TwoClassGroupRank := AssociativeArray();
TrueCurveRank := AssociativeArray();
FalseCurveRankLowerBound := AssociativeArray();
FalseCurveRankUpperBound := AssociativeArray();
WashingtonsBound := AssociativeArray();
TwoClassGroupRank[0] := [ 1, 2, 4, 7, 8, 10, 13, 14, 16, 19, 20, 22, 28, 31, 32, 34, 35, 37, 38, 40, 43, 46, 47, 49, 50, 52, 53, 56, 58, 61, 62, 65, 68, 70, 73, 74, 76, 77, 79, 80, 82, 86, 88, 89, 91, 92, 94, 97, 98, 104, 106, 107, 109, 110, 112, 115, 116, 119, 121, 122, 124, 125, 128, 131, 134, 140, 145, 148, 155, 158, 160, 161, 164, 167, 172, 173, 175, 178, 182, 185, 190, 193, 196, 197, 199, 200, 202, 203, 205, 206, 208, 209, 211, 212, 214, 215, 217, 221, 224, 226, 232, 233, 238, 239, 241, 244, 245, 247, 251, 253, 254, 256, 257, 259, 260, 265, 266, 268, 272, 278, 281, 289, 293, 295, 296, 298, 302, 304, 314, 316, 317, 319, 320, 322, 323, 325, 326, 328, 331, 337, 338, 340, 343, 344, 346, 349, 353, 355, 361, 362, 364, 367, 368, 373, 376, 379, 380, 383, 385, 386, 388, 392, 394, 401, 403, 409, 410, 413, 415, 416, 421, 422, 424, 425, 430, 431, 436, 437, 443, 445, 448, 451, 452, 455, 463, 464, 466, 467, 469, 476, 478, 481, 484, 485, 487, 488, 490, 493, 497, 506, 508, 509, 518, 520, 521, 526, 527, 529, 530, 536, 539, 541, 550, 551, 553, 554, 562, 563, 566, 568, 569, 572, 574, 581, 586, 587, 589, 590, 592, 595, 596, 598, 599, 601, 604, 605, 608, 610, 613, 620, 622, 623, 628, 631, 632, 634, 635, 638, 640, 643, 647, 650, 652, 656, 658, 659, 661, 662, 664, 665, 667, 670, 673, 674, 676, 677, 679, 680, 685, 686, 688, 689, 692, 694, 695, 697, 700, 703, 706, 707, 713, 715, 718, 721, 725, 728, 730, 731, 733, 736, 739, 743, 746, 749, 751, 752, 754, 755, 757, 760, 761, 763, 764, 766, 767, 769, 770, 775, 778, 779, 781, 782, 785, 787, 788, 790, 797, 799, 802, 811, 812, 814, 817, 818, 821, 823, 826, 827, 829, 833, 836, 841, 847, 850, 851, 853, 854, 857, 859, 860, 862, 863, 865, 866, 868, 869, 871, 872, 877, 881, 883, 884, 886, 889, 890, 893, 896, 898, 901, 902, 905, 907, 908, 910, 913, 916, 917, 919, 920, 925, 929, 931, 932, 935, 940, 946, 947, 949, 950, 952, 953, 955, 965, 967, 968, 973, 974, 976, 979, 980, 986, 988, 994, 997, 998, 1000, 1001, 1004, 1006, 1007, 1009, 1010, 1013, 1015, 1018, 1019, 1022, 1024, 1031, 1036, 1042, 1045, 1046, 1048, 1051, 1052, 1060, 1061, 1063, 1064, 1067, 1069, 1072, 1073, 1079, 1082, 1084, 1087, 1088, 1091, 1093, 1094, 1097, 1099, 1100, 1105, 1106, 1108, 1109, 1111, 1115, 1117, 1120, 1123, 1124, 1126, 1136, 1138, 1139, 1141, 1144, 1148, 1151, 1153, 1156, 1157, 1162, 1169, 1171, 1172, 1174, 1175, 1178, 1183, 1190, 1195, 1196, 1202, 1204, 1205, 1211, 1213, 1219, 1222, 1223, 1225, 1228, 1231, 1234, 1238, 1240, 1241, 1244, 1246, 1250, 1256, 1262, 1264, 1267, 1268, 1271, 1273, 1274, 1276, 1277, 1280, 1282, 1285, 1286, 1288, 1289, 1291, 1292, 1294, 1295, 1297, 1300, 1303, 1304, 1306, 1307, 1309, 1313, 1318, 1319, 1321, 1322, 1324, 1325, 1327, 1330, 1333, 1337, 1340, 1342, 1343, 1345, 1346, 1348, 1349, 1351, 1354, 1357, 1360, 1361, 1363, 1366, 1372, 1373, 1375, 1378, 1379, 1381, 1388, 1391, 1396, 1399, 1402, 1405, 1412, 1415, 1417, 1420, 1423, 1424, 1429, 1430, 1432, 1436, 1438, 1439, 1444, 1447, 1448, 1454, 1456, 1457, 1460, 1465, 1468, 1469, 1471, 1472, 1477, 1478, 1480, 1481, 1483, 1486, 1487, 1489, 1492, 1493, 1495, 1496, 1498, 1504, 1507, 1510, 1513, 1514, 1516, 1517, 1519, 1520, 1522, 1523, 1525, 1526, 1528, 1529, 1531, 1532, 1534, 1535, 1537, 1538, 1540, 1543, 1546, 1549, 1552, 1553, 1555, 1558, 1559, 1562, 1564, 1567, 1568, 1571, 1574, 1576, 1577, 1580, 1583, 1585, 1588, 1591, 1592, 1595, 1597, 1600, 1601, 1603, 1604, 1610, 1615, 1616, 1625, 1628, 1630, 1631, 1636, 1640, 1645, 1649, 1655, 1660, 1663, 1664, 1666, 1669, 1670, 1672, 1675, 1676, 1679, 1681, 1682, 1684, 1685, 1687, 1691, 1696, 1699, 1700, 1703, 1708, 1714, 1715, 1721, 1723, 1726, 1727, 1730, 1732, 1738, 1741, 1742, 1745, 1748, 1754, 1757, 1762, 1763, 1766, 1768, 1772, 1774, 1777, 1778, 1780, 1781, 1783, 1786, 1787, 1789, 1792, 1793, 1795, 1796, 1799, 1807, 1808, 1810, 1813, 1814, 1816, 1820, 1822, 1823, 1825, 1826, 1828, 1829, 1832, 1834, 1835, 1843, 1846, 1847, 1850, 1858, 1862, 1864, 1868, 1870, 1871, 1873, 1876, 1877, 1879, 1880, 1891, 1892, 1894, 1895, 1898, 1906, 1912, 1913, 1915, 1918, 1922, 1928, 1930, 1934, 1936, 1939, 1940, 1942, 1946, 1948, 1949, 1951, 1954, 1955, 1960, 1961, 1963, 1966, 1967, 1970, 1972, 1975, 1976, 1982, 1987, 1988, 1990, 1991, 1993, 1994, 1996, 1999, 2002, 2005, 2006, 2008, 2017, 2018, 2021, 2024, 2029, 2030, 2032, 2033, 2035, 2036, 2038, 2039, 2051, 2053, 2054, 2056, 2057, 2065, 2066, 2068, 2069, 2071, 2075, 2077, 2078, 2080, 2086, 2089, 2092, 2093, 2095, 2096, 2098, 2102, 2104, 2107, 2108, 2116, 2117, 2119, 2122, 2123, 2126, 2131, 2134, 2135, 2137, 2138, 2140, 2141, 2143, 2147, 2149, 2150, 2152, 2155, 2156, 2158, 2162, 2164, 2167, 2168, 2170, 2171, 2174, 2177, 2179, 2183, 2185, 2186, 2188, 2191, 2192, 2194, 2198, 2200, 2203, 2206, 2207, 2209, 2212, 2215, 2216, 2218, 2219, 2221, 2224, 2225, 2228, 2230, 2231, 2233, 2237, 2239, 2242, 2248, 2249, 2252, 2255, 2260, 2261, 2264, 2267, 2270, 2275, 2279, 2282, 2284, 2285, 2287, 2288, 2290, 2291, 2293, 2294, 2303, 2305, 2306, 2309, 2311, 2312, 2314, 2315, 2317, 2324, 2326, 2327, 2329, 2332, 2335, 2336, 2341, 2342, 2345, 2347, 2348, 2350, 2351, 2353, 2354, 2356, 2359, 2360, 2362, 2363, 2366, 2369, 2375, 2377, 2378, 2381, 2383, 2386, 2387, 2392, 2398, 2399, 2401, 2404, 2405, 2408, 2411, 2414, 2417, 2422, 2423, 2425, 2428, 2429, 2434, 2435, 2440, 2441, 2443, 2446, 2447, 2449, 2456, 2458, 2461, 2464, 2468, 2470, 2471, 2476, 2477, 2480, 2483, 2485, 2488, 2494, 2495, 2500, 2503, 2509, 2510, 2512, 2515, 2518, 2525, 2527, 2530, 2533, 2534, 2536, 2539, 2542, 2543, 2545, 2548, 2549, 2554, 2558, 2560, 2561, 2564, 2566, 2567, 2569, 2570, 2575, 2576, 2578, 2582, 2584, 2585, 2587, 2590, 2591, 2593, 2594, 2596, 2597, 2599, 2600, 2603, 2608, 2611, 2615, 2617, 2621, 2623, 2627, 2629, 2632, 2636, 2639, 2641, 2642, 2647, 2653, 2654, 2656, 2657, 2659, 2666, 2668, 2671, 2672, 2674, 2675, 2677, 2678, 2680, 2683, 2684, 2686, 2690, 2693, 2695, 2696, 2699, 2701, 2702, 2704, 2705, 2707, 2708, 2711, 2714, 2716, 2722, 2723, 2725, 2729, 2732, 2734, 2735, 2737, 2738, 2740, 2741, 2743, 2744, 2746, 2747, 2750, 2755, 2756, 2758, 2765, 2767, 2768, 2771, 2773, 2776, 2777, 2779, 2780, 2782, 2783, 2786, 2788, 2792, 2795, 2797, 2800, 2801, 2806, 2809, 2813, 2816, 2818, 2822, 2825, 2828, 2830, 2831, 2833, 2839, 2840, 2842, 2843, 2845, 2846, 2849, 2851, 2852, 2854, 2858, 2860, 2861, 2863, 2864, 2866, 2867, 2872, 2873, 2875, 2876, 2878, 2879, 2882, 2885, 2887, 2888, 2893, 2900, 2903, 2905, 2906, 2911, 2912, 2914, 2915, 2918, 2923, 2924, 2929, 2930, 2933, 2935, 2938, 2941, 2944, 2947, 2948, 2950, 2953, 2956, 2957, 2959, 2960, 2962, 2965, 2966, 2968, 2971, 2972, 2975, 2977, 2978, 2983, 2984, 2987, 2993, 2996, 2999, 3002, 3005, 3007, 3008, 3010, 3011, 3013, 3014, 3019, 3022, 3025, 3031, 3038, 3046, 3049, 3050, 3055, 3056, 3058, 3059, 3062, 3064, 3065, 3067, 3073, 3074, 3077, 3080, 3082, 3083, 3088, 3089, 3091, 3094, 3097, 3098, 3100, 3107, 3109, 3115, 3116, 3121, 3130, 3131, 3133, 3136, 3139, 3143, 3145, 3146, 3148, 3151, 3152, 3154, 3155, 3158, 3160, 3161, 3163, 3166, 3167, 3169, 3172, 3173, 3176, 3178, 3179, 3181, 3184, 3188, 3191, 3193, 3196, 3197, 3199, 3200, 3202, 3205, 3206, 3209, 3211, 3212, 3214, 3220, 3221, 3223, 3229, 3235, 3236, 3238, 3242, 3244, 3247, 3251, 3262, 3266, 3268, 3269, 3271, 3272, 3278, 3280, 3281, 3283, 3284, 3286, 3289, 3296, 3298, 3301, 3302, 3310, 3313, 3316, 3317, 3319, 3320, 3325, 3331, 3334, 3335, 3340, 3341, 3344, 3346, 3349, 3350, 3353, 3355, 3356, 3358, 3361, 3365, 3367, 3370, 3374, 3376, 3379, 3380, 3382, 3383, 3385, 3389, 3391, 3395, 3398, 3401, 3406, 3407, 3409, 3410, 3412, 3413, 3415, 3416, 3419, 3421, 3424, 3425, 3427, 3431, 3436, 3439, 3442, 3445, 3448, 3451, 3454, 3457, 3463, 3469, 3470, 3472, 3473, 3475, 3476, 3479, 3482, 3488, 3490, 3491, 3493, 3494, 3496, 3497, 3499, 3500, 3502, 3503, 3509, 3512, 3514, 3515, 3517, 3518, 3523, 3524, 3527, 3529, 3530, 3538, 3539, 3541, 3545, 3548, 3550, 3551, 3554, 3559, 3562, 3563, 3565, 3566, 3568, 3574, 3575, 3577, 3580, 3581, 3583, 3584, 3587, 3590, 3592, 3595, 3596, 3610, 3613, 3617, 3620, 3622, 3626, 3628, 3629, 3635, 3638, 3640, 3643, 3644, 3650, 3655, 3656, 3661, 3662, 3665, 3668, 3670, 3673, 3682, 3688, 3692, 3694, 3701, 3703, 3704, 3706, 3718, 3719, 3721, 3722, 3724, 3727, 3728, 3733, 3737, 3739, 3740, 3745, 3748, 3751, 3752, 3758, 3761, 3767, 3776, 3785, 3787, 3788, 3790, 3791, 3794, 3796, 3799, 3800, 3802, 3803, 3811, 3815, 3821, 3824, 3826, 3829, 3830, 3832, 3833, 3835, 3836, 3838, 3841, 3842, 3844, 3850, 3851, 3854, 3856, 3857, 3859, 3860, 3865, 3866, 3868, 3871, 3874, 3875, 3877, 3880, 3881, 3883, 3886, 3887, 3889, 3893, 3896, 3898, 3905, 3907, 3908, 3910, 3913, 3914, 3916, 3919, 3920, 3923, 3929, 3932, 3937, 3940, 3943, 3944, 3946, 3947, 3955, 3958, 3962, 3964, 3968, 3970, 3971, 3973, 3976, 3977, 3979, 3989, 3992, 3995, 3998, 4000, 4003, 4004, 4006, 4012, 4013, 4016, 4019, 4021, 4022, 4028, 4030, 4031, 4033, 4034, 4037, 4042, 4043, 4045, 4048, 4049, 4051, 4052, 4054, 4055, 4057, 4060, 4063, 4064, 4066, 4069, 4070, 4075, 4076, 4078, 4079, 4081, 4082, 4084, 4085, 4087, 4090, 4091, 4093, 4094, 4099, 4100, 4102, 4103, 4109, 4111, 4115, 4118, 4120, 4126, 4127, 4129, 4133, 4135, 4138, 4141, 4142, 4145, 4148, 4150, 4151, 4160, 4162, 4166, 4169, 4172, 4174, 4180, 4181, 4184, 4186, 4187, 4189, 4193, 4198, 4202, 4205, 4207, 4208, 4210, 4213, 4216, 4217, 4222, 4223, 4226, 4231, 4234, 4235, 4237, 4238, 4240, 4247, 4249, 4250, 4252, 4253, 4258, 4259, 4261, 4265, 4267, 4273, 4276, 4277, 4279, 4282, 4283, 4286, 4288, 4289, 4294, 4301, 4303, 4306, 4312, 4315, 4318, 4319, 4321, 4322, 4333, 4334, 4337, 4339, 4342, 4343, 4345, 4346, 4348, 4351, 4352, 4357, 4363, 4364, 4367, 4372, 4373, 4376, 4378, 4379, 4381, 4382, 4385, 4387, 4388, 4390, 4391, 4393, 4397, 4400, 4403, 4405, 4406, 4408, 4409, 4411, 4412, 4417, 4420, 4421, 4424, 4427, 4429, 4430, 4432, 4433, 4438, 4439, 4441, 4442, 4445, 4450, 4453, 4454, 4457, 4459, 4463, 4466, 4469, 4472, 4474, 4487, 4490, 4492, 4493, 4496, 4498, 4502, 4505, 4507, 4510, 4514, 4517, 4519, 4520, 4523, 4525, 4529, 4531, 4535, 4538, 4541, 4546, 4547, 4552, 4553, 4556, 4558, 4564, 4567, 4573, 4576, 4579, 4580, 4583, 4586, 4588, 4589, 4597, 4600, 4601, 4606, 4607, 4610, 4612, 4613, 4615, 4616, 4618, 4621, 4622, 4627, 4628, 4630, 4634, 4636, 4637, 4646, 4648, 4649, 4654, 4655, 4658, 4664, 4667, 4672, 4673, 4679, 4681, 4684, 4688, 4691, 4697, 4699, 4700, 4702, 4711, 4712, 4714, 4717, 4718, 4720, 4721, 4726, 4727, 4729, 4730, 4732, 4742, 4744, 4750, 4756, 4759, 4760, 4763, 4769, 4771, 4774, 4775, 4778, 4780, 4783, 4784, 4786, 4787, 4789, 4792, 4799, 4802, 4804, 4811, 4813, 4817, 4819, 4820, 4822, 4823, 4826, 4828, 4829, 4831, 4834, 4837, 4841, 4846, 4850, 4853, 4855, 4858, 4861, 4862, 4867, 4868, 4870, 4876, 4880, 4882, 4885, 4886, 4889, 4891, 4894, 4895, 4898, 4903, 4904, 4907, 4909, 4910, 4912, 4915, 4916, 4922, 4927, 4930, 4934, 4937, 4939, 4942, 4943, 4946, 4949, 4952, 4958, 4960, 4963, 4964, 4970, 4973, 4975, 4976, 4979, 4981, 4982, 4987, 4991, 4994, 4996, 4997, 4999, 5000, 5006, 5011, 5012, 5017, 5018, 5020, 5023, 5026, 5029, 5035, 5041, 5042, 5044, 5045, 5048, 5051, 5054, 5056, 5057, 5059, 5062, 5065, 5066, 5068, 5069, 5071, 5072, 5075, 5080, 5081, 5084, 5087, 5095, 5098, 5102, 5104, 5105, 5111, 5113, 5114, 5117, 5119, 5122, 5125, 5126, 5128, 5132, 5134, 5135, 5138, 5143, 5144, 5152, 5153, 5155, 5162, 5167, 5171, 5173, 5174, 5180, 5182, 5188, 5192, 5194, 5195, 5198, 5203, 5209, 5210, 5212, 5213, 5216, 5218, 5225, 5227, 5228, 5231, 5239, 5240, 5242, 5243, 5245, 5246, 5252, 5254, 5257, 5260, 5263, 5266, 5267, 5269, 5270, 5272, 5273, 5275, 5278, 5285, 5288, 5290, 5293, 5296, 5299, 5300, 5302, 5306, 5311, 5312, 5314, 5315, 5323, 5324, 5329, 5330, 5332, 5335, 5341, 5342, 5344, 5353, 5354, 5356, 5357, 5359, 5360, 5362, 5363, 5368, 5369, 5372, 5377, 5384, 5389, 5392, 5393, 5398, 5399, 5401, 5402, 5404, 5410, 5419, 5420, 5422, 5426, 5428, 5429, 5437, 5438, 5440, 5443, 5447, 5449, 5453, 5455, 5458, 5459, 5464, 5468, 5470, 5471, 5473, 5476, 5477, 5482, 5483, 5485, 5492, 5494, 5497, 5498, 5501, 5503, 5506, 5509, 5510, 5518, 5519, 5521, 5522, 5528, 5533, 5537, 5540, 5543, 5545, 5548, 5551, 5552, 5554, 5557, 5560, 5561, 5564, 5566, 5575, 5581, 5582, 5584, 5587, 5588, 5590, 5593, 5594, 5596, 5597, 5599, 5600, 5603, 5606, 5608, 5611, 5612, 5614, 5617, 5618, 5620, 5621, 5623, 5624, 5630, 5632, 5633, 5635, 5636, 5638, 5641, 5642, 5644, 5648, 5651, 5657, 5659, 5662, 5663, 5665, 5666, 5668, 5669, 5672, 5675, 5680, 5683, 5686, 5690, 5695, 5698, 5699, 5702, 5710, 5711, 5716, 5717, 5719, 5720, 5722, 5728, 5729, 5731, 5734, 5744, 5746, 5747, 5749, 5752, 5753, 5755, 5756, 5758, 5759, 5761, 5762, 5764, 5765, 5770, 5771, 5776, 5777, 5779, 5780, 5782, 5786, 5788, 5789, 5791, 5795, 5797, 5798, 5801, 5803, 5804, 5806, 5807, 5821, 5827, 5828, 5830, 5831, 5833, 5839, 5842, 5845, 5848, 5849, 5851, 5852, 5854, 5855, 5858, 5860, 5861, 5863, 5864, 5866, 5867, 5869, 5873, 5875, 5879, 5882, 5884, 5887, 5890, 5891, 5896, 5897, 5900, 5902, 5903, 5905, 5906, 5908, 5909, 5911, 5914, 5915, 5923, 5926, 5927, 5933, 5935, 5936, 5944, 5945, 5947, 5950, 5951, 5957, 5959, 5960, 5963, 5965, 5968, 5969, 5971, 5972, 5974, 5975, 5977, 5984, 5986, 5987, 5989, 5990, 5993, 5996, 5998, 5999, 6001, 6011, 6013, 6014, 6016, 6020, 6022, 6025, 6031, 6034, 6035, 6037, 6040, 6044, 6046, 6047, 6053, 6055, 6056, 6059, 6061, 6062, 6067, 6070, 6076, 6079, 6080, 6082, 6086, 6091, 6092, 6094, 6095, 6100, 6101, 6106, 6109, 6110, 6113, 6116, 6121, 6125, 6131, 6134, 6136, 6137, 6142, 6146, 6148, 6151, 6152, 6157, 6158, 6160, 6163, 6164, 6167, 6170, 6173, 6175, 6176, 6178, 6181, 6185, 6187, 6188, 6191, 6194, 6197, 6199, 6200, 6202, 6206, 6208, 6212, 6220, 6224, 6226, 6227, 6229, 6230, 6235, 6236, 6238, 6242, 6244, 6245, 6247, 6251, 6253, 6260, 6262, 6263, 6265, 6268, 6272, 6275, 6278, 6281, 6284, 6286, 6290, 6292, 6293, 6295, 6296, 6298, 6299, 6301, 6302, 6307, 6310, 6311, 6314, 6317, 6320, 6322, 6323, 6325, 6328, 6329, 6331, 6332, 6334, 6337, 6340, 6346, 6347, 6349, 6350, 6355, 6356, 6365, 6367, 6370, 6374, 6376, 6377, 6379, 6380, 6382, 6385, 6386, 6388, 6391, 6392, 6394, 6400, 6401, 6403, 6404, 6407, 6412, 6413, 6415, 6416, 6418, 6419, 6422, 6425, 6430, 6431, 6433, 6436, 6437, 6440, 6445, 6448, 6449, 6451, 6452, 6454, 6455, 6457, 6458, 6461, 6464, 6469, 6470, 6476, 6479, 6484, 6485, 6491, 6493, 6494, 6496, 6499, 6503, 6505, 6506, 6508, 6511, 6517, 6520, 6521, 6523, 6524, 6526, 6527, 6532, 6536, 6538, 6539, 6542, 6544, 6545, 6547, 6548, 6550, 6551, 6553, 6554, 6556, 6559, 6560, 6565, 6566, 6569, 6572, 6574, 6575, 6577, 6578, 6581, 6583, 6584, 6592, 6601, 6604, 6610, 6613, 6617, 6619, 6622, 6623, 6626, 6628, 6629, 6631, 6632, 6634, 6637, 6644, 6650, 6653, 6659, 6662, 6664, 6668, 6670, 6673, 6674, 6676, 6677, 6680, 6686, 6688, 6689, 6694, 6697, 6703, 6704, 6706, 6709, 6713, 6716, 6719, 6721, 6722, 6725, 6731, 6733, 6734, 6736, 6739, 6740, 6742, 6743, 6745, 6751, 6752, 6757, 6758, 6760, 6761, 6764, 6766, 6769, 6772, 6773, 6775, 6776, 6779, 6782, 6784, 6785, 6787, 6790, 6791, 6793, 6794, 6796, 6800, 6802, 6806, 6808, 6811, 6814, 6817, 6820, 6821, 6823, 6824, 6829, 6830, 6833, 6836, 6838, 6839, 6842, 6844, 6847, 6848, 6850, 6853, 6856, 6857, 6859, 6862, 6868, 6869, 6874, 6875, 6877, 6884, 6890, 6896, 6899, 6902, 6904, 6907, 6913, 6916, 6919, 6923, 6925, 6928, 6929, 6935, 6937, 6938, 6941, 6943, 6946, 6949, 6952, 6953, 6956, 6962, 6964, 6967, 6971, 6973, 6974, 6976, 6980, 6983, 6985, 6986, 6988, 6989, 6994, 6997, 6998, 7000, 7003, 7004, 7006, 7007, 7010, 7015, 7016, 7021, 7024, 7025, 7027, 7034, 7037, 7039, 7042, 7043, 7045, 7046, 7049, 7051, 7052, 7054, 7057, 7058, 7067, 7070, 7072, 7073, 7076, 7078, 7082, 7087, 7090, 7093, 7094, 7099, 7100, 7102, 7103, 7105, 7106, 7108, 7111, 7114, 7115, 7117, 7118, 7120, 7121, 7123, 7124, 7126, 7127, 7129, 7132, 7135, 7142, 7144, 7145, 7150, 7151, 7154, 7157, 7162, 7166, 7168, 7171, 7172, 7174, 7175, 7178, 7180, 7181, 7183, 7184, 7187, 7189, 7190, 7192, 7196, 7199, 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TwoClassGroupRank[2] := [ 11, 17, 23, 25, 26, 29, 44, 55, 59, 64, 67, 71, 83, 85, 95, 101, 113, 118, 127, 130, 133, 136, 137, 142, 146, 149, 151, 163, 166, 169, 170, 176, 179, 181, 184, 187, 191, 194, 218, 220, 223, 227, 229, 230, 236, 242, 248, 262, 263, 274, 275, 277, 280, 283, 284, 287, 290, 292, 301, 305, 307, 308, 310, 311, 313, 329, 332, 334, 341, 350, 352, 358, 359, 365, 370, 371, 377, 382, 389, 391, 395, 400, 406, 407, 412, 418, 427, 428, 434, 440, 442, 449, 454, 457, 458, 460, 461, 470, 472, 475, 479, 491, 494, 496, 499, 500, 502, 503, 505, 511, 512, 514, 517, 523, 524, 532, 533, 535, 538, 542, 545, 547, 548, 556, 557, 559, 560, 571, 575, 578, 583, 584, 614, 616, 619, 625, 626, 637, 641, 644, 646, 649, 653, 655, 668, 671, 682, 683, 698, 701, 704, 709, 710, 712, 719, 722, 724, 734, 737, 745, 748, 758, 772, 773, 784, 791, 793, 794, 796, 800, 803, 805, 806, 808, 809, 815, 820, 824, 832, 835, 839, 842, 845, 848, 875, 878, 880, 892, 895, 899, 904, 914, 922, 928, 934, 937, 938, 941, 944, 956, 958, 959, 962, 964, 970, 971, 977, 982, 983, 989, 991, 995, 1003, 1012, 1016, 1025, 1027, 1028, 1030, 1033, 1037, 1039, 1040, 1043, 1049, 1054, 1055, 1057, 1058, 1066, 1075, 1076, 1078, 1081, 1085, 1090, 1102, 1112, 1121, 1127, 1129, 1130, 1133, 1135, 1142, 1145, 1147, 1150, 1154, 1159, 1160, 1163, 1165, 1166, 1177, 1180, 1184, 1186, 1187, 1189, 1192, 1193, 1198, 1199, 1201, 1207, 1208, 1214, 1216, 1220, 1226, 1229, 1232, 1243, 1247, 1252, 1255, 1258, 1261, 1270, 1298, 1301, 1310, 1312, 1316, 1331, 1334, 1336, 1339, 1352, 1355, 1358, 1367, 1369, 1370, 1376, 1382, 1384, 1385, 1387, 1393, 1394, 1397, 1400, 1403, 1406, 1409, 1411, 1414, 1421, 1427, 1433, 1441, 1442, 1450, 1451, 1453, 1459, 1463, 1466, 1474, 1484, 1499, 1501, 1502, 1505, 1508, 1541, 1544, 1547, 1550, 1556, 1561, 1565, 1570, 1579, 1582, 1586, 1589, 1594, 1606, 1607, 1612, 1613, 1618, 1619, 1624, 1633, 1634, 1637, 1639, 1642, 1643, 1646, 1651, 1652, 1654, 1657, 1661, 1667, 1673, 1678, 1688, 1690, 1693, 1694, 1702, 1705, 1706, 1709, 1712, 1717, 1718, 1724, 1729, 1733, 1735, 1739, 1744, 1747, 1750, 1751, 1753, 1759, 1765, 1771, 1775, 1784, 1798, 1801, 1802, 1804, 1811, 1817, 1819, 1831, 1838, 1840, 1841, 1844, 1849, 1852, 1853, 1856, 1859, 1861, 1865, 1874, 1882, 1883, 1885, 1886, 1888, 1889, 1897, 1900, 1901, 1904, 1907, 1909, 1910, 1919, 1921, 1924, 1927, 1931, 1933, 1937, 1943, 1945, 1957, 1964, 1969, 1973, 1978, 1979, 1981, 1984, 1985, 1997, 2000, 2003, 2011, 2012, 2015, 2020, 2023, 2026, 2027, 2041, 2042, 2044, 2045, 2047, 2048, 2059, 2060, 2062, 2072, 2074, 2081, 2083, 2084, 2087, 2090, 2101, 2105, 2110, 2111, 2113, 2114, 2120, 2125, 2129, 2132, 2144, 2153, 2159, 2165, 2173, 2176, 2180, 2182, 2189, 2195, 2204, 2213, 2222, 2227, 2234, 2236, 2245, 2251, 2254, 2257, 2258, 2266, 2269, 2272, 2273, 2276, 2281, 2296, 2299, 2300, 2302, 2318, 2323, 2333, 2338, 2339, 2365, 2368, 2371, 2372, 2374, 2380, 2384, 2390, 2395, 2396, 2402, 2407, 2410, 2413, 2416, 2419, 2420, 2431, 2437, 2438, 2444, 2450, 2452, 2453, 2462, 2465, 2467, 2473, 2479, 2482, 2486, 2489, 2492, 2497, 2501, 2506, 2507, 2516, 2521, 2522, 2528, 2531, 2537, 2546, 2551, 2552, 2555, 2557, 2563, 2572, 2573, 2581, 2605, 2609, 2612, 2614, 2618, 2620, 2624, 2626, 2630, 2633, 2644, 2645, 2648, 2650, 2660, 2662, 2665, 2669, 2689, 2692, 2698, 2713, 2719, 2720, 2726, 2728, 2752, 2753, 2759, 2761, 2762, 2774, 2789, 2791, 2794, 2803, 2807, 2810, 2812, 2815, 2819, 2821, 2824, 2827, 2836, 2837, 2848, 2855, 2857, 2869, 2881, 2884, 2890, 2891, 2894, 2897, 2899, 2902, 2908, 2917, 2920, 2921, 2926, 2927, 2936, 2942, 2951, 2954, 2969, 2974, 2980, 2986, 2989, 2990, 2992, 2995, 2998, 3001, 3004, 3016, 3017, 3020, 3023, 3026, 3028, 3029, 3034, 3035, 3037, 3040, 3041, 3044, 3047, 3052, 3053, 3061, 3068, 3070, 3071, 3076, 3085, 3086, 3095, 3101, 3103, 3104, 3106, 3110, 3113, 3122, 3124, 3127, 3134, 3137, 3149, 3157, 3170, 3175, 3182, 3185, 3187, 3194, 3203, 3208, 3215, 3218, 3224, 3227, 3230, 3232, 3233, 3241, 3245, 3248, 3250, 3253, 3254, 3256, 3259, 3260, 3263, 3265, 3274, 3287, 3290, 3292, 3293, 3295, 3299, 3304, 3307, 3308, 3314, 3322, 3323, 3326, 3328, 3329, 3332, 3338, 3343, 3347, 3352, 3359, 3362, 3364, 3368, 3371, 3377, 3388, 3392, 3394, 3397, 3400, 3418, 3428, 3430, 3433, 3434, 3437, 3440, 3443, 3449, 3458, 3460, 3464, 3466, 3478, 3481, 3487, 3505, 3506, 3508, 3511, 3521, 3526, 3535, 3536, 3542, 3544, 3547, 3553, 3556, 3557, 3560, 3571, 3572, 3578, 3586, 3589, 3593, 3598, 3599, 3601, 3602, 3604, 3605, 3607, 3608, 3611, 3614, 3616, 3619, 3623, 3625, 3634, 3637, 3641, 3646, 3647, 3652, 3653, 3658, 3659, 3664, 3671, 3674, 3676, 3685, 3686, 3689, 3691, 3695, 3698, 3700, 3707, 3709, 3712, 3713, 3715, 3725, 3731, 3734, 3736, 3742, 3746, 3749, 3754, 3755, 3757, 3760, 3763, 3766, 3769, 3770, 3772, 3773, 3775, 3779, 3781, 3782, 3793, 3797, 3805, 3806, 3808, 3809, 3812, 3817, 3820, 3823, 3845, 3847, 3848, 3853, 3862, 3869, 3872, 3878, 3884, 3890, 3892, 3895, 3899, 3901, 3902, 3904, 3911, 3917, 3922, 3926, 3928, 3931, 3934, 3935, 3941, 3949, 3950, 3952, 3956, 3965, 3967, 3980, 3982, 3986, 3988, 3991, 3994, 3997, 4001, 4009, 4015, 4018, 4024, 4025, 4027, 4036, 4039, 4040, 4046, 4067, 4073, 4088, 4096, 4097, 4106, 4112, 4114, 4117, 4123, 4124, 4132, 4136, 4139, 4144, 4147, 4153, 4154, 4159, 4163, 4165, 4168, 4171, 4178, 4183, 4192, 4195, 4196, 4199, 4201, 4204, 4211, 4214, 4220, 4225, 4228, 4232, 4241, 4243, 4244, 4246, 4256, 4262, 4264, 4270, 4271, 4274, 4280, 4285, 4295, 4297, 4300, 4307, 4309, 4313, 4316, 4324, 4327, 4328, 4330, 4331, 4336, 4340, 4349, 4354, 4355, 4358, 4369, 4370, 4375, 4384, 4394, 4396, 4399, 4414, 4418, 4423, 4426, 4435, 4436, 4444, 4447, 4448, 4456, 4462, 4465, 4468, 4471, 4475, 4477, 4478, 4480, 4483, 4484, 4489, 4495, 4499, 4501, 4504, 4511, 4516, 4522, 4526, 4528, 4532, 4534, 4537, 4540, 4543, 4544, 4550, 4555, 4559, 4561, 4565, 4568, 4570, 4571, 4577, 4585, 4591, 4592, 4594, 4595, 4603, 4604, 4609, 4619, 4624, 4625, 4631, 4633, 4639, 4640, 4643, 4645, 4651, 4652, 4657, 4661, 4666, 4669, 4675, 4676, 4678, 4682, 4685, 4687, 4690, 4694, 4703, 4705, 4706, 4708, 4715, 4723, 4724, 4733, 4735, 4736, 4738, 4739, 4741, 4747, 4748, 4751, 4753, 4754, 4757, 4762, 4765, 4766, 4768, 4772, 4777, 4781, 4790, 4795, 4796, 4801, 4805, 4808, 4810, 4814, 4816, 4825, 4835, 4838, 4840, 4844, 4852, 4859, 4864, 4865, 4871, 4873, 4879, 4888, 4900, 4901, 4906, 4918, 4921, 4924, 4925, 4928, 4931, 4936, 4940, 4945, 4948, 4951, 4957, 4961, 4966, 4969, 4972, 4978, 4984, 4985, 4988, 4993, 5002, 5005, 5008, 5009, 5014, 5015, 5021, 5024, 5027, 5030, 5032, 5047, 5050, 5053, 5060, 5063, 5074, 5077, 5078, 5083, 5086, 5089, 5090, 5092, 5093, 5096, 5107, 5108, 5110, 5116, 5120, 5123, 5129, 5140, 5141, 5146, 5147, 5149, 5158, 5159, 5164, 5168, 5176, 5177, 5183, 5185, 5189, 5191, 5197, 5200, 5201, 5204, 5206, 5207, 5219, 5221, 5222, 5224, 5230, 5233, 5234, 5237, 5249, 5251, 5255, 5261, 5264, 5276, 5279, 5281, 5287, 5291, 5294, 5308, 5309, 5317, 5318, 5320, 5326, 5336, 5338, 5345, 5347, 5348, 5350, 5365, 5366, 5371, 5374, 5375, 5378, 5380, 5381, 5383, 5386, 5387, 5390, 5405, 5411, 5413, 5414, 5416, 5417, 5423, 5425, 5432, 5434, 5435, 5441, 5446, 5450, 5452, 5456, 5461, 5462, 5465, 5467, 5479, 5486, 5488, 5489, 5491, 5495, 5500, 5504, 5507, 5512, 5513, 5516, 5524, 5525, 5527, 5530, 5531, 5534, 5536, 5539, 5546, 5549, 5555, 5558, 5563, 5570, 5572, 5573, 5576, 5579, 5585, 5602, 5605, 5609, 5615, 5626, 5629, 5639, 5645, 5647, 5650, 5654, 5656, 5660, 5671, 5674, 5678, 5684, 5687, 5692, 5693, 5696, 5701, 5704, 5705, 5707, 5708, 5713, 5714, 5723, 5726, 5732, 5737, 5741, 5743, 5767, 5768, 5773, 5792, 5794, 5800, 5809, 5810, 5813, 5815, 5816, 5818, 5819, 5822, 5824, 5825, 5834, 5837, 5840, 5857, 5870, 5876, 5881, 5888, 5893, 5894, 5899, 5917, 5918, 5920, 5924, 5932, 5938, 5941, 5942, 5948, 5953, 5956, 5962, 5966, 5978, 5992, 5995, 6002, 6004, 6005, 6007, 6008, 6010, 6017, 6023, 6026, 6028, 6029, 6038, 6041, 6049, 6050, 6052, 6058, 6064, 6065, 6071, 6073, 6074, 6077, 6083, 6085, 6088, 6089, 6097, 6098, 6103, 6104, 6107, 6112, 6115, 6118, 6119, 6127, 6133, 6139, 6140, 6143, 6145, 6149, 6154, 6155, 6169, 6172, 6190, 6193, 6196, 6203, 6211, 6217, 6218, 6221, 6223, 6232, 6241, 6248, 6250, 6254, 6256, 6257, 6259, 6266, 6269, 6271, 6274, 6280, 6283, 6287, 6289, 6304, 6305, 6308, 6316, 6335, 6338, 6343, 6344, 6352, 6361, 6364, 6371, 6373, 6389, 6395, 6397, 6398, 6406, 6409, 6410, 6421, 6427, 6428, 6434, 6439, 6442, 6443, 6446, 6463, 6466, 6467, 6475, 6481, 6482, 6487, 6490, 6497, 6500, 6502, 6512, 6515, 6518, 6529, 6530, 6533, 6541, 6562, 6568, 6580, 6587, 6589, 6590, 6593, 6595, 6596, 6598, 6599, 6602, 6605, 6608, 6614, 6616, 6625, 6635, 6638, 6640, 6641, 6643, 6646, 6647, 6649, 6655, 6658, 6661, 6665, 6667, 6671, 6679, 6682, 6683, 6685, 6692, 6698, 6700, 6701, 6707, 6710, 6712, 6715, 6724, 6727, 6730, 6746, 6748, 6749, 6755, 6770, 6778, 6781, 6788, 6797, 6799, 6805, 6809, 6812, 6815, 6818, 6832, 6835, 6841, 6845, 6851, 6854, 6863, 6866, 6871, 6872, 6880, 6881, 6883, 6886, 6887, 6889, 6892, 6893, 6895, 6898, 6905, 6908, 6910, 6911, 6917, 6920, 6922, 6926, 6931, 6934, 6940, 6944, 6947, 6955, 6958, 6961, 6970, 6977, 6979, 6982, 6991, 6992, 7001, 7018, 7019, 7022, 7028, 7030, 7031, 7033, 7036, 7055, 7060, 7064, 7066, 7069, 7075, 7079, 7081, 7085, 7088, 7096, 7109, 7112, 7130, 7133, 7136, 7138, 7139, 7141, 7147, 7148, 7153, 7156, 7160, 7163, 7165, 7169, 7177, 7186, 7193, 7202, 7204, 7210, 7217, 7223, 7232, 7234, 7249, 7252, 7255, 7259, 7262, 7264, 7265, 7267, 7270, 7271, 7273, 7274, 7277, 7280, 7282, 7286, 7288, 7289, 7300, 7318, 7319, 7324, 7325, 7327, 7330, 7340, 7343, 7346, 7349, 7354, 7357, 7358, 7366, 7370, 7372, 7382, 7385, 7393, 7396, 7406, 7409, 7412, 7414, 7415, 7417, 7426, 7429, 7435, 7438, 7444, 7445, 7451, 7454, 7456, 7460, 7463, 7477, 7478, 7484, 7492, 7493, 7496, 7498, 7501, 7505, 7507, 7511, 7514, 7517, 7519, 7522, 7526, 7532, 7543, 7544, 7550, 7555, 7556, 7559, 7564, 7568, 7570, 7571, 7576, 7579, 7583, 7585, 7586, 7588, 7589, 7594, 7601, 7607, 7612, 7616, 7621, 7622, 7628, 7630, 7645, 7648, 7651, 7658, 7664, 7666, 7669, 7675, 7688, 7691, 7699, 7700, 7702, 7703, 7708, 7709, 7718, 7723, 7727, 7729, 7732, 7733, 7736, 7744, 7754, 7757, 7760, 7766, 7769, 7772, 7775, 7777, 7781, 7784, 7787, 7798, 7799, 7801, 7802, 7808, 7811, 7813, 7819, 7826, 7828, 7834, 7835, 7846, 7847, 7856, 7859, 7873, 7879, 7883, 7885, 7886, 7897, 7898, 7910, 7922, 7924, 7934, 7937, 7945, 7948, 7958, 7967, 7975, 7981, 7982, 7984, 7985, 8002, 8006, 8008, 8011, 8012, 8015, 8017, 8021, 8023, 8029, 8030, 8033, 8036, 8039, 8045, 8047, 8050, 8053, 8054, 8059, 8063, 8068, 8080, 8081, 8084, 8089, 8098, 8102, 8104, 8108, 8110, 8111, 8113, 8117, 8119, 8122, 8132, 8137, 8147, 8155, 8156, 8161, 8167, 8170, 8171, 8185, 8186, 8191, 8200, 8204, 8209, 8210, 8213, 8218, 8219, 8225, 8227, 8230, 8233, 8236, 8242, 8243, 8254, 8261, 8269, 8272, 8278, 8282, 8287, 8288, 8293, 8294, 8296, 8297, 8299, 8306, 8323, 8326, 8338, 8339, 8342, 8344, 8345, 8348, 8353, 8357, 8360, 8363, 8369, 8374, 8377, 8383, 8389, 8392, 8398, 8402, 8404, 8405, 8407, 8410, 8419, 8426, 8428, 8431, 8440, 8441, 8443, 8444, 8446, 8449, 8453, 8465, 8467, 8468, 8476, 8480, 8485, 8491, 8494, 8495, 8500, 8504, 8509, 8510, 8519, 8524, 8530, 8543, 8548, 8554, 8557, 8561, 8572, 8576, 8579, 8584, 8591, 8593, 8594, 8596, 8599, 8602, 8603, 8608, 8609, 8611, 8614, 8617, 8621, 8623, 8630, 8633, 8636, 8647, 8648, 8650, 8651, 8653, 8657, 8662, 8666, 8671, 8672, 8681, 8687, 8689, 8693, 8702, 8710, 8716, 8723, 8725, 8729, 8735, 8740, 8744, 8747, 8750, 8752, 8756, 8761, 8767, 8768, 8773, 8791, 8792, 8795, 8797, 8806, 8813, 8816, 8819, 8827, 8828, 8831, 8833, 8836, 8840, 8842, 8843, 8846, 8848, 8849, 8852, 8857, 8858, 8864, 8867, 8881, 8887, 8890, 8891, 8894, 8897, 8903, 8905, 8914, 8918, 8930, 8932, 8936, 8942, 8944, 8950, 8957, 8960, 8963, 8965, 8968, 8974, 8975, 8981, 8983, 8987, 8990, 8993, 8995, 9004, 9010, 9011, 9017, 9020, 9026, 9028, 9031, 9034, 9038, 9041, 9044, 9049, 9050, 9052, 9056, 9061, 9068, 9071, 9074, 9076, 9077, 9083, 9091, 9095, 9098, 9100, 9112, 9116, 9118, 9122, 9127, 9133, 9145, 9149, 9157, 9160, 9173, 9175, 9178, 9181, 9188, 9190, 9197, 9199, 9209, 9218, 9220, 9221, 9223, 9230, 9235, 9238, 9241, 9242, 9247, 9256, 9263, 9268, 9274, 9278, 9283, 9286, 9289, 9290, 9293, 9298, 9310, 9317, 9319, 9323, 9326, 9328, 9331, 9334, 9337, 9343, 9346, 9347, 9349, 9352, 9356, 9365, 9368, 9374, 9379, 9383, 9385, 9388, 9394, 9397, 9401, 9403, 9404, 9406, 9424, 9427, 9428, 9431, 9433, 9434, 9437, 9440, 9442, 9445, 9451, 9463, 9464, 9466, 9467, 9475, 9478, 9479, 9481, 9482, 9484, 9491, 9494, 9500, 9502, 9508, 9514, 9529, 9533, 9538, 9542, 9544, 9548, 9551, 9554, 9557, 9562, 9568, 9572, 9574, 9575, 9577, 9580, 9584, 9592, 9593, 9595, 9602, 9604, 9605, 9607, 9608, 9614, 9619, 9622, 9623, 9626, 9629, 9631, 9640, 9644, 9650, 9653, 9655, 9659, 9662, 9673, 9676, 9682, 9685, 9688, 9691, 9700, 9704, 9706, 9709, 9710, 9716, 9718, 9719, 9721, 9724, 9725, 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TwoClassGroupRank[4] := [ 143, 157, 347, 419, 439, 473, 611, 617, 830, 856, 943, 961, 1103, 1118, 1235, 1253, 1390, 1408, 1435, 1445, 1490, 1627, 1697, 1711, 1736, 1760, 1837, 1855, 1958, 2146, 2201, 2240, 2243, 2321, 2330, 2474, 2498, 2513, 2519, 2579, 2588, 2606, 2663, 2717, 2764, 2870, 2909, 2963, 3032, 3119, 3125, 3140, 3164, 3217, 3257, 3305, 3404, 3452, 3455, 3467, 3532, 3632, 3677, 3679, 3683, 3697, 3710, 3743, 3839, 3938, 3959, 3983, 3985, 4007, 4058, 4105, 4130, 4177, 4190, 4229, 4292, 4298, 4310, 4360, 4361, 4508, 4574, 4642, 4670, 4693, 4793, 4849, 4874, 4877, 4883, 4913, 4919, 4933, 5033, 5036, 5038, 5131, 5156, 5165, 5179, 5215, 5236, 5282, 5303, 5321, 5327, 5351, 5396, 5408, 5515, 5567, 5653, 5681, 5735, 5740, 5783, 5785, 5843, 5878, 5912, 5929, 5939, 5954, 6043, 6128, 6182, 6205, 6214, 6233, 6239, 6358, 6359, 6383, 6472, 6478, 6514, 6535, 6557, 6563, 6611, 6695, 6728, 6737, 6763, 6827, 6932, 6959, 6965, 6968, 7009, 7040, 7084, 7091, 7214, 7376, 7387, 7427, 7450, 7469, 7486, 7573, 7753, 7852, 7928, 7960, 8005, 8014, 8095, 8123, 8141, 8144, 8179, 8222, 8285, 8305, 8327, 8378, 8408, 8489, 8492, 8513, 8585, 8620, 8674, 8711, 8737, 8777, 8783, 8786, 8804, 8872, 8893, 9062, 9086, 9121, 9128, 9158, 9257, 9260, 9377, 9458, 9505, 9512, 9517, 9550, 9647, 9677, 9679, 9689, 9713, 9763, 9859, 9970, 10025, 10100, 10108, 10123, 10190, 10205, 10226, 10237, 10244, 10315, 10334, 10378, 10456, 10457, 10486, 10507, 10553, 10679, 10696, 10739, 10897, 10898, 10939, 10949, 10951, 10958, 11000, 11050, 11132, 11189, 11209, 11216, 11236, 11323, 11366, 11393, 11396, 11447, 11525, 11575, 11584, 11587, 11590, 11594, 11701, 11758, 11794, 11824, 11984, 11992, 12151, 12233, 12239, 12278, 12323, 12361, 12401, 12419, 12469, 12496, 12509, 12521, 12535, 12584, 12601, 12653, 12665, 12737, 12743, 12797, 12866, 12904, 12946, 12947, 12959, 13108, 13115, 13121, 13126, 13165, 13211, 13334, 13379, 13411, 13484, 13544, 13601, 13616, 13670, 13684, 13819, 13853, 13873, 13940, 13948, 13972, 13985, 14009, 14144, 14168, 14207, 14219, 14279, 14290, 14333, 14486, 14501, 14510, 14522, 14560, 14590, 14596, 14614, 14618, 14629, 14642, 14686, 14711, 14714, 14743, 14750, 14762, 14767, 14791, 14801, 14944, 14975, 14993, 15145, 15169, 15199, 15271, 15281, 15311, 15386, 15464, 15482, 15490, 15523, 15556, 15557, 15602, 15701, 15737, 15761, 15785, 15823, 15844, 15880, 16063, 16103, 16160, 16187, 16195, 16238, 16262, 16279, 16288, 16319, 16390, 16421, 16481, 16490, 16514, 16517, 16639, 16745, 16877, 16895, 16901, 16949, 16984, 17065, 17128, 17201, 17233, 17245, 17272, 17282, 17315, 17522, 17540, 17591, 17600, 17620, 17650, 17669, 17672, 17690, 17707, 17725, 17798, 17812, 17819, 17827, 17840, 17846, 17906, 18064, 18071, 18170, 18176, 18224, 18343, 18406, 18428, 18449, 18475, 18559, 18649, 18695, 18724, 18743, 18787, 18829, 18925, 18967, 18997, 19000, 19037, 19105, 19144, 19169, 19177, 19222, 19244, 19270, 19301, 19303, 19307, 19343, 19369, 19388, 19523, 19663, 19669, 19688, 19799, 19849, 19867, 19883, 19904, 19937, 19955, 20000 ];
TwoClassGroupRank[6] := [ 3461, 9955, 12563, 13349, 14963, 16627, 17279, 19181, 19466, 19681 ];
TrueCurveRank[1] := [ 1, 2, 4, 7, 8, 10, 13, 14, 16, 19, 20, 22, 28, 31, 32, 34, 35, 37, 38, 40, 43, 46, 47, 49, 50, 52, 53, 56, 58, 61, 62, 65, 68, 70, 73, 74, 76, 77, 79, 80, 82, 86, 88, 89, 91, 92, 94, 97, 98, 104, 106, 107, 109, 110, 112, 115, 116, 119, 121, 122, 124, 125, 128, 131, 134, 140, 145, 148, 155, 158, 160, 161, 164, 167, 170, 172, 173, 175, 178, 182, 184, 185, 190, 193, 196, 197, 199, 200, 202, 203, 205, 206, 208, 209, 211, 212, 214, 215, 217, 221, 224, 226, 232, 233, 238, 239, 241, 244, 245, 247, 251, 253, 254, 256, 257, 259, 260, 262, 265, 266, 268, 272, 278, 280, 281, 284, 289, 290, 293, 295, 296, 298, 301, 302, 304, 310, 313, 314, 316, 317, 319, 320, 322, 323, 325, 326, 328, 331, 332, 334, 337, 338, 340, 343, 344, 346, 349, 352, 353, 355, 361, 362, 364, 367, 368, 370, 373, 376, 379, 380, 382, 383, 385, 386, 388, 392, 394, 401, 403, 409, 410, 412, 413, 415, 416, 418, 421, 422, 424, 425, 427, 430, 431, 436, 437, 443, 445, 448, 449, 451, 452, 454, 455, 460, 463, 464, 466, 467, 469, 476, 478, 481, 484, 485, 487, 488, 490, 493, 496, 497, 502, 505, 506, 508, 509, 514, 518, 520, 521, 524, 526, 527, 529, 530, 536, 539, 541, 547, 550, 551, 553, 554, 556, 560, 562, 563, 566, 568, 569, 572, 574, 581, 586, 587, 589, 590, 592, 595, 596, 598, 599, 601, 604, 605, 608, 610, 613, 614, 620, 622, 623, 628, 631, 632, 634, 635, 638, 640, 643, 646, 647, 650, 652, 656, 658, 659, 661, 662, 664, 665, 667, 670, 673, 674, 676, 677, 679, 680, 682, 685, 686, 688, 689, 692, 694, 695, 697, 700, 703, 706, 707, 713, 715, 718, 721, 725, 728, 730, 731, 733, 734, 736, 739, 743, 746, 748, 749, 751, 752, 754, 755, 757, 760, 761, 763, 764, 766, 767, 769, 770, 772, 775, 778, 779, 781, 782, 785, 787, 788, 790, 794, 797, 799, 802, 805, 811, 812, 814, 817, 818, 820, 821, 823, 826, 827, 829, 832, 833, 836, 841, 842, 847, 850, 851, 853, 854, 857, 859, 860, 862, 863, 865, 866, 868, 869, 871, 872, 877, 881, 883, 884, 886, 889, 890, 893, 895, 896, 898, 901, 902, 905, 907, 908, 910, 913, 916, 917, 919, 920, 922, 925, 929, 931, 932, 935, 937, 940, 944, 946, 947, 949, 950, 952, 953, 955, 962, 964, 965, 967, 968, 971, 973, 974, 976, 979, 980, 986, 988, 994, 997, 998, 1000, 1001, 1004, 1006, 1007, 1009, 1010, 1013, 1015, 1018, 1019, 1022, 1024, 1031, 1036, 1042, 1045, 1046, 1048, 1051, 1052, 1054, 1060, 1061, 1063, 1064, 1066, 1067, 1069, 1072, 1073, 1076, 1079, 1082, 1084, 1085, 1087, 1088, 1091, 1093, 1094, 1097, 1099, 1100, 1105, 1106, 1108, 1109, 1111, 1115, 1117, 1120, 1123, 1124, 1126, 1127, 1136, 1138, 1139, 1141, 1142, 1144, 1148, 1150, 1151, 1153, 1156, 1157, 1162, 1165, 1169, 1171, 1172, 1174, 1175, 1178, 1180, 1183, 1190, 1192, 1193, 1195, 1196, 1202, 1204, 1205, 1207, 1208, 1211, 1213, 1219, 1222, 1223, 1225, 1228, 1231, 1234, 1238, 1240, 1241, 1244, 1246, 1250, 1256, 1262, 1264, 1267, 1268, 1270, 1271, 1273, 1274, 1276, 1277, 1280, 1282, 1285, 1286, 1288, 1289, 1291, 1292, 1294, 1295, 1297, 1300, 1301, 1303, 1304, 1306, 1307, 1309, 1313, 1318, 1319, 1321, 1322, 1324, 1325, 1327, 1330, 1333, 1336, 1337, 1340, 1342, 1343, 1345, 1346, 1348, 1349, 1351, 1354, 1355, 1357, 1360, 1361, 1363, 1366, 1370, 1372, 1373, 1375, 1378, 1379, 1381, 1384, 1387, 1388, 1391, 1393, 1396, 1399, 1400, 1402, 1405, 1406, 1412, 1415, 1417, 1420, 1423, 1424, 1429, 1430, 1432, 1436, 1438, 1439, 1442, 1444, 1447, 1448, 1450, 1454, 1456, 1457, 1460, 1465, 1468, 1469, 1471, 1472, 1477, 1478, 1480, 1481, 1483, 1484, 1486, 1487, 1489, 1492, 1493, 1495, 1496, 1498, 1504, 1507, 1508, 1510, 1513, 1514, 1516, 1517, 1519, 1520, 1522, 1523, 1525, 1526, 1528, 1529, 1531, 1532, 1534, 1535, 1537, 1538, 1540, 1543, 1546, 1549, 1552, 1553, 1555, 1556, 1558, 1559, 1562, 1564, 1567, 1568, 1571, 1574, 1576, 1577, 1580, 1582, 1583, 1585, 1588, 1589, 1591, 1592, 1594, 1595, 1597, 1600, 1601, 1603, 1604, 1610, 1615, 1616, 1625, 1628, 1630, 1631, 1636, 1640, 1645, 1646, 1649, 1652, 1655, 1657, 1660, 1663, 1664, 1666, 1669, 1670, 1672, 1675, 1676, 1679, 1681, 1682, 1684, 1685, 1687, 1691, 1693, 1694, 1696, 1699, 1700, 1702, 1703, 1705, 1706, 1708, 1712, 1714, 1715, 1721, 1723, 1726, 1727, 1729, 1730, 1732, 1735, 1738, 1741, 1742, 1745, 1747, 1748, 1754, 1757, 1762, 1763, 1766, 1768, 1772, 1774, 1777, 1778, 1780, 1781, 1783, 1786, 1787, 1789, 1792, 1793, 1795, 1796, 1798, 1799, 1804, 1807, 1808, 1810, 1813, 1814, 1816, 1820, 1822, 1823, 1825, 1826, 1828, 1829, 1832, 1834, 1835, 1841, 1843, 1846, 1847, 1849, 1850, 1856, 1858, 1861, 1862, 1864, 1868, 1870, 1871, 1873, 1874, 1876, 1877, 1879, 1880, 1891, 1892, 1894, 1895, 1897, 1898, 1906, 1912, 1913, 1915, 1918, 1919, 1922, 1924, 1927, 1928, 1930, 1934, 1936, 1939, 1940, 1942, 1945, 1946, 1948, 1949, 1951, 1954, 1955, 1960, 1961, 1963, 1966, 1967, 1970, 1972, 1975, 1976, 1982, 1987, 1988, 1990, 1991, 1993, 1994, 1996, 1997, 1999, 2002, 2005, 2006, 2008, 2017, 2018, 2020, 2021, 2023, 2024, 2029, 2030, 2032, 2033, 2035, 2036, 2038, 2039, 2042, 2045, 2051, 2053, 2054, 2056, 2057, 2062, 2065, 2066, 2068, 2069, 2071, 2075, 2077, 2078, 2080, 2081, 2084, 2086, 2089, 2092, 2093, 2095, 2096, 2098, 2101, 2102, 2104, 2105, 2107, 2108, 2116, 2117, 2119, 2120, 2122, 2123, 2126, 2131, 2134, 2135, 2137, 2138, 2140, 2141, 2143, 2147, 2149, 2150, 2152, 2155, 2156, 2158, 2162, 2164, 2165, 2167, 2168, 2170, 2171, 2174, 2176, 2177, 2179, 2180, 2183, 2185, 2186, 2188, 2191, 2192, 2194, 2198, 2200, 2203, 2204, 2206, 2207, 2209, 2212, 2215, 2216, 2218, 2219, 2221, 2224, 2225, 2228, 2230, 2231, 2233, 2234, 2237, 2239, 2242, 2245, 2248, 2249, 2252, 2255, 2258, 2260, 2261, 2264, 2267, 2269, 2270, 2275, 2279, 2282, 2284, 2285, 2287, 2288, 2290, 2291, 2293, 2294, 2296, 2302, 2303, 2305, 2306, 2309, 2311, 2312, 2314, 2315, 2317, 2324, 2326, 2327, 2329, 2330, 2332, 2335, 2336, 2341, 2342, 2345, 2347, 2348, 2350, 2351, 2353, 2354, 2356, 2359, 2360, 2362, 2363, 2365, 2366, 2369, 2372, 2374, 2375, 2377, 2378, 2381, 2383, 2384, 2386, 2387, 2392, 2396, 2398, 2399, 2401, 2404, 2405, 2408, 2410, 2411, 2414, 2416, 2417, 2422, 2423, 2425, 2428, 2429, 2434, 2435, 2440, 2441, 2443, 2444, 2446, 2447, 2449, 2452, 2456, 2458, 2461, 2462, 2464, 2468, 2470, 2471, 2476, 2477, 2479, 2480, 2483, 2485, 2488, 2492, 2494, 2495, 2500, 2503, 2506, 2509, 2510, 2512, 2515, 2518, 2525, 2527, 2528, 2530, 2533, 2534, 2536, 2537, 2539, 2542, 2543, 2545, 2548, 2549, 2554, 2558, 2560, 2561, 2564, 2566, 2567, 2569, 2570, 2575, 2576, 2578, 2582, 2584, 2585, 2587, 2590, 2591, 2593, 2594, 2596, 2597, 2599, 2600, 2603, 2605, 2608, 2611, 2612, 2614, 2615, 2617, 2618, 2620, 2621, 2623, 2627, 2629, 2632, 2636, 2639, 2641, 2642, 2644, 2647, 2648, 2653, 2654, 2656, 2657, 2659, 2665, 2666, 2668, 2671, 2672, 2674, 2675, 2677, 2678, 2680, 2683, 2684, 2686, 2689, 2690, 2692, 2693, 2695, 2696, 2699, 2701, 2702, 2704, 2705, 2707, 2708, 2711, 2714, 2716, 2719, 2722, 2723, 2725, 2729, 2732, 2734, 2735, 2737, 2738, 2740, 2741, 2743, 2744, 2746, 2747, 2750, 2752, 2755, 2756, 2758, 2762, 2765, 2767, 2768, 2771, 2773, 2776, 2777, 2779, 2780, 2782, 2783, 2786, 2788, 2792, 2795, 2797, 2800, 2801, 2806, 2809, 2812, 2813, 2816, 2818, 2821, 2822, 2824, 2825, 2828, 2830, 2831, 2833, 2836, 2839, 2840, 2842, 2843, 2845, 2846, 2849, 2851, 2852, 2854, 2858, 2860, 2861, 2863, 2864, 2866, 2867, 2872, 2873, 2875, 2876, 2878, 2879, 2882, 2884, 2885, 2887, 2888, 2890, 2893, 2900, 2902, 2903, 2905, 2906, 2908, 2911, 2912, 2914, 2915, 2918, 2920, 2923, 2924, 2929, 2930, 2933, 2935, 2938, 2941, 2942, 2944, 2947, 2948, 2950, 2951, 2953, 2956, 2957, 2959, 2960, 2962, 2965, 2966, 2968, 2971, 2972, 2974, 2975, 2977, 2978, 2980, 2983, 2984, 2986, 2987, 2989, 2993, 2996, 2999, 3002, 3005, 3007, 3008, 3010, 3011, 3013, 3014, 3019, 3020, 3022, 3023, 3025, 3031, 3038, 3041, 3044, 3046, 3049, 3050, 3055, 3056, 3058, 3059, 3062, 3064, 3065, 3067, 3068, 3070, 3073, 3074, 3077, 3080, 3082, 3083, 3086, 3088, 3089, 3091, 3094, 3097, 3098, 3100, 3106, 3107, 3109, 3110, 3115, 3116, 3121, 3124, 3130, 3131, 3133, 3136, 3137, 3139, 3143, 3145, 3146, 3148, 3151, 3152, 3154, 3155, 3157, 3158, 3160, 3161, 3163, 3166, 3167, 3169, 3170, 3172, 3173, 3176, 3178, 3179, 3181, 3184, 3188, 3191, 3193, 3196, 3197, 3199, 3200, 3202, 3205, 3206, 3208, 3209, 3211, 3212, 3214, 3220, 3221, 3223, 3229, 3232, 3235, 3236, 3238, 3242, 3244, 3247, 3251, 3262, 3266, 3268, 3269, 3271, 3272, 3274, 3278, 3280, 3281, 3283, 3284, 3286, 3289, 3292, 3296, 3298, 3299, 3301, 3302, 3304, 3310, 3313, 3316, 3317, 3319, 3320, 3325, 3326, 3331, 3334, 3335, 3340, 3341, 3344, 3346, 3349, 3350, 3352, 3353, 3355, 3356, 3358, 3361, 3365, 3367, 3370, 3374, 3376, 3379, 3380, 3382, 3383, 3385, 3389, 3391, 3395, 3397, 3398, 3400, 3401, 3406, 3407, 3409, 3410, 3412, 3413, 3415, 3416, 3419, 3421, 3424, 3425, 3427, 3430, 3431, 3433, 3434, 3436, 3437, 3439, 3440, 3442, 3445, 3448, 3451, 3452, 3454, 3457, 3463, 3466, 3469, 3470, 3472, 3473, 3475, 3476, 3479, 3481, 3482, 3487, 3488, 3490, 3491, 3493, 3494, 3496, 3497, 3499, 3500, 3502, 3503, 3508, 3509, 3511, 3512, 3514, 3515, 3517, 3518, 3521, 3523, 3524, 3527, 3529, 3530, 3538, 3539, 3541, 3545, 3548, 3550, 3551, 3554, 3557, 3559, 3562, 3563, 3565, 3566, 3568, 3571, 3574, 3575, 3577, 3580, 3581, 3583, 3584, 3587, 3590, 3592, 3595, 3596, 3605, 3610, 3613, 3617, 3619, 3620, 3622, 3625, 3626, 3628, 3629, 3635, 3638, 3640, 3643, 3644, 3646, 3647, 3650, 3653, 3655, 3656, 3661, 3662, 3664, 3665, 3668, 3670, 3673, 3682, 3685, 3686, 3688, 3692, 3694, 3695, 3698, 3701, 3703, 3704, 3706, 3715, 3718, 3719, 3721, 3722, 3724, 3727, 3728, 3733, 3736, 3737, 3739, 3740, 3745, 3748, 3751, 3752, 3758, 3761, 3766, 3767, 3770, 3775, 3776, 3782, 3785, 3787, 3788, 3790, 3791, 3794, 3796, 3799, 3800, 3802, 3803, 3809, 3811, 3815, 3817, 3820, 3821, 3824, 3826, 3829, 3830, 3832, 3833, 3835, 3836, 3838, 3841, 3842, 3844, 3847, 3850, 3851, 3854, 3856, 3857, 3859, 3860, 3862, 3865, 3866, 3868, 3869, 3871, 3872, 3874, 3875, 3877, 3878, 3880, 3881, 3883, 3886, 3887, 3889, 3892, 3893, 3896, 3898, 3901, 3902, 3905, 3907, 3908, 3910, 3913, 3914, 3916, 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19979, 19981, 19982, 19985, 19987, 19988, 19991, 19993, 19994, 19996, 19999 ];
TrueCurveRank[3] := [ 11, 17, 23, 25, 26, 29, 44, 55, 59, 64, 67, 71, 83, 85, 95, 101, 113, 118, 127, 130, 133, 136, 137, 142, 146, 149, 151, 157, 163, 166, 169, 176, 179, 181, 187, 191, 194, 218, 220, 223, 227, 229, 230, 236, 242, 248, 263, 274, 275, 277, 283, 287, 292, 305, 307, 308, 311, 329, 341, 350, 358, 359, 365, 371, 377, 389, 391, 395, 400, 406, 407, 428, 434, 440, 442, 457, 458, 461, 470, 472, 475, 479, 491, 494, 499, 500, 503, 511, 512, 517, 523, 532, 533, 535, 538, 542, 545, 548, 557, 559, 571, 575, 578, 583, 584, 616, 617, 619, 625, 626, 637, 641, 644, 649, 653, 655, 668, 671, 683, 698, 701, 704, 709, 710, 712, 719, 722, 724, 737, 745, 758, 773, 784, 791, 793, 796, 800, 803, 806, 808, 809, 815, 824, 830, 835, 839, 845, 848, 856, 875, 878, 880, 899, 904, 914, 928, 934, 938, 941, 943, 956, 958, 959, 961, 970, 977, 982, 983, 989, 991, 995, 1003, 1012, 1016, 1025, 1027, 1028, 1030, 1033, 1037, 1039, 1040, 1043, 1049, 1055, 1057, 1058, 1075, 1078, 1081, 1090, 1102, 1112, 1118, 1121, 1129, 1130, 1133, 1135, 1145, 1147, 1154, 1159, 1160, 1163, 1166, 1177, 1184, 1186, 1187, 1189, 1198, 1199, 1201, 1214, 1216, 1220, 1226, 1229, 1232, 1243, 1247, 1252, 1255, 1258, 1261, 1298, 1310, 1312, 1316, 1331, 1334, 1339, 1352, 1358, 1367, 1369, 1376, 1382, 1385, 1390, 1394, 1397, 1403, 1408, 1409, 1411, 1414, 1421, 1427, 1433, 1435, 1441, 1451, 1453, 1459, 1463, 1466, 1474, 1490, 1499, 1501, 1502, 1505, 1541, 1544, 1547, 1550, 1561, 1565, 1570, 1579, 1586, 1606, 1607, 1612, 1613, 1618, 1619, 1624, 1627, 1633, 1634, 1637, 1639, 1642, 1643, 1651, 1654, 1661, 1667, 1673, 1688, 1690, 1697, 1709, 1711, 1717, 1718, 1724, 1733, 1736, 1739, 1744, 1750, 1751, 1753, 1759, 1765, 1771, 1775, 1784, 1802, 1811, 1817, 1819, 1831, 1837, 1838, 1840, 1844, 1852, 1853, 1855, 1859, 1865, 1882, 1883, 1885, 1886, 1888, 1889, 1901, 1904, 1907, 1909, 1910, 1921, 1931, 1937, 1943, 1957, 1958, 1964, 1969, 1973, 1978, 1979, 1981, 1984, 1985, 2000, 2003, 2011, 2012, 2015, 2026, 2027, 2041, 2044, 2047, 2048, 2059, 2060, 2072, 2074, 2083, 2087, 2090, 2111, 2113, 2114, 2125, 2129, 2132, 2144, 2146, 2153, 2159, 2173, 2182, 2189, 2195, 2213, 2222, 2227, 2236, 2240, 2251, 2254, 2257, 2266, 2272, 2273, 2276, 2281, 2299, 2300, 2318, 2323, 2333, 2338, 2339, 2368, 2371, 2380, 2390, 2395, 2402, 2407, 2413, 2419, 2420, 2431, 2437, 2438, 2450, 2453, 2465, 2467, 2473, 2482, 2486, 2489, 2497, 2498, 2501, 2507, 2513, 2516, 2521, 2522, 2531, 2546, 2551, 2552, 2555, 2557, 2563, 2572, 2573, 2581, 2588, 2606, 2609, 2624, 2626, 2633, 2645, 2650, 2660, 2662, 2669, 2713, 2717, 2720, 2726, 2728, 2753, 2759, 2761, 2764, 2774, 2789, 2791, 2794, 2803, 2807, 2810, 2815, 2819, 2827, 2837, 2848, 2855, 2857, 2869, 2870, 2881, 2891, 2894, 2897, 2899, 2917, 2921, 2926, 2927, 2936, 2954, 2969, 2990, 2992, 2995, 3001, 3004, 3016, 3017, 3026, 3028, 3029, 3032, 3034, 3035, 3037, 3047, 3052, 3053, 3061, 3071, 3076, 3085, 3095, 3101, 3103, 3104, 3113, 3125, 3127, 3134, 3140, 3149, 3164, 3175, 3182, 3185, 3187, 3194, 3203, 3215, 3217, 3218, 3224, 3227, 3230, 3233, 3241, 3245, 3248, 3250, 3253, 3254, 3256, 3257, 3259, 3260, 3263, 3265, 3287, 3290, 3293, 3295, 3305, 3307, 3308, 3314, 3322, 3323, 3328, 3329, 3332, 3338, 3343, 3347, 3359, 3362, 3364, 3371, 3377, 3388, 3392, 3394, 3404, 3418, 3428, 3443, 3449, 3458, 3460, 3464, 3478, 3505, 3526, 3535, 3536, 3542, 3544, 3547, 3553, 3556, 3560, 3578, 3586, 3589, 3593, 3598, 3599, 3601, 3602, 3604, 3607, 3608, 3611, 3614, 3616, 3623, 3632, 3634, 3637, 3641, 3652, 3658, 3659, 3671, 3674, 3676, 3679, 3689, 3691, 3697, 3700, 3707, 3709, 3710, 3712, 3713, 3725, 3731, 3734, 3746, 3749, 3754, 3755, 3757, 3763, 3769, 3772, 3773, 3779, 3793, 3797, 3805, 3806, 3808, 3812, 3823, 3845, 3848, 3853, 3884, 3890, 3895, 3899, 3904, 3911, 3917, 3922, 3928, 3931, 3935, 3941, 3949, 3950, 3952, 3967, 3983, 3985, 3986, 3991, 3997, 4001, 4015, 4024, 4027, 4036, 4040, 4058, 4067, 4073, 4088, 4096, 4106, 4114, 4136, 4139, 4144, 4147, 4153, 4154, 4159, 4163, 4168, 4171, 4178, 4183, 4190, 4192, 4196, 4199, 4201, 4204, 4211, 4214, 4225, 4228, 4229, 4232, 4241, 4243, 4244, 4271, 4285, 4292, 4295, 4300, 4307, 4310, 4313, 4316, 4324, 4327, 4328, 4330, 4336, 4349, 4355, 4358, 4361, 4384, 4396, 4399, 4418, 4423, 4426, 4447, 4462, 4465, 4475, 4477, 4478, 4483, 4484, 4489, 4495, 4499, 4501, 4504, 4508, 4511, 4516, 4522, 4532, 4534, 4537, 4543, 4544, 4555, 4559, 4565, 4568, 4571, 4574, 4592, 4603, 4619, 4624, 4625, 4631, 4640, 4642, 4643, 4645, 4651, 4652, 4657, 4661, 4669, 4670, 4675, 4678, 4682, 4685, 4687, 4690, 4693, 4694, 4703, 4708, 4715, 4723, 4724, 4733, 4735, 4736, 4738, 4739, 4741, 4747, 4748, 4751, 4754, 4757, 4768, 4793, 4796, 4805, 4835, 4849, 4859, 4864, 4865, 4874, 4877, 4883, 4888, 4901, 4906, 4913, 4918, 4924, 4931, 4933, 4951, 4957, 4961, 4969, 4972, 4984, 4985, 4993, 5005, 5008, 5009, 5014, 5015, 5021, 5027, 5030, 5033, 5036, 5038, 5053, 5063, 5074, 5077, 5083, 5090, 5093, 5096, 5107, 5108, 5110, 5116, 5123, 5131, 5140, 5141, 5147, 5156, 5159, 5164, 5168, 5176, 5177, 5179, 5185, 5189, 5191, 5200, 5201, 5204, 5215, 5219, 5234, 5236, 5237, 5249, 5251, 5261, 5264, 5279, 5282, 5291, 5294, 5308, 5309, 5318, 5321, 5338, 5347, 5351, 5371, 5374, 5375, 5380, 5381, 5386, 5387, 5396, 5405, 5408, 5414, 5416, 5417, 5423, 5425, 5432, 5434, 5435, 5441, 5452, 5461, 5462, 5465, 5467, 5479, 5486, 5489, 5491, 5495, 5500, 5507, 5512, 5513, 5515, 5525, 5527, 5531, 5534, 5536, 5539, 5546, 5549, 5555, 5563, 5567, 5576, 5579, 5585, 5609, 5615, 5629, 5639, 5645, 5647, 5654, 5671, 5674, 5684, 5687, 5692, 5693, 5701, 5704, 5705, 5723, 5726, 5732, 5737, 5740, 5741, 5743, 5767, 5773, 5783, 5785, 5792, 5800, 5813, 5819, 5822, 5825, 5834, 5840, 5843, 5857, 5870, 5876, 5878, 5899, 5912, 5924, 5932, 5938, 5948, 5956, 5962, 5995, 6004, 6005, 6010, 6023, 6026, 6028, 6029, 6038, 6049, 6050, 6052, 6058, 6064, 6065, 6071, 6074, 6077, 6083, 6085, 6089, 6097, 6098, 6103, 6107, 6115, 6118, 6119, 6127, 6133, 6140, 6143, 6145, 6149, 6155, 6169, 6182, 6193, 6203, 6205, 6211, 6214, 6218, 6221, 6239, 6248, 6254, 6257, 6259, 6269, 6271, 6274, 6283, 6287, 6305, 6335, 6338, 6343, 6359, 6361, 6364, 6371, 6395, 6398, 6406, 6427, 6428, 6434, 6439, 6442, 6446, 6463, 6466, 6467, 6478, 6487, 6490, 6497, 6500, 6502, 6512, 6514, 6515, 6518, 6533, 6535, 6563, 6587, 6589, 6590, 6593, 6595, 6596, 6602, 6614, 6616, 6625, 6635, 6638, 6643, 6646, 6647, 6649, 6655, 6661, 6665, 6667, 6671, 6679, 6683, 6692, 6695, 6698, 6700, 6701, 6707, 6710, 6712, 6727, 6728, 6746, 6755, 6770, 6788, 6799, 6805, 6809, 6812, 6815, 6827, 6851, 6854, 6863, 6871, 6872, 6880, 6881, 6883, 6887, 6889, 6898, 6905, 6908, 6911, 6917, 6920, 6922, 6926, 6932, 6934, 6940, 6944, 6947, 6955, 6961, 6965, 6977, 6991, 7001, 7009, 7019, 7028, 7031, 7033, 7036, 7040, 7055, 7064, 7066, 7069, 7075, 7079, 7084, 7085, 7088, 7091, 7109, 7112, 7136, 7138, 7139, 7147, 7148, 7163, 7165, 7186, 7193, 7210, 7214, 7217, 7223, 7232, 7234, 7249, 7255, 7259, 7267, 7274, 7277, 7280, 7282, 7286, 7300, 7318, 7319, 7324, 7325, 7340, 7343, 7349, 7354, 7358, 7382, 7385, 7387, 7393, 7396, 7409, 7415, 7417, 7426, 7427, 7450, 7451, 7454, 7456, 7463, 7478, 7486, 7493, 7496, 7505, 7514, 7517, 7519, 7522, 7526, 7543, 7544, 7550, 7555, 7556, 7559, 7564, 7568, 7570, 7571, 7573, 7576, 7583, 7585, 7588, 7589, 7601, 7607, 7612, 7616, 7622, 7645, 7648, 7664, 7666, 7675, 7699, 7700, 7702, 7703, 7709, 7718, 7727, 7733, 7754, 7772, 7775, 7777, 7781, 7787, 7799, 7801, 7802, 7811, 7819, 7826, 7835, 7846, 7852, 7856, 7859, 7879, 7883, 7885, 7886, 7897, 7928, 7934, 7937, 7945, 7948, 7958, 7960, 7967, 7981, 7982, 7985, 8005, 8006, 8014, 8015, 8017, 8021, 8023, 8029, 8030, 8033, 8039, 8047, 8050, 8053, 8063, 8084, 8089, 8102, 8108, 8110, 8111, 8113, 8117, 8119, 8132, 8137, 8141, 8144, 8147, 8155, 8161, 8170, 8171, 8185, 8186, 8191, 8209, 8210, 8213, 8218, 8219, 8222, 8227, 8230, 8243, 8254, 8261, 8269, 8272, 8278, 8294, 8297, 8299, 8305, 8306, 8326, 8327, 8338, 8339, 8342, 8345, 8353, 8357, 8360, 8363, 8369, 8377, 8378, 8383, 8389, 8405, 8407, 8408, 8419, 8431, 8440, 8443, 8444, 8449, 8453, 8465, 8468, 8480, 8485, 8489, 8492, 8495, 8500, 8504, 8509, 8524, 8543, 8548, 8554, 8557, 8579, 8584, 8591, 8593, 8599, 8602, 8608, 8617, 8623, 8636, 8647, 8650, 8657, 8671, 8674, 8681, 8693, 8710, 8723, 8729, 8735, 8737, 8744, 8747, 8752, 8756, 8761, 8767, 8768, 8773, 8777, 8786, 8795, 8804, 8806, 8813, 8819, 8827, 8828, 8831, 8833, 8836, 8843, 8846, 8852, 8858, 8864, 8867, 8872, 8887, 8891, 8893, 8897, 8903, 8914, 8918, 8942, 8950, 8957, 8960, 8974, 8975, 8981, 8983, 8987, 8993, 9004, 9026, 9034, 9041, 9044, 9049, 9052, 9062, 9071, 9074, 9076, 9083, 9098, 9116, 9121, 9122, 9127, 9128, 9149, 9157, 9173, 9181, 9188, 9197, 9199, 9218, 9221, 9223, 9230, 9235, 9247, 9263, 9268, 9274, 9283, 9286, 9293, 9298, 9317, 9326, 9331, 9334, 9347, 9349, 9356, 9365, 9368, 9374, 9379, 9383, 9394, 9397, 9403, 9424, 9427, 9431, 9433, 9442, 9451, 9458, 9463, 9466, 9467, 9478, 9479, 9481, 9491, 9494, 9500, 9505, 9508, 9517, 9529, 9533, 9544, 9548, 9550, 9551, 9554, 9557, 9580, 9593, 9595, 9602, 9604, 9605, 9607, 9608, 9614, 9619, 9623, 9626, 9629, 9650, 9653, 9655, 9659, 9662, 9673, 9677, 9679, 9688, 9689, 9691, 9706, 9713, 9718, 9719, 9721, 9724, 9725, 9739, 9748, 9749, 9752, 9754, 9757, 9758, 9767, 9769, 9773, 9781, 9790, 9793, 9794, 9802, 9811, 9815, 9826, 9827, 9838, 9839, 9842, 9844, 9851, 9857, 9859, 9863, 9866, 9874, 9881, 9887, 9911, 9923, 9925, 9928, 9932, 9941, 9944, 9953, 9956, 9962, 9967, 9970, 9979, 9985, 9986, 9989, 10007, 10015, 10021, 10025, 10039, 10057, 10067, 10069, 10073, 10075, 10076, 10085, 10091, 10096, 10100, 10103, 10109, 10120, 10121, 10123, 10126, 10127, 10138, 10145, 10151, 10153, 10163, 10165, 10175, 10177, 10186, 10187, 10189, 10190, 10196, 10201, 10205, 10207, 10213, 10223, 10225, 10226, 10229, 10231, 10237, 10244, 10247, 10249, 10253, 10259, 10267, 10270, 10271, 10277, 10285, 10286, 10292, 10303, 10304, 10307, 10309, 10315, 10319, 10325, 10327, 10334, 10336, 10337, 10343, 10349, 10372, 10378, 10379, 10384, 10394, 10403, 10406, 10427, 10439, 10441, 10445, 10456, 10459, 10460, 10466, 10468, 10471, 10475, 10480, 10483, 10489, 10490, 10498, 10511, 10517, 10519, 10522, 10537, 10541, 10559, 10565, 10577, 10582, 10595, 10600, 10603, 10615, 10619, 10621, 10637, 10642, 10645, 10646, 10649, 10651, 10676, 10685, 10690, 10691, 10696, 10697, 10706, 10711, 10721, 10726, 10732, 10733, 10739, 10742, 10744, 10745, 10751, 10754, 10760, 10769, 10774, 10784, 10790, 10792, 10798, 10801, 10802, 10805, 10822, 10825, 10831, 10840, 10841, 10844, 10847, 10861, 10868, 10873, 10879, 10886, 10889, 10891, 10895, 10897, 10898, 10901, 10904, 10907, 10909, 10912, 10934, 10936, 10937, 10939, 10942, 10949, 10951, 10955, 10958, 10961, 10963, 10964, 10967, 10973, 10975, 10990, 10991, 10996, 11003, 11005, 11011, 11021, 11029, 11036, 11038, 11048, 11050, 11056, 11072, 11078, 11080, 11081, 11084, 11093, 11099, 11125, 11138, 11155, 11159, 11174, 11185, 11188, 11191, 11192, 11194, 11197, 11198, 11201, 11203, 11204, 11216, 11228, 11231, 11234, 11236, 11243, 11261, 11267, 11270, 11278, 11297, 11309, 11315, 11320, 11323, 11329, 11332, 11333, 11341, 11356, 11357, 11363, 11374, 11378, 11384, 11393, 11399, 11401, 11413, 11419, 11431, 11432, 11443, 11444, 11449, 11450, 11453, 11456, 11468, 11479, 11483, 11485, 11486, 11495, 11500, 11504, 11509, 11513, 11521, 11525, 11534, 11543, 11546, 11554, 11563, 11567, 11575, 11584, 11585, 11587, 11593, 11594, 11597, 11600, 11617, 11620, 11629, 11639, 11648, 11653, 11675, 11681, 11690, 11701, 11719, 11741, 11747, 11755, 11758, 11762, 11777, 11788, 11789, 11804, 11807, 11815, 11824, 11842, 11848, 11849, 11861, 11870, 11872, 11875, 11884, 11885, 11891, 11905, 11908, 11911, 11924, 11932, 11933, 11936, 11945, 11951, 11953, 11957, 11966, 11969, 11971, 11972, 11980, 11983, 11990, 11992, 12001, 12007, 12011, 12017, 12019, 12028, 12029, 12035, 12040, 12041, 12070, 12077, 12083, 12089, 12091, 12092, 12098, 12100, 12110, 12115, 12119, 12127, 12133, 12142, 12148, 12151, 12155, 12170, 12191, 12202, 12217, 12226, 12235, 12236, 12239, 12245, 12253, 12265, 12269, 12271, 12275, 12283, 12284, 12292, 12293, 12296, 12307, 12328, 12329, 12331, 12356, 12359, 12374, 12379, 12392, 12395, 12401, 12416, 12421, 12424, 12452, 12463, 12466, 12469, 12473, 12484, 12491, 12496, 12505, 12509, 12520, 12521, 12527, 12529, 12530, 12535, 12550, 12551, 12554, 12557, 12584, 12590, 12601, 12602, 12605, 12607, 12608, 12611, 12613, 12614, 12617, 12638, 12653, 12662, 12665, 12682, 12685, 12694, 12704, 12706, 12707, 12724, 12727, 12731, 12737, 12755, 12767, 12772, 12773, 12785, 12791, 12797, 12808, 12811, 12820, 12823, 12826, 12835, 12842, 12844, 12848, 12851, 12862, 12875, 12877, 12893, 12895, 12898, 12901, 12902, 12904, 12931, 12938, 12940, 12943, 12946, 12961, 12968, 12973, 12976, 12979, 12983, 12986, 12991, 13001, 13012, 13013, 13016, 13019, 13043, 13049, 13052, 13066, 13067, 13073, 13078, 13096, 13099, 13100, 13103, 13123, 13126, 13129, 13132, 13157, 13165, 13178, 13184, 13204, 13205, 13207, 13211, 13228, 13237, 13240, 13241, 13246, 13247, 13249, 13253, 13261, 13274, 13283, 13298, 13307, 13322, 13327, 13328, 13330, 13331, 13343, 13345, 13348, 13354, 13355, 13364, 13367, 13387, 13390, 13423, 13430, 13444, 13465, 13475, 13484, 13499, 13507, 13519, 13525, 13535, 13544, 13553, 13589, 13591, 13595, 13598, 13601, 13613, 13616, 13628, 13639, 13640, 13645, 13652, 13654, 13661, 13670, 13679, 13682, 13684, 13688, 13696, 13702, 13703, 13708, 13711, 13723, 13724, 13727, 13729, 13739, 13745, 13748, 13750, 13759, 13768, 13772, 13775, 13786, 13787, 13793, 13796, 13798, 13801, 13808, 13811, 13835, 13843, 13855, 13861, 13865, 13871, 13873, 13882, 13886, 13889, 13891, 13906, 13912, 13913, 13915, 13928, 13934, 13936, 13940, 13943, 13961, 13966, 13967, 13972, 13985, 13993, 13997, 14000, 14011, 14018, 14021, 14032, 14033, 14035, 14036, 14041, 14042, 14051, 14053, 14054, 14065, 14077, 14080, 14090, 14092, 14099, 14108, 14111, 14116, 14123, 14132, 14141, 14144, 14152, 14155, 14156, 14167, 14168, 14173, 14179, 14185, 14186, 14197, 14237, 14242, 14248, 14255, 14258, 14261, 14266, 14270, 14273, 14290, 14299, 14305, 14315, 14327, 14329, 14345, 14353, 14356, 14365, 14369, 14371, 14375, 14378, 14417, 14419, 14420, 14423, 14426, 14443, 14444, 14461, 14471, 14477, 14482, 14483, 14486, 14491, 14495, 14498, 14500, 14510, 14519, 14522, 14528, 14534, 14539, 14542, 14552, 14560, 14563, 14567, 14579, 14596, 14608, 14614, 14620, 14623, 14629, 14630, 14638, 14642, 14650, 14657, 14675, 14686, 14689, 14695, 14696, 14699, 14714, 14722, 14726, 14729, 14731, 14738, 14740, 14743, 14746, 14747, 14750, 14753, 14762, 14767, 14768, 14779, 14789, 14798, 14800, 14801, 14804, 14813, 14836, 14845, 14861, 14863, 14873, 14876, 14878, 14887, 14893, 14894, 14897, 14900, 14902, 14905, 14908, 14915, 14941, 14942, 14951, 14953, 14956, 14957, 14978, 14983, 14984, 14993, 14995, 15014, 15020, 15029, 15043, 15046, 15061, 15065, 15082, 15085, 15091, 15140, 15151, 15170, 15173, 15185, 15197, 15199, 15202, 15203, 15218, 15221, 15226, 15227, 15236, 15251, 15263, 15281, 15286, 15287, 15298, 15299, 15301, 15302, 15305, 15307, 15308, 15319, 15320, 15332, 15350, 15371, 15386, 15397, 15409, 15430, 15431, 15436, 15439, 15446, 15455, 15466, 15467, 15469, 15472, 15487, 15491, 15509, 15511, 15514, 15515, 15517, 15523, 15542, 15545, 15551, 15553, 15557, 15559, 15565, 15566, 15571, 15577, 15601, 15602, 15647, 15649, 15664, 15671, 15676, 15701, 15709, 15730, 15733, 15736, 15737, 15739, 15740, 15751, 15755, 15760, 15761, 15763, 15764, 15773, 15781, 15785, 15788, 15797, 15802, 15808, 15814, 15818, 15821, 15823, 15830, 15836, 15851, 15863, 15875, 15877, 15880, 15883, 15884, 15887, 15890, 15895, 15901, 15907, 15908, 15914, 15938, 15949, 15955, 15961, 15964, 15970, 15989, 15995, 15997, 15998, 16000, 16004, 16007, 16019, 16033, 16048, 16054, 16055, 16063, 16067, 16070, 16073, 16081, 16085, 16090, 16094, 16099, 16100, 16103, 16106, 16109, 16112, 16117, 16147, 16151, 16159, 16160, 16166, 16189, 16204, 16208, 16219, 16237, 16238, 16243, 16246, 16247, 16259, 16262, 16279, 16286, 16294, 16295, 16298, 16303, 16307, 16325, 16328, 16331, 16351, 16354, 16379, 16385, 16387, 16390, 16394, 16405, 16411, 16421, 16423, 16424, 16426, 16433, 16444, 16445, 16466, 16472, 16474, 16478, 16487, 16490, 16498, 16502, 16511, 16513, 16514, 16517, 16522, 16535, 16547, 16552, 16565, 16588, 16606, 16607, 16609, 16634, 16637, 16639, 16643, 16648, 16649, 16655, 16661, 16663, 16673, 16675, 16676, 16679, 16684, 16685, 16687, 16711, 16721, 16723, 16727, 16730, 16739, 16742, 16745, 16748, 16757, 16759, 16766, 16769, 16775, 16786, 16801, 16811, 16819, 16840, 16841, 16847, 16850, 16858, 16864, 16870, 16874, 16877, 16889, 16898, 16901, 16907, 16909, 16913, 16921, 16924, 16931, 16937, 16943, 16954, 16957, 16964, 16969, 16979, 16984, 16997, 16999, 17002, 17009, 17015, 17023, 17026, 17032, 17033, 17035, 17039, 17041, 17053, 17062, 17063, 17065, 17071, 17078, 17083, 17090, 17092, 17105, 17107, 17110, 17111, 17116, 17128, 17137, 17138, 17158, 17159, 17167, 17173, 17176, 17185, 17195, 17197, 17198, 17207, 17210, 17219, 17221, 17225, 17231, 17236, 17237, 17243, 17246, 17255, 17257, 17263, 17272, 17282, 17300, 17303, 17308, 17314, 17315, 17329, 17345, 17348, 17360, 17366, 17375, 17398, 17399, 17407, 17413, 17416, 17417, 17419, 17426, 17431, 17434, 17438, 17443, 17450, 17471, 17477, 17479, 17483, 17488, 17491, 17501, 17510, 17516, 17518, 17525, 17530, 17531, 17543, 17549, 17551, 17552, 17555, 17564, 17567, 17576, 17579, 17585, 17591, 17600, 17605, 17611, 17614, 17618, 17629, 17633, 17644, 17651, 17666, 17669, 17672, 17675, 17678, 17689, 17690, 17699, 17707, 17711, 17719, 17726, 17740, 17747, 17750, 17758, 17759, 17762, 17776, 17794, 17795, 17797, 17798, 17804, 17807, 17809, 17810, 17812, 17831, 17837, 17840, 17846, 17851, 17867, 17869, 17876, 17885, 17888, 17894, 17896, 17897, 17903, 17906, 17909, 17924, 17927, 17929, 17930, 17935, 17948, 17962, 17966, 17969, 17972, 17977, 17978, 17984, 17995, 17998, 17999, 18005, 18008, 18011, 18041, 18043, 18052, 18058, 18061, 18062, 18064, 18071, 18089, 18091, 18101, 18107, 18112, 18115, 18127, 18128, 18140, 18161, 18164, 18167, 18170, 18176, 18178, 18187, 18188, 18194, 18199, 18206, 18211, 18218, 18224, 18226, 18238, 18239, 18241, 18248, 18250, 18257, 18272, 18275, 18296, 18314, 18325, 18326, 18335, 18343, 18346, 18353, 18359, 18362, 18368, 18371, 18377, 18389, 18395, 18403, 18406, 18407, 18415, 18419, 18425, 18428, 18439, 18448, 18466, 18469, 18475, 18499, 18505, 18512, 18518, 18524, 18526, 18530, 18535, 18539, 18544, 18547, 18551, 18559, 18569, 18574, 18578, 18586, 18587, 18589, 18590, 18595, 18596, 18601, 18604, 18608, 18623, 18629, 18637, 18638, 18649, 18673, 18689, 18695, 18701, 18703, 18716, 18722, 18725, 18751, 18760, 18764, 18779, 18787, 18791, 18793, 18794, 18803, 18811, 18812, 18815, 18841, 18845, 18848, 18901, 18931, 18944, 18970, 18979, 18986, 18995, 18997, 18998, 19000, 19018, 19037, 19040, 19042, 19048, 19049, 19051, 19052, 19058, 19063, 19064, 19070, 19072, 19078, 19079, 19091, 19094, 19096, 19109, 19129, 19133, 19135, 19142, 19144, 19156, 19169, 19183, 19187, 19198, 19199, 19202, 19205, 19210, 19228, 19244, 19253, 19255, 19256, 19264, 19267, 19270, 19283, 19286, 19288, 19292, 19294, 19301, 19307, 19313, 19316, 19343, 19348, 19349, 19352, 19361, 19363, 19364, 19369, 19372, 19373, 19385, 19387, 19399, 19400, 19403, 19415, 19427, 19436, 19453, 19457, 19466, 19471, 19477, 19487, 19490, 19493, 19496, 19499, 19514, 19516, 19517, 19523, 19529, 19531, 19537, 19547, 19553, 19573, 19577, 19582, 19583, 19603, 19616, 19618, 19624, 19630, 19639, 19640, 19663, 19669, 19675, 19676, 19685, 19687, 19688, 19691, 19721, 19723, 19727, 19729, 19730, 19744, 19745, 19748, 19750, 19751, 19780, 19786, 19789, 19793, 19816, 19820, 19831, 19843, 19844, 19849, 19859, 19862, 19865, 19867, 19871, 19876, 19883, 19891, 19904, 19907, 19912, 19916, 19919, 19922, 19924, 19925, 19931, 19939, 19943, 19945, 19951, 19952, 19955, 19957, 19990, 20000 ];
TrueCurveRank[5] := [ 143, 347, 419, 439, 473, 611, 1103, 1235, 1253, 1445, 1760, 2201, 2243, 2321, 2474, 2519, 2579, 2663, 2909, 2963, 3119, 3455, 3461, 3467, 3532, 3677, 3683, 3743, 3839, 3938, 3959, 4007, 4105, 4360, 4919, 5165, 5303, 5327, 5653, 5681, 5735, 5929, 5939, 5954, 6043, 6128, 6233, 6383, 6557, 6611, 6737, 6763, 6959, 6968, 7376, 7469, 7753, 8095, 8123, 8179, 8285, 8513, 8585, 8711, 8783, 9086, 9158, 9257, 9377, 9647, 9763, 9955, 10457, 10486, 10553, 10679, 11000, 11132, 11189, 11209, 11366, 11396, 11447, 12233, 12278, 12323, 12419, 12743, 12947, 12959, 13108, 13115, 13121, 13349, 13379, 13411, 13819, 13948, 14009, 14207, 14219, 14279, 14333, 14501, 14618, 14711, 14944, 14975, 15145, 15169, 15271, 15311, 16187, 16195, 16319, 16481, 16627, 16895, 16949, 17279, 17540, 17620, 17725, 17819, 18743, 18925, 18967, 19181, 19303, 19388, 19681, 19799 ];
TrueCurveRank[7] := [ 12563, 14963 ];
FalseCurveRankLowerBound[1] := [ 892, 1678, 1801, 1900, 1933, 2110, 2630, 2698, 2998, 3040, 3122, 3368, 3506, 3572, 3742, 3760, 3781, 4009, 4246, 4270, 4354, 4375, 4825, 4840, 4900, 4936, 4940, 4948, 5050, 5197, 5230, 5326, 5504, 5524, 5530, 5572, 5920, 6104, 6196, 6266, 6280, 6316, 6481, 6562, 6580, 6685, 6730, 6886, 6970, 7022, 7204, 7330, 7366, 7370, 7429, 7460, 7628, 7736, 7744, 7798, 8011, 8054, 8122, 8204, 8225, 8282, 8374, 8428, 8620, 8716, 8848, 9056, 9061, 9100, 9220, 9242, 9278, 9310, 9475, 9575, 9704, 9836, 9920, 10006, 10048, 10051, 10198, 10382, 10388, 10888, 11170, 11221, 11233, 11264, 11272, 11492, 11542, 11548, 11590, 11647, 11662, 11717, 11734, 11738, 11852, 11866, 12184, 12185, 12187, 12244, 12286, 12350, 12358, 12457, 12565, 12592, 12593, 12604, 12676, 12703, 12710, 12742, 12845, 12872, 12886, 13021, 13033, 13040, 13042, 13147, 13270, 13400, 13448, 13457, 13502, 13832, 13978, 14122, 14246, 14320, 14332, 14360, 14374, 14396, 14429, 14464, 14467, 14569, 14621, 14624, 14968, 15094, 15266, 15452, 15463, 15496, 15548, 15562, 15568, 15580, 15622, 15640, 15694, 15778, 15985, 16123, 16201, 16271, 16316, 16321, 16346, 16372, 16378, 16429, 16480, 16672, 16813, 16814, 16822, 16882, 16894, 16940, 17029, 17074, 17188, 17276, 17383, 17425, 17428, 17465, 17486, 17656, 17705, 17866, 17986, 18044, 18070, 18136, 18169, 18172, 18268, 18392, 18436, 18445, 18464, 18560, 18632, 18653, 18664, 18686, 18740, 18781, 18910, 18937, 18982, 19025, 19324, 19417, 19544, 19594, 19658, 19738, 19753, 19835, 19940 ];
FalseCurveRankLowerBound[2] := [ 16120 ];
FalseCurveRankLowerBound[3] := [ 10108 ];
FalseCurveRankUpperBound[3] := [ 892, 1678, 1801, 1900, 1933, 2110, 2630, 2698, 2998, 3040, 3122, 3368, 3506, 3572, 3742, 3760, 3781, 4009, 4246, 4270, 4354, 4375, 4825, 4840, 4900, 4936, 4940, 4948, 5050, 5197, 5230, 5326, 5504, 5524, 5530, 5572, 5920, 6104, 6196, 6266, 6280, 6316, 6481, 6562, 6580, 6685, 6730, 6886, 6970, 7022, 7204, 7330, 7366, 7370, 7429, 7460, 7628, 7736, 7744, 7798, 8011, 8054, 8122, 8204, 8225, 8282, 8374, 8428, 8620, 8716, 8848, 9056, 9061, 9100, 9220, 9242, 9278, 9310, 9475, 9575, 9704, 9836, 9920, 10006, 10048, 10051, 10198, 10382, 10388, 10888, 11170, 11221, 11233, 11264, 11272, 11492, 11542, 11548, 11590, 11647, 11662, 11717, 11734, 11738, 11852, 11866, 12184, 12185, 12187, 12244, 12286, 12350, 12358, 12457, 12565, 12592, 12593, 12604, 12676, 12703, 12710, 12742, 12845, 12872, 12886, 13021, 13033, 13040, 13042, 13147, 13270, 13400, 13448, 13457, 13502, 13832, 13978, 14122, 14246, 14320, 14332, 14360, 14374, 14396, 14429, 14464, 14467, 14569, 14621, 14624, 14968, 15094, 15266, 15452, 15463, 15496, 15548, 15562, 15568, 15580, 15622, 15640, 15694, 15778, 15985, 16120, 16123, 16201, 16271, 16316, 16321, 16346, 16372, 16378, 16429, 16480, 16672, 16813, 16814, 16822, 16882, 16894, 16940, 17029, 17074, 17188, 17276, 17383, 17425, 17428, 17465, 17486, 17656, 17705, 17866, 17986, 18044, 18070, 18136, 18169, 18172, 18268, 18392, 18436, 18445, 18464, 18560, 18632, 18653, 18664, 18686, 18740, 18781, 18910, 18937, 18982, 19025, 19324, 19417, 19544, 19594, 19658, 19738, 19753, 19835, 19940 ];
FalseCurveRankUpperBound[5] := [ 10108 ];
WashingtonsBound[1] := [ 1, 2, 4, 7, 8, 10, 13, 14, 16, 19, 20, 22, 28, 31, 32, 34, 35, 37, 38, 40, 43, 46, 47, 49, 50, 52, 53, 56, 58, 61, 62, 65, 68, 70, 73, 74, 76, 77, 79, 80, 82, 86, 88, 89, 91, 92, 94, 97, 98, 104, 106, 107, 109, 110, 112, 115, 116, 119, 121, 122, 124, 125, 128, 131, 134, 140, 145, 148, 155, 158, 160, 161, 164, 167, 172, 173, 175, 178, 182, 185, 190, 193, 196, 197, 199, 200, 202, 203, 205, 206, 208, 209, 211, 212, 214, 215, 217, 221, 224, 226, 232, 233, 238, 239, 241, 244, 245, 247, 251, 253, 254, 256, 257, 259, 260, 265, 266, 268, 272, 278, 281, 289, 293, 295, 296, 298, 302, 304, 314, 316, 317, 319, 320, 322, 323, 325, 326, 328, 331, 337, 338, 340, 343, 344, 346, 349, 353, 355, 361, 362, 364, 367, 368, 373, 376, 379, 380, 383, 385, 386, 388, 392, 394, 401, 403, 409, 410, 413, 415, 416, 421, 422, 424, 425, 430, 431, 436, 437, 443, 445, 448, 451, 452, 455, 463, 464, 466, 467, 469, 476, 478, 481, 484, 485, 487, 488, 490, 493, 497, 506, 508, 509, 518, 520, 521, 526, 527, 529, 530, 536, 539, 541, 550, 551, 553, 554, 562, 563, 566, 568, 569, 572, 574, 581, 586, 587, 589, 590, 592, 595, 596, 598, 599, 601, 604, 605, 608, 610, 613, 620, 622, 623, 628, 631, 632, 634, 635, 638, 640, 643, 647, 650, 652, 656, 658, 659, 661, 662, 664, 665, 667, 670, 673, 674, 676, 677, 679, 680, 685, 686, 688, 689, 692, 694, 695, 697, 700, 703, 706, 707, 713, 715, 718, 721, 725, 728, 730, 731, 733, 736, 739, 743, 746, 749, 751, 752, 754, 755, 757, 760, 761, 763, 764, 766, 767, 769, 770, 775, 778, 779, 781, 782, 785, 787, 788, 790, 797, 799, 802, 811, 812, 814, 817, 818, 821, 823, 826, 827, 829, 833, 836, 841, 847, 850, 851, 853, 854, 857, 859, 860, 862, 863, 865, 866, 868, 869, 871, 872, 877, 881, 883, 884, 886, 889, 890, 893, 896, 898, 901, 902, 905, 907, 908, 910, 913, 916, 917, 919, 920, 925, 929, 931, 932, 935, 940, 946, 947, 949, 950, 952, 953, 955, 965, 967, 968, 973, 974, 976, 979, 980, 986, 988, 994, 997, 998, 1000, 1001, 1004, 1006, 1007, 1009, 1010, 1013, 1015, 1018, 1019, 1022, 1024, 1031, 1036, 1042, 1045, 1046, 1048, 1051, 1052, 1060, 1061, 1063, 1064, 1067, 1069, 1072, 1073, 1079, 1082, 1084, 1087, 1088, 1091, 1093, 1094, 1097, 1099, 1100, 1105, 1106, 1108, 1109, 1111, 1115, 1117, 1120, 1123, 1124, 1126, 1136, 1138, 1139, 1141, 1144, 1148, 1151, 1153, 1156, 1157, 1162, 1169, 1171, 1172, 1174, 1175, 1178, 1183, 1190, 1195, 1196, 1202, 1204, 1205, 1211, 1213, 1219, 1222, 1223, 1225, 1228, 1231, 1234, 1238, 1240, 1241, 1244, 1246, 1250, 1256, 1262, 1264, 1267, 1268, 1271, 1273, 1274, 1276, 1277, 1280, 1282, 1285, 1286, 1288, 1289, 1291, 1292, 1294, 1295, 1297, 1300, 1303, 1304, 1306, 1307, 1309, 1313, 1318, 1319, 1321, 1322, 1324, 1325, 1327, 1330, 1333, 1337, 1340, 1342, 1343, 1345, 1346, 1348, 1349, 1351, 1354, 1357, 1360, 1361, 1363, 1366, 1372, 1373, 1375, 1378, 1379, 1381, 1388, 1391, 1396, 1399, 1402, 1405, 1412, 1415, 1417, 1420, 1423, 1424, 1429, 1430, 1432, 1436, 1438, 1439, 1444, 1447, 1448, 1454, 1456, 1457, 1460, 1465, 1468, 1469, 1471, 1472, 1477, 1478, 1480, 1481, 1483, 1486, 1487, 1489, 1492, 1493, 1495, 1496, 1498, 1504, 1507, 1510, 1513, 1514, 1516, 1517, 1519, 1520, 1522, 1523, 1525, 1526, 1528, 1529, 1531, 1532, 1534, 1535, 1537, 1538, 1540, 1543, 1546, 1549, 1552, 1553, 1555, 1558, 1559, 1562, 1564, 1567, 1568, 1571, 1574, 1576, 1577, 1580, 1583, 1585, 1588, 1591, 1592, 1595, 1597, 1600, 1601, 1603, 1604, 1610, 1615, 1616, 1625, 1628, 1630, 1631, 1636, 1640, 1645, 1649, 1655, 1660, 1663, 1664, 1666, 1669, 1670, 1672, 1675, 1676, 1679, 1681, 1682, 1684, 1685, 1687, 1691, 1696, 1699, 1700, 1703, 1708, 1714, 1715, 1721, 1723, 1726, 1727, 1730, 1732, 1738, 1741, 1742, 1745, 1748, 1754, 1757, 1762, 1763, 1766, 1768, 1772, 1774, 1777, 1778, 1780, 1781, 1783, 1786, 1787, 1789, 1792, 1793, 1795, 1796, 1799, 1807, 1808, 1810, 1813, 1814, 1816, 1820, 1822, 1823, 1825, 1826, 1828, 1829, 1832, 1834, 1835, 1843, 1846, 1847, 1850, 1858, 1862, 1864, 1868, 1870, 1871, 1873, 1876, 1877, 1879, 1880, 1891, 1892, 1894, 1895, 1898, 1906, 1912, 1913, 1915, 1918, 1922, 1928, 1930, 1934, 1936, 1939, 1940, 1942, 1946, 1948, 1949, 1951, 1954, 1955, 1960, 1961, 1963, 1966, 1967, 1970, 1972, 1975, 1976, 1982, 1987, 1988, 1990, 1991, 1993, 1994, 1996, 1999, 2002, 2005, 2006, 2008, 2017, 2018, 2021, 2024, 2029, 2030, 2032, 2033, 2035, 2036, 2038, 2039, 2051, 2053, 2054, 2056, 2057, 2065, 2066, 2068, 2069, 2071, 2075, 2077, 2078, 2080, 2086, 2089, 2092, 2093, 2095, 2096, 2098, 2102, 2104, 2107, 2108, 2116, 2117, 2119, 2122, 2123, 2126, 2131, 2134, 2135, 2137, 2138, 2140, 2141, 2143, 2147, 2149, 2150, 2152, 2155, 2156, 2158, 2162, 2164, 2167, 2168, 2170, 2171, 2174, 2177, 2179, 2183, 2185, 2186, 2188, 2191, 2192, 2194, 2198, 2200, 2203, 2206, 2207, 2209, 2212, 2215, 2216, 2218, 2219, 2221, 2224, 2225, 2228, 2230, 2231, 2233, 2237, 2239, 2242, 2248, 2249, 2252, 2255, 2260, 2261, 2264, 2267, 2270, 2275, 2279, 2282, 2284, 2285, 2287, 2288, 2290, 2291, 2293, 2294, 2303, 2305, 2306, 2309, 2311, 2312, 2314, 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WashingtonsBound[5] := [ 143, 157, 347, 419, 439, 473, 611, 617, 830, 856, 943, 961, 1103, 1118, 1235, 1253, 1390, 1408, 1435, 1445, 1490, 1627, 1697, 1711, 1736, 1760, 1837, 1855, 1958, 2146, 2201, 2240, 2243, 2321, 2330, 2474, 2498, 2513, 2519, 2579, 2588, 2606, 2663, 2717, 2764, 2870, 2909, 2963, 3032, 3119, 3125, 3140, 3164, 3217, 3257, 3305, 3404, 3452, 3455, 3467, 3532, 3632, 3677, 3679, 3683, 3697, 3710, 3743, 3839, 3938, 3959, 3983, 3985, 4007, 4058, 4105, 4130, 4177, 4190, 4229, 4292, 4298, 4310, 4360, 4361, 4508, 4574, 4642, 4670, 4693, 4793, 4849, 4874, 4877, 4883, 4913, 4919, 4933, 5033, 5036, 5038, 5131, 5156, 5165, 5179, 5215, 5236, 5282, 5303, 5321, 5327, 5351, 5396, 5408, 5515, 5567, 5653, 5681, 5735, 5740, 5783, 5785, 5843, 5878, 5912, 5929, 5939, 5954, 6043, 6128, 6182, 6205, 6214, 6233, 6239, 6358, 6359, 6383, 6472, 6478, 6514, 6535, 6557, 6563, 6611, 6695, 6728, 6737, 6763, 6827, 6932, 6959, 6965, 6968, 7009, 7040, 7084, 7091, 7214, 7376, 7387, 7427, 7450, 7469, 7486, 7573, 7753, 7852, 7928, 7960, 8005, 8014, 8095, 8123, 8141, 8144, 8179, 8222, 8285, 8305, 8327, 8378, 8408, 8489, 8492, 8513, 8585, 8620, 8674, 8711, 8737, 8777, 8783, 8786, 8804, 8872, 8893, 9062, 9086, 9121, 9128, 9158, 9257, 9260, 9377, 9458, 9505, 9512, 9517, 9550, 9647, 9677, 9679, 9689, 9713, 9763, 9859, 9970, 10025, 10100, 10108, 10123, 10190, 10205, 10226, 10237, 10244, 10315, 10334, 10378, 10456, 10457, 10486, 10507, 10553, 10679, 10696, 10739, 10897, 10898, 10939, 10949, 10951, 10958, 11000, 11050, 11132, 11189, 11209, 11216, 11236, 11323, 11366, 11393, 11396, 11447, 11525, 11575, 11584, 11587, 11590, 11594, 11701, 11758, 11794, 11824, 11984, 11992, 12151, 12233, 12239, 12278, 12323, 12361, 12401, 12419, 12469, 12496, 12509, 12521, 12535, 12584, 12601, 12653, 12665, 12737, 12743, 12797, 12866, 12904, 12946, 12947, 12959, 13108, 13115, 13121, 13126, 13165, 13211, 13334, 13379, 13411, 13484, 13544, 13601, 13616, 13670, 13684, 13819, 13853, 13873, 13940, 13948, 13972, 13985, 14009, 14144, 14168, 14207, 14219, 14279, 14290, 14333, 14486, 14501, 14510, 14522, 14560, 14590, 14596, 14614, 14618, 14629, 14642, 14686, 14711, 14714, 14743, 14750, 14762, 14767, 14791, 14801, 14944, 14975, 14993, 15145, 15169, 15199, 15271, 15281, 15311, 15386, 15464, 15482, 15490, 15523, 15556, 15557, 15602, 15701, 15737, 15761, 15785, 15823, 15844, 15880, 16063, 16103, 16160, 16187, 16195, 16238, 16262, 16279, 16288, 16319, 16390, 16421, 16481, 16490, 16514, 16517, 16639, 16745, 16877, 16895, 16901, 16949, 16984, 17065, 17128, 17201, 17233, 17245, 17272, 17282, 17315, 17522, 17540, 17591, 17600, 17620, 17650, 17669, 17672, 17690, 17707, 17725, 17798, 17812, 17819, 17827, 17840, 17846, 17906, 18064, 18071, 18170, 18176, 18224, 18343, 18406, 18428, 18449, 18475, 18559, 18649, 18695, 18724, 18743, 18787, 18829, 18925, 18967, 18997, 19000, 19037, 19105, 19144, 19169, 19177, 19222, 19244, 19270, 19301, 19303, 19307, 19343, 19369, 19388, 19523, 19663, 19669, 19688, 19799, 19849, 19867, 19883, 19904, 19937, 19955, 20000 ];
WashingtonsBound[7] := [ 3461, 9955, 12563, 13349, 14963, 16627, 17279, 19181, 19466, 19681 ];
MsChecked := [ 1, 2, 4, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 101, 104, 106, 107, 109, 110, 112, 113, 115, 116, 118, 119, 121, 122, 124, 125, 127, 128, 130, 131, 133, 134, 136, 137, 140, 142, 143, 145, 146, 148, 149, 151, 155, 157, 158, 160, 161, 163, 164, 166, 167, 169, 170, 172, 173, 175, 176, 178, 179, 181, 182, 184, 185, 187, 190, 191, 193, 194, 196, 197, 199, 200, 202, 203, 205, 206, 208, 209, 211, 212, 214, 215, 217, 218, 220, 221, 223, 224, 226, 227, 229, 230, 232, 233, 236, 238, 239, 241, 242, 244, 245, 247, 248, 251, 253, 254, 256, 257, 259, 260, 262, 263, 265, 266, 268, 272, 274, 275, 277, 278, 280, 281, 283, 284, 287, 289, 290, 292, 293, 295, 296, 298, 301, 302, 304, 305, 307, 308, 310, 311, 313, 314, 316, 317, 319, 320, 322, 323, 325, 326, 328, 329, 331, 332, 334, 337, 338, 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19906, 19907, 19909, 19910, 19912, 19913, 19915, 19916, 19918, 19919, 19921, 19922, 19924, 19925, 19927, 19928, 19930, 19931, 19933, 19934, 19936, 19937, 19939, 19940, 19942, 19943, 19945, 19946, 19949, 19951, 19952, 19954, 19955, 19957, 19958, 19960, 19961, 19963, 19964, 19966, 19969, 19970, 19973, 19975, 19976, 19978, 19979, 19981, 19982, 19985, 19987, 19988, 19990, 19991, 19993, 19994, 19996, 19999, 20000 ];
FalseCurveRankList:= [ 892, 1678, 1801, 1900, 1933, 2110, 2630, 2698, 2998, 3040, 3122, 3368, 3506, 3572, 3742, 3760, 3781, 4009, 4246, 4270, 4354, 4375, 4825, 4840, 4900, 4936, 4940, 4948, 5050, 5197, 5230, 5326, 5504, 5524, 5530, 5572, 5920, 6104, 6196, 6266, 6280, 6316, 6481, 6562, 6580, 6685, 6730, 6886, 6970, 7022, 7204, 7330, 7366, 7370, 7429, 7460, 7628, 7736, 7744, 7798, 8011, 8054, 8122, 8204, 8225, 8282, 8374, 8428, 8620, 8716, 8848, 9056, 9061, 9100, 9220, 9242, 9278, 9310, 9475, 9575, 9704, 9836, 9920, 10006, 10048, 10051, 10108, 10198, 10382, 10388, 10888, 11170, 11221, 11233, 11264, 11272, 11492, 11542, 11548, 11590, 11647, 11662, 11717, 11734, 11738, 11852, 11866, 12184, 12185, 12187, 12244, 12286, 12350, 12358, 12457, 12565, 12592, 12593, 12604, 12676, 12703, 12710, 12742, 12845, 12872, 12886, 13021, 13033, 13040, 13042, 13147, 13270, 13400, 13448, 13457, 13502, 13832, 13978, 14122, 14246, 14320, 14332, 14360, 14374, 14396, 14429, 14464, 14467, 14569, 14621, 14624, 14968, 15094, 15266, 15452, 15463, 15496, 15548, 15562, 15568, 15580, 15622, 15640, 15694, 15778, 15985, 16120, 16123, 16201, 16271, 16316, 16321, 16346, 16372, 16378, 16429, 16480, 16672, 16813, 16814, 16822, 16882, 16894, 16940, 17029, 17074, 17188, 17276, 17383, 17425, 17428, 17465, 17486, 17656, 17705, 17866, 17986, 18044, 18070, 18136, 18169, 18172, 18268, 18392, 18436, 18445, 18464, 18560, 18632, 18653, 18664, 18686, 18740, 18781, 18910, 18937, 18982, 19025, 19324, 19417, 19544, 19594, 19658, 19738, 19753, 19835, 19940 ];TrueCurveRankList:= [ 1, 2, 4, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 101, 104, 106, 107, 109, 110, 112, 113, 115, 116, 118, 119, 121, 122, 124, 125, 127, 128, 130, 131, 133, 134, 136, 137, 140, 142, 143, 145, 146, 148, 149, 151, 155, 157, 158, 160, 161, 163, 164, 166, 167, 169, 170, 172, 173, 175, 176, 178, 179, 181, 182, 184, 185, 187, 190, 191, 193, 194, 196, 197, 199, 200, 202, 203, 205, 206, 208, 209, 211, 212, 214, 215, 217, 218, 220, 221, 223, 224, 226, 227, 229, 230, 232, 233, 236, 238, 239, 241, 242, 244, 245, 247, 248, 251, 253, 254, 256, 257, 259, 260, 262, 263, 265, 266, 268, 272, 274, 275, 277, 278, 280, 281, 283, 284, 287, 289, 290, 292, 293, 295, 296, 298, 301, 302, 304, 305, 307, 308, 310, 311, 313, 314, 316, 317, 319, 320, 322, 323, 325, 326, 328, 329, 331, 332, 334, 337, 338, 340, 341, 343, 344, 346, 347, 349, 350, 352, 353, 355, 358, 359, 361, 362, 364, 365, 367, 368, 370, 371, 373, 376, 377, 379, 380, 382, 383, 385, 386, 388, 389, 391, 392, 394, 395, 400, 401, 403, 406, 407, 409, 410, 412, 413, 415, 416, 418, 419, 421, 422, 424, 425, 427, 428, 430, 431, 434, 436, 437, 439, 440, 442, 443, 445, 448, 449, 451, 452, 454, 455, 457, 458, 460, 461, 463, 464, 466, 467, 469, 470, 472, 473, 475, 476, 478, 479, 481, 484, 485, 487, 488, 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19192, 19193, 19195, 19196, 19198, 19199, 19201, 19202, 19204, 19205, 19207, 19208, 19210, 19211, 19214, 19216, 19217, 19219, 19220, 19222, 19223, 19225, 19226, 19228, 19229, 19231, 19232, 19234, 19235, 19237, 19238, 19240, 19241, 19243, 19244, 19246, 19247, 19250, 19252, 19253, 19255, 19256, 19258, 19259, 19261, 19264, 19265, 19267, 19268, 19270, 19271, 19273, 19274, 19276, 19277, 19279, 19280, 19282, 19283, 19285, 19286, 19288, 19289, 19291, 19292, 19294, 19295, 19297, 19300, 19301, 19303, 19304, 19306, 19307, 19309, 19310, 19312, 19313, 19315, 19316, 19318, 19319, 19321, 19322, 19325, 19327, 19328, 19330, 19331, 19333, 19334, 19336, 19339, 19340, 19342, 19343, 19345, 19346, 19348, 19349, 19351, 19352, 19354, 19355, 19357, 19358, 19361, 19363, 19364, 19367, 19369, 19370, 19372, 19373, 19375, 19376, 19378, 19379, 19381, 19382, 19384, 19385, 19387, 19388, 19390, 19391, 19393, 19394, 19397, 19399, 19400, 19402, 19403, 19405, 19406, 19408, 19411, 19412, 19414, 19415, 19418, 19420, 19421, 19423, 19424, 19426, 19427, 19429, 19430, 19432, 19433, 19435, 19436, 19438, 19439, 19441, 19442, 19444, 19447, 19448, 19450, 19451, 19453, 19454, 19456, 19457, 19459, 19460, 19462, 19463, 19465, 19466, 19468, 19469, 19471, 19472, 19474, 19475, 19477, 19478, 19480, 19481, 19483, 19484, 19486, 19487, 19489, 19490, 19492, 19493, 19495, 19496, 19498, 19499, 19502, 19504, 19505, 19508, 19510, 19511, 19513, 19514, 19516, 19517, 19519, 19520, 19522, 19523, 19525, 19526, 19528, 19529, 19531, 19532, 19534, 19537, 19538, 19541, 19546, 19547, 19549, 19550, 19552, 19553, 19555, 19558, 19559, 19561, 19562, 19564, 19565, 19567, 19568, 19570, 19571, 19573, 19574, 19577, 19579, 19580, 19582, 19583, 19585, 19586, 19588, 19589, 19591, 19595, 19597, 19598, 19600, 19601, 19603, 19604, 19606, 19607, 19609, 19610, 19612, 19613, 19615, 19616, 19618, 19619, 19621, 19622, 19624, 19625, 19627, 19628, 19630, 19631, 19633, 19634, 19636, 19637, 19639, 19640, 19642, 19643, 19645, 19646, 19649, 19651, 19652, 19655, 19657, 19660, 19661, 19663, 19664, 19666, 19667, 19669, 19672, 19673, 19675, 19676, 19678, 19679, 19681, 19682, 19684, 19685, 19687, 19688, 19691, 19693, 19694, 19696, 19697, 19699, 19700, 19702, 19705, 19706, 19708, 19709, 19711, 19712, 19714, 19715, 19717, 19718, 19720, 19721, 19723, 19724, 19726, 19727, 19729, 19730, 19732, 19733, 19735, 19736, 19741, 19742, 19744, 19745, 19747, 19748, 19750, 19751, 19754, 19756, 19757, 19760, 19762, 19763, 19765, 19766, 19768, 19769, 19771, 19772, 19774, 19775, 19777, 19778, 19780, 19781, 19783, 19784, 19786, 19787, 19789, 19790, 19792, 19793, 19795, 19796, 19798, 19799, 19802, 19804, 19805, 19807, 19808, 19810, 19811, 19813, 19814, 19816, 19817, 19820, 19823, 19825, 19826, 19828, 19829, 19831, 19832, 19834, 19838, 19840, 19841, 19843, 19844, 19846, 19847, 19849, 19852, 19853, 19855, 19856, 19858, 19859, 19861, 19862, 19865, 19867, 19868, 19870, 19871, 19874, 19876, 19877, 19879, 19880, 19882, 19883, 19885, 19888, 19889, 19891, 19892, 19894, 19895, 19897, 19898, 19900, 19901, 19903, 19904, 19906, 19907, 19909, 19910, 19912, 19913, 19915, 19916, 19918, 19919, 19921, 19922, 19924, 19925, 19927, 19928, 19930, 19931, 19933, 19934, 19936, 19937, 19939, 19942, 19943, 19945, 19946, 19949, 19951, 19952, 19954, 19955, 19957, 19958, 19960, 19961, 19963, 19964, 19966, 19969, 19970, 19973, 19975, 19976, 19978, 19979, 19981, 19982, 19985, 19987, 19988, 19990, 19991, 19993, 19994, 19996, 19999, 20000 ];

//Creates the TrueSharp sequence. 
TrueSharp := [];
for k in Keys(WashingtonsBound) do
    for m in VectorMeet(WashingtonsBound[k],TrueCurveRank[k]) do
        Append(~TrueSharp, m);
    end for;
end for;
TrueSharp := Sort(TrueSharp);


//This computes the intersection of two sequence V1 and V2.
function VectorMeet(V1,V2)
    return [k : k in V1 | k in V2];
end function;



//Takes as its input a set I (usually an interval) and returns Sharp(I) defined in section 6.1.
function TrueSharpness(I)
    a := #VectorMeet(TrueSharp,I);
    b := #VectorMeet(MsChecked,I);
    return RealField(5)!(a/b);
end function;

//Takes as its input an integer m and returns the rank of E_m. If m is in MsChecked, then it uses
//the database, otherwise it computes the rank from scratch.
function RankOfM(m)
    if m in TrueCurveRankList then
        for k in Keys(TrueCurveRank) do
        if m in TrueCurveRank[k] then
            return k;
        end if;
        end for;
    end if;
    if m in FalseCurveRankList then
        for k in Keys(FalseCurveRankLowerBound) do
            if m in FalseCurveRankLowerBound[k] then
            rl := k;
            end if;
        end for;
        for k in Keys(FalseCurveRankUpperBound) do
            if m in FalseCurveRankLowerBound[k] then
            ru := k;
            end if;
        end for;
        return [rl,ru];
    end if;
    if not m in MsChecked then
        f := Polynomial([1,-(m+3),m,1]);
        E := EllipticCurve(f);
        return RankBounds(E);
    end if;
end function;

//Takes as its input an integer m and returns Washington's bound for the rank of E_m. If m is
//in MsChecked, then it uses the database, otherwise it computes the bound from scratch.
function WashingtonsBoundForM(m)
    if m in MsChecked then
    for k in Keys(WashingtonsBound) do
        if m in WashingtonsBound[k] then
            return k;
        end if;
    end for;
    else
        f := Polynomial([1,-(m+3),m,1]);
        Lm := NumberField(f);
        G := ClassGroup(Lm);
        mult2 := hom<G -> G | g :-> 2*g>;
        return 1 + Integers()!(Log(#Kernel(mult2))/Log(2));
    end if;
end function;

//Takes as its input an integer m and returns the dimension of CL(L_m)[2]. If m is in MsChecked,
//then it uses the database, otherwise it computes the dimension from scratch.
function TwoClassGroupRankForM(m)
    if  m in MsChecked then
    for k in Keys(TwoClassGroupRank) do
        if m in TwoClassGroupRank[k] then
            return k;
        end if;
    end for;
    else
        f := Polynomial([1,-(m+3),m,1]);
        Lm := NumberField(f);
        G := ClassGroup(Lm);
        mult2 := hom<G -> G | g :-> 2*g>;
        return 1 + Integers()!(Log(#Kernel(mult2))/Log(2));
    end if;
end function;
