weierstrass_point_bound := [<1, 0>, <2, 0>, <3, 0>, <4, 0>, <5, 0>, <6, 0>, <7, 0>, <8, 0>, <9, 0>, <10, 0>, <11, 0>, <12, 0>, <13, 0>, <14, 0>, <15, 0>, <16, 0>, <17, 0>, <18, 0>, <19, 0>, <20, 0>, <21, 0>, <22, 0>, <23, 0>, <24, 0>, <25, 0>, <26, 0>, <27, 0>, <28, 0>, <29, 0>, <30, 0>, <31, 0>, <32, 0>, <33, 0>, <34, 0>, <35, 0>, <36, 0>, <37, 0>, <38, 0>, <39, 0>, <40, 0>, <41, 0>, <42, 0>, <43, 0>, <44, 0>, <45, 0>, <46, 0>, <47, 0>, <48, 0>, <49, 0>, <50, 0>, <51, 0>, <52, 0>, <53, 0>, <54, 1>, <55, 0>, <56, 0>, <57, 0>, <58, 0>, <59, 0>, <60, 0>, <61, 0>, <62, 0>, <63, 0>, <64, 1>, <65, 0>, <66, 0>, <67, 0>, <68, 0>, <69, 0>, <70, 0>, <71, 0>, <72, 1>, <73, 0>, <74, 0>, <75, 0>, <76, 0>, <77, 0>, <78, 0>, <79, 0>, <80, 0>, <81, 0>, <82, 0>, <83, 0>, <84, 0>, <85, 0>, <86, 0>, <87, 0>, <88, 0>, <89, 0>, <90, 0>, <91, 0>, <92, 0>, <93, 0>, <94, 0>, <95, 0>, <96, 1>, <97, 0>, <98, 1>, <99, 0>, <100, 1>, <101, 0>, <102, 0>, <103, 0>, <104, 0>, <105, 0>, <106, 0>, <107, 0>, <108, 2>, <109, 0>, <110, 0>, <111, 0>, <112, 0>, <113, 0>, <114, 0>, <115, 0>, <116, 0>, <117, 0>, <118, 0>, <119, 0>, <120, 1>, <121, 1>, <122, 0>, <123, 0>, <124, 0>, <125, 1>, <126, 0>, <127, 0>, <128, 2>, <129, 0>, <130, 0>, <131, 0>, <132, 0>, <133, 0>, <134, 0>, <135, 1>, <136, 0>, <137, 0>, <138, 0>, <139, 0>, <140, 0>, <141, 0>, <142, 0>, <143, 0>, <144, 2>, <145, 0>, <146, 0>, <147, 1>, <148, 0>, <149, 0>, <150, 1>, <151, 0>, <152, 0>, <153, 0>, <154, 0>, <155, 0>, <156, 0>, <157, 0>, <158, 0>, <159, 0>, <160, 1>, <161, 0>, <162, 1>, <163, 0>, <164, 0>, <165, 0>, <166, 0>, <167, 0>, <168, 1>, <169, 1>, <170, 0>, <171, 0>, <172, 0>, <173, 0>, <174, 0>, <175, 0>, <176, 0>, <177, 0>, <178, 0>, <179, 0>, <180, 1>, <181, 0>, <182, 0>, <183, 0>, <184, 0>, <185, 0>, <186, 0>, <187, 0>, <188, 0>, <189, 1>, <190, 0>, <191, 0>, <192, 3>, <193, 0>, <194, 0>, <195, 0>, <196, 1>, <197, 0>, <198, 0>, <199, 0>, <200, 2>, <201, 0>, <202, 0>, <203, 0>, <204, 0>, <205, 0>, <206, 0>, <207, 0>, <208, 0>, <209, 0>, <210, 0>, <211, 0>, <212, 0>, <213, 0>, <214, 0>, <215, 0>, <216, 4>, <217, 0>, <218, 0>, <219, 0>, <220, 0>, <221, 0>, <222, 0>, <223, 0>, <224, 1>, <225, 1>, <226, 0>, <227, 0>, <228, 0>, <229, 0>, <230, 0>, <231, 0>, <232, 0>, <233, 0>, <234, 0>, <235, 0>, <236, 0>, <237, 0>, <238, 0>, <239, 0>, <240, 3>, <241, 0>, <242, 1>, <243, 2>, <244, 0>, <245, 0>, <246, 0>, <247, 0>, <248, 0>, <249, 0>, <250, 4>, <251, 0>, <252, 1>, <253, 0>, <254, 0>, <255, 0>, <256, 3>, <257, 0>, <258, 0>, <259, 0>, <260, 1>, <261, 0>, <262, 0>, <263, 0>, <264, 1>, <265, 0>, <266, 0>, <267, 0>, <268, 0>, <269, 0>, <270, 4>, <271, 0>, <272, 0>, <273, 0>, <274, 0>, <275, 0>, <276, 0>, <277, 0>, <278, 0>, <279, 0>, <280, 1>, <281, 0>, <282, 0>, <283, 0>, <284, 0>, <285, 0>, <286, 0>, <287, 0>, <288, 4>, <289, 1>, <290, 0>, <291, 0>, <292, 0>, <293, 0>, <294, 1>, <295, 0>, <296, 0>, <297, 1>, <298, 0>, <299, 0>, <300, 3>, <301, 0>, <302, 0>, <303, 0>, <304, 0>, <305, 0>, <306, 0>, <307, 0>, <308, 0>, <309, 0>, <310, 0>, <311, 0>, <312, 1>, <313, 0>, <314, 0>, <315, 0>, <316, 0>, <317, 0>, <318, 0>, <319, 0>, <320, 3>, <321, 0>, <322, 0>, <323, 0>, <324, 5>, <325, 0>, <326, 0>, <327, 0>, <328, 0>, <329, 0>, <330, 0>, <331, 0>, <332, 0>, <333, 0>, <334, 0>, <335, 0>, <336, 3>, <337, 0>, <338, 1>, <339, 0>, <340, 1>, <341, 0>, <342, 0>, <343, 4>, <344, 0>, <345, 0>, <346, 0>, <347, 0>, <348, 0>, <349, 0>, <350, 0>, <351, 1>, <352, 1>, <353, 0>, <354, 0>, <355, 0>, <356, 0>, <357, 0>, <358, 0>, <359, 0>, <360, 5>, <361, 2>, <362, 0>, <363, 1>, <364, 0>, <365, 0>, <366, 0>, <367, 0>, <368, 0>, <369, 0>, <370, 0>, <371, 0>, <372, 0>, <373, 0>, <374, 0>, <375, 3>, <376, 0>, <377, 0>, <378, 4>, <379, 0>, <380, 0>, <381, 0>, <382, 0>, <383, 0>, <384, 4>, <385, 0>, <386, 0>, <387, 0>, <388, 0>, <389, 0>, <390, 0>, <391, 0>, <392, 4>, <393, 0>, <394, 0>, <395, 0>, <396, 1>, <397, 0>, <398, 0>, <399, 0>, <400, 4>, <401, 0>, <402, 0>, <403, 0>, <404, 0>, <405, 4>, <406, 0>, <407, 0>, <408, 1>, <409, 0>, <410, 0>, <411, 0>, <412, 0>, <413, 0>, <414, 0>, <415, 0>, <416, 1>, <417, 0>, <418, 0>, <419, 0>, <420, 1>, <421, 0>, <422, 0>, <423, 0>, <424, 0>, <425, 0>, <426, 0>, <427, 0>, <428, 0>, <429, 0>, <430, 0>, <431, 0>, <432, 8>, <433, 0>, <434, 0>, <435, 0>, <436, 0>, <437, 0>, <438, 0>, <439, 0>, <440, 1>, <441, 4>, <442, 0>, <443, 0>, <444, 0>, <445, 0>, <446, 0>, <447, 0>, <448, 3>, <449, 0>, <450, 5>, <451, 0>, <452, 0>, <453, 0>, <454, 0>, <455, 0>, <456, 1>, <457, 0>, <458, 0>, <459, 1>, <460, 0>, <461, 0>, <462, 0>, <463, 0>, <464, 0>, <465, 0>, <466, 0>, <467, 0>, <468, 1>, <469, 0>, <470, 0>, <471, 0>, <472, 0>, <473, 0>, <474, 0>, <475, 0>, <476, 0>, <477, 0>, <478, 0>, <479, 0>, <480, 6>, <481, 0>, <482, 0>, <483, 0>, <484, 4>, <485, 0>, <486, 5>, <487, 0>, <488, 0>, <489, 0>, <490, 1>, <491, 0>, <492, 0>, <493, 0>, <494, 0>, <495, 0>, <496, 0>, <497, 0>, <498, 0>, <499, 0>, <500, 7>, <501, 0>, <502, 0>, <503, 0>, <504, 5>, <505, 0>, <506, 0>, <507, 2>, <508, 0>, <509, 0>, <510, 0>, <511, 0>, <512, 8>, <513, 1>, <514, 0>, <515, 0>, <516, 0>, <517, 0>, <518, 0>, <519, 0>, <520, 2>, <521, 0>, <522, 0>, <523, 0>, <524, 0>, <525, 1>, <526, 0>, <527, 0>, <528, 3>, <529, 3>, <530, 0>, <531, 0>, <532, 0>, <533, 0>, <534, 0>, <535, 0>, <536, 0>, <537, 0>, <538, 0>, <539, 1>, <540, 7>, <541, 0>, <542, 0>, <543, 0>, <544, 1>, <545, 0>, <546, 0>, <547, 0>, <548, 0>, <549, 0>, <550, 0>, <551, 0>, <552, 1>, <553, 0>, <554, 0>, <555, 0>, <556, 0>, <557, 0>, <558, 0>, <559, 0>, <560, 2>, <561, 0>, <562, 0>, <563, 0>, <564, 0>, <565, 0>, <566, 0>, <567, 4>, <568, 0>, <569, 0>, <570, 0>, <571, 0>, <572, 0>, <573, 0>, <574, 0>, <575, 0>, <576, 10>, <577, 0>, <578, 1>, <579, 0>, <580, 1>, <581, 0>, <582, 0>, <583, 0>, <584, 0>, <585, 0>, <586, 0>, <587, 0>, <588, 5>, <589, 0>, <590, 0>, <591, 0>, <592, 0>, <593, 0>, <594, 4>, <595, 0>, <596, 0>, <597, 0>, <598, 0>, <599, 0>, <600, 8>, <601, 0>, <602, 0>, <603, 0>, <604, 0>, <605, 1>, <606, 0>, <607, 0>, <608, 1>, <609, 0>, <610, 0>, <611, 0>, <612, 1>, <613, 0>, <614, 0>, <615, 0>, <616, 1>, <617, 0>, <618, 0>, <619, 0>, <620, 0>, <621, 1>, <622, 0>, <623, 0>, <624, 3>, <625, 1>, <626, 0>, <627, 0>, <628, 0>, <629, 0>, <630, 2>, <631, 0>, <632, 0>, <633, 0>, <634, 0>, <635, 0>, <636, 0>, <637, 1>, <638, 0>, <639, 0>, <640, 7>, <641, 0>, <642, 0>, <643, 0>, <644, 0>, <645, 0>, <646, 0>, <647, 0>, <648, 9>, <649, 0>, <650, 1>, <651, 0>, <652, 0>, <653, 0>, <654, 0>, <655, 0>, <656, 0>, <657, 0>, <658, 0>, <659, 0>, <660, 1>, <661, 0>, <662, 0>, <663, 0>, <664, 0>, <665, 0>, <666, 0>, <667, 0>, <668, 0>, <669, 0>, <670, 0>, <671, 0>, <672, 6>, <673, 0>, <674, 0>, <675, 8>, <676, 4>, <677, 0>, <678, 0>, <679, 0>, <680, 2>, <681, 0>, <682, 0>, <683, 0>, <684, 1>, <685, 0>, <686, 9>, <687, 0>, <688, 0>, <689, 0>, <690, 0>, <691, 0>, <692, 0>, <693, 0>, <694, 0>, <695, 0>, <696, 1>, <697, 0>, <698, 0>, <699, 0>, <700, 2>, <701, 0>, <702, 4>, <703, 0>, <704, 3>, <705, 0>, <706, 0>, <707, 0>, <708, 0>, <709, 0>, <710, 0>, <711, 0>, <712, 0>, <713, 0>, <714, 0>, <715, 0>, <716, 0>, <717, 0>, <718, 0>, <719, 0>, <720, 8>, <721, 0>, <722, 2>, <723, 0>, <724, 0>, <725, 0>, <726, 2>, <727, 0>, <728, 1>, <729, 5>, <730, 0>, <731, 0>, <732, 0>, <733, 0>, <734, 0>, <735, 3>, <736, 1>, <737, 0>, <738, 0>, <739, 0>, <740, 1>, <741, 0>, <742, 0>, <743, 0>, <744, 1>, <745, 0>, <746, 0>, <747, 0>, <748, 0>, <749, 0>, <750, 8>, <751, 0>, <752, 0>, <753, 0>, <754, 0>, <755, 0>, <756, 8>, <757, 0>, <758, 0>, <759, 0>, <760, 1>, <761, 0>, <762, 0>, <763, 0>, <764, 0>, <765, 0>, <766, 0>, <767, 0>, <768, 10>, <769, 0>, <770, 0>, <771, 0>, <772, 0>, <773, 0>, <774, 0>, <775, 0>, <776, 0>, <777, 0>, <778, 0>, <779, 0>, <780, 1>, <781, 0>, <782, 0>, <783, 1>, <784, 7>, <785, 0>, <786, 0>, <787, 0>, <788, 0>, <789, 0>, <790, 0>, <791, 0>, <792, 5>, <793, 0>, <794, 0>, <795, 0>, <796, 0>, <797, 0>, <798, 0>, <799, 0>, <800, 10>, <801, 0>, <802, 0>, <803, 0>, <804, 0>, <805, 0>, <806, 0>, <807, 0>, <808, 0>, <809, 0>, <810, 7>, <811, 0>, <812, 0>, <813, 0>, <814, 0>, <815, 0>, <816, 3>, <817, 0>, <818, 0>, <819, 2>, <820, 1>, <821, 0>, <822, 0>, <823, 0>, <824, 0>, <825, 0>, <826, 0>, <827, 0>, <828, 1>, <829, 0>, <830, 0>, <831, 0>, <832, 3>, <833, 0>, <834, 0>, <835, 0>, <836, 0>, <837, 1>, <838, 0>, <839, 0>, <840, 3>, <841, 3>, <842, 0>, <843, 0>, <844, 0>, <845, 1>, <846, 0>, <847, 0>, <848, 0>, <849, 0>, <850, 1>, <851, 0>, <852, 0>, <853, 0>, <854, 0>, <855, 0>, <856, 0>, <857, 0>, <858, 0>, <859, 0>, <860, 0>, <861, 0>, <862, 0>, <863, 0>, <864, 16>, <865, 0>, <866, 0>, <867, 3>, <868, 0>, <869, 0>, <870, 0>, <871, 0>, <872, 0>, <873, 0>, <874, 0>, <875, 3>, <876, 0>, <877, 0>, <878, 0>, <879, 0>, <880, 2>, <881, 0>, <882, 8>, <883, 0>, <884, 1>, <885, 0>, <886, 0>, <887, 0>, <888, 1>, <889, 0>, <890, 0>, <891, 4>, <892, 0>, <893, 0>, <894, 0>, <895, 0>, <896, 6>, <897, 0>, <898, 0>, <899, 0>, <900, 11>, <901, 0>, <902, 0>, <903, 0>, <904, 0>, <905, 0>, <906, 0>, <907, 0>, <908, 0>, <909, 0>, <910, 0>, <911, 0>, <912, 3>, <913, 0>, <914, 0>, <915, 0>, <916, 0>, <917, 0>, <918, 4>, <919, 0>, <920, 1>, <921, 0>, <922, 0>, <923, 0>, <924, 1>, <925, 0>, <926, 0>, <927, 0>, <928, 1>, <929, 0>, <930, 0>, <931, 1>, <932, 0>, <933, 0>, <934, 0>, <935, 0>, <936, 5>, <937, 0>, <938, 0>, <939, 0>, <940, 0>, <941, 0>, <942, 0>, <943, 0>, <944, 0>, <945, 3>, <946, 0>, <947, 0>, <948, 0>, <949, 0>, <950, 0>, <951, 0>, <952, 1>, <953, 0>, <954, 0>, <955, 0>, <956, 0>, <957, 0>, <958, 0>, <959, 0>, <960, 8>, <961, 3>, <962, 0>, <963, 0>, <964, 0>, <965, 0>, <966, 0>, <967, 0>, <968, 7>, <969, 0>, <970, 0>, <971, 0>, <972, 14>, <973, 0>, <974, 0>, <975, 0>, <976, 0>, <977, 0>, <978, 0>, <979, 0>, <980, 4>, <981, 0>, <982, 0>, <983, 0>, <984, 1>, <985, 0>, <986, 0>, <987, 0>, <988, 0>, <989, 0>, <990, 2>, <991, 0>, <992, 1>, <993, 0>, <994, 0>, <995, 0>, <996, 0>, <997, 0>, <998, 0>, <999, 1>, <1000, 9>, <1001, 0>, <1002, 0>, <1003, 0>, <1004, 0>, <1005, 0>, <1006, 0>, <1007, 0>, <1008, 9>, <1009, 0>, <1010, 0>, <1011, 0>, <1012, 0>, <1013, 0>, <1014, 2>, <1015, 0>, <1016, 0>, <1017, 0>, <1018, 0>, <1019, 0>, <1020, 1>, <1021, 0>, <1022, 0>, <1023, 0>, <1024, 11>, <1025, 0>, <1026, 4>, <1027, 0>, <1028, 0>, <1029, 9>, <1030, 0>, <1031, 0>, <1032, 1>, <1033, 0>, <1034, 0>, <1035, 0>, <1036, 0>, <1037, 0>, <1038, 0>, <1039, 0>, <1040, 2>, <1041, 0>, <1042, 0>, <1043, 0>, <1044, 1>, <1045, 0>, <1046, 0>, <1047, 0>, <1048, 0>, <1049, 0>, <1050, 2>, <1051, 0>, <1052, 0>, <1053, 4>, <1054, 0>, <1055, 0>, <1056, 7>, <1057, 0>, <1058, 3>, <1059, 0>, <1060, 1>, <1061, 0>, <1062, 0>, <1063, 0>, <1064, 1>, <1065, 0>, <1066, 0>, <1067, 0>, <1068, 0>, <1069, 0>, <1070, 0>, <1071, 0>, <1072, 0>, <1073, 0>, <1074, 0>, <1075, 0>, <1076, 0>, <1077, 0>, <1078, 2>, <1079, 0>, <1080, 11>, <1081, 0>, <1082, 0>, <1083, 2>, <1084, 0>, <1085, 0>, <1086, 0>, <1087, 0>, <1088, 3>, <1089, 4>, <1090, 0>, <1091, 0>, <1092, 1>, <1093, 0>, <1094, 0>, <1095, 0>, <1096, 0>, <1097, 0>, <1098, 0>, <1099, 0>, <1100, 2>, <1101, 0>, <1102, 0>, <1103, 0>, <1104, 3>, <1105, 0>, <1106, 0>, <1107, 1>, <1108, 0>, <1109, 0>, <1110, 0>, <1111, 0>, <1112, 0>, <1113, 0>, <1114, 0>, <1115, 0>, <1116, 1>, <1117, 0>, <1118, 0>, <1119, 0>, <1120, 3>, <1121, 0>, <1122, 0>, <1123, 0>, <1124, 0>, <1125, 10>, <1126, 0>, <1127, 1>, <1128, 1>, <1129, 0>, <1130, 0>, <1131, 0>, <1132, 0>, <1133, 0>, <1134, 9>, <1135, 0>, <1136, 0>, <1137, 0>, <1138, 0>, <1139, 0>, <1140, 1>, <1141, 0>, <1142, 0>, <1143, 0>, <1144, 1>, <1145, 0>, <1146, 0>, <1147, 0>, <1148, 0>, <1149, 0>, <1150, 0>, <1151, 0>, <1152, 17>, <1153, 0>, <1154, 0>, <1155, 0>, <1156, 6>, <1157, 0>, <1158, 0>, <1159, 0>, <1160, 2>, <1161, 1>, <1162, 0>, <1163, 0>, <1164, 0>, <1165, 0>, <1166, 0>, <1167, 0>, <1168, 0>, <1169, 0>, <1170, 2>, <1171, 0>, <1172, 0>, <1173, 0>, <1174, 0>, <1175, 0>, <1176, 15>, <1177, 0>, <1178, 0>, <1179, 0>, <1180, 0>, <1181, 0>, <1182, 0>, <1183, 1>, <1184, 1>, <1185, 0>, <1186, 0>, <1187, 0>, <1188, 9>, <1189, 0>, <1190, 0>, <1191, 0>, <1192, 0>, <1193, 0>, <1194, 0>, <1195, 0>, <1196, 0>, <1197, 2>, <1198, 0>, <1199, 0>, <1200, 13>, <1201, 0>, <1202, 0>, <1203, 0>, <1204, 0>, <1205, 0>, <1206, 0>, <1207, 0>, <1208, 0>, <1209, 0>, <1210, 0>, <1211, 0>, <1212, 0>, <1213, 0>, <1214, 0>, <1215, 7>, <1216, 3>, <1217, 0>, <1218, 0>, <1219, 0>, <1220, 1>, <1221, 0>, <1222, 0>, <1223, 0>, <1224, 5>, <1225, 3>, <1226, 0>, <1227, 0>, <1228, 0>, <1229, 0>, <1230, 0>, <1231, 0>, <1232, 2>, <1233, 0>, <1234, 0>, <1235, 0>, <1236, 0>, <1237, 0>, <1238, 0>, <1239, 0>, <1240, 1>, <1241, 0>, <1242, 4>, <1243, 0>, <1244, 0>, <1245, 0>, <1246, 0>, <1247, 0>, <1248, 7>, <1249, 0>, <1250, 9>, <1251, 0>, <1252, 0>, <1253, 0>, <1254, 0>, <1255, 0>, <1256, 0>, <1257, 0>, <1258, 0>, <1259, 0>, <1260, 3>, <1261, 0>, <1262, 0>, <1263, 0>, <1264, 0>, <1265, 0>, <1266, 0>, <1267, 0>, <1268, 0>, <1269, 1>, <1270, 0>, <1271, 0>, <1272, 1>, <1273, 0>, <1274, 0>, <1275, 0>, <1276, 0>, <1277, 0>, <1278, 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