squares.py

squares = [
    (1, 1, 1), (2, 4, 3), (3, 9, 5), (4, 16, 7), (5, 25, 9), (6, 36, 11),
    (7, 49, 13), (8, 64, 15), (9, 81, 17), (10, 100, 19), (11, 121, 21),
    (12, 144, 23), (13, 169, 25), (14, 196, 27), (15, 225, 29), (16, 256, 31),
    (17, 289, 33), (18, 324, 35), (19, 361, 37), (20, 400, 39), (21, 441, 41),
    (22, 484, 43), (23, 529, 45), (24, 576, 47), (25, 625, 49), (26, 676, 51),
    (27, 729, 53), (28, 784, 55), (29, 841, 57), (30, 900, 59), (31, 961, 61),
    (32, 1024, 63), (33, 1089, 65), (34, 1156, 67), (35, 1225, 69),
    (36, 1296, 71), (37, 1369, 73), (38, 1444, 75), (39, 1521, 77),
    (40, 1600, 79), (41, 1681, 81), (42, 1764, 83), (43, 1849, 85),
    (44, 1936, 87), (45, 2025, 89), (46, 2116, 91), (47, 2209, 93),
    (48, 2304, 95), (49, 2401, 97), (50, 2500, 99), (51, 2601, 101),
    (52, 2704, 103), (53, 2809, 105), (54, 2916, 107), (55, 3025, 109),
    (56, 3136, 111), (57, 3249, 113), (58, 3364, 115), (59, 3481, 117),
    (60, 3600, 119), (61, 3721, 121), (62, 3844, 123), (63, 3969, 125),
    (64, 4096, 127), (65, 4225, 129), (66, 4356, 131), (67, 4489, 133),
    (68, 4624, 135), (69, 4761, 137), (70, 4900, 139), (71, 5041, 141),
    (72, 5184, 143), (73, 5329, 145), (74, 5476, 147), (75, 5625, 149),
    (76, 5776, 151), (77, 5929, 153), (78, 6084, 155), (79, 6241, 157),
    (80, 6400, 159), (81, 6561, 161), (82, 6724, 163), (83, 6889, 165),
    (84, 7056, 167), (85, 7225, 169), (86, 7396, 171), (87, 7569, 173),
    (88, 7744, 175), (89, 7921, 177), (90, 8100, 179), (91, 8281, 181),
    (92, 8464, 183), (93, 8649, 185), (94, 8836, 187), (95, 9025, 189),
    (96, 9216, 191), (97, 9409, 193), (98, 9604, 195), (99, 9801, 197),
    (100, 10000, 199), (101, 10201, 201), (102, 10404, 203), (103, 10609, 205),
    (104, 10816, 207), (105, 11025, 209), (106, 11236, 211), (107, 11449, 213),
    (108, 11664, 215), (109, 11881, 217), (110, 12100, 219), (111, 12321, 221),
    (112, 12544, 223), (113, 12769, 225), (114, 12996, 227), (115, 13225, 229),
    (116, 13456, 231), (117, 13689, 233), (118, 13924, 235), (119, 14161, 237),
    (120, 14400, 239), (121, 14641, 241), (122, 14884, 243), (123, 15129, 245),
    (124, 15376, 247), (125, 15625, 249), (126, 15876, 251), (127, 16129, 253),
    (128, 16384, 255), (129, 16641, 257), (130, 16900, 259), (131, 17161, 261),
    (132, 17424, 263), (133, 17689, 265), (134, 17956, 267), (135, 18225, 269),
    (136, 18496, 271), (137, 18769, 273), (138, 19044, 275), (139, 19321, 277),
    (140, 19600, 279), (141, 19881, 281), (142, 20164, 283), (143, 20449, 285),
    (144, 20736, 287), (145, 21025, 289), (146, 21316, 291), (147, 21609, 293),
    (148, 21904, 295), (149, 22201, 297), (150, 22500, 299), (151, 22801, 301),
    (152, 23104, 303), (153, 23409, 305), (154, 23716, 307), (155, 24025, 309),
    (156, 24336, 311), (157, 24649, 313), (158, 24964, 315), (159, 25281, 317),
    (160, 25600, 319), (161, 25921, 321), (162, 26244, 323), (163, 26569, 325),
    (164, 26896, 327), (165, 27225, 329), (166, 27556, 331), (167, 27889, 333),
    (168, 28224, 335), (169, 28561, 337), (170, 28900, 339), (171, 29241, 341),
    (172, 29584, 343), (173, 29929, 345), (174, 30276, 347), (175, 30625, 349),
    (176, 30976, 351), (177, 31329, 353), (178, 31684, 355), (179, 32041, 357),
    (180, 32400, 359), (181, 32761, 361), (182, 33124, 363), (183, 33489, 365),
    (184, 33856, 367), (185, 34225, 369), (186, 34596, 371), (187, 34969, 373),
    (188, 35344, 375), (189, 35721, 377), (190, 36100, 379), (191, 36481, 381),
    (192, 36864, 383), (193, 37249, 385), (194, 37636, 387), (195, 38025, 389),
    (196, 38416, 391), (197, 38809, 393), (198, 39204, 395), (199, 39601, 397),
    (200, 40000, 399), (201, 40401, 401), (202, 40804, 403), (203, 41209, 405),
    (204, 41616, 407), (205, 42025, 409), (206, 42436, 411), (207, 42849, 413),
    (208, 43264, 415), (209, 43681, 417), (210, 44100, 419), (211, 44521, 421),
    (212, 44944, 423), (213, 45369, 425), (214, 45796, 427), (215, 46225, 429),
    (216, 46656, 431), (217, 47089, 433), (218, 47524, 435), (219, 47961, 437),
    (220, 48400, 439), (221, 48841, 441), (222, 49284, 443), (223, 49729, 445),
    (224, 50176, 447), (225, 50625, 449), (226, 51076, 451), (227, 51529, 453),
    (228, 51984, 455), (229, 52441, 457), (230, 52900, 459), (231, 53361, 461),
    (232, 53824, 463), (233, 54289, 465), (234, 54756, 467), (235, 55225, 469),
    (236, 55696, 471), (237, 56169, 473), (238, 56644, 475), (239, 57121, 477),
    (240, 57600, 479), (241, 58081, 481), (242, 58564, 483), (243, 59049, 485),
    (244, 59536, 487), (245, 60025, 489), (246, 60516, 491), (247, 61009, 493),
    (248, 61504, 495), (249, 62001, 497), (250, 62500, 499), (251, 63001, 501),
    (252, 63504, 503), (253, 64009, 505), (254, 64516, 507), (255, 65025, 509),
    (256, 65536, 511), (257, 66049, 513), (258, 66564, 515), (259, 67081, 517),
    (260, 67600, 519), (261, 68121, 521), (262, 68644, 523), (263, 69169, 525),
    (264, 69696, 527), (265, 70225, 529), (266, 70756, 531), (267, 71289, 533),
    (268, 71824, 535), (269, 72361, 537), (270, 72900, 539), (271, 73441, 541),
    (272, 73984, 543), (273, 74529, 545), (274, 75076, 547), (275, 75625, 549),
    (276, 76176, 551), (277, 76729, 553), (278, 77284, 555), (279, 77841, 557),
    (280, 78400, 559), (281, 78961, 561), (282, 79524, 563), (283, 80089, 565),
    (284, 80656, 567), (285, 81225, 569), (286, 81796, 571), (287, 82369, 573),
    (288, 82944, 575), (289, 83521, 577), (290, 84100, 579), (291, 84681, 581),
    (292, 85264, 583), (293, 85849, 585), (294, 86436, 587), (295, 87025, 589),
    (296, 87616, 591), (297, 88209, 593), (298, 88804, 595), (299, 89401, 597),
    (300, 90000, 599), (301, 90601, 601), (302, 91204, 603), (303, 91809, 605),
    (304, 92416, 607), (305, 93025, 609), (306, 93636, 611), (307, 94249, 613),
    (308, 94864, 615), (309, 95481, 617), (310, 96100, 619), (311, 96721, 621),
    (312, 97344, 623), (313, 97969, 625), (314, 98596, 627), (315, 99225, 629),
    (316, 99856, 631), (317, 100489, 633), (318, 101124, 635),
    (319, 101761, 637), (320, 102400, 639), (321, 103041, 641),
    (322, 103684, 643), (323, 104329, 645), (324, 104976, 647),
    (325, 105625, 649), (326, 106276, 651), (327, 106929, 653),
    (328, 107584, 655), (329, 108241, 657), (330, 108900, 659),
    (331, 109561, 661), (332, 110224, 663), (333, 110889, 665),
    (334, 111556, 667), (335, 112225, 669), (336, 112896, 671),
    (337, 113569, 673), (338, 114244, 675), (339, 114921, 677),
    (340, 115600, 679), (341, 116281, 681), (342, 116964, 683),
    (343, 117649, 685), (344, 118336, 687), (345, 119025, 689),
    (346, 119716, 691), (347, 120409, 693), (348, 121104, 695),
    (349, 121801, 697), (350, 122500, 699), (351, 123201, 701),
    (352, 123904, 703), (353, 124609, 705), (354, 125316, 707),
    (355, 126025, 709), (356, 126736, 711), (357, 127449, 713),
    (358, 128164, 715), (359, 128881, 717), (360, 129600, 719),
    (361, 130321, 721), (362, 131044, 723), (363, 131769, 725),
    (364, 132496, 727), (365, 133225, 729), (366, 133956, 731),
    (367, 134689, 733), (368, 135424, 735), (369, 136161, 737),
    (370, 136900, 739), (371, 137641, 741), (372, 138384, 743),
    (373, 139129, 745), (374, 139876, 747), (375, 140625, 749),
    (376, 141376, 751), (377, 142129, 753), (378, 142884, 755),
    (379, 143641, 757), (380, 144400, 759), (381, 145161, 761),
    (382, 145924, 763), (383, 146689, 765), (384, 147456, 767),
    (385, 148225, 769), (386, 148996, 771), (387, 149769, 773),
    (388, 150544, 775), (389, 151321, 777), (390, 152100, 779),
    (391, 152881, 781), (392, 153664, 783), (393, 154449, 785),
    (394, 155236, 787), (395, 156025, 789), (396, 156816, 791),
    (397, 157609, 793), (398, 158404, 795), (399, 159201, 797),
    (400, 160000, 799), (401, 160801, 801), (402, 161604, 803),
    (403, 162409, 805), (404, 163216, 807), (405, 164025, 809),
    (406, 164836, 811), (407, 165649, 813), (408, 166464, 815),
    (409, 167281, 817), (410, 168100, 819), (411, 168921, 821),
    (412, 169744, 823), (413, 170569, 825), (414, 171396, 827),
    (415, 172225, 829), (416, 173056, 831), (417, 173889, 833),
    (418, 174724, 835), (419, 175561, 837), (420, 176400, 839),
    (421, 177241, 841), (422, 178084, 843), (423, 178929, 845),
    (424, 179776, 847), (425, 180625, 849), (426, 181476, 851),
    (427, 182329, 853), (428, 183184, 855), (429, 184041, 857),
    (430, 184900, 859), (431, 185761, 861), (432, 186624, 863),
    (433, 187489, 865), (434, 188356, 867), (435, 189225, 869),
    (436, 190096, 871), (437, 190969, 873), (438, 191844, 875),
    (439, 192721, 877), (440, 193600, 879), (441, 194481, 881),
    (442, 195364, 883), (443, 196249, 885), (444, 197136, 887),
    (445, 198025, 889), (446, 198916, 891), (447, 199809, 893),
    (448, 200704, 895), (449, 201601, 897), (450, 202500, 899),
    (451, 203401, 901), (452, 204304, 903), (453, 205209, 905),
    (454, 206116, 907), (455, 207025, 909), (456, 207936, 911),
    (457, 208849, 913), (458, 209764, 915), (459, 210681, 917),
    (460, 211600, 919), (461, 212521, 921), (462, 213444, 923),
    (463, 214369, 925), (464, 215296, 927), (465, 216225, 929),
    (466, 217156, 931), (467, 218089, 933), (468, 219024, 935),
    (469, 219961, 937), (470, 220900, 939), (471, 221841, 941),
    (472, 222784, 943), (473, 223729, 945), (474, 224676, 947),
    (475, 225625, 949), (476, 226576, 951), (477, 227529, 953),
    (478, 228484, 955), (479, 229441, 957), (480, 230400, 959),
    (481, 231361, 961), (482, 232324, 963), (483, 233289, 965),
    (484, 234256, 967), (485, 235225, 969), (486, 236196, 971),
    (487, 237169, 973), (488, 238144, 975), (489, 239121, 977),
    (490, 240100, 979), (491, 241081, 981), (492, 242064, 983),
    (493, 243049, 985), (494, 244036, 987), (495, 245025, 989),
    (496, 246016, 991), (497, 247009, 993), (498, 248004, 995),
    (499, 249001, 997), (500, 250000, 999), (501, 251001, 1001),
    (502, 252004, 1003), (503, 253009, 1005), (504, 254016, 1007),
    (505, 255025, 1009), (506, 256036, 1011), (507, 257049, 1013),
    (508, 258064, 1015), (509, 259081, 1017), (510, 260100, 1019),
    (511, 261121, 1021), (512, 262144, 1023), (513, 263169, 1025),
    (514, 264196, 1027), (515, 265225, 1029), (516, 266256, 1031),
    (517, 267289, 1033), (518, 268324, 1035), (519, 269361, 1037),
    (520, 270400, 1039), (521, 271441, 1041), (522, 272484, 1043),
    (523, 273529, 1045), (524, 274576, 1047), (525, 275625, 1049),
    (526, 276676, 1051), (527, 277729, 1053), (528, 278784, 1055),
    (529, 279841, 1057), (530, 280900, 1059), (531, 281961, 1061),
    (532, 283024, 1063), (533, 284089, 1065), (534, 285156, 1067),
    (535, 286225, 1069), (536, 287296, 1071), (537, 288369, 1073),
    (538, 289444, 1075), (539, 290521, 1077), (540, 291600, 1079),
    (541, 292681, 1081), (542, 293764, 1083), (543, 294849, 1085),
    (544, 295936, 1087), (545, 297025, 1089), (546, 298116, 1091),
    (547, 299209, 1093), (548, 300304, 1095), (549, 301401, 1097),
    (550, 302500, 1099), (551, 303601, 1101), (552, 304704, 1103),
    (553, 305809, 1105), (554, 306916, 1107), (555, 308025, 1109),
    (556, 309136, 1111), (557, 310249, 1113), (558, 311364, 1115),
    (559, 312481, 1117), (560, 313600, 1119), (561, 314721, 1121),
    (562, 315844, 1123), (563, 316969, 1125), (564, 318096, 1127),
    (565, 319225, 1129), (566, 320356, 1131), (567, 321489, 1133),
    (568, 322624, 1135), (569, 323761, 1137), (570, 324900, 1139),
    (571, 326041, 1141), (572, 327184, 1143), (573, 328329, 1145),
    (574, 329476, 1147), (575, 330625, 1149), (576, 331776, 1151),
    (577, 332929, 1153), (578, 334084, 1155), (579, 335241, 1157),
    (580, 336400, 1159), (581, 337561, 1161), (582, 338724, 1163),
    (583, 339889, 1165), (584, 341056, 1167), (585, 342225, 1169),
    (586, 343396, 1171), (587, 344569, 1173), (588, 345744, 1175),
    (589, 346921, 1177), (590, 348100, 1179), (591, 349281, 1181),
    (592, 350464, 1183), (593, 351649, 1185), (594, 352836, 1187),
    (595, 354025, 1189), (596, 355216, 1191), (597, 356409, 1193),
    (598, 357604, 1195), (599, 358801, 1197), (600, 360000, 1199),
    (601, 361201, 1201), (602, 362404, 1203), (603, 363609, 1205),
    (604, 364816, 1207), (605, 366025, 1209), (606, 367236, 1211),
    (607, 368449, 1213), (608, 369664, 1215), (609, 370881, 1217),
    (610, 372100, 1219), (611, 373321, 1221), (612, 374544, 1223),
    (613, 375769, 1225), (614, 376996, 1227), (615, 378225, 1229),
    (616, 379456, 1231), (617, 380689, 1233), (618, 381924, 1235),
    (619, 383161, 1237), (620, 384400, 1239), (621, 385641, 1241),
    (622, 386884, 1243), (623, 388129, 1245), (624, 389376, 1247),
    (625, 390625, 1249), (626, 391876, 1251), (627, 393129, 1253),
    (628, 394384, 1255), (629, 395641, 1257), (630, 396900, 1259),
    (631, 398161, 1261), (632, 399424, 1263), (633, 400689, 1265),
    (634, 401956, 1267), (635, 403225, 1269), (636, 404496, 1271),
    (637, 405769, 1273), (638, 407044, 1275), (639, 408321, 1277),
    (640, 409600, 1279), (641, 410881, 1281), (642, 412164, 1283),
    (643, 413449, 1285), (644, 414736, 1287), (645, 416025, 1289),
    (646, 417316, 1291), (647, 418609, 1293), (648, 419904, 1295),
    (649, 421201, 1297), (650, 422500, 1299), (651, 423801, 1301),
    (652, 425104, 1303), (653, 426409, 1305), (654, 427716, 1307),
    (655, 429025, 1309), (656, 430336, 1311), (657, 431649, 1313),
    (658, 432964, 1315), (659, 434281, 1317), (660, 435600, 1319),
    (661, 436921, 1321), (662, 438244, 1323), (663, 439569, 1325),
    (664, 440896, 1327), (665, 442225, 1329), (666, 443556, 1331),
    (667, 444889, 1333), (668, 446224, 1335), (669, 447561, 1337),
    (670, 448900, 1339), (671, 450241, 1341), (672, 451584, 1343),
    (673, 452929, 1345), (674, 454276, 1347), (675, 455625, 1349),
    (676, 456976, 1351), (677, 458329, 1353), (678, 459684, 1355),
    (679, 461041, 1357), (680, 462400, 1359), (681, 463761, 1361),
    (682, 465124, 1363), (683, 466489, 1365), (684, 467856, 1367),
    (685, 469225, 1369), (686, 470596, 1371), (687, 471969, 1373),
    (688, 473344, 1375), (689, 474721, 1377), (690, 476100, 1379),
    (691, 477481, 1381), (692, 478864, 1383), (693, 480249, 1385),
    (694, 481636, 1387), (695, 483025, 1389), (696, 484416, 1391),
    (697, 485809, 1393), (698, 487204, 1395), (699, 488601, 1397),
    (700, 490000, 1399), (701, 491401, 1401), (702, 492804, 1403),
    (703, 494209, 1405), (704, 495616, 1407), (705, 497025, 1409),
    (706, 498436, 1411), (707, 499849, 1413), (708, 501264, 1415),
    (709, 502681, 1417), (710, 504100, 1419), (711, 505521, 1421),
    (712, 506944, 1423), (713, 508369, 1425), (714, 509796, 1427),
    (715, 511225, 1429), (716, 512656, 1431), (717, 514089, 1433),
    (718, 515524, 1435), (719, 516961, 1437), (720, 518400, 1439),
    (721, 519841, 1441), (722, 521284, 1443), (723, 522729, 1445),
    (724, 524176, 1447), (725, 525625, 1449), (726, 527076, 1451),
    (727, 528529, 1453), (728, 529984, 1455), (729, 531441, 1457),
    (730, 532900, 1459), (731, 534361, 1461), (732, 535824, 1463),
    (733, 537289, 1465), (734, 538756, 1467), (735, 540225, 1469),
    (736, 541696, 1471), (737, 543169, 1473), (738, 544644, 1475),
    (739, 546121, 1477), (740, 547600, 1479), (741, 549081, 1481),
    (742, 550564, 1483), (743, 552049, 1485), (744, 553536, 1487),
    (745, 555025, 1489), (746, 556516, 1491), (747, 558009, 1493),
    (748, 559504, 1495), (749, 561001, 1497), (750, 562500, 1499),
    (751, 564001, 1501), (752, 565504, 1503), (753, 567009, 1505),
    (754, 568516, 1507), (755, 570025, 1509), (756, 571536, 1511),
    (757, 573049, 1513), (758, 574564, 1515), (759, 576081, 1517),
    (760, 577600, 1519), (761, 579121, 1521), (762, 580644, 1523),
    (763, 582169, 1525), (764, 583696, 1527), (765, 585225, 1529),
    (766, 586756, 1531), (767, 588289, 1533), (768, 589824, 1535),
    (769, 591361, 1537), (770, 592900, 1539), (771, 594441, 1541),
    (772, 595984, 1543), (773, 597529, 1545), (774, 599076, 1547),
    (775, 600625, 1549), (776, 602176, 1551), (777, 603729, 1553),
    (778, 605284, 1555), (779, 606841, 1557), (780, 608400, 1559),
    (781, 609961, 1561), (782, 611524, 1563), (783, 613089, 1565),
    (784, 614656, 1567), (785, 616225, 1569), (786, 617796, 1571),
    (787, 619369, 1573), (788, 620944, 1575), (789, 622521, 1577),
    (790, 624100, 1579), (791, 625681, 1581), (792, 627264, 1583),
    (793, 628849, 1585), (794, 630436, 1587), (795, 632025, 1589),
    (796, 633616, 1591), (797, 635209, 1593), (798, 636804, 1595),
    (799, 638401, 1597), (800, 640000, 1599), (801, 641601, 1601),
    (802, 643204, 1603), (803, 644809, 1605), (804, 646416, 1607),
    (805, 648025, 1609), (806, 649636, 1611), (807, 651249, 1613),
    (808, 652864, 1615), (809, 654481, 1617), (810, 656100, 1619),
    (811, 657721, 1621), (812, 659344, 1623), (813, 660969, 1625),
    (814, 662596, 1627), (815, 664225, 1629), (816, 665856, 1631),
    (817, 667489, 1633), (818, 669124, 1635), (819, 670761, 1637),
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