312, 1352, 520, 2393, 2393, 1560, 3017, 1248, 1248, 208, 728, 624, 3121, 520, 208, 312, 208, 2497, 0, 1456, 2081, 1352, 1977, 1769, 2601, 208, 3225, 2081, 1977, 3017, 3225, 1977, 2289, 2393, 1977, 1769, 416, 1248, 0, 2497, 728, 3017, 2289, 104, 520, 1248, 2913, 1560, 2497]
sHat: [[2575, 622, 1476, 1098, 1189, 1089, 1866, 441, 2652, 2085, 1880, 3074, 669, 1124, 2462, 837, 588, 2767, 518, 2266, 2355, 2574, 2578, 2620, 2929, 711, 2363, 162, 1287, 2081, 2321, 3136, 2764, 3150, 1183, 467, 941, 1917, 2772, 882, 2342, 353, 2988, 2967, 3300, 145, 2156, 394, 1308, 2111, 1872, 1013, 1632, 2117, 3233, 2651, 2109, 600, 884, 3157, 1589, 1473, 1870, 685, 159, 1391, 325, 663, 1537, 1743, 16, 1277, 1118, 2603, 2028, 1827, 2537, 2276, 1181, 1212, 3005, 1818, 3003, 3021, 1532, 2952, 1537, 771, 2697, 1550, 1519, 2158, 737, 398, 2060, 2851, 1255, 2667, 1598, 125, 2889, 3152, 2746, 1415, 2988, 451, 782, 2404, 114, 3184, 664, 2304, 1259, 287, 1154, 920, 3310, 2280, 2401, 2850, 344, 990, 3090, 2839, 90, 3248, 1659, 2260, 832, 2898, 2825, 2487, 46, 2485, 2128, 2318, 2998, 1139, 2055, 1940, 609, 2538, 1304, 1750, 210, 2541, 2922, 2179, 579, 2126, 1084, 2139, 2127, 273, 366, 2007, 987, 1360, 423, 853, 690, 1696, 3189, 2274, 383, 2287, 2575, 916, 796, 2042, 2907, 3266, 2440, 2460, 1204, 1918, 1104, 1628, 3143, 126, 618, 348, 560, 711, 2554, 1663, 409, 3222, 2182, 3128, 2902, 370, 204, 2072, 326, 602, 2418, 2908, 1535, 417, 1195, 1045, 265, 2112, 1550, 1058, 1849, 3160, 736, 2285, 2802, 1342, 1514, 2398, 542, 2758, 1403, 397, 953, 168, 3149, 3307, 874, 1625, 2705, 2286, 1522, 119, 2442, 1840, 2693, 1234, 1043, 2384, 3024, 1008, 1313, 344, 153, 457, 2557, 879, 1155, 3204, 528, 756, 254, 2218, 3053, 428, 895, 1581, 1631, 2818, 308, 760],
[1955, 2736, 44, 2370, 1364, 1350, 365, 2611, 1089, 26, 317, 2200, 1460, 255, 232, 2662, 2664, 3197, 945, 1088, 1566, 505, 206, 3163, 945, 1247, 1522, 2446, 2246, 3325, 2144, 1611, 3093, 1792, 2877, 3042, 2988, 9, 538, 266, 1921, 2788, 2667, 2792, 1836, 2327, 2523, 1390, 2497, 2863, 2564, 343, 2422, 1072, 1671, 1216, 58, 440, 2317, 3224, 1430, 3322, 163, 299, 1217, 900, 953, 1343, 3084, 1520, 2217, 2547, 2832, 1007, 753, 30, 2099, 1043, 2911, 471, 436, 2769, 3321, 1841, 1462, 1716, 2920, 1994, 3068, 3223, 1065, 1262, 2904, 846, 202, 2785, 49, 959, 2860, 2659, 716, 2026, 3251, 2837, 2615, 313, 3082, 2170, 2275, 1883, 719, 1342, 943, 3136, 2237, 1015, 1304, 2604, 2552, 692, 3263, 1383, 1415, 2437, 1713, 1019, 3046, 108, 148, 1165, 268, 3210, 1784, 1992, 2065, 3067, 819, 714, 1824, 2555, 1180, 2154, 1669, 264, 1969, 2105, 1982, 2127, 3007, 246, 3205, 424, 377, 769, 2522, 1398, 754, 561, 2382, 2156, 377, 1208, 2536, 3059, 2833, 1104, 2241, 2108, 3308, 989, 2227, 559, 1956, 3103, 1573, 1765, 1745, 854, 2152, 1052, 60, 461, 1570, 1956, 213, 418, 3082, 1901, 1332, 2595, 1483, 3280, 196, 1831, 937, 1796, 1269, 843, 3319, 117, 395, 1428, 2195, 1358, 477, 1982, 1727, 3080, 2502, 2620, 1316, 808, 729, 316, 926, 3199, 2906, 3177, 2195, 263, 3168, 2797, 2607, 1423, 3289, 1356, 2447, 3089, 974, 1605, 3208, 2032, 3253, 3184, 190, 1332, 1554, 3277, 916, 1888, 792, 2191, 196, 2809, 399, 2966, 1204, 1216, 2807, 1477, 2775, 337, 2949, 1523, 726, 1218],
[1387, 2313, 1509, 24, 466, 1064, 2304, 412, 1010, 3272, 2347, 2772, 2699, 1471, 682, 2426, 895, 2080, 63, 2534, 1275, 610, 1785, 3123, 1794, 152, 1659, 2941, 1725, 1932, 1378, 2184, 2947, 1437, 2132, 64, 2345, 3291, 2562, 2412, 3260, 3249, 475, 533, 2271, 95, 688, 1192, 2542, 2537, 2859, 731, 1410, 995, 2669, 771, 519, 1929, 2064, 3157, 1902, 159, 906, 1419, 78, 1578, 30, 818, 2685, 2419, 861, 3321, 2098, 1749, 362, 2599, 3012, 2859, 2050, 1339, 2559, 3136, 1031, 955, 2332, 2833, 3268, 2956, 2081, 724, 2013, 882, 1921, 2727, 383, 1926, 3145, 1015, 2490, 1815, 1107, 2248, 2909, 496, 1344, 1259, 413, 2357, 2704, 772, 575, 1527, 3084, 1644, 3270, 2844, 1368, 104, 1029, 1747, 2996, 2162, 2429, 3309, 1701, 2511, 530, 539, 3271, 1310, 1792, 1631, 2439, 2107, 75, 3180, 833, 2293, 2179, 1470, 2483, 208, 3002, 3263, 267, 391, 3327, 2423, 745, 1589, 21, 1047, 3320, 1034, 82, 1037, 53, 3264, 2127, 2374, 1877, 1225, 3051, 117, 103, 2569, 80, 2878, 2038, 679, 1911, 1350, 1567, 2927, 2683, 466, 1876, 2080, 1798, 1668, 1679, 163, 299, 1136, 1847, 1814, 2345, 2848, 1319, 2230, 1510, 1924, 1096, 1036, 373, 1671, 2054, 2177, 3160, 2825, 2394, 2537, 2389, 1652, 401, 427, 1778, 1712, 2744, 1868, 352, 3141, 2664, 176, 960, 2087, 2625, 2946, 952, 410, 2011, 2380, 1757, 2380, 3007, 2077, 63, 2904, 651, 535, 1677, 1245, 3068, 2589, 2219, 2708, 2639, 2263, 714, 1641, 1485, 2625, 2861, 2649, 2043, 1654, 1449, 1317, 1388, 208, 2530, 2229, 2577, 690, 2576, 2595],
[209, 1551, 1647, 2222, 2389, 481, 3061, 771, 3119, 407, 802, 28, 2766, 2446, 666, 310, 64, 2697, 1632, 1911, 1135, 1130, 1831, 795, 1635, 1400, 1898, 2070, 629, 395, 1254, 2095, 2997, 3170, 2818, 3047, 1715, 2436, 185, 760, 1750, 839, 2497, 1242, 1492, 3292, 3145, 1774, 1581, 1526, 1906, 2071, 3281, 270, 1706, 1711, 2008, 2482, 667, 1231, 2201, 1886, 1260, 857, 1581, 89, 250, 3251, 2877, 616, 134, 923, 1905, 1546, 1459, 944, 1076, 1747, 269, 2887, 2893, 2008, 1582, 426, 92, 2705, 819, 2237, 932, 872, 369, 1857, 340, 1142, 3028, 660, 2068, 1391, 2441, 3101, 191, 880, 1991, 895, 2428, 781, 1743, 255, 132, 2603, 3328, 997, 1534, 3189, 2865, 433, 609, 1891, 651, 2309, 1752, 2947, 1067, 1084, 3011, 1266, 1772, 41, 2841, 541, 1842, 2463, 1546, 2125, 675, 2551, 2621, 705, 2794, 499, 484, 619, 1141, 2204, 1007, 403, 399, 2576, 6, 1768, 2300, 2350, 1053, 1772, 3223, 161, 1546, 1189, 1529, 1742, 1959, 2674, 3172, 1377, 1420, 2729, 1625, 2325, 2059, 2114, 2089, 239, 743, 1762, 1181, 108, 1150, 2371, 1615, 2336, 1133, 2852, 1999, 1608, 1015, 1425, 1083, 660, 3064, 2290, 204, 1910, 408, 1721, 2945, 2309, 920, 227, 1219, 659, 2061, 3083, 2123, 976, 2803, 268, 1486, 1875, 7, 643, 1257, 2601, 1883, 654, 2424, 756, 1761, 2411, 3258, 2837, 935, 407, 2874, 643, 1188, 1039, 2222, 725, 711, 1276, 1511, 468, 1638, 567, 2347, 1563, 1221, 192, 670, 21, 938, 3295, 1101, 174, 2517, 1402, 1418, 655, 1296, 2363, 489, 1512, 1571, 1023, 86, 1556]]
w: [1740, 3246, 1647, 44, 19, 3261, 2, 20, 1595, 3296, 110, 1684, 48, 81, 1566, 1653, 30, 3215, 137, 1688, 1685, 3285, 1601, 3240, 3245, 4, 1683, 1611, 3292, 1659, 1736, 1630, 135, 1607, 1654, 51, 65, 1611, 47, 3, 3293, 1747, 1678, 2, 1817, 3266, 1618, 3283, 1701, 1574, 3287, 1667, 1758, 8, 14, 49, 1692, 3185, 1628, 1648, 3315, 1749, 1745, 26, 5, 3249, 3217, 1781, 1620, 1588, 48, 1654, 70, 33, 3304, 1692, 1762, 3292, 58, 3241, 76, 23, 1609, 14, 1617, 1629, 1721, 1696, 3260, 9, 3322, 1663, 1684, 1668, 3326, 1641, 1729, 1599, 75, 1573, 3275, 26, 1652, 1550, 3256, 1567, 1647, 1724, 3226, 1704, 3294, 3296, 85, 54, 3263, 1654, 3293, 1685, 3318, 3296, 1758, 3222, 3227, 1648, 1724, 3314, 39, 1734, 3270, 1729, 1655, 1702, 8, 3273, 3233, 35, 52, 3304, 1681, 43, 1637, 1701, 1738, 3257, 99, 3305, 1574, 3220, 3281, 3290, 80, 1631, 1657, 1674, 1692, 190, 1683, 3291, 25, 3289, 3248, 54, 3313, 1695, 1613, 3290, 1604, 3296, 1576, 1635, 1737, 1575, 1781, 1685, 1636, 142, 3237, 25, 1565, 1683, 3132, 1612, 1598, 1580, 51, 6, 3253, 1693, 1610, 1580, 3257, 134, 1643, 3205, 51, 21, 115, 1593, 3326, 1714, 42, 83, 3293, 1620, 23, 1648, 73, 3327, 1630, 1665, 56, 1717, 3286, 3198, 1563, 140, 1569, 1761, 3299, 1660, 1652, 1661, 82, 1654, 1770, 1606, 1676, 1541, 3272, 107, 1671, 3284, 1622, 18, 3324, 1639, 1723, 1613, 1653, 1725, 3297, 15, 1673, 3253, 3306, 1647, 1668, 1595, 3305, 47, 0, 1574, 1587, 1692, 1761, 3278]
mPrime: 05C958EC26561B6DB818F4B8CB2E28990E748417587FEC38A1284BBB4FF9E478

KPrime: C61F73D2BFB18594E1BA5D3B58B4C934206D3A6F8EC91395AB7779C61FA1DD6F
rPrime: 6DC410C18448882046E2162045D93FE36D6F9C6B27F2A04E04050E9985617B1D

tHat: [[1188, 120, 2593, 2579, 176, 2297, 1867, 1265, 1414, 1853, 1274, 896, 2148, 3049, 2408, 2275, 653, 215, 295, 280, 472, 1851, 3, 678, 918, 1534, 2902, 607, 3095, 1267, 842, 3232, 2346, 3068, 3193, 2749, 2934, 3300, 68, 1025, 30, 305, 742, 2245, 460, 309, 1333, 1912, 986, 1880, 992, 1074, 3088, 664, 548, 1373, 3102, 3157, 161, 1243, 2287, 808, 1357, 1272, 3273, 1186, 3295, 567, 769, 2019, 69, 3058, 1475, 1382, 1647, 150, 1582, 1955, 1766, 288, 1652, 1332, 3009, 1150, 752, 152, 593, 2586, 588, 1428, 1033, 211, 1927, 386, 2702, 138, 1764, 1928, 2200, 1892, 208, 2256, 2478, 25, 1627, 1587, 3069, 1836, 343, 1332, 779, 2204, 347, 1569, 780, 2894, 791, 522, 2273, 312, 3257, 569, 90, 1788, 85, 246, 2200, 2083, 191, 47, 54, 1969, 592, 1348, 2907, 1910, 2136, 2790, 2555, 2903, 2453, 1685, 1538, 2492, 2718, 988, 3125, 1560, 254, 878, 2258, 2753, 2627, 1019, 82, 1708, 2191, 424, 1918, 61, 1158, 705, 1466, 3276, 3076, 3135, 1566, 625, 374, 3301, 3117, 1292, 1556, 2991, 346, 1481, 2067, 2099, 1102, 1871, 438, 1431, 3091, 1963, 2382, 965, 1896, 1640, 1965, 109, 920, 2027, 1286, 926, 789, 2143, 3128, 600, 1732, 1506, 1052, 1275, 227, 413, 465, 2786, 588, 1075, 1871, 2819, 2980, 1692, 3271, 2396, 880, 1287, 2499, 980, 271, 459, 212, 2557, 3113, 1389, 3008, 3207, 3051, 3328, 2824, 1042, 324, 1106, 3174, 531, 939, 836, 2407, 1515, 1986, 2116, 291, 2236, 3314, 1806, 2878, 2607, 2700, 3037, 1858, 2955, 1331, 209, 621, 1514, 2736, 2096],
[40, 745, 2093, 2480, 1621, 2477, 2733, 2377, 2264, 609, 1100, 2821, 333, 1238, 2580, 775, 3243, 63, 729, 2521, 2710, 2043, 1665, 1496, 931, 3141, 2644, 1963, 2215, 424, 1209, 3095, 184, 2111, 2334, 3143, 1601, 1608, 1001, 2645, 2381, 814, 2323, 1830, 1153, 467, 1335, 143, 3048, 2796, 317, 2136, 1285, 1652, 3294, 2287, 3131, 2731, 1858, 2308, 2172, 948, 2959, 2113, 1203, 3090, 2727, 2124, 2882, 1725, 635, 2241, 899, 3041, 543, 1406, 145, 2482, 2694, 996, 282, 2262, 1878, 269, 982, 3071, 1365, 265, 3094, 1127, 2892, 2486, 1163, 2316, 184, 926, 37, 989, 2830, 1502, 1912, 2369, 2856, 2059, 3027, 335, 136, 1796, 412, 324, 2170, 1782, 3273, 3035, 1997, 3199, 3306, 775, 1275, 246, 3056, 1877, 2873, 2746, 2416, 664, 2312, 974, 969, 1148, 3320, 2186, 1694, 1125, 906, 1457, 1433, 1143, 312, 1534, 1870, 2006, 1523, 3063, 795, 1540, 3178, 1138, 2872, 256, 416, 1228, 2088, 965, 387, 419, 1064, 2853, 937, 505, 214, 2150, 1985, 1168, 1267, 1395, 1919, 189, 2385, 1291, 1888, 1296, 409, 2483, 3135, 2903, 1970, 771, 1836, 163, 1827, 1505, 334, 960, 2134, 434, 687, 3054, 671, 1448, 1584, 2742, 2699, 1403, 659, 494, 2170, 2420, 1676, 207, 2825, 497, 128, 3116, 1080, 2609, 1807, 1543, 2656, 3297, 427, 539, 82, 2368, 2575, 351, 546, 151, 1389, 2260, 3328, 61, 927, 1714, 1831, 2898, 1672, 556, 1796, 2510, 1605, 2065, 1247, 270, 1262, 700, 1140, 1449, 1004, 304, 419, 2377, 298, 2846, 1826, 1233, 2494, 2741, 2334, 195, 2518, 1044, 3139, 1878, 681, 963],
[1641, 1050, 2184, 1792, 763, 2059, 947, 1979, 2363, 2093, 2488, 1362, 2914, 112, 2179, 747, 393, 2630, 2820, 3187, 3318, 230, 2802, 1509, 977, 613, 504, 1768, 1118, 362, 2174, 3070, 1638, 1110, 285, 1459, 1324, 327, 1857, 705, 807, 8, 550, 1560, 3271, 1784, 1548, 1380, 2343, 2871, 2465, 1777, 903, 1528, 3193, 2943, 3040, 2588, 1619, 3267, 387, 1390, 709, 640, 2183, 154, 1158, 2507, 1819, 1621, 660, 794, 578, 1190, 703, 1157, 290, 2244, 353, 2304, 594, 2054, 613, 1175, 1869, 1331, 704, 2070, 487, 2031, 2317, 1735, 1751, 2039, 2524, 30, 2046, 289, 2720, 976, 2870, 1070, 2366, 2146, 1672, 2356, 1066, 793, 2744, 1644, 271, 2428, 862, 2674, 2651, 1300, 222, 1681, 1491, 2554, 2926, 686, 1884, 686, 1673, 2897, 1000, 1142, 2670, 3158, 626, 2553, 2348, 3010, 1878, 2978, 409, 1588, 974, 1453, 951, 448, 2304, 116, 1316, 1445, 1741, 318, 1198, 3131, 2537, 2073, 3014, 1490, 2502, 2874, 1883, 2346, 1056, 866, 137, 1438, 1609, 2137, 1148, 1488, 2407, 977, 414, 436, 847, 2527, 3087, 968, 10, 2775, 2743, 1794, 801, 1758, 2916, 671, 845, 697, 292, 2606, 3004, 3136, 2588, 2612, 3253, 974, 1776, 1838, 1246, 241, 1864, 820, 765, 3064, 2312, 834, 181, 2660, 1077, 1164, 2200, 2750, 1678, 1104, 2672, 2645, 385, 2231, 577, 3139, 551, 2041, 1454, 3063, 1686, 2641, 3138, 516, 2848, 3166, 463, 3020, 270, 1629, 1338, 14, 1882, 1345, 1560, 513, 183, 1759, 881, 310, 2819, 2931, 42, 1604, 2938, 749, 870, 1799, 2034, 1276, 1243, 1065, 1037, 2266, 2001, 2515],
[2490, 2725, 2082, 1407, 482, 3155, 960, 664, 1536, 3158, 1608, 439, 2271, 1523, 1327, 2072, 379, 514, 870, 2557, 1795, 2043, 1166, 303, 1049, 3070, 441, 748, 2383, 2188, 1792, 469, 2594, 2707, 554, 3187, 675, 2684, 3279, 2457, 90, 2686, 949, 2329, 2814, 1273, 781, 950, 2555, 2247, 1844, 699, 2746, 2550, 1046, 316, 2094, 2904, 1392, 2231, 469, 3221, 539, 2781, 1003, 2677, 1578, 2732, 2051, 2518, 3030, 52, 2391, 2688, 1711, 2132, 2883, 380, 2870, 3229, 3015, 1314, 158, 1431, 2157, 2833, 1692, 2282, 2657, 327, 2172, 2513, 2600, 1907, 3176, 2808, 2708, 1453, 2830, 1593, 2584, 1025, 1979, 3038, 2113, 2598, 1869, 1074, 2329, 2362, 2748, 2222, 191, 1525, 744, 294, 662, 2905, 2237, 1182, 2803, 3222, 303, 1815, 2277, 1427, 1585, 67, 490, 188, 2274, 1783, 1523, 2968, 2247, 337, 2120, 1905, 1839, 2954, 153, 1260, 2301, 2689, 2561, 1945, 1718, 1247, 2651, 713, 1877, 2126, 1995, 3236, 2089, 1380, 2664, 2665, 3239, 3104, 3195, 518, 468, 3197, 1065, 156, 2512, 603, 3268, 768, 1984, 1927, 1813, 1904, 2121, 2228, 141, 927, 1286, 2745, 1243, 2240, 380, 2142, 566, 2640, 1357, 961, 1522, 362, 1047, 1976, 1553, 974, 1612, 407, 1382, 2781, 1427, 211, 2746, 1197, 277, 588, 189, 2184, 2417, 1017, 1479, 2919, 228, 3121, 2438, 245, 2675, 2272, 1993, 1508, 494, 1289, 2361, 446, 1135, 606, 1721, 1664, 3270, 1322, 1880, 2811, 2832, 2547, 862, 178, 2929, 3001, 1801, 472, 705, 342, 2583, 683, 3203, 2409, 1706, 1098, 1802, 1512, 172, 2857, 1688, 445, 979, 2767, 1161, 91]]

bHat = aHat^T: [[[2624, 568, 2343, 2233, 2805, 2899, 2873, 862, 1680, 1122, 2223, 1232, 675, 223, 877, 554, 3109, 1566, 1221, 2974, 631, 3155, 353, 85, 3205, 916, 3125, 2800, 13, 2810, 1568, 429, 563, 1252, 1415, 2283, 2688, 1290, 3302, 649, 589, 1319, 2435, 655, 549, 2025, 2435, 1070, 995, 3155, 1026, 2083, 974, 2385, 93, 1256, 2492, 2678, 3138, 1863, 1159, 1109, 2613, 662, 2632, 1104, 1563, 1378, 2425, 1369, 611, 236, 2763, 2290, 3078, 2556, 386, 1806, 735, 831, 2924, 2003, 2871, 2522, 2509, 914, 1083, 1197, 1758, 2568, 1334, 2933, 543, 2137, 3112, 434, 776, 1395, 2779, 2681, 439, 1404, 2186, 2413, 3163, 34, 1561, 2114, 2889, 2952, 1819, 2707, 2234, 2185, 2329, 1552, 2269, 1453, 3081, 2519, 2289, 539, 806, 1893, 3036, 2448, 283, 2499, 117, 677, 994, 1962, 461, 2927, 2741, 331, 2486, 2447, 1930, 2426, 2701, 2778, 224, 772, 2444, 97, 0, 12, 626, 2491, 3044, 655, 2045, 738, 1645, 1426, 1334, 936, 2424, 192, 3313, 334, 1788, 1179, 149, 2674, 2776, 3000, 3129, 606, 732, 1811, 636, 355, 702, 3041, 2996, 1356, 1668, 2856, 3297, 2606, 2095, 973, 488, 2087, 532, 662, 2483, 528, 1732, 1731, 2227, 307, 1570, 2730, 2661, 512, 2669, 1085, 376, 2425, 1357, 2493, 1542, 2905, 27, 2645, 1219, 3235, 964, 825, 1505, 1674, 2035, 2117, 883, 961, 338, 1483, 1964, 2875, 731, 817, 164, 1113, 2260, 1775, 3152, 2447, 2146, 322, 1161, 3061, 1272, 2586, 46, 1580, 2792, 1404, 2247, 479, 1185, 268, 2075, 1355, 2787, 159, 3022, 14, 2382, 15, 2529, 815, 3234, 2762],
[2629, 1997, 2999, 1097, 137, 1577, 1900, 1104, 1001, 1440, 2424, 609, 2363, 1592, 130, 3142, 2673, 3040, 1280, 3295, 1901, 2413, 3046, 2832, 201, 439, 1201, 2413, 1883, 622, 92, 13, 1687, 2757, 1880, 1234, 2632, 560, 251, 396, 1783, 2916, 1138, 2990, 361, 2641, 27, 2237, 2272, 2193, 3129, 886, 1795, 1779, 2149, 2804, 2857, 1854, 1378, 3054, 394, 1916, 845, 2223, 158, 30, 3243, 277, 2010, 2276, 2939, 2488, 1972, 1670, 950, 1919, 1914, 2179, 2793, 782, 1729, 765, 2667, 364, 373, 2127, 2856, 291, 1981, 1220, 3128, 1221, 1286, 642, 2538, 2719, 2928, 1831, 26, 215, 3185, 2281, 518, 306, 1696, 1186, 2416, 3172, 1707, 761, 1563, 2160, 64, 2901, 1932, 2750, 2014, 3232, 1255, 2255, 60, 155, 2295, 1060, 279, 761, 1916, 835, 1373, 582, 1286, 2901, 1228, 2238, 611, 299, 1915, 22, 2933, 337, 2796, 2308, 2280, 1388, 2764, 1312, 1073, 3084, 2467, 2918, 1874, 3254, 3078, 2895, 2580, 2327, 1351, 1919, 1337, 409, 3067, 1023, 2327, 413, 1829, 2534, 2638, 1918, 3215, 35, 3248, 3325, 1764, 1766, 1393, 745, 82, 1052, 1128, 3070, 1811, 802, 679, 241, 2434, 1471, 1158, 1994, 3075, 2179, 2694, 579, 16, 2918, 2980, 1404, 168, 1251, 3011, 2492, 1835, 2206, 1910, 1589, 1495, 2248, 699, 522, 1341, 1561, 2988, 3196, 1256, 1345, 508, 252, 211, 1764, 203, 1641, 1042, 396, 1582, 1581, 3321, 1317, 1307, 3201, 2143, 3186, 1067, 2674, 1455, 2192, 1017, 2701, 2103, 513, 1084, 2345, 1712, 2798, 2048, 880, 851, 2992, 2355, 48, 4, 1212, 2558, 2978, 715, 2217, 2388, 2088],
[2987, 273, 1770, 1102, 1971, 3319, 510, 2205, 3078, 1835, 191, 851, 89, 2463, 3156, 2065, 3103, 872, 3160, 1639, 2774, 945, 875, 2723, 2952, 3094, 2384, 837, 1586, 2229, 1725, 2179, 3081, 2650, 2181, 1175, 1049, 1294, 90, 1765, 555, 3164, 2556, 1274, 796, 2802, 1471, 1642, 2526, 1128, 3287, 976, 671, 2519, 1954, 1740, 1026, 1812, 2252, 845, 1144, 1595, 648, 2181, 1608, 1664, 830, 695, 3260, 1279, 2937, 2090, 1488, 1583, 930, 1576, 1832, 1167, 564, 1811, 1975, 2946, 1567, 1744, 416, 624, 2742, 275, 2330, 261, 2551, 1218, 275, 1296, 3056, 2183, 245, 1847, 1705, 874, 914, 565, 1927, 501, 2152, 2471, 3211, 2397, 2891, 1258, 2064, 1753, 999, 1006, 3315, 2414, 1949, 1231, 2831, 3146, 1703, 2372, 2345, 156, 3078, 343, 2771, 1873, 1709, 2947, 1945, 1644, 1648, 547, 1193, 1949, 2797, 827, 3136, 310, 636, 2212, 71, 2744, 1694, 3218, 1367, 2236, 2096, 2133, 2509, 1490, 2800, 2296, 3096, 3200, 2041, 813, 2231, 3255, 2686, 3180, 995, 2066, 748, 3059, 1857, 1182, 2027, 708, 1658, 2201, 647, 2114, 2442, 629, 3146, 1167, 2999, 3254, 2345, 740, 3109, 716, 1227, 740, 3188, 220, 443, 2741, 1181, 634, 2402, 2461, 804, 1544, 224, 345, 449, 2810, 688, 1900, 172, 941, 667, 1613, 1424, 764, 26, 1666, 974, 2352, 2772, 397, 3037, 1452, 1423, 927, 2881, 2724, 3182, 2090, 784, 1973, 780, 794, 1469, 2338, 3118, 826, 2391, 2938, 172, 2039, 1162, 1330, 138, 3133, 1518, 2500, 1571, 2412, 3111, 2600, 1767, 1177, 935, 1238, 1054, 2788, 3015, 52, 1839, 1319, 1638, 3304],
[2564, 46, 3039, 1265, 664, 3080, 3046, 737, 1933, 895, 2587, 227, 480, 254, 1794, 3059, 1222, 477, 833, 387, 1745, 3025, 1713, 2893, 1063, 11, 3121, 724, 404, 3122, 1214, 1049, 496, 1828, 1278, 960, 3093, 639, 2967, 2987, 1777, 1251, 193, 1933, 319, 2372, 2975, 2140, 584, 454, 3118, 1832, 2460, 1921, 571, 981, 1009, 1318, 2167, 851, 1839, 3154, 2923, 2121, 3192, 2486, 3268, 1020, 449, 1355, 1720, 2757, 616, 3262, 3237, 585, 2873, 1484, 2566, 1664, 2767, 2250, 1187, 3278, 1661, 329, 634, 606, 2877, 2035, 975, 433, 445, 14, 1683, 157, 25, 3075, 1176, 2831, 945, 1947, 744, 1907, 2585, 2300, 2869, 2347, 113, 281, 429, 694, 1261, 3221, 2524, 2928, 2528, 474, 2659, 2178, 2044, 2418, 2623, 1366, 1110, 2711, 1449, 453, 1862, 3086, 1665, 1522, 45, 900, 2857, 3286, 1714, 2597, 109, 2432, 2006, 562, 3247, 2119, 1769, 422, 1348, 2281, 898, 755, 2120, 359, 2189, 2682, 589, 442, 1435, 2438, 3315, 241, 142, 2907, 25, 1337, 724, 2767, 2929, 492, 1136, 533, 1590, 321, 575, 1052, 2051, 902, 3208, 626, 2637, 1349, 945, 1624, 1225, 928, 968, 438, 1202, 1447, 1819, 499, 1134, 1702, 141, 1522, 1259, 3188, 2952, 2275, 1974, 2385, 1084, 2399, 3150, 403, 1802, 615, 2440, 1036, 3114, 2179, 1054, 2675, 232, 1358, 673, 1759, 1779, 53, 1113, 862, 1907, 2112, 1388, 752, 1247, 3067, 2591, 2477, 440, 323, 1086, 1599, 3174, 3179, 2493, 375, 365, 2496, 2012, 3239, 624, 3187, 490, 2254, 1256, 2758, 2170, 317, 1619, 2913, 3150, 2862, 1356, 259, 249, 192]],
[[381, 2010, 2217, 1935, 3124, 1918, 3067, 2709, 2398, 1950, 949, 3173, 1987, 2300, 3321, 3290, 2006, 3170, 2635, 3264, 2064, 1442, 1427, 197, 2613, 988, 2821, 2533, 2379, 3066, 1247, 2768, 2704, 3307, 3222, 2868, 46, 14, 177, 3281, 3083, 2638, 1200, 1130, 1336, 2347, 2636, 2717, 1414, 1911, 3073, 2977, 2154, 700, 2743, 2137, 865, 1748, 2420, 3187, 2830, 429, 2817, 995, 3232, 2409, 366, 571, 597, 2748, 999, 1717, 3245, 1510, 520, 1472, 1571, 1308, 2647, 2104, 2201, 3127, 2504, 3313, 1963, 3236, 3132, 1973, 1926, 2273, 1464, 433, 990, 1395, 1439, 1944, 118, 245, 1968, 73, 2213, 2863, 1629, 1291, 2108, 919, 2326, 1607, 1124, 2463, 1063, 1909, 548, 990, 843, 1599, 2128, 1820, 1629, 580, 729, 1649, 1041, 1857, 2661, 1263, 117, 1986, 2337, 1459, 3305, 3041, 88, 3314, 685, 1898, 3303, 662, 845, 2607, 894, 3200, 1403, 2958, 999, 1700, 2838, 781, 1807, 2331, 2205, 2672, 2411, 856, 185, 1136, 228, 3177, 2475, 932, 3264, 1968, 1843, 2819, 1970, 245, 464, 1845, 2761, 1190, 1102, 1581, 1915, 621, 1083, 452, 3092, 1567, 1436, 2040, 953, 155, 2788, 314, 1167, 1017, 422, 917, 3286, 1063, 1086, 208, 460, 2537, 93, 2322, 2852, 1876, 2207, 2289, 2385, 2937, 2935, 1774, 411, 1893, 897, 2465, 1228, 204, 1036, 299, 3140, 1190, 2309, 3125, 143, 188, 569, 2166, 1952, 1963, 2791, 2692, 1003, 1272, 671, 212, 3204, 1518, 1627, 2391, 2481, 1162, 891, 234, 3160, 33, 1095, 1921, 1902, 586, 1479, 256, 3005, 14, 1312, 2855, 1017, 2588, 1662, 2974, 2668, 2186, 1232, 2454],
[2762, 243, 107, 2437, 1701, 3113, 1491, 1412, 59, 1936, 1069, 143, 1822, 3004, 1307, 2896, 591, 2456, 3104, 3228, 2832, 1517, 1186, 801, 1049, 1786, 293, 2898, 2994, 2183, 1966, 2133, 1823, 1015, 2101, 854, 1381, 11, 1377, 2887, 1587, 270, 1719, 2804, 2076, 595, 3158, 1782, 2244, 1967, 1156, 2483, 2271, 2011, 2829, 2783, 933, 1300, 3312, 66, 594, 1992, 2471, 792, 3224, 240, 2242, 1235, 305, 1374, 130, 1248, 3130, 1380, 3075, 3224, 1643, 269, 560, 2250, 3156, 1084, 3316, 1254, 2705, 1011, 852, 1665, 2469, 51, 2986, 1126, 3080, 322, 3263, 306, 284, 69, 432, 3307, 1563, 2270, 2650, 118, 2398, 1171, 3073, 377, 2549, 1390, 1255, 2624, 1885, 2614, 289, 1373, 2201, 875, 490, 3300, 1697, 2130, 2387, 230, 3106, 964, 1618, 1786, 2565, 717, 2280, 2892, 2662, 355, 478, 2333, 37, 2236, 83, 862, 2302, 1349, 3050, 1944, 1096, 86, 3182, 2964, 2045, 2845, 2654, 3261, 1209, 706, 1881, 665, 2871, 939, 993, 1598, 1160, 2792, 3021, 398, 2892, 938, 2505, 2795, 2316, 2641, 2867, 2979, 677, 1050, 3313, 2851, 120, 1476, 615, 1299, 3185, 1919, 528, 590, 1317, 2059, 572, 1579, 3018, 1104, 1557, 706, 3294, 154, 1592, 1195, 1587, 1498, 2034, 1586, 1425, 2087, 1068, 2078, 1673, 1391, 1534, 1126, 2936, 2390, 334, 1332, 1738, 2686, 1195, 564, 1864, 1712, 2155, 740, 1529, 494, 3117, 3118, 2098, 503, 440, 977, 1407, 2450, 2408, 1645, 2068, 160, 1809, 2710, 606, 776, 680, 918, 1485, 2401, 163, 488, 856, 1283, 445, 2185, 1773, 3004, 975, 1157, 234, 800, 3266, 2201],
[2117, 656, 1637, 514, 414, 3033, 3278, 927, 1965, 2351, 2372, 2572, 2285, 1624, 1529, 2780, 2665, 3015, 1022, 303, 1509, 2229, 897, 368, 52, 337, 1722, 2719, 1336, 2374, 2388, 1094, 318, 481, 3276, 2700, 39, 3112, 2367, 3010, 3220, 1094, 3203, 61, 3264, 1979, 2048, 292, 1475, 1328, 1112, 2813, 375, 1839, 1986, 2295, 1697, 2070, 112, 674, 921, 1719, 1195, 1767, 1483, 924, 703, 1606, 1365, 694, 3098, 3120, 2285, 1212, 2531, 401, 1093, 2550, 676, 2945, 465, 1061, 3053, 750, 2714, 2615, 2047, 2270, 3069, 1945, 1286, 2207, 2170, 2816, 1972, 299, 1068, 1767, 1968, 1078, 2544, 2320, 236, 3019, 1531, 2493, 1717, 1885, 2289, 2477, 2462, 1624, 2352, 2360, 2580, 2544, 3134, 902, 2502, 3233, 1789, 252, 197, 1803, 372, 1343, 922, 856, 633, 130, 2445, 1149, 1796, 381, 16, 2159, 2764, 3185, 2271, 2513, 1133, 1126, 1096, 272, 30, 1062, 3126, 676, 3236, 2500, 1695, 95, 2682, 2890, 3286, 3301, 2070, 1087, 1976, 2259, 692, 1612, 1169, 1045, 3022, 1192, 1469, 2662, 1868, 2545, 1135, 3258, 5, 2323, 1039, 2021, 1337, 931, 1029, 557, 2597, 2287, 955, 1463, 2298, 685, 2263, 310, 708, 2283, 3234, 1586, 20, 357, 2502, 2507, 1812, 2436, 271, 736, 1490, 2144, 718, 367, 2901, 1572, 1384, 2268, 875, 1557, 745, 2024, 1149, 2133, 1916, 2525, 469, 1764, 470, 1399, 386, 2296, 1765, 3046, 976, 1578, 1532, 1111, 3047, 690, 2033, 2307, 1834, 1736, 630, 2184, 1893, 1516, 658, 2016, 2476, 361, 2781, 62, 789, 677, 758, 1460, 891, 2299, 2601, 1327, 1484, 1102, 13, 1328],
[227, 2881, 2934, 1877, 1445, 1035, 841, 1422, 2771, 2429, 439, 32, 3042, 2410, 2433, 3047, 342, 159, 2687, 164, 2746, 514, 1542, 185, 815, 3173, 417, 2081, 1736, 2824, 3188, 166, 1176, 227, 499, 834, 829, 2850, 872, 109, 1051, 3219, 1974, 2581, 246, 2085, 276, 784, 2832, 2893, 1818, 1162, 3156, 2671, 1458, 1269, 516, 1650, 1956, 152, 81, 650, 405, 1885, 1425, 2756, 1080, 1575, 1526, 1370, 1159, 2365, 2244, 3219, 1231, 391, 2300, 836, 2430, 2808, 2017, 2430, 2782, 1098, 721, 2547, 223, 2068, 2136, 303, 1057, 830, 446, 1691, 2516, 953, 2930, 2537, 2846, 1274, 1762, 982, 945, 1742, 376, 1052, 1974, 2328, 354, 474, 1604, 2917, 1202, 1867, 1998, 2692, 3228, 2207, 3013, 3192, 1731, 2191, 2099, 1237, 2132, 767, 2776, 650, 2881, 2442, 561, 1370, 143, 2114, 312, 1124, 2301, 1839, 3214, 1812, 697, 534, 3285, 346, 698, 103, 1895, 1926, 1233, 2431, 2814, 1204, 2568, 538, 1855, 2019, 1934, 3319, 2912, 2543, 1651, 2416, 2303, 416, 2725, 1484, 611, 727, 1756, 2115, 1847, 647, 3133, 2504, 158, 832, 1346, 2857, 350, 1722, 1583, 936, 1232, 3297, 1156, 1933, 1842, 439, 728, 2141, 612, 325, 731, 2358, 1969, 1649, 1438, 886, 691, 2115, 1323, 552, 421, 2834, 1097, 625, 2630, 814, 265, 1019, 3063, 208, 1734, 2395, 1264, 2214, 2112, 1205, 159, 2197, 2168, 2655, 764, 3128, 603, 241, 973, 2703, 1961, 1396, 2123, 264, 2771, 440, 2114, 288, 1235, 108, 2591, 341, 2753, 851, 879, 0, 2593, 1439, 368, 2797, 1415, 2834, 2179, 1599, 2494, 3285, 2028, 3323]],
[[3236, 336, 469, 393, 681, 1084, 2197, 49, 1351, 3173, 375, 300, 2754, 1981, 2260, 1105, 3152, 1208, 2983, 499, 1136, 3164, 2357, 657, 605, 1497, 2533, 1348, 2158, 806, 694, 1567, 1923, 3087, 473, 2114, 2185, 908, 3164, 2866, 3141, 3277, 3216, 854, 1591, 729, 1452, 961, 161, 355, 443, 2223, 3317, 1304, 1652, 1442, 2772, 1720, 951, 1645, 130, 3033, 2055, 670, 832, 2254, 220, 1226, 2317, 1560, 349, 945, 771, 1444, 1982, 144, 2894, 1534, 1865, 828, 856, 1426, 1475, 2268, 3175, 546, 3296, 2563, 3319, 423, 704, 1344, 2872, 129, 164, 986, 2004, 1171, 3029, 133, 1575, 1335, 1751, 2557, 1109, 453, 3193, 271, 2591, 216, 600, 2636, 1672, 283, 27, 1953, 812, 755, 968, 2653, 2349, 2087, 1150, 1463, 3035, 1365, 2749, 1326, 2790, 2920, 2242, 1955, 847, 1397, 15, 1378, 944, 3321, 1966, 1229, 720, 318, 728, 928, 257, 3173, 1205, 2681, 1333, 3228, 1533, 320, 2894, 1949, 1272, 1989, 1736, 811, 496, 782, 1947, 644, 606, 1791, 1273, 71, 3315, 592, 518, 1533, 1808, 2655, 2309, 665, 1545, 1743, 2915, 1705, 2116, 505, 2412, 1350, 1864, 317, 3213, 10, 1706, 3272, 1106, 2320, 1374, 3164, 314, 314, 1038, 1136, 611, 2173, 2909, 2481, 738, 103, 451, 438, 2576, 2561, 1511, 2263, 2636, 1168, 2942, 191, 603, 860, 2554, 1244, 139, 2014, 2121, 2244, 2104, 1900, 329, 1029, 1442, 1570, 3179, 2639, 1979, 2676, 2442, 3151, 141, 1884, 2742, 291, 2484, 2689, 394, 2867, 2908, 2791, 1525, 2209, 2755, 191, 1586, 2448, 972, 2742, 252, 1519, 1568, 546, 623, 2252],
[832, 1602, 2989, 2379, 2113, 3210, 609, 473, 1515, 2815, 2191, 945, 160, 937, 499, 2405, 3261, 651, 2491, 3309, 3122, 1898, 2484, 3252, 961, 1596, 837, 222, 1565, 488, 2795, 2389, 2828, 2079, 2018, 742, 1034, 1403, 343, 290, 2825, 3298, 2511, 568, 2218, 1521, 2638, 1424, 3058, 704, 370, 3135, 620, 2591, 319, 1525, 755, 2292, 2693, 331, 426, 2079, 993, 3254, 1230, 191, 145, 408, 1872, 20, 1920, 769, 2126, 1916, 3021, 1857, 2011, 420, 1694, 2362, 1954, 395, 720, 1531, 2266, 2108, 413, 1245, 2026, 3217, 1376, 119, 2314, 625, 2097, 1104, 2393, 2683, 2226, 2676, 2280, 3312, 1804, 1114, 1523, 1992, 392, 1907, 285, 568, 513, 708, 657, 1423, 3133, 3307, 1207, 8, 2310, 2378, 2873, 2270, 2854, 1284, 2285, 641, 816, 454, 1325, 468, 2772, 190, 1505, 3255, 1251, 2992, 2894, 116, 2457, 1064, 2312, 973, 3258, 935, 3064, 173, 2050, 3168, 1692, 1068, 2453, 2082, 548, 3262, 2125, 440, 2306, 1938, 2384, 1955, 233, 280, 118, 1222, 274, 2085, 1908, 2087, 2212, 448, 2353, 252, 391, 3048, 777, 1508, 424, 2206, 1898, 2551, 2808, 477, 1657, 3179, 1966, 54, 1419, 2285, 2237, 188, 270, 280, 2891, 968, 905, 962, 96, 2227, 1891, 1156, 1500, 355, 2003, 2275, 2870, 3184, 3323, 1906, 1972, 190, 568, 660, 2809, 2041, 1645, 1081, 3094, 409, 2276, 2356, 1609, 1728, 828, 955, 2498, 1505, 3211, 2375, 2869, 488, 2156, 52, 653, 729, 2382, 718, 1951, 2230, 2240, 1783, 2121, 2923, 3155, 979, 242, 2043, 1017, 133, 2810, 2374, 1782, 2345, 2054, 1872, 815, 1463],
[1532, 932, 1476, 3209, 1469, 237, 1495, 518, 809, 1710, 792, 2096, 907, 458, 1013, 1682, 1325, 399, 315, 3121, 1584, 2286, 1284, 325, 682, 1028, 2536, 1911, 736, 3288, 2873, 1554, 3216, 2288, 42, 175, 3233, 913, 1911, 2404, 1242, 1113, 1228, 379, 2127, 1083, 39, 193, 2582, 1882, 1649, 1818, 2640, 2071, 1623, 235, 2732, 1679, 2441, 535, 420, 1138, 1195, 302, 1432, 308, 2467, 656, 1366, 3041, 1086, 1934, 1208, 1024, 3308, 2488, 1767, 1120, 2926, 1963, 2864, 2933, 80, 2866, 3030, 1695, 2909, 67, 65, 1636, 1089, 738, 2700, 3084, 2695, 1058, 1656, 3319, 224, 1451, 41, 1593, 1178, 1662, 840, 552, 3181, 2575, 2166, 1850, 2973, 2995, 634, 2451, 1441, 2762, 1771, 1929, 2412, 1112, 3004, 1852, 716, 2652, 959, 2800, 1101, 496, 3037, 2905, 2802, 202, 1202, 571, 512, 585, 2866, 850, 743, 486, 2687, 1888, 1106, 573, 78, 1063, 2228, 1641, 245, 919, 697, 2634, 1610, 780, 936, 1039, 1543, 1284, 1462, 1004, 354, 1155, 1687, 1840, 859, 2896, 3315, 1318, 130, 989, 1124, 2040, 2413, 2674, 710, 338, 1893, 1198, 2660, 1998, 2285, 1665, 2538, 1650, 475, 3049, 2349, 309, 758, 2224, 2565, 3254, 3207, 684, 1966, 1513, 1737, 2758, 2642, 644, 1096, 2784, 1586, 460, 1021, 758, 2654, 305, 880, 325, 2425, 1223, 1939, 215, 3120, 1573, 291, 2409, 995, 510, 1129, 291, 2608, 98, 2270, 2947, 2485, 2283, 1842, 1011, 2585, 1730, 317, 3132, 3157, 1118, 3262, 951, 2089, 1881, 1864, 2404, 2086, 1387, 1269, 1862, 975, 1230, 557, 2111, 1776, 966, 1184, 951, 3275, 2089],
[672, 2087, 876, 1898, 2630, 2142, 1294, 333, 2333, 1969, 1052, 2146, 1713, 600, 1682, 1838, 1185, 3287, 8, 1757, 600, 1574, 2145, 130, 165, 1300, 2361, 782, 968, 124, 2840, 2632, 3301, 2035, 944, 2758, 2208, 2858, 896, 1722, 3067, 2068, 2749, 823, 934, 3185, 2817, 1438, 1056, 1542, 2048, 3004, 1705, 1925, 956, 639, 2097, 3047, 1673, 911, 11, 2913, 1860, 1988, 735, 2807, 953, 739, 835, 2894, 453, 1245, 1892, 1397, 2048, 2611, 895, 2964, 2164, 2358, 286, 3100, 3160, 1177, 475, 1861, 2092, 1461, 551, 521, 2237, 406, 2330, 3247, 1019, 1857, 2175, 2319, 3028, 2994, 3148, 927, 3292, 121, 334, 1440, 2360, 2535, 2291, 1598, 2794, 2630, 2406, 1884, 451, 3040, 3277, 2540, 3198, 2417, 1351, 2159, 2963, 2971, 257, 113, 3206, 1765, 1616, 1436, 2958, 1010, 1102, 96, 879, 725, 1885, 1827, 943, 255, 1519, 950, 372, 1401, 224, 1102, 1767, 2568, 352, 794, 2799, 147, 1226, 129, 2321, 1896, 957, 2396, 1043, 3202, 3159, 2915, 2073, 2125, 1919, 1750, 725, 79, 3244, 151, 2732, 1865, 1394, 314, 764, 315, 402, 2059, 353, 2167, 1815, 1438, 1038, 269, 2779, 2334, 1444, 2011, 1586, 1529, 2333, 463, 3234, 1181, 1051, 407, 751, 2725, 1613, 1009, 2313, 1004, 2877, 2238, 80, 2864, 538, 2178, 1243, 3061, 1563, 868, 2781, 2727, 461, 3117, 455, 2223, 2366, 2862, 725, 2922, 924, 1900, 1060, 2, 692, 472, 2799, 3034, 1025, 2992, 1863, 3261, 3099, 1175, 1786, 1076, 1511, 693, 1215, 359, 807, 1408, 1766, 183, 324, 819, 259, 2641, 3319, 1578, 348, 349, 2057, 608]],
[[1206, 1314, 1500, 1288, 2199, 664, 813, 1904, 2451, 461, 2466, 2183, 2431, 776, 2967, 3088, 3049, 1792, 933, 1003, 2293, 1341, 1359, 3259, 2973, 1400, 612, 1613, 952, 2484, 1818, 404, 2014, 647, 1432, 2797, 1457, 1290, 2649, 1943, 718, 900, 790, 1446, 389, 889, 781, 462, 977, 1974, 2606, 2918, 2488, 237, 2308, 3095, 1012, 2124, 2726, 1336, 1792, 3305, 3093, 2377, 1547, 2182, 2880, 2633, 848, 1158, 300, 3027, 2569, 2545, 1263, 1963, 2641, 1932, 3147, 2821, 2944, 3076, 686, 1868, 1204, 1014, 1952, 1683, 1059, 3135, 268, 1244, 1507, 3095, 1571, 2442, 1178, 1159, 1042, 879, 144, 1099, 2983, 3234, 725, 381, 426, 1419, 1041, 128, 832, 3274, 124, 3283, 1727, 1904, 313, 1167, 2242, 1296, 2870, 1383, 2064, 501, 1913, 2534, 2438, 672, 2274, 1915, 1455, 2594, 1279, 159, 3243, 3280, 2797, 259, 445, 2811, 142, 2013, 783, 696, 1631, 558, 345, 1168, 1955, 1078, 1947, 2936, 2788, 1081, 2559, 462, 1620, 2475, 1728, 377, 1544, 1050, 3024, 2876, 1432, 1121, 699, 1533, 2260, 1408, 1831, 930, 2100, 71, 1666, 3261, 1884, 2231, 1354, 3024, 2044, 2449, 538, 1509, 618, 1669, 2663, 1719, 3081, 2214, 239, 2467, 1059, 3227, 1923, 1552, 1728, 1338, 2181, 2189, 2258, 2682, 1700, 2020, 625, 2116, 1856, 2870, 477, 978, 1114, 1294, 1468, 2735, 1811, 1152, 1660, 1107, 184, 1583, 2037, 2539, 1350, 1879, 534, 705, 275, 305, 203, 2815, 1902, 3067, 2206, 1811, 3204, 3132, 852, 1501, 47, 1, 661, 104, 2152, 2150, 1737, 740, 551, 1825, 1997, 1544, 2819, 712, 44, 1701, 261, 3035],
[619, 3204, 369, 1810, 1593, 84, 1721, 875, 3204, 56, 1919, 604, 3290, 2766, 2033, 2417, 2425, 313, 2004, 746, 1985, 2051, 1234, 1054, 1320, 1098, 1955, 262, 1348, 39, 527, 417, 2256, 3202, 2238, 499, 3139, 144, 3139, 2389, 2404, 1092, 699, 1025, 2972, 3318, 2298, 2652, 223, 1688, 3268, 2887, 2294, 557, 23, 155, 285, 414, 2557, 2945, 2210, 156, 2850, 141, 2659, 2339, 1480, 883, 2049, 1994, 1178, 1484, 3275, 1799, 3166, 1711, 2050, 872, 1574, 932, 3071, 177, 1168, 883, 472, 2145, 1423, 1457, 1918, 2797, 2903, 1729, 341, 3128, 2575, 1996, 2388, 1188, 1157, 301, 1138, 2038, 907, 2812, 1922, 1428, 1018, 2401, 3232, 3317, 2160, 974, 1329, 3191, 676, 972, 2908, 1875, 2224, 1555, 694, 760, 997, 502, 1563, 594, 889, 2186, 1065, 577, 2396, 335, 1544, 975, 599, 564, 910, 2978, 2913, 1944, 2351, 3219, 134, 2920, 1204, 69, 2971, 72, 2134, 463, 1935, 3206, 2809, 2857, 923, 2603, 1448, 800, 3001, 458, 1507, 2955, 765, 1677, 567, 2614, 1233, 1110, 2627, 5, 2068, 3101, 2636, 1418, 2125, 1039, 2024, 3150, 842, 1494, 311, 2810, 2003, 1067, 2904, 774, 1501, 1649, 564, 343, 946, 1037, 2142, 1504, 2264, 1407, 1013, 1114, 1872, 2516, 1986, 124, 2125, 1631, 2711, 1541, 3135, 2558, 1044, 35, 546, 3296, 1710, 705, 1986, 570, 306, 136, 2041, 3159, 1077, 965, 2006, 1172, 3097, 2706, 1766, 1822, 1975, 2586, 2887, 2441, 694, 3029, 2763, 3325, 646, 2618, 1128, 795, 2460, 913, 38, 466, 1841, 740, 2563, 1556, 1531, 425, 2553, 2570, 2341, 3193, 862, 1921],
[3248, 2199, 1872, 1800, 252, 2561, 1433, 1415, 610, 3292, 2771, 2753, 2871, 1735, 2797, 131, 1348, 2221, 1271, 2042, 1041, 2476, 1145, 1854, 3229, 1441, 2327, 2990, 2265, 998, 2400, 841, 248, 138, 231, 2486, 1360, 1079, 2207, 2606, 1258, 2862, 2262, 1495, 2776, 1520, 291, 2184, 1988, 947, 926, 2727, 1929, 971, 934, 962, 2360, 1037, 758, 2801, 2759, 2321, 2593, 986, 1858, 1963, 791, 1722, 957, 1547, 879, 2237, 1133, 738, 1404, 2684, 458, 2263, 2855, 2170, 963, 1821, 1563, 1524, 1223, 1441, 1606, 737, 158, 1859, 2721, 1756, 2168, 368, 1219, 828, 2155, 479, 1680, 1180, 2964, 811, 1681, 126, 1166, 1691, 694, 2515, 1890, 963, 1987, 2789, 79, 424, 1082, 365, 3216, 781, 1788, 3091, 2053, 2677, 593, 2000, 3020, 1884, 2396, 284, 2489, 3223, 1520, 2460, 2438, 2583, 2285, 663, 2540, 1668, 2208, 3087, 1751, 30, 1930, 1544, 1688, 3052, 3326, 452, 3232, 1905, 1960, 2547, 909, 1030, 774, 357, 3114, 1973, 1607, 2624, 236, 2273, 308, 507, 1123, 616, 1083, 127, 1848, 1701, 808, 220, 1735, 3153, 1223, 2654, 1719, 2409, 2233, 1793, 420, 3238, 1927, 460, 2615, 27, 1242, 2823, 2504, 1706, 2352, 1916, 1257, 2408, 1232, 3174, 1401, 1517, 518, 1072, 2849, 728, 293, 1397, 1844, 1830, 2559, 75, 492, 2869, 2848, 1265, 2524, 1421, 358, 3202, 1837, 2925, 932, 2859, 389, 1295, 1920, 488, 2459, 1364, 2853, 1247, 289, 2486, 2806, 807, 1535, 2870, 29, 2879, 3195, 1054, 2148, 422, 2057, 585, 88, 1290, 1579, 2426, 1553, 976, 517, 1857, 2045, 475, 3117, 2334, 1878, 2771],
[1351, 279, 2141, 1097, 1906, 3306, 776, 1713, 3070, 2649, 1632, 996, 469, 552, 952, 714, 2772, 1663, 2450, 233, 939, 3077, 2355, 879, 1038, 1875, 2196, 1381, 3011, 3159, 1812, 2979, 2788, 1530, 2606, 2497, 433, 2491, 2733, 263, 2487, 194, 1191, 770, 2073, 1575, 3291, 1698, 2815, 2684, 2822, 1770, 2092, 42, 2484, 2177, 2609, 2743, 3036, 2211, 1958, 2673, 1232, 1046, 1748, 3250, 3243, 2517, 1274, 3124, 2877, 2737, 3012, 2560, 1170, 2219, 2189, 2855, 585, 2168, 992, 3051, 1151, 2110, 2031, 658, 781, 3158, 906, 349, 140, 1103, 38, 388, 1605, 1860, 1049, 229, 1512, 476, 2634, 33, 2385, 1801, 665, 2179, 2441, 1095, 1406, 214, 1005, 1809, 1883, 1220, 1491, 2155, 2349, 3199, 62, 748, 580, 2035, 1474, 365, 1455, 967, 1337, 2746, 2766, 3124, 1666, 3308, 2553, 2952, 3309, 1779, 2683, 2204, 2239, 664, 2049, 3317, 3129, 786, 1448, 2343, 3312, 1591, 2325, 2021, 1646, 164, 822, 419, 1237, 1989, 2556, 1951, 3134, 1162, 206, 1566, 1846, 2440, 663, 1801, 2154, 835, 1901, 2141, 410, 1820, 1170, 967, 2540, 630, 205, 1623, 209, 2169, 3196, 2962, 1241, 2218, 1372, 179, 1672, 1089, 282, 552, 38, 2889, 1454, 331, 1075, 2603, 1851, 1004, 1580, 837, 2250, 1390, 2129, 69, 1183, 2592, 2701, 2512, 2779, 1930, 167, 1678, 687, 2626, 3029, 518, 1729, 1466, 2969, 1638, 3243, 509, 1912, 2760, 722, 2714, 1012, 1370, 1733, 3288, 1646, 2526, 1406, 1304, 1442, 1755, 549, 1627, 1479, 2781, 2842, 525, 973, 499, 888, 413, 3097, 2384, 173, 520, 1527, 2000, 2653, 318, 1623, 386]]]

r: [[0, 3328, 0, 0, 3328, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 3328, 0, 0, 1, 0, 1, 2, 0, 2, 3328, 0, 3328, 1, 1, 0, 3328, 0, 3327, 1, 0, 1, 3327, 1, 3328, 0, 0, 1, 3328, 3328, 0, 3327, 0, 0, 0, 1, 3328, 3328, 1, 0, 1, 0, 0, 3328, 0, 2, 2, 0, 3328, 3327, 1, 1, 0, 0, 3327, 2, 0, 3327, 1, 3328, 1, 0, 3328, 1, 1, 0, 0, 2, 3327, 0, 0, 0, 3327, 3328, 1, 0, 3328, 3327, 0, 0, 0, 0, 3328, 3328, 0, 3328, 2, 1, 1, 0, 1, 0, 3328, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 3328, 3328, 2, 0, 0, 3327, 1, 3328, 0, 0, 3328, 3328, 3328, 0, 1, 3328, 3328, 3328, 0, 0, 0, 1, 0, 3328, 3328, 1, 0, 0, 0, 1, 1, 2, 1, 1, 3328, 1, 3328, 1, 1, 3327, 3328, 1, 0, 2, 3328, 1, 0, 0, 3328, 3328, 1, 3328, 3328, 3328, 0, 2, 1, 0, 3327, 1, 0, 1, 1, 2, 2, 0, 3327, 1, 3327, 0, 0, 1, 0, 3328, 3328, 1, 0, 0, 1, 3328, 2, 1, 0, 0, 2, 1, 3328, 3328, 0, 1, 0, 0, 0, 3328, 1, 3328, 0, 3328, 0, 3328, 0, 0, 1, 3328, 3328, 1, 0, 3328, 0, 1, 0, 3328, 3327, 1, 3327, 3328, 1, 3327, 0, 1, 0, 0, 3328, 0, 1, 3328, 3328, 0, 1, 0, 3328, 0, 0, 1, 0, 1, 3328, 3328],
[1, 1, 2, 1, 1, 1, 0, 0, 1, 1, 1, 3328, 3328, 0, 3328, 3328, 3328, 1, 1, 0, 3328, 0, 3328, 0, 1, 3328, 3328, 0, 1, 1, 3328, 1, 3328, 2, 0, 3328, 0, 3328, 1, 0, 3328, 0, 0, 1, 0, 1, 1, 0, 3327, 3328, 3328, 3327, 3328, 1, 0, 3328, 3328, 3328, 1, 0, 1, 3327, 3328, 3328, 3327, 3328, 3328, 0, 0, 0, 3327, 0, 0, 1, 0, 1, 0, 0, 3328, 3328, 0, 1, 0, 3328, 0, 1, 0, 1, 3328, 2, 0, 0, 3328, 3328, 3328, 3328, 0, 3328, 0, 0, 3328, 0, 3328, 3328, 2, 3327, 3328, 3327, 2, 1, 2, 0, 0, 3328, 3328, 0, 3327, 0, 1, 3327, 1, 0, 3328, 1, 0, 3327, 0, 0, 3328, 0, 3328, 3327, 1, 3327, 0, 1, 0, 3328, 0, 0, 1, 0, 0, 1, 0, 1, 0, 3328, 1, 1, 1, 0, 0, 1, 3328, 3327, 1, 0, 1, 3328, 0, 1, 0, 1, 0, 3328, 3327, 0, 3327, 3328, 1, 3328, 1, 3328, 1, 0, 0, 3328, 0, 3328, 3328, 0, 0, 0, 3327, 0, 0, 2, 0, 1, 3328, 2, 1, 0, 3328, 0, 0, 0, 1, 3327, 0, 0, 3327, 0, 1, 0, 0, 2, 0, 3328, 1, 1, 3328, 3328, 1, 0, 3327, 1, 0, 3327, 0, 0, 0, 3328, 0, 1, 1, 0, 0, 3328, 0, 0, 3328, 1, 2, 3327, 1, 1, 2, 1, 0, 1, 3328, 3328, 0, 1, 1, 1, 1, 1, 3328, 0, 2, 3327, 2, 1],
[3328, 0, 0, 1, 0, 3328, 1, 1, 1, 1, 3328, 0, 1, 0, 0, 0, 3328, 3328, 3328, 1, 0, 1, 0, 0, 3328, 0, 3328, 1, 0, 1, 3328, 3328, 3327, 1, 0, 0, 0, 3328, 3328, 2, 0, 1, 1, 1, 3328, 0, 1, 0, 1, 0, 3328, 1, 3328, 3328, 0, 1, 3328, 3328, 3328, 1, 2, 0, 3328, 1, 3327, 0, 1, 0, 1, 3327, 0, 3328, 3328, 0, 0, 3328, 3328, 3328, 0, 3328, 3327, 0, 0, 1, 3328, 0, 0, 0, 1, 0, 0, 3328, 0, 1, 0, 3328, 0, 1, 3328, 3328, 3328, 0, 0, 1, 1, 3327, 3327, 1, 1, 1, 0, 0, 3328, 0, 0, 3328, 3328, 3328, 3327, 3328, 1, 2, 0, 0, 1, 0, 3327, 0, 0, 0, 0, 0, 3327, 3328, 3328, 3328, 0, 0, 1, 2, 3327, 1, 0, 2, 1, 0, 3327, 0, 0, 3328, 1, 3328, 3328, 0, 0, 0, 1, 0, 1, 3328, 3328, 3328, 0, 3327, 3328, 1, 3328, 2, 1, 1, 1, 0, 3327, 3327, 3328, 3328, 0, 1, 3328, 0, 3327, 3327, 1, 1, 3327, 1, 1, 1, 3328, 0, 0, 3327, 3327, 1, 3328, 3328, 3328, 3327, 0, 0, 0, 3328, 3328, 1, 3327, 1, 0, 1, 3328, 0, 0, 0, 3327, 3328, 2, 0, 3328, 1, 2, 0, 3328, 0, 2, 1, 0, 2, 0, 3328, 1, 3328, 0, 3328, 1, 0, 3328, 3328, 1, 3328, 3328, 0, 3327, 1, 0, 3328, 0, 3328, 0, 1, 1, 3327, 0, 3327, 1, 3328, 2, 0],
[1, 3328, 0, 1, 3327, 1, 1, 1, 2, 0, 0, 0, 1, 0, 0, 3328, 0, 1, 2, 0, 0, 0, 0, 0, 0, 3328, 1, 1, 0, 1, 3328, 0, 3328, 0, 0, 2, 3328, 3328, 0, 3328, 3328, 0, 1, 0, 3328, 3327, 1, 3328, 1, 2, 3328, 1, 0, 0, 3328, 3328, 0, 0, 1, 0, 3328, 3328, 3328, 0, 2, 1, 2, 3328, 0, 3328, 0, 0, 1, 2, 1, 0, 2, 3328, 3328, 0, 0, 3328, 0, 0, 0, 2, 3328, 3328, 2, 3327, 2, 0, 0, 1, 0, 3328, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 3328, 3328, 3327, 0, 1, 0, 1, 2, 1, 0, 0, 0, 3328, 1, 3328, 3328, 0, 1, 3328, 3328, 1, 0, 3328, 2, 1, 3327, 1, 3328, 1, 2, 1, 0, 0, 2, 3328, 3328, 1, 2, 3328, 1, 3328, 0, 0, 1, 1, 0, 0, 3328, 0, 1, 0, 3328, 0, 1, 3328, 1, 2, 2, 2, 1, 1, 3328, 0, 1, 3328, 0, 0, 0, 1, 3328, 1, 1, 3327, 3328, 0, 1, 3328, 0, 0, 3327, 0, 0, 2, 0, 0, 3327, 1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3328, 1, 0, 2, 2, 3328, 0, 1, 1, 3327, 1, 1, 0, 3328, 3328, 0, 0, 3328, 3328, 3328, 1, 3328, 3328, 0, 1, 0, 2, 3328, 3328, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 3328, 3328, 1, 3327, 3327, 1, 0, 0, 3328, 1, 0]]

e1: [[0, 3328, 3328, 3328, 3328, 3327, 0, 3328, 2, 3327, 3328, 3328, 0, 0, 2, 3328, 3328, 0, 1, 3328, 1, 0, 1, 0, 1, 3328, 1, 3328, 3328, 0, 0, 2, 2, 1, 1, 0, 0, 0, 0, 3327, 1, 3327, 0, 3328, 1, 3327, 3328, 3328, 1, 1, 0, 1, 0, 0, 3328, 0, 3328, 3328, 2, 0, 3328, 0, 3328, 3327, 0, 3328, 0, 0, 0, 3328, 3328, 2, 3327, 2, 0, 3327, 0, 1, 3327, 3328, 3328, 3327, 1, 1, 3328, 0, 3328, 0, 0, 1, 3328, 0, 3328, 3328, 3328, 1, 2, 0, 3328, 3328, 0, 0, 1, 3328, 3328, 1, 1, 1, 0, 0, 3328, 0, 1, 1, 0, 1, 0, 3328, 3328, 2, 3328, 0, 0, 0, 0, 3328, 0, 1, 0, 0, 3328, 0, 3328, 1, 0, 3328, 1, 1, 0, 1, 1, 0, 1, 3327, 3328, 1, 3328, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 3328, 0, 0, 0, 0, 0, 3328, 1, 3328, 3327, 3328, 0, 3327, 1, 0, 0, 0, 3328, 1, 0, 1, 3328, 0, 0, 0, 1, 0, 3328, 0, 0, 2, 3328, 1, 1, 1, 0, 0, 1, 3328, 2, 0, 1, 3328, 1, 1, 0, 3328, 3327, 1, 1, 1, 3328, 3328, 3328, 2, 0, 0, 0, 3328, 0, 3328, 0, 0, 0, 0, 0, 0, 3327, 1, 3327, 1, 0, 0, 1, 3328, 3328, 3328, 0, 0, 2, 2, 0, 1, 0, 0, 3328, 3328, 0, 3328, 3327, 1, 3327, 1, 1, 0, 0, 0, 1],
[0, 2, 3328, 0, 1, 3328, 0, 0, 0, 3328, 1, 0, 0, 0, 3328, 0, 2, 3327, 3328, 0, 1, 0, 1, 0, 3328, 1, 3328, 3328, 3328, 0, 0, 0, 3328, 3328, 3328, 1, 3328, 1, 0, 3327, 1, 3328, 2, 3328, 0, 1, 0, 3327, 0, 3328, 0, 0, 3328, 3328, 3327, 0, 3327, 0, 3328, 1, 0, 0, 3328, 3328, 1, 2, 1, 3328, 0, 3328, 3328, 1, 3328, 3328, 0, 1, 0, 3328, 0, 1, 1, 1, 0, 0, 3327, 1, 1, 0, 1, 3328, 2, 3328, 3328, 3328, 3327, 2, 3328, 1, 0, 3328, 3328, 0, 3327, 0, 3328, 1, 1, 2, 0, 1, 3328, 0, 0, 0, 1, 3328, 1, 0, 0, 0, 3328, 0, 0, 3328, 1, 1, 0, 1, 3328, 0, 3328, 1, 3327, 1, 0, 1, 0, 0, 1, 1, 1, 3328, 1, 3327, 2, 0, 1, 3328, 3327, 1, 3328, 2, 2, 1, 0, 1, 3327, 0, 0, 0, 3328, 3328, 0, 1, 1, 1, 3328, 3328, 1, 1, 1, 3328, 3328, 0, 1, 1, 3328, 0, 0, 0, 2, 0, 0, 2, 0, 3328, 1, 0, 3328, 2, 0, 3327, 0, 2, 3328, 0, 0, 0, 1, 3328, 2, 1, 1, 3328, 3328, 3327, 3328, 0, 3328, 1, 2, 0, 0, 0, 1, 3327, 3328, 0, 3328, 2, 0, 1, 3327, 3328, 1, 3328, 0, 1, 0, 3328, 3328, 3328, 3327, 2, 0, 3327, 3328, 0, 0, 3328, 3328, 0, 2, 3328, 3327, 1, 0, 3328, 1, 0, 3328, 3328, 0, 1, 0, 1],
[3328, 0, 1, 3328, 1, 3328, 3328, 2, 3327, 1, 1, 3328, 0, 3328, 0, 3327, 0, 3328, 1, 3328, 1, 2, 1, 0, 0, 3328, 3328, 2, 3327, 1, 3328, 1, 0, 0, 2, 0, 0, 1, 0, 1, 3328, 0, 0, 1, 3328, 3327, 1, 0, 0, 3328, 3328, 1, 3328, 3328, 0, 1, 0, 0, 0, 1, 3327, 0, 3328, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3327, 3328, 3328, 0, 2, 0, 3328, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 3328, 0, 3328, 2, 1, 0, 3328, 0, 0, 0, 0, 3328, 3328, 0, 3328, 1, 1, 0, 1, 3327, 3327, 2, 1, 1, 0, 1, 3328, 3328, 1, 1, 3328, 1, 0, 3328, 2, 3328, 3328, 0, 3328, 3328, 3328, 3327, 0, 3328, 1, 0, 0, 0, 3327, 0, 1, 3327, 2, 0, 1, 1, 0, 3328, 1, 3328, 0, 0, 3328, 1, 0, 1, 3328, 3328, 1, 1, 0, 0, 0, 3328, 3328, 3327, 0, 3328, 3328, 3328, 0, 0, 2, 1, 0, 0, 0, 0, 1, 2, 3327, 0, 2, 2, 1, 0, 3328, 1, 3328, 0, 1, 1, 3328, 0, 0, 0, 0, 0, 0, 1, 0, 1, 3328, 3328, 3328, 0, 3328, 0, 0, 1, 0, 3327, 1, 0, 3328, 3328, 3328, 0, 0, 3327, 0, 1, 1, 2, 3328, 2, 1, 1, 1, 0, 3328, 1, 3327, 3328, 0, 3327, 2, 1, 1, 3328, 0, 1, 0, 3328, 0, 3328, 2, 3327, 3328, 3328, 3328, 0],
[3328, 0, 0, 1, 0, 1, 1, 3328, 0, 0, 1, 3328, 1, 1, 0, 3328, 3327, 2, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 3328, 0, 1, 1, 3328, 1, 0, 3328, 2, 0, 0, 3328, 3328, 0, 3328, 0, 3328, 0, 0, 0, 0, 0, 0, 0, 3328, 3327, 3328, 1, 2, 0, 3328, 3328, 1, 1, 1, 2, 3328, 2, 3328, 0, 0, 3328, 2, 3327, 0, 0, 1, 1, 1, 3328, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 3328, 3328, 3328, 3328, 1, 1, 1, 0, 2, 1, 0, 1, 3328, 1, 1, 2, 0, 2, 0, 3328, 3328, 0, 3328, 1, 0, 2, 2, 0, 3328, 1, 1, 0, 3328, 1, 3328, 3328, 0, 3328, 3328, 3328, 3327, 1, 1, 1, 0, 3328, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 0, 3327, 2, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 3328, 2, 1, 3328, 0, 3328, 3328, 3327, 1, 1, 0, 3327, 0, 0, 2, 3328, 3327, 0, 1, 1, 3327, 3328, 0, 0, 0, 1, 3328, 3328, 0, 2, 3327, 1, 1, 3328, 0, 3327, 0, 3328, 3328, 1, 0, 0, 1, 3328, 3328, 1, 3328, 0, 3328, 1, 2, 3328, 3327, 1, 3327, 0, 3328, 1, 1, 0, 0, 0, 3328, 1, 0, 3327, 1, 0, 1, 0, 2, 0, 1, 1, 3328, 0, 1, 1, 0, 1, 1, 3327, 3327, 0, 3328, 1, 0, 0, 0, 2, 3327, 2, 1, 3328, 2, 0, 1]]

e2: [0, 3327, 1, 3328, 1, 2, 0, 1, 0, 0, 0, 3327, 0, 1, 0, 3328, 1, 2, 0, 0, 0, 1, 0, 2, 1, 2, 0, 3327, 2, 3328, 3327, 2, 1, 1, 0, 0, 0, 3328, 0, 1, 3328, 0, 3327, 1, 1, 1, 3328, 3328, 0, 1, 3327, 3328, 3328, 3327, 0, 0, 0, 0, 0, 3328, 0, 3328, 3327, 1, 3328, 0, 2, 1, 3328, 0, 0, 2, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 2, 3328, 0, 0, 3328, 0, 2, 3328, 3328, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 3327, 1, 1, 0, 1, 3328, 1, 0, 0, 0, 0, 3327, 1, 1, 0, 0, 0, 0, 3328, 0, 3328, 0, 0, 0, 0, 1, 0, 1, 3328, 3327, 1, 0, 2, 3328, 1, 1, 0, 1, 0, 3328, 1, 3328, 1, 0, 3328, 1, 1, 2, 3328, 1, 0, 1, 3328, 1, 3328, 0, 1, 3328, 1, 1, 0, 1, 3328, 0, 0, 0, 0, 1, 3328, 1, 3328, 1, 3328, 3328, 3328, 0, 0, 3328, 1, 3328, 3328, 1, 0, 3328, 2, 0, 2, 3328, 0, 0, 0, 3327, 2, 3328, 3328, 3327, 0, 0, 0, 3328, 0, 3328, 3328, 0, 1, 3328, 3328, 0, 3327, 0, 3328, 3328, 3328, 0, 3328, 1, 0, 1, 3328, 0, 3328, 3328, 1, 0, 3328, 0, 3327, 3328, 3328, 3328, 3328, 3328, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 1, 0, 1, 3327, 3328, 1, 1, 3328, 3327, 1, 0]
rHat: [[2961, 3151, 3250, 2522, 466, 1490, 1030, 1206, 2334, 2137, 1753, 2041, 2417, 1536, 2849, 2167, 2109, 919, 3056, 1731, 1659, 1875, 2419, 2016, 2710, 1881, 2237, 2309, 2798, 1029, 2844, 3148, 2249, 2078, 1804, 1091, 3190, 1373, 3122, 2914, 1641, 358, 2751, 1763, 206, 424, 2254, 2358, 1224, 3280, 2695, 2390, 2284, 274, 1151, 2264, 172, 2380, 1036, 2592, 2833, 2022, 1622, 491, 1655, 2741, 3282, 290, 206, 175, 2374, 1809, 908, 779, 1458, 305, 2308, 2476, 3075, 811, 2695, 2671, 1230, 782, 1376, 1540, 2642, 928, 1982, 864, 1397, 2176, 138, 1232, 898, 340, 2206, 2730, 1402, 2119, 2834, 1508, 2641, 1930, 288, 1599, 2775, 490, 1978, 1969, 3010, 2127, 1484, 2233, 3010, 1764, 690, 2285, 779, 1092, 859, 1627, 566, 502, 314, 1790, 2788, 771, 1950, 2163, 250, 718, 756, 239, 1797, 508, 2590, 2409, 2409, 3069, 1069, 219, 606, 618, 2155, 2175, 1603, 2041, 1765, 3072, 1492, 2660, 1511, 982, 2442, 2669, 735, 685, 1153, 1729, 2108, 2742, 1146, 1168, 2604, 2012, 796, 766, 1232, 2440, 2645, 1584, 2624, 892, 402, 1440, 1987, 2819, 457, 3142, 1976, 2606, 345, 3267, 465, 3282, 472, 882, 1081, 409, 614, 1273, 1904, 1507, 344, 496, 2426, 1611, 1595, 191, 2808, 2900, 1971, 269, 2413, 1656, 1031, 3323, 3094, 1094, 710, 1983, 1669, 1443, 19, 2852, 168, 3199, 1599, 393, 1722, 2438, 914, 2791, 1879, 1726, 889, 2821, 1074, 2815, 1281, 2225, 1240, 1544, 3134, 768, 3268, 1102, 2173, 133, 1603, 3152, 2293, 2947, 2342, 2474, 314, 157, 2066, 2186, 749, 967, 1908, 2, 1503, 747],
[1189, 2551, 2100, 2299, 2054, 2162, 3251, 1612, 2462, 3169, 915, 103, 2714, 3276, 2159, 3154, 3152, 2348, 559, 1071, 2421, 2154, 1575, 2261, 2653, 468, 1337, 662, 907, 2087, 527, 541, 549, 1961, 1239, 2163, 727, 490, 393, 2693, 1601, 757, 487, 990, 555, 1418, 298, 354, 1450, 1595, 1914, 1794, 1274, 1825, 1624, 1290, 3162, 1400, 1705, 1487, 3041, 2435, 1288, 1391, 3147, 825, 842, 1775, 1484, 2047, 500, 1973, 878, 1261, 60, 2102, 236, 558, 2754, 2788, 682, 434, 1646, 1171, 2657, 2727, 2339, 2040, 2008, 1623, 1963, 2666, 934, 1717, 39, 778, 1289, 960, 1094, 2293, 614, 3234, 1820, 1398, 575, 1580, 1041, 2844, 2708, 3137, 1537, 2148, 408, 2415, 1547, 2957, 2357, 409, 1685, 491, 3119, 129, 2576, 183, 487, 2265, 2827, 3032, 2544, 2631, 3182, 474, 2093, 2298, 1329, 2063, 296, 1911, 3148, 133, 1214, 1762, 3081, 1864, 2522, 1331, 1523, 1694, 1563, 1370, 1183, 38, 638, 1960, 2711, 2801, 2339, 2802, 535, 1774, 2869, 1522, 2765, 2201, 3262, 410, 1833, 588, 421, 2501, 3156, 494, 1935, 106, 970, 1266, 1488, 3260, 2111, 2712, 3199, 1525, 2672, 3109, 732, 2472, 861, 1811, 1910, 1641, 499, 2052, 1771, 787, 1658, 231, 124, 1770, 2701, 645, 3203, 3029, 1169, 2875, 1435, 2968, 2212, 308, 232, 3289, 2018, 1813, 1815, 3203, 61, 822, 2652, 250, 990, 2565, 175, 1404, 2600, 3175, 100, 2623, 1234, 1411, 1116, 1753, 767, 3180, 2619, 829, 1328, 2731, 1207, 2624, 872, 497, 2731, 2358, 3038, 3214, 2936, 2091, 1250, 1210, 3167, 3138, 246, 1191, 1091, 239, 1618, 451],
[125, 1510, 2110, 3009, 1778, 1285, 938, 1419, 68, 809, 2600, 491, 492, 1897, 978, 2401, 2711, 779, 348, 752, 2074, 3128, 1260, 1871, 1244, 1799, 735, 1223, 2239, 1419, 791, 1997, 2045, 3275, 2715, 3147, 250, 3157, 878, 1816, 1889, 3318, 1364, 1787, 2863, 1533, 1639, 1559, 2493, 1826, 2511, 1427, 844, 2177, 428, 1155, 1057, 3018, 207, 43, 2134, 602, 3327, 3013, 179, 1926, 838, 3004, 3158, 90, 2275, 534, 3006, 2862, 2681, 1791, 3046, 2263, 3065, 985, 2779, 732, 2646, 2516, 2047, 79, 1034, 2434, 1120, 1250, 2537, 609, 2270, 3287, 786, 2528, 344, 2972, 1448, 1516, 275, 128, 2558, 1660, 1027, 2989, 3241, 2639, 2732, 227, 362, 1615, 591, 2044, 1780, 1745, 550, 536, 2711, 628, 1441, 1748, 1709, 1869, 2078, 687, 3015, 1322, 1432, 2658, 3140, 2281, 2191, 323, 138, 654, 1176, 850, 2368, 2482, 12, 3080, 1749, 1813, 3322, 3027, 65, 298, 2844, 1375, 3116, 728, 1257, 1884, 890, 2929, 1469, 3037, 2862, 2379, 672, 1024, 2695, 1775, 1282, 542, 2094, 531, 1913, 3001, 2015, 1040, 2433, 2971, 140, 2241, 1209, 636, 836, 2245, 592, 823, 3328, 1526, 459, 1862, 3120, 2843, 1484, 3174, 1490, 3225, 1991, 740, 415, 2169, 1873, 3322, 795, 2649, 3272, 418, 1002, 2662, 2162, 1275, 2861, 2247, 2890, 134, 2181, 1308, 2549, 976, 574, 2913, 1394, 2749, 3158, 2666, 2592, 1712, 725, 1962, 171, 1324, 2697, 718, 1202, 1190, 3133, 3115, 2979, 221, 433, 1932, 801, 1204, 1392, 46, 1184, 3102, 1601, 1880, 3110, 2858, 3208, 461, 1577, 3170, 1715, 2465, 3150, 2297, 542, 1373],
[129, 3281, 1891, 987, 608, 1105, 536, 193, 517, 1519, 230, 2266, 1852, 1290, 1686, 1876, 1797, 2312, 2503, 556, 420, 1266, 2259, 2616, 230, 1176, 2515, 291, 3169, 1769, 1159, 3237, 2988, 934, 2904, 1271, 570, 2276, 2989, 2393, 1965, 695, 2379, 1903, 971, 165, 210, 2288, 1241, 243, 1719, 551, 1060, 1233, 1384, 2422, 2036, 3001, 425, 2274, 307, 1758, 2723, 2651, 1423, 1577, 395, 610, 1573, 2921, 2026, 584, 1903, 2244, 3222, 520, 1770, 811, 1289, 1722, 786, 2263, 2679, 2071, 2698, 1651, 1006, 2944, 1272, 726, 2615, 1124, 440, 2276, 2512, 574, 2680, 1050, 1004, 45, 2342, 1647, 2928, 1933, 2311, 148, 1034, 2048, 1445, 1002, 15, 136, 2344, 1942, 109, 291, 656, 2244, 2034, 305, 2914, 1130, 1918, 305, 587, 932, 1431, 1574, 47, 2833, 3201, 2256, 1489, 961, 2810, 2670, 2188, 1434, 2185, 1288, 2792, 3142, 2263, 2399, 2350, 115, 2424, 2344, 2261, 1936, 1724, 2299, 446, 2972, 1929, 780, 1832, 835, 1574, 1361, 2763, 2881, 313, 3294, 1868, 2936, 1533, 1264, 553, 2251, 1071, 2463, 3150, 2330, 826, 3275, 1284, 1996, 2776, 925, 847, 1197, 3217, 2821, 2864, 1138, 915, 2495, 14, 1451, 3150, 927, 1371, 1069, 1247, 121, 1147, 1844, 1608, 1240, 1748, 1637, 3270, 1827, 3217, 837, 2605, 1693, 2588, 2886, 901, 1535, 459, 428, 154, 2854, 1067, 2096, 2589, 55, 396, 1053, 46, 154, 1228, 3036, 328, 128, 72, 204, 2303, 3104, 112, 489, 377, 1990, 145, 2473, 2994, 859, 1758, 1730, 291, 517, 2892, 3093, 1430, 2643, 1636, 837, 59, 1968, 460, 1939, 3307, 185]]

BHat * rHat: [[3177, 2307, 2045, 211, 502, 2182, 280, 2061, 1553, 1500, 2903, 1612, 1218, 2202, 3131, 26, 1881, 1487, 3171, 1176, 1953, 232, 887, 2834, 2475, 1504, 1778, 1293, 194, 1958, 1224, 1530, 1718, 1679, 1414, 390, 1106, 1685, 416, 399, 1732, 1013, 2278, 1386, 3112, 1003, 516, 1180, 2108, 962, 633, 2541, 2704, 2031, 2667, 203, 3160, 2046, 477, 887, 448, 1666, 742, 2912, 2329, 56, 1688, 2262, 1513, 1327, 709, 2954, 395, 630, 661, 941, 2012, 1957, 1816, 1923, 918, 1565, 1838, 859, 1923, 2054, 58, 1737, 2812, 1887, 2569, 108, 2063, 971, 1718, 2233, 1898, 344, 517, 2919, 955, 16, 1172, 2114, 620, 382, 1751, 3232, 3138, 2853, 2268, 615, 3031, 188, 2982, 1177, 494, 14, 2450, 3270, 2362, 2313, 1171, 2530, 3105, 2013, 726, 507, 626, 2708, 405, 3037, 2565, 43, 2351, 858, 1215, 1800, 268, 2370, 2945, 1237, 2408, 125, 156, 651, 2315, 2590, 3107, 2172, 2577, 2998, 2058, 1320, 282, 1180, 2891, 3096, 174, 2048, 20, 3163, 1973, 844, 283, 3136, 732, 1697, 409, 906, 2185, 812, 1788, 738, 2249, 1968, 1649, 2209, 2856, 1061, 775, 1351, 746, 556, 1226, 1770, 2504, 2836, 1207, 2312, 2080, 275, 2630, 2516, 1272, 1101, 2973, 1436, 1524, 3035, 454, 2458, 1753, 1931, 1964, 92, 1254, 3250, 2434, 2808, 2506, 1511, 325, 464, 1494, 2469, 207, 1521, 2190, 2403, 239, 3050, 1137, 423, 574, 355, 655, 1042, 2432, 259, 310, 2204, 1840, 2348, 1549, 2843, 1785, 1748, 239, 2160, 1567, 776, 1617, 1229, 2520, 421, 3261, 3065, 1618, 2951, 654, 2350, 867, 386, 1073, 366],
[1396, 3277, 3123, 1246, 892, 1821, 416, 1095, 2313, 2155, 2538, 2380, 1873, 1203, 2992, 2095, 2261, 1877, 2457, 2468, 495, 1649, 1243, 1662, 2288, 2281, 2418, 1597, 2094, 3288, 1542, 806, 2473, 903, 1672, 90, 2657, 1705, 1626, 1477, 487, 919, 1259, 3171, 1721, 857, 1687, 346, 1801, 1593, 1652, 660, 1968, 97, 2612, 2233, 2873, 2963, 1398, 472, 1926, 1154, 2078, 269, 3280, 1349, 2388, 93, 1133, 165, 1737, 1830, 2177, 1312, 2229, 1327, 488, 2667, 1459, 1308, 1783, 2551, 2327, 1986, 1383, 1908, 107, 2509, 2191, 3272, 3040, 3279, 3275, 1218, 2459, 1888, 87, 1165, 1375, 1875, 2271, 2946, 2299, 1128, 495, 552, 688, 3004, 152, 410, 1706, 632, 2611, 2036, 1790, 2214, 1592, 844, 1472, 2743, 1792, 252, 585, 359, 2170, 1522, 1900, 65, 74, 2510, 2767, 2301, 372, 1756, 549, 1051, 1007, 72, 2808, 1828, 3141, 2584, 200, 563, 3181, 1327, 368, 3293, 257, 774, 221, 26, 308, 2068, 578, 272, 1610, 1013, 468, 1070, 220, 1664, 1234, 601, 1194, 2200, 2547, 2965, 1694, 534, 2042, 1404, 2826, 2958, 1936, 3262, 1578, 1323, 2605, 457, 2837, 669, 2711, 2288, 2007, 773, 1257, 2458, 943, 240, 190, 3281, 3227, 2377, 69, 1314, 1833, 1513, 2404, 2121, 3097, 1291, 2166, 3246, 2954, 1836, 1516, 2412, 72, 833, 101, 2060, 157, 1939, 885, 1336, 3167, 2181, 206, 2808, 334, 1889, 1535, 767, 2805, 732, 2998, 356, 160, 3208, 1443, 1173, 193, 1504, 2434, 3227, 183, 82, 2620, 3273, 3081, 767, 1207, 607, 2747, 1262, 972, 2984, 2697, 203, 1905, 962, 744, 2490, 542, 3117],
[36, 2141, 2507, 2722, 695, 674, 2402, 2411, 1481, 2602, 3005, 1950, 2693, 1536, 873, 2707, 1997, 527, 885, 22, 2263, 994, 415, 2981, 386, 1029, 2066, 274, 3196, 441, 273, 3108, 1768, 2146, 2047, 2282, 2835, 1038, 385, 2576, 2918, 208, 255, 2576, 2187, 874, 3139, 835, 2396, 1696, 63, 2747, 3205, 242, 96, 457, 2308, 3260, 1349, 2451, 1719, 2309, 967, 407, 2934, 293, 2298, 3205, 1763, 614, 124, 77, 973, 136, 549, 118, 637, 2582, 169, 1297, 3001, 1396, 1595, 761, 759, 433, 729, 27, 1740, 1629, 1811, 542, 2412, 322, 844, 137, 2249, 2113, 21, 2530, 612, 1769, 249, 2471, 3212, 2598, 2453, 3208, 329, 1930, 937, 2077, 57, 735, 2468, 3244, 3315, 374, 2168, 142, 2230, 475, 1683, 838, 2564, 2306, 102, 3014, 3063, 21, 3024, 2846, 1269, 3079, 224, 2172, 2107, 1115, 3317, 3328, 1378, 923, 401, 1672, 618, 1277, 377, 2658, 513, 1936, 666, 702, 584, 2002, 36, 3017, 207, 2434, 549, 1219, 2350, 2086, 2559, 756, 628, 805, 1905, 3150, 2897, 2029, 2765, 247, 1230, 1896, 2107, 2033, 1011, 915, 1524, 140, 1635, 2194, 2348, 2336, 2280, 2779, 3115, 1641, 1595, 2152, 2749, 1450, 2547, 3306, 2367, 586, 1598, 717, 1996, 779, 764, 2292, 3140, 1476, 2384, 308, 1295, 1623, 1989, 548, 796, 1048, 1658, 2125, 2501, 2980, 530, 1418, 1004, 275, 8, 712, 3316, 1078, 1101, 2937, 616, 2132, 2592, 2561, 2491, 2334, 1656, 1386, 2760, 809, 1606, 1941, 3010, 593, 1688, 1666, 2927, 1582, 2431, 1202, 1691, 2145, 1046, 2138, 1407, 1859, 645, 1954, 198, 527],
[1506, 379, 1200, 924, 1096, 407, 3201, 2679, 1175, 2383, 151, 1150, 1101, 3211, 1477, 2148, 1078, 2363, 3224, 2756, 1525, 2512, 583, 785, 328, 2669, 895, 2307, 949, 2127, 1386, 1876, 2459, 1636, 686, 2969, 2242, 2840, 1416, 826, 2899, 885, 2234, 37, 425, 1235, 1578, 1055, 2907, 525, 858, 430, 1908, 15, 3221, 933, 1880, 2226, 2412, 2800, 1729, 959, 820, 2324, 15, 1322, 3226, 1066, 2086, 1501, 2703, 2905, 3003, 1714, 241, 2339, 1210, 1327, 3154, 1245, 1820, 1694, 1151, 1516, 1575, 1272, 1425, 2292, 618, 809, 2588, 988, 2176, 1135, 2106, 2675, 924, 1053, 1126, 2056, 2818, 1862, 1974, 818, 379, 2933, 2314, 1803, 862, 2891, 934, 2381, 842, 446, 3241, 142, 2881, 550, 2934, 3284, 989, 1467, 2565, 2278, 1305, 245, 708, 2434, 1235, 1982, 1056, 2099, 459, 2260, 2464, 2604, 2231, 2657, 2326, 842, 1833, 3224, 395, 72, 1997, 3071, 1006, 2584, 685, 1198, 1230, 939, 909, 2634, 1056, 2503, 2068, 3074, 3163, 2885, 1216, 2512, 1366, 1287, 497, 3168, 1704, 1239, 2795, 829, 1926, 1073, 1499, 1657, 3278, 1090, 1274, 809, 535, 1055, 2486, 3073, 2668, 2030, 2353, 1250, 3195, 696, 493, 1422, 2327, 971, 464, 1228, 115, 827, 2712, 631, 1340, 69, 2131, 505, 503, 879, 1769, 3048, 1737, 937, 2082, 2227, 183, 2823, 20, 2032, 559, 157, 2032, 2079, 2871, 1940, 1468, 2682, 2785, 2394, 2195, 3067, 2872, 2930, 2607, 3300, 1986, 3165, 3308, 282, 397, 2735, 1390, 2599, 1483, 315, 2720, 1197, 2965, 2466, 1095, 1057, 1383, 1411, 2811, 247, 2240, 1499, 2765, 2881, 144, 2083]]
NTTInverse(BHat * rHat): [[3070, 1403, 2569, 1535, 2889, 2555, 885, 3020, 1056, 2040, 995, 873, 2394, 1510, 2542, 2103, 689, 51, 1822, 3032, 2675, 2707, 2636, 1256, 3207, 2846, 1050, 1173, 636, 530, 1794, 746, 1513, 286, 2642, 2601, 3062, 2961, 1264, 818, 388, 194, 2629, 1173, 973, 1503, 1815, 1303, 1481, 548, 2909, 1001, 1315, 869, 1852, 2329, 1081, 1718, 2971, 2064, 1649, 1337, 3030, 1542, 145, 243, 1749, 559, 2441, 1805, 2460, 49, 2615, 1890, 1190, 2547, 2409, 1359, 1717, 3221, 369, 639, 964, 682, 232, 375, 1578, 1223, 248, 1212, 1333, 599, 998, 234, 1285, 324, 3145, 2356, 642, 766, 19, 2276, 2553, 3123, 146, 2823, 2051, 2636, 2687, 2320, 6, 2552, 2385, 902, 2438, 1118, 3145, 2935, 58, 485, 2846, 2641, 2949, 181, 2455, 2681, 390, 534, 55, 3226, 1641, 2901, 567, 2387, 765, 2375, 1468, 442, 1303, 1543, 97, 70, 2844, 577, 323, 2056, 1844, 2345, 3185, 1016, 265, 672, 958, 570, 2765, 693, 2210, 1849, 1092, 2915, 502, 164, 1522, 2167, 2705, 1425, 967, 271, 1125, 1629, 3157, 1363, 1959, 784, 63, 2079, 551, 305, 3022, 1790, 438, 1106, 1757, 17, 1650, 3176, 3066, 923, 1911, 2003, 2754, 1085, 1952, 1946, 354, 1958, 418, 2788, 56, 1736, 2304, 449, 3114, 14, 2888, 1925, 2867, 2199, 1207, 2101, 310, 2433, 3082, 1564, 1887, 3159, 2687, 1239, 1243, 2119, 1375, 330, 1968, 1013, 3003, 2343, 1979, 2092, 3238, 925, 3011, 841, 2468, 753, 3189, 1128, 366, 2024, 1769, 2850, 3171, 964, 1213, 3029, 1350, 304, 568, 1149, 1915, 2239, 1087, 3040, 935, 1720, 1562, 139],
[607, 2205, 1165, 535, 1987, 2768, 2696, 3197, 1435, 2405, 88, 919, 2087, 1426, 2285, 2705, 2061, 620, 176, 1481, 2653, 1231, 3007, 1679, 1172, 209, 682, 3254, 118, 272, 1751, 2843, 2706, 1229, 3072, 442, 364, 1148, 1240, 1159, 1924, 1797, 266, 1967, 464, 2058, 712, 711, 3231, 1476, 1509, 1240, 1097, 1483, 1814, 2360, 797, 1204, 10, 3184, 2085, 2110, 1238, 2570, 2151, 1553, 2796, 2378, 606, 1974, 2380, 334, 2562, 846, 581, 2588, 85, 1957, 2392, 1270, 1319, 2175, 1335, 1388, 2066, 1459, 1225, 231, 883, 636, 2465, 1757, 2869, 2989, 1844, 2453, 174, 2735, 960, 3092, 1892, 1581, 2203, 1849, 760, 486, 1781, 324, 1399, 1515, 1252, 3060, 3171, 2483, 3214, 2381, 3245, 673, 300, 2373, 641, 1877, 1933, 1040, 2106, 2787, 729, 2182, 1399, 2782, 1603, 651, 2753, 1199, 563, 1160, 3327, 1613, 2774, 929, 750, 2673, 224, 1304, 1344, 1447, 3078, 807, 2259, 3128, 690, 2352, 390, 2291, 247, 3002, 2703, 2380, 1648, 712, 1004, 181, 725, 1689, 1460, 1599, 320, 105, 1158, 3174, 1670, 2567, 1327, 1997, 2759, 1048, 2583, 2, 1594, 2143, 2779, 514, 263, 1083, 2990, 1320, 857, 320, 823, 3180, 863, 1403, 1455, 1183, 359, 1238, 881, 2343, 2934, 2977, 1768, 1878, 1486, 1744, 1995, 1156, 1071, 2892, 347, 69, 3113, 1485, 1068, 34, 175, 2608, 1207, 2821, 2819, 266, 2754, 2746, 2543, 2045, 3263, 1163, 2036, 1822, 1520, 821, 2146, 1432, 2671, 2500, 2942, 629, 1701, 1012, 1352, 2367, 1684, 3211, 641, 1344, 3014, 2212, 3179, 2455, 2922, 65, 2953, 2558, 1974, 463, 1995, 2380],
[1770, 3266, 3043, 128, 261, 2123, 2318, 1679, 2312, 2908, 1415, 2106, 952, 231, 1318, 2672, 2033, 2343, 2062, 1271, 2885, 2749, 2830, 1397, 1458, 619, 156, 3146, 13, 712, 2290, 2997, 2389, 285, 2680, 215, 1442, 237, 311, 281, 2575, 1402, 734, 3001, 1319, 279, 1769, 2017, 1170, 2232, 2479, 719, 2499, 2068, 2674, 2293, 1093, 2012, 2581, 2347, 2686, 625, 2527, 1482, 2950, 3198, 1910, 743, 1169, 1634, 1515, 3039, 2747, 2298, 1090, 1486, 789, 1648, 2771, 2658, 3058, 673, 3189, 1781, 2653, 106, 71, 1122, 2394, 3152, 1859, 3062, 157, 1835, 1027, 1134, 2264, 3036, 2598, 2207, 781, 40, 1023, 1027, 2254, 2111, 2079, 2093, 2120, 2697, 595, 3042, 1497, 465, 1059, 82, 256, 412, 2995, 1587, 368, 2826, 2505, 2406, 1566, 2634, 2034, 1682, 2483, 1108, 651, 1706, 3294, 3012, 3213, 1568, 1147, 650, 1416, 2066, 43, 2743, 396, 2903, 2214, 3254, 639, 113, 1157, 84, 60, 2678, 357, 720, 2255, 427, 847, 3204, 268, 737, 2590, 1831, 2037, 2516, 2417, 2553, 1542, 2758, 2190, 962, 3068, 2659, 2086, 3133, 1740, 2634, 180, 1791, 930, 1437, 1946, 923, 2351, 2992, 293, 2512, 1552, 2326, 2340, 539, 1345, 1565, 1101, 1365, 3161, 2904, 382, 1654, 814, 2694, 17, 1715, 1013, 901, 569, 2283, 2331, 1325, 1572, 535, 2094, 991, 1320, 228, 884, 135, 2421, 97, 1859, 3246, 3280, 2695, 2668, 2268, 1157, 2547, 2436, 385, 805, 801, 944, 2865, 1279, 1857, 1461, 1916, 2123, 495, 1284, 1453, 1985, 2046, 1624, 3183, 2364, 30, 1537, 1862, 2739, 80, 2579, 1215, 2397, 2192, 932, 2914],
[1604, 907, 2780, 2896, 1440, 1196, 865, 2226, 1719, 2596, 1431, 1360, 2267, 2487, 547, 1929, 1366, 1922, 1848, 2866, 1071, 2029, 2971, 2938, 92, 1243, 2389, 1985, 1817, 3303, 1704, 2386, 124, 1364, 2576, 727, 450, 944, 1975, 793, 436, 3138, 2370, 811, 330, 27, 977, 2684, 509, 2572, 1129, 656, 2651, 3175, 2299, 2138, 1874, 1231, 1038, 2930, 954, 324, 1412, 3221, 578, 2157, 157, 2462, 147, 835, 1855, 1831, 3277, 3186, 2064, 3310, 2081, 1046, 1255, 2715, 784, 3111, 821, 2619, 161, 2911, 2020, 427, 1280, 1918, 582, 2287, 3104, 1504, 2902, 1566, 1491, 1947, 1901, 3135, 3252, 3142, 8, 1941, 457, 3045, 2681, 2888, 2211, 816, 624, 432, 1698, 64, 2915, 916, 744, 394, 1448, 1090, 2144, 1006, 813, 692, 987, 2205, 1951, 3121, 1438, 671, 1765, 2188, 2533, 246, 3109, 2501, 2362, 3007, 590, 2924, 2032, 2371, 2796, 3178, 442, 665, 1942, 2701, 787, 1384, 1107, 1575, 157, 1914, 2380, 3203, 890, 1299, 2312, 1837, 2649, 1035, 349, 2949, 342, 313, 1645, 1191, 415, 521, 2850, 1227, 1525, 2183, 1291, 2753, 2684, 3300, 1842, 1332, 984, 2275, 98, 3213, 956, 2387, 2654, 3212, 1764, 2884, 907, 584, 3036, 2211, 314, 465, 1722, 397, 2501, 2477, 337, 1110, 2683, 3042, 1210, 1275, 2964, 867, 692, 1958, 2356, 1419, 1437, 541, 2149, 2496, 1907, 477, 2210, 1782, 1923, 2141, 1793, 734, 1486, 3237, 2369, 72, 892, 893, 922, 179, 2550, 3256, 1785, 781, 3317, 3235, 2821, 3205, 1024, 3101, 913, 856, 2667, 3290, 3034, 1088, 1053, 1942, 1973, 769, 1307, 895, 2929, 2976]]
u = NTTInverse(BHat * rHat) + e1: [[3070, 1402, 2568, 1534, 2888, 2553, 885, 3019, 1058, 2038, 994, 872, 2394, 1510, 2544, 2102, 688, 51, 1823, 3031, 2676, 2707, 2637, 1256, 3208, 2845, 1051, 1172, 635, 530, 1794, 748, 1515, 287, 2643, 2601, 3062, 2961, 1264, 816, 389, 192, 2629, 1172, 974, 1501, 1814, 1302, 1482, 549, 2909, 1002, 1315, 869, 1851, 2329, 1080, 1717, 2973, 2064, 1648, 1337, 3029, 1540, 145, 242, 1749, 559, 2441, 1804, 2459, 51, 2613, 1892, 1190, 2545, 2409, 1360, 1715, 3220, 368, 637, 965, 683, 231, 375, 1577, 1223, 248, 1213, 1332, 599, 997, 233, 1284, 325, 3147, 2356, 641, 765, 19, 2276, 2554, 3122, 145, 2824, 2052, 2637, 2687, 2320, 5, 2552, 2386, 903, 2438, 1119, 3145, 2934, 57, 487, 2845, 2641, 2949, 181, 2455, 2680, 390, 535, 55, 3226, 1640, 2901, 566, 2388, 765, 2374, 1469, 443, 1303, 1544, 98, 70, 2845, 575, 322, 2057, 1843, 2345, 3185, 1016, 265, 673, 958, 571, 2766, 693, 2210, 1851, 1091, 2915, 502, 164, 1522, 2167, 2704, 1426, 966, 269, 1124, 1629, 3155, 1364, 1959, 784, 63, 2078, 552, 305, 3023, 1789, 438, 1106, 1757, 18, 1650, 3175, 3066, 923, 1913, 2002, 2755, 1086, 1953, 1946, 354, 1959, 417, 2790, 56, 1737, 2303, 450, 3115, 14, 2887, 1923, 2868, 2200, 1208, 2100, 309, 2432, 3084, 1564, 1887, 3159, 2686, 1239, 1242, 2119, 1375, 330, 1968, 1013, 3003, 2341, 1980, 2090, 3239, 925, 3011, 842, 2467, 752, 3188, 1128, 366, 2026, 1771, 2850, 3172, 964, 1213, 3028, 1349, 304, 567, 1147, 1916, 2237, 1088, 3041, 935, 1720, 1562, 140],
[607, 2207, 1164, 535, 1988, 2767, 2696, 3197, 1435, 2404, 89, 919, 2087, 1426, 2284, 2705, 2063, 618, 175, 1481, 2654, 1231, 3008, 1679, 1171, 210, 681, 3253, 117, 272, 1751, 2843, 2705, 1228, 3071, 443, 363, 1149, 1240, 1157, 1925, 1796, 268, 1966, 464, 2059, 712, 709, 3231, 1475, 1509, 1240, 1096, 1482, 1812, 2360, 795, 1204, 9, 3185, 2085, 2110, 1237, 2569, 2152, 1555, 2797, 2377, 606, 1973, 2379, 335, 2561, 845, 581, 2589, 85, 1956, 2392, 1271, 1320, 2176, 1335, 1388, 2064, 1460, 1226, 231, 884, 635, 2467, 1756, 2868, 2988, 1842, 2455, 173, 2736, 960, 3091, 1891, 1581, 2201, 1849, 759, 487, 1782, 326, 1399, 1516, 1251, 3060, 3171, 2483, 3215, 2380, 3246, 673, 300, 2373, 640, 1877, 1933, 1039, 2107, 2788, 729, 2183, 1398, 2782, 1602, 652, 2751, 1200, 563, 1161, 3327, 1613, 2775, 930, 751, 2672, 225, 1302, 1346, 1447, 3079, 806, 2257, 3129, 689, 2354, 392, 2292, 247, 3003, 2701, 2380, 1648, 712, 1003, 180, 725, 1690, 1461, 1600, 319, 104, 1159, 3175, 1671, 2566, 1326, 1997, 2760, 1049, 2582, 2, 1594, 2143, 2781, 514, 263, 1085, 2990, 1319, 858, 320, 822, 3182, 863, 1401, 1455, 1185, 358, 1238, 881, 2343, 2935, 2976, 1770, 1879, 1487, 1743, 1994, 1154, 1070, 2892, 346, 70, 3115, 1485, 1068, 34, 176, 2606, 1206, 2821, 2818, 268, 2754, 2747, 2541, 2044, 3264, 1162, 2036, 1823, 1520, 820, 2145, 1431, 2669, 2502, 2942, 627, 1700, 1012, 1352, 2366, 1683, 3211, 643, 1343, 3012, 2213, 3179, 2454, 2923, 65, 2952, 2557, 1974, 464, 1995, 2381],
[1769, 3266, 3044, 127, 262, 2122, 2317, 1681, 2310, 2909, 1416, 2105, 952, 230, 1318, 2670, 2033, 2342, 2063, 1270, 2886, 2751, 2831, 1397, 1458, 618, 155, 3148, 11, 713, 2289, 2998, 2389, 285, 2682, 215, 1442, 238, 311, 282, 2574, 1402, 734, 3002, 1318, 277, 1770, 2017, 1170, 2231, 2478, 720, 2498, 2067, 2674, 2294, 1093, 2012, 2581, 2348, 2684, 625, 2526, 1483, 2950, 3198, 1910, 743, 1169, 1634, 1515, 3039, 2747, 2298, 1090, 1484, 788, 1647, 2771, 2660, 3058, 672, 3189, 1781, 2653, 106, 72, 1123, 2395, 3152, 1860, 3063, 158, 1835, 1026, 1134, 2263, 3038, 2599, 2207, 780, 40, 1023, 1027, 2254, 2110, 2078, 2093, 2119, 2698, 596, 3042, 1498, 463, 1057, 84, 257, 413, 2995, 1588, 367, 2825, 2506, 2407, 1565, 2635, 2034, 1681, 2485, 1107, 650, 1706, 3293, 3011, 3212, 1566, 1147, 649, 1417, 2066, 43, 2743, 394, 2903, 2215, 3252, 641, 113, 1158, 85, 60, 2677, 358, 719, 2255, 427, 846, 3205, 268, 738, 2589, 1830, 2038, 2517, 2417, 2553, 1542, 2757, 2189, 960, 3068, 2658, 2085, 3132, 1740, 2634, 182, 1792, 930, 1437, 1946, 923, 2352, 2994, 291, 2512, 1554, 2328, 2341, 539, 1344, 1566, 1100, 1365, 3162, 2905, 381, 1654, 814, 2694, 17, 1715, 1013, 902, 569, 2284, 2330, 1324, 1571, 535, 2093, 991, 1320, 229, 884, 133, 2422, 97, 1858, 3245, 3279, 2695, 2668, 2266, 1157, 2548, 2437, 387, 804, 803, 945, 2866, 1280, 1857, 1460, 1917, 2121, 494, 1284, 1451, 1987, 2047, 1625, 3182, 2364, 31, 1537, 1861, 2739, 79, 2581, 1213, 2396, 2191, 931, 2914],
[1603, 907, 2780, 2897, 1440, 1197, 866, 2225, 1719, 2596, 1432, 1359, 2268, 2488, 547, 1928, 1364, 1924, 1849, 2866, 1073, 2029, 2971, 2938, 93, 1243, 2389, 1985, 1818, 3304, 1703, 2386, 125, 1365, 2575, 728, 450, 943, 1977, 793, 436, 3137, 2369, 811, 329, 27, 976, 2684, 509, 2572, 1129, 656, 2651, 3175, 2298, 2136, 1873, 1232, 1040, 2930, 953, 323, 1413, 3222, 579, 2159, 156, 2464, 146, 835, 1855, 1830, 3279, 3184, 2064, 3310, 2082, 1047, 1256, 2714, 784, 3111, 821, 2619, 161, 2912, 2021, 429, 1281, 1918, 581, 2286, 3103, 1503, 2903, 1567, 1492, 1947, 1903, 3136, 3252, 3143, 7, 1942, 458, 3047, 2681, 2890, 2211, 815, 623, 432, 1697, 65, 2915, 918, 746, 394, 1447, 1091, 2145, 1006, 812, 693, 986, 2204, 1951, 3120, 1437, 670, 1763, 2189, 2534, 247, 3109, 2500, 2363, 3008, 590, 2925, 2032, 2373, 2796, 3179, 443, 665, 1942, 2699, 789, 1384, 1108, 1576, 158, 1914, 2380, 3203, 890, 1299, 2313, 1836, 2651, 1036, 348, 2949, 341, 312, 1643, 1192, 416, 521, 2848, 1227, 1525, 2185, 1290, 2751, 2684, 3301, 1843, 1330, 983, 2275, 98, 3213, 957, 2386, 2653, 3212, 1766, 2882, 908, 585, 3035, 2211, 312, 465, 1721, 396, 2502, 2477, 337, 1111, 2682, 3041, 1211, 1274, 2964, 866, 693, 1960, 2355, 1417, 1438, 539, 2149, 2495, 1908, 478, 2210, 1782, 1923, 2140, 1794, 734, 1484, 3238, 2369, 73, 892, 895, 922, 180, 2551, 3255, 1785, 782, 3318, 3235, 2822, 3206, 1022, 3099, 913, 855, 2668, 3290, 3034, 1088, 1055, 1940, 1975, 770, 1306, 897, 2929, 2977]]

mu: [1665, 0, 1665, 0, 0, 0, 0, 0, 1665, 0, 0, 1665, 0, 0, 1665, 1665, 0, 0, 0, 1665, 1665, 0, 1665, 0, 0, 0, 1665, 1665, 0, 1665, 1665, 1665, 0, 1665, 1665, 0, 0, 1665, 0, 0, 0, 1665, 1665, 0, 1665, 0, 1665, 0, 1665, 1665, 0, 1665, 1665, 0, 0, 0, 1665, 0, 1665, 1665, 0, 1665, 1665, 0, 0, 0, 0, 1665, 1665, 1665, 0, 1665, 0, 0, 0, 1665, 1665, 0, 0, 0, 0, 0, 1665, 0, 1665, 1665, 1665, 1665, 0, 0, 0, 1665, 1665, 1665, 0, 1665, 1665, 1665, 0, 1665, 0, 0, 1665, 1665, 0, 1665, 1665, 1665, 0, 1665, 0, 0, 0, 0, 0, 1665, 0, 1665, 0, 0, 1665, 0, 0, 1665, 1665, 0, 0, 1665, 0, 1665, 1665, 1665, 0, 0, 0, 0, 0, 0, 1665, 0, 1665, 1665, 1665, 0, 0, 0, 1665, 0, 0, 0, 0, 1665, 1665, 1665, 1665, 0, 1665, 0, 0, 0, 0, 0, 0, 1665, 1665, 0, 1665, 0, 1665, 1665, 1665, 1665, 1665, 1665, 1665, 0, 0, 0, 1665, 1665, 0, 1665, 1665, 1665, 0, 0, 0, 1665, 1665, 1665, 0, 0, 1665, 0, 0, 0, 0, 1665, 0, 1665, 0, 0, 0, 1665, 0, 1665, 0, 0, 1665, 1665, 0, 1665, 0, 0, 1665, 0, 1665, 1665, 0, 1665, 1665, 1665, 0, 1665, 1665, 1665, 1665, 1665, 0, 0, 1665, 0, 1665, 0, 0, 1665, 1665, 1665, 1665, 1665, 0, 0, 1665, 0, 0, 1665, 1665, 1665, 0, 0, 0, 1665, 1665, 1665, 1665, 0]
tHat^T * rHat: [2521, 1369, 68, 1528, 885, 2690, 1603, 1010, 2439, 2475, 3038, 2950, 2802, 515, 997, 2224, 265, 2892, 1640, 1056, 2648, 2894, 761, 3110, 1444, 809, 1776, 153, 1273, 2927, 1206, 474, 1024, 1319, 709, 1223, 372, 1046, 702, 2886, 1740, 1983, 3267, 3286, 2119, 119, 2873, 2020, 2698, 873, 388, 2392, 1860, 1105, 1484, 296, 2039, 103, 2512, 3108, 1212, 476, 1874, 422, 2025, 1328, 59, 2041, 835, 2678, 1733, 2812, 1648, 1426, 420, 1770, 2865, 218, 3125, 3324, 2568, 66, 2746, 1487, 2559, 2516, 2680, 3000, 3225, 1933, 2058, 565, 2699, 2311, 436, 989, 1998, 455, 2658, 3143, 1628, 1347, 400, 1533, 526, 2834, 337, 1605, 2508, 2211, 2642, 727, 600, 2363, 1027, 2666, 1051, 592, 1384, 1563, 1353, 2589, 3316, 2491, 3246, 1824, 487, 1599, 1557, 2240, 2645, 601, 78, 1153, 2842, 2609, 2477, 914, 2910, 1203, 795, 1324, 1369, 1941, 350, 3231, 1514, 2083, 1753, 2156, 2885, 2080, 532, 2189, 1530, 1072, 3173, 1407, 2806, 2507, 3309, 1225, 1431, 728, 1562, 183, 1475, 2509, 3181, 3023, 632, 1610, 630, 2779, 1042, 1494, 698, 2106, 2687, 63, 1288, 1777, 1555, 1383, 2064, 1961, 2394, 689, 3249, 500, 656, 2249, 2442, 331, 2729, 2280, 1736, 111, 1669, 1719, 1198, 1197, 2329, 1953, 1931, 2421, 856, 2272, 2114, 412, 597, 2752, 2077, 1388, 2382, 207, 2363, 3299, 3038, 1663, 2261, 3147, 2806, 2432, 2666, 398, 2874, 1470, 2710, 98, 186, 2820, 1241, 3283, 601, 85, 37, 2846, 627, 1262, 238, 816, 1033, 2485, 602, 816, 1408, 2509, 1723, 511, 2256, 1595, 2550, 654, 1254, 780]
NTTInverse(tHat^T * rHat): [1412, 1558, 3294, 2350, 2981, 2714, 1658, 564, 2631, 244, 2252, 431, 1955, 3100, 2202, 38, 3093, 2809, 1095, 2136, 2259, 15, 1706, 78, 857, 458, 1099, 1767, 2837, 522, 1536, 1544, 1508, 3242, 1050, 3077, 1549, 2401, 574, 1124, 1293, 3307, 1429, 1156, 1855, 3243, 3173, 2230, 1721, 1805, 2457, 640, 482, 1742, 937, 1105, 1233, 572, 2803, 2059, 1081, 1098, 1681, 1665, 2498, 2846, 536, 2773, 241, 2365, 300, 3112, 1536, 788, 2196, 831, 1930, 406, 2239, 656, 1550, 929, 2924, 195, 622, 43, 77, 2653, 751, 1284, 1538, 25, 1757, 1150, 2694, 811, 2783, 3181, 2082, 1504, 964, 324, 2392, 2445, 1646, 2211, 1253, 1008, 3252, 301, 128, 3261, 1039, 2807, 1094, 2214, 590, 1086, 2116, 1952, 1537, 2226, 3127, 361, 808, 2908, 268, 2253, 1765, 1000, 2632, 3179, 2911, 2830, 2241, 2390, 2276, 2450, 2395, 2700, 1280, 948, 1321, 1284, 1198, 1808, 1192, 1179, 1561, 1365, 1414, 338, 718, 3056, 1338, 281, 2380, 2232, 2846, 2442, 548, 141, 2880, 2664, 1288, 3179, 2325, 647, 2925, 747, 2703, 1598, 1759, 3080, 1446, 2048, 980, 2228, 79, 2430, 1390, 3251, 451, 422, 2767, 700, 3242, 3123, 2623, 3128, 2298, 2766, 2336, 2637, 380, 1826, 783, 1534, 2157, 3240, 2149, 2461, 3317, 623, 1529, 2295, 368, 326, 3064, 2141, 2387, 775, 1550, 3068, 2961, 1202, 1899, 2383, 652, 1455, 2205, 1921, 322, 1857, 784, 1673, 3138, 465, 1388, 1943, 110, 2634, 1909, 3214, 2062, 276, 1304, 1535, 358, 593, 2391, 1968, 108, 449, 1268, 1701, 833, 2384, 3020, 2241, 69, 2209, 2960, 1240, 3207, 2501]
e2 + mu: [1665, 3327, 1666, 3328, 1, 2, 0, 1, 1665, 0, 0, 1663, 0, 1, 1665, 1664, 1, 2, 0, 1665, 1665, 1, 1665, 2, 1, 2, 1665, 1663, 2, 1664, 1663, 1667, 1, 1666, 1665, 0, 0, 1664, 0, 1, 3328, 1665, 1663, 1, 1666, 1, 1664, 3328, 1665, 1666, 3327, 1664, 1664, 3327, 0, 0, 1665, 0, 1665, 1664, 0, 1664, 1663, 1, 3328, 0, 2, 1666, 1664, 1665, 0, 1667, 0, 1, 0, 1665, 1666, 1, 0, 1, 0, 1, 1666, 0, 1667, 1664, 1665, 1665, 3328, 0, 2, 1664, 1664, 1665, 0, 1665, 1665, 1665, 1, 1667, 0, 0, 1666, 1663, 1, 1666, 1665, 1666, 3328, 1666, 0, 0, 0, 0, 3327, 1666, 1, 1665, 0, 0, 1665, 3328, 0, 1664, 1665, 0, 0, 1665, 1, 1665, 1666, 1664, 3327, 1, 0, 2, 3328, 1, 1666, 0, 1666, 1665, 1664, 1, 3328, 1, 1665, 3328, 1, 1, 2, 1664, 1666, 1665, 1666, 3328, 1666, 3328, 0, 1, 3328, 1, 1, 1665, 1666, 3328, 1665, 0, 1665, 1665, 1666, 1664, 1666, 1664, 1666, 3328, 3328, 3328, 1665, 1665, 3328, 1666, 1664, 1664, 1, 0, 3328, 1667, 1665, 1667, 3328, 0, 1665, 0, 3327, 2, 3328, 1664, 3327, 1665, 0, 0, 3328, 1665, 3328, 1664, 0, 1, 1664, 1664, 0, 1663, 0, 3328, 1664, 3328, 1665, 1664, 1, 1665, 1666, 1664, 0, 1664, 1664, 1666, 1665, 1664, 0, 3327, 1664, 3328, 1664, 3328, 3328, 1665, 1665, 1665, 1666, 1665, 2, 1, 1665, 0, 0, 1666, 1665, 1666, 3327, 3328, 1, 1666, 1664, 1663, 1666, 0]
v = NTTInverse(tHat^T * rHat) + e2 + mu: [3077, 1556, 1631, 2349, 2982, 2716, 1658, 565, 967, 244, 2252, 2094, 1955, 3101, 538, 1702, 3094, 2811, 1095, 472, 595, 16, 42, 80, 858, 460, 2764, 101, 2839, 2186, 3199, 3211, 1509, 1579, 2715, 3077, 1549, 736, 574, 1125, 1292, 1643, 3092, 1157, 192, 3244, 1508, 2229, 57, 142, 2455, 2304, 2146, 1740, 937, 1105, 2898, 572, 1139, 394, 1081, 2762, 15, 1666, 2497, 2846, 538, 1110, 1905, 701, 300, 1450, 1536, 789, 2196, 2496, 267, 407, 2239, 657, 1550, 930, 1261, 195, 2289, 1707, 1742, 989, 750, 1284, 1540, 1689, 92, 2815, 2694, 2476, 1119, 1517, 2083, 3171, 964, 324, 729, 779, 1647, 548, 2918, 2674, 3251, 1967, 128, 3261, 1039, 2807, 1092, 551, 591, 2751, 2116, 1952, 3202, 2225, 3127, 2025, 2473, 2908, 268, 589, 1766, 2665, 969, 1514, 2909, 2831, 2241, 2392, 2275, 2451, 732, 2700, 2946, 2613, 2985, 1285, 1197, 1809, 2857, 1178, 1562, 1366, 1416, 2002, 2384, 1392, 3004, 280, 717, 2231, 2846, 2443, 547, 142, 2881, 1000, 2954, 3178, 661, 647, 1261, 2412, 1040, 3262, 96, 1415, 3112, 2047, 979, 2227, 1744, 766, 1389, 1588, 2115, 2086, 2768, 700, 3241, 1461, 959, 1466, 2297, 2766, 672, 2637, 378, 1828, 782, 3198, 2155, 1576, 2149, 2461, 3316, 2288, 1528, 630, 368, 327, 1399, 476, 2387, 2438, 1550, 3067, 1296, 1201, 235, 718, 653, 3120, 542, 256, 322, 192, 2448, 10, 1474, 2129, 1388, 1941, 1774, 2633, 244, 3213, 2061, 1941, 2969, 3200, 2024, 2258, 2393, 1969, 1773, 449, 1268, 38, 2498, 721, 3018, 2240, 70, 546, 1295, 2903, 1544, 2501]

KBar: 62C86B23A76F753CD161DAE4D4B44E900BAACE3D758C356D534FBFAFF6BDCCFA
cPrime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

Accepted, returning KPrime
